Introduction to 

Autogyros, Helicopters, and Other 

V/STOL Aircraft 

Volume II: Helicopters 
Edited by 

Catherine Dow, Dow Technical Services

Cover Design by 

Susan O 

Cover Photo 

On June 26, 1936, Henrich Focke’s F.61 astounded the world. This was the first truly 

practical helicopter. A year later, the F.61 had captured all of the helicopter world records. 
NASA/SP–2012-215959 Vol II 

Introduction to 

Autogyros, Helicopters, and Other 

V/STOL Aircraft 

Volume II: Helicopters 

Franklin D. Harris 

Piedmont, Oklahoma 

National Aeronautics and

Space Administration 

Ames Research Center 

Moffett Field, California 94035-1000 

October 2012 
Prepared for Monterey Technologies, Inc. 

under NASA Contract NNA07BB01C 

Subcontract 200703.NNA07BB01C 

Task Order 01C-53 

ISBN: 978-0-615-71562-9

Available from: 

NASA Center for AeroSpace Information 

7115 Standard Drive 

Hanover, MD 21076-1320 

(301) 621-0390 

National Technical Information Service 

5285 Port Royal Road 

Springfield, VA 22161 

(703) 487-4650 
v 

DEDICATION 

To two terrific offspring whom I am very proud of: 

 Leslie B. Harris Doyle—She chided me about my very first try at an opening sentence, 

“A helicopter is not an airplane.” And even laughed. Without knowing it, she encouraged me 

to respect the general wisdom of every reader. Just as important, she helped me transition 

from tennis in Arizona to horseback riding in Oklahoma. Now I own a horse and a saddle and 

bridle. She “boards” my horse on her property, includes me on trail rides, and has taught me 

how to barrel race so I can occasionally participate in our local rodeo along with her other 

students. 

 Glenn J. Harris III—He bought me my first computer in 1992, set it up, showed me 

how to use Microsoft®

 Word and Excel®, and is now my full-time IT guy. Based on this 

Volume II, he upgraded me to a solid state hard drive, Windows®

 7, Office 2003, and threw in 

a color printer for good measure. When I visit NASA Ames Research Center, he puts me up 

for a night on his houseboat—at no charge! 

Grit and the author near the end of a trail ride. 

 
vi 
vii 

TABLE OF CONTENTS 

PREFACE .................................................................................................................................. xi 

ACKNOWLEDGMENTS ....................................................................................................... xiii 

1 PIONEERING EFFORTS ............................................................................................... 1

1.1 EARLY HOVERING PERFORMANCE .................................................................. 5

1.2 STABILITY AND CONTROL .................................................................................. 9

1.3 POWER-OFF LANDING ........................................................................................ 23

1.3.1 Power-Off Landing ........................................................................................... 23

1.3.2 Power Failure in and Near Hover ..................................................................... 37

1.4 CLOSING REMARKS ............................................................................................ 43

2 MODERN RESULTS ..................................................................................................... 49

2.1 ENGINES ................................................................................................................. 53

2.1.1 Piston Engines .................................................................................................. 53

2.1.2 Turbine Engines ................................................................................................ 63

2.2 WEIGHT .................................................................................................................. 87

2.2.1 A Helicopter Sizing Method ........................................................................... 110

2.3 HOVER PERFORMANCE .................................................................................... 119

2.3.1 Hover Power Margin ...................................................................................... 119

2.3.2 Hover Ceiling Versus Gross Weight ............................................................... 122

2.3.3 UTTAS and AAH Hover Performance .......................................................... 138

2.3.4 Tail Rotor Performance in Hover ................................................................... 141

2.3.5 Other Anti-torque Devices .............................................................................. 146

2.3.6 Bell Model 222 and Aerospatiale Dauphin 2 Hover Performance ................. 151

2.3.7 Blade Element Momentum Theory Revisited ................................................ 152

2.3.8 Single Rotor Helicopter Summary ................................................................. 172

2.3.9 Twin-Rotor Helicopters .................................................................................. 178

2.3.10 Ground Effect ................................................................................................. 198

2.3.11 Closing Remarks ............................................................................................ 200

2.4 FORWARD-FLIGHT PERFORMANCE .............................................................. 207

2.4.1 Airplane .......................................................................................................... 211

2.4.2 Single Rotor Helicopter .................................................................................. 230

2.4.3 Twin-Rotor Helicopter .................................................................................... 238

2.4.4 Takeoff Following an Engine Failure ............................................................. 251

2.4.5 Closing Remarks ............................................................................................ 265

2.5 FUEL EFFICIENCY .............................................................................................. 267

2.5.1 Helicopter Lift-to-Drag Ratio (L/D) ............................................................... 277

2.5.2 Equivalent Parasite Drag Flat Plate Area (fe) ................................................. 278

2.5.3 Rotor Hub Parasite Drag Area ........................................................................ 295
viii 

2.5.4 The Doorhinge Rotor Hub .............................................................................. 310

2.5.5 Closing Remarks ............................................................................................ 314

2.6 VIBRATION .......................................................................................................... 315

2.6.1 Occupant Vibration, Humans Complain ......................................................... 319

2.6.2 Structural Fatigue, Parts Break ....................................................................... 332

2.6.3 Hub Vibratory Loads, Aircraft Response ....................................................... 343

2.6.4 Blade Vibratory Response, Hub Vibratory Loads .......................................... 396

2.6.5 Blade Airloads, Blade Vibratory Response .................................................... 420

2.6.6 Closing Remarks ............................................................................................ 434

2.7 NOISE .................................................................................................................... 437

2.7.1 Sound, Noise, and Human Hearing ................................................................ 437

2.7.2 Loudness Curves, Sound Pressure Level, and the Decibel ............................ 440

2.7.3 Weighted Loudness Curves ............................................................................ 442

2.7.4 Propellers and Rotors at Zero Speed .............................................................. 444

2.7.5 Overall Sound Pressure Level (OSPL) in Hover ............................................ 468

2.7.6 The Quiet Helicopter Program ....................................................................... 498

2.7.7 Government Noise Regulations for Helicopters ............................................. 509

2.7.8 Noise in Forward Flight .................................................................................. 514

2.7.9 Closing Remarks ............................................................................................ 535

2.8 PURCHASE PRICE ............................................................................................... 539

2.8.1 Civil Marketplace ........................................................................................... 539

2.8.2 Military Procurement ...................................................................................... 550

2.8.3 Concluding Remarks ...................................................................................... 570

2.9 OPERATING COSTS ............................................................................................ 579

2.9.1 Airplanes ......................................................................................................... 579

2.9.2 Helicopters ...................................................................................................... 595

2.9.3 A Direct Operating Cost (DOC) Calculator ................................................... 602

2.9.4 S-61 Direct Operating Costs in 2011 .............................................................. 616

2.9.5 Fuel and Maintenance DOCs in 2011 ............................................................. 617

2.9.6 Parts and Prices, Limited-Life Parts, and Scheduled Maintenance ................ 637

2.9.7 Total Operating Cost (TOC) ........................................................................... 653

2.9.8 Concluding Remarks ...................................................................................... 660

2.10 ACCIDENT RECORD ........................................................................................... 663

2.10.1 History, Accident Rate, and Predictions ......................................................... 663

2.10.2 In All, 11,426 Accidents From 1964 Through 2011 ...................................... 675

2.10.3 Detailed Accident Analysis ............................................................................. 683

2.10.4 Concluding Remarks ...................................................................................... 696

3 CONCLUDING REMARKS ....................................................................................... 699

4 REFERENCES ............................................................................................................. 703
ix 

APPENDIX A—Rotorcraft Stability and Control in Hover .................................................. 741 

APPENDIX B—Self-Induced Velocity Generated by a Lifting Line Wing or 

Rotor Blade ................................................................................................. 755 

APPENDIX C—Ad Hoc Committee ..................................................................................... 815 

APPENDIX D—Rotor Hubs .................................................................................................. 833 

APPENDIX E—Fatigue Article ............................................................................................. 869 

APPENDIX F—Dynamics of a Free-Free Uniform Beam .................................................... 875 

APPENDIX G—Project Hummingbird ................................................................................. 889 

AIRPLANES, ENGINES, AND HELICOPTERS ................................................................. 933 

INDIVIDUALS ...................................................................................................................... 937 

INDEX ................................................................................................................................... 941 
x 
xi 

PREFACE 

 There are hundreds of histories and tens of thousands of technical works about 

helicopters; more than enough topics to fill many books bigger and heavier than the one you 

have in hand. From this storehouse of literature, I decided that subjects dealing with 

helicopter shortcomings would be of most value for this introduction to helicopters. In my 

mind, the short list only includes engines, weight, performance, vibration, noise, purchase 

price, operating costs, and safety record. Here, in a nutshell, is why I chose these eight topics. 

 Engines—Without knowing at least a smattering of how piston and turbine engines 

operate (and what their limitations are), you are placed at a severe disadvantage when talking 

to engine manufacturers. These manufacturers have, more often than not, saved a helicopter 

development program from the scrap pile. They have done this by upping the takeoff rating of 

the chosen engine to make up for an overweight, underperforming helicopter prototype. 

 

 Weight—The track record for meeting estimated weight empty and design takeoff 

gross weight is no better for helicopters than for fixed-wing aircraft. Where we get our eternal 

optimism, given our historical trend data and weight estimating methodology, is beyond me. 

 Performance—Hover performance cannot, even today, be predicted to within ±5 

percent, and it always seems to come out minus given flight test data. The helicopter’s 

forward flight performance is severely limited by excessive profile and induced power, 

disproportionately high hub drag, and non-retractable landing gear. With these configuration 

burdens, it is no wonder that helicopter fuel efficiency is poor when compared to fixed-wing 

aircraft. 

 Vibration—Despite enormous theoretical progress that has identified many sources of 

vibration, no lightweight, low-cost invention to reduce helicopter vibration to airliner levels 

has been devised. Vibration suppressors and absorbers are the Band-Aid of choice, and these 

solutions are trotted out shortly after a prototype’s first flight when the test pilot says he 

cannot read the instrument panel above 100 knots. It has, in fact, been the use of many 

different types of anti-vibration devices, added to the basic machine by each manufacturer, 

that has saved the day as the rotorcraft industry expanded. 

 Noise—High tip speeds, especially of tail rotors, and no engine exhaust mufflers lead 

to very noisy helicopters, which, in turn, continue to dampen community acceptance of these 

machines. The design choice to wring out every pound of airframe weight empty per installed 

engine horsepower has relegated lower-noise configurations to an undeserved place on the 

priority list. Noise research by a very small, but staunch, band of advocates has been 

shortchanged by the low priority on noise set by the rotorcraft industry. A design approach 

yielding high performance and low noise was demonstrated by Hughes with its OH-6. No 

manufacturer of note has applied the Hughes’ technology and design approach that became 

available in the early 1970s. 
xii 

 Purchase Price—Helicopter fleet size continues to grow despite the 50 percent 

premium paid (over comparable fixed-wing aircraft) to have vertical and forward flight 

capability in one machine. The fact that the purchase price of a helicopter appears to depend 

about equally on weight empty and installed power may be an eye-opener, but this fact does 

not offer much insight into how to make the initial purchase price low enough to attract major 

airline companies that could best establish helicopter service on short-haul routes. Only 

recently has there been a helicopter airline service established that has stayed in business. If 

you get to Vancouver, British Columbia, go see Helijet’s operation. 

 Operating Costs—To say that helicopter operating costs are excessive compared to 

fixed-wing standards is a real understatement. Of the 5,000 to 7,000 parts and/or components 

in a helicopter, about 50 to 75 have to be replaced for every 1,500 to 5,000 hours of flight 

time. And, as you probably guessed, these must-be-replaced components are the most 

expensive, which lays a foundation for unacceptably high maintenance costs. Throw in low 

miles per gallon of fuel used, and many potential buyers say, “No thanks.” 

 Safety Record—The quite favorable trend of fewer and fewer helicopter accidents per 

year, even as the number of helicopters flying has increased over the past six decades, is a 

heartwarming story to relate. However, the industry did learn an expensive lesson when it 

introduced helicopters powered by single turbine engines, which caused a wide spike in 

accidents per year. This spike distorted the yearly trend in accidents per 100,000 flight hours. 

The current trend is to sell four helicopters and have an accident with one of them. Loss of 

engine power due to running out of gas is quite common, and the upward trend in loss-ofcontrol accidents per year is very, very disturbing. 

 So there you have it. 

 This introduction to these yet-to-be-improved helicopter shortcomings will show you 

why they are so difficult to solve. I hope you will be a part of their solution, and I hope you 

will start with the efforts offered in the Concluding Remarks of this volume. 
xiii 

ACKNOWLEDGMENTS 

 In the acknowledgments in the first volume of this three volume set, I expressed my 

gratitude to the many men and women who gave me their help when I really needed it. And 

each and every one has continued giving me their help as this second volume unfolded. In this 

second volume, I found that I needed even more expert assistance, particularly when 

confronted by several stone walls. For example: 

 In dealing with helicopter weights, I was able to rely on Mike Scully, who is, I 

believe, the world’s authority on the subject. Mike also helped shape what you will read about 

engines. 

 The subject of performance is very dear to my heart, and I thought it would be a rather 

straightforward subject to address. But thanks to Tom Wood and Jack Gallagher (who was 

President of New York Helicopter Airways) you have much more information about poweroff landings and about the FAA’s requirement for Category A takeoffs and landings from 

heliports. Also, Jack told me he preferred tandem rotor machines to the single rotor 

configuration because they are much less sensitive to crosswinds during takeoff and landing. 

 The vibration chapter would have been considerably less useful to you if Tom 

Norman, Bob Kufeld, Ethan Romander, Carl Russell, Randy Peterson, Wayne Johnson, and 

several others from the NASA Ames Research Center Aeromechanics Branch, headed up by 

Bill Warmbrodt, hadn’t jumped in when they did. 

 There is no question that writing in some depth about noise took me out of my 

technical comfort zone. Fortunately Wayne Johnson clarified more than a few key technical 

points that I had lost track of over the years. And then Ben Sim, Ken Brentner, Charlie Cox, 

and, of course, Fred Schmidt (who has been an acknowledged expert in the subject for 

decades) helped me expand the scope of this rather difficult subject. 

 Opening up the subject of helicopter purchase price, which Mike Scully and I had 

written a paper about, put me back in touch with Sharon Desfor, President of HeliValue$, Inc. 

She and her staff publish The Official Helicopter Blue Book®. Sharon is one person who really

keeps her ear to the ground about commercial helicopters. We were able to reminisce about 

several manufacturers, and their trials and tribulations in bringing new helicopters to the 

marketplace. You have much more history and authoritative selling price data about civil 

helicopters because of her. For the world of military helicopter procurement, I turned to Webb 

Joiner (past President of Bell Helicopter) for history about the Huey program. And for the 

Army’s side of procurement, Bud Patnode (Colonel Clarence A. Patnode Jr., retired) and Bud 

Forster (Lieutenant General William H. Forster, retired) filled in several blanks in my 

memory. Webb and both retired U.S. Army officers allowed me to include some of their 

written thoughts about keeping a very tight rein on requirements and specifications, 

particularly during development, which is invaluable advise. 
xiv 

 Newly minted helicopter engineers, and even many practicing engineers, have too 

little exposure to helicopter operating costs, which is very disappointing to me. With Bill 

de Decker’s help, this chapter may fill in a serious educational gap. Bill and his cohort Alan 

Conklin (now departed) brought the firm of Conklin & de Decker into the world. They 

created an invaluable data bank of operating cost data (for both fixed-wing and rotary wing 

aircraft) with their software called Aircraft Cost Evaluator (ACE). ACE is acknowledged by 

the worldwide aviation community as the leading product of its type, and it is still expanding 

as new aircraft arrive on the scene. Bill gave me unbelievable access to their company’s data 

bank, and this privilege put realistic operating cost data at your fingertips. 

 Reading about accidents with commercially manufactured helicopters and amateurbuilt autogyros in the cold light of day is always a sobering experience. Fortunately, I was 

able to turn to Eugene Kasper (Test and Evaluation Engineer, Flight Control and Cockpit 

Integration Division, U.S. Army Aeroflightydynamics Directorate at NASA Ames Research 

Center). Gene has maintained National Transportation Safety Board reports in his massive 

Microsoft®

 Word and Excel® files that we began in the late 1990s. His continued interest in 

rotorcraft safety, and his thoroughness in studying accident reports, provides you with an 

invaluable source. 

 I would be quite remiss if I did not again thank three marvelous women who have 

done so much to bring this Volume II to completion. Kathy Ponce at the NASA Ames 

Research Center library has not once failed to find some obscure reference that the world has 

forgotten, but is of immense value to you. Cathy Dow has edited this Volume II with superb 

professional skill, as she did in Volume I, while continuing to managed me with both timely 

suggestions and gentle persuasion. And, of course, I thank my wife, Sue, for her patience with 

me through the ups and downs during another year and a half of writing. 
1

1 PIONEERING EFFORTS 

 There is a wealth of history documenting the origins of powered lift and the many 

inventors who struggled for over 250 years to give the helicopter a place in the world’s 

transportation system. A fascinating glimpse of the struggle is provided by Gene Liberatore in 

Helicopters Before Helicopters [1]. Efforts to create a man-carrying, powered lift system 

began well before the airplane was conceived as Fig. 1-1 suggests. Despite over 40 powered 

lift attempts up to 1903, no promising results comparable to the achievement of the Wright 

brothers can be pinpointed. This state of affairs continued until the early 1920s. 

 The struggle to achieve a truly operational helicopter that rivaled the Cierva C.30 

autogyro finally ended when Henrich Focke, Anton Flettner, and Igor Sikorsky were each able 

to begin production deliveries of their separate designs during the early part of World War II. 

Excellent accounts of this struggle are provided by Boulet [2] and Gablehouse [3]. The story 

is well summarized by Brooks [4] and Gibbs-Smith [5], and by Apostolo [6], with beautiful 

illustrations, one of which is of the Sikorsky R-4, Fig. 1-2. 

0

10

20

30

40

50

60

70

80

90

100

1650 1700 1750 1800 1850 1900 1950

Helicopters

Tries

Year

Wright Bros.

Dec. 17, 1903

Airplanes

Fig. 1-1. Pursuing the helicopter was the real goal of early inventors. 
1. PIONEERING EFFORTS 

2 

Fig. 1-2. The Sikorsky R-4 was the first production helicopter in the U.S. [6]. 

 In reading these histories and many others, one must conclude that the practical 

helicopter was pursued with every bit as much energy (and money) as the airplane—at least 

up until the achievements of the Wright brothers really took root in Europe in 1909. Many 

inventive geniuses such as Bréguet and Sikorsky struggled unsuccessfully with the helicopter 

in the very early 1900s before turning their skill to evolving the airplane. Fortunately, many of 

these pioneers returned to help make rotorcraft what they are today. 

 Boulet’s history [2], even as brief as it is, describes over 70 different helicopters that 

evolved prior to 1945. A common thread clearly exists for this long period that stretches back 

to at least 1784. In that year, Launoy and Bienvenue flew a simple, stick model, coaxial rotor 

system. What followed were, with one very notable exception, helicopters that used rotors of 

the same size, in pairs, to ensure equilibrium in applied torque. From Boulet, the 

configurations tried were distributed as shown in Fig. 1-3. 

 Of this group of pre-1945 helicopters (and a few models), only three types were 

produced in quantity. The first was the side-by-side configuration pioneered by Henrich Focke 

and designated as the FA 223. Out of 30 aircraft ordered by the German Government, 9 were 

completed by the end of World War II. The Focke-Achgelis FA 223 was based on the truly 

successful F. 61, which hovered in late June of 1936. By June of the following year, the F. 61 

held the altitude record (2,100 meters) and easily flew 100 kilometers cross country.1 The 

 

1 Boulet (page 61 of reference [2]) suggests that “the helicopter enthusiasts, in 1934, must have been rather 

discouraged. Ten years after the first flight in a closed circuit by Oehmichen, the official altitude world record 

was only 18 meters (+2 meters compared with the altitude reached by Oehmichen) and the straight line record 

barely reached over one kilometer. Nobody then suspected the progress which would be made during the ten 

following years.” 
1. PIONEERING EFFORTS 

3 

second type to go into production was created by Anton Flettner and designated the FL 282. 

The two main rotors of his design were nearly coaxial but, in fact, were intermeshed like an 

eggbeater. This configuration is referred to technically as a synchropter. Out of a German 

Government order for 30, 24 were delivered. Flettner developed his configuration with the 

FL 265. Six of this very successful earlier model were ordered by the German Navy, and the 

first prototype flew in May of 1939. You can read a superb story of German helicopter 

development in Helicopters of the Third Reich written by Steve Coates [7]. 

 The third type was produced in the United States. The single-main-rotor plus antitorque tail rotor configuration was developed by Igor Sikorsky with his VS 300. The first 

flight of the VS 300 was in September of 1939, and by December 1941 Sikorsky had refined 

the design to what most laymen think of as the modern helicopter. The success of the VS 300 

led to production orders from the U.S. Army Air Corps for 126 of the Sikorsky Model R-4s. 

The prototype, the XR-4, first flew in January of 1942, and the production order was filled in 

18 months. The R-4 was quickly followed by the R-6. Four prototypes, and 416 out of 900 

R-6s ordered by the U.S. Army Air Corps, were delivered by the end of World War II. The 

success of the R-4 also led to the R-5, whose prototype first flew in late August of 1943. By 

the end of World War II, 123 of this larger model had been delivered. 

0 5 10 15 20 25 30

Coaxial

Side by side

Tandem

Quad

Single +Tail Rotor

Single + Props on Blades

Synchropter

Number of Rotorcraft

Fig. 1-3. At least 72 different helicopters were built by 1945. 
1. PIONEERING EFFORTS 

4 

 In many ways, World War II stimulated helicopter evolution and production just as 

World War I gave impetus to the airplane. Out of some 70-plus configurations, 3 basic types 

survived the weeding-out development process that started around 1784. And of the roughly 

700 rotorcraft produced by 1945, about 665 (or over 95 percent) were the single-main-rotor 

plus anti-torque tail rotor configuration. In contrast to this 160-year rotorcraft development 

cycle, the first modern airplanes—albeit a model glider flown by Cayley in 1804 and, more 

comparably, a stable, rubber-band-powered model flown by Penaud in 1871—were developed 

in about 50 years. 

 There is another interesting parallel between airplane and rotorcraft development. 

While the Wright brothers were successful with a biplane having canard control surfaces, it 

was the mono-plane with control surfaces on the tail that became the production choice. 

Similarly, Boulet (page 44 of reference [2]) asks that “three men share the glory to be the first 

to fly and control a helicopter” and he suggests the following: 

• Pescara with a coaxial helicopter. First controlled flight of about one minute. By January of 

1922, the several times rebuilt and modified aircraft had demonstrated hover for 

approximately ten minutes. 

• De Bothezat’s quad rotor helicopter. First flight of more than one minute in December of 

1922. 

• Oehmichen with a quad rotor helicopter. First kilometer flown in a closed circuit in May of 

1924. 

To this list one could add: 

• Florine’s tandem rotor helicopter. Raised the airborne record to nearly 10 minutes and 

reached somewhat over 15-feet altitude in October of 1933. 

• The Bréguet–Dorand coaxial design. By December of 1936 had demonstrated forward 

flight to about 500-feet altitude, endurance slightly over 1 hour, top speed of 108 km/hr, but 

with maximum hover time of 10 minutes. 

History records that none of these configurations went into production during the first step in 

bringing the helicopter into practical use. 

dont delete this 
5 

1.1 EARLY HOVERING PERFORMANCE 

 During the struggle to get the preproduction helicopters off the ground, finding a 

reliable engine, transmitting power to the pair (or pairs) of rotors, and getting control of the 

“machine” was an ever-recurring theme. With respect to installing enough power to hover, the 

pioneers appear to have taken a very reasonable approach. They had available, for example, at 

least one basic theory. This theory defined the ideal horsepower required to hover out of 

ground effect (HPideal) in terms of the rotor thrust (T) (somewhat in excess of takeoff weight), 

the rotor or rotors swept disc area (A), and the density of air (ρ). The theory gives the quite 

simple result that 

(1.1) ideal

T T HP

550 2 A = ρ

 (hover out of ground effect). 

 Accounting correctly for rotor(s) area (A) requires some care when using Eq. (1.1), 

because it was originally derived for one thrusting rotor disc. For example, the area is πR2

 for 

a single main rotor having a blade radius (R). With the coaxial configuration, the area is also 

πR2 even though there are two rotor discs. This is true for the coaxial rotor system because the 

same column of air that passes through the upper rotor passes through the lower rotor. In the 

case of two rotors not overlapped (i.e., the tandem or side-by-side arrangements), the 

applicable area would be 2 πR2

. Obviously then, the area for the nonoverlapped quad-rotor 

would be 4 πR2. 

 When two rotors are overlapped as in the Flettner synchropter design, there is 

considerable mixing of the two columns of air, and the problem becomes rather difficult. But 

to a first approximation, the applicable area to use in Eq. (1.1) is given as 

(1.2) ( ) ( ) 2

2 1 1 d A 2 R 1 1 sin d d

2 2R 2R 2R −     π

=π − − − −       π   . 

The distance between the centerlines of the two rotor hubs is denoted by (d ) in Eq. (1.2), and 

the rotor discs are assumed to be in about the same horizontal plane. 

 This theory for hover power required, Eq. (1.1), was derived from basic fluid dynamic 

principles established by W. J. Macquorn Rankine, R. E. Froude, and W. Froude in the years 

from 1865 to 1889. It was subsequently improved by Albert Betz and Ludwig Prandtl in 

1920.2 The pioneers must have quickly become aware that this available theory had more than 

a few shortcomings because they generally installed about twice the power specified by 

Eq. (1.1). More precisely, they took the most readily available engine and then built 

helicopters with rotor diameters nearly twice that suggested by the simple theory. Because 

belt-drive transmissions were the most common means of reducing engine RPM to rotor RPM 

 

2 You will find that references [8], [9], [10], [11], and [12] provide an excellent window into some of the great 

aerodynamic, structures, dynamics, and mathematical work that formed such an important part of rotorcraft 

development. 
1.1 EARLY HOVERING PERFORMANCE 

6 

in the early 1900s, as much as one-half of the engine power never reached the rotors. And 

even with the use of gears and shafts, Boulet’s history also recounts several instances (for 

example, read the Bartram Kelley story, page 104 of reference [2]) when the engine did not 

deliver the power claimed by the manufacturer. 

 The relation between actual installed horsepower and the ideal horsepower to hover 

provides an interesting capsule view of what the early inventors were doing to demonstrate a 

feasible helicopter. Fig. 1-4 provides this view by using the historically available data. All but 

one pioneer (the Luyties large model of Dec. 1907) installed more power than required by the 

ideal theory given in Eq. (1.1) as Fig. 1-4 shows. One has to assume that each inventor fully 

expected his “machine” to hover out of ground effect (HOGE), that is, at altitudes many times 

the rotor diameter. However, about one-half of the inventors were, at best, in a marginal 

power—not to mention control—situation. If it had not been that the early efforts were to just 

get in the air so that stability and control could be demonstrated, progress would have been 

even slower. Boulet carefully points out the progressive improvement in hover altitude. By 

1922, the record for hovering altitude was still only about 15 meters or 45 feet. This is a very 

important technical point because it raises the question of ground effect and its augmentation 

of lifting capability for a given design. 

0

200

400

600

800

1,000

1,200

1,400

0 100 200 300 400 500 600

Actual 

Horsepower 

Installed

Ideal Horsepower Required to Hover

Ideal 

Power

Two Times 

Ideal Power

Fig. 1-4. In the period from 1907 to 1922, some early inventors installed enough 

power to hover.
1.1 EARLY HOVERING PERFORMANCE 

7 

 The effect of the ground on reducing the power required to hover becomes 

progressively more pronounced as the distance from the rotor hub plane to the ground is 

decreased. A formal theory for hover performance in ground effect had to wait until 1937 

when Betz [13] was able to provide an approximation that modified Eq. (1.1) to 

(1.3) ideal

T T 2Z HP

550 2 A R

  =  

ρ  

 (hover in ground effect). 

The distance from the rotor hub plane to the ground is denoted by Z in Eq. (1.3), and the Betz 

approximation only applies when the helicopter is below an altitude where Z/R is on the order 

of one-fourth or less. This criteria was, in fact, the situation for most of the early inventors. It 

would seem that these several first attempts to hover encountered a situation where (1) the 

rotors themselves were about 50 percent efficient relative to the ideal power given by 

Eq. (1.1), (2) only half the installed power was transmitted to the rotors, and (3) the benefit of 

ground effect reduced power required by perhaps one-half. 

 Looking back with this technical perspective, you have to say that the early inventors 

(in the 1907 to 1922 period that Boulet singles out) were fighting a real uphill battle. 

 By the end of 1922, the helicopter was beginning to reflect both the hardware and 

theoretical progress that was improving fixed-wing aircraft. The Boulet photographs show, for 

example, that propeller shapes for rotors became more common. There was a progressive 

reduction in the number of blades per rotor, and the individual blades became quite a bit 

narrower in chord (c) for any given radius (R). Clearly the beneficial concept of higher bladeaspect ratio (AR, the ratio of blade radius to blade chord, or R/c) was being applied. The blade 

cross section or airfoil shape changed from simple, flat slabs that were more characteristic of 

windmills into at least “modern” airfoils. These vintage airfoils were carefully curved on the 

upper surface, but the bottom surface was basically flat. This evolution of blades and airfoil 

shapes has been traced well back in time by Jan Drees [14] and is a fascinating story of its 

own. 

 Significant theoretical progress was also made in estimating the power required to 

hover. The subject in itself was not of major importance to fixed-wing propeller designers in 

this period because it was airplane cruise and maximum speed they sought. Static thrust for 

takeoff was simply a by-product of their designs. But, of course, to rotorcraft inventors just 

the reverse was true. Groundwork for this important theoretical advancement was first laid by 

W. Froude and S. Drzewiecki before 1900. It was brought to fruition by Betz in 1925 as 

Glauert summarizes in volume IV of reference [10]. Thus, the ideal power required to hover 

out of ground effect as provided by Eq. (1.1) was updated to include an additional term and a 

touch of empiricism to give the more practical result of 

(1.4) HOGE

3

t do

i

T T bcRV C HP k

550 2 A 8 550

  ρ = +  

ρ ×  

. 

The empiricism was introduced by the coefficient (ki) which designers increased from the 

ideal value of 1.00. Values of k i

 from 1.10 to 1.25 were most often used. 
1.1 EARLY HOVERING PERFORMANCE 

8 

 The final term in Eq. (1.4) became known as the profile power (HPo) term. This 

addition acknowledged that it takes some power just to drag the blades around even if they are 

not lifting. This power is very dependent on the drag coefficient3 of the airfoil (Cdo), on the tip 

speed cubed (Vt), and on the total blade physical area (bcR). 

 The power-required formula provided by Eq. (1.4) led to having two areas that 

described a rotor—one being the swept disc area (πR2

) and the other being the physical total 

blade area (bcR) for rectangular blades. These two areas were formed into a ratio referred to 

as solidity (σ). This descriptive parameter remains in use to this day, so remember that 

(1.5) 2

bcR bc Solidity for rectangular blades R R

≡ σ≡ =

π π . 

Equation (1.4) also suggested a number of nondimensional forms that were finally resolved to 

some extent by the N.A.C.A. [15]. Two key coefficients were adopted—one for thrust and one 

for power—and both were based on the swept disc area. For the thrust coefficient 

(1.6) T 2

t

T C

AV = ρ

and for the power coefficient 

(1.7) P 3

t

P C

AV = ρ . 

With these coefficients in hand, the hover power required provided by Eq. (1.4) was made less 

cumbersome (in fact, disguised to some) and became 

(1.8) 

P PP HOGE i o

T do

i

3

2

2

C CC

C C k

8

= +

σ

= +

. 

 From 1922 to mid-1936—when the truly successful helicopter, the F. 61, first 

hovered—you will see an apparent lack of progress made with helicopters. This period, which 

was the subject of Volume I, was discussed in detail by Brooks [4] and mentioned by Boulet 

[2] in passing, and was dominated by Cierva, Pitcairn, and Kellett and their development and 

production of the autogyro. Perhaps most importantly, the modern rotor system—having a 

few blades that are long and slender (i.e., high-aspect ratio)—was evolved during this period. 

It was also during this period that autogyros incorporated lead-lag dampers to preclude the 

destructive ground resonance phenomenon, and practical demonstrations of blade feathering 

through a swashplate gave future helicopter pilots firm control. Thus, the 12 or so years that 

were spent in creating hubs, blades, and control systems, and solving many structural dynamic 

and aerodynamic problems, were clearly one of the most fruitful periods in rotorcraft, if not 

helicopter, development. 

 

3 The drag of airfoils, while clearly seen in experiments, was calculated as zero up until the early 1910s. With the 

work of Prandtl and his students, a realistic theory finally became available that showed that Cdo was on the 

order of 0.01 to 0.015. This began to bridge the gap between test and theory. Improvements to the theory are still 

being made today. 
9 

1.2 STABILITY AND CONTROL 

 The period from mid-1936 to March 1946, when the Bell Model 47 received the first 

Civil Aviation Authority (the CAA, which proceeded the FAA) certification for civilian use in 

the United States, must have been a very exciting 10 years for the pioneers. For example, Igor 

Sikorsky’s triumph in evolving the VS-300, the prototype of modern, single-main-rotor plus 

anti-torque tail rotor helicopters, is just one of the fascinating stories found in Boulet’s history. 

Threaded within this history is the underlying story of helicopter stability and control. The 

early helicopters, although helped by autogyro development, were not at all stable. The tale 

related by Frank Gregory4 on first flying the Sikorsky VS-300 in 1940 when he was a U.S. 

Army captain, captures the essence of the stability and control problem. 

 Captain Gregory, after learning how to use the collective stick to get the aircraft off the 

ground, recounts that 

“once in the air there was a slight disturbance and the nose of the aircraft seemed to come up 

too quickly, so I moved the [cyclic] stick forward. In so doing the nose went down all right, 

but to my complete surprise, the aircraft started moving forward and climbing. In all my 

experience with flying heretofore, when I pushed the stick forward the airplane had always 

gone down. I was halfway across the airport before I finally stopped the machine. After about 

eight minutes of flying, I finally got the craft back on the ground, much to the relief of 

Sikorsky, although, of the group which had been watching my flight, he was most 

enthusiastic in his congratulations.” 

 The inherent instability of all early helicopters was only overcome by the skill of the 

pilot when given an adequate control system. The Wright brothers, assisted by glider testing, 

solved most of their stability and control problems before the onset of their successful 

powered flying, as many historians have pointed out. In contrast, the early helicopter pioneers 

seemed to be tackling the power, stability, and control problems all at the same time. 

 Stability and control of the helicopter was formally studied by analysis at least as early 

as 1923 judging by the work of G. A. Crocco published by the N.A.C.A. in reference [17]. His 

work and that of Kurt Hohenemser [18] in 1939, plus Igor Sikorsky’s personal, but perhaps 

too brief, ground instructions, may be all that Captain Gregory had at hand before his first 

flight. But, in retrospect, a simple understanding of the VS-300 control and inherent 

instability in hovering flight is relatively easy to recreate. 

 The simplified force and moment diagram for the situation Captain Gregory found 

himself in, once he added enough collective pitch to hover, is shown in Fig. 1-5. Based on 

advanced theory, the equations for all six components of motion can be reduced to (1) fore 

and aft or longitudinal motion at nearly constant height, and (2) helicopter pitching motion for 

the hovering helicopter. The two equations describing the motion of the aircraft center of 

gravity (cg ) are 

 

4 Reference [2], page 95–96. The pioneering experiences of Colonel H. Franklin Gregory are more fully related 

in his own book titled Anything A Horse Can Do [16]. 
1.2 STABILITY AND CONTROL 

10 

(1.9) 

2

cg

x cg S 2

W x

FW H 0

g t

∂

=− ×θ − − =

∂ 

and 

(1.10) 

2

cg M hH M I 0 cg S P cg 2

t

∂ θ

=× + − =

∂  . 

These two equations of motion assume that rotor thrust (TS) is equal to helicopter weight (W) 

and that the body pitch angle (θcg) is a small angle. The rotor inplane force, called the rotor 

H-force (HS), acts in the rotor plane perpendicular to the rotor shaft. Thus, the H-force acts at 

the hub, which is a distance (h ) above the center of gravity. The rotor blades can introduce a 

hub pitching moment (MP) as discussed in detail in Volume I. This hub moment is 

approximated as 

(1.11) C

P 1S

Frb

M a

2

β =

where the blade centrifugal force is (FC) in pounds, the flapping hinge offset is (rβ) in feet, the 

number of blades is (b), and the longitudinal flapping is (a1S) in radians. 

 Classically, engineers search for the stability of the system and then review the control 

aspects. But from Captain Gregory’s point of view, one could say that he was in trouble from 

the onset—that is, at time equals zero (i.e., t = 0). He stated that “.... there was a slight 

disturbance and the nose of the aircraft seemed to come up too quickly, so I moved the 

[cyclic] stick forward.” 

θcg

Ts

w

Hs

θcg

Ts

w

Hs

Fig. 1-5. The primary forces and moments involved in longitudinal helicopter stability 

and control in hover. 
1.2 STABILITY AND CONTROL 

11 

 If you assume that the “slight disturbance” was a longitudinal gust of wind (Vgust) 

while Captain Gregory held the longitudinal cyclic stick fixed, then the initial helicopter 

response is, from Eq. 15 in Appendix A, quite simply approximated as 

(1.12) P s 2

cg gust

cg

M Vh H V V t

2I

  ∂ ∂ + ×∂ ∂ θ= × ×  

 

. 

Both the hub moment (MP) and H-force speed derivatives introduced here depend on the 

longitudinal flapping. That is, because 

(1.11) C

P 1S

Frb

M a

2

β =

and 

(1.13) H Wa S 1 ≈ S , 

it follows that 

(1.14) P C 1S S 1S M Frb a Ha and W

V 2V V V

∂   β ∂ ∂∂ = ≈   ∂ ∂ ∂∂  

. 

Therefore, the initial helicopter response to a gust becomes 

(1.15) C 1S 2

cg gust

cg

F r b 2hW a V t

4I V

β   +   ∂ θ =      ∂  

. 

In Volume I, the longitudinal flapping was found to be very sensitive to speed, being on the 

order of 

(1.16) 1S 0 t 1C a 2 VV B =θ − . 

Therefore, the partial derivative of longitudinal flapping (a1S) with respect to speed (V ) is 

(1.17) 1S 0

t

a 2

V V

∂ θ = ∂ . 

With this last substitution, the initial helicopter response to a gust is approximated in the first 

few seconds of pitch motion by 

(1.18) C 0 2

cg gust

cg t

F r b 2hW 2 V t

4I V

β   +   θ θ =      

. 

 
1.2 STABILITY AND CONTROL 

12 

 The VS-300 configuration Captain Gregory was flying that day in late 1940 is not 

absolutely recorded. However, the data5 of primary interest suggests that, for a gust of 5 feet 

per second, he experienced an initial response, in degrees, of about 

(1.19) 

2

cg

cg

1.15 t in degrees

d dt 2.3 t in deg/ sec

θ ≈ °×

θ ≈× . 

 Fig. 1-6 gives you some idea of what Captain Gregory experienced (and, in fact, what 

most student pilots first experience). Had he not “moved the stick forward,” the helicopter 

would have begun the unstable oscillation shown by the open circles in Fig. 1-6. The period 

of this oscillation (i.e., the time to complete one cycle) is on the order of 12 seconds. 

Furthermore, the amplitude doubles every 3.6 seconds! The fact that Captain Gregory just 

stayed above the ground for his first 8-minute flight would seem to be a major miracle. 

-30

-25

-20

-15

-10

-5

0

5

10

15

20

0 2 4 6 8 10 12 14

Pitch 

Attitude 

(deg)

+ Nose Up Approximate Response 

per Eq. 1.19

Exact Response 

per Appendix K

Time (sec)

Fig. 1-6. The Sikorsky VS-300 was a challenge to hover (response to a 5-ft/sec wind 

gust with controls fixed). 

 

5 Technical information provided by Harold Ulisnik, Sikorsky Aircraft, allowed the following data on the 

VS-300 to be compiled: W = 1,290 lb, Icg = 1,000 slug-ft2

, h = 5 ft, R = 15 ft 1 in., c = 12 in., b = 3, σ = 0.0633, 

Vt

 = 353 ft/sec, Ω = 23.4 rad/sec, FC = 3,892 lb, rβ = 2.125 in., If = 81 slug-ft2, γ = 9.27, B1C = ± 10 deg, δcyclic = 

± 10 in., ρ = 0.002378 slug/ft3

, CT = 0.00609, and θ = 0.19 rad. 
1.2 STABILITY AND CONTROL 

13 

 What Captain Gregory learned quickly was to make smooth, but small, control 

movements roughly in proportion to the helicopter pitch rate, not pitch attitude. In effect, he 

first became a rate gyro. His control of the VS-300 went from the longitudinal cyclic stick 

(δcyclic) through the control linkage to the blade longitudinal feathering angle, (B1C), which 

then changed the longitudinal flapping angle (a1S). Stated in an engineering way 

(1.20) 1C

1S 0 t 1C 0 t cyclic

cyclic

B a 2 VV B 2 VV ∂ =θ − =θ − δ ∂δ . 

The control ratio of the VS-300 was on the order of –1 degree of B1C per 1 inch of aft stick. 

Thus, aft stick produced rearward flapping and a nose-up moment about the helicopter center 

of gravity as Fig. 1-5 suggests. Acting with both a sense of pitch rate and, to a lesser extent, 

pitch attitude, Captain Gregory’s control inputs can be described as 

(1.21) cyclic cyclic

cyclic cg cg

cg cg

∂δ ∂δ δ = θ+ θ ∂θ ∂θ

  , 

and the control of rotor forces and moments through longitudinal flapping then becomes 

(1.22) cyclic cyclic 1C

1S 0 t cg cg

cyclic cg cg

B a 2 VV ∂   ∂δ ∂δ

=θ − θ+ θ   ∂ δ ∂θ ∂θ  

  . 

By reacting to pitch rate, the pilot introduces sufficient damping to control the inherently 

unstable helicopter. Additional control motions can then be made to precisely hover the 

rotorcraft over any given spot. 

 I have taken some license in the story of VS-300 stability and control development. A 

more factual account, based on the aircraft log, was provided by a letter5

 from Harold 

Ulisnick as follows: 

 “The VS-300 was first flown 14 September 1939 with full cyclic control on the 

main rotor. The aircraft was nearly uncontrollable not so much because of lack of skill 

on the part of the pilot, but due to the fact that the controls were rigged about 60o

 out of 

phase [a longitudinal stick input resulted in considerable lateral aircraft response, etc.]. 

Cyclic control was non-linear, and spongy. Additionally, aircraft vibratory levels were 

extremely high. 

 Following the crash on 9 December 1939, the VS-300 was rebuilt with main rotor 

collective control only, single tail rotor anti-torque/directional control, and twin 

horizontal tail rotors for longitudinal and lateral control. The first reference I have to 

Lieut. Gregory piloting the VS-300 is on 24 July 1940. Several very short duration 

flights were made. The aircraft was configured as above. 

 Following many changes to the geometry of the two horizontal tail rotor support 

structures [directed at improving control characteristics], Captain Gregory again flew the 

machine on 16 April 1941. Stability and control were adequate enough to permit 

Mr. Sikorsky on 6 May to set a world endurance record [in hover] for helicopters of 

1 hr., 5 min., and 14.5 sec. Maj. Gregory again flew the aircraft on 7 May 1941. Forward 

flight stability was still poor due to main rotor downwash impinging on the two 
1.2 STABILITY AND CONTROL 

14 

horizontal tail rotors. Lateral control was marginal. Also, there was a lateral ‘shuffle’ that 

continued to plague development. 

 Experiments were made with lateral cyclic in the main rotor, but twin horizontal 

tail rotors were retained for longitudinal control and for just-in-case. Confusion over 

control precession angle still remained. 

 Maj. Gregory next flew the VS-300 on 14 August 1941 by which time the two 

horizontal tail rotors had been removed to be replaced by one horizontal tail rotor for 

longitudinal control. The main rotor now had lateral/collective control. Lateral control 

was now satisfactory and control phase angle was finally understood. Note that, by this 

time, the mechanism for inputting control to the main rotor from stationary coordinates 

to rotating coordinates had been completely revised relative to the manner in which it 

had been accomplished in the aircraft as it was originally flown. In effect, the swashplate 

had now been partially invented. 

 Return to full cyclic control in the main rotor due to success experienced with 

main rotor lateral cyclic was made in late November 1941. On 8 December 1941 first 

flight was made with the new control system. Much work was done ‘refining’ the control 

system (stiffening, collective/throttle synchronization, fine tuning phase angle, etc.). 

 Lt. Col. Gregory next flew the machine on 20 November 1942 with a two bladed 

29 foot diameter main rotor. Decision was made to return to a 3-bladed main rotor. A 

new 30 foot diameter main rotor was constructed. On 23 April 1943 Lt. Col. Gregory 

flew the machine in its final configuration. The basic overall geometry had now been 

established. The XR-4, (Sikorsky VS-316), contracted for back on 21 December 1942 

quickly followed.” 

The several configuration steps Sikorsky took in arriving at the prototype of the modern, 

single rotor helicopter today are illustrated with photographs in Boulet’s history [2].6

 The next major step in helicopter development also improved helicopter stability and 

control. In January of 1943, Arthur Young successfully flew a unique helicopter having a 

single, two-bladed main rotor plus anti-torque tail rotor. His design incorporated a mechanical 

gyroscope rotating with, and partially controlling, the blade feathering motion. This 

“stabilizer bar” changed the helicopter from an inherently unstable “machine” into a more 

controllable aircraft. From model helicopter tests begun in early 1940, Art Young found that 

the stability augmentation in hover could be so complete that his model would simply drift 

with the wind. (Art Young describes his pioneering work with models in reference [21] and 

then again, more completely, in reference [22].) His accomplishment was greeted with 

enthusiasm by Lawrence Bell, president of Bell Aircraft Company and an aviation pioneer in 

his own right. The result of this collaboration, after three prototypes and several accidents, 

was the now-familiar Bell Model 47. This helicopter received the world’s first civil 

certification (from the then CAA) on March 8, 1946.7 

 

6 You will find more fascinating test pilot tales about the VS-300 in the book by Charles Morris, Pioneering the 

Helicopter [19]. He was hired by Sikorsky in early 1941 as the chief flight test pilot and, fortunately, Igor 

Sikorsky provided a history in his famous book, Story of the Winged-S [20]. 

7 The Young rotor system was further discussed and explained by Klemin in the popular magazine Aero Digest 

[23]. The stability and control aspects of the invention were tried on the Sikorsky H-19 with great success [24]. 

Richard Tipton [25] recounts the early history of the trailblazing efforts of Larry Bell and Art Young. Art Young 
1.2 STABILITY AND CONTROL 

15 

 The Bell rotor system (with the Young Stabilizer Bar) as it came to be known, is 

illustrated schematically in Fig. 1-7. The Bell Model 47 hardware is shown in Fig. 1-8. The 

inputs from the pilot through the swashplate are mixed with the stabilizer bar inputs before 

being passed on to the blade. 

Fig. 1-7. Arthur Young invented the stabilizer bar, which significantly improved 

helicopter stability and control [28]. 

 left what was to become Bell Helicopter in June of 1945. Bart Kelley, a lifelong friend to Young and himself a 

leader in the birth of this evolving technology [26, 27], became the technical director of the newly created 

helicopter company in 1946. 
1.2 STABILITY AND CONTROL 

16 

Fig. 1-8. The Young Stabilizer Bar and ground-resonance free, two-bladed rotor system 

put Bell Helicopter in business [28]. 
1.2 STABILITY AND CONTROL 

17 

 What is too often missed in the discussion of the work by Art Young is the fact that his 

two-bladed rotor system completely solved the ground resonance problem (see Volume I) that 

had plagued rotorcraft nearly from the beginning. The lag hinge was removed, and the bladed 

attachment was made very strong in the inplane direction. It virtually uncoupled the lead-lag 

motion from the landing gear degree of freedom. In my view, this was the more rewarding 

benefit to the rotorcraft industry. More helicopters have been delivered with the two-bladed 

rotor system than any other type. 

 Stanley Hiller Jr., also working with a small group of very talented individuals, made 

the next major step to improved helicopter stability and control. Hiller’s story is related by Jay 

Spenser in an excellent book, Vertical Challenge, The Hiller Aircraft Story [29]. Working 

somewhat in isolation on the west coast of the United States, Hiller initially began with a 

reasonably successful coaxial helicopter that evolved into the UH-4 Commuter. But it was 

with his UH-5, a conventional, single-main-rotor plus tail rotor design, that Joe Stuart III, 

Ed Bennett, and Hiller made a real breakthrough. The two-bladed rotor system they pioneered 

is shown in Fig. 1-9 and Fig. 1-10. The engineering fundamentals of this most successful 

mechanical stability and control invention were explained by Joe Stuart [30-32]. 

Fig. 1-9. Joe Stuart III, Ed Bennett, and Stanley Hiller developed the servo paddle 

control system that solved the helicopter stability problem [30, 31]. 
1.2 STABILITY AND CONTROL 

18 

 The application of Stuart’s theory to the Hiller UH-12 (i.e., the Model 360) was 

conveyed by Don Jacoby [33], and Klemin [34] wrote glowingly about the door that had been 

opened. 

 The pilot controlled the feathering of the servo paddles (the control rotor airfoil), and 

the servo paddles controlled blade feathering. The results were that pilot control loads were 

very, very low. This encouraged the direct control of longitudinal and lateral cyclic by a 

stick directly connected to the swashplate. The collective control was conventional. This 

combination of aerodynamic surfaces at the ends of a gyro bar provided the most stability in 

the early helicopters. For Hiller, it led to the very successful Model 360 product line that 

helped support some of the most innovative research and development the rotorcraft industry 

saw during the 1950s. 

 

Fig. 1-10. The Hiller Servo Paddle Control Bar and Bell two-bladed rotor system put 

Hiller in business (photo from author’s collection). 
1.2 STABILITY AND CONTROL 

19 

 The Hiller rotor system, like Young’s, was also two bladed with very stiff joining of 

the blades to the teetering hub. Both were free of the ground resonance “phenomena.” (In my 

opinion, the Hiller system should be resurrected for use in the small, one- or two-place 

helicopters that frequently come to pass. The low-cost advantage of inherent stability with a 

simple aeromechanical system plus the cost of only two blades is just the place to start.) 

 The subject of helicopter stability and control was addressed in considerable detail by 

Rene Miller in his classic paper, Helicopter Control and Stability in Hovering Flight [35]. 

And the behavior of the three basic rotor systems available to future helicopter development 

was thoroughly summarized by Gerhard J. Sissingh [36, 37], starting with his work in 

Germany in 1939.8 In the engineering terminology of this book, the longitudinal flapping for 

each rotor system can be uniquely described as follows: 

For the “normal” rotor blade as Sissingh called it, that is, the three-bladed, articulated rotor 

system adapted by Focke, Sikorsky, and Piasecki 

(1.23) 1C

1S 0 t cyclic

cyclic

B a 2 VV ∂ =θ − δ ∂δ for articulated rotor system. 

For the Young, two-bladed, stabilizer bar rotor system, both the pilot’s stick (δcyclic ) and bar 

motion (δstab. bar ) can make an input to blade feathering. Therefore, 

(1.24) 1C 1C

1S 0 t cyclic stab. bar

cyclic stab. bar

B B a 2 VV ∂ ∂ =θ − δ + δ ∂ δ ∂δ

where the stabilizer bar input (δstab. bar) depends on both body pitch angle and body pitch rate 

according to 

(1.25) stab. bar stab. bar

stab. bar cg cg

cg cg

∂δ ∂δ δ = θ+ θ

∂θ ∂θ

  . 

For the Hiller, two-bladed, servo paddle rotor system, the pilot’s cyclic stick motion (δcyclic ) 

goes first to create the servo paddle motion (δservo paddle) so that 

(1.26) 1C

1S 0 t servo pad

servo paddle

B a 2 VV ∂ =θ − δ

∂δ . 

The servo paddle motion is then described as 

(1.27) servo pad. servo pad. servo pad.

servo pad. cyclic cg cg

cyclic cg cg

∂δ ∂δ ∂δ δ = δ + θ+ θ

∂δ ∂θ ∂θ

  . 

 

8 At the end of World War II, several members of the United States aircraft industry toured through Germany to 

gain insight into the many accomplishments made there. Dick Prewitt summed up rotary wing development [38]. 

A similar assessment was made by Liptrot in Britain [39]. Both Kurt Hohenemser and Gerhard Sissingh [40, 41] 

found their way to the U.S. and contributed enormously to the technology of rotorcraft, and both were members 

in good standing of the American Helicopter Society. 
1.2 STABILITY AND CONTROL 

20 

Of course similar equations can be written for lateral control and stability, and the behavior of 

the helicopter about that axis system. 

 The work by Sissingh [37] shows the essence of these two, pioneering, mechanical 

stability augmentation systems. Several linkage ratios and key derivatives are given that will 

reduce the inherent instability of the helicopter as it evolves into a more manageable machine. 

 The advent of hydromechanical control systems was followed by powerful electronics 

and computers. The industry first saw the stability augmentation system [42, 43] on a 

Sikorsky H-19 late in the summer of 1950. This was followed with successful application on a 

Piasecki XHJP-1, the prototype of the HUP-1. Today, the industry thinks in terms of an 

automatic flight control system (AFCS). 

 This introduction to helicopter stability and control would not be complete without 

acknowledging the role that model helicopters have played. Spenser, on page 166 of reference 

[29], points out that 

“another interesting use of the [Hiller Servo Paddle] Rotormatic system in more recent years 

would underscore its value: almost all radio-controlled gasoline-powered scale model 

helicopters—be they models of Sikorskys, Bells, Agustas, Bölkows, or whatever—require 

Hiller Rotormatic paddles for sufficient stability and control to fly. Without Hiller’s patented 

paddles, model helicopter flight would probably not have been able to evolve parallel to 

radio-controlled model airplanes as a hobby.” 

This important point can be reinforced by the pioneering efforts of John Burkam,9 a truly 

creative engineer. His very simple, small, and light, rubber-band-powered model helicopter is 

shown in Fig. 1-11. The plans for this model first appeared in the January 1970 issue of 

American Aircraft Modeler [44]. The lead-in to the construction details in the article reads: 

Penni Helicopter 

World’s first, real, rubber powered copter is simple but a scientifically developed free-flight 

demonstrating all principles of rotor-wing operation. Build it from scrap! 

 As originally conceived, Burkam used a Young Stabilizer Bar with the 16-inchdiameter rotor. Later, in 1982, a scaled-up version of the “Penni,” called the “Nicki,” was 

developed. It had a 24-inch-diameter rotor. Among other modifications, John incorporated the 

Hiller Servo Paddle. He explained9

 that “the reason for that [change] was that with 9 degrees 

or so of positive [pitch] angle on the paddles, it would tend to pull the helicopter out of a 

shallow dive and restore it to level flight.” 

 

9 John spent his career at what is now the Boeing Helicopter Division and retired in 1987. In private letters and 

telephone discussions, John explained that he had delivered well over a 1,000 kits of the Penni, the larger sized 

Nicki, and also a tandem rotor model called the Tricki. 
1.2 STABILITY AND CONTROL 

21 

Fig. 1-11. The widely built “Penni” model helicopter was created in 1970 by 

John Burkam to demonstrate the stability of various hub types. 
22 
23 

1.3 POWER-OFF LANDING 

 Power failures in a helicopter were not then, or are they today, as benign a situation as 

they were with an autogyro. The reasons for this statement are twofold. First, the helicopter 

inventors now had the possibility of power failure during hovering flight, and second, the 

powered rotor used in the helicopter required additional time, following the power failure, to 

transition into the autogyro mode. Two distinct critical regimes where power failure could be 

especially serious soon became clear. These two regimes were: 

1. Power failure in forward flight while flying at low heights above the ground. 

Speeds from about 25 miles per hour up to maximum speed (Vmax ) where full-rated 

engine shaft horsepower (ESHPrated) was required. In fact, this regime could 

become critical whenever full ESHPrated was used. 

2. Power failure in hover at heights from 10 to 500 feet above the ground. This 

regime was quickly expanded to include flight at low speeds up to 25 miles per 

hour. 

 As more flight testing and operational experience was gained, a diagram of height 

versus airspeed was established for each model (Fig. 1-12). This H-V diagram, as it came to 

be known, conveyed the two flight regimes that the pilot should avoid. Later, the diagram 

became a standard chart found in the emergency procedures section of the pilot’s flight 

manual. The diagram is occasionally referred to as the “deadman’s curve.” 

 Consider the low-altitude, forward-flight regime first and then later the hover and lowspeed flight regime. 

1.3.1 Power-Off Landing 

 You will recall from Volume I that Henrich Focke [45] set the number-one design 

requirement to provide for the “possibility of a forced landing in case of engine failure.” 

Focke went on [46] to say that “on 10th May 1937 he [Rohlfs, the test pilot] performed the 

very first auto-rotational landing, with engine off; a perfect 3-point, tail-down landing.” 

 Sikorsky came to this same point of success in April of 1942 with the XR-4, the first 

production helicopter to follow the VS-300. The story is told by test pilot Charles Morris in 

Boulet’s history.10 Morris recounts a telephone call in late March of 1942 from Lieutenant 

 

10 See reference [2], pages 96–99. The Sikorsky VS-300 success led to an Army Air Corps contract for 

development of the XR-4, signed in December 1940. Ralph Alex, with a 16-member team, translated the 5-page 

technical specification into the first observation helicopter in 1 year. It flew first on January 14, 1942. The major 

acceptance demonstration was conducted April 20, 1942, and the helicopter was flown cross country to Wright 

Field (Ohio) arriving on May 17, 1942. The flight covered 760 miles in 16 flying hours over 5 days. By January 

5, 1943, the XR-4 had successfully completed tests at Wright Field. The helicopter designation was changed 

from XR-4 to YR-4, and an initial order for 29 was placed. In all, 126 R-4s were built in 18 months. (Now that is 

a story of progress.) 
1.3 POWER-OFF LANDING 

24 

0

100

200

300

400

500

0 10 20 30 40 50 60 70 80 90 100

Height 

(ft)

Horizontal Velocity (mph)

AVOID

AVOID

Fig. 1-12. Typical flight regions to avoid when flying a helicopter. 

Colonel Frank Gregory (by then the Army chief of helicopters) requesting the demonstration 

of this first observation helicopter before an Army board as soon as possible. He described a 

full envelope of speed and altitude. Gregory concluded with the desire to “see it up to 500 or 

1,000 feet anyway, but of course 5,000 feet would be excellent!” 

 Morris goes on to say, after gasping, “But we haven’t even found out yet how it 

handles in autorotation, when the engine quits. We have a lot of investigation still for forward 

speed. It seems too early to set a date.” Gregory’s response was, “Nonsense. Suppose we 

make it April 20. That will give you practically a full month to learn all you need to.” (The 

response of the Sikorsky team to this type of need is characteristic of the rotorcraft industry 

even today.) Morris recalls the ensuing effort as follows: 

 “We had no knowledge of the mysteries of high-speed flight, engine failure, and 

altitude. The last two were inseparable; it would be bordering on suicide to go even 100 feet 

off the ground without first investigating how the ship would handle without power. We 

knew, theoretically, that the rotor should keep right on turning, but theory and practice 

sometimes need a little coercing to get together. Nevertheless, we redoubled our efforts. On 

April 3rd, I flew the XR-4 to a nearby airfield. There, over the long paved runways, I would 

try to approach the power-off condition. 
1.3 POWER-OFF LANDING 

25 

 We decided that the safest procedure would be to fly forty to fifty miles an hour, 

about 100 feet high. Pitch [collective] would be reduced as rapidly as possible, and when the 

ship was within twenty feet of the ground, a so-called flare-out would be made by tilting 

rearward and slowing down the ship. We could tell when we had reached autorotation by 

watching the tachometers that showed engine and rotor speed. 

 These tests were the most difficult of any I have ever done. Active coordination of 

the throttle was required as pitch [collective] was quickly reduced. The rudder [tail rotor antitorque thrust] had to be readjusted because of the changing power applied to the main rotor. I 

had to watch the airspeed indicator (to be sure I was not slowing down or speeding up), 

glance at the pitch indicator (to see how close it was to five degrees), keep an eye on the two 

tachometers (for signs of autorotation), and watch the ground, all this in a very short period 

of time! 

 Several attempts were made this first day, but the results were inconclusive. Their 

primary value was in the training I received, and I couldn’t concentrate so hard for more than 

a few minutes at a time. 

 The second day of trials, I was able to secure actual autorotation by starting about 

200 feet high. The glide, with the engine slightly throttled was quite pleasant, and it was 

obvious that the ship lost no part of its excellent control. We were greatly relieved, too, that 

the change from powered flight to autorotation and vice versa, was free from transitional 

vibrations. The completion of this test marked the casting aside of our last fetters–we could 

now feel free to fly at higher altitudes without fear of serious trouble if the engine should fail. 

 A few days later, Gregory (Lieutenant Colonel by now) dropped in to arrange final 

details of the official demonstration. I took him up for his first ride in the XR-4, and he spent 

more than twenty minutes flying it himself, handling the controls, getting the feel of it. 

 Finally I shouted, “I’ll show you a power-off glide.” He nodded his head and 

watched intently as I climbed to 300 feet above the airport, then lowered the pitch lever to 

three degrees, and throttled back. We glided down smoothly, and a broad grin lit his face as I 

banked slightly to one side and to the other. “I think I’ll land her,” I said, when we were 

about 100 feet high. I had never before actually landed a helicopter without power, but 

everything felt so right that it seemed quite natural to carry it through. 

 “Okay,” he smiled. At about twenty feet I eased back slightly on the [longitudinal 

cyclic] control stick to sense its effectiveness, and at five feet from the ground, I moved the 

stick backward again. The glide decreased, the ship flared out as it tilted rearward, and we 

settled softly onto the runway. The tail wheel touched first, and the ship rocked forward onto 

the main landing gear, then rolled about ten feet to a stop. Our first power-off landing was a 

definite success.” 

 From these two accounts of the importance of a power-off situation, you can 

appreciate more fully why it is such an important design consideration, and the detailed 

description provided by Morris emphasizes how pilot-sensitive the emergency procedures 

can be. 

 The engineering description of a landing following power failure in forward flight is 

relatively easy to set up and to understand. Broadly stated, this is a problem in energy 

management during four distinct phases as follows: 
1.3 POWER-OFF LANDING 

26 

1. An awareness of the power failure, 

2. A reaction to the failure with a rapid transition to gliding or autogyro flight, 

3. A well-timed flaring out of the glide as the ground is approached, and 

4. A judicious use of the last amount of stored energy in the rotor system. 

The primary equation that governs the outcome starts with the power required from the 

engine. In this case where maneuvering is going to happen, the basic equation for engine shaft 

horsepower required (ESHPreq’d ) is 

(1.28) 

req'd

R

550ESHP Power Required in Steady Level Flight (550 HP)

Power for Steady Climb (W dh dt)

Power for Accelerating Airspeed (W g V dV dt)

Power for Accelerating Rotor Speed (I d dt)

=

+

+

+ Ω Ω

. 

A positive sign convention has been established in Eq. (1.28) for the three additional demands 

for engine power that are involved in the power-off maneuver. 

 It is not necessary for the moment to think about the details of how to estimate the 

horsepower required in steady, level flight (HP). Therefore, consider the first additional power 

required. This is the power required to change height above the ground. The term deals, of 

course, with the change in potential energy. This additional demand on the engine power 

depends on the weight (W) and the increase in height (h) above ground level with time (t). A 

positive rate of climb (VRC) means that dh/dt is positive. Conversely, in the power-off situation 

a negative change in height with time occurs. This leads to a rate of descent (VRD) and a 

negative value for dh/dt. 

 The second additional demand on the engine comes from a positive increase in 

airspeed (V ) due to acceleration of dV/dt. Because, by definition 

(1.29) ( ) ( )

()( )

2 2

2 2

H RC RD

V Horizontal Speed Rate of Climb or Descent

V V or V

= +

= +

, 

it follows for the positive situation of climbing that 

(1.30) V dV dt V dV dt V dV dt = + H H RC RC . 

In the power-off situation, it does not necessarily follow that the horizontal speed (VH) is 

always reducing or that some rate of climb might not briefly occur during the complete 

maneuver. 

 The third demand from the engine comes from an acceleration in rotor speed (Ω). This 

power depends on the polar moment of inertia (IR) of the rotor system, principally of the 

blades, plus many of the smaller rotating components that go along as rotor speed is 
1.3 POWER-OFF LANDING 

27 

increased. Again, it is not a foregone conclusion that potential energy from height and kinetic 

energy from airspeed might not be used to accelerate rotor speed during the maneuver. 

 A very good engineering view of the time Charles Morris spent giving Lieutenant 

Colonel Gregory a complete power-off demonstration of the XR-4 in early April 1942 can be 

obtained from the previous three equations. Rather than amplifying the details, consider first 

the simple integration of the engine power, Eq. (1.28), with respect to time. Suppose at t = 0, 

the engine power is instantaneously reduced to zero. (A driveshaft failure would do this, for 

example, while simply throttling back quickly would not be a very close approximation.) 

Then, with zeroed engine shaft horsepower in Eq. (1.28), the power-required expression in 

integral form becomes 

(1.31) 

( ) ( ) ( )

f 2 2 2

1 1 1

t t h V

R 0 h V

1 1 22 22

2 1 2 2 2 1 R 2 1

550 HP dt W dh W g V dV I d

W h h Wg V V I

= Ω

Ω =− − − Ω Ω

=− − − − − Ω −Ω

   . 

 Now consider some physical data for the XR-4 and some estimates for the initial and 

final conditions. The XR-4 had a normal takeoff gross weight of about 2,000 pounds, and the 

early engine was rated at 165 horsepower. The three-bladed, 36-foot-diameter rotor turned at 

about 225 rpm giving Ω = 23.5 rad/sec and a tip speed of 420 ft/sec. The XR-4 rotor system 

polar moment of inertia (IR) was on the order of 450 slug-ft2

. 

 With respect to the initial and final conditions, suppose you assume that Morris began 

the demonstration at 300 feet above the ground and at a cruise speed perhaps as high as 

60 miles per hour or 88 ft/sec. This would put the advance ratio (μ) around 0.20. From 

references [47-50], the power required for steady, level flight would have been roughly 

120 hp or about three-fourths of the rated engine power. The initial conditions, therefore, 

become 

(1.32) 11 1 1

2

1 R

t t 0, h 300 ft, V 88 ft / sec, 23.5 rad / sec

550 HP 66,000 ft lb / sec with I 450 slug ft

= = = = Ω=

=− =− . 

The final conditions are much easier to set, of course, because the XR-4 was stopped on the 

ground. Therefore, 

(1.33) f2 2 2 2 t t , h 0, V 0, 0, HP 0 = = = Ω= = . 

 The horsepower required will vary with time, but for this simple illustration assume 

the power is constant over the complete demonstration at a value of HPref. Then the integral 

required by Eq. (1.31) has the first-order estimate of 

(1.34) f t

ref f f 0 550 HP dt 550 HP t 66, 000 t for the XR 4 example = =× −  . 

With this last rough approximation you see the relation between the three sources of energy as 

an expression in time of 
1.3 POWER-OFF LANDING 

28 

(1.35) 

1 1 2 2

1 1R1 2 2

f

ref

Wh W g V I t

550 HP

+ 9.1 seconds from the 300 feet initial height

+ 3.6 seconds from the 60 mph initial airspeed

+ 1.8 seconds from the 225 initial rpm

+ +Ω =

= . 

The power-off maneuver Morris demonstrated was, therefore, over in about 15 to 20 seconds. 

 Within this introductory framework you can now better appreciate the comments 

Morris made about the total concentration it took to develop the emergency procedure and to 

visually record data while he learned. Just as interesting is the speculation about Lieutenant 

Colonel Gregory’s confidence. After all, Gregory, as an established autogyro pilot, had 

performed the full autorotation to a successful landing hundreds of times, but in this 

demonstration he was the passenger with a pilot who was doing it for the first time. 

 The introduction of Eq. (1.35) provides a step to defining a flight envelope in which an 

experienced pilot is likely to land successfully following a complete loss of power. This 

envelope has evolved into a chart of height versus airspeed that is normally placed in the 

flight manual as part of the Emergency Procedures section. A preliminary basis for this 

height-velocity diagram is to use time as a fixed parameter and find the line that relates height 

and velocity. From Eq. (1.35), this means solving for height (h) in terms of airspeed (V ) for a 

given time (tf ). Thus, 

(1.36) 

2 2

ref f R 550 HP t V I h

W 2g 2 W

Ω = −− . 

The results of applying Eq. (1.36) for the Sikorsky XR-4 example are shown in 

Fig. 1-13. The configuration data used for this example are a weight (W) of 2,000 pounds, a 

reference horsepower (HPref) of 120 hp, an initial rotor speed (Ω) of 23.5 radians per second, 

and a rotor polar moment of inertia (IR) of 450 slug-feet2

. 

 With Fig. 1-13 in hand, you can better appreciate the progressive increase in height 

that Morris selected as he developed the emergency procedures. He said that 

1. “We decided that the safest procedure would be to fly forty to fifty miles per hour, 

about 100 feet high.”.....“Several attempts were made this first day, but the results were 

inconclusive.” 

2. “The second day of the trials, I was able to secure actual autorotation by starting about 

200 feet high. The glide, with the engine slightly throttled [presumably at flight idle], was 

quite pleasant... .” 

3. A few days later, Morris demonstrated the XR-4 to Lt. Col. Gregory after climbing “to 

300 feet above the airport [and probably at about 50 miles per hour], then lowered the 

[collective] pitch lever to three degrees, and throttled back.” 
1.3 POWER-OFF LANDING 

29 

0

100

200

300

400

500

0 10 20 30 40 50 60 70 80 90 100

Height 

(ft)

Horizontal Velocity (mph)

Manevuer Time

15 seconds

5 sec

10 sec

2.5 sec

Fig. 1-13. The XR-4 power-off envelopes for four different maneuver times, tf. 

Morris, of course, was not dealing with a complete engine failure so the first second, or 

perhaps two, of becoming aware of the emergency was not demonstrated. This is the first of 

the four distinct phases outlined earlier and, in fact, he was only approximating the second 

phase in which the pilot must react rather quickly to make the transition to autogyro mode. 

 The first second or two following complete failure of power to the rotor system 

imposes a clear design constraint. You can see this from the rather simple analysis that 

follows. The important general characteristic is that the torque that reduces rotor speed goes 

down from the initial value in approximately a linear fashion. That is, 

(1.37) ( ) ( ) Q Q 1 tt t = − 0 1 . 

The reasoning behind this rather fundamental behavior is simple physics. When the engine 

quits, the energy per second (i.e., the power) is supplied almost entirely by the kinetic energy 

from rotor inertia. The rotorcraft follows F = ma in the horizontal and vertical directions much 

slower. Thus, little kinetic energy becomes available until a second or two after the power 

failure. The full potential energy available from a loss in height follows even later. The 

deceleration in rotor speed reduces rotor thrust roughly in proportion to the square of rotor 
1.3 POWER-OFF LANDING 

30 

speed, so the rotorcraft begins to fall first and slow down second. The rate of descent velocity 

(VRD), therefore, supplies the next source of energy to help offset the decaying rotor speed. 

The net result of this somewhat complex transient behavior is, perhaps surprisingly, the linear 

variation in rotor torque approximated by Eq. (1.37). 

 Even though the engine power goes instantaneously to zero at t = 0, the rotor winds 

down in a slower manner, and zero torque equilibrium is not reached until the time of t = t1. 

Interestingly, the time to reach zero torque is on the order of t1 = 2 seconds (for no pilot input 

and from a straight and level flight condition). Accepting this first-order characteristic makes 

the problem easy. The rotor speed (Ω) is then determined by the simple equation 

(1.38) ( ) ( )

2

R R 01 2 t

d d I I Q Q 1 tt dt dtψ Ω = =− =− − . 

This rotor speed equation is integrated to give 

(1.39) ( ) ( ) 2

R 00 1 t I Q   Ω −Ω =− −t t 2t  

from which it follows that 

(1.40) ( ) ( ) ( ) t 0 2 2 0

1 1 2

0 R0 R0

Q P 1 t t 2t 1 t t 2t

I I

Ω =− − =− − ΩΩ Ω . 

With the postulated linear variation in torque with time suggested by Eq. (1.37), the rotor 

speed decreases from t = 0 to t = t1 . Then the rotor RPM begins to increase again. This droop 

in RPM reaches a minimum at t = t1 and has the value 

(1.41) ( )t 0

2 1

0 R 0

P 1 t

2I

  Ω

  = −     Ω Ω . 

For the XR-4 example, this becomes 

(1.42) ( )t

2

0

66,000 1 2 1 0.266 0.734

2 450 23.5

  Ω

  = − × =− =

  Ω ××  

. 

There are several reasons, as you will see later, for not purposely allowing the rotor speed to 

drop below normal RPM by more than 20 to 30 percent. Charles Morris was demonstrating a 

helicopter that, in retrospect, was on pretty safe ground in this regard. 

 There is, of course, a loss in rotor thrust as the rotor speed decays in the first several 

seconds. This thrust variation is roughly in proportion to the square of rotor speed. Because 

thrust is approximately equal to weight at time zero, it follows that 

(1.43) ( ) ( )

2 2

t 2 0

2 1

0 R0

P Thrust (Weight) 1 t t 2t (Weight) I

  Ω   ≈ =− −         Ω Ω  

. 
1.3 POWER-OFF LANDING 

31 

This loss in thrust leads immediately to the rotorcraft falling with an acceleration proportional 

to the difference between weight and thrust. A rate of descent velocity (VRD), therefore, builds 

up in accordance with the solution to F = ma of 

(1.44) ( ) t t

RD 0 0

W T V dt g 1 T W dt W g− = =−   . 

This equation is directly integrated because the ratio of thrust to weight is approximated from 

Eq. (1.43). The simple result is that 

(1.45) 

23 4

2 0 0

RD 222

R0 1 R0 1 1

P P t tt t V gt 1 I 3t I 3 4t 20t

     

= −− −+         Ω Ω     . 

The rate of descent when the torque is about zero (i.e., t = t1 ≈ 2 sec) then will be on the order 

of 

(1.46) 

0 0

RD 1 2 2

R0 R0

P P 8 16 V g at t t 2 sec

I 3 15 I

20 ft/sec for the XR-4 example.

    = − ==       Ω Ω  

=

 The rate of descent leads naturally to a loss in height, which, if the power failure 

happens near the ground, obviously becomes extremely important. This height lost is found 

by integrating Eq. (1.46) to find that 

(1.47) 

3 2 3

0 0

22 2

R0 1 R0 1 1

g t P P t t 3t t h 1

3 I 4t I 4 20t 40t

      Δ= − − − +         Ω Ω     . 

Assuming again the t = t1 ≈ 2 sec situation means that the loss of height the pilot would have 

to deal with is about 

(1.48) 

0 0

2 2 1

R 0 R 0

P P 1 h 2g 1 at t t 2 sec

I I 3

16 feet for the XR-4 example.

  

Δ= −    = =

 Ω Ω  

=

 Now go back to the first and second distinct phases that follow an abrupt loss of power 

using the results obtained above. To repeat, these first two phases are: 

 1. An awareness of the power failure, and 

 2. A reaction to the failure with a rapid transition to gliding or autogyro flight. 

These two phases could easily take 2 seconds. Furthermore, in that time the rotorcraft could 

well drop 15 to 20 feet and pick up a rate of descent velocity of 20 to 25 feet per second. And 

this situation could be expected at any horizontal airspeed from hover up to an airspeed where 

the full rated power of the engine was required. This rather simple overview illuminates, 
1.3 POWER-OFF LANDING 

32 

therefore, a portion of the height-velocity diagram (begun with Fig. 1-13) that should be 

avoided. 

 The height-velocity diagram can show the area to be avoided. For example, continue 

the XR-4 illustration by replacing HPref of 120 hp with ESHPrated = 165 hp. Then Morris 

might have conservatively experienced an excessive droop in RPM down to 64 percent of 

normal RPM at the 2-second time. The rate of descent would then be about 27 ft/sec and the 

height loss more on the order of 21 feet. On this basis, Fig. 1-13 would be revised to show an 

AVOID area as illustrated in Fig. 1-14. 

 The AVOID area shown in Fig. 1-14 tapers down at low speed. This reflects a modern 

view that came with operational experience and theoretical work begun in the 1950s by 

I. C. Cheeseman in England [51] and pursued by Harry H. Heyson at NASA in the U.S.A. 

[52]. The low-speed region is somewhat more favorable because of ground effect that 

provides a beneficial cushioning and reduced power required. 

0

100

200

300

400

500

0 10 20 30 40 50 60 70 80 90 100

Height 

(ft)

Horizontal Velocity (mph)

AVOID

Manevuer Time

15 seconds

5 seconds

10 seconds

2.5 sec

Fig. 1-14. The XR-4 low-height AVOID region predicted with a simple theory. 
1.3 POWER-OFF LANDING 

33 

 The second distinct phase of the power failure emergency deals with the reaction of 

the pilot after becoming aware of the situation. In the AVOID area, the reaction is likely to be 

rather instinctive upon seeing the loss in height. That is, the pilot would increase collective 

pitch to get thrust (even as the rotor speed is decaying). The simultaneous response must be to 

flare the rotorcraft nose up by moving the longitudinal cyclic stick aft. This control motion, if 

done quickly at high speed, can actually get the rotorcraft to climb and bring the rotor speed 

back to near normal RPM. After this 1- to 2-second period, the pilot has some opportunity to 

land safely. 

 The reaction—the second phase, when the rotorcraft is well out of the AVOID area of 

the height-velocity diagram—would be different. Generally, the procedure would be as Morris 

described. That is, a quick lowering of the collective pitch accompanied by some aft 

longitudinal cyclic to avoid an excessive droop in RPM as the transition to the autogyro 

gliding state is made. 

 The actual power-off glide, the third distinct phase, can be rather uneventful as 

autogyros demonstrated (and Morris records about his second day). The pilot has considerable 

latitude in glide speed. You can see this from data for the PCA-2 autogyro shown in 

Fig. 2-114 in Volume I. The glide can be stretched by gliding at an airspeed for the best lift-todrag ratio just as is done with a fixed-wing aircraft. And as the ground is approached, a slight 

flare will reduce airspeed to the point where rate of descent is minimized. However, a major 

problem of this third distinct phase of the emergency can occur in this period. If the rotorcraft 

has an excessive minimum rate of descent (say upwards of 1,800 feet per minute or 30 feet 

per second), the skill and judgment of the pilot in the final 3 to 5 seconds become the deciding 

factor. 

 To this day, I am not aware of any simple theory (comparable to that developed for the 

AVOID area) that captures the period from flaring the glide to the final touchdown. Factors 

such as flaring nose-up reduces visibility and the pilot may lose reference to how close the tail 

is to the ground, or the few seconds of flight available from rotor inertia may be given up too 

soon in reducing rate of descent velocity. This last phase is entirely in the hands of the pilot. 

 You can read many technical articles about power-off landings. I doubt, however, that 

they will be as informative as what you can learn from an experienced pilot. To emphasize 

this point, consider a most recent book, To Fly Like a Bird, which tells many operational 

stories of the first Bell helicopters. In the last chapter, Joe Mashman11 discusses autorotation. 

He highlights the efforts he and Floyd Carlson made to bring Larry Bell, Art Young, and Bart 

Kelley (with their pioneering Model 30) up to the point that Charles Morris and Sikorsky had 

reached earlier. Mashman relates that in late 1943: 

 

11 Joe Mashman, in reference [53], pages 170–172, provides another pioneering story that you can learn so much 

from. Joe switched over from flight testing Bell fixed-wing aircraft and was taught to fly helicopters by Floyd 

Carlson. Joe relates a great deal of the history of the Bell Model 47. The operational experiences he passes on are 

absolutely fascinating and provide key design considerations for a useful rotorcraft. 
1.3 POWER-OFF LANDING 

34 

 “We knew that if you lost your engine, you had to go to a low blade angle to keep 

the rotor turning. That’s what determined our minimum collective pitch setting in the 

helicopter, the setting that would keep the rotor blades turning at the optimal rpm due to the 

inflow of air up through the rotor. It wasn’t too hard to figure out, using what little 

aeronautical knowledge we already had. 

 What we didn’t know was how effective rotor inertia would be and how effective 

the flare would be. We did know how much inertia we’d get to a certain extent, because we 

could hover just above the ground and chop the throttle. As the aircraft began to settle, we 

would abruptly pull up the collective pitch lever and utilize the main rotor inertia to cushion 

the landing. That gave us an effective feel for the inertia and how much collective had to be 

pulled. But we didn’t have knowledge of the interaction between the flare and the collective 

pitch pull needed to make a safe power-off landing. 

 Sikorsky had already successfully demonstrated autorotation with their machines. 

But their helicopters had articulated rotor heads [on] which [the blades] were mounted with a 

slight [flapping hinge] offset. The articulated rotor follows the pitch of the fuselage as the tail 

hits the ground and then pitches forward. When the fuselage pitches forward, it carries the 

rotor forward. With the semi-rigid, seesaw-type Bell rotor, there’s no resistance to prevent 

teetering between the rotor and the mast. It’s just free to flap, so if you hit the tail and 

violently pitch forward, the rotor can’t follow fast enough, and that’s when it hits the tail 

boom, with what can be devastating results.” 

With this background about the differences between the Sikorsky articulated rotor system with 

flapping hinge offset and the Young teetering rotor system, Mashman continues with: 

 “Early during the development program, Floyd Carlson had tried an autorotation in 

the original single-place Model 30, Ship 1. As he flared, his tail hit the ground and the main 

rotor sliced into the tail boom, cutting it right off. The helicopter was repaired [it became 

Model 30, Ship 1A], four wheels were put on, and the seat was widened so that another 

person could sit next to Floyd to read the instruments for him while he flew the aircraft. Now 

it was my turn to accompany him on the next autorotation attempts. 

 Floyd and I flew over to a little grass strip close to our Gardenville [New York] 

facility and began our flight test procedure. Starting in forward flight we reduced power by 

small increments and did a running touch-down landing preceded by a moderate flare. Floyd 

was doing the flying; there was only one set of controls. I’d call out the manifold pressure 

and the airspeed to him so he didn’t have to look down at the instrument panel. On the first 

one, we did a rolling touchdown, at about 60 percent power. Then we took off, went around 

again and cut the power back another inch or two of manifold pressure. We came in at the 

theoretically best autorotating speed, did a flare, and then touched down as we rolled off 

power. We just sort of gradually worked our way down in power settings until we achieved a 

complete power-off landing. It took about 45 minutes and involved about 15 takeoffs and 

landings.... .” 
1.3 POWER-OFF LANDING 

35 

Mashman goes on to point out a key design philosophy that Bell Helicopter adopted for its 

future products. He says: 

 “To improve the helicopter’s autorotative capability, the engineers intentionally 

increased rotor inertia so that, in a steep flare, we could just slowly ease the nose forward 

while maintaining a decelerating attitude. With a low inertia rotor system, you can’t keep the 

helicopter in a flare very long. This is why the rotor systems of two-bladed Bell helicopters 

have high inertia, which provides outstanding power-off landing capability.” 

 Now, given what Morris and Mashman wrote, think again about the last phases of 

landing after power failure. These phases are: 

3. A well-timed flaring out of the glide as the ground is approached, and 

4. A judicious use of the last amount of stored energy in the rotor system. 

The flaring portion of the maneuver is really a flaring of the tip path plane (αtpp) discussed 

earlier in relation to autogyros (see Fig. 2-28, Volume I). To arrest the rate of descent with a 

flare really means to increase αtpp from about 10 degrees up to perhaps 20 to 30 degrees. 

During the glide, the tip path plane is flapped slightly aft relative to the hub plane, however, 

the rotorcraft fuselage attitude (θcg) relative to the ground is nearly zero (not terribly 

uncomfortable as Morris pointed out). Now to increase αtpp in the final flare without 

increasing the fuselage attitude would require perhaps 15 to 20 degrees of longitudinal 

flapping (a1S). The Cierva-type hub, which has a flapping hinge offset (rβ ), would introduce a 

very large nose-up pitching moment to the body with this much flapping. Therefore, a 

combination of fuselage attitude and flapping (i.e., αhp + a1S = αtpp ) that produced a reasonable 

flare had to be found by Morris. His configuration led to rather large nose-up body attitudes 

when the tail wheel touched down. In contrast, Carlson and Mashman, with the teetering rotor 

having zero flapping hinge offset, found they could introduce a great deal of flapping and 

much lower nose-up fuselage attitude to achieve the same αtpp. The restraint for them was 

clearance between the rotor blades and the tail boom. 

 Mashman explained the final phase of the power failure procedure when he discussed 

not letting the helicopter slam down on its main gear after the tail wheel touched down. 

Without any horizontal velocity, and with zero rate of descent, the only energy left is from 

rotor inertia. As you saw from the XR-4 numerical example, rotor inertia provided less than 

2 seconds in which to complete the final touchdown. 

 To completely analyze all four phases of the maneuver requires some form of 

simulation that has the pilot in the loop. In the pioneering days, that meant the pilots flew the 

prototype. Fortunately, today we can do much better. However, even a simple first-order 

simulation has a serious shortcoming that still exists today. The shortcoming is that thrust, and 

particularly power required at high αtpp, is poorly predicted even with empirical modifications 

based on experiments. 

 
1.3 POWER-OFF LANDING 

36 

 Despite the complexity of the maneuver, some hint of test procedures was evolved. 

For example, the throttle chops done in a low hover that Mashman described helped 

succeeding pioneers approach evaluation of their configuration more safely. And from a 

design criteria point of view, the importance of rotor inertia and minimum rate of descent 

became clearer with each succeeding helicopter. In Fig. 1-15, I have created a sweeping 

generality of a design criteria. The figure reflects the success of (1) Cierva, Pitcairn, and 

Kellett with their autogyros, and (2) Focke, Flettner, Sikorsky, Young/Bell, Hiller, Piasecki, 

and Kaman with their helicopters. 

 Rotor energy, as used on the ordinate of Fig. 1-15, is expressed in units of horsepower. 

That is, 

(1.49) normal

2

RI

Rotor Energy in horsepower 550

Ω ≡ . 

For the abscissa, I chose the installed rated shaft horsepower of the engine at sea level as an 

all encompassing measure of the configuration. Two lines, suggesting the importance of 

minimum rate of descent to the safe landing, are added to Fig. 1-15. This follows from the 

experiences of Mashman. 

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

0 50 100 150 200 250 300 350

Rotor 

Energy 

(hp)

Installed Engine Horsepower (Rated hp)

2 sec. Time Delay

Min. Rate of 

Descent

1,200 fpm

900 fpm

Fig. 1-15. Both low, minimum rate of descent, and high rotor kinetic energy are 

important to a safe, power-off landing. 
1.3 POWER-OFF LANDING 

37 

 In addition to minimum rate of descent, the drop in rotor speed immediately following 

an abrupt loss of power is reflected in Fig. 1-15. I suggest that a more conservative design 

criteria might have been chosen by the pioneers. Because any of their helicopters were 

capable of flying at the full rated shaft horsepower of the engine (ESHPrated ), letting P0 equal 

550 times ESHPrated in Eq. (1.40) would better cover the power failure situation for the 

complete flight envelope. 

 Accept again that t1 is on the order of 2 seconds, and say the rotor-speed ratio should 

not go below 70 percent of normal RPM. Then the product of rotor inertia and rotor-speed 

squared should be selected so that 

(1.50) 2

R normal rated I ESHP

550 0.3

Ω

≥ . 

1.3.2 Power Failure in and Near Hover 

 The more serious side of the height-velocity diagram centers on a power failure when 

the rotorcraft is hovering. Performance in a vertical descent was hotly debated even for the 

autogyro as you found by reading the Glauert lecture of January 20, 1927 [54]. Early model 

rotor systems were tested in a wind tunnel and in free-flight drop tests [55-60]. More 

applicable data came from full-scale testing such as that provided by Wheatley [61]. The net 

result was that (1) early model tests were found not to be representative of full scale, and that 

(2) the bare essentials could only be empirically captured in crude theory. This left the 

problem of studying power-off vertical descent squarely in the laps of flight test and 

experimental test pilots. 

 What came from this early work was the conclusion that, in power-off vertical 

descent, the rotor had the performance of a parachute. Glauert advanced this finding at the end 

of his January 1927 lecture saying: 

“Before concluding I wish to say just a few words about the possibility of the vertical descent 

of a gyroplane. The condition in which the windmill is then operating is unfortunately 

outside the scope of airscrew theory at present, and our conclusions must be based wholly on 

empirical results. In light of wind tunnel experiments and of dropping tests it appears that the 

velocity of steady vertical descent of a windmill is of the order of 25 w [the paper has a 

typographical error and the correct expression is 25 w1⁄2 ], where w is the loading per sq. ft. of 

disc area, and for a loading of 2 lbs. per sq. ft. this means a vertical velocity of 35 f.p.s. I see 

no reason for believing that the rate of descent of a full scale windmill can be appreciably 

less than this value, and so I do not believe that it would be safe for a gyroplane to descend 

vertically to the ground for any considerable height in still air. Of course, with the wind 

blowing and for a descent from low height, from which the full vertical velocity would not 

be attained, it might be possible to perform this manœuvre, but genuine steady vertical 

descent at a safe speed does not seem to be possible.” 
1.3 POWER-OFF LANDING 

38 

 The conclusion that Glauert advanced and that Wheatley confirmed with tests of the 

Pitcairn PCA-2 autogyro [see Volume I, Fig. 2-102, and Eq. 2.276] was simply 

(1.51) ( )( ) ( )

2 2 hp

horizontal 1 2

2 D

T

R/D V

C R

+ =

ρ π

and that 

(1.52) ( ) ( )

2 2

R 1 2 2

W 2 RD

LD D T C 1.2 for vertical descent

q A S qA V R

+ = == ≈ + ρ π

from which it follows that the minimum vertical rate of descent velocity will be on the order 

of 

(1.53) 2 2

RD 1

2 R max

1 Min. V T R 26.5 T R in ft / sec

C

≈ π= π

ρ

when the density of air is taken as 0.002378 slugs per cubic foot, and the maximum rotor drag 

coefficient is 1.2. Glauert’s use of 25 rather than 26.5 reflects a modest impression that the 

maximum rotor drag coefficient was somewhat higher than the 1.20 I have used here. 

 What is so interesting about the discussion that followed Glauert’s January 1927 

lecture was that many in the audience were quite convinced that they had clearly witnessed 

the Cierva Autogiro perform vertical descents on landing. Others argued that even if it was 

not vertical descent, operationally controlled descent at 30-degree glide path angles was quite 

satisfactory.12 More model experiments were requested and additional, more carefully 

conducted flight testing was demanded—all to be reported as soon as possible, of course. 

 The crux of the situation really centered around the rate of descent versus horizontal 

velocity performance at low speed. You can see this from typical flight data for the PCA-2 

autogyro that was shown in Volume I, Fig. 2-102. The low-speed end of this data is presented 

here as Fig. 1-16. 

 From Fig. 1-16 you can see that landing into the wind would give the appearance of a 

much steeper glide angle while the rate of descent would still be rather low. This point was 

brought out by several members of the audience at Glauert’s January 1927 lecture. In 

addition, the ground had the effect of increasing thrust to some extent which also softened the 

tail-down landing. 

 

12 The more important issue raised by the lecture was the position reiterated by Glauert that gyroplane highspeed performance and efficiency was not ever going to be comparable to fixed-wing aircraft. Cierva felt that 

Glauert was dismissing his Autogiro quite prematurely, and only on the basis of theory and some model tests that 

were currently in progress. Cierva stated that Glauert was wrong on all counts and was adamant about it in his 

letter that replaced his attendance at the lecture. Mr. Handley Page, a senior member of the aircraft industry, was 

in the audience. He expressed his opinion saying, “When the next paper comes I hope it will be a paper from 

Senor de la Cierva, but I suppose it will be replied to by letter from Mr. Glauert, who will be unable to be 

present. I do hope, however, that then we shall have the facts of the whole thing.” 
1.3 POWER-OFF LANDING 

39 

0

10

20

30

40

0 10 20 30 40 50

Rate of 

Descent 

(ft/sec)

Horizontal Velocity (ft/sec)

Approximate Tip 

Path Plane Angle

 of Attack 60 deg. Nose Up

45 deg.

30 deg.

( ) ( ) ( ) 2 2 2

R / D V 36.5 + = horizontal

Fig. 1-16. The PCA-2 low-speed gliding performance showed that the rotor had the drag 

of a parachute (power off, constant rotor speed, and hover out of ground effect). 

 The solid line I have added to Fig. 1-16 provides a first extension from vertical 

descent of power-off performance. By assuming that 

(1.54) ( ) ( )( )

2 2

R 1 22 2

W 2 RD H

LD W C 1.2 at low speed qA S VV R+ == ≈ + ρ+π , 

it follows that the relation between vertical rate of descent velocity (VRD) and horizontal 

velocity (VH) will be graphically a circle described as 

(1.55) ( ) ( )

2 2

RD H 1 2 2

2

W W V V at low speed 1.2 R 0.6 R

+= =

ρπ ρπ . 

Thus, the early rotorcraft technology aspects of terminal velocity in vertical descent were laid 

for the helicopter pioneers. 
1.3 POWER-OFF LANDING 

40 

 What soon became apparent to the helicopter community was that this low-speed, high 

tip-path-plane angle-of-attack (αttp) region had a number of very adverse operational 

characteristics. The primary up-flow through and about the rotor was very turbulent. This 

caused erratic control of vertical and near-vertical descent, and significantly increased overall 

helicopter vibration. In reality, rotorcraft did have a low-speed stall region using a definition 

based on highly turbulent flow. The region was bounded by αttp greater than 30 (or perhaps 

45) degrees and combinations of VRD and VH near and within the circle given in Eq. (1.55). 

 Henrich Focke conveyed early exploration of power-off test results in figure 4 of his 

1965 Cierva lecture [46]. He chose to make his point with power-off data from low speed. 

Pilot Rohlfs landed starting with a throttle chop in low-speed, level flight at about 4 meters 

per second (13 ft/sec) and at a height of roughly 160 meters (525 feet). The time history 

Focke included shows that Rohlfs chose to exchange altitude for horizontal velocity and avoid 

a vertical descent from such a height. The time history, in English units, becomes more 

informative by plotting height versus horizontal velocity as Fig. 1-17 shows. 

 The transition by pilot Rohlfs initially appears to be toward a vertical descent but, by 

350 feet and about 5 seconds into the landing, he had already started to nose the F. 61 into a 

dive that took him well into forward flight. During this power-off landing, the vertical rate of 

descent reached a maximum of about 80 ft/sec at the 6-second point. After building up nearly 

100 ft/sec of flight path airspeed, he pulled out of the dive and made the landing as if from a 

power failure in forward flight. Data from Focke suggests that Rohlfs nearly touched down at 

a very high speed, but apparently he simply glided parallel to the ground and let horizontal 

airspeed bleed off. 

 This interchange in VRD and VH for the Focke F. 61 helicopter is shown in Fig. 1-18. 

The first 3 seconds were spent well within the rotor turbulent flow region. The subsequent 

nose-down dive increased rate of descent and flight path airspeed, and took the helicopter out 

of the turbulent flow region. By 9 seconds the pull-up was well underway, and he was clearly 

back in control of the situation with still 150 feet of height available. Focke’s time history, 

however, does show a rather hard landing. 

 As the pioneers gathered more experience in power-off landings from, and near, hover, 

a low-speed AVOID area was mapped out. It took the shape of a pear as illustrated in 

Fig. 1-19 for the XR-4 example. The character and design criteria related to both AVOID 

regions have received considerable attention [62-75]. 

 The reliability of engines and drivetrain components rapidly improved as the pioneers 

gained and applied field experience. But to this day, Focke’s number-one design requirement 

to provide for the “possibility of a forced landing in case of engine failure” has remained of 

paramount importance to the rotorcraft industry.
1.3 POWER-OFF LANDING 

41 

0

100

200

300

400

500

600

0 20 40 60 80 100 120

t=0

t=3 seconds

Altitude 

Above

The

Ground

(ft)

t=18 seconds

t=15

t=12

t=9

t=6

Horizontal Velocity (ft/sec)

Fig. 1-17. Power-off vertical descents from high altitudes were avoided by pilots of early 

helicopters and still are today. 

-20

0

20

40

60

80

100

0 20 40 60 80 100 120

Rate of 

Descent 

(ft/sec)

t=15 t=12

t=9

t=6 sec.

t=3

t=0

t=18

Horizontal 

Velocity 

(ft/sec)

60 deg.

( ) ( ) ( ) 2 2 2

R / D V 36.5 + = horizontal

Fig. 1-18. Transition from vertical descent to descent in forward flight avoided the 

turbulence region of the rotor. 
1.3 POWER-OFF LANDING 

42 

0

100

200

300

400

500

0 10 20 30 40 50 60 70 80 90 100

Height 

(ft)

Horizontal Velocity (mph)

AVOID

AVOID

Manevuer Time

15 seconds

5 seconds

10 seconds

Fig. 1-19. The XR-4 had two AVOID regions but only one could be predicted with a 

simple theory. 
43 

1.4 CLOSING REMARKS 

 The rotorcraft industry completed the transition from autogyro to helicopter product 

line by the end of 1945. In Germany, the pre-World War II, 1936 experimental Focke F. 61 led 

to government war orders for the larger Focke Achgelis Fa-223. The German Government 

also placed war production orders for the Flettner Fl-282, which was based on the successful 

Flettner FL-265 experimental helicopter of 1939. Based on Focke’s success, the Weir 

Company in England discontinued autogyro development and began its experimentation with 

the W.4 and W.5. And in the United States, the Army Air Corps led the transition when they 

selected the Sikorsky R-4 for production in 1942. 

 This transition from autogyro to helicopter product line is shown in Fig. 1-20. While 

the history may seem rather complex when presented graphically, it was, in fact, driven by 

two main factors. First, the commercial success of the autogyro did not carry over to 

enthusiastic military use. In fact, several evaluations of the autogyro versus the observation 

balloon were conducted by the U.S. Army Air Corps. Their conclusions, even before World 

War II began, were quite unfavorable with regard to the autogyro as Butler points out [76, 77]. 

Field evaluation was impeded by accidents with both the Kellett YG-1 and Pitcairn YG-2 

direct control autogyros. Persistent occurrences of ground and air resonance complicated 

confidence in rotary wing technology by the decision makers of the day. 

 The second factor was, of course, Focke’s success with the helicopter. This technology 

advancement, which gave a true rotorcraft hovering capability, was brought to the attention of 

Major General Oscar Westover (then Chief of Air Corps) by Lawrence LePage in early 1938. 

By the end of 1938, the U.S. Government had authorized $2,000,000 for rotary wing and 

slow-speed, high-lift aircraft. The War Department was assigned as the lead agency. They 

issued a request for information (RFI) proposal in December 1939. The industry response led 

to the U.S. Air Corps Material Division at Wright Field issuing a request for proposal (RFP) 

to buy aircraft. From the several proposals submitted, the evaluation board selected two 

winners in June of 1940. They were: 

a. The Stinson Aircraft Company’s C-105 fixed-wing, short-range, liaison aircraft, 

and 

b. The Platt–LePage Aircraft Corporation’s larger variation of the Focke F. 61. 

As Butler notes on page 10 of reference [77], neither the Pitcairn or Kellett autogyros, nor the 

Sikorsky helicopter designs were selected. The Platt–LePage helicopter was designated the 

XR-1, and the company was funded $199,075 for one rotorcraft. Stinson received about 

$3,000 each for immediate delivery of six off-the-shelf aircraft. 

 Despite best efforts by Haviland Platt and Laurence LePage, progress in developing 

their 440-horsepower, 5,200-pound-gross-weight helicopter was painfully slow. The XR-1 

first hovered on May 18, 1941, but delivery dates kept being missed. An additional contract 

for $144,662 led to a second, improved model designated the XR-1A. The U.S. Army finally 

took delivery of this helicopter in early August 1944. However, in April 1945, the U.S. Army 

terminated all contracts with the Platt–LePage Corporation. 
1.4 CLOSING REMARKS 

44 

 Technical difficulties experienced by Platt–LePage, from contract award well into late 

1944, kept the door open for Sikorsky. His progress in solving the problems of the VS-300 

and translating the configuration into the VS-300A laid the foundation for the Sikorsky XR-4. 

It was this helicopter, developed under the leadership of Ralph Alex, that gained the ultimate 

procurement support for the first successful incorporation of the helicopter into the Army 

Aviation force structure. 

Igor

Sikorsky

1938

VS 300A

Dec. 31, 1941

XR-4

Jan. 14 XR-6

Oct. 15, 1943

XR-5

Aug. 31, 1943

900 Ordered

416 Built

200 Ordered

123 Built

131 Ordered

131 Built

W - 5

June 6

Weir Ltd

1937

XR - 1

June 23, 1941

XR - 1A

Oct. 15, 1943

Havilland H. Platt

W. Laurence LePage

1938

H. Focke & G. Wulf

Flugzengban A.G.

Heinrich Focke

1933

F. 61

2 Built

June 26, 1936

H. Focke

1937

Fa 266

Renamed

Fa 223

100 Ordered

Plus Parts For 30

17 Built

Ivan

Bratukhin

1940

2 MG Omega

Omega II

Frank N.

Piasecki

1943

1942

Stanley

1941 Hiller, Jr.

Arthur Young

Larry Bell

Sept. 14

VS 300

1939

1942

K. Achgelis

One Fa 223

Delievered To

U.S. Troops

·

Parts For 30 To ·Russian Troops

One Fa 223 ·Flown to 

England

1938

Oct. 27

W - 6

1939

August

1940

FL - 265

6 Built 24 Built

Anton 30 Ordered

Flettner

1937

FL - 288

August

1940 May 19

1939

Two Fl-282 ·Taken To U.S.A.

Spring

1945

·One Removed

By Russian Army

Type 314 1 Built

June 26, 1935

Societe Anonyme 

Louis Brequet

 des Avions

Le Syndict d'Etudes 

du Gyroplane

Rene Dorand

1932

Pitcairn

Autogiro

Company

PA-33

Renamed

YG-2

Kellett

Autogiro

Corporation

YG-1 XO/YO

-60

XR-2

XR-3

Fig. 1-20. The rotorcraft industry made the transition from autogyros to helicopters 

before the end of World War II. 
1.4 CLOSING REMARKS 

45 

 The U.S. Air Corps had made good use of the autogyro before selecting the helicopter 

for its future and, in fact, this first rotorcraft gained significant support at the operational 

level. This support was strongly stated by First Lieutenant Erickson S. Nichols in a paper he 

presented at the Second Annual Rotating Wing Aircraft Meeting held on November 30 and 

December 1, 1939.13 Lieutenant Nichols was introduced by session Chairman, Captain 

Franklin Gregory. Lieutenant Nichols noted in his introduction that 

“Captain Gregory, at the meeting held here last year, gave a report on the history in the Army 

of the autogiro, and this year I have been asked to tell its tactical use for the Army and its 

military value and the tests which were made to determine the same.” 

The points made by Lieutenant Nichols on Nov. 30, 1939, might simply be repeated today. He 

notes, for example, that 

“the results of these tests, show that the autogiro could be used to great advantage for all types 

of reconnaissance, convoy duty, liaison, courier and command work. Also that due to its ability 

to hover over a particular spot [what an interesting choice of words!] it can provide almost 

constant observation of the terrain in the vicinity of a command either halted or on the march 

during daylight”. [A nighttime and all-weather capability was to come much later.] 

These statements, plus a host of other important lessons, are invaluable reading and certainly 

justify Lieutenant Nichols’ closing remarks that 

“being the only Air Corps Officer to be with the autogiro during all the tests described, from 

the results experienced I feel I have a right to be enthusiastic about the military and tactical 

value of autogiros, and as I am enthusiastic, it can readily be seen why I am known as the 

‘Windmill Salesman’ among my friends in the Air Corps.” 

You will find, not only in the histories related by Butler but in others as well, that the autogyro 

was not so favorably compared to conventional fixed-wing aircraft as Lieutenant Nichols was 

selling. For example, Cyrus W. Hardy [82]14 points out that 

“the [early] autogiro’s difficult flying characteristics and low pay load were undesirable. Their 

landing and takeoff distances were only a small advantage [and that even by late 1944] the 

autogiro still offered only minor advantages over the airplane and it was abandoned for the 

helicopter. The autogiro, however, left a wealth of technical information which provided a good 

foundation for future helicopter development.” 

 

13 Both the First Annual Meeting, October of 1938, and the second [79] were sponsored by the Philadelphia 

Chapter of the Institute of the Aeronautical Sciences. They were held at the Franklin Institute in Philadelphia, 

Pennsylvania. Proceedings of the two meetings were edited by Ralph McClarren, who was then the Assistant 

Associate Director in charge of aviation for the Franklin Institute. In corresponding with Mr. McClarren in 

March 1993, he sent me more details of these meetings plus the highlights of his career [80]. Dr. Alexander 

Klemin, a frequent contributor to Aero Digest, wrote a very positive summary article about the first meeting that 

appeared in the December 1938 issue of that popular magazine [81]. These meetings were the forerunner of the 

Annual Forum of the American Helicopter Society today and happened because of the vigorous efforts of 

E. Burke Wilford who was then Chairman of the Philadelphia Chapter. 

14 The first volume of the Journal of the American Helicopter Society was published in January of 1956. The 

then Technical Director of the Society, Alfred Gessow, became Editor. A subscription for one year was $4.00, 

but the quarterly publication was included in AHS membership dues. This first journal, a premiere history and 

development issue, was devoted to the story of the birth and development of the helicopter industry. It makes for 

absolutely fascinating reading because of the articles from both military and commercial users. This historic 

volume was reprinted by the American Helicopter Society in May 2006. 
1.4 CLOSING REMARKS 

46 

 The autogyro also created a passionate group of rotary wing advocates within the 

military, and it established a fundamental, military operational use of rotorcraft that has been 

continually repeated over the last 50 years. Of course additional missions have been added 

through the years as rotorcraft capability expanded. You will also find the view of the Army in 

the mid-1950s expressed by Lieutenant Colonel Edgar C. Wood in the Journal of the 

American Helicopter Society (AHS), vol. 1, no. 1. 

 There were a number of Army leadership reasons for selecting the helicopter over the 

autogiro that Butler points out [76, 77]. There were just as many operational and technical 

reasons as well. For example, the helicopter could truly hover. Operationally, this capability, 

relative to the autogyro, does not appear as overwhelming as you might think. What hovering 

really allowed was looking over the landing spot before touching down. With the autogyro, 

the pilots were committed to land once they got close enough to the ground to see the terrain 

details. With the helicopter, even with wheels on what might appear as firm ground, the pilot 

could still “pull collective” if the situation warranted it and then search for a better spot. This 

was a very important point to the Army aviator. 

 The actual performance differences between one of the best autogyros available for 

evaluation, the Kellett YO-60 (Fig. 1-21) discussed earlier [84], and Sikorsky’s experimental 

XR-4, and then the YR-4B pre-production upgrade that followed [47-50], is quite illuminating 

as Table 1-1 and Fig. 1-22 show. 

 The differences in power required with airspeed shown in Fig. 1-22 are particularly 

interesting. The helicopter, with its high airframe drag and low installed engine horsepower, 

clearly would not compete at speeds above 75 miles per hour. The autogyro, with its loss in 

propeller efficiency at low speed (and despite its high installed power), would never compete 

at speeds below 75 miles per hour. 

Fig. 1-21. The 1943 Kellett YO-60 was the last autogyro the U.S. Army Air Force 

would purchase (photo from author’s collection). 
1.4 CLOSING REMARKS 

47 

Table 1-1. Autogyro vs. Helicopter in 1942 

 Configuration Autogyro Helicopter 

Manufacturer Kellett Sikorsky 

Model YO-60 YR-4B 

Design Gross Weight 2800 lb 2450 lb 

Operating Weight Empty 2180 lb 1980 lb 

Normal Fuel 36 gal. 30 gal. 

Parasite Drag Area at Cruise 13 sq ft 23 sq ft 

 Performance 

Cruise Speed 70 to 94 mph 65 mph 

Maximum Speed 134 mph 85 mph 

Minimum Speed 26 mph 0 mph 

Maximum Range 210 statute miles 200 statute miles 

Average Cruising Speed for Max Range 70 mph 65 mph 

Maximum Endurance 2.2 hours 2.2 hours 

Service Ceiling 13750 ft 8000 ft 

 Dimensions 

Main Rotor 3 blades 3 blades 

 Diameter 43.2 ft 38 ft 

 Chord at 70% Radius 12.92 in. 13.8 in. 

 Solidity 0.0476 0.0578 

 Airfoil (root) 23016 NACA 0012 NACA 

 Airfoil (tip) 23010 NACA 0012 NACA 

 Rotor Speed at Maximum Speed 241 rpm 241 rpm 

 Rotor Speed at Minimum Speed 189 rpm 241 rpm 

Horizontal Tail One None 

 Span 10 ft n/a 

 Chord 30 in. n/a 

Fuselage 

 Number of Seats 2 (in tandem) 2 (side-by-side) 

 Overall Length 21 ft 5 in. 27 ft 11 in. 

Propeller or Tail Rotor 2 blades 3 blades 

 Hamilton Standard, Constant Speed 2150 rpm 1275 rpm 

 Hub Model 2B20 Articulated 

 Blade Design 6135A-6 0012 NACA 

 Diameter 8.5 ft 7.92 ft 

 Solidity n/a 0.0998 

Engine Jacobs I-6MB-8 Warner R-550-1 

 Maximum Rated Power 320 bhp 190 bhp 

 Operating Speed 2150 rpm 2250 rpm 
1.4 CLOSING REMARKS 

48 

0

50

100

150

200

250

300

350

0 30 60 90 120 150

Horsepower

Airspeed (mph)

YO-60 Engine Power Available

ηP

D×V

550

YO-60 Engine HP 

Required

GW = 2,800 lbs

YR-4B Engine HP 

Required

GW = 2,550 lbs

YR-4B Engine Power Available

D×V

550

Fig. 1-22. The U.S. Army had chosen the helicopter over the autogyro by the 

end of 1944. 

 It took another 20 years before Army aviators got the best of both worlds, and more, in 

a Light Observation Helicopter powered with a gas turbine engine. You will encounter that 

story and others as you read about the modern results achieved with the helicopter in the next 

section. 
49 

2 MODERN RESULTS 

 In the November 1924 issue of Mechanical Engineering [85], Dr. Alexander Klemin, 

one of the most respected and enthusiastic spokesmen in the rotorcraft industry, published a 

technical article entitled An Introduction to the Helicopter. The third introductory paragraph 

he wrote reads as follows: 

 “To achieve utility, the helicopter must climb vertically with a moderate degree of 

useful load; attain a reasonable ceiling; achieve vertical descent with motors in action; 

achieve safe descent—if not vertically, then at least on a steep path with dead motor; have a 

reasonable speed in horizontal flight; be fairly stable and completely controllable; and have 

reasonable assurance of correct functioning of its mechanism. In these requirements we have 

the whole of the subject.” 

It was in the period after World War II that the industry was able to meet “these 

requirements.” 

 In late 1961 the American Helicopter Society (AHS) devoted its October, November, 

and December issues of its NEWSLETTER magazine, now called Vertiflite, to updating 

technical data about as many helicopters and VTOLs as possible. The three-part summation, 

[86-88] was authored by Ralph Alex, the first and eighth president of the AHS. The articles 

were entitled Helicopters From ‘A to Z’. (In my opinion these 3 issues are real collectibles, 

not just for the 135 configuration descriptions, but because the photographs were printed with 

superb clarity.) In his introduction, Alex included a number of statistics that quickly capture 

how the industry was doing. With some of my condensing, he noted that: 

• The multitude of military uses has provided [the industry with] the basic support of the 

Armed Forces and has supplied most of the development motivation which has been 

responsible for the current state of the art. Military sales over the past 6 years were 

$1,665,000,000. From 1941 through 1960, over 7,000 (1,200 Air Force, 1,800 Navy, 

3,200 Army) helicopters were delivered to the Armed Forces. 

• The vast commercial future predicted has progressed but not as rapidly as envisioned due 

to excessive manufacturing and operating cost. Commercial sales over the past 6 years 

were $456,000,000. Over 1,500 helicopters for commercial use had been delivered since 

1941. Orders for 182 helicopters had been placed for delivery in 1961. 

• In 1960, the 235 commercial operators in the U.S. and Canada operated 882 helicopters, 

provided 56 flight schools and had annual sales gross of $50 million. 

• The scheduled airlines had 20 helicopters in service during 1960. They carried a total of 

490,000 passengers and amassed 1,054,000,000 revenue ton miles including airmail and 

freight. 

• The industry employed approximately 24,000 people directly and had a backlog of 

$350,000,000 in unfilled orders. It exported 82 helicopters valued at 7.7 million dollars. 

 In addition to the articles by Alex and the often-referenced book, Helicopters and 

Autogyros by Gablehouse [3], you will find the period from 1945 on up to at least 1967 is
2. MODERN RESULTS 

50 

particularly well documented by Paul Lambermont and Anthony Pirie in their survey of 

Helicopters and Autogyros of the World, [89]. Their initial publication came out in 1958. A 

revised and enlarged book was published in 1970. The table of contents of the second edition 

lists over 500 rotorcraft (i.e., initial autogyros, helicopters, convertiplanes, and their product 

improvement models). An overview, including many photographs, is provided for each 

rotorcraft, and a brief historical introduction recaps the period from 1784 to 1903. 

 An excellent complement to the survey by Lambermont and Pirie is The Illustrated 

Encyclopedia of Helicopters, [6], by Giorgio Apostolo. His encyclopedia not only revisits the 

early history of rotorcraft, but it includes many superb artist renditions, three-dimensional 

views, and photographs. More recently, Jay Spenser has updated the early rotorcraft industry 

in Whirlybirds: A History of the U.S. Helicopter Pioneers, [90], which has many exceptional 

photographs. Taken together, these publications from Alex, Gablehouse, Lambermont and 

Pirie, Apostolo, and Spenser show that the rotorcraft industry has been steadily expanding as 

summarized earlier in Fig. 1-1. 

 In the United States, for example, Frank Piasecki succeeded in developing and then 

producing the tandem rotor helicopter starting with the XHRP-1 prototype that first flew in 

March of 1945. Arthur Young, assisted by Bartram Kelley and supported by the Lawrence 

Bell Corporation, significantly improved the inherent stability of the single-main-rotor 

helicopter with a prototype that first flew in free flight in early 1943. This prototype led to the 

Bell Model 30 and then to the very well-known Bell Model 47 that, in January of 1946, was 

the first helicopter to receive a civil certification. Charles Kaman started his company with the 

Flettner rotor system and had his prototype K-125 flying in January of 1947. By October of 

1948, Stanley Hiller had decided against further development of the coaxial configuration and 

began deliveries of his Model 360, a single-main-rotor plus anti-torque tail rotor design that 

also improved the inherent stability of the helicopter. And, of course, Sikorsky’s company 

grew by translating its early military helicopters into commercial models. 

 In Europe, consolidation of many diverse efforts also occurred. Great Britain saw 

Westland Aircraft Limited evolve from the groundwork of Cierva, A. V. Roe, Weir, Bristol, 

Fairey, and others. The cooperation between Sikorsky and Westland, begun in early 1947, led 

to a broad product line. In Italy, Augusta became the primary producer through a licensing 

agreement with the then Bell Aircraft Corporation. This led to the Bell Model 47 production 

in Italy starting early in 1955. The German and Austrian work of Focke, Flettner, Doblhoff, 

Dornier, Derschmidt, and others culminated in the formation of Bölkow and production of the 

first, practical, hingeless rotor system, which led to the BO-105 in the late 1960s.15 Finally, in 

 

15 In May of 1993, while at an air show in California, I ran across a thin booklet by Heinz J. Nowarra [91]. It is 

packed with early photos and key history about German and Austrian helicopter activities from 1928 to 1945. I 

learned a great deal from this work and highly recommend it. In late 1994, while going through the Wayne 

Wiesner collection, I came across the U.S. Air Force test report of the Flettner-282 [92]. It was a fine helicopter 

and a tribute to its inventor, Anton Flettner. Certainly Focke and Flettner were the leaders in helicopter 

development until the disruption of World War II. In 1983, Gunter Reichert, a very good friend, gave me a 

marvelous book tracing the history of the Messerschmitt–Bölkow–Blohn (MBB) company up to the BO-105 

(written in German with superb photos, although I cannot read German) [93]. Steve Coates’ book [7] really 

rounds out the picture. 
2. MODERN RESULTS 

51 

France, the pioneering work of Bréguet, Oemichen, Dorand, and others ultimately created Sud 

Aviation which led to Aerospatiale. More recently, Eurocopter has been established by 

combining the Bölkow and Aerospatiale teams. This has given the world a European 

rotorcraft product line that is quite comparable to what is available from the United States. 

 In Russia, a number of design teams formed to produce several rotorcraft types. This 

story of Soviet Helicopters was brought to light in 1983 by John Everett-Heath [94]. Heath 

traces progress from 1754 up to the modern efforts of Nikolai Kamov and Mikhail Mil [95, 

96]. The influence of the Russian climate on design becomes rather clear when you read these 

books, and it explains why the very heaviest lifting helicopters have evolved in what is again 

Russia. 

 It is well known that helicopter development has been paced by military needs, and 

this has given the world some very powerful weapon systems [97]. However, the industry 

founders always saw their inventions helping mankind as Frank McGuire of Bell Helicopter 

carefully points out [98]. Progress throughout the decades since the 1940s confirms that the 

worldwide rotorcraft industry is in business to stay. Part of the industry has chosen product 

lines designed for larger transport and heavy-lift capability. Several 30-passenger 

configurations are available, and payloads of 25,000 kg (55,000 lb) can be lifted. The other 

side of the industry has proliferated the light- and medium-weight product lines. Cruise 

speeds of 150 miles per hour are common, and the speed record is over 400 km/h (249 mph or 

216 knots). Ranges of 660 km (400 statute miles or 350 nautical miles) with internal fuel are 

the norm, and hover endurance is limited only by fuel capacity. Helicopters, regardless of 

manufacturer, have demonstrated their ability to perform a multitude of tasks and, from a 

user’s point of view: 

1. Engines have become more efficient and reliable. 

2. Weight empty is more productively used. 

3. Hover performance at high altitudes is routine. 

4. Forward flight at higher speeds in comfort is possible. 

5. Fuel efficiency has been significantly improved. 

6. Costs, both initial and operational, are major factors in design and production. 

7. Safety has steadily improved. 

 Modern results, from each of these preceding seven areas, will tell you just how 

mature the helicopter has become. The engineering explanations and analyses that follow are 

tied to the configuration evolution to help round out your appreciation of what has been 

accomplished in creating the rotorcraft industry. The second objective is to continue 

expanding your understanding of the (1) physical and mechanical aspects, (2) basic 

nomenclature, (3) engineering symbols, and (4) fundamental equations. 
52 
53 

2.1 ENGINES 

 An engine is the heart of any aircraft propulsion system. This is not a simplistic or trite 

statement. The progress in aviation is so intertwined with what has been accomplished in this 

field that it too often is just taken for granted. Because of this intertwining, you will find some 

history about several helicopters in the engine discussion that follows. 

 For rotorcraft, the engine is, if it is possible, even more important than for fixed-wing 

aircraft. In fact, even conceptual rotorcraft design rarely proceeds without first having at least 

one proven engine in mind. Igor Sikorsky clearly understood this fact in 1908 before he had 

become 20 years old. You will find his recollections in Boulet’s history very pointed (pages 24 

through 30 of reference [2]). He traveled to Paris in January 1909, expressly “to make a 

correct decision on the type of motor to use.” He finally selected one Anzani 25-horsepower 

engine to take home. It was a choice he described as, “Less bad than the rest.” However, you 

may recall that it was this power plant that Louis Blériot used a few months later to make the 

first flight across the English Channel. 

 There are primarily two types of engines available to, and used by, the rotorcraft 

industry. One is the four stroke, spark ignition, internal combustion, reciprocating piston 

engine. The other is the gas turbine. You need to understand both of these power plants so 

consider the piston engine first. 

2.1.1 Piston Engines 

 In 1862 Beau de Rochas, a Frenchman, proposed and patented a sequence of four 

operations, or strokes, that a spark ignition piston engine could have to produce power. 

Fig. 2-1 schematically illustrates these four strokes. Each stroke is 180 degrees of crankshaft 

rotation. This means that the crankshaft goes through two revolutions to produce one impulse 

of power. Referring to Fig. 2-1, Rochas proposed that: 

1. There would first be an intake stroke to suck a fuel-air mixture through the open 

intake valve into a cylinder; 

2. The second stroke would be a compression stroke with both valves closed to raise 

the temperature and pressure of the fuel-air mixture; 

3. The third stroke, with both valves closed, would start with a spark to ignite the 

fuel-air mixture, which expands on combustion and forces the piston down; and 

finally 

4. The fourth stroke would exhaust the cylinder free of the burned gases through the 

open exhaust valve. 

 The internal combustion engine that Rochas described came into being in Germany. In 

1876 a German engineer, Nikolaus A. Otto, used these principles to create a 1-cylinder, 

3-horsepower engine. The cylinder bore was 6.3 inches and the stroke was 11.8 inches. The 
2.1 ENGINES 

54 

output shaft speed was 180 rpm. A countryman, Gottlieb Daimler,16 followed with an 

8-horsepower engine and then built a 16-horsepower engine nearly entirely of aluminum. The 

Daimler company, spurred on by a car racing enthusiast named Emil Jellinek, later created the 

Mercedes engine. (You might not know that Mercedes was the middle name of one of 

Jellinek’s daughters.) These and other early engines were used to power dirigibles before the 

turn of the 20th century, and aviation had a power plant. 

Fig. 2-1. The internal combustion engine became a reality for aviation just before 

the turn of the 20th century. 

 

16 You will find the Daimler–Mercedes-Benz story of car and engine development in references [99] and [100] 

very interesting. Both Benz and Daimler were rather poorly treated by business associates, and it was not until 

1926 that the forerunner of today’s company was in place. However, the push for higher touring-car speeds (and 

then racing cars) was a prime motivation for improving early gasoline engines. 
2.1 ENGINES 

55 

Despite the progress made with automobile and motorcycle engines, early aviation 

pioneers found them quite heavy for the amount of power they produced. Both the Wright 

brothers and Samuel Langley found that they had to build their own engines to reach the goal 

of powered flight. The Wright engine barely did the job. Their engine dropped from 16 to 

about 12 horsepower at 1090 rpm after it warmed up. With four cylinders of 4-inch bore and 

4-inch stroke, it weighed nearly 180 pounds. In contrast, the engine that Langley’s assistant, 

Charles Manly, developed from a design started by Stephen Balzar, a New York City 

automobile builder, was a major step forward. Manley’s engine produced 52 horsepower at 

950 rpm with five cylinders. It had pistons of 5-inch bore and 5.5-inch stroke, and weighed 

135 pounds. It was not until 1918 that another piston engine came along that outperformed the 

0.385-horsepower-per-pound Manley engine. Most importantly, the Manly engine was very 

reliable. One can only wonder how much faster the Wright brothers and others would have 

progressed had they been able to use the Manly engine. 

 To understand the general trends in piston engine improvements, you need some 

background about the key parameters that govern piston engine performance. The brake 

horsepower (BHP) that a piston engine will produce is rather easy to calculate. The power 

stroke begins with an explosion. The explosion creates a very high initial pressure that moves 

the piston downward. During the power stroke, the top of the piston feels an average pressure 

that engine designers refer to as the indicated, mean, effective pressure (IMEP). This pressure, 

say in pounds per square inch, acts on the piston face of area (A) in square inches to produce a 

force in pounds. This force moves through a distance (L), say in feet, that is the length of a 

stroke. The piston force (P×A) times the stroke distance is the work done (in foot-pounds) by 

one cylinder during a power stroke. Thus, 

(2.1) Work done Piston A L = ( ) IMEP piston stroke ( )( ). 

Now think about the time it takes to do this work. In a four-cycle engine, the power stroke for 

each cylinder occurs only once every two revolutions of the crankshaft. Thus, the power 

stroke time (T) is the time it takes the crankshaft to turn 180 degrees or π radians. This relates 

to engine RPM as 

(2.2) seconds 120 2 seconds

Work time T

radians 2 radians RPM

t t == = = π π . 

The indicated horsepower, based on IMEP, is work done per unit of time by one cylinder 

(n = 1) or simply 

(2.3) ( ) IMEP piston stroke ( )( )

work done in foot pounds Indicated HP per piston 550 work time in seconds

Piston A L RPM

550 120

− =

= ×

. 
2.1 ENGINES 

56 

 This indicated horsepower per cylinder is transmitted from each piston assembly along 

the crankshaft to an output shaft where it becomes useful power, which is called brake 

horsepower (BHP). BHP is somewhat less than indicated horsepower because of losses such 

as the friction drag of the pistons against the cylinder walls and internal pumping. In addition, 

some of the indicated power might be used to drive engine accessories like a supercharger, 

which I will discuss shortly. The key point here is that BHP depends on a piston pressure 

(Ppressure), i.e., the brake, mean effective pressure; the piston face area (Apiston) and stroke length 

(Lstroke), which is a volume; the engine speed (RPM); and the number of cylinders (n). Thus, 

(2.4) ( )( ) 3 P in psi A L in inches RPM pressure piston stroke BHP n

792,000 = . 

 Despite the simplifications presented by Eq. (2.4), it does capture the fundamentals of 

piston engine performance. The vast majority of aviation engines run in a very narrow RPM 

range centered around 2700 rpm. There is also a finite pressure and temperature that a 

cylinder can withstand without an enormous weight penalty. Thus, the BHP is primarily a 

function of the number of cylinders and the size or displacement (i.e., the volume in cubic 

inches or liters) that each piston will create. 

 Fig. 2-2 illustrates the fundamental trend suggested by Eq. (2.4) for a number of 

aircraft piston engines available during the first half of the 20th century. The majority of data 

shown in this figure have come from the first six editions of Lionel S. Marks’ Mechanical 

Engineers’ Handbook, [101]. Perhaps the most authoritative stories of aircraft piston engine 

evolution, from an engineering viewpoint, are provided by Charles Fayette Taylor [102] and 

L. J. K. Setright [103].17 These histories discuss the use of gearboxes to better optimize engine 

speed with propeller speed. They also point out the basic limitations to maximum piston 

speed. 

 The data in Fig. 2-2 reflects an increase in piston pressure as used in Eq. (2.4) from 

about 100 pounds per square inch with the early, small engines, up to about 300 pounds per 

square inch for the large engines of the mid-1950s. Thus, one could expect that new, small 

engines in the power range suited to small (i.e., one- to four-person) rotorcraft would perform 

above the historical trend line shown in the figure if advanced technology ensued. 

 It is not too unreasonable to think that a piston engine’s weight would be in proportion 

to its size and the density of steel from which most engines were, and are, made. In turn, the 

size would be in proportion to the piston engine’s total displacement. Fig. 2-3 basically 

confirms this reasoning. This weight trend can also be related to the rated BHP as shown in 

 

17 You will find a popular history of engines in the July 1953 issue of Aero Digest [104]. A more detailed 

engineering review is included in a terrific book called The Lore of Flight [105]. The illustrations are wonderful, 

and it is an invaluable guide for both laymen and experts. My friends at the Boeing Vertol V/STOL wind tunnel 

gave me a copy of this book when I left in 1974. It has been a continual source of enjoyment and knowledge ever 

since. 
2.1 ENGINES 

57 

0

500

1,000

1,500

2,000

2,500

3,000

3,500

0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000

Total Displacement times (RPM/1,000) (cubic inches - rpm)

Rated Brake 

Horsepower 

(BHP)

Fig. 2-2. The piston engine provides power nearly in proportion to its cubic inches of 

displacement and to RPM. 

Fig. 2-4. The trend is not linear, however, because power improved with both size and 

increases in mean pressure as the technology evolved. This was suggested by Fig. 2-2. 

 A normal characteristic of the un-supercharged piston engine is to lose power output 

nearly in proportion to the density of air in which the engine is operating. Rated BHP is 

generally quoted by a manufacturer at standard sea-level conditions. Therefore, to extrapolate 

the power output of a piston engine, you can use an empirical, first approximation to the 

actual thermodynamic process given for an un-supercharged engine as 

(2.5) S.L rated

Density Ratio 0.145 BHP BHP

0.845 σ

  − =     . 

 You will remember that both ambient atmospheric pressure (Pam) and temperature 

(Tam) determine the density (ρam). These properties of air are conventionally expressed in 

ratios. That is, 

(2.6) 

5.255876113

am

o

p H in feet 1 0.00687558563

p 1,000

    δ= = −         . 

Similarly, an absolute-temperature ratio is commonly used in the form 
2.1 ENGINES 

58 

(2.7) am am am

o

T T in F 459.67 T in C 273.15

T 518.67 288.15

°+ °+ θ= = = . 

These properties of air are widely published [106]. In addition, a density ratio (σ) equation 

that comes in very handy is 

(2.8) 

5.255876113

am

3

am

H in ft. 518.67 1 0.00687558563

1,000

0.002378 slug / ft T in F 459.67

    −     ρ δ     σ = = ≈ θ ° +

where H is pressure altitude expressed in feet. A standard day assumes that temperature 

decreases with altitude as 

(2.9) am

H T 59 F 3.566

1,000

  ≈ °−    

so that density varies with pressure altitude in feet on a standard day approximately as 

(2.10) 

5.255876113

am

3

H in ft. 518.67 1 0.00687558563

1,000

0.002378 slug / ft H in ft. 518.67 3.566

1,000

    −     ρ     σ= ≈   −    

. 

 The loss in power output with altitude has frequently been offset by adding a 

supercharger to the engine. This device compresses the intake air and makes the engine think 

(so to speak) and operate as if it were at sea level. However, running the engine at sea level 

with a supercharger on may require operation at partial throttle to avoid overheating the 

engine, or to avoid predetonation, which is called “knock.” With a supercharged engine, the 

pilot can draw the sea-level-rated power to altitudes of 10,000 feet or better. An engine 

manufacturer would state this feature by saying that its engine is “flat rated” from sea level up 

to some design altitude. A supercharged piston engine can be an ideal solution for rotorcraft 

operations such as hovering at high altitudes. For the supercharged engine, BHP empirically 

varies slightly differently with density above the design altitude. Thus Eq. (2.5) becomes, for 

the supercharged engine, 

(2.11) Design Altitude

Design Altitude for supercharged engine

0.1 BHP BHP

0.9 σ

  σ − =  

 

. 

 Today the aviation piston engine has found itself powering light planes, small 

autogyros, and one- to four-place helicopters. The two major U.S. piston engine 

manufacturers are Lycoming and Continental whose products span the range from 100 to 

slightly over 400 rated horsepower. Output engine shaft speeds range from 2,400 to 3,400 

rpm. Both companies offer four- and six-cylinder engines, and many are supercharged. This 

gives an extremely broad choice in horsepower for any design altitude. For example, in 
2.1 ENGINES 

59 

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

0 500 1,000 1,500 2,000 2,500 3,000 3,500

Uninstalled 

 Dry 

Weight 

(lbs)

Total Displacement (cubic inches)

Fig. 2-3. Smaller piston engines weigh about 0.75 pounds per cubic inch of 

total displacement. 

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

0 500 1,000 1,500 2,000 2,500 3,000 3,500

Uninstalled 

 Dry 

Weight 

(lbs)

Rated Brake Horsepower (BPH)

Fig. 2-4. Piston engines would have improved if gas turbine engines had not 

become practical. 
2.1 ENGINES 

60 

Aviation Week & Space Technology [107] you will find a data list of U.S.-produced 

reciprocating engines that covers two pages (in small print). Data from this reference give the 

approximate bounds in available piston engine performance shown in Fig. 2-5. 

 A very important characteristic of piston engines is their fuel consumption. This 

characteristic is shown in Fig. 2-6, again using historical data [107]. The specific fuel 

consumption (SFC) at rated horsepower is a frequently quoted ratio for engines. SFC is 

simply the ratio of fuel flow in pounds per hour to rated BHP. This is the slope of the data as 

presented in Fig. 2-6. Historically, smaller piston engines are not as fuel efficient as larger 

engines, as the figure suggests. (It is worth remembering that one U.S. gallon of piston engine 

fuel weighs in the range of 5.9 to 6.1 pounds.) 

 Engine manufacturers obtain their engine’s performance in a test cell using as close to 

an ideal setup as possible. This provides all potential users with a firm baseline. But when a 

given engine is installed in a rotorcraft (or any aircraft for that matter), its performance is 

compromised as you might expect. Getting air and fuel into the engine and getting exhaust 

overboard become very practical design issues that impact both maximum power available 

and fuel flow. Consider Fig. 2-7 and the data from three U.S. Army helicopters shown as an 

example. 

 The U.S. Army introduced two piston-powered cargo helicopters into service in the 

1950s. One was the Piasecki H-21 that began life as the XHRP-X in 1945 and was developed 

under U.S. Navy contract. (The H-21 evolved into a turbine-powered commercial version, the 

Vertol Model 44, by the early 1960s). The 11,500-pound H-21 set the world speed record over 

a 3-kilometer course at 236 kilometers per hour (146 mph or 127 knots) in September 1953. 

The other helicopter was the 13,000-pound Sikorsky S-58 or H-34 that first flew in 1954. This 

helicopter was derived from the S-55 or H-19 that first flew in 1949 and was developed under 

U.S. Army contract. In July of 1956, an H-34 set world speed records over 100-, 500-, and 

1,000-kilometer closed circuits. The highest speed was 219 kilometers per hour (136 mph or 

about 118 knots). The S-58 was re-engined with a gas turbine in 1971. Both of these 15- to 

20-passenger helicopters used the Wright R-1820 reciprocating engine with supercharging. 

 Both the Piasecki H-21 and the Sikorsky H-34 were thoroughly evaluated by the Air 

Force for the Army at the Air Force Flight Test Center located at Edwards Air Force Base in 

California [108, 109]. The fuel flow versus BHP data recorded in these reports covers a range 

in engine RPM from 2300 to 2700 and altitudes from nearly sea level up to 15,000 feet.18 

 

18 The Air Force Flight Test Center at Edwards Air Force Base in California is not just the world’s leading flight 

research center for airplanes. It has supported rotorcraft development of all types for several decades. Major 

General Peter Odgers traces the history of Edwards from a little-known lakebed at the turn of the century up to 

the first landing of the Space Shuttle Columbia in April 1981 [110]. Hundreds of detailed engineering flight test 

reports for military helicopters alone have been published. There is, in my opinion, no better source for rotorcraft 

data than the pilot-oriented results that come from this organization. The good, bad, and unacceptable features of 

a helicopter are clearly written up. In short, these reports are probably the best “design manuals” you could read. 

In October 1996, the Army moved their flight testing operation from Edwards to Fort Rucker, Alabama, and 

renamed it Army Aviation Technical Test Center. The library at the center contains a wealth of test reports. 
2.1 ENGINES 

61 

0

50

100

150

200

250

300

350

400

0 5,000 10,000 15,000 20,000

220 Pound

No Supercharge

550 Pound

Supercharged

Brake 

Horsepower

Pressure Altitude, Standard Day (feet)

Fig. 2-5. U.S.-produced piston engines provide a wide choice of options for light plane 

and rotorcraft manufacturers. 

0

200

400

600

800

1,000

1,200

1,400

1,600

0 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000

Fuel 

Flow 

(lbs/hr)

Rated Brake Horsepower (BHP)

Fig. 2-6. Piston engines burn fuel at a rate of about 0.5 pounds per hour for each rated 

horsepower delivered. 
2.1 ENGINES 

62 

This composite of engine performance is shown by the square, open symbols in Fig. 2-7. As 

you can see, fuel consumption does not vary linearly with the horsepower output of this 

engine. Furthermore, the optimum SFC is at partial power, not at rated power. The difference 

between uninstalled engine performance (as quoted by manufacturers and published in trade 

magazines) and performance when installed in a rotorcraft can be substantial. You can see this 

by comparing Fig. 2-6 with Fig. 2-7. 

 Fig. 2-7 also shows fuel consumption for an engine at the other end of the size 

spectrum. In the early 1960s, the Army bought a very small training helicopter that was 

developed by Hughes as its Model 269A. (The October 1961 advertisement [86] suggests that 

Hughes sold its 269A for $22,500 and that it could be flown for just 13-cents-per-mile total 

direct operating costs. This product is offered today as the Schweizer Model 269A/A1.) This 

two-man, 1,550-pound helicopter used the Lycoming O-360-C2B, which was not 

supercharged. The helicopter was evaluated with the military designation of YHO-2HU [111]. 

Again, the installed engine performance was obtained over a range in RPM and altitudes. The 

fuel flow variation with BHP is not linear for this small engine either (although the data is 

rather compressed because of the scale). 

 The fuel flow at a given power setting with a piston engine depends on a raft of 

variables, not the least of which are density and RPM. More fundamentals of reciprocating 

engine design and operation is beyond the rudiments discussed previously and requires a book 

in itself. 

 

0

100

200

300

400

500

600

700

800

900

1,000

0 200 400 600 800 1,000 1,200 1,400

SFC

0.50

0.75

Fuel 

Flow 

(lbs/hr)

Brake Horsepower (BHP)

Lycoming O-360-C2B

Hughes TH-55A

Wright R-1820

Piasecki H-21

and

Sikorsky H-34

Fig. 2-7. SFC improves when a piston engine is operated at partial power. 
2.1 ENGINES 

63 

2.1.2 Turbine Engines 

 Now turn your attention to turboshaft gas turbine engines. This power plant evolved 

after practical, pure jet propulsion became a reality just before World War II.19 The shaft 

turbine that followed was a leap forward in simplicity as Fig. 2-8 suggests. Air enters the 

engine inlet and encounters a large capacity compressor, identical in principle to a piston 

engine supercharger. The compressed air flows into the combustion chamber where fuel is 

injected and the mixture is burned. This converts the fuel-air mixture into a supply of hot gas 

of greatly increased energy. The high-energy gas expands through the turbine wheels and then 

out the exhaust. The first turbine direct drives the compressor. The second turbine, called the 

power turbine, drives the output shaft. 

 The arrangement shown in Fig. 2-8 is generally referred to as a free turbine because 

the compressor/turbine assembly can turn separately from the output shaft/power turbine 

assembly. There are many fixed-shaft turbine engines however. With fixed turbine engines, 

the output shaft, compressor, and power turbine are all hard-mounted to one shaft. About 

65 percent of the available power created in the thermodynamic process is used to turn the 

compressor. Another 30 to 35 percent of the power turns the output shaft. The remaining 

power is exhausted at high velocity out the tail pipe in the form of very hot jet thrust. 

 The shaft turbine engine turns in the range of 20,000 to 40,000 rpm with very small 

engines operating at over 60,000 rpm. These speeds are far in excess of what normal 

propellers use (i.e., about 1,000 rpm) or helicopter and other rotorcraft need (i.e., 250 to 

350 rpm) and so some gear reduction is required. Tabulated engine characteristics such as 

those periodically provided by trade magazines [107] rarely include this key data. Instead the 

type of engine is more often classified as to (a) its compressor type–—axial and/or 

centrifugal, and (b) its output—shaft, prop, fan, or pure jet. The implication of output type 

infers that the manufacturer may include a mechanical gearbox to bring down the output 

speed to something more useful to the airframe manufacturer. 

 A standard designation of stages or partitions of the gas turbine engine along with 

nomenclature was established by the military with MIL-E-5007 in 1949 [112]. The system 

description has been further detailed by the Society of Automotive Engineering in its 

publication ARP-681B [113]. These numbered stations or points along the engine are shown 

in Fig. 2-8 and Fig. 2-9. The nomenclature is in common use and is well worth remembering. 

 

19 You will recall that the first World War was called The Great War or The War to End All Wars. Apparently 

these were just working titles until we could number them. But, technology leaps do get made during these 

terrible periods. In January 1930 Commodore Frank Whittle patented the jet engine in England at his own 

expense. He found little interest in his practical ideas, but with capital from private friends, he successfully ran 

the first turbojet engine on April 12, 1937. A specially built Gloster E. 28/39 fighter, using a Whittle modified 

engine, first flew on May 15, 1941. Although Germany started later, the Pabst von Ohain turbojet ran in 

September of 1937. It was quickly developed into the He S3B and flown in the Heinkel He 178 on August 27, 

1939, and the world was introduced to jet propulsion. 
2.1 ENGINES 

64 

For example: 

• Pam – Ambient pressure far ahead or far behind the engine. 

• PS 2 – Static pressure at the compressor inlet. 

• PT 3 – Total pressure at the compressor outlet. 

• T4 – Temperature at the turbine inlet, written as TIT. 

• T5 – Temperature at the turbine outlet, written as TOT. 

• N1 – Compressor rotational speed, sometimes written as Ng. 

• N2 – Power turbine rotational speed, written as Nf. 

In general, the subscript “s” means static and “T” means total. If no subscript to pressure is 

used, it probably means a static pressure. 

 The calculation of power from a gas turbine is not quite as straightforward as it is for a 

piston engine. However, it is worth your time to understand this power plant because it is the 

current engine of choice for most rotorcraft. A gas turbine in its most basic form operates 

schematically as shown in Fig. 2-9. The available energy level at any station in the cycle is 

derived from basic thermodynamic gas laws. 

 The general thermodynamic energy equation, found in any number of propulsion 

books, is the basic starting point for any propulsion system.20 As a reminder, this fundamental 

is reproduced here, simply stated in differential equation form, as follows: 

(2.12) V

vdP Pdv VdV dh dL dQ C dT J J gJ J

+= + + + +

where dL Mechanical work input, dQ Heat energy input, C dT Internal energy, V

vdP Pdv VdV dh and Flow work, Kinetic energy, and Potential energy. J J gJ J

= ==

== =

 

20 You will recall that the perfect gas equations are normally summarized as: 

P

P V P

V

R C P RT, C C , , JC R JC 1

γ ν= − = γ= =

γ −

The several gas constants, in the English system, are: R = 53.3524117 ft-lb/lb-°R, J = 778.02922 ft-lb/BTU, 

CP = 0.24 BTU/lb-°R at sea level standard temperature of Tam = 59 °F = (459.67 + 59 °F) degrees Rankine = 

518.67 °R. Remember that thermodynamic equations always use temperature in the absolute Rankine degrees 

system where absolute zero is 0 °R or minus 459.67 °F. The ratio of specific heats for air is γ = 1.4 at nominal 

temperatures. 
2.1 ENGINES 

65 

Gear Box

Output

Shaft

Engine

Inlet

Power

Turbine

Combustor

Chamber

3 Stage Axial

Compressor Exhaust

Compressor

Turbine

1 2 3 4 567 Station

Fig. 2-8. A free-shaft turbine has one turbine “wheel” driving the output shaft and a 

separate turbine “wheel” driving the compressor.

Heat Source

(Combustor)

Compressor Expander

Work (Turbine)

To Compressor

Useful

Work Out

Intake Exhaust

Ambient Air

Station 1 2 3 4 5 6 7

Fig. 2-9. All thermal power plants can be schematically approximated as shown here. 
2.1 ENGINES 

66 

 You can analyze the cycle characteristic of a gas turbine engine using this fundamental 

thermodynamic concept. That is, you can progress from the outside ambient air conditions to 

the engine inlet, through the engine, and out the exhaust. Thinking in terms of Eq. (2.12), you 

can also calculate the horsepower, temperature, and pressure situation at each station. 

Consider the following very simple example.21 Suppose the rotorcraft is hovering at some 

altitude where the total pressure and temperature are just the outside, ambient conditions, say 

at 4,000-feet pressure altitude on a hot day when the temperature is 95 o

F. Then, 

( ) P 25.84 inches of Hg and T 95 F 459.67 554.67 R am = = °+ = ° am . 

 As the air comes in, it is gathered up by the inlet, sent on to the compressor face, and 

then compressed. The compressor raises the gas (air in this case) temperature and pressure, 

and this takes horsepower that is supplied by its power turbine. The temperature rise depends 

on what compression you need. This compression is generally expressed as a pressure ratio. 

So to continue the example, suppose the air gets all the way from the outside to the 

compressor face with no losses. Then PT2 = Pam and TT2 = Tam. (Admittedly, this is rather ideal 

because getting air into the engine is a joint job for the rotorcraft designer and engine 

manufacturer. Both a pressure loss and a temperature rise generally occur in practice.) Now 

assume you have an engine whose compressor increases the pressure by a factor of 5.2. Then, 

T3

T2

Total pressure behind compressor P PR 5.2

Total pressure ahead of compressor P = == . 

The horsepower that the compressor needs to do this work becomes, with constants added to 

provide a numerical example, simply 

(2.13) ( )( )

( )( )

( )

1

compressor P T3

T2

C T2

0.2857

T2

C

0.2857

HP J C P T 1

Airflow lbs / sec 550 P

0.33949 459.67 T in F PR 1

0.4 459.67 95 F 5.2 1

133.3 hp / lbs / sec of airflow

γ−

γ

      = ×× −   η        

≈ +° −

η

≈ +° −

=

. 

 

21 During the mid-1950s, the engineers at Hiller were very active in teaching a rotary wing course at Stanford 

University in Palo Alto, California. Course notes were prepared and, thanks to Wayne Wiesner, the AHS Library 

and I have a copy. John B. Nichols gave the lecture on helicopter propulsion. His notes, dated May 5, 1954, 

contain the most concise, understandable transformation of thermodynamic laws into useful, simple engineering 

theory for any type of “engine” that I have ever seen. He never once uses words like adiabatic, reversible, 

isentropic, enthalpy, or entropy! The gas turbine example you are about to read is my condensation of Nichols’ 

37-page, superbly lucid lecture. The information is too important to relegate to an appendix. Understanding the 

gas turbine engine is vital to rotorcraft engineering. 

 John Nichols passed away in mid-June of 1993. The AHS recognized his career on page 58 of the 

September/October 1993 issue of Vertiflite [114]. On the same page, the AHS noted the addition to its technical 

library of the lecture notes given by Wayne Wiesner. I missed the chance to ask John for permission to include 

his lecture notes in this book. However, I did get “permission” from Wayne who organized the Stanford course. 
2.1 ENGINES 

67 

(This step assumes that compression begins at a relatively low temperature where CP ≈ 0.24 

and γ ≈ 1.4. An average of the gas constants over the compression would be more correct. The 

compressor is assumed to be only 0.85 efficient in this example.) 

 The temperature rises through the compressor due to the compression of the air. When 

the air comes out from behind the compressor, it is at a higher total temperature of TT3 given 

approximately by 

(2.14) 

1

T3 T3 0.2857

T2 C T2

T P 1 1 1 1 1 5.2 1 1 .7078 1.71

TP 0.85

γ−

γ

      =+ − =+ − =+ ≈       η        

. 

Because the air went into the compressor at 

 T T 459.67 95 F 554.67 R T2 am ≈ = + °= °

it comes out at 

 T3

T3 T2

T2

T T T 1.71 554.67 R 947.67 R 488 F

T

= = × °= °= ° . 

The air pressure will have been increased so that behind the compressor (station 3) 

(2.15) 

P P Compressor Pressure Ratio P PR T3 T2 T2

25.84 5.2 134.4 inches of Hg

12.7 5.2 66 pounds per square inch

= × = ×

= ×=

= ×=

. 

Now the airflow through the compressor, for a medium-sized turbine engine, could be on the 

order of 10 pounds per second. Using this illustrative value and the results from Eq. (2.13), 

this example compressor would “steal” some 1,333 horsepower from the following combustor 

and power turbine stages where the real power is produced. 

 Next, go from behind the compressor, through the combustor, to the front of the first 

turbine “wheel” that powers the compressor. Injecting fuel and igniting the mixture in the 

combustor raises the gas temperature to very high values as you will quickly understand. As 

this very hot fuel-air gas mixture comes out of the combustor, it moves to the turbine stage. 

The inlet or entrance to the power turbine stage sees temperatures on the order of 

(2.16) ( )( )

( ) T4 T3

P

Fuel Flow lbs / sec Fuel Heating Value BTU / lb T T

C Air Flow in lbs / sec

= +

× . 

 Continuing the example, again assume the air flow is 10 pounds per second for this 

medium-sized gas turbine engine. This type of engine uses aviation fuel which has a heating 

value of approximately 18,500 BTU/pound. The fuel flow could easily be on the order of 1/80 

of the airflow. This gives roughly 0.125 pounds per second or about 450 pounds per hour for 

the rate of fuel consumption. With this fuel flow, the temperature at the turbine inlet stage has 

become very hot, being on the order of 
2.1 ENGINES 

68 

 

( )( )

( ) T4 T3

0.125 lbs / sec 18,500 BTU / lb T T

0.2474 10 lbs / sec

947.67 R 934.00 R 1882.67 R 1423 F

= +

= °+ °= °= °

. 

With no pressure losses in the combustor, the fuel-air gas mixture will have the same pressure 

leaving the combustor as it did going in. Using this ideal assumption again, it follows that the 

total pressure at the turbine inlet will be 

 P P 134.4 inches of Hg T4 T3

66 pounds per square inch

≈ =

= . 

The engine manufacturer is clearly dealing with very high temperatures and pressures. The 

environment that the turbine has to perform in is harsh to say the very least. 

 Now consider the turbine stage. This stage takes energy out in the same sense as a 

windmill. It behaves as a compressor in reverse. Therefore, the shaft horsepower (SHP) that 

the turbine stage can produce depends on the pressure drop across the stage. Suppose, in the 

extreme, that the engine design allows the pressure to drop all the way down to the ambient 

pressure as it goes through the several turbine “wheels.” That is, assume PT 5 = 25.84 inches of 

Hg. This is an extreme assumption because then there would be no pressure to force the 

burned fuel-air residues out the exhaust nozzle. Still, this gives you a high-side feeling of the 

potential turbine power. Because the pressure at the turbine inlet was found to be PT 4 ≈ PT 3 = 

134.4 inches of Hg, it follows that the pressure ratio across the turbine stage is 

 T5

T4

P 25.84 inch Hg 0.1923

P 134.4 inch Hg = = . 

In addition, the temperature at the entrance to the turbine stage was found with Eq. (2.16) to 

be TT 4 = 1423 °F. Thus, the turbine horsepower per lb/sec of gas mixture flow becomes 

(2.17) ( )

( )( )

( )

1

turbine T5 P T

T4

T4

1

T5

T T4

T4

0.2497

HP J C P T 1

Flow 550 P

P 0.389 459.67 T in F 1

P

0.389 0.85 459.67 1423 F 1 0.1923

209.7 hp / lbs / sec of gas mixtureflow

γ−

γ

γ−

γ

 

η     = × ×−         

      ≈ ×η × + ° × −       

≈ ×× + °−

=

. 

(Because the temperature is so high in this turbine stage, the gas constants have changed to 

CP ≈ 0.2746 and γ ≈ 1.3328. The turbine is assumed to be only 0.85 efficient in this example.) 
2.1 ENGINES 

69 

 The gas mixture flow in the turbine stage is actually slightly greater than the airflow 

alone because of the fuel that is added. The difference is, however, only by the fuel-air ratio of 

1/80 or about 1 percent. Therefore, to a first approximation the SHP that the turbine can 

provide, using the 10-pounds-per-second airflow I assumed, is 

 SHPturbine = 2097 hp. 

But of this available SHP from, say, two turbine “wheels,” the turbine that drives the 

compressor takes 1,333 horsepower. That leaves only 764 horsepower for the turbine that 

drives the output gearbox. This may startle you, however it is a rather typical result. To 

reinforce this point, the example is not complete without 

(2.18) Useable Shaft Horsepower SHP SHP turbine compressor

2097 1333 764 shp

= −

= −= . 

 Keep in mind that I chose a situation where the rotorcraft was hovering at 4,000-feet 

pressure altitude and the outside air temperature was assumed to be 95 °F. The performance of 

the turbine engine can be found at any other pressure altitude and temperature quite simply. 

Suppose you want to know what power a given engine will produce at sea level on a standard 

day. Because the engine performance is so tied to pressure and temperature ratios, the basic 

first-order parameters that allow converting from one altitude and temperature to another 

ambient condition are 

(2.19) Useable SHP SHP Fuel Flow or just and δθ δθ δθ . 

These ratios are called the referred power and referred fuel flow. Now, from Eq. (2.6) and 

Eq. (2.7), you will calculate for 4,000-feet pressure altitude and 95 °F outside air temperature 

that 

25.84 95 F 459.67 0.8636 1.0694 0.8931

29.92 518.67

° + δ= = θ= = δ θ= . 

Therefore, the referred performance of this example engine becomes 

SHP 764 850 referred shaft horsepower 0.893 = ≈ δ θ . 

Then, the power at any other operating condition is simply 

(2.20) 1 1 1

SHP SHP = ×δ θ

δ θ . 

Thus, the usable SHP at sea level and 59 °F, where δ1 and θ1 are 1.0, is about 850 horsepower. 

In a like manner, the fuel flow can be referred as 

W 450 ff 500 referred fuel flow in lbs hr

0.893 = ≈ δ θ . 
2.1 ENGINES 

70 

Then this referred fuel flow can be used to find the fuel flow at sea level and 59 °F as follows 

(2.21) 1

ff

ff 1 1

W W = ×δ θ

δ θ . 

Thus, the rate of fuel consumption is roughly 500 pounds per hour at sea level and 59 °F 

where δ1 and θ1 are 1.0. 

The SFC is, of course, simply 

(2.22) 

ff

SHP 500 SFC 0.592 lbs / hr per horsepower W 850

δ θ = ≈= δ θ . 

 To produce this power at sea level on a standard day where Tam = 59 °F, the 

compressor ratio (PR) and turbine inlet temperature (T4, or quite commonly TIT) will also 

adjust in a referred manner so that 

T5

PR 5.2 6.0213 referred compressor ratio 0.8636

and

T 1882.67 R 1760.49 R referred TIT.

1.0694

= == δ

° = = °=

θ

 The preceding elementary discussion of turboshaft engine performance can be very 

helpful to the rotorcraft designer in at least two ways. First of all, you get a much better feel 

for the constraints on an engine manufacturer recommending an engine to fill a need. Second, 

it lets you see what the engine manufacturer might do to increase power available when the 

rotorcraft requires more power than originally estimated! This second situation is, 

unfortunately, all too common. 

 Consider first the preliminary design task for the engine manufacturer to fill a new 

rotorcraft need. Thinking in terms of preliminary sizing, the number-one parameter that 

governs how much power the gas turbine will produce is the airflow that the engine will be 

designed to handle. This is because the fundamental thermodynamic equations such as 

Eq. (2.13) and (2.17) yield performance on a per pound/second of airflow or gas mixture flow, 

respectively. Current technology defines compressor pressure ratios, mechanical efficiencies, 

and the very important TIT. 

 You should understand that the TIT is perhaps the most important design and 

operating constraint to the engine manufacturer. Considerable progress has, of course, been 

made in raising this limiting temperature as the gas turbine has been refined. Early TIT limits 

of about 1,000 °F or 1,459.67 °R have been increased to 2,000 °F or 2,459.67 °R. Today, 

advanced materials and actual internal cooling of individual turbine blades are raising the TIT 

limits another 500 °F. As this key temperature limit has risen, there has been a corresponding 

increase in the compressor pressure ratio. 
2.1 ENGINES 

71 

 The very simple gas turbine equations just discussed illustrate the basic preliminary 

design trends that underlay this engine and the reasons engine manufacturers see things the 

way they do. Consider the situation where the turbine inlet temperature (TIT) is fixed (by 

technology) at some value, and the compressor pressure ratio is varied. The usable SHP per 

pound of airflow will then peak at a corresponding pressure ratio as shown in Fig. 2-10. The 

trend of increased power as TIT is increased is quite spectacular as Fig. 2-10 also shows. In 

essence, a whole family of gas turbine engines is presented in Fig. 2-10. 

 Now look at the lowest curve on Fig. 2-10 where TIT = 1,500 °R. In the first place, if 

the compressor ratio is 1.0, there will be no flow through the engine. Fuel burned in the 

combustor will just turn the engine into a furnace. The turbine wheels will not turn, and the 

pilot will get no usable SHP. That is why the curves all start at zero power when the pressure 

ratio is 1.0. The importance of this point is not just academic as you might think. When the 

pilot starts the engine, he must be rather careful to get the compressor turning with the starter 

motor before he adds the fuel, otherwise the engine can get a “hot start” and damage the 

turbine. Automation of the starting process has significantly helped to make this problem a 

thing of the past. 

 By following the TIT = 1,500 °R curve over the maximum power region to the point 

where PR = 11.5 in Fig. 2-10, you will see that the SHP is again zero. At this point the 

temperature rise is so great in the compressor stage of the cycle that the only fuel that can be 

burned in the combustor gets used to turn the compressor turbine. No additional 

thermodynamic energy (i.e., additional fuel flow) can be introduced to get usable shaft turbine 

without going over the TIT limit of 1,500 °R used as an example level. 

 Fig. 2-10 shows just how much the engine usable SHP per pound/second of airflow 

can be increased given the technology to operate the turbine stage at very high temperatures. 

You should note that as the allowable TIT is increased, the preliminary design engine trend 

will “optimize” at successively higher compressor pressure ratios. However, the maximum 

power is achieved over a greater range in pressure ratio as higher TITs are allowed. 

 The companion curves to usable SHP are SFC curves. The preliminary design trends 

for this key engine performance characteristic are shown in Fig. 2-11; you can see that the rate 

of fuel consumption does not continually benefit from increasing TIT limits. This is in 

contrast to the trend in SHP shown in Fig. 2-10. 

 You will notice that Fig. 2-11 gives the distinct impression that there is an asymptotic 

lower limit to SFC; perhaps about 0.3 pounds per hour per horsepower. In fact, there is an 

absolute minimum to SFC on the order of 0.138 pounds per hour per horsepower assuming 

gas turbine jet fuel currently in use.22 The logic is as follows: 

 

22 In discussing this rather simple result with Mike Scully in September of 2009, he refined my numbers 

somewhat and added that “there are many definitions for BTU. The ISO BTU definition (exactly 1,055.056 

Joules per BTU) is also the official U.S. value (see NIST SP-1038). The ISO BTU quotes the lower heating 

values (LHV) for aviation fuels from MIL-STD-3013. The fuel density (lb/gal.) values in system specs are often 

higher than the minimums in MIL-STD-3013. DoD uses JP-8 on land and JP-5 on ships. JP-4 is only used for 
2.1 ENGINES 

72 

1. JP-8 jet fuel weights approximately 6.7 pounds per U.S. gallon. 

2. The heat content of JP-8 is about 18,400 BTUs per pound. 

3. One horsepower is equivalent to 42.44 BTUs per minute or 2,546 BTUs per hour. 

4. Thus, one hp = 2,546/18,400 pounds per hour or 0.138 lb/hr. 

5. The lowest possible SFC is 0.1376 lb/hr/hp assuming JP-8. 

Keep in mind that actual SFC must be higher than ideal because a significant amount of fuel 

is used to power the compressor as Eq. (2.18) shows. 

 The SFC and SHP preliminary design trends shown in Fig. 2-10 and Fig. 2-11 can be 

combined into one very informative data set as shown in Fig. 2-12. The primary variable is 

the four TIT limits used in this example. Both compressor pressure ratio and fuel-air ratio are 

adjusted, for a constant TIT, to move along any given line. The preliminary designs presented 

in this form help pinpoint the “optimum” performance at each TIT. 

 Given this background in preliminary design performance of the gas turbine, consider 

the actual engine performance currently available from engine manufacturers. The tabulated 

data [107], for example, provide trends in fuel flow at rated power with engine size for about 

200 turboshaft and turboprop gas turbine engines. This important engine performance 

characteristic is shown in Fig. 2-13. Data for both turboshaft and turboprop engines are 

included in this survey. Note that this uninstalled engine performance is presented at sea level 

on a standard day where the outside air temperature is 59 °F. This is in contrast to the 

preliminary design example where I used 4,000-feet pressure altitude and an outside air 

temperature of 95 °F. 

 Based on the SFC of 0.60 upper boundary shown in Fig. 2-13, the smaller (and earlier) 

gas turbine engines have yet to benefit from technology that allows higher turbine inlet 

temperatures. The SFC line of 0.50 shows that engine manufacturers have made great 

progress in raising turbine inlet temperature limits in the medium-sized engines that mark a 

second generation. The fact that some engines are now beginning to operate at SFCs below 

0.45 shows that a point of diminishing returns is near for SFC. This is not to suggest, 

however, that work has been discontinued on improving future turbine engines. 

 Finally, consider the issue of engine weight. The trends in gas turbine weight with 

rated SHP using tabulated data [107] are shown in Fig. 2-14. There is a distinction between 

turboshaft and turboprop made in this figure. However, the line is blurred between the two 

types because of the weight of the gearbox. Tabulated data give no details about a gearbox. In 

general, a turboshaft engine does not have a gearbox while the designation turboprop suggests 

the weight of a gearbox is included. This is particularly evident in the high-power region of 

the graph where the gearbox weight appears to be of the same magnitude as the turbine engine 

itself. 

 

operations at very low temperature (e.g., Alaska in winter) because it is almost as dangerous as gasoline. 

Commercial jets use Jet A-1, which is very similar to JP-8. The use of these fuels is not driven by BTU/lb 

because the world will not pay a high price in $ and operational limitations for modest performance gains.” 
2.1 ENGINES 

73 

0

50

100

150

200

250

0 2 4 6 8 10 12 14 16 18 20

Turbine Inlet Temperature

1500 °R

2000 °R

2500 °R

3000 °R

SHP per 

lbs/sec of 

Air Flow

Compressor Pressure Ratio

Fig. 2-10. Dramatic engine performance increases are obtained by raising TIT limits.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 2 4 6 8 10 12 14 16 18 20

Turbine 

Inlet

Temperature

3000 °R

2500 °R

2000 °R

1500 °R

Specific Fuel 

Consumption 

(lbs/hr per 

SHP)

Compressor Pressure Ratio

Fig. 2-11. There is a diminishing return to reducing fuel consumption as TIT limits 

are increased. 
2.1 ENGINES 

74 

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 50 100 150 200 250 300

Turbine Inlet

Temperature

1500 °R

2000 °R

3000 °R

2500 °R

3.0 to 4.5

5.5 to 7.0

8 to 11

12 to 16 

Compressor

Pressure

Ratio

Specific

Fuel 

Consumption

Shaft Horsepower per lbs/sec of Air Flow

Fig. 2-12. Airflow and TIT are the key parameters of the gas turbine engine.

0

500

1,000

1,500

2,000

2,500

3,000

0 1,000 2,000 3,000 4,000 5,000 6,000 7,000

0.45 SFC

Fuel 

Flow

at 

Rated 

Power 

(lbs/hr)

Rated Shaft Horsepower

0.60 0.50

0.40

Fig. 2-13. Gas turbine engines burn fuel at a rate of approximately 0.45 pounds per hour 

for each rated SHP delivered. 
2.1 ENGINES 

75 

0

500

1,000

1,500

2,000

2,500

0 1,000 2,000 3,000 4,000 5,000 6,000 7,000

Uninstalled 

Dry Weight 

(lbs)

Rated Shaft Horsepower

Turboprop 

(Incl. Gearbox)

Turboshaft 

(No Gearbox)

Fig. 2-14. Turboshaft engines without a gearbox are lighter than turboprop engines 

with a gearbox. 

 This issue of who is furnishing the gearbox is a rather important distinction to the 

rotorcraft industry. Helicopters, for example, use large rotors that turn in the range of 250 to 

350 rpm. This means a speed reduction from a power turbine speed on the order of 

20,000 rpm. Most helicopter manufacturers have the technology, created from the piston 

engine era, to design a 10-to-1 speed-reducing gearbox. However, a 100-to-1 gearbox 

definitely requires a joint effort on the part of rotorcraft and engine manufacturers. 

 With the preceding background, let me now discuss turbine engines as they have come 

into use—and how they perform—when installed in rotorcraft. The turboshaft gas turbine 

found its way more slowly into the rotorcraft industry than it did in the fixed-wing field. In 

1951, Charles Kaman experimented with two 175-horsepower Boeing 505 industrial gas 

turbines installed in his Navy HTK, the forerunner of his H-43 synchropter. In France, the 

Turbomeca engine company produced the Artouste II turboshaft engine. This was the first gas 

turbine specifically designed for a helicopter. It was installed in the then Sud-Aviation 

Company helicopter that became the Alouette II and made its maiden flight December 3, 

1955. (You will find the fascinating story of the French rotorcraft industry in Boulet’s history 

[2]. The combination of Turbomeca engines and Sud-Aviation, soon to become Aérospatiale, 

helicopters quickly made France a world leader in the industry.) Other members of the 

industry shortly followed suit proving that the high power-to-weight ratio offered by the 

turboshaft was here to stay. 
2.1 ENGINES 

76 

 In the late 1950s, the Department of the Army (through the Air Force) awarded the 

Bell Helicopter Corporation a contract for what became the first in the long line of Hueys. 

The experimental XH-40, powered by a Lycoming YT-53-L-1, was flight tested at Edwards 

Air Force Base in May and June of 1957. The test report [115] was delayed for nearly a year 

because of a 50-horsepower discrepancy (over the 300- to 700-hp range) between Lycoming 

test stand calibration of the engine and power available as measured with the engine installed 

in the XH-40.23 The helicopter’s performance was finally evaluated and published assuming 

the installed power measured at Edwards was representative [116]. 

 The fuel flow for the installed Lycoming YT-53-L-1 free-shaft turbine engine is shown 

as a function of SHP delivered in Fig. 2-15. The two parameters are used in the referred sense 

that allows one curve to describe the effects of altitude and temperature. That is, the engine 

performance parameters include the δ√θ term discussed earlier. 

0

100

200

300

400

500

600

700

800

0 100 200 300 400 500 600 700 800 900 1,000

Referred 

Fuel 

Flow 

(lbs/hr)

Referred Shaft Horsepower

Lycoming YT-53-L-1

Installed in Bell XH-40

Installed in Test Cell

Allison T63-A-5A

Installed in

Hughes OH-6A

Hiller OH-5A

Bell OH-4A

Fig. 2-15. Gas turbine engines burn fuel at zero SHP to power their compressor. 

 

23 The engine was returned to Bell for installation and flight test in the other two XH-40 helicopters. In one 

helicopter, the engine performed nearly identically in accordance with the test stand calibration. In the third 

helicopter, “the engine appeared to produce more power for a given gas producer speed than was determined 

during test stand calibration.” The problem finally went into “the too hard file” with the conclusion that “these 

discrepancies will probably be determined as service experience is gained on the H-40.” As it turned out, the first 

three XH-40s grew to a fleet of over 10,000 UH-1s or, more popularly, the Huey helicopter. Service experience 

from nearly two million flight hours has been gathered. The Huey helicopter is considered a success. 
2.1 ENGINES 

77 

 You will note in Fig. 2-15 that fuel flow varies nearly linearly with SHP. However, 

there is an apparent zero shift so that fuel needs to be burned even when no usable SHP is 

provided. This is a measure of how much thermodynamic energy is used by the compressor 

just to make the engine even run. You can also see from the figure that the slopes for both the 

larger Lycoming YT-53 engine and the smaller Allison T-63 engine (which I will discuss next) 

are about the same. This measure suggests that both engines were of the same technology 

level. 

 Gas turbine engines operate in such a way that, to the first approximation, fuel flow 

and power are related simply as 

(2.23) Wff SHP a b   = +   δθ δθ   . 

This handy approximation is quite useful for estimating mission fuel weight in rotorcraft 

preliminary design. The constant (a) in Eq. (2.23) reflects primarily the compressor and the 

turbine “wheel” that drives it. For the early T-63, which was nominally rated at 270 SHP, this 

constant is a referred fuel flow of 40 pounds per hour. The larger T-53, rated at 850 SHP, 

intercepts at 230 pounds per hour. The slope [for these two engines (b) is 0.545 lbs/hr per 

SHP] in the equation represents the useful energy that the fuel is providing. Virtually all gas 

turbine engines behave in the nearly linear fashion suggested by Fig. 2-15. 

 The smaller Allison T-63 engine shown in Fig. 2-15 was the power plant selected by 

the Army when they began a competition for a new Light Observation Helicopter in the early 

1960s. The objective was to replace the piston-powered fleet of Hiller H-23s and Bell H-13s. 

This time the Department of the Army, rather than the Air Force, was the procurement agency. 

The “fly-off” competition began in January/February 1964 with the Hughes OH-6A, the 

Hiller OH-5A, and the Bell OH-4A. The development costs of about $20 million for the three 

manufacturers and $7 million for engines was paid by the Army. The helicopters were built to 

Federal Aviation Agency (FAA) civil regulations with only minor military requirements 

superimposed. The Army was buying “off-the-shelf products.” These helicopters were 

evaluated and results published in references [117], [118], and [119], respectively. (By this 

time the Air Force had turned over rotorcraft testing at Edwards Air Force Base to the Army, 

and this created the U.S. Army Aviation Systems Test Activity.) 

 The competition was, to say the very least, hard fought not only from the technical 

side but from the business side. The Hiller OH-5A and Hughes OH-6A appeared to receive 

the better product evaluation compared to the Bell OH-4A in the test reports. As it turned out, 

the Hughes OH-6A was the first-round winner (May 26, 1965), and the Army bought some 

1,000 helicopters at just under $20,000 a piece. However, both Bell and Hiller proceeded to 

quickly turn their helicopters into commercial products. Hiller came out with its FH-1100 and 

Bell began the very successful Model 206 line. Hughes soon followed with its Model 500. 

This onset of three, turbine-powered, “advanced technology” commercial products was 

highlighted in the 14th Annual Helicopter Edition of Flight Magazine [120]. 
2.1 ENGINES 

78 

 When the Vietnam War started, the Army decided to buy another batch of 121 OH-6A 

light observation helicopters. However, they ended up buying the Bell commercial Model 

206B (a great improvement over its original OH-4A), and it was designated as the Army’s 

OH-58A. The flight evaluation of this helicopter was reported [121]. Despite the rough start 24

the world now had three exceptional, light helicopters, and they were each powered with the 

Allison 250-series shaft turbine. 

 This competition story of the 1960s was repeated again in the late 1970s in a 

somewhat different form. In this period the General Electric YT-700-GE-700 engine became 

available (through an Army-led competition) for consideration by the U.S. Army. The Army 

also found the need to update both its attack helicopter and utility helicopter fleets during this 

period. (At this time, Bell Helicopter Textron had a virtual monopoly on nearly every 

helicopter the U.S. Army was flying. The Bell OH-58As through Cs were being used for light 

observation, the Bell Huey UH-1Bs through Ds served for utility, and the Bell Cobra AH-1, 

prototyped in 9 months, provided the attack capability. In the Vietnam conflict, these 

rotorcraft demonstrated beyond any doubt just how valuable helicopters had become.) 

 Using the General Electric YT-700-GE-700 engine, the mid-1970s saw a “fly off” 

between helicopters prototyped by each of the four major United States rotorcraft 

manufacturers. The Army’s new utility helicopter was to be either the Sikorsky YUH-60A or 

the Boeing Vertol YUH-61A. The attack helicopter competition was between the Bell YAH-63 

and the Hughes YAH-64. Each helicopter was tested by the Army at Edwards Air Force Base, 

and results were published at the end of 1976 in references [123-126], respectively. This 

competition really tested the industry’s capability in every aspect of modern rotorcraft 

engineering and manufacturing, as well as business management. The results of the 

competition, with respect to installed engine performance, were quite extraordinary. 

 Two YT-700-GE-700 engines were installed in each of the four prototype helicopters 

that were delivered for Army flight evaluation at Edwards in 1975. The evaluation of engine 

power available—uninstalled versus installed—for hovering at 4,000-feet pressure altitude 

with an ambient temperature of 95 °F is summarized in Table 2-1. Each evaluation concluded 

 

24 On July 24, 1968, the San Francisco Chronicle carried a United Press article from Washington that summed 

up a Congressional, House Armed Services Committee investigation into both the original award and the 

supplementary buy. It read in part: “The [original] contract award was marked by allegations including 

misconduct, prejudice, information leaks, influence peddling and industrial espionage. The report accused 

Hughes of building 1,000 light observation helicopters for the Army at the bargain basement rate of $19,860 

each, then quoting a price of $55,000 each for 121 additional machines needed for Vietnam. Rather than pay the 

higher price, the Army canceled its supplementary order and met war needs with other existing models. The 

subcommittee said Hughes won the [original] contract over Hiller Aircraft Corp. by buying in or making a below 

cost bid in the hope of recovering an estimated $10 million loss by pricing the same machine much higher for 

commercial buyers. Hiller’s price was $24,000 per helicopter. The Army had estimated each would cost $30,000 

to $40,000. The subcommittee’s 10-month-long investigation began when the Army asked Hughes to build the 

extra helicopters. The company, headed by Howard Hughes, denied that the loss would be recovered in prices of 

follow up Army contracts. The House investigators reprimanded the Army and urged that the Air Force and 

Navy take over its procurement of aircraft.” The subcommittee’s findings became a matter of Congressional 

record [122]. 
2.1 ENGINES 

79 

that roughly 31⁄2 percent of the engine’s power was lost on installation. Further, the test 

conclusion comparison showed that the installed SHP only varied 15 horsepower between the 

four designs which, in itself, is quite remarkable. This represents a difference between the 

four helicopters of less than three-quarters of 1 percent (of the 2,365 hp) uninstalled power 

available. 

 The evaluation of the YT-700-GE-700 engine fuel flow as a function of SHP when 

installed in these four helicopters is examined in Fig. 2-16 and Fig. 2-17. The data is shown in 

the referred coordinates applicable to gas turbine engines. The YUH-60A engine performance 

data shown in Fig. 2-16 indicates that minimum SFC of 0.48 was obtained at high power in 

the range of 1,300 to 1,500 referred SHP. The scatter in the data is rather typical of flight 

measurements. This scatter, when both engines are included, amounts to ±35 pounds per hour 

in fuel flow at 1,400 SHP or about ±5 percent. At constant fuel flow of 700 pounds per hour, 

the scatter in power is ±70 horsepower or about ±5 percent. The engine prime item 

development specification (commonly called a PIDS) reflects the performance that the 

manufacture had to meet, or exceed, in nearly ideal test cell conditions. In this particular 

example, both right and left engines met “spec” in the test cell. The engine performance 

degraded when installed in the helicopter, although the right engine appears to have had better 

installed performance than the left engine. 

 I have scrutinized all the engines tested in the four development helicopters in 

Fig. 2-17 by just looking at the upper end of engine performance where the scatter in data has 

expanded considerably. The uncertainties in both power and fuel flow have increased to 

slightly over ±7 percent. The importance of, and confidence in, a company’s product 

performance claims are rather compromised when these facts are introduced into published 

data. The only satisfactory recourse I have found is to turn to the pilot’s flight handbook. 

Table 2-1. Installing Engines in Rotorcraft With a Minimum of Losses and 

a Maximum of Confidence Was Finally Proven in the 1970s 

Parameter Utility Attack 

Model YUH-60A YUH-61A YAH-63 YAH-64 

Mission Weight, lb 16,853 16,411 16,054 14,242 

Weight Empty, lb 12,113 11,704 13,338 11,556 

Main Rotor Diameter, ft 53.67 49.00 51.50 48.00 

Tail Rotor Diameter, ft 11.00 10.17 9.50 8.33 

Uninstalled Shaft Horsepower 

Available at 4,000 ft/95 °F 

2 × 1,178 

or 2,356 

2 × 1,178 

or 2,356 

2 × 1,178 

or 2,356 

2 × 1,178 

or 2,356 

Installed Shaft Horsepower 

Available at 4,000 ft/95 °F 2,285 2,275 2,275 2,290 

Installation Loss, Δ SHP 71 81 81 66 
2.1 ENGINES 

80 

0

100

200

300

400

500

600

700

800

900

0 200 400 600 800 1,000 1,200 1,400 1,600 1,800

Left Engine

Right Engine

Prime Item 

Development

Specification

AMC-CP-2222-02000

Referred 

Fuel 

Flow 

(lbs/hr)

Referred Shaft 

Fig. 2-16. In 1974, two General Electric YT700-GE-700 engines installed in the Sikorsky 

YUH-60A gave an SFC of 0.48 lbs/hr fuel flow per SHP. 

500

550

600

650

700

750

800

1,000 1,100 1,200 1,300 1,400 1,500 1,600 1,700 1,800

YUH-60A

YUH-61A

YAH-63A

YAH-64A

± 45 lbs/hr

± 95 SHP

Prime Item Development Specification

AMC-CP-2222-02000

Referred 

Fuel 

Flow 

(lbs/hr)

Referred Shaft Horsepower

Fig. 2-17. There is about a 7 percent performance uncertainty when engines are 

installed in rotorcraft. 
2.1 ENGINES 

81 

 The U.S. Army invested heavily again in engines and rotorcraft in the mid- to late 

1980s. The first step was funding of an Advanced Technology Demonstrator Engine (ATDE) 

program that would improve upon the Lycoming T-53 turboshaft gas turbine. The objective 

was an even more maintainable, lighter weight engine, still within the 750 to 1,000 SHP 

range. The farsighted ATDE program provided the technology for the Light Turbine 

Helicopter Engine Company T-800 engine. This engine is produced by the team of Allison 

Gas Turbine Corporation and the Garret Division of the Allied-Signal Aerospace Company 

(they go by the shorter name of LHTEC.) The LHTEC T-800 was selected as the Government 

Furnished Equipment (GFE) for the Army-funded development of a modern Light Helicopter, 

the Boeing-Sikorsky RAH-66 Comanche. 

 The RAH-66 came into being after a hard-fought competition managed by the U.S. 

Army. Two teams of major companies, Boeing/Sikorsky and McDonnell Douglas/Bell 

Helicopter, submitted massive proposals with their “paper” designs. There was no competitive 

“fly-off”—a marked departure from previous Army procurements. The Boeing/Sikorsky 

design and program was selected on April 5, 1991, and a final contract for $2.8 billion was 

signed on April 12th. The May 1991 issue of Rotor & Wing magazine, page 10 of reference 

[127], provided a one-page summary of key factors in the competition and included the major 

specifications to be met by Boeing/Sikorsky. These were: 

• 52-month development program with four prototypes 

• Initial operating capability (IOC) in December of 1998 

• 1,292 helicopters produced at the rate of 10 aircraft per month 

• $8.505 million per helicopter in 1988 dollars 

• Unit and depot parts and labor (including the GFE T-800) costing $492 per flight 

hour 

• Total operating cost per flight hour under $1,000 

• Mission weight [empty] of 7,500 pounds 

• Top speed of 190 knots 

While the design emphasized reliability, maintainability, and overall user friendliness, the 

most advanced stealth and sensor technology was incorporated. Other, more classical 

technical features such as basic airframe, drivetrain, and rotor configuration were considered 

secondary to the costs and mission weight-empty specification requirements. This was a 

measure of how mature helicopter technology was thought to be in the late 1980s.25 

 

25 Many of the highly classified aspects of the design have yet to reach the public domain. I was the “Chief 

Engineer” for the McDonnell/Bell Super Team which lost to the Boeing/Sikorsky First Team. It was one of the 

most fascinating experiences of my career. The RAH-66 program began, rather early in its history, to run into 

budget problems [128]. The program was cancelled on Monday, February 23, 2004 [129]. One lesson the 

program taught was that development problems bring “help” from Congress. 
2.1 ENGINES 

82 

0

1

2

3

4

5

6

7

0 1,000 2,000 3,000 4,000 5,000 6,000 7,000

Brake

or

Shaft

Horsepower 

per

Pound of 

Dry Weight

Rated Brake or Shaft Horsepower

Turboshaft

Turboprop

4 Cycle Piston

Fig. 2-18. The gas turbine engine enjoys an enormous weight advantage over the 

piston engine. 

 This introduction to engines would not be complete without contrasting piston and 

shaft turbine engines. For example, consider the comparisons in rated horsepower available at 

sea level per pound of dry weight shown in Fig. 2-18. Piston engines now are capable of about 

0.75 BHP per pound in their mature, high-powered form. Turboprop turbines that include a 

gear box appear limited to about 2.5 to 3.0 SHP per pound in their mature, high-powered 

form. Turboshaft gas turbines—without a gearbox—show no obvious limit with size. Of 

course this leaves the burden of a 100-to-1 speed-reducing gearbox to the turboshaft engine 

user. 

 The modern turbine engine offers a very significant weight advantage compared to the 

four-cycle piston engine. It did not initially offer a comparable fuel-flow advantage as 

Fig. 2-19 shows. The small, Lycoming O-360 piston engine burns fuel at about one-half the 

rate of the nearly comparable Allison T-63, a vintage, 1960s, small gas turbine with a gearbox. 

In the larger engine category, the supercharged Wright R-1820 has a fuel flow again about 

one-half of the late 1950s Lycoming YT-53. But with two decades of development to draw on, 

both the General Electric YT-700 and LHTEC T-800 gas turbine engines have demonstrated 

fuel efficiency quite comparable to the piston engine at the end of its era. 
2.1 ENGINES 

83 

 What has happened, of course, is that only minor product performance improvements 

have been made to piston engines since the late 1950s. The industry has, instead, concentrated 

its resources on maturing the gas turbine, and they have been very successful. This does not 

mean, however, that the rotorcraft industry has forsaken the piston engine, as a quick review 

of any number of trade magazines and manufacturers’ brochures will show. The number of 

new piston engines available for sport and experimental aircraft [130] is quite amazing. A 

large market still exists for used Bell Model 47s powered with the Lycoming VO-435 piston 

engine that is now rated at 260 BHP. The Hughes two-place Model 269A (i.e., the Army T-55 

trainer) is still in production by the Schweizer Company and uses the Lycoming O-360-C2D 

piston engine. The Enstrom Company delivers its three-place, F-28 series with Lycoming 

HIO-360-C1A to F1AD engines. And, most encouragingly, Frank Robinson—beginning in the 

early 1979 with his R-22—has completely captured the small, two-place, light helicopter 

market. (In 1979, Robinson delivered 10 R-22s; in 1980, 78; and in 1981, 156, and he had 

captured 57 percent of the market.) The R-22 is powered by the Lycoming O-320-A2C rated 

at 150 horsepower for takeoff and 124 horsepower for continuous operation. The natural next 

step, a four-place, piston-engine-powered helicopter has followed with the R-44. This 

helicopter is delivered with a Lycoming VO-435 rated at 265 horsepower for takeoff. The 

spirited and innovative efforts demonstrated by Robinson and his company are reminiscent of 

the best efforts given by our rotorcraft pioneers. 

0

100

200

300

400

500

600

700

800

900

1,000

0 200 400 600 800 1,000 1,200 1,400 1,600

Referred 

Fuel 

Flow 

(lbs/hr)

Referred Shaft Horsepower

Lycoming HO-360-C2B 

in Hughes YHO-2HU

Allison T 63-A-5A 

in Hughes OH-6A

Lycoming YT-53-L-1 

in Bell XH-40

Wright R-1820-84 

in Sikorsky H-34A

General Electric

YT700-GE-700

in YUH-61A

& YAH-64A

Fig. 2-19. The piston engine enjoyed a fuel flow advantage over the turboshaft 

engine until the mid-1970s. 
2.1 ENGINES 

84 

 You should also be aware that small helicopters fitting into the FAA Part 103 

certification category for ultra-light aircraft are frequently created. This FAA category is 

designated for recreation and sport aircraft uses only. In late 1993 for example, Harry 

Parkinson (President of Advanced Technologies Inc.) announced the Ultrasport 254 in the 

October 1993 issue of Rotor & Wing. This one-place helicopter is sold for around $30,000. It 

has a single, two-bladed main rotor and a weight empty of slightly less than 254 pounds, 

which is the upper limit restriction for FAA Part 103 aircraft. The takeoff gross weight of 

482 pounds includes the 200-pound pilot and 30 pounds of fuel. The test helicopter was 

initially powered with a Rotax 503, two-cycle, piston engine. This two-cylinder engine has 

pistons of 2.834-inch bore and 2.40-inch stroke. It produces a maximum 50 BHP at 6,600 rpm 

and weighs 82 pounds with carburetors and exhaust system. The fuel flow at 50 horsepower is 

6.8 U.S. gallons per hour (about 41 pounds per hour, which gives an SFC of 0.816. A Hirth 

2703 engine is used in the production Ultrasport 254. This two-cylinder engine has pistons of 

2.755-inch bore and 2.52-inch stroke. It produces 55 BHP at 6200 rpm and weighs 

70.5 pounds. The fuel flow at 55 horsepower is 6.2 U.S. gallons per hour (about 37.2 pounds 

per hour) which gives an SFC of 0.676. 

 Finally, the small autogyro still has a very strong following. A noteworthy example of 

this rotorcraft class was offered by the Farrington Aircraft Corporation as the Model 18-A 

Gyroplane. This two-seats-in-tandem rotorcraft was originally developed by the Umbaugh 

Aircraft Corporation in the late 1950s and early 1960s. Production began again in April of 

1991 when the very much improved Model 18-A was fully recertified by the FAA. The 1800- 

pound-gross-weight autogyro is powered with a Lycoming O-360-A1D and can be thought of 

as a direct competitor to the Robinson R-22. A more recent autogyro example is the Groen 

Brothers’ Hawk. 

 The progress made by the propulsion industry can be summarized in several ways. For 

example, in February 1992 Dr. Richard Carlson was invited to address the National Academy 

of Engineering, which was honoring Dr. Alexander H. Flax. Dr. Carlson spoke about the 

future of rotary wing aircraft [131]. He used a particularly illuminating comparison between 

engines in the 1000-horsepower range that I have embellished here in Fig. 2-20. Another 

technical comparison is shown in Fig. 2-21 where SFC and shaft (or brake) horsepower per 

pound are summarized for both piston and gas turbine engines. This figure captures some of 

the historical trends and emphasizes how different the two engine classes are. Historically, the 

older engines fall towards the higher SFC and lower horsepower-per-pound range. 

 The contrast between piston and turboshaft engines is exemplified by their relative 

costs. In general, pricing information is rather difficult to come by. Yet, it is just this 

competitively sensitive data that engineers, in particular, need in order to balance their 

preoccupation with rotorcraft technology. Data from reference [132]26 shows that, at equal 

 

26 An absolutely mandatory reference for rotorcraft study is published by HeliValue$, Inc. [132]. Their Official 

Helicopter Blue Book® provides an enormous amount of configuration and pricing data that has been heavily 

relied on by the commercial marketplace for nearly two decades. I think the value of this reference to 

understanding helicopter technology, and seeing where engineers, in particular, can make very significant 

contributions to reduce product costs, is not realized by the technical community. 
2.1 ENGINES 

85 

R-1300 (940 lbs) 1949

T-53 (490 lbs) 1953

ATDE (230 lbs) 1980

Fig. 2-20. Progress in the engine industry has been impressive [131]. 

0

1

2

3

4

5

6

7

0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85

Turboprop

With Gearbox

Turboshaft

Without Gearbox

4 Cycle Piston

Rated 

Horsepower 

per Pound 

of Dry 

Weight

SFC (at cruise power for piston, at maximum power for turbine)

Fig. 2-21. Gas turbine engines have given the helicopter its most significant 

step forward. 
2.1 ENGINES 

86 

power, the piston engine price is about one-third of the turbine engine price. The compilation 

shown in Fig. 2-22 emphasizes this difference. 

 The corner of a black square data symbol (for turbines) immersed in the open circle 

piston engine data is just visible on Fig. 2-22. This was the first suggestion of offering the 

turboprop engine at piston engine prices. The suggestion was made by the Allison Engine 

Company in the early 1990s with its very well proven, Model 250-series engine. You will 

recall that this gas turbine engine with a gearbox giving about 6600 rpm output started the 

Hughes Model 500, Hiller FH-1100, and Bell Model 206B product lines. The engine started 

as the Model 250-C18B, which later grew into the 250-C20. Allison has derated the growth 

engine back down to the original level of about 320 SHP at sea level on a standard day. The 

full influence (of what might be a very competitive move by Allison) on both Lycoming and 

Continental piston engine product lines has yet to be seen. 

You may conclude from this introduction to engines that, at equal power: 

1. Piston engines weigh at least three times what comparable turboshaft engines 

weigh. 

2. Early turboshaft engines burned twice as much fuel as advanced piston engines. 

3. Improvements in gas turbine engine performance have come by increasing turbine 

inlet temperatures. 

4. Engine manufacturers can change a turboshaft to a turboprop by adding a gearbox. 

5. Turboshaft engines presently cost three times what piston engines cost (but they 

have become much more reliable). 

You should also appreciate that the single, most important factor that has improved rotorcraft 

is progress in engine technology. 

0

200,000

400,000

600,000

800,000

0 500 1,000 1,500 2,000 2,500 3,000

Low Time 

Used 

Engine 

Price

 (1992 

dollars)

Takeoff Rated Horsepower

Shaft Turbine 

$360/hp

4 Cycle Pistons 

$130/hp

Fig. 2-22. Turboshaft engines are priced about three times higher than four-cycle 

piston engines.
87 

2.2 WEIGHT 

 Rotorcraft weight is perhaps the clearest measure the industry has of its technological 

progress. This is because all facets of design and manufacturing finally come to light when 

you study modern helicopter weight results in some detail. 

 To understand and appreciate the progress made by the rotorcraft industry in reducing 

helicopter weight and obtaining a more efficient “machine,” you need to: 

a. Start with a framework for the discussion, 

b. Understand the terminology used, 

c. See two general trends that have appeared over five decades, 

d. Review detailed results for one specific helicopter class, and then 

e. Apply this background understanding to a broad range of products that the 

industry has created. 

After absorbing these five points you will see a simple method of conceptually sizing and 

weighing a new, modern helicopter. This chapter on weights will then conclude with a short 

discussion of helicopter productivity. Let me start with a framework for the discussion. 

 A framework in which to discuss, examine, and evaluate modern helicopter weights is 

shown in Fig. 2-23. All manner of manufacturers’ brochures, specifications, and handbooks, 

as well as a similar array of trade magazines and military reports, can provide modern 

helicopter weights, performance, and configuration data relative to Fig. 2-23. Fortunately, 

these sources have become relatively consistent in using terms such as takeoff gross weight, 

useful load, and empty weight (or weight empty as used by the U.S. military). Unfortunately, 

the actual components and equipment that are included within the weight terms of Fig. 2-23 

are far from consistent. 

 You might think that design weight enjoys special attention because of its placement 

in the top box on Fig. 2-23. In practice, this is generally not the case. A design weight is 

frequently first established as a configuration emerges from conceptual and preliminary 

design. Its specific weight value is influenced not only by customer needs but by engineering 

facts and regulatory requirements. In some cases, upper management may simply legislate a 

design weight value and even associate a “design-to-cost” or selling price for the product as 

well. From an engineering point of view, the design weight is a needed reference “number” by 

many individual contributors as the detail design progresses. 

 The design weight will generally be the highest reference weight during preliminary 

and detail design. It does not stand alone however. Associated with the design weight are a 

minimum of two limit load factors as suggested by Fig. 2-23. Positive and negative load 

factors on the order of +3.0 g and –0.5 g have been common practice in the rotorcraft industry 

for some time. These load factors and design weight combine to give one set of primary 

design loads. To understand this point a little better, consider a simple example. 
2.2 WEIGHT 

88 

Fig. 2-23. Takeoff gross weight is the sum of weight empty and useful load. 

 The Bell Helicopter XH-40, the beginning of the Huey series, had a design gross 

weight of 5,400 pounds with limit flight load factors of +3.0 g and –0.5 g. This implies that a 

steep bank, sharp pull-up, or other maneuver will increase the rotor thrust from about 

5,400 pounds to somewhat over 16,200 pounds. A primary component such as the main rotor 

shaft would have to be designed for the 16,200-pound tensile load. (The rotor shaft would also 

have to be strong enough for a negative or compressive load of –2,700 pounds.) Thus, a 

primary load for many components could be defined as 

(2.24) 

Design Load Design Weight Limit Load Factor

5, 400 lbs 3.0 g for Bell XH 40 rotor shaft

16, 200 lbs

= ×

=× −

= +

.

Of course the complete set of design loads for all components does not remain constant as the 

rotorcraft completes the several design phases. In fact, it is not until the rotorcraft has 

completed its comprehensive military qualification or civil certification that the multitude of 

design loads settle down. 

 The takeoff gross weight depends on the design loads. It may surprise you to learn that 

the takeoff gross weight can frequently exceed the design weight. Fig. 2-23 suggests this by 

listing a number of different military missions or civilian applications. The reason for this 

apparent inconsistency is that a restricted flight load factor can be defined for the pilot in his 

flight manual so that the design load is not exceeded. In an engineering sense then, the 

definition of takeoff gross weight that I prefer is 

DESIGN WEIGHT 

Limit Load Factors 

TAKEOFF GROSS WEIGHT 

 ·Primary Mission 

 ·Maximum Payload 

 ·Maximum Range 

 ·External Load 

 ·Ferry Range 

 ·Maximum Alternate 

 ·Minimum Operating 

USEFUL LOAD WEIGHT EMPTY 
2.2 WEIGHT 

89 

(2.25) 

Primary Design Load Takeoff Gross Weight Allowable or Restricted Load Factor

Design Weight Design Limit Load Factor

Allowable Load Factor

=

× =

. 

An example of Eq. (2.25) at work can be found in any experimental flight test program. For 

instance, during flight testing of the XH-40 [115], the experimental helicopter was flown at 

takeoff gross weights as high as 5,720 pounds. This was 320 pounds greater than its design 

weight of 5,400 pounds. Care was taken, therefore, to not maneuver the helicopter up to the 

+3.0 g limit. Rather, the pilot restricted maneuvers to below +2.83 g as determined by 

 5,400 3.0 5,720 2.83

× = . 

 The testing of the experimental XH-40 at flight weights higher than design weight 

followed a classical process of envelope expansion. In this case, the XH-40 became the H-40 

and was the first production helicopter in the Huey series.27 The design weight of the H-40 or 

HU-1A was increased to 5,725 pounds. Testing [116] was conducted with flight weights as 

high as 6,400 pounds. Again, care was taken not to exceed reduced maneuvering load factors 

so that primary design loads (i.e., maximum rotor-shaft tensile load) would not be violated. 

 By late 1964 the XH-40 had progressed through the UH-1A and reached the UH-1D 

model stage. The design weight was then 6,600 pounds while the positive limit load factor 

had been maintained at +3.0 g. The negative load factor had gone from –0.5 g to +0.5 g.28 An 

ultimate load factor of +4.5 g had been introduced.29 To accomplish these successive growth 

steps, the rotor blade chord was increased from 15 inches to 21 inches. The preproduction 

model of the UH-1D, the YUH-1D, was tested [133] at flight weights as high as 

8,800 pounds. During testing at flight weight above the design weight of 6,600 pounds, the 

limit load factor was restricted to +2.2 g. The pilot was careful to fly the helicopter more 

gently in maneuvers. 

 Perhaps a pattern is now becoming clear to you. Modern helicopters, and most aircraft 

for that matter, are designed for loads well in excess of those that come with just straight and 

level flying. Flight can be attempted, and has been accomplished, at well beyond the design 

weight with almost all helicopters. Because all components have been designed including 

 

27 The U.S. Army designated this model as the HU-1 and later reversed the helicopter (H) and utility (U) 

nomenclature while adding a reference letter (A) to indicated that this would be the “A” model. This created the 

UH-1A designation. 

28 The ability of the teetering rotor system, regardless of the number of blades, to safely perform negative g 

maneuvers that come with, say, an aggressive push-over, began to be questioned. The flapping motion could 

become erratic and cause the hub to hit the rotor mast. This motion could cause extremely high loads and 

potentially severe damage to flight-critical components. Later, Bell two-bladed, teetering rotor systems 

incorporated modifications to reduce this problem. 

29 You may recall that a part that is loaded up to its limit load can be unloaded, and little or no damage to the 

part will have occurred. A part loaded to its ultimate load is expected to break. 
2.2 WEIGHT 

90 

limit load factors, there is a “factor of safety” inherent in the reference number associated 

with the design weight. 

 There are, as you might now also suspect, many other safety factors that come into 

play for each individual part that is designed and built. Thus, the weight of any given part, and 

its cost, is very influenced by its detail design loads. When the helicopter is flown, the 

measured loads for a multitude of flight conditions can frequently show that the established 

design loads were too high. Of course flight test measurements can, and often do, show that 

the part is under designed. Rather than restrict the flight envelope of the helicopter, the underdesigned part is generally redesigned. On the other hand, it is quite rare that an over-designed 

part will be resized to a lighter version. This is because “re-qualification of the part is more 

expensive than living with what we have” as upper management often says. 

 With the framework of Fig. 2-23 and the introduction to design weight, limit load 

factors, and design loads in hand, let me proceed to discuss takeoff gross weight. 

 The helicopter is the most utilitarian aircraft mankind currently has flying. Several 

roles or missions that can lead to a variety of takeoff gross weights are listed below the dashed 

line in the box in Fig. 2-23 to reflect this inherent, utilitarian characteristic. The highest 

takeoff gross weight likely occurs with a ferry range mission or a job where an external load 

is carried at the end of a sling. At the other end of the spectrum lies the minimum operating 

takeoff gross weight. This weight would only include a pilot, virtually no fuel and, of course, 

zero payload. 

 The takeoff gross weight for the overwhelming majority of helicopters introduced 

during the last 50 years is well below 50,000 pounds. However, this does not mean that there 

is an inherent limitation to helicopter size. These two points are emphasized in Fig. 2-24. The 

over 600 data points shown in Fig. 2-24 were collected over 45 years; they come from too 

many sources for me to reference. A reasonably representative summary starts with references 

[86-89, 94]. As you can see from Fig. 2-24, large helicopters capable of takeoff gross weights 

well above 50,000 pounds have already been built by the Mil and Kamov design bureaus in 

Russia. The Mil Mi-6 and Mi-10 are single rotor configurations with a main rotor diameter of 

just under 115 feet. The Mil Mi-12 was a side-by-side configuration that used components 

from the Mil Mi-6/-10. The Mi-12 had a cabin about 95 feet long and 14 feet wide, which is 

comparable to medium-sized commercial jet transports. The Mil Mi-26 is currently in service 

with Aeroflot and has a 70- to 100-passenger cabin. The Kamov Ka-22 was an experimental 

transport that could carry 100 passengers. The Ka-22 was a side-by-side “compound” 

helicopter having a fixed wing and two forward thrusting propellers, as well as two 65-foot, 

7-inch-diameter main rotors. It set the rotorcraft world speed record in October of 1961 at 

227 miles per hour or nearly 200 knots. 

 In the United States, the Boeing Helicopter Division had virtually completed, but not 

fully assembled, the YCH-62A, a tandem helicopter designed for external load, “sky crane” 

missions. The YCH-62A was to have a 148,000-pound takeoff gross weight and a rotor 
2.2 WEIGHT 

91 

100

1,000

10,000

100,000

1,000,000

1935 1945 1955 1965 1975 1985 1995 2005

Maximum 

Takeoff 

Gross 

Weight 

(lbs)

Year of First Flight

Fig. 2-24. There is no inherent limitation to helicopter size. 

diameter of 92 feet. The Sikorsky CH-53E (at about 70,000-pounds takeoff gross weight) 

grew over 15 years from the lighter CH-53A model of just under 40,000-pounds takeoff gross 

weight when it went into service in 1965.30 

 Finally, you should be aware that Henrich Focke had a scaled-up version of his Fa-223 

on the drawing board in 1941. This side-by-side helicopter, the Fa-284, was to have a takeoff 

gross weight of about 26,000 pounds. One can only marvel at the giant strides Focke was 

taking after his F. 61 demonstrated a path to true rotary wing flight. 

 The historical trend of takeoff gross weights shown in Fig. 2-24 immediately raises a 

question. Just how well has the rotorcraft industry done in producing helicopters that do 

useful work? To explore one facet of this question requires definitions of useful load and 

empty weight. 

 

30 The rotorcraft industry has excelled in growing the capability of an initial product. The CH-53 series is just 

one outstanding example. Another is the Boeing CH-47 series. This heavy-lift, tandem rotor, cargo helicopter 

began as the YHC-1B with a gross weight of 25,000 pounds in 1959. This preproduction helicopter grew slightly 

and entered service in 1962 as the CH-47A at 33,000 pounds. By 1985, the CH-47D had arrived and was capable 

of taking off at 50,000 pounds. 
2.2 WEIGHT 

92 

100

1,000

10,000

100,000

1,000,000

100 1,000 10,000 100,000 1,000,000

Primary Mission Takeoff Gross Weight (lbs)

Useful 

Load 

(lbs)

Fraction Of 

TOGW

0.50

0.40

0.30

Fig. 2-25. On average, the rotorcraft industry can obtain 40 percent useful load from 

takeoff gross weight. 

 Consider the following definitions for weight empty and useful load. These categories, 

shown in boxes on Fig. 2-23, break down takeoff gross weight into two main elements. An 

introductory definition of weight empty is that (1) it accounts for all components that are not 

intended to be removed from the helicopter, and (2) it does not account for items loaded 

and/or unloaded (nor for materials that are consumed) during a flight. It follows then that 

useful load includes whatever is not in weight empty. 

 These rudimentary definitions of takeoff gross weight and its two subgroups are 

sufficient, for the moment, to understand the data presented in Fig. 2-25. This trend of useful 

load as a function of takeoff gross weight shows how well the rotorcraft industry has done 

over the last 50 years. 

 The takeoff gross weight I have chosen as the abscissa in Fig. 2-25 is for the primary 

mission.31 However, it is by no means a certainty that the values I used are truly correct for 

anything more than a majority of the helicopters. Still, the message is clear. The industry is 

 

31 As I suggested earlier, the takeoff gross weight can vary considerably for any given helicopter depending on 

the allowable load factors given in the pilot’s flight handbook. However, the empty weight does not vary 

appreciably for obvious, practical reasons. Therefore, there can be a variety of useful loads quoted for a given 

helicopter. Many sources are inconsistent in their tabulated weight data and few rarely define associated load 

factors. 
2.2 WEIGHT 

93 

capable, on average, of producing helicopters that give about 40 percent of takeoff gross 

weight to useful load. 

 Historically, there appears to be an upper bound to the percentage of takeoff gross 

weight available for useful load. For helicopters with a shaft-driven rotor system, Fig. 2-25 

suggests a value of approximately 50 percent. You may be aware that there have been a few 

small helicopters built that had rotor-blade-tip jet propulsion. This class has yielded a useful 

load percentage well above the 50 percent level. Unfortunately, fuel consumption has been so 

high for non-shaft-driven rotor systems that little useful load has been left over for more than 

the pilot. 

 The list of items that might be included in useful load is really not too long. The 

reference for the most authoritative list today (at least for U.S. helicopters) would be Military 

Standard (MIL-STD) 1374A. This guiding document [134] provides a one-sheet format to 

itemize no more than 54 lines of weight and other information. The MIL-STD set of forms is 

used in conjunction with a set of weight definitions given in MIL-W-25140 [135]. In Table 

2-2, I have taken some poetic license to show the most common items MIL-STD-1374A and 

MIL-W-25140 suggest be included in useful load. 

Table 2-2. Useful Load as Suggested by MIL-STD-1374A 

Load Condition 

Crew (no.) 

Passengers (no.) 

Fuel 

 Unusable 

 Internal (type/gals.) 

 External (type/gals.) 

Oil 

 Trapped 

 Engine 

Auxiliary Fuel Tanks 

Baggage 

Cargo 

 Internal 

 External 

Gun Installations 

 Guns 

 Ammo 

Weapons Installed 

 Fixed Devices 

 Expendables 

Other Equipment 

 Survival Kits 

 Armor (removable) 

 Etc. 

Total Useful Load 

Weight Empty 

Gross Weight 
2.2 WEIGHT 

94 

 You can see from Table 2-2 that the useful load definition always starts with a load 

condition. After that comes the item and some room to add information about the item. All 

this goes in the first column. The following columns are used to fill in the weight for any 

other defined load condition. Generally, the first load condition is associated with the primary 

mission. The last three lines are used to total the useful load from the lines above, record the 

weight empty as enumerated on other sheets, and then add the two together to get the takeoff 

gross weight. 

 The discussion so far has given you a framework, some terminology, and two general 

trends to introduce you to the world of helicopter weight. Unfortunately, I may have left you 

with a somewhat misleading impression that is suggested by Fig. 2-25. There is, in fact, a 

widely held perception that a high ratio of useful load to gross weight or, alternately, a low 

ratio of weight empty to gross weight is a measure of “goodness.” However, as you will see, 

these ratios have varied considerably, both upwards and downwards, over the last several 

decades of modern helicopter development. What has happened is that more and more useful 

features and equipment have been added to the helicopter over this period. This has been 

made possible because of the gas turbine engine, improvements in materials, and innovative 

structural design that has reduced the weight of mandatory components needed to just fly. 

Therefore, to qualify this impression I may have given you, consider the evolution of light 

rotorcraft used by the U.S. Army for observation and scouting. 

 You will recall that the predecessor to the U.S. Army Air Corps, the Air Service of 

World War I, funded George DeBothezat’s development of a quadrotor in June of 1921. By 

May of 1923, despite having demonstrated a “flyable machine,” the results were less than 

encouraging, and DeBothezat left McCook Field with apparently poor feelings on both sides. 

Army interest in rotorcraft was not revived until the autogyro burst on the scene, although it 

did not perform well in the Army’s observation and scouting missions. The transition from 

autogyros to helicopters began in the early 1940s when Haviland Platt and Lawrence Le Page 

convinced the Air Corps to fund development of their version of Henrich Focke’s F. 61. 

Ultimately, the transition pitted the older Kellett YG-1B and newer YO-60 autogyros (and 

corresponding Pitcairn autogyro models) against the Platt–Le Page XR-1 side-by-side 

helicopter and the Sikorsky XR-4 single-main-rotor helicopter. The Sikorsky XR-4 ultimately 

won the Army’s confidence when it was accepted by Colonel H. Franklin Gregory on May 12, 

1942. 

 One interesting aspect of this early period was the evolving definition of the military 

helicopter’s tactical mission and the meaning of the words “light observation/scout 

helicopter.”32 The February 1941 specification for the Kellett XR-2/XR-3 autogyro [136, 137] 

(the prototype of the Kellett XO-60/YO-60) contains a paragraph that states: 

 

32 I am deeply indebted to Bernie Lindenbaum for copies of the autogyro and helicopter specifications [136-

144]. These documents provided much more accurate technical insight into our rotorcraft history. Bernie was 

one of the earliest members of the American Helicopter Society. He was also the staunchest supporter of VTOL 

within the U.S. Air Force. 
2.2 WEIGHT 

95 

 “B-4.0. The tactical mission of this [autogyro] aircraft is for experimentation and 

investigation into new and novel features which will improve the performance of this type of 

aircraft, and will increase its value as a reconnaissance and observation type of craft for work 

with ground troops.” 

Similarly, the specification for the Sikorsky XR-4 dated January 1, 1942, [138] also has a 

paragraph B-4.0 that reads (with my italics): 

 “B-4.0. The tactical mission of this [helicopter] aircraft is as yet undetermined, due 

to its completely novel characteristics. It is presumed, however, to have excellent values in 

observation, liaison, communication, reconnaissance, gun-fire control, convoy and defense of 

ground objects, smoke screen, tree transport, life-saving, short-range light bombing and 

attack.” 

Even in the May 4, 1942, specification for the YR-4A/YR-4B [139], the October 20, 1942, 

specification for the Sikorsky XR-6 [140], and still in the March 1945 specifications for the 

Sikorsky R-4A/-4B [141] (the very much improved production version of the preproduction 

YR-4A/-4B, which grew from the XR-4) there is still a note of skepticism. Paragraph B-4.0 

reads: 

 “B-4.0. The tactical mission of this [helicopter] aircraft shall be short range liaison, 

observation, performance of courier mission, adjustment of artillery fire and general 

cooperation with the ground forces, and for general investigation of utilities of this type of 

completely new and novel aircraft.” 

When the specification for the Sikorsky XR-5 [142] was submitted (dated June 1, 1942) and 

followed with the production for the R-5A [143] dated February 1, 1944, things were 

sounding more positive because the word “completely” had been dropped. Paragraph B-4.0 

reads: 

 “B-4.0. The tactical mission of this aircraft shall be observation liaison, general 

cooperation with the various Ground Arms assisting the Artillery by locating suitable 

objectives and adjusting fire and for general investigation of the utility of this type of new 

and novel type of aircraft.” 

 The B-4.0 paragraph included with the January 17, 1944, specification for the 

Platt–Le Page YR-1A [144] was much more encouraging. It reads as follows: 

 “B-4.0. The tactical mission of this helicopter includes reconnaissance missions for 

surface forces for the purpose of observing and reporting on the disposition and activities of 

hostile ground, air and naval forces. In addition, it assists the artillery by locating suitable 

objectives and adjusting fire, and is a liaison agency for the use of ground commanders. It is 

also capable of operating off the decks of freighters, etc., to serve in convoy duty as an aerial 

spotter of enemy submarines and raiders.” 

At least in this specification the word “aircraft” had been replaced with “helicopter” and 

words like “completely new and novel” had been deleted. You get the feeling that perhaps the 

new U.S. Army Air Forces felt that a helicopter rather that an autogyro was the “machine” to 

fill their requirement. 
2.2 WEIGHT 

96 

 This specific example you are reading about does not stop here, of course. Sikorsky 

quickly followed the R-4 series with a much improved derivative, the R-6. These rotorcraft, 

along with the R-5,33 comprised the Army Air Corps helicopter fleet until the late 1940s. 

During the next decade, which included the Korean War, the Army replaced its firstgeneration Sikorsky helicopters with militarized Bell Model 47s (the H-13 series) and Hiller 

Model 360s (the H-23 series). The 1960s produced the Vietnam War, and the Army moved to 

gas-turbine-powered helicopters (see footnote 24, page 78). You will recall that the Army 

conducted a “fly off ” competition between the Bell OH-4A, Hiller OH-5A, and Hughes 

OH-6A. The Hughes OH-6A and, later, the Bell OH-58A were chosen for this modernization 

step. In the late 1970s, after a modest upgrade that produced the OH-58C, the Army initiated a 

further helicopter improvement program leading to the Bell OH-58D, which entered 

operational service in the mid-1980s. 

 These five generations of early rotorcraft performed basically the same primary 

tactical mission for the Army that was defined in the midst of World War II.34 This role was, 

and continues to be, a scouting mission that calls for aerial observation. As the helicopter 

proved itself and the turbine engine improved the product, mini guns were added for some 

missions. Aeroscouts could then locate and suppress enemy forces. The added feature of the 

1960’s OH-6As and OH-58As was a passenger compartment that could hold two to four 

soldiers. The 1980’s OH-58D introduced a very sophisticated mission equipment package 

(MEP) to replace the voice radio, maps, and binoculars that earlier scout crews used [145, 

146]. 

 These five generations of rotorcraft are quite comparable and serve as a specific 

measure of progress over nearly 50 years, at least within this narrow size and aeroscouting 

category. The five decades of progress is summarized in Table 2-3. The primary scouting 

mission outlined in Table 2-3 is for aerial reconnaissance with an endurance on the order of 

2.5 to 3 hours. 

 The historical data provided in Table 2-3 is not quite as informative as you might 

think, however. For one thing, it is not clear what the trend in useful load as a percent of 

primary-mission takeoff gross weight means. This trend, shown in Fig. 2-26, does suggest that 

in the early helicopter years the ratio was “improving,” but then, in the modernization, the 

industry produced a less efficient product! 

 

33 Almost in parallel with the R-4 and R-6 light helicopters, Sikorsky developed the larger R-5 that grew into his 

first commercial product, the S-51. 

34 During World War II, about 5,700 L-4 Piper Cub airplanes were bought for the scouting mission. The L-4 

scout crew consisted of a pilot and observer, and their MEP consisted of voice radio, maps, and binoculars. The 

use of airplanes was a marked success. Counting the L-4s, L-5s, L-16s, and L-19s, the Army used a total of 

about 10,800 light airplanes before turning to the helicopter. About 100 early models of the H-13 were on hand 

when the Korean War began, and nearly 1,000 were produced during the war years (1950–1953). Another 600 

H-13s were produced for operational use through 1965. Additional requirements for 400 TH-13 trainers 

continued production through 1970. Nearly 400 Hiller H-23s were produced during the Korean War with another 

400 bought in the period from 1954 through 1958. During the nearly 7 years between September 1966 and July 

1973 the Army received a total of 3,600 Light Observation Helicopters. About 1,400 were OH-6As and 2,200 

were OH-58As. The seeds of true aeroscouting were sown by these early helicopters even though the crews had 

minimal mission equipment. The OH-58D updated the MEP. 
2.2 WEIGHT 

97 

 One fact suggested by both Table 2-3 and Fig. 2-26 is that, for its engine power, the 

Hughes OH-6A was one of the most (if not the most) structurally efficient rotorcraft ever 

produced in quantity. 

 This specific example should now have you alert to the possibility that the ratio of 

useful load to takeoff gross weight is not necessarily a measure of “goodness” or industry 

success. In many cases, such as special purpose helicopters used by the military, the ratio is 

quite misleading. 

 The real insight into the world of rotorcraft weights comes from a careful and 

thorough review of empty weight.35 The majority of the industry’s progress can best be seen 

by comparing the detailed group weight-empty statements available in MIL-STD-1374A 

format. In Part I, this MIL-STD provides a summary of the weight empty in several groups. 

This portion of the MIL-STD is rarely more than three pages long. A detailed accounting 

supporting the Part I summary is provided in a longer Part II. 

 Weight empty by groups can be broken down into three subheadings as shown in 

Fig. 2-27. Again, I have taken some liberty in rearranging the format of MIL-STD-1374A, 

Part I. In this case I have chosen the three subheadings so that weight empty is partitioned into 

approximately three equal groups by weight. The first subheading of Structural Groups 

gathers up 7 MIL-STD subgroups. The second subheading contains just the single Propulsion 

Group with its 11 subsystems and/or installations. The third subheading accounts for the 

remaining 12 other groups listed by MIL-STD-1374A, Part I. In practice, even the summary 

weight-empty statement required by the MIL-STD is going to be several pages long. This is 

Table 2-3. Evolution of U.S. Army Scout Rotorcraft 

Model YG-1B YO-60 R-4B R-6 OH-13S OH-23G OH-6A OH-58C OH-58D

Crew (no. 2) 400 400 400 400 400 400 400 400 470 

Passengers 0 0 0 0 0 0 0 0 0 

Fuel 188 216 86 127 257 284 402 466 654 

Oil 25 34 31 53 32 29 7 16 18 

Cargo 0 0 0 0 220 0 139 178 0 

Weapons Install. 0 0 0 0 0 0 0 0 114 

Other Equip. 0 0 0 8 0 0 0 0 4 

Useful Load 613 650 517 588 909 713 948 1060 1260 

Weight Empty 1619 2180 2020 2034 1941 1914 1212 1885 3093 

Gross Weight 2232 2830 2537 2622 2850 2627 2160 2945 4353 

 

35 Most authors, when discussing rotorcraft weight information and data, are very careful to point out that they 

have misgivings about the numbers they are quoting. The reasons for the misgivings are really too numerous to 

list. I have the most faith in data from helicopters that I was directly involved with. After that, I consider 

contractual data provided in U.S. Military documents as most authoritative. This restriction means that less than 

100 helicopters, out of over 500 rotorcraft that can be identified, are well documented. And after that, weight 

data does become quite “iffy” in my mind; I then share the misgivings of all authors who have the courage to 

tackle the subject in some depth. 
2.2 WEIGHT 

98 

0

5

10

15

20

25

30

35

40

45

YG1BYO60R-4B R-6 OH13SOH23GOH6AOH58COH58D

Ratio 

Useful 

Load 

to 

Gross 

Weight

(%)

1937 1942 1942 1943 1948 1950 1966 1968 1986

Fig. 2-26. The ratio of useful load to takeoff gross weight is not necessarily a measure 

of “goodness.” 

Fig. 2-27. The summary weight-empty statement in U.S. MIL-STD-1374A, Part I 

format, starts with 30 line items. 

Weight Empty 

Structural Groups Propulsion Group All Other Groups 

· Wing 

· Rotor 

· Tail 

· Body 

· Alighting Gear 

· Engine Section 

· Air Induction 

· Engine Installation 

· Accessory Gearboxes 

· Exhaust Systems 

· Engine Cooling 

· Water Injection 

· Engine Control 

· Starting System 

· Propeller Installation 

· Lubricating System 

· Fuel System 

· Drive System 

· Flight Controls 

· Aux. Power Plant 

· Instruments 

· Hydraulic & Pneumatic 

· Electrical 

· Avionics 

· Armament 

· Furnishings & Equipment 

· Air Conditioning 

· Anti-icing 

· Photographic 

· Load & Handling 
2.2 WEIGHT 

99 

because most of the 30 major line items shown in Fig. 2-27 have from two to five subitems—

and that is just for the Part I summary. A complete report satisfying MIL-STD-1374A 

requirements for a modern military rotorcraft will included the detailed weight statement in 

Part II. The Part II section of MIL-STD-1374A can be several hundred pages long. 

 This specific example of U.S. Army aeroscout evolution from the autogyro to the most 

modern scout helicopter can now be continued in more depth using data from the Military 

Standards. Consider a first step that takes you to the subheading level of Fig. 2-27. A 

summary of this historical data is shown in Table 2-4. Additional dimensional data is provided 

in Table 2-5. 

 As you review these two data tables, you may first notice that the OH-6A has the 

lowest Structural Groups and Propulsion Group weights. The OH-6A is also the smallest of 

the nine rotorcraft under study. Secondly, you should note that the OH-58D doubled the 

engine rated horsepower, and its weight for the All Other Groups is many times that of any of 

the other rotorcraft. 

 Now let me use the data from these tables to illustrate several modern results that the 

rotorcraft industry has achieved. The first and clearest point is the effect that the arrival of the 

turbine engine had on Propulsion Group weight. As shown in Fig. 2-28, the reduction in 

Propulsion Group weight from about 2.8 to nearly 1.1 pounds per horsepower is dramatic. 

This was probably a bigger step forward for the rotary wing industry than for the fixed-wing 

industry. 

 An equally interesting fact is that the piston-powered autogyros and helicopters 

needed about the same Propulsion Group weight. The reason for this is that autogyros used a 

heavy, metal propeller but had no main-rotor drive system to speak of. For example, the 

YG-1B propeller installation weighed about 80 pounds, and the YO-60 propeller installation 

was just over 110 pounds. These propeller installation weights are quite comparable to the 

early helicopter’s main rotor transmission weight for the same engine power rating. 

Table 2-4. Evolution of U.S. Army Scout Rotorcraft 

Model 

Structural 

Groups 

Propulsion 

Group 

All Other 

Groups 

Weight 

Empty 

Useful 

Load 

Gross 

Weight 

YG-1B 756 654 209 1619 613 2232 

YO-60 944 905 331 2180 650 2830 

R-4B 900 970 200 2019 517 2537 

R-6 966 769 299 2034 588 2622 

OH-13S 630 795 515 1940 910 2850 

OH-23G 769 765 380 1914 713 2627 

OH-6A 529 327 357 1212 948 2160 

OH-58C 725 382 431 1885 1060 2945 

OH-58D 1020 714 1359 3093 1260 4353 
2.2 WEIGHT 

100 

 A final point is illustrated in Fig. 2-29. Historical data shows that the rotorcraft 

industry has successfully reduced the weight of drive-system components accounted for in the 

Propulsion Group. Thus, the use of the gas turbine engine plus the reduction in drive-system 

weight accomplished over five decades was a major step in arriving at the modern helicopter. 

Table 2-5. U.S. Army Scout Rotorcraft Dimensions 

Model Engine 

Type Engine Model Rated Power (hp) 

Rotor Dia

(ft) 

Fuselage 

Length (ft) 

Gross 

Weight (lb) 

YG-1B Piston Jacobs R-755-A3 245 40.00 26.00 2,232 

YO-60 Piston Jacobs R-915-A1 325 42.00 21.42 2,830 

R-4B Piston Warner R-550-3 200 38.00 35.50 2,537 

R-6 Piston Franklin O-405-9 235 38.00 34.60 2,622 

OH-13S Piston Lycoming VO-435 260 37.17 32.67 2,850 

OH-23G Piston Lycoming VO-540 305 35.42 27.67 2,627 

OH-6A Turbine Allison T63-A-5A 317 26.33 22.79 2,160 

OH-58C Turbine Allison 250-C20 400 33.33 29.60 2,945 

OH-58D Turbine Allison T703-AD 650 35.00 30.20 4,353 

0

100

200

300

400

500

600

700

800

900

1,000

0 100 200 300 400 500 600 700

Propulsion 

Group 

(lbs)

Maximum Engine Rated Horsepower

R-4B

OH-13S

R-6 OH-23G

YG-1B

YO-60

OH-58D

OH-58C

OH-6A

Piston

Turbine

Fig. 2-28. Turbine engines helped cut Propulsion Group weight by nearly 60 percent. 
2.2 WEIGHT 

101 

0

0.2

0.4

0.6

0.8

1

1.2

1.4

R-4B R-6 OH-13S OH-23G OH-6A OH-58C OH-58D

Drive 

System 

Weight 

per 

Engine 

Horsepower 

(lbs/hp)

1942 1943 1948 1950 1966 1968 1986

Fig. 2-29. The reduction in helicopter drive-system weight over 50-plus years has 

been impressive. 

 One industry accomplishment not captured by the drive-system weight data in 

Fig. 2-29 is the improvement in reliability and reduction in maintenance costs of this major 

system. The first step was made by Sikorsky in going from the R-4 series to the R-6 series. 

You can appreciate this dramatic first improvement when you read the last 60 pages of 

Pioneering the Helicopter [19] by Charles Morris. Morris first recounts the XR-4 flight from 

Bridgeport, Connecticut, to Dayton, Ohio, and delivery of the first, truly successful, single 

rotor helicopter to the U.S. Army Air Corps on May 17, 1942. The 16-hour-and-10-minute 

flight, spread over 5 days, was performed with a continuous eye on the main transmission oil 

temperature gauge. The transmission, it seems, was continually on the verge of overheating. 

The demonstrations, given the day after arriving, were done with the Sikorsky team 

(particularly Ralph Alex) having “fingers crossed.” Three days later, a major overhaul of the 

XR-4 was completed; it showed that the main transmission had been slowly “chewing itself to 

pieces.” It was replaced, and Morris went on—with 100 more flight hours—to train five Air 

Force officers. The XR-4 successfully completed its Wright Field testing on January 5, 1943. 

 Drive system and other improvements came with the R-6. Morris notes [19] that the 

R-6 was “conceived as a cleaned-up version of the R-4 type, with a 250-horsepower Franklin 

engine supplying a good margin of power. As it took shape, however, the effort to save weight 

and to smooth out the box-like contours of her predecessor resulted in a brand new machine.” 

Morris took the XR-6 for its first flight on October 15, 1943. He credits several months of 

development work for the unofficial record, long-distance flight that Colonel Frank Gregory 
2.2 WEIGHT 

102 

and Ralph Alex made on March 2, 1944.36 On that day, Gregory and Alex [the “aeroscout 

crew”] flew nonstop from Washington, D. C., to Dayton, Ohio, (387 miles) in 4 hours and 

55 minutes. Transmission overheating was not reported; the 260-pound, XR-4 drive system 

that handled an inadequate 185-horsepower engine was advanced to the lighter, R-6, 200-

pound drive system that could absorb 250 horsepower. 

 The rotorcraft industry did not, and has not, stopped its drive-system development 

work. You only need to read about the OH-6A world record program [147] to appreciate a real 

success story. Using one preproduction YOH-6A helicopter, a Hughes Tool Company/Army 

team captured 23 world helicopter records between March 12 and April 7 of 1966. I believe 

the nonstop, long-distance record was a real milestone. Robert Ferry started with a normal 

hover liftoff on April 6 at 2:20 p.m. (PST) from Culver City, California. He landed, 

2,277 statute miles away, on the sand at Ormond Beach, Florida, on April 7 at 8:28 a.m. 

(EST). The record was set at 2,213 miles in 15 hours and 8 minutes for an average speed of 

150 miles per hour. At that time, the YOH-6A was FAA certified (for the U.S. Army Light 

Helicopter competition) at a takeoff weight of 2,100 pounds. On the record-breaking flight, 

Ferry lifted off at 3,235 pounds, which was more than three times the basic weight empty of 

the helicopter. About 1,860 pounds of JP-5 fuel, contained mostly in auxiliary fuel tanks 

placed in the passenger compartment, were onboard. Ferry used all but 10 pounds of this fuel. 

Thus, the average fuel consumption was on the order of 1-1/4 statute miles per pound of fuel 

or about 8.5 statute miles per gallon. And the transmission did not overheat. 

 Today the rotorcraft industry expects propulsion and drive-system components to run 

2,000 trouble-free hours between overhauls. The time between overhaul (TBO) on most 

components of the Allison 250-series gas turbines is at least 1,500 hours. The more expensive 

parts are already at or above 3,500 hours between overhaul. The rest of the Propulsion Group 

systems have TBOs well above 2,000 hours, and improvements are still being made. As you 

will see later in this introduction to weights, the industry has already demonstrated it can 

produce excellent propulsion systems with multi-engines totaling at least 25,000 horsepower. 

 Now let me proceed to the Structural Groups subheading in Fig. 2-27. The innovation 

in engineering design approaches, the advancements in materials, and the improvements in 

safety as well as many other factors come to the forefront here. However, they are so 

intertwined that it is more difficult to fully appreciated the progress of the rotorcraft industry 

in this area. But, for a starting point, consider Fig. 2-30. I have used primary mission takeoff 

gross weight as the abscissa on this figure. This is a direct, but rather crude, first 

approximation to a much more complex set of parameters. 

 

36 Colonel Gregory, in his book Anything A Horse Can Do [16], relates a number of improvements achieved 

with the R-6 including an early use of composites and successful sound proofing. He also discusses a rather 

typical array of development problems that were overcome. 
2.2 WEIGHT 

103 

0

200

400

600

800

1,000

1,200

1,400

0 1,000 2,000 3,000 4,000 5,000

Primary Mission Takeoff Gross Weight (lbs)

Structural 

Groups 

Weight 

(lbs)

YG-1B

R-6 OH-58D

R-4B

OH-23G

OH-13S

YO-60

OH-58C

OH-6A

0.25 of TOGW

Fig. 2-30. The Structural Groups amount to about 25 percent of primary mission 

takeoff gross weight. 

 On the surface it would appear from Fig. 2-30 that little, if any, progress has been 

made by the rotorcraft industry over the past six decades. This, of course, is not the case. The 

industry has slowly but surely redistributed the structural weight between the six groups listed 

in Fig. 2-27. (I say six for this specific case because no wing group is involved with the scout 

rotorcraft under study here.) The magnitude of this redistribution is summarized in Fig. 2-31. 

 The improvements made to the body group have increased the crash worthiness of the 

basic structure, allowed for higher landing speeds without damage, increased visibility, 

provided more internal volume, and made getting in and out easier with additional, larger 

doors. These improvements were paid for by a somewhat reduced autorotational capability 

that came with less rotor inertia. The alighting gear weight reduction came by changing to a 

skid tube rather than the wheeled landing gear that autogyros and the first Sikorsky 

helicopters used. 

 Now let me discuss the All Other Groups weight-empty category that is shown in 

Fig. 2-27. It is here that lightweight, aeroscout helicopters have seen the most increase in 

usable features. In five decades, the percentage of weight empty devoted to All Other Groups 

has nearly tripled as Fig. 2-32 clearly shows. 
2.2 WEIGHT 

104 

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

YG-1B

YO-60

R-4B

R-6

OH-13S

OH-23G

OH-6A

OH-58C

OH-58D

Rotor Body Gear Tail+Eng. Sect.+Air

Structural Groups Distribution (fraction)

Fig. 2-31. Over six decades, the industry has shifted weight from the rotor and alighting 

gear groups to improve the body group. 

 The major elements of the All Other Groups for aeroscout rotorcraft are summarized 

in Fig. 2-33. The initial growth element was the addition of an hydraulic system that gave the 

scout crew “power steering.” This, in turn, allowed installation of an autopilot. The number 

and quality of flight instruments also grew over the decades. Some improvement in the 

furnishing and interior equipment, along with heating and cooling systems, was also 

forthcoming. (I would say that comfortable seats have yet to be installed though!) The major 

step forward in added features came from evolutions in the electronic world. These electronic 

items fall in the subheading of avionics as Fig. 2-27 shows. 

 The increase of avionics on the OH-58D was dramatic as references [145, 146] point 

out in considerable detail. These avionics gave the modern scout crew the most up-to-date 

“eyeballs” to replace their binoculars, an electronic navigation system to replace their paper 

maps, and the most all-encompassing communication system possible at the time. Finally, the 

OH-58D was equipped with a real, offensive, air-to-ground missile weapons system.37 

 

37 I was honored to receive the AHS 1986 Grover E. Bell Award for my “direction and leadership in the design 

and fielding of the United States Army Helicopter Improvement Program (OH-58D).” But, with no false 

modesty, I felt that it was one of the most splendid total team efforts the industry had seen for quite a while. It 

was for that team effort that I felt the award was appropriate, and I tried to say so in my acceptance remarks. I 

wrote the paper [145] to recognize the effort and spirit that went into the OH-58D program. My personal “high” 

came when I got to fly the OH-58D for an hour. A person is lucky to be a part of such an adventure even once in 

a lifetime. 
2.2 WEIGHT 

105 

 Fig. 2-33 shows that the historically “normal trend” would have about doubled the All 

Other Groups’ weight by the time the OH-58D came along. Instead, the rotorcraft industry 

was able to incorporate electronic and computer technology as fast, and sometimes faster, 

than the fixed-wing industry. 

 By the 1980s, the light aeroscout helicopter was thought of more as a “mission 

platform.” This thinking carried forward to the Army’s development of its most modern, 

armed, aeroscout helicopter in the 1990s—the RAH-66 Comanche. Again, every 

improvement in avionics, flight control technology, and attack armament (including stealth 

shaping) was sought. You would be quite mislead about the capabilities of the RAH-66 if you 

looked at it from only a historical weight trend view. 

 I have used the preceding material about aeroscout rotorcraft as a specific example to 

introduce you to the world of weights. However, in many ways the military light helicopter—

and its larger, military, attack helicopter companion—do not represent the more commonly 

available utility and transport helicopters the industry offers. It is true that few modern 

helicopters have been developed solely to fulfill commercial marketplace needs. In fact, most 

commercial helicopters today are product derivatives using components developed for the 

military. With this thought in mind then, let me now broaden your view of modern helicopters 

to include a much wider range in takeoff gross weight and installed engine horsepower. 

 You have already seen from Fig. 2-24 that the overwhelming majority of modern 

helicopters fall well below a 50,000-pound takeoff gross weight. Fig. 2-25 showed you that, 

on average, the industry can obtain at least 40 percent useful load from takeoff gross weight. 

So now consider the distribution of weight empty between the three subheadings I selected in 

Fig. 2-27. As I mentioned in footnote 35, page 97, I prefer to illustrate modern weight results 

using data primarily from U.S. MIL-STD-1374A reports. This limits the number of post-1940 

helicopters that can be studied. However, as Table 2-6 shows, the distribution of types is 

representative of the industry’s products. 

Table 2-6. A Sample of 92 Post-1940 Helicopters 

Commercial and/or 

Military Use 

Military Use 

Primarily 

Weight Passengers/Cargo Scout Attack 

Very Light 4 Pistons None None 

Light 10 Pistons 

11 Turbines 

8 Pistons 

7 Turbines None 

Medium 5 Pistons 

26 Turbines None 7 Turbines 

Heavy 2 Pistons 

11 Turbines None None 

Very Heavy 3 Turbine None None 
2.2 WEIGHT 

106 

0

200

400

600

800

1,000

1,200

1,400

1,600

0 500 1,000 1,500 2,000 2,500 3,000 3,500

OH-58D

R-6 R-4B

YG-1B

OH-6A YO-60

OH-58C

OH-13S

OH-23G

1980s

0.45 of WE

1940s

0.15 of WE

1960s

0.30 of WE

All Other 

Groups 

Weight 

(lbs)

Weight Empty (lbs)

Fig. 2-32. The industry has increased the weight of All Other Groups to add aeroscout 

helicopter features. 

0 200 400 600 800 1,000 1,200 1,400

YG-1B

YO-60

R-4B

R-6

OH-13S

OH-23G

OH-6A

OH-58C

OH-58D

Flight Controls, Hydraulic System

And Instruments

Furnishing & Equipment, Air

Conditioning, Anti-ice, Etc.

Electrical & Avionics

Armament

Weight of All Other Groups (lbs)

Fig. 2-33. The industry dramatically increased electrical and avionics features in the 

1980’s aeroscout helicopter. 
2.2 WEIGHT 

107 

 Taken as a group, the 92 post-1940 (i.e., modern) helicopters show you that the 

rotorcraft industry has made considerable progress in maturing its current rotary wing 

products. The progress is most dramatic in the Propulsion Group as you learned from the 

specific aeroscout helicopters example. Fig. 2-34 emphasizes this view with a larger, more 

representative group of helicopters and uses a log-log axis system. 

 The reduction in Propulsion Group weight over five decades can be overstated 

somewhat (as I have in Fig. 2-34) by going from “top of scatter” of piston-powered, early 

helicopters to “bottom of scatter” for turbine-powered helicopters. The industry, on this 

overstated basis, has achieved a weight reduction on the order of 1.8/6.5 or nearly 75 percent. 

That is, Propulsion Group weight is approximated as 

(2.26) ( ) ( ) 0.9 0.9 Pistons at 6.5 HP Turbines at 1.8 HP . 

 Industry progress in reducing the Structural Groups portion of empty weight is 

appreciable when the broader range of helicopters from Table 2-6 is considered. This is 

confirmed in Fig. 2-35. Not only has the industry redistributed the several group weights 

within the Structural Groups, it has also succeeded in reducing weight. This weight reduction 

of about 30 percent has been accomplished with very innovative design and the application of 

advanced materials, and has not come at the expense of foregoing key features. Just the 

opposite trend has occurred. The industry has created a more crashworthy and reliable 

structure with modern interiors and improved accessibility. 

(2.27) Pistons at 0.36 TOGW Turbines at 0.24 TOGW . ( )  ( )

100

1,000

10,000

100,000

10 100 1,000 10,000 100,000

Piston

6.5 (HP)0.9

Turbine

1.8 (HP)0.9

VS-300

Propulsion 

Group 

(lbs)

Maximum Engine(s) Rated Horsepower

Fig. 2-34. The gas turbine engine allowed the industry to reduce Propulsion Group 

weight dramatically. 
2.2 WEIGHT 

108 

100

1,000

10,000

100,000

100 1,000 10,000 100,000 1,000,000

0.24 (TOGW)

0.36 (TOGW)

VS-300

Structural 

Groups 

(lbs)

Normal Takeoff Gross Weight (lbs)

Fig. 2-35. Innovative designs with advanced materials have reduced the weight of 

the Structural Group.

 The weight reductions achieved in the Structural Groups and the Propulsion Group 

have permitted the rotorcraft industry to increase the weight allocated to All Other Groups. 

The hydraulic-powered flight control system, which allowed an autopilot, was just the first of 

many added features to enhance the helicopter. Improvements in electronics have led to more 

automated flight instruments. Auxiliary power plants have been added to the larger 

helicopters, anti-icing is more frequently incorporated, and air conditioning is a quite 

commonly offered accessory. Fig. 2-36 shows that the industry has more than doubled the 

weight allocated to All Other Groups. 

(2.28) Pistons at 0.13 WE Turbines at 0.30 WE . ( )  ( )

 As you can now appreciate, the rotorcraft industry has made considerable progress in 

the important area of helicopter weights since (1) Focke astounded the world with his F. 61 

side-by-side and produced his Fa 223, (2) Flettner produced his Fl 282 synchropter, and (3) 

Sikorsky developed his VS-300 single rotor and delivered his R-4 series to the U.S. Army Air 

Corps. You have seen that the weights38 of the Propulsion Group and Structural Groups have 

 

38 You will have noted in Fig. 2-34, Fig. 2-35, and Fig. 2-36 that I included data for the Sikorsky VS-300. The 

industry is (and most certainly I am) indebted to Harold Ulisnik for recapturing information about such a 

historically significant rotorcraft. Harold sent me a letter [148] that contained the VS-300 weight breakdown in 

MIL-STD-1374A. He obtained the actual weight data when he refurbished the VS-300 for its place in the 

Smithsonian Institute. This contribution, after retiring from Sikorsky Aircraft, is worth its weight in gold. 
2.2 WEIGHT 

109 

10

100

1,000

10,000

100,000

100 1,000 10,000 100,000

Turbine

0.30 (WE)

Piston

0.13 (WE)

VS-300

All Other 

Groups 

(lbs)

Weight Empty (lbs)

Fig. 2-36. The industry has more than doubled the weight allocated to All 

Other Groups. 

been reduced to provide additional weight for more and better features in the All Other 

Groups. And along the way you have: 

1. Seen a framework for the discussion as shown in Fig. 2-23, 

2. Added weight terminology to your vocabulary, 

3. Reviewed two general trends that have appeared over five decades; namely that 

 (a) There is no inherent limitation to helicopter size and 

 (b) The industry can obtain 40 percent useful load from takeoff gross weight, 

4. Reviewed detailed results for the military aeroscout helicopters, and then 

5. Seen this understanding applied to a broad range of products that the industry has 

created. 
2.2 WEIGHT 

110 

2.2.1 A Helicopter Sizing Method 

 Let me now introduce you to a very abbreviated, helicopter sizing method by way of 

an example. The method itself is patterned after two very comprehensive and detailed 

methods that are widely used in the rotorcraft industry today. The sizing method you will see 

here is simply a very scaled down version of references [149-151] and is typical of an 

engineering problem. First, a group of known and, if necessary, assumed facts are given as 

input. Second, a sequence of equations that will lead to the problem’s solution are constructed. 

Then third, the calculations with real numbers are completed giving an answer. 

 To begin the sizing method, suppose you tell me the design requirements are as 

follows: 

You want a helicopter that transports eight passengers and their baggage, in 

safety and comfort, on a 2-hour flight at top cruise speed. Civil regulations 

require a pilot and a copilot. 

The conceptual design method I will use to “rough out” a helicopter that meets your 

requirement is guided by Table 2-7 on page 111. The process starts by translating your design 

requirements into the Useful Load items outlined in Table 2-2. (In your design problem, only 

a few of the Useful Load items have been defined, so I have made assumptions about what 

you did not tell me.) 

 Frequently, a few items of Useful Load are “holy” (i.e., are held constant or fixed) 

during the conceptual sizing process. This is the case for your design problem. I have assumed 

that each crew member and passenger weighs 200 pounds. Ten bags at 20 pounds apiece 

seems reasonable. These fixed items are listed as the first set of inputs to the design problem 

and are shown at the top of Table 2-7. 

 For the moment, the unknown portion of Useful Load will be how much fuel and oil 

will be used during the 2-hour flight. Prudence says that some fuel reserve for flight beyond 

2 hours should be included in the design. Therefore, I have added a half hour of fuel reserve 

to your design requirement. What this total, possible flight time of 2.5 hours means in pounds 

of fuel is yet to be determined, but it will be accounted for shortly. 

 At this point in the conceptual design process the oil is a very minor weight, and I will 

assume that 20 pounds of oil will be enough. No additional cargo is carried. Because this is a 

civil helicopter, there are no guns, weapons, or other equipment. 

 The Useful Load is, therefore, set at 2,220 pounds plus fuel weight when it is 

determined. 

 Now consider the second item of input to the design method outlined in Table 2-7 

under Design Parameters. Because you stated no preference for your helicopter’s 

configuration, I will select a single main rotor with a tail rotor. (We could just as easily be 
2.2 WEIGHT 

111 

Table 2-7. A Simple Conceptual Design Example 

DESIGN INPUT DATA

 Useful Load

 Crew 400 lb 

 Passengers 1600 

 Fuel 2.5 hrs (lb TBD) 

 Oil 20 

 Baggage 200 

 Cargo 0 

 Guns/Weapons 0 

 Other Equipment 0 

Total Useful Load 2,220 lb + fuel

 Design Parameters

 Configuration Single Rotor 

 Disc Loading 8 lb/sq ft 

 Engine Twin Turbines 

 Engine SFC 0.40 lb/hr per hp 

 Lift-Drag Ratio 3.19 at Vcruise 

 Weight Factors

 Propulsion Group 1.80 

 Structural Groups 0.24 

 All Other Groups 0.30 

 Installed Power 2.70 

CALCULATION STEPS RESULTS NOTES 

 Iteration Number 1,2,3 ... final Converges Quickly 

 1. Start Gross Weight 10,341 lb Started with 9,000 lb 

 2. Rated Horsepower 2,082 hp = Eq. 1-131 

 3. Fuel for 2.5 Hours 2,082 lb = SFC × ESHP × Flt Time 

 4. Propulsion Group 1,745 lb = Eq. 1-129 

 5. Structural Groups 2,482 lb = Eq. 1-129 

 6. All Other Groups 1,812 lb = Eq. 1-130 

 7. Weight Empty 6,039 lb = Steps 4 + 5 + 6 

 8. Useful Load 4,302 lb = 2,220 + Step 3 

 9. End Gross Weight 10,341 lb = Steps 7 + 8 

10. Iteration Difference 0 lb = Step 9 minus Step 1

11. Rotor Diameter 40.57 ft = 4 GW DL π

12. Continuous Cruise Speed 178 kts From Eq. 1-132 

discussing a tandem, coaxial, or synchropter configuration for this illustration.) You also did 

not specify a disc loading, so I will choose a representative value for you.39 The disc loading 

of modern helicopters ranges from 6 to 12 pounds per square foot of main rotor(s) area. I will 

assume a disc loading of 8 pounds per square foot to start with. (Before closing this design 

illustration, results obtained by assuming disc loading values from 1 to 12 pounds per square 

foot will show you a rather interesting trend that has influenced the industry for five decades.) 

 

39 You will recall that disc loading is the ratio of helicopter gross weight to the area of the rotor or rotors, 

depending on the helicopter configuration. This was discussed in the section titled Early Hovering Performance

on page 5. 
2.2 WEIGHT 

112 

It seems reasonable to select a pair of gas turbine engines to power your helicopter. They will 

be more expensive than piston engines as you will recall. However, I have in mind a new 

engine model that is very fuel efficient. It has a specific fuel consumption (SFC) of only 0.40 

pounds per hour per horsepower as suggested by Fig. 2-13. 

 The third part of input to the design process is the four items listed as weight factors. 

Some rational calculation of the three, major elements of weight empty shown in Fig. 2-27 

must be made. To do this I will assume that the historical trends shown in Fig. 2-34, Fig. 2-35, 

and Fig. 2-36 are an adequate starting point. This means that I intend to assume a very modern 

design and calculate the three elements of weight empty from the three equations of 

(2.29) 

0.9 0.9 Pr opulsion Group Wgt. PG Wgt. Factor HP 1.8HP

Structural Groups Wgt. SGs Wgt. Factor GW 0.24GW

All Other Groups Wgt. AOGs Wgt. Factor WE 0.30WE

≡= × =

≡= ×=

≡ = ×=

.

There is a little algebra required here because I want the weight of All Other Groups directly, 

not in terms of weight empty as given by Eq. (2.29). Therefore, because 

(2.30) WE PG SGs AOGs =+ + ( ) and AOGs Wgt. Factor WE = × , 

solving these two equations in two unknowns gives 

(2.31) Wgt.Factor PG SGs ( ) AOGs

1 Wgt. Factor

+ = − . 

On this basis, I will choose the weight factors for Propulsion Group, Structural Groups, and 

All Other Groups as 1.8, 0.24, and 0.30, respectively, as shown in Table 2-7.40

 There is now only one last item to include in the input. Some estimate of horsepower 

needs to be made so that Propulsion Group weight can be calculated with Eq. (2.29). You will 

recall from Fig. 1-4 that some early inventors did not install enough engine horsepower to 

hover. In the chapters about modern hover and forward-flight performance that follow this 

discussion about modern helicopter weights, you will read that modern designs install 

maximum engine rated horsepower at sea level on a standard day approximately as 

(2.32) ( )

Max. SLS ( ) Installed Power Factor GW GW ESHP 14.7

550 A = . 

The earlier inventors sometimes ended up with an installed power factor of 1.0 in Eq. (2.32). 

Their “machines” could just barely hover, in ground effect, at sea level on a standard day. 

Modern designers have used a factor of 1.7 to as high as 2.7 for helicopters that have high 

altitude hover and fast cruise performance. 

 

40 You should be aware that the industry has, over the decades, developed a detailed set of semiempirical weight 

trend equations that parallel Eq. (2.29). These detailed equations estimate the weight of every line item listed in 

Fig. 2-27. References [152-156] are just a fraction of what has been published. Furthermore, each major 

manufacturer has a Weights Department that closely guards a proprietary set of historical weight trend data. 
2.2 WEIGHT 

113 

 I should mention that if you had stated a cruise speed requirement for your helicopter, 

I would have calculated the installed engine horsepower simply as 

(2.33) ( ) Max. SLS ( )

Hel

Gross Weight ESHP Speed in ft / sec 0.85 550 L D

= ×

× × . 

Without any more information I would have guessed the lift-drag ratio of your helicopter at 

about 3.0 to 4.0, depending on speed. This would be based on the forward-flight portion of the 

performance chapter that follows this discussion of weights. The 0.85 factor in the 

denominator of Eq. (2.33) says that top cruise speed will be set with the engine designed to 

operate continuously at 85 percent of maximum turbine inlet temperature. This is a “wear and 

tear” or time between overhaul issue. 

 The simple form of estimating engine horsepower, Eq. (2.32), is suitable for this 

helicopter sizing illustration. I need only to choose a disc loading (i.e., GW/A) and an 

installed power factor. Table 2-7 shows that a disc loading of 8 and an installed power factor 

of 2.7 seem reasonable. (An alternate approach might be for you to specify what engines to 

use; then rotor diameter would have to be found using Eq. (2.32) and speed determined from 

Eq. (2.33)). Fuel quantity will be estimated as given at calculation step 3 in Table 2-7. 

 With all the input defined, it now becomes a simple matter to “turn the crank” and 

calculate some numbers that show what your helicopter will look like. The actual calculation 

proceeds in 3 or 4 iterations of 11 steps each, as described in the lower portion of Table 2-7. 

The reason for needing some iteration is because the Structural Groups’ weight depends on 

gross weight, but gross weight has yet to be determined.41

 The calculation part of the design method starts by guessing a gross weight at iteration 

1, step 1. My tendency is to guess low and hope for a light design that will be less costly. I 

chose 9,000 pounds, and after three iterations the process converges to a takeoff gross weight 

of just over 10,300 pounds. 

 Based on the design requirements you gave me a few pages back (plus a few 

assumptions on my part), your helicopter will 

a. Be a single rotor configuration, 

b. Have two turbine engines with a maximum rated horsepower of 1,040 hp each, 

c. Need a fuel tank that holds 2,040 pounds or about 315 gals, 

d. Have a 40.6-foot rotor diameter, and 

e. Enjoy a continuous cruise speed of 175-plus knots at 85 percent of maximum 

engine rated horsepower. 

 

41 In doing this simple engineering problem, I “programmed” Table 2-7 on the spreadsheet software called 

Microsoft®

 Excel®. Excel includes a Goal Seek routine under the Tools menu that performs the iteration in short 

order. 
2.2 WEIGHT 

114 

You can expect a quiet, climate controlled, modern interior and a “jet smooth ride” for your 

passengers, the latest flight instruments and autopilot for the crew, and high reliability and 

low maintenance. As to the purchase price, well, that is another subject. 

 There is one classical helicopter design trend that you should be aware of. The trend 

deals with the influence of disc loading on the overall results. In the previous design study 

illustration, a disc loading of 8 pounds per square foot was assumed. What is interesting, as 

Fig. 2-37 shows, is that varying disc loading significantly affects gross weight and the 

required engine horsepower, but only begins to significantly affect the rotor diameter below a 

disc loading of 6.0. What this says is that the smallest helicopter falls in the disc loading range 

around 8. Very low disc loading drives the diameter up, while higher disc loading drives up 

the engine power and Propulsion Group weight. This increases the weight empty and gross 

weight. The increasing gross weight increases the Structural Groups and the weight empty, 

and the cycle continues. 

 The early pioneers had a narrow choice from a comparatively short list of relatively 

low-powered piston engines. As a consequence, their helicopters were low-disc-loading 

“machines.” The modern industry has a wide range of gas turbine engines to use and, 

accepting the cost, could even offer higher-disc-loading products with greater installed 

horsepower. The benefit, however, seems to be only 5- to 15-knots greater cruise speeds. The 

issue of helicopter maximum efficient cruise speed has been with the industry ever since 

Glauert raised the issue, and argued with Cierva about it, in the mid-1920s. 

4,000

6,000

8,000

10,000

12,000

14,000

16,000

18,000

0 2 4 6 8 10 12 14

Total Engine

Horsepower = 2,082 

1453

2,916

4,043

40.6 ft = Diameter

42.1

40.6

41.9

956

46.2 740

50.5

327

76.5

Takeoff 

Gross 

Weight 

(lbs)

Disc Loading (lbs/ft2

)

534

58.1

Fig. 2-37. The industry avoids high-disc-loading helicopters. Example for a constant, 

fixed useful load of 2,220 pounds per Table 2-7. 
2.2 WEIGHT 

115 

 The rotorcraft industry has, over six decades, nearly doubled the level flight speed 

record. Today, that record stands at just over 216 knots. Unfortunately, the record was 

achieved by brute power because the record-setting helicopter had a lift-to-drag ratio of less 

than 2.6. This is not impressive at all from an aerodynamic efficiency point of view, as 

Glauert would be quick to point out. You can see the issue and the problem easily from the 

trend shown in Fig. 2-38 and the parameters of Eq. (2.33). 

 Now let me proceed to a final point—helicopter productivity—in this introduction to 

modern helicopter weights. A frequently used definition of productivity is work per unit of 

time. Work has the English units of pound-feet and time has the unit of seconds. The pound in 

question here is generally taken as payload in the transportation industry. Payload is the part 

of Useful Load that the user perceives as useful. For “your commercial helicopter” this would 

be the eight, paying passengers and I suppose their baggage, which together total 

1,800 pounds. This leaves the feet and seconds to account for; but this is just velocity or, in 

the world of productivity, speed. Thus, 

(2.34) Work Productivity Payload Speed PV Time

≡ = ×= . 

0

20

40

60

80

100

120

140

160

180

200

0 2 4 6 8 10 12 14

Cruise L / D = 3.19

4

4

3.98

3.84

3.49

2.96 2.77

Maximum 

Continous 

Cruise Speed 

(knots)

Disc Loading (lbs/ft2

)

Fig. 2-38. The lift-to-drag ratio of current helicopters drops rapidly at speeds above 

150 knots. Example for a constant, fixed useful load of 2,220 pounds per Table 2-7. 
2.2 WEIGHT 

116 

 So far the rotorcraft industry, unlike the fixed-wing industry, has been unable to 

significantly increase helicopter productivity by increases in speed. The brief discussion about 

disc loading, the current world speed record, and Fig. 2-38 give you a hint of what the 

industry has apparently come to accept as a serious limitation inherent in the helicopter. But if 

increasing helicopter productivity by doubling or tripling cruise speed is not practical, there 

appears to be no such limitation to increasing productivity by raising payload. Raising the 

payload of “your commercial helicopter” by a factor of 10 or 20 to provide 100- or even 200-

passenger helicopters is well within the industry’s capability. Of course the question just 

behind this open door is one of user cost, and this means that the more appropriate measure 

would be productivity per unit of money. In United States units that means 

(2.35) Payload Speed PV Productivity Per Dollar User Dollars $

× = = . 

 The subject of helicopter cost and price is addressed later. However, there is one 

bridge to costs that you may see used in published studies of helicopter productivity. The 

bridge is to imagine that (1) helicopter manufacturing costs, (2) the purchase price, (3) the 

user or operator’s costs, and (4) the end-benefactor cost (say a passenger’s ticket price) ALL

are proportional to the helicopter’s weight empty.42 This presumption leads to 

(2.36) Payload Speed PV Productivity Per Dollar Weight Empty WE

× ∝ = . 

 If this proportionality as stated by Eq. (2.36) was followed, then Fig. 2-37 suggests 

that disc loadings approaching 1.0 would have the lowest weight empty. One would blindly 

ignore the fact that the rotor diameter had become quite large. Using the design method in 

Table 2-7, even with all its simplicity, gives you the trend of the parameter PV/WE with disc 

loading shown in Fig. 2-39. On this basis, “your optimum helicopter” should be designed with 

a disc loading of 3, a rotor diameter of 50.5 feet, and a cruise speed of around 136 knots. I 

believe you would say this conceptual design was too slow and too big to be called a modern, 

low-drag, twin-turbine helicopter. 

 The other end of the conceptual design spectrum emphasizes low aerodynamic drag, 

high speed, and the installation of higher-powered engines to get that speed. The disc loading 

becomes higher, the helicopter stays small, but the parameter PV/WE is significantly reduced. 

This trend, shown in Fig. 2-40, uses the previous data but graphed with cruise speed as the 

abscissa. Again, the low productivity per dollar, measured by PV/WE, at high disc loading 

comes about because the industry has not succeeded in raising the helicopter lift-to-drag ratio 

much above 4.0. At the high speeds potentially possible with disc loadings approaching 12, 

the lift-drag ratio is falling from 4.0 to something on the order of 2.5. This aerodynamic 

performance problem has deprived the rotorcraft industry of a development path enjoyed by 

the fixed-wing industry. 

 

42 To say that I am not in favor of these assumptions would be an understatement! On more than one occasion I 

have seen the focus placed solely on reducing weight empty regardless of the manufacturing or material costs; 

ignoring the issue of rotorcraft costs is not something I recommend. 
2.2 WEIGHT 

117 

30

40

50

60

70

80

90

0 2 4 6 810 12 14

Cruise Speed

178 kts

79

111

136

151

168

184

189

76.5

58.1 50.5

46.2

42.1

40.6

41.9

40.6 ft

Diameter

PV/WE 

(knots)

Disc Loading (lbs/ft2

)

Fig. 2-39. The industry avoids low-disc-loading helicopters because they are too big and 

too slow. Example for a constant, fixed useful load of 2,220 pounds per Table 2-7. 

30

40

50

60

70

80

90

60 80 100 120 140 160 180 200

1

2

3

4

6

10

12

 Disc Loading

8 lbs/ft Cruise L/D 2

3.19

4

4

3.98

3.84

3.49

2.96

2.77

PV/WE 

(knots)

Cruise Speed (knots)

Fig. 2-40. The industry avoids high-disc-loading helicopters because of excessive costs to 

get speed. Example for a constant, fixed useful load of 2,220 pounds per Table 2-7. 
2.2 WEIGHT 

118 

 This introduction to modern helicopter weights has given you a framework and 

associated terminology to discuss the industry’s progress in a very vital area. You have seen 

that: 

1. There is no limitation to helicopter size, 

2. The overwhelming number of helicopters have takeoff gross weights well below 

50,000 pounds, 

3. The modern helicopter grew from the small “machines” that replaced the autogyro, 

and these early helicopters gave the military a true aerial scout capability, 

4. The ratio of useful load to gross weight is not always a measure of “goodness,” 

particularly for special-purpose helicopters that the military use, 

5. The application of the turbine engine was a major step, 

6. Weight reduction in Propulsion Group and Structural Groups was used to add 

features in the All Other Groups, 

7. Simple methods can be used to roughly size a helicopter, 

8. Helicopter productivity depends on payload and speed, and 

9. Efficient helicopter aerodynamic performance at high speed has yet to be 

achieved, and this has impeded the industry. 

 In closing this discussion about weight, it is probable that further weight-empty 

reductions will be made as the modern helicopter continues to mature. It would be my hope 

that these reductions in weight will be accompanied by reductions in costs and improvements 

in performance. However, it is well to keep in mind Lieutenant Alexander Klemin’s statement 

opening Chapter III of his book, Aeronautical Engineering and Airplane Design [157]. In 

1918, Lieutenant Klemin43 wrote: 

“Hardly any branch of practical airplane design offers such difficulties as the estimates of 

weight. A manufacturer – who has built a number of machines and has kept careful weight 

schedules has valuable data in his possession, but is, as a rule, chary of making such data 

public. Even an experienced manufacturer, however, may be at a loss when building an 

entirely new type, particularly if the new type is of a very different size from that to which he 

has been accustomed. 

Theoretical considerations apply only to a limited extent. Empirical formulas have been 

suggested by several authorities, but are only partly satisfactory. The authors’ thanks are due 

to manufacturers and others for such data as they have permission to publish.” 

 

43 Dr. Alexander Klemin became a staunch supporter of rotorcraft. He was born in London on May 15th, 1888, 

and died unexpectedly on March 14th, 1950. An obituary by Group Captain R. N Liptrot was published in the 

Journal of the Helicopter Association of Great Britain, vol. 4, no. 1. Each year the American Helicopter Society 

gives an award—The Klemin Award—to a very deserving society member. 
119 

2.3 HOVER PERFORMANCE 

 The improvements in rotorcraft performance over the past five decades have been 

nothing short of astounding. Cruise speeds, under 75 miles per hour in the early 1940s, have 

doubled to modern speeds ranging from 150 to 170 miles per hour (130 to 150 knots). Many 

helicopters are available that can do useful work at altitudes from 10,000 to 20,000 feet thanks 

to the turbocharged piston engine and the transition to gas turbine engines. Payloads of 

20,000 pounds can easily be moved well over 100 nautical miles. Extended range beyond 

600 nautical miles is common place, and aerial refueling permits comfortable, long-distance, 

over-water flights such as California to Hawaii (2,100 nautical miles). Helicopters have flown 

around the world. In short, over 50 years the helicopter has matured in the category of 

performance. 

 To appreciate the progress made by the rotorcraft industry in reaching this mature 

level of performance, it helps to understand helicopter performance in the three major areas 

of: 

1. Hovering, including takeoff, 

2. Forward flight and landing, and 

3. Fuel efficiency. 

These topics, combined with the previous background about engines and weights, form at 

least a minimum basis to see the modern progress made with the helicopter. Consider hover 

performance first. 

2.3.1 Hover Power Margin 

 The takeoff and hovering performance of modern helicopters has established the 

unique character of these “machines.” When you see a hovering helicopter rescue a mountain 

climber stranded at 10,000 feet, you quickly appreciate the progress made since the early 

pioneering efforts to just get off the ground. The “performance secret” to these humanitarian 

successes lies in (a) installing an engine or engines with enough power, (b) minimizing the 

power required to takeoff and hover, (c) selecting the design horsepower and gear reduction 

for the transmission, and (d) achieving a structurally efficient helicopter. You already have 

some insight into engine performance from the earlier discussion, and from your introduction 

to modern helicopter weights you should be convinced that structurally efficient helicopters 

have been achieved. So consider the progress that has been made in ensuring an ample power 

margin between power available and power required for useful flight. 

 Let me first use some history as a broad introduction to power margin. The early 

pioneers, as you will recall from Fig. 1-4, had begun to appreciate just how much horsepower 

the helicopter would need to achieve a bare minimum of hovering performance. However, the 

transition to the modern era of consistently installing enough power to hover did not begin 

until the mid-1930s. The beginning of the modern era came when Maurice Claisse 

demonstrated a coaxial “gyroplane” designed by René Dorand, but guided by Louis Bréguet 
2.3 HOVER PERFORMANCE 

120 

himself. These two French pioneers worked at Louis Bréguet’s Société des Avions. Their 

efforts to develop the Bréguet Type 314 in the mid-1930s are recounted by Claisse in Jean 

Boulet’s history [2]. The initial, inadequate ground runs with the Type 314 were followed by 

a disastrous, first hovering attempt on a Sunday in late November of 1933. During this initial, 

unsuccessful period, Claisse noted that they “found an engine made at Bréguet’s for the 

Leviathan, called the Bréguet-Bugatti. It was a 500 HP engine. We cut it in two sections and 

we had an engine of 250 HP which seemed to fit our needs.” The “machine” was rebuilt, more 

thorough ground testing was completed, and in June of 1935 flight testing began again. The 

4,500-pound-gross-weight helicopter with 52.5-foot-diameter, two-bladed, coaxial rotors was 

readied in August of 1935 for a serious demonstration. Unfortunately, the 250-horsepower 

piston engine threw a connecting rod. Claisse went on to say that “fortunately, there was in 

Bréguet’s hanger a Wright 90 engine, which was an excellent engine. It had a little too much 

power (420 HP), and the speed [RPM] was not exactly right. But we adjusted it, and then we 

had more power than necessary.” Between December 1935 and December 22, 1936, Claisse 

went on to capture all the helicopter world records. These demonstrations earned the Bréguet 

airplane company a 3.2-million-Franc subsidy from the French Government for follow-on 

development. The Type 314 was damaged during subsequent autorotation testing, and with 

the coming of World War II Bréguet and his company had to concentrate on airplane 

deliveries. Claisse concluded his personal history with: 

 “We were not able to do it all. We gave up.” 

 Fortunately, Focke, Flettner, Platt and Le Page, Sikorsky, and several others picked up 

the pioneers’ legacy and development continued. After World War II, Bréguet and Dorand 

began anew. Bréguet continued with the coaxial configuration. His G-11E, a 28-footdiameter, 2,915-pound-takeoff-gross-weight helicopter was powered with a 240-horsepower 

engine. It flew in early December of 1948. The G-11E was uprated to the Type III having a 

31.5-foot-diameter, 450-horsepower engine, and a 4,630-pound, fully loaded flying weight. 

The Type III was the last helicopter for Bréguet. This great French aviation pioneer died in 

1956. 

 Dorand became the head of the SNCAC, one of several French nationalized aircraft 

organizations. He favored Flettner’s synchropter approach and launched his less-thansuccessful NC-2001. One of three prototypes briefly hovered in ground effect in June of 1948. 

The SNCAC was subsequently shut down, and Dorand formed his own company and began 

experimenting with single rotors turned by tip jet propulsion. 

 It is worth taking a moment to get a rough idea of the power margin of the Bréguet–

Dorand Type 314. A first-order index of power margin comes from the power available and 

the ideal horsepower required to hover out of ground effect as discussed earlier in relation to 

the pioneering efforts. Applying Eq. (1.1) on page 5, but now using the Bréguet–Dorand Type 

314 as the example, shows that 
2.3 HOVER PERFORMANCE 

121 

(2.37) 

ideal

T T HP Hover out of ground effect 550 2 A

4500 4500 172 hp 550 2 0.002378 2140

= ρ

= = × ×

. 

Imagine now that Claisse and Dorand had proceeded with the original, 250-horsepower 

engine. The ratio of installed engine power to ideal would have been a miserly 1.45. I believe 

that the smaller engine did these French pioneers a favor when it threw a connecting rod. By 

turning to the 420-horsepower Wright 90 engine, Bréguet and Dorand gave Claisse a ratio of 

installed to ideal power of 2.44, and then they “had more power than necessary.” Considering 

that the Type 314 (vintage 1935) had a mechanical hydraulic-powered control system, and the 

controls were phased so that longitudinal stick motion gave equal roll and pitch response, 

Maurice Claisse certainly did not need the complication of an underpowered “machine.” 

 Before “giving up” as Claisse concludes, Bréguet presented a paper in November of 

1936 [158] that summarized his work. This work really began in the very early 1900s. 

Interestingly, he provides only two photos of his Type 314 and devotes less than 2 pages out 

of 35 to what he refers to as “only a laboratory gyroplane.” Instead he indirectly comments 

that concepts of flapping, lead-lagging, and feathering were established well before Cierva 

began. Then he proceeds to outline his aerodynamic performance theory for the “gyroplane” 

in considerable detail. This lays the groundwork for his next design. 

 Bréguet proposes [158] “the gyroplane of the future.” His conceptual design envisions 

a coaxial, 25-meter-diameter (82.02-foot) rotor system to be used with a 12-passenger, airlinetype fuselage. The design includes a retractable landing gear. An alternate fuselage appears to 

be a seaplane fuselage similar to the Boeing Clipper. He estimated the takeoff gross weight at 

15 to 17 [metric] tons but used 15 tons or 33,069 pounds in all his figures. Four engines 

giving a combined output of 3,600 horsepower at an altitude of 3,000 meters (9,843-feet 

pressure altitude on a standard day) were to be “housed in one compartment of the aircraft.” 

Each of these piston engines (remember Bréguet presented this paper in November of 1936 

before the gas turbine engine became an option) would have to be rated at about 1,300 

horsepower at sea level to give the power he wanted at altitude. Based on his aerodynamic 

theory, Bréguet believed that the power required to hover at 3,000 meters would be 2,650 

horsepower and that at a high-speed cruise power of 2,400 horsepower, his gyroplane would 

cruise at 400 kilometers per hour or 248 miles per hour (about 216 knots). There can be little 

doubt, however, that Bréguet intended to install enough engine horsepower. At sea level the 

ideal horsepower to hover for his design is 2,181 horsepower. He was, therefore, proposing a 

ratio of installed to ideal power of 4×1,300/2,181 or around 2.38.44

 

44 I found Bréguet’s paper fascinating although the definition of symbols was hard to follow, and the mixture of 

metric and English units complicated my understanding of his results. The ideal power to hover out of ground 

effect at 3,000 meters is 2,181 horsepower given the weight and diameter he proposed. This would suggest a 

hover efficiency of 2,181 ÷ 2,650 or about 82 percent, which modern helicopters have yet to achieve. Bréguet’s 

theory led to a 216-knot cruise speed that I can only imagine Glauert would have scoffed at. I suspect that Cierva 

would have seriously disagreed with Bréguet’s theory but liked the answer. 
2.3 HOVER PERFORMANCE 

122 

Table 2-8. The Rotorcraft Industry Has Flown Over 550 

Separate Models as the Helicopter Matured 

Configurations Piston Turbine Row Totals 

Single Rotor 197 217 414 

Tandem Rotors 31 22 53 

Coaxial Rotors 37 10 47 

Synchropter 11 9 20 

Side-by-Side 16 2 18 

Tri-Rotor 1 0 1 

Quad-Rotor 1 0 1 

Column Totals 294 260 554 

 

 I have compiled a survey of about 600 helicopters known to have flown since Bréguet 

and Dorand began what I believe to be the modern era of helicopter development. The shaftdriven configurations, numbering slightly over 550, are distributed as shown in Table 2-8. 

Modern results illustrating a simple view of power margin are summarized in Fig. 2-41. The 

results of this survey confirm Bréguet’s accuracy in 1936. 

 The trend that this survey of over 550 shaft-driven helicopters suggests is an average 

installed-to-ideal-power ratio of 2.25. Designers who started out at a lower ratio generally 

uprated the engine before serious production was begun. Very few configurations were 

attempted below a ratio of 1.50, and none of these helicopters went beyond Bréguet’s 

“laboratory model” stage. The rotorcraft industry learned the value of power margin, and each 

generation of helicopter model improved as Fig. 2-41 suggests. 

 A more definitive power margin criteria for U.S. Army helicopters became available 

in April 1974 [159]. This Army design requirement called for a 500-foot-per-minute vertical 

rate of climb at 4,000-feet pressure altitude with an outside air temperature of 95 o

F using 

military rated power. The presumption was that future Army helicopters would at least be able 

to hover at this high/hot condition, hopefully with enough spare power to maneuver. 

2.3.2 Hover Ceiling Versus Gross Weight 

 Although historically very informative, the surveys shown in Fig. 2-41 and Fig. 2-42 

do not display hover performance in the way you are most likely to see it. Nor do they convey 

the fundamental physics behind these modern helicopter trends. Hover performance for a 

given helicopter is most often shown graphically as in Fig. 2-43. The envelope of the highest 

altitude that the helicopter can takeoff and hover out of ground effect (HOGE) is defined for a 

practical range in takeoff gross weight (TOGW). In general, the available engine horsepower 

decreases from its sea-level rating as altitude increases. Naturally, this limits takeoff from 

high-altitude heliports at heavy weight. The transmission may limit the TOGW at low altitude 

as Fig. 2-43 suggests. Finally, in combination with a minimal weight statement, you can 

quickly establish what the gross weight means in terms of useful load. 
2.3 HOVER PERFORMANCE 

123 

10

100

1,000

10,000

100,000

10 100 1,000 10,000 100,000

Actual 

Engine(s) 

Rated 

Horsepower

Ideal Horsepower To Hover (S.L. Std. Day)

Average Of 602 

Helicopters Is 

2.24(Ideal)

2.75(Ideal)

1.5(Ideal)

Fig. 2-41. Rotorcraft always benefit from a healthy margin between engine power 

available and power required. 

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

1930 1940 1950 1960 1970 1980 1990 2000

Ratio 

Rated 

ESHP 

To 

Ideal 

HP

Introductory Year

Probably Requires In 

Ground Effect 

Takeoff

Solid symbols are Turbine 

Open symbols are Piston

Fig. 2-42. Power margin has continually increased. 
2.3 HOVER PERFORMANCE 

124 

 Fig. 2-43 does a fair job of summarizing the characteristic trend of rotorcraft hovering 

performance, particularly if you are comparing one product to another.45 However, it only 

begins to suggest what key factors and fundamental physics influence helicopter hovering 

performance. It will be a real help to your introduction to rotorcraft if you understand the 

details behind the typical summary presented in Fig. 2-43. After you see these details, I will 

come back to the format of Fig. 2-43 and then add a bit more. 

 The physics behind and leading to Fig. 2-43 are, fortunately, really quite easy to 

understand although it does take several pages to convey. The most important hover 

performance fundamentals are: 

a. The variation, with altitude and temperature, of power required to hover, 

b. The variation, with altitude and temperature, of engine power available, and 

c. The power that the transmission system is designed for. 

 Because the majority of the 600 helicopters surveyed are single rotor helicopters with 

a tail rotor for anti-torque, I will use this configuration to illustrate these 3 hover performance 

fundamentals. 

 Within the single-rotor group, the Sikorsky UH-60A, designated by the U.S. Army as 

the Black Hawk, has a great deal of information available in the public domain. This utility, 

tactical, transport helicopter emerged as the winner in the competition for a modern helicopter 

to replace the Bell UH-1 “Huey” series. The Army UH-60A is a measure of early 1970’s 

technology. The preproduction model, the YUH-60A, was flight evaluated [160] by the U.S. 

Army Aviation Engineering Flight Activity at Edwards Air Force Base from April 7 to 

September 17 of 1976. The production configuration, the UH-60A, was qualified [161] from 

October 27, 1979, to October 9, 1980. The final report was published in September of 1981 

and contained the statement that the UH-60A had “undergone the most extensive qualification 

program of any helicopter in the history of the industry.” It would be hard to argue with the 

Army’s statement. 

 In my opinion, there is only one book worth reading about the complete history of the 

Sikorsky UH-60. Ray Leoni wrote it. He titled the saga Black Hawk: The Story of a World 

Class Helicopter [162], and it was published by the American Institute of Aeronautics and 

Astronautics (A.I.A.A.) in 2007. Ray was the leading figure behind Sikorsky’s helicopter 

 

45 Perhaps a word of caution is needed here. You will frequently see tables comparing helicopter characteristics 

published in trade magazines. These tables, until recently, could be most misleading. Very often the collection of 

numbers I have seen presented is an “apples-to-oranges” comparison. For example, under the weight columns, 

the maximum takeoff gross weight might well be quoted. Then, in the performance columns, the hover altitude 

might be quoted—but for the normal gross weight. If you look at Fig. 2-43, you can see that the maximum 

takeoff gross weight at which this helicopter can HOGE is just under 22,000 pounds. This corresponds to a sea 

level takeoff. But the comparative table may well quote the hover ceiling as 8,000 feet. Fig. 2-43 says this hover 

ceiling is associated with a “normal” gross weight of 18,500 pounds. The next helicopter product listed on the 

table could mix and match numbers from its hover ceiling chart and include in ground effect (HIGE) takeoff 

hover ceiling performance. The second product may appear to be superior, but you would be deceived. 
2.3 HOVER PERFORMANCE 

125 

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

12 14 16 18 20 22 24

Hovering 

Ceiling

(ft)

Gross Weight (1,000 lbs)

Minimum

Operating

TOGW

Normal

TOGW

Limited By 

Engine(s) 

Rated 

Horsepower

Limited By 

Transmission 

Rating

Fig. 2-43. The most common display of hovering performance defines hover ceiling 

vs. takeoff gross weight. 

development—from conceptual design, to winning the U.S. Army competition with the entrée 

from the now Boeing Helicopter Division, to worldwide use of the UH-60 today. The insight 

about engineering details, company strategy, working with the U.S. Army, trials and 

tribulations—it is all there. The Foreword to Ray’s book was written by Sergei Sikorsky 

(Igor’s son), and the Preface was contributed by Charlie Crawford, who was Ray’s 

counterpart on the Army’s side. Charlie ate, slept, and breathed the Black Hawk program 

along with Ray. As Charlie wrote, “If you want to understand rotorcraft development, this is a 

must read book.” 

 After winning the fly-off competition against the Boeing-Vertol YUH-61A, the 

preproduction YUH-60A was considerably improved before entering into production. Table 

2-9 shows that the combined efforts of the Sikorsky Aircraft Division and the General Electric 

Aircraft Engines Division gave the U.S. Army a superior helicopter.46 Most importantly, the 

UH-60A has performed well in the field.47

 

46 Preparing Table 2-9 required careful review of both the flight qualification reports [160, 161] and weight 

reports [163, 164]. 

47 Further flight research of a production UH-60A to evaluate the rotor system in more detail was accomplished 

in the first half of 1987. This effort [165] in 1988 provided extensive data for performance, loads, and stability 

and control, as well as vibration levels throughout the airframe. More recently, NASA and the U.S. Army 

teamed up to provide the industry with the most comprehensive set of blade airloads data imaginable [166, 167]. 
2.3 HOVER PERFORMANCE 

126 

 With this background about a representative single rotor helicopter, the UH-60 series, 

in hand, let me discuss hovering performance from the power-required perspective. 

 The power required to HOGE was obtained with the YUH-60A/UH-60A wheels about 

100 feet above the ground. The distance from the bottom of the wheels to the main-rotor hub 

adds another 12 feet. This gives a height-to-diameter ratio over 2.0, which is representative of 

HOGE testing. While the final Army evaluation was based on the UH-60A results, I have 

chosen to include data from the YUH-60A evaluation as well to give you an appreciation of 

experimental “data scatter.” The results shown in Fig. 2-44 provide the power required versus 

altitude on a standard day for two gross weights. The lower weight is the primary mission 

gross weight of 16,260 pounds while the alternate gross weight of 20,250 pounds is near the 

maximum weight for the “A model” of the UH-60 series. 

 The fundamental trend is for hover power required to increase with altitude, and the 

UH-60A design is no exception. You saw earlier [from Eq. (1.4), repeated here for 

convenience] that a simple engineering approximation to the physics involved is given by 

1,800

2,000

2,200

2,400

2,600

2,800

3,000

3,200

0 2,000 4,000 6,000 8,000 10,000 12,000 14,000

Shaft 

Horsepower 

Required

Altitude On A Standard Day (ft)

TOGW

20,250 lbs

TOGW

16,260 lbs

Fig. 2-44. UH-60 power required to hover out of ground effect increases with altitude.

(Open symbols for the YUH-60A; solid symbols for the UH-60A.) 

 

The combination of thorough reporting of the flight qualification coupled with subsequent flight research really 

benchmarked helicopter technical progress as it had evolved by the mid-1970s. 
2.3 HOVER PERFORMANCE 

127 

Table 2-9. The UH-60A Improved Upon the YUH-60A 

Basic Aircraft Information YUH-60A UH-60A 

Power Installed 

 Twin Engines YT700-GE-700 T700-GE-700 

 30 Min Rating SL, Std (installed) 1516 hp 1553 hp 

 100% RPM 20,000 rpm 20,900 rpm 

 Main Transmission Continuous Limit 2,791 hp 2,828 hp 

 Tail Transmission Continuous Limit 420 hp Not quoted 

Weights 

 Weight Empty 11,182 lb 10,495 lb 

 Trapped Fluids 42 lb 50 lb 

 Crew (pilot, copilot, and gunner) 725 lb 725 lb 

 Weapons and Ammunition 164 lb 159 lb 

 Operating Empty Weight 12,113 lb 11,429 lb 

 Payload (11 combat-equipped troops) 2,640 lb 2,640 lb 

 Fuel (troop assault mission/includes a reserve) 2,100 lb 2,065 lb 

 Primary Mission Gross Weight (PEG) 16,853 lb 16,134 to 16,260 lb 

 Alternate Gross Weight (AGE) 19,930 lb 20,250 lb 

 Fuel Capacity/Weight 350 gal./2,275 lb 364 gal./2,366 lb 

 Test A/C EW With Inst, Full Oil, Fuel Drained 13,121 lb 11,820 lb 

Dimensions 

 Main Rotor 

 Diameter 53 ft, 8 in. Same 

 Blade Number 4 Same 

 Blade Chord 1.73 ft 1.73/1.75 ft 

 Solidity 0.0821 0.0826 

 100% RPM 263 rpm 257.9 rpm 

 100% Tip Speed 739.1 ft/sec 724.7 ft/sec 

 Tail Rotor 

 Diameter 11 ft Same 

 Blade Number 4 Same 

 Blade Chord 0.81 ft Same 

 Solidity 0.1875 Same 

 100% RPM 1,214 rpm 1,189.8 rpm 

 100% Tip Speed 699.2 ft/sec 685.3 ft/sec 

 Airframe 

 Nose-to-Tail Length Not Avail 50 ft, 0.75 in. 

 Hub-to-Hub Distance Not Avail 32.567 ft 

 Main/Tail Rotor(s) Clearance Not Avail 2.8 in. 

 Vertical Tail Span 8 ft, 2 in. Same 

 Vertical Tail Area 32.3 sq ft Same 

 Horizontal Stabilator Span 172 in. Same 

 Horizontal Stabilator Area 45 sq ft Same 

Performance 

 PMGW (equal payload of 2,640 lb) 

 Standard Day HOGE 8,800 ft 11,200 ft 

 Hot Day (35 °C at all pressure alts) HOGE 4,000 ft 5,900 ft 

 Cruise Speed (4,000 ft, 35 °C at eng MCP) 138 kts 147 kts 

 Economical Cruise Speed (4,000 ft, 35 °C) 130 kts 133 kts 

 AGW 

 Standard Day HOGE 3,650 ft 5,000 ft 

 Hot Day (35 °C at all pressure alts) HOGE Unable to HOGE 700 ft 
2.3 HOVER PERFORMANCE 

128 

(2.38) HOGE

3

t do

i

T T bcRV C HP k

550 2 A 8 550

  ρ = +  

ρ ×  

. 

The induced-power term is the first part of Eq. (2.38). It accounts for the power required by, 

say, the main rotor to support the helicopter weighing W pounds with a thrust of T pounds. 

The second term makes sure that the power to drag the main rotor blades around is included. 

The same equation can be used to approximate the power needed by the tail rotor to account 

for its anti-torque thrust. Because the engine generally provides power for accessories such as 

generators, hydraulic pumps, and cabin cooling or heating, an additional accessory power 

(that does not vary much with altitude) is frequently added. 

 A usable but very empirical “curve fit” to the UH-60A test results was created by 

Nagata [161]. It took the dimensional form 

(2.39) Re qd.

3

t W W bcRV ESHP 1.4572 0.005897

550 2 A 8 550

  ρ = +   ×

ρ ×  

. 

This curve-fit equation was used by Nagata primarily to interpolate among the hover test data 

acquired out of ground effect at density altitudes below 2,160 feet. It failed to capture the 

measured results at density altitudes between 4,000 and 11,000 feet. An auxiliary graph was 

included in the report [161] to add a power increment reflecting this surprising and 

unexplained altitude effect.48 

 The effect of altitude on hover power required is clear enough when you study 

Eq. (2.38) for a moment. As you know, the density of air (ρ) diminishes with increasing 

altitude. Therefore, the induced power will go up nearly as 1 ρ . The lesser power, used 

primarily to turn the blades, varies directly with density and, therefore, decreases with 

altitude. The proportions of the two, power-required elements, when calculated with UH-60A 

dimensions from Table 2-9 and with Eq. (2.39), for the primary mission gross weight of 

16,260 pounds are 

Re qd.

Re qd.

or Sea Level, Std Day)

or 5, 000 ft, Std Day)

ESHP 1,675 226 1, 900 hp (f

ESHP 1,804 195 2,000 hp ( f

= +=

= += . 

Thus, the helicopter’s hovering power required is dominated by the induced-power term. 

Based on the UH-60A flight test results, the crudest, first approximation that captures the 

physics would simply be 

 

48 During early flight testing of the OH-58D [145], I learned not to use the word “phenomena” for such initially 

unexplainable results. Teddy Hoffman (our OH-58D program leader whom I revere) told me—in the most 

humorous way—that upper management and other laymen absolutely quake in their shoes when the chief 

engineer calmly says, “the pilot won’t go above 60 knots because the tail wag vibration is so bad. Must be some 

phenomena.” Up until then I thought everyone had the problem-solving confidence that engineers have. Teddy 

also recommended keeping an active “too hard file.” He also defined and quantified the word “features” for me 

in a way I will never forget. 
2.3 HOVER PERFORMANCE 

129 

(2.40) Re qd.

W W Ideal Horsepower ESHP 1.6

550 2 A 0.625

  = =  

ρ  

. 

 No doubt you are aware that experimental data virtually always contains some 

“scatter.” Rotorcraft flight testing offers no exception to this engineering fact. The results 

presented in Fig. 2-44 are for the most part quite representative of what the modern rotorcraft 

industry deals with on an everyday basis. The power-required differences between two 

virtually identical helicopters is frequently as large as Fig. 2-44 suggests. Engineering 

analysis just as frequently fails to pinpoint all the reasons. The data scatter during a given test 

period for one helicopter frequently is as large as Fig. 2-44 shows. Efforts by everyone to 

reduce or explain the scatter just as frequently fail to improve the situation. I have brought this 

fact of life to your attention using engine performance as an example in Fig. 2-45. Here you 

see an expanded ordinate (i.e., the referred shaft horsepower axis) and not starting from zero 

power. In short, I have “blown up” the data presentation in Fig. 2-45. This scale makes an 

error band of ±100 horsepower or roughly ±5 percent appear quite large. However, this is a 

realistic situation because even the most modern theories and experimental instrumentation 

rarely can reduce the uncertainty in how much power it takes to hover. 

700

800

900

1,000

1,100

1,200

1,300

1,400

1,500

1,600

1,700

600 650 700 750 800 850

Referred Turbine Inlet Temperature (deg. C)

S/N 207211

S/N 207213

S/N 207226

S/N 207270

Referred 

Shaft 

Horsepower 100 HP

25o

 C

Fig. 2-45. “Identical” engines vary in performance. 
2.3 HOVER PERFORMANCE 

130 

 The real-life uncertainty of ±100 horsepower at the primary mission gross weight of 

16,260 pounds is hardly comforting to those who produce or use helicopters today. When 

viewed as if the power required were accurately known, the uncertainty translates to not 

knowing what weight can be lifted. Consider this view. The UH-60 requires roughly 

2,000 horsepower to hover at low altitudes. This translates to about 8 pounds of lifted weight 

per horsepower. The uncertainty of ±100 horsepower, therefore, equates to about 

±800 pounds in gross weight. But this ±800-pound uncertainty strikes at the useful load that 

contains the payload (2,640 pounds) and fuel (2,065 pounds). Plus or minus 800 pounds out 

of 4,705 pounds, therefore, is an uncertainty of ±17 percent! 

 With this understanding of hover power required, let me proceed to examine engine 

power available in some detail. Two T700-GE-700 engines are installed in the UH-60A. Each 

engine is nominally rated at 1,553 installed horsepower at the sea level, standard day 

condition. The rating is called an intermediate rated power (good for no longer than 

30 minutes at a time) or IRP by the U.S. Army. The total of 3,106 installed horsepower at sea 

level decreases with altitude as you learned earlier from the discussion about engines. 

Fig. 2-46 adds the final power-available line, but not its data scatter, to the power-required 

graph of Fig. 2-44. (I have removed the YUH-60A power-required data and put them in the 

“too hard file.”) 

 The power margin, as noted in Fig. 2-46, is the difference between engine power 

available and helicopter power required. At the point where this difference shrinks to zero, the 

helicopter has reached the altitude where it can just hover out of ground effect. This altitude is 

referred to as the hover ceiling. You might note in passing that the power margin index that I 

used in the broad survey of 550 shaft-driven helicopters can now be related to the practical 

power margin in Fig. 2-46. For example, at a gross weight of 16,260 pounds the ideal HOGE 

horsepower required for the UH-60A is

ideal

16, 260 16, 260 HP 1,150 hp 550 2 0.0023769 2, 262 = = × × . 

The simple power-margin index becomes 3,106/1,150 = 2.7. At 20,250 pounds the index 

(about 1.94) is still favorable, although I have never talked to a pilot who said he ever had 

enough power margin. 

 As it turned out, the Sikorsky/General Electric team made some reasonable and cost 

effective changes in going from the YUH-60A to the UH-60A. For example, the engine speed 

was increased and the rotor system was slowed down as Table 2-9 notes. This increased the 

practical power margin in production by about 40-plus horsepower. 

 While the data scatter in power available is not shown in Fig. 2-46, that does not mean 

it does not exist. The flight qualification test report for the YUH-60A provided a very clear 

data-scatter example as you saw in Fig. 2-17, page 80. In addition, Fig. 2-45 shows how four 

preproduction engines performed in General Electric’s test cell before delivery. The variation 
2.3 HOVER PERFORMANCE 

131 

1,800

2,000

2,200

2,400

2,600

2,800

3,000

3,200

0 2,000 4,000 6,000 8,000 10,000 12,000 14,000

Engine 

Shaft 

Horsepower

Altitude On A Standard Day (ft)

Power Available

Twin T700-GE-700

At IRP (30 min.)

Rating

Power

Margin

Power Required

At 20,250 lbs

Power Required

At 16,260 lbs

Hover Ceiling

Of 5,000 ft.

Hover Ceiling

Of 11,200 ft.

Fig. 2-46. Power margin of the UH-60A decreases with altitude. 

(Solid symbols for the UH-60A; open symbols for the YUH-60A removed for clarity.) 

in turbine inlet temperature required to produce 1,250 horsepower is about 25 oC. This 

illustrates a representative difference that can be expected in production. Although I have not 

differentiated it, each engine was tested at turbine speeds from 19,000 to 21,000 rpm. 

 Before introducing transmission-limited power, let me use the power-available data 

from Fig. 2-45 to raise a very important point. The question posed by the figure is this: If you 

were the engine manufacturer, what turbine inlet temperature would you pick to ensure 

consistent delivery of engines rated at 1,250 horsepower? Apparently, as you can see from the 

figure, all four prototype engines could be delivered if you chose a temperature of 755 °C. A 

helicopter producer would, quite naturally—in view of the power required to hover and his 

uncertainties—strongly suggest that he get delivery of engines with an extra 100 horsepower 

(i.e., the 1,350 horsepower at 755 °C capability achieved by the YT700-GE-700, Serial 

Number 207211 engine). Then his helicopter might have the more competitive hover 

performance. But you, as the engine manufacturer, probably could deliver only 10 out of 1000 

production engines to this helicopter producer. This important point does not stop here. 
2.3 HOVER PERFORMANCE 

132 

 You, as the helicopter manufacturer, must assure the certifying agency and the 

user/pilot that the flight handbook performance will be achievable for a reasonable period 

after delivery. Keep in mind that the engine will deteriorate over 1,000 hours of operating 

time. While more than 1,250 horsepower will be available at 755 °C when your helicopter is 

delivered, the pilot, after a year or two of operation, will quite likely see 755 °C plus another 

15 °C (or 770 °C) on his turbine temperature gauge just to lift off at the same conditions. This 

means that both manufacturers must keep the user in mind by including a field degradation 

allowance before settling on engine performance used to create the pilot’s handbook. 

 The engine manufacturer needs to profitably deliver virtually all engines he makes, the 

helicopter producer needs to be profitably competitive, and the user needs to have economical 

performance over the long haul. All these needs are influenced by the data presented in 

Fig. 2-45 and Fig. 2-46. A compromise might easily be a 1,200-horsepower engine that 

operates at or below 740 °C when delivered. The pilot would be informed (in the flight 

handbook) that when the turbine temperature starts reading close to 755 °C, a check liftoff 

should be performed, and an engine overhaul is imminent. 

 Now on to the part that transmissions play in hover performance. 

 The third key factor involved in the physics of hover performance is the rating of the 

transmission. The limit is frequently expressed in terms of the engine shaft horsepower. 

However, it is primarily a limit torque in some particular gear that defines the limit. This 

torque and an associated rotational speed are really closer to the heart of a transmission limit. 

The main-rotor-transmission output torque is displayed to the pilot, usually on a percent 

gauge. The pilot, therefore, monitors both a turbine gas temperature gauge for thermodynamic 

limits and a torque meter gauge for mechanical limits. 

 The YUH-60A main rotor transmission was uprated from 2,791 engine shaft 

horsepower (ESHP) at 263 main rotor rpm to 2,828 ESHP at 257.9 rpm for the production 

UH-60A. Fig. 2-47 shows this higher rating added (as the horizontal dashed line) to the 

power-required and power-available example you have seen developing. For this modern 

helicopter the transmission was designed and qualified to allow for growth in takeoff gross 

weight. The margin between power required at the UH-60A alternate gross weight of 

20,250 pounds and the transmission-limited ESHP of 2,828 horsepower is sufficient for a sealevel takeoff at a higher weight of 21,800 pounds. More practically, this margin allows for 

reasonable flying and maneuvering in turbulent air at the alternate, 20,250-pound gross 

weight. 

 Over the decades, mechanical drive system technology—both engineering and 

manufacturing—has been impressive. It is quite rare to have a transmission not perform in the 

field as advertised. When failures have occurred, they have generally been traced to a minor 

detail that did not quite fit all previous experience. The design is repaired, and the new 

experience is incorporated in the “don’t ever forget file.” This experience has, in a large 

measure, accounted for the very much improved safety record of helicopters. 
2.3 HOVER PERFORMANCE 

133 

1,800

2,000

2,200

2,400

2,600

2,800

3,000

3,200

0 2,000 4,000 6,000 8,000 10,000 12,000 14,000

Engine 

Shaft 

Horsepower

Altitude On A Standard Day (ft)

Power Available

Twin T700-GE-700

At IRP (30 min.)

Rating

Power

Margin

Power Required

At 20,250 lbs

Power Required

At 16,260 lbs

Hover Ceiling

Of 5,000 ft.

Hover Ceiling

Of 11,200 ft.

Limit Power Due To Main Rotor Transmission

(Turbine at 20,900 rpm; main rotor at 257.9 rpm)

Fig. 2-47. The transmission limit can put a cap on rotorcraft hovering performance as 

the dashed line shows for the UH-60A. 49

 The final display of modern helicopter hovering performance is not in the engineering 

form of Fig. 2-47. The more useful final graph is hovering ceiling (i.e., pressure altitude in 

feet) versus gross weight. For example, UH-60A test data provided in appendix E of reference 

[161] displays the hover capability in the more common form you saw in Fig. 2-43, which 

opened this hover performance discussion several pages ago. This summary for the UH-60A 

is shown in Fig. 2-48 for both a standard day and an Army-defined hot day (where the outside 

air temperature is 35 °C at all pressure altitudes). I have added the YUH-60A hot-day results 

from reference [160] to complete this example. 

 

49 In setting the torque limits, transmission designers are most concerned with the loads acting on each tooth of 

each gear. These loads act to both bend and shear a gear tooth from its “hub.” Tooth-bending stresses are high, 

and there can be a great deal of scrubbing involved. Long, maximum-power runs “on the bench” using several 

transmissions are generally made before a transmission is installed in the first helicopter. I doubt you can find 

any other transmission that converts as much torque per pound of weight empty. In my opinion, these designers 

stand head and shoulders above those who design transmissions for lesser applications. 
2.3 HOVER PERFORMANCE 

134 

 Fig. 2-48 clearly shows that the UH-60A hover ceiling was an improvement over the 

preproduction YUH-60A. There is, however, an even better way to see successive product 

improvements. This more informative picture comes by showing hover ceiling as a function 

of useful load (not gross weight as in Fig. 2-48). Then the comparative results between the 

two UH-60A-series helicopters used in this illustration are much more impressive as you can 

appreciate from Fig. 2-49. 

 Let me complete this portion of your introduction to modern helicopter hovering 

performance with another survey result. The background you have just finished reading 

should let you quickly understand and then appreciate Fig. 2-50. The 150-plus different 

helicopter models (out of 550) form an envelope of product capability offered by the 

rotorcraft industry up to 1995. This envelope has continually expanded over the last five 

decades. Turbocharged piston engines gave early helicopters high-altitude performance with a 

very useful load. Turbine engines quickly led to larger helicopters that increased useful load 

tenfold, and then tenfold again. 

 The modern results achieved by the rotorcraft industry shown in Fig. 2-50 have come, 

in part, by investing heavily in aerodynamic research. Perhaps a disproportionate share of this 

aerodynamic research money has gone to reducing hover power required. Two facts have, 

however, clearly emerged from this long effort to mature the helicopter. They are: 

1. A reduction in the uncertainty of initial power-required estimates has been achieved 

over five decades. 

2. When power required is viewed in a nondimensional form,50 it is not at all obvious 

that substantial progress in hovering efficiency has been achieved. 

 In May 1980, a measure of rotorcraft aerodynamic theory versus experimental results 

was provided by the aerodynamic staff at Bell [168]. The uncertainty in predicting a hover 

ceiling/gross weight result such as Fig. 2-48 was shown to be about ±3 percent. The power 

available was assumed to be known exactly in this study of 17 helicopters. Therefore, the 

uncertainty lay in predicting power required to hover. Considering the complexities of this 

engineering problem, you may well think that ±3 percent is rather good. However, the Bell 

analysis [168] notes that this uncertainty amplifies to ±18 percent of fuel load, ±6.7 percent of 

useful load, or ±10.5 percent of payload when applied to a Bell Model 206A. 

 

50 You will remember this nondimensional form from Eqs. (1.6), (1.7), and (1.8) on page 8. Two coefficients 

were defined that remove—to a first-order approximation—effects of wide ranges in helicopter size and 

configuration. The nondimensional, coefficient forms for rotor thrust, Eq. (1.6), and power, Eq. (1.7), can be 

used for a complete helicopter by simply changing the subscripts. That is, 

Re qd.

Reqd.

TW PP 22 3 2

tt t t

TW P 550 ESHP

C C and C C

AV AV AV AV

×

= →= = → =

ρρ ρ ρ
2.3 HOVER PERFORMANCE 

135 

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

12 14 16 18 20 22 24

Hover 

Ceiling 

(Pressure 

Altitude in 

feet)

Gross Weight (in 1,000s of pounds)

UH-60A

Engine IRP

Limit On A

Std. Day

Engine IRP

Limit On A

35o

 C Day

UH-60A

YUH-60A

UH-60A

Transmission

Limit On A

Std. Day

Fig. 2-48. The final output of the engineering analysis of Fig. 2-47 is found in this 

more common format.

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

10,000

0 2 4 6 8 10 12

Hover 

Ceiling

(Pressure 

altitude in 

feet on a 

35o

 C day 

with 

engines at 

IRP)

Useful Load (in 1,000s of pounds)

UH-60A

YUH-60A

1,600 More 

Pounds

2,700 Feet 

Higher

Fig. 2-49. The UH-60A was a major improvement on the YUH-60A when compared 

on a useful-load basis. 
2.3 HOVER PERFORMANCE 

136 

500 5,000 50,000

0

4,000

8,000

12,000

16,000

20,000

100 1,000 10,000 100,000

Useful Load (lbs)

Hover 

Ceiling 

(Pressure 

altitude in 

feet on a 

standard 

day)

The

Worldwide 

Capability

as of

1994/1995

1942 USA

Sikorsky R-4B

1940 German

Focke Fa-223

1968 Russian

Mil-12

1977 Russian

Mil-26

1979 USA

Boeing CH-47D

1980 USA

Sikorsky CH-53E

1990 USA

Kaman SH-2G

1936 Germany

Focke Fa-61

1980 USA

UH-60A

Fig. 2-50. The industry has continually expanded the hover ceiling and useful load 

capabilities of helicopters. (Note: UH-60A at 11,200 feet with PMGW = 16,260 

and WE = 10,465.) 

 The question of how much helicopter performance has improved is continually asked. 

In overall product terms, I believe you should be impressed, but an assessment of Army 

helicopter performance trends [169] gave a somewhat mixed opinion. Richard Lewis,51 the 

author of this April 1972 review, concluded that 

“...the nondimensional performance of Army rotorcraft is essentially independent of aircraft 

configuration. This is not meant to imply that progress is lacking. It should be kept in mind 

that the data represent only the current generation of Army rotorcraft and they are close 

contemporaries. It does suggest that drastic variations in demonstrated performance levels 

are not easily achieved and warrant examination. 

It is hoped that the data presented herein will be of use to rotorcraft designers and evaluators. 

The understanding that performance trends are closely grouped will permit attention to be 

focused toward important technical areas such as noise, directional control and vibration, 

where breakthroughs in rotorcraft design are both necessary and desirable.” 

 

51 Dick was then Deputy Director of Flight Test for the U. S. Army Aviation Systems Test Activity at Edwards 

Air Force Base in California. When he wrote his paper, he and his group had a wealth of flight test data from 

every helicopter that had passed through. He was able to support his conclusions using data from just six 

helicopters. 
2.3 HOVER PERFORMANCE 

137 

 Fig. 2-51 provides a somewhat different conclusion 20 years later. This hover-enginehorsepower-required versus takeoff-weight survey (but in the classical CP versus CW

coefficient form) includes 54 different flight tests [108, 109, 115, 116, 118, 121, 124, 125, 

133, 170-188, 190-206] and [207-210]. Every CP – CW data point for each test is included in 

Fig. 2-51. Thus, “data scatter” in both configuration and experiment is apparent. A ±12 

percent spread from the semiempirical result of 

(2.41) Reqd.

3/2 C 0.0157C 1.045C P WW = +

captures hover-power-required technology for today’s helicopter types. 

 Equation (2.41) is handy and rather easy to derive when you start with the 

nondimensional form of the basics. Equation (2.38), in nondimensional form, becomes 

(2.42) i 3 2 do

P T

k C C C

2 8

σ

= + . 

Suppose now that the airfoil drag coefficient (Cdo) is calculated as 

(2.43) ( )

do T TT do

do do

Airfoil

C C 6C 6C C 6 C C where C so that C

C C LD = = == σ σσ

 

 

. 

Then it follows that 

(2.44) ( ) ( )

ii T 3 2 do 3 2 i 3 2

P T T T T

Airfoil Airfoil

kk C k C 6 6 CC C CC

2 2 8 8 LD 8LD 2

σ σ  

= += + = +  

σ    

. 

A rational value for the airfoil lift-to-drag ratio of around 50, and a just as rational value for 

the induced-power correction factor (ki) of 1.48, leads to Eq. (2.41). Using engine power and 

weight for the coefficients completes the insight. The implication of this result is that the 

equation describes an envelope of best performance for any typical modern helicopter. In the 

ideal case, ki = 1.0, which shows that improvement is possible! 

 There is another way to compare optimum performance of several helicopters. This 

frequently employed view is shown in Fig. 2-52 and uses the system aircraft hover Figure of 

Merit (FM) as the measure of optimum. You will recall that this parameter is defined as the 

ratio of ideal power to actual power. In aircraft terms, this amounts to 

(2.45) 

3 2

W

SHP

1 C

2 A/C Hover Figure of Merit Actual C = . 

The conventional approach to displaying aircraft FM is versus the weight coefficient (CW). 

This choice for the abscissa is not used in Fig. 2-52 because the many helicopters shown all 

have a considerable difference in solidity (σ). The basis for using CW

3/2 divided by solidity is 

arrived at as follows: 
2.3 HOVER PERFORMANCE 

138 

(2.46) 

3 2 3 2

W W

do i 3 2 SHP do

W 3 2 i

W

1 1 C C

2 2 1 A/C Hover Figure of Merit Actual C C k 2 C C k 8 2 8 C

== = σ   σ +   +

 

. 

Because the group of helicopters use nominally the same airfoil for the main rotor blades (i.e., 

Cdo is about 0.01), the primary variable is CW

3/2/σ. This keeps all helicopters in the same 

range on the abscissa. Furthermore, Fig. 2-52 shows that CW

3/2/σ must approach 0.01 to 

maximize FM. The limit is, of course, that CW /σ must not be too high or the airfoil average 

lift coefficient [per Eq. (2.43)] giving maximum airfoil lift-to-drag ratio will be exceeded. 

Equation (2.46) obviously says the maximum FM cannot exceed 1/ki , which occurs if it were 

possible to have a zero airfoil drag coefficient. The heavy, solid line on Fig. 2-52 using 

Eq. (2.46) was computed with Cdo = 0.01 and ki = 1.48, which places the line in the 

semiempirical category. Clearly, a much more detailed engineering calculation is required to 

explain the spread in FM for the 54 examples. 

 A more detailed engineering estimate of engine horsepower required to hover takes 

the form 

(2.47) Main Rotor(s) TailRotor(s)

Accessory

Main Rotor(s) TailRotor(s)

RHP RHP

ESHP SHP = ++

η η . 

In this approach, the engine delivers power to the main rotor (RHPmr) but a transmission 

efficiency (η), on the order of 0.97, is charged. This is true if the helicopter has a tail rotor as 

well. Of course the engine also delivers power to run accessories such as the electrical and 

hydraulic subsystems as well. All computations are made for the helicopter at a given weight, 

which means that rotor thrust is greater than the weight. This helps to accounted for rotor 

downwash on the helicopter fuselage and appendages. With Eq. (2.47) in mind, consider the 

amount of engine power required by the total helicopter and then by the tail rotor in the single 

rotor configuration for four helicopters evaluated in 1976. 

2.3.3 UTTAS and AAH Hover Performance 

 Perhaps the most extraordinary hover performance experimental results I ever 

encountered came when the competitive flight test data for the utility tactical transport aircraft 

system (UTTAS) and advanced attack helicopter (AAH) became available. The Sikorsky 

YUH-60A [123] competed with the Boeing-Vertol YUH-61[124] for the utility helicopter, and 

the Bell YAH-63A [125] competed with the Hughes YAH-64A [126]. The experimental 

engine power required to hover as a function of weight for the four configurations is shown in 

Fig. 2-53. The data, in aircraft coefficient form, shows that the two utility helicopters are 

nearly indistinguishable from Eq. (2.41) in nondimensional performance. What deviates are 

the two attack helicopters; the YAH-63A being on the low side of Eq. (2.41) by about 

–5 percent and the YAH-64A being on the high side by +5 percent. 
2.3 HOVER PERFORMANCE 

139 

0

20

40

60

80

100

120

140

0 20 40 60 80 100 120

52 Helicopters Total

46 Single Rotor

 4 Tandem

 1 Synchropter

 1 Coaxial

XH-59A(ABC)

Coaxial

Engine 

Shaft 

Power 

Required 

Coeff.

 CP × 105

Weight Coeff. CW × 104

Fig. 2-51. The industry has established conventional helicopter hover power required to 

within ±12 percent (single rotors are open circles; tandems are black squares). 

0.4

0.5

0.6

0.7

0 0.002 0.004 0.006 0.008 0.01 0.012

Figure

Of

Merit

Coaxial

ABC (XH-59A)

Compressiblity

Effect On HH-53C SH-2F

Single

(ServoTabs)

HH-43B

Synchropter

(Weight Coeff.)3/2/Solidity

Fig. 2-52. Modern helicopter aircraft FM is far from ideal. 
2.3 HOVER PERFORMANCE 

140 

 The primary differences between the four configurations are due to tail rotor 

horsepower required and the secondary differences are in main rotor solidity. The test reports 

for the four helicopters included tail rotor power measurements. Thus, measured tail rotor 

power can be subtracted from the measured total power illustrated by Fig. 2-53, and this leads 

to Fig. 2-54, which was observed in 1987[211]. 

50

60

70

80

90

100

110

50 55 60 65 70 75 80 85 90 95

YUH-60A

YUH-61A

YAH-63A

YAH-64A

Engine Eq. 2.41

Shaft 

Power 

Required 

Coeff.

 CP × 105

Weight Coeff. CW × 

Fig. 2-53. All four helicopter hover performance results were extraordinarily close. 

Fig. 2-54. Without tail rotor power, all four helicopters had the same CP–CW

performance when solidity differences were accounted for [211]. 
2.3 HOVER PERFORMANCE 

141 

 I find it quite amazing that both UTTAS and AAH helicopters could have their HOGE 

performance results estimated from such a simple engineering approximation as 

(2.48) 3 2

P W

1.254 C 0.001261 C

2

= σ+ . 

The comparative tail rotor performance for these four helicopters is also interesting. 

2.3.4 Tail Rotor Performance in Hover 

 As a reminder, the evolution of the helicopter up until Igor Sikorsky’s breakthrough in 

the early 1940s was dominated by inventors who used large main rotors in pairs. These early 

twin-rotor helicopters arranged the rotors in coaxial, side-by-side, tandem, and quadrotor 

configurations. The early inventors sought to achieve equilibrium with the engine input power 

and torque with both rotors lifting—in the belief that this was the most efficient helicopter 

that could be achieved. In fact, the side-by-side arrangement was used by Henrich Focke 

when he stunned the world in 1936 with the first truly successful helicopter, his F. 61. Focke 

went into production with his FA 223. A countryman, Anton Flettner, followed shortly with 

his equally successful FL 282. Flettner’s design intermeshed the two main rotors in the 

fashion of an eggbeater, and this became the synchropter configuration. 

 It was in defense of this progress made in Germany at the start of World War II that 

Sikorsky developed his now famous VS-300. He used a large, single main rotor for lifting and 

a much smaller rotor to produce an anti-torque force. The tail rotor, as originally developed, 

contributed little lift; it served only to provide a basic anti-torque force and a measure of 

directional control. This comparatively small rotor was placed at the end of a tail boom, and 

its thrust was directed to the side as Fig. 2-55 shows. 

 Surprisingly, in the configuration Sikorsky pioneered, the distance aft (ltr)—measured 

from the main rotor shaft—at which the tail rotor thrust (i.e., Ttr or the anti-torque force) acts 

is not a major factor in the tail rotor power required to hover. This is because the moment arm 

is conventionally about equal to the main rotor radius (R). That is, ltr is approximately equal to 

R. With this rough approximation, the simplest aerodynamic theory shows that 

Fig. 2-55. Single rotor helicopter torque equilibrium. 

Main Rotor 

Plane 

Tail Rotor 

Plane 

Tail Boom 

Tail Rotor Thrust 

Moment (antitorque force)

Arm

Input Torque

to 

Main Rotor 
2.3 HOVER PERFORMANCE 

142 

(2.49) 

mr

mr

mr

mr mr mr mr mr

tr

tr mr t t

3/2 3/2

tr mr

tr

tr tr t

P Q main-rotor torque

Q Q P P 550HP T tail-rotor thrust

l RR V V

T 1 550HP HP tail-rotor horsepower 550 2 A 550 2 A V

= = Ω

= ≈ = == = Ω

  ≈ =   = ρ ρ  

. 

Thus, the tail rotor horsepower (HPtr) is more influenced by its own size (Atr), the main rotor 

horsepower (HPmr), and the main rotor tip speed (Vt). 

 Completing the comparison of the four UTTAS/AAH configurations is quite 

informative. Consider the hover out of ground effect (HOGE) situation at the U.S. Army hotday design condition where the pressure altitude is 4,000 feet and the outside air temperature 

is 95o

 F. At this ambient air condition, the density is 0.00192 slugs per cubic foot. Suppose 

you accept that the main rotor horsepower can be calculated from Eq. (2.48). Ignore 

transmission efficiency and accessory power for this example. Then, with the data from 

Table 2-10, a new table of results, Table 2-11, can be constructed. The Army’s test reports 

[123-126] each give the gross weight that can be hovered out of ground effect on this hot-day 

condition. These weights are tabulated across the first row of Table 2-11. Using these weights, 

the main rotor “thrust” coefficient is calculated, based on gross weight from 

(2.50) W 2

mr t mr

GW C

A V−

= ρ

where (ρ) is the air density, (Amr = πR2

) is the main rotor disc area, and (R) is the main rotor 

radius. The main rotor tip speed (Vt) is the reference velocity. You should be aware that the 

true main rotor thrust is generally 2 to 5 percent greater than the gross weight because the 

rotor downwash creates an airframe vertical drag. 

 Given the weight coefficient, I have obtained the total engine power coefficient (CPeng) 

for each configuration from the flight test data given in each report. Then, for the sake of 

completeness, the engine horsepower required to hover is calculated with 

(2.51) 3

mr t mr

Peng

A V SHP C

550

ρ − = . 

The main rotor power coefficient (CPmr) has been calculated in accordance with Eq. (2.48) and 

recorded on line 5 of Table 2-11. This leads to the main rotor horsepower (HPmr) and the 

main rotor torque—which the tail rotor thrust (Ttr), acting at the moment arm (ltr), must 

counterbalance—being calculated by 

(2.52) 

3

mr t mr mr

mr Pmr mr tr tr

t mr mr

A V 550HP HP C and therefore Q T l 550 V R

−

−

ρ = == . 
2.3 HOVER PERFORMANCE 

143 

Table 2-10. UTTAS and AAH Parameters 

Parameter YUH-60A YUH-61A YAH-63A YAH-64A 

Primary Mission GW (lb) 16,853 16,410 16,054 14,242 

Main Rotor 

Diameter (ft) 53.67 49 51.5 48 

Design RPM 263 286 276 289 

Tip Speed (fps) 739 734 744 726 

Blade No. 4 4 2 4 

Chord (ft) 1.73 1.917 3.55 1.75 

Solidity 0.0821 0.0996 0.0878 0.092 

Disc Area (ft2) 2,262.3 1,885.7 2,083.1 1,809.6 

Tail Rotor 

Diameter (ft) 11 10.167 9.5 8.33 

Design RPM 1,214 1,297 1,446 1,411 

Tip Speed (fps) 699.2 688 719 615 

Blade No. 4 4 2 4 

Chord at 0.75 R (ft) 0.81 0.7326 1.4167 0.8333 

Taper Ratio 1.0 0.6966 1.0 1.0 

Solidity 0.188 0.1832 0.1899 0.2475 

Disc Area (ft2) 95.03 81.18 70.88 54.50 

Moment Arm (ft) 32.567 29.917 30.82 28.49 

This gives the tail rotor thrust (Ttr = Qmr/ltr) and, therefore, the tail rotor thrust coefficient 

(CTtr) simply as 

(2.53) tr

Ttr 2

tr t tr

T C

A V−

= ρ . 

Of course I have taken liberty in calling the anti-torque force the tail rotor thrust. In the single 

rotor configuration, the interference between the tail rotor and the airframe’s vertical fin, 

body, and other appendages can be rather large [212]. This means that the actual tail rotor 

thrust could easily be 10 to 15 percent higher than the required anti-torque force. 

 The tail rotor power coefficient (CPtr), given the tail rotor thrust coefficient, has been 

obtained from the flight test data for each configuration. This power coefficient is recorded on 

line 10, Table 2-11. This gives the tail rotor horsepower (HPtr) calculated from 

(2.54) 3

tr t tr

tr Ptr

A V HP C

550

ρ − = . 

 The next to the last line on Table 2-11, the ratio of tail rotor horsepower to main rotor 

horsepower, shows the wide variation that can occur between design approaches. The last line 

of Table 2-11 shows the simple sum of main- and tail-rotor horsepower, which is less than the 

total engine shaft horsepower. This indicates that transmission efficiencies and accessory 

power have not been accounted for. However, I must warn you that, because of experimental 

accuracy and data scatter, the end results might easily have gone 100 horsepower the other 

way [213]. 
2.3 HOVER PERFORMANCE 

144 

Table 2-11. UTTAS and AAH Comparison 

Parameter YUH-60A YUH-61A YAH-63A YAH-64A 

GW hovered at 4,000 ft, 95 °F 16,193 15,130 16,500 15,000 

CW 0.006825 0.007755 0.007451 0.008189 

CPeng from test report 0.000686 0.000828 0.000761 0.000941 

Total SHP 2,187 2,156 2,280 2,275 

CPmr 0.000603 0.000731 0.000681 0.000773 

HPmr 1,924 1,904 2,040 1,869 

Qmr 38,423 34,948 38,833 33,987 

Ttr 1,180 1,168 1,260 1,193 

CTtr 0.01322 0.01583 0.01672 0.03013 

CPtr from test report 0.00196 0.00225 0.00177 0.00226 

HPtr 222 208 180 100 

HPtr/HPmr 0.116 0.109 0.088 0.054 

HPmr + HPtr 2,146 2,112 2,220 1,969 

 A tail rotor has its own CP versus CT behavior in hover. This data, for the UTTAS and 

AAH examples under discussion, is shown in Fig. 2-56. This performance data is for HOGE 

(specifically at 100-feet wheels-to-ground distance). Tail rotor performance when the aircraft 

is hovering in ground effect (HIGE) varies somewhat from performance in HOGE. The line 

shown on this figure is given by 

(2.55) 3 2

Ptr Ttr

1.49 C 0.001261 C

2

= σ+ . 

 As the single main rotor plus tail rotor became the dominant configuration for most 

applications, more important issues of tail rotor placement and design became clearer. For 

example, roll angle trim of the helicopter was now tied to the tail rotor thrust. The main rotor 

thrust was tilted in the opposite lateral direction to keep the helicopter from drifting sideways. 

Even so, many early, small, single rotor helicopters hovered with “one wing low.” Tail rotor 

placement higher up above the boom lessened this adverse roll-trim characteristic because the 

anti-torque thrust acted closer to the main rotor plane. This placement added another gearbox 

in the tail rotor drivetrain of most single rotor helicopters. 

 A most important factor in the design and operation of tail rotors for the single-mainrotor helicopter has been safety. Unfortunately, the tail rotor, particularly on smaller 

helicopters operating on or near the ground, is quite accessible. People have inadvertently 

walked into it. Fortunately, special illuminating blade paint schemes, guard rings, flight and 

ground crew alertness, and educated awareness by passengers has significantly reduced 

injuries to people from tail rotors. 
2.3 HOVER PERFORMANCE 

145 

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

YUH-60A

YUH-61A

YAH-63A

YAH-64A

Eq. 2.55

Tail 

Rotor 

Power 

Coeff.

Tail Rotor Net Force Coeff.

Fig. 2-56. UTTAS and AAH tail rotor performance in HOGE.

 Pioneering study of tail rotors came with the analytical work of Ken Amer and 

Al Gessow in 1953 [214]. Toward the end of the 1960s, enough field experience had been 

gained with the single rotor helicopter to appreciate the very complex aerodynamic 

environment in which the tail rotor operates. Downwash from the main rotor, turbulent flow 

from the upstream fuselage, and flying in quartering winds all took on special importance to 

the designer and operator. The decades of the 1970s and 1980s saw intense engineering 

theoretical analysis, wind tunnel experiments, and flight testing [212, 214-232]. This research 

was rewarding. It uncovered (a) recommendations for tail rotor rotational direction, 

(b) advantages of the pulling tail rotor over the pushing placement, (c) adverse effects of the 

vertical fin, (d) ground effects, (e) losses in tail rotor effectiveness due to vortex ring flight 

conditions, and (f) regions of flight where complete loss of directional control could, and did, 

occur. This accumulating knowledge led to “over designing” newer tail rotors in relation to 

earlier design standards. 

 The last decade has seen the introduction of bearingless tail rotors through the use of 

composite materials [225]. These most modern tail rotors have helped to hold down 

manufacturing costs and are virtually maintenance free. The propeller-like noise of older-type 

tail rotors can now be significantly reduced by a combination of more blades and lower 

rotational speeds. Coupled with advanced flight control systems, the modern tail rotor reduces 

pilot workload in all but the most demanding flight conditions. Finally, canting the thrust axis 

of the tail rotor slightly upwards lets this primary anti-torque device add lift equal to its own 

weight. 
2.3 HOVER PERFORMANCE 

146 

2.3.5 Other Anti-torque Devices 

 The propeller-like tail rotor is not the only way that modern, single rotor helicopters 

achieve yawing moment equilibrium in hover. Aerospatiale (the French helicopter 

manufacturer that merged with Germany’s Messerschmitt-Bölkow-Blohm (MBB) in January 

1992 to form Eurocopter) uses a ducted propeller or ducted fan called a Fenestron (Fig. 2-57) 

on several of its smaller helicopters. McDonnell Douglas, before merging with Boeing in the 

U.S. in August 1997, developed a nozzle exhaust called NOTAR (Fig. 2-58). The jet velocity 

of the NOTOR is created by a ducted fan located near the engine compartment. The fan air is 

ducted through the tail boom to the swiveling nozzle. A relatively small portion of the ductedfan flow is used for boundary layer control (BLC) along the tail boom. In conjunction with the 

main rotor downwash over the tail boom, the BLC forces the tail boom to develop a lateral 

side force, which becomes added anti-torque. 

 It is worth noting that the NOTAR concept is not new. The concept was first tested on 

the Nord 1700 under the direction of André Bruel, with first flight in September 1948 [233]. A 

private company, Société Nationale de Constructions Aéronautiques du Nord, was established 

to develop the Nord 1700. Bruel patented the anti-torque by nozzle concept. 

Fig. 2-57. The SA 365 N-1 Dauphin 2 uses a Fenestron ducted-fan anti-torque device 

(photo from author’s collection). 
2.3 HOVER PERFORMANCE 

147 

Fig. 2-58. The MD Explorer uses a NOTAR nozzle anti-torque device 

(drawing from author’s collection). 

 The relationship between anti-torque force and the horsepower required to obtain this 

force is quite simple. The ideal horsepower (ideal HP) depends on the thrust (T) desired, the 

ambient air density, and the area of the jet exhaust. From simple momentum theory, the 

system thrust and ideal horsepower required are given by 

(2.56) 3

2 exit exit

exit exit

A V T A V and ideal HP

2 550

ρ =ρ =

×

and, therefore, the fundamental relationship for each device is that 

(2.57) 

3 2

exit

T ideal HP

550 4 A

= ρ . 

 Now consider the three ways (so far) that an anti-torque force is produced with 

modern helicopters (see Fig. 2-59). For a tail rotor configured as an unducted fan, the air 

passing through the rotor quickly contracts to a column of air having an area equal to one-half 

of the rotor area. That is, Aexit = 1⁄2 Atr. For a well-designed ducted fan, which the Fenestron 

closely approximates, the air passing through the fan does not contract downstream. Thus, for 

the Fenestron ducted fan, the exit area and the fan area are equal (Aexit = Afan). The total thrust 

is the sum of the fan’s thrust and the duct’s lift, which comes primarily from the lip of the 

duct. In the ideal ducted-fan system, one-half of the total thrust comes from the fan and onehalf comes from the duct. For the NOTAR anti-torque device, behaving as a nozzle, the exit 

area can be as large as the designer can achieve, given the configuration constraints. At 
2.3 HOVER PERFORMANCE 

148 

present, the NOTAR exit area is less than the fan area. That is, the ratio of nozzle area to fan 

area is less than one (An < Afan). These three anti-torque devices each have a different ideal 

horsepower equation. Following Eq. (2.57), you immediately have 

(2.58) 

3 2

tr

tr

T ideal HP for the unducted tail rotor,

550 2 A

= ρ

(2.59) 

3 2

df

f

T ideal HP for the ducted tail rotor,

550 4 A

= ρ

 and 

(2.60) 

3 2

n

n

T ideal HP for the nozzle

550 4 A

= ρ . 

 The primary advantage of the Fenestron and the NOTAR is, in my opinion, safety. 

Walking into either and getting hurt is a remote possibility. A person is met with just a blast of 

air with the NOTAR. Both configurations offer considerable protection should the pilot 

inadvertently swing the tail into a post or other grounded object. However, there is a 

perceivable performance difference between the three anti-torque devices. To begin with, 

ducting a free tail rotor (a shrouded tail rotor, if you prefer) can offer a diameter reduction. 

Suppose a comparison is made at equal anti-torque force (i.e., thrust). Then thrust from 

Eq. (2.58) can be substituted into Eq. (2.59), and a little arithmetic gives 

(2.61) ( ) tr

df tr

f

D ideal HP ideal HP

2D = . 

The diameter of the ducted fan (Df) can be one-half of the diameter of the tail rotor (Dtr) and 

have equal ideal horsepower at equal thrust. 

 The static performance comparison between two tail rotors and an advanced Fenestron 

with stators is quite interesting and illustrates the effect of both diameter and solidity 

differences. Note from Table 2-12 that I have selected a comparison where the Fenestron 

diameter is about one-half of the diameter of the two tail rotors. 

Fig. 2-59. Three ways of producing an anti-torque force.
2.3 HOVER PERFORMANCE 

149 

 The power coefficient (CP) versus thrust coefficient (CT) for the two tail rotors is 

displayed in Fig. 2-60. The Fenestron’s performance is shown separately in Fig. 2-61 because 

of the large-scale difference. Keep in mind that identical power and thrust coefficients are 

used for the three anti-torque devices. That is, 

(2.62) ( ) ( ) T P 22 23

t t

T 550SHP C and C

R V R V = =ρ π ρ π

Table 2-12. Anti-torque Device Comparison 

Parameter Bell Westland Aerospatiale 

Helicopter Early Model 222 Early Lynx SA 365N-1 

Reference [168] [226] [227] 

Diameter (ft) 6.5 6.89 3.58 

Blades 2 4 11 

Chord (ft) 0.8333 0.5906 0.2525 

Reference Solidity (bc/πR) 0.1632 0.2183 0.4939 

Stators No No Yes 

Root Cutout (r/R) 0.1 0.384 0.333 

RPM 1,881 1,824 4,009 

Tip Speed (fps) 640 658 751 

Reference Disc Area (ft2) 33.183 37.282 10.660 

0

0.001

0.002

0.003

0.004

0.005

0.006

-0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02 0.025 0.03

Tail 

Rotor 

Power 

Coeff.

Tail Rotor Thrust Coeff.

Bell Model 222

Westland Lynx

Fig. 2-60. Isolated performance of two tail rotors.
2.3 HOVER PERFORMANCE 

150 

0

0.01

0.02

0.03

0.04

0.05

0.06

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18

Fenestron 

Power 

Coeff.

Eq. 2.63

Fenestron Thrust Coeff.

Fig. 2-61. Isolated Fenestron performance. 

where the thrust (T) is the system total thrust, which, for the Fenestron, includes both the fan 

thrust and the duct lift. The shaft horsepower (SHP) is, of course, the power required by the 

device, whether tail rotor or Fenestron. 

 The isolated Fenestron performance shown in Fig. 2-61 is accompanied by a 

semiempirical curve-fit equation given by 

(2.63) ( )

3 2

P T 2 3

t

550SHP C 0.001375 1.31C

R V

= = σ+

ρ π . 

The Westland Lynx isolated tail rotor performance, Fig. 2-60, in the working thrust range is 

approximated by 

(2.64) ( )

3 2

P T 2 3

t

550SHP C 0.001875 1.60C

R V

= = σ+

ρ π . 

The Bell 222 isolated tail rotor performance, Fig. 2-60, in the working thrust range is 

approximated by 

(2.65) ( )

3 2

P T 2 3

t

550SHP C 0.001 1.45C

R V

= = σ+

ρ π . 
2.3 HOVER PERFORMANCE 

151 

0

100

200

300

400

500

600

700

800

900

1,000

0 500 1,000 1,500 2,000 2,500

Fenestron, Diameter = 3.58 ft, Tip Speed = 751 fps

Bell 222, Diameter = 6.5 ft, Tip Speed = 640 fps

Westland Lynx, Diameter = 6.89 ft, Tip Speed = 658 fps

Shaft

Horsepower 

Required 

by 

Anti-torque 

Device

Anti-torque Force Produced by Device (lb)

Fig. 2-62. Isolated anti-torque device performance at sea level, standard day. 

 The preceding three approximate equations really do little to compare the three 

configurations. A more direct view is simply horsepower versus thrust as shown in Fig. 2-62. 

 In the NOTAR case, the logic is the same as for a ducted fan. The ducted fan 

producing the nozzle flow is small compared to an unducted tail rotor. The small size allows 

the fan to be installed before the tail boom, but aft of the engine compartment, as shown 

schematically in Fig. 2-58. 

2.3.6 Bell Model 222 and Aerospatiale Dauphin 2 Hover Performance 

 Having compared the Aerospatiale Fenestron ducted fan and the Bell Model 222 tail 

rotor, it is worth a moment to compare the complete helicopter performance of the two aircraft 

[168, 170]. First, some background. In 1979 the U.S. Coast Guard completed a competition 

for a new search and rescue helicopter. They selected the Aerospatiale SA 365 N-1 Dauphin 2 

over the Bell Model 222. The contract called for delivery of 90 Dauphins. After some 

relatively minor setbacks caused primarily by trouble with the Lycoming LTS 101 engines, 

which caused a switch to Turbomecca ARRIEL 1C1 engines, the Dauphin performed well in 

the field. Bell continued offering its Model 222 (with the Lycoming LTS 101 engines) 

commercially, but the engine troubles persisted and initial customers were discouraged. 
2.3 HOVER PERFORMANCE 

152 

30

35

40

45

50

55

60

65

70

75

40 45 50 55 60 65 70

Aerospatiale Dauphin 2

Bell Model 222

Eq. 2.41

Engine 

Shaft 

Power 

Required 

Coeff.

 CP × 105

Weight Coeff. CW × 104

Fig. 2-63. Performance difference primarily due to anti-torque device. 

 Regarding comparative hover performance, the nondimensional performance in 

coefficient form is shown in Fig. 2-63. The difference between the two machines is due 

almost entirely to the anti-torque horsepower difference given in Fig. 2-62. That is, the 

roughly 40-horsepower difference between the Fenestron and the Bell Model 222 tail rotors 

shown in Fig. 2-62 equates to a 0.0025 increment in the Dauphin CP shown in Fig. 2-63. 

2.3.7 Blade Element Momentum Theory Revisited 

 The rotorcraft industry has used blade element momentum theory to predict power 

required by hovering helicopter rotors for nearly a century. Despite its shortcomings, the 

theory has served the industry quite well. Recent decades have seen an increase in the use of 

powerful computers to obtain greater accuracy in predicting airflow through and about the 

rotor (or rotors). This improved flow-field calculation, particularly of induced velocity, has 

led to more accurate prediction of power required to produce a given thrust. However, the 

knowledge to be gained from blade element momentum theory and applied to these advancing 

methods is not yet exhausted. 
2.3 HOVER PERFORMANCE 

153 

 One very specific use of blade element momentum theory is identification of 

similarity parameters for thrust, power, and collective pitch for both single and multirotor 

configurations. The theory has, of course, been most frequently used to predict performance 

of a specific configuration, but in December 1937 rotary wing aerodynamicists were reminded 

of just how helpful the theory could be in its more nondimensional form. The purpose of this 

portion of Volume II is to bring attention to that fact again. 

 The derivation and use of blade element momentum theory are described in many 

well-known books [85, 234-242]. These works do not, however, emphasize a nondimensional 

form of the theory that Montgomery Knight and Ralph Hefner used with considerable success 

in 1937. Knight and Hefner’s work was published in NACA TN No. 626 and entitled Static 

Thrust Analysis of the Lifting Airscrew [243]. In this report they used their form of the blade 

element momentum theory to eliminate solidity as an independent parameter. Experimental 

results supported their view. They continued to apply their understanding to the in-groundeffect performance problem and published NACA TN No. 835 in December of 1941 [244]. 

This later report, entitled Analysis of Ground Effect on the Lifting Airscrew, further 

substantiated their interpretation and use of blade element momentum theory. Today, the 

nearly complete development of free-wake hover performance theory provides an opportunity 

to reaffirm Knight and Hefner’s approach, and extend their results beyond rotor performance 

characteristics to the spanwise distribution of key aerodynamic parameters [245]. 

 The basis of blade element momentum theory (see chapter 4 of reference [234] for 

example) is formed by equating an element of thrust (dT) calculated by momentum theory to 

the same element of thrust obtained by blade element theory. In hover, this amounts to 

(2.66) ( )

2 2 1 2

(r) 2 r l(r) dT 4 v rdr bc r C dr = πρ = ρ Ω . 

This fundamental assumption immediately simplifies to 

(2.67) 

2

(r)

l(r) 2

(r)

8 v

C

bc r

π = Ω . 

 When (a) the spanwise blade station is nondimensionalized using r = R x; (b) a local 

blade element solidity is defined as 2

(x) (x) σ= π bcR R ; and (c) the tip speed, V R t = Ω , is 

taken as a reference velocity, the concise form of blade element momentum theory becomes 

(2.68) 

2

(x) (x)

l(x) (x) 2

(x) t

8 1 v bc R

C where

V x R

    = σ     = σ π     . 

To obtain an explicit expression for spanwise induced velocity scaled to tip speed, the 

classical assumption that 

(2.69) (x)

l(x) (x) (x) (x) (x) (x)

t

v

Ca a a

xV

  = α ≈ θ −φ ≈ θ −        

is used. Then the resulting quadratic from equating Eqs. (2.68) and (2.69) is solved to give 
2.3 HOVER PERFORMANCE 

154 

(2.70) (x) (x) (x)

t (x)

v a 16

12 1

V 16 a

  σ θ  

=+ −       σ    

. 

 The beginnings of Knight and Hefner’s view of blade element momentum theory are 

apparent in Eq. (2.70). The key is to see the appearance of (x) a 16 σ , its reciprocal, or this 

parameter, raised to some power. Therefore, the foundation for defining several useful 

similarity parameters is established by rewriting the induced velocity of Eq. (2.70) as 

(2.71) (x) (x)

(x) t (x)

16 v 16

1 2x 1 .

aV a

    θ

=+ −    

σ σ      

The first similarity parameter to emerge from Eq. (2.71) is scaling of the blade element pitch 

angle by airfoil lift-curve slope and local solidity. That is, 

(2.72) (x)

(x)

(x)

16

a

θ

Θ ≡

σ . 

Both Eqs. (2.71) and (2.72), when introduced into Eq. (2.69), redefine the blade element angle 

of attack and then the blade element lift coefficient, so that the second key similarity 

parameter is 

(2.73) l(x)

2 (x) (x)

(x)

16C 1 1 1 2x

a xx

=Θ + − + Θ

σ . 

This equation forms the basis of Knight and Hefner’s approach, and their view of rotor 

performance similarity parameters to both thrust and power coefficients. They chose constant 

chord, untwisted blades to show how solidity could be removed as an independent parameter 

from both performance coefficients. 

 Knight and Hefner approached the thrust problem first by reformatting blade element 

thrust so that Eq. (2.73) could be used. In modern notation, they preceded as follows: 

(2.74) ( )( ) ( )( )

2

1 1 2 2 l

2 2 l t 2

a 16C dT r bcdr C xV bcRdx

16 a

σ    = ρΩ = ρ       σ 

. 

Because 2 bcR R =π σ for a constant-chord blade, they could factor out solidity and disc area 

prior to spanwise integration so that 

(2.75) ( )( ) c

2 2 B

1 2 2 l 2

2 t 2

x

a 16C T V R x dx

16 a

σ   = ρπ     σ





 . 

From this point they saw that the thrust problem, using Eq. (2.73), would lead to 

(2.76) ( ) c

c

B

B T l 2 2

2 2 2 x x

32C 16C x dx x x x 1 2x dx

a a

  = = Θ +− + Θ   σ σ 





  . 
2.3 HOVER PERFORMANCE 

155 

 Knight and Hefner52 did not use a tip loss factor (i.e., B = 1) and also ignored loss of 

lift at the blade root (i.e., xc = 0). Another possible conclusion can be drawn, however. For 

example, Gessow and Myers [234] note that Sissingh (who referenced Prandtl) suggested that 

the tip loss factor should vary with thrust coefficient as 

(2.77) 

1/2

T T

2

2C 2 C B1 1

b AR

  =− =−   π σ  . 

There have been many discussions, some quite heated, as to what semiempirical factors such 

as tip loss, root cutout, and airfoil aerodynamic properties are most generally applicable when 

using blade element momentum theory to predict performance of a new helicopter product. So 

far, the rotary wing aerodynamic community has never guessed the right answer. One thing 

does seem clear, however. The tip loss factor depends on 2 C T σ , which favors Knight and 

Hefner’s similarity parameters, but the tip loss factor also depends on the blade-aspect ratio 

(AR). In their work, Knight and Hefner only varied the number of blades at equal bladeaspect ratio. While the influence of blade-aspect ratio is not large, some experimental data and 

a modern theory [245] will show that two wide-chord blades have slightly worse performance 

than four narrow-chord blades—at equal solidity. 

 To proceed then, the integrated result for untapered, untwisted blades is 

(2.78) ( ) ( ) ( ) ( ) 22 33 5 5 3 3

c c T

22 2 2

32C Bx Bx FH FH

a 2 3 10 6

− −Θ − −

=+ −+

σ ΘΘ

where, F 1 2B and H 1 2x ≡+Θ ≡+ Θc and, as a reminder, 16 . a

θ Θ =

σ

 Knight and Hefner, rather than see thrust versus collective pitch as CΤ = f (θ,σ), sought 

confirmation that ( ) 2 C f T σ = θσ through experiment. They tested two-, three-, four-, and fivebladed rotor configurations. All blades were manufactured as identically as possible. Each 

 

52 The view suggested by Knight and Hefner can also be arrived at another way. From Gessow and Myers’ wellknown textbook [234] (chapter 8, eq. 21), the simplest calculation of thrust coefficient at any advance ratio starts 

with 

1 11 1 2 2 T 11 1

T 2 32 2 64 4

C C a or a . = σ θ+   μ θ+ λ = θ+ μ θ+ λ   σ

In hover, advance ratio (μ) is zero, and inflow ratio (λ) is frequently set to its ideal, uniform, downwash value of 

λ = – (1⁄2CT)1⁄2. Thus, for hover 

C a C T

T

σ = − θ1

6

1

4

1

2 .

This classical result says that comparing different solidity rotors with CT/σ versus θ will not remove the solidity 

parameter. However, by dividing through by solidity, the thrust and collective pitch similarity parameters are 

revealed because 

T T T

2 2 T 2

C CC 1 1 1 1 11 a C or a .

6 4 2 6 42

  θ θ       =− =−         σ σσ     σσ σ     
2.3 HOVER PERFORMANCE 

156 

blade had a 30-inch radius, no twist, a NACA 0015 airfoil, and a 2-inch constant chord from 

the 5-inch radius station to the tip. The tests were conducted at 960 rpm, which is a tip speed 

of about 250 feet per second. Their report includes an appendix with tabulations of all 

measurements. 

 Knight and Hefner illustrated their transformation by first plotting CT versus θ for each 

rotor set. This commonly obtained result is reproduced in Fig. 2-64. They did not include a 

comparison of their data in the coordinates of CT/σ versus θ as suggested by footnote 52. This 

comparison is shown in Fig. 2-65. This CT/σ view can be of interest when blade stall is 

suspected. Knight and Hefner thoroughly discussed how blade stall was apparent in their data. 

They (and other investigators) refer to a loud, buzzing noise from the model at high thrust as 

an audible indication of blade stall. A quantitative barometric parameter of blade stall is 

average blade element lift coefficient. This blade-stall indicator is frequently defined as 

(2.79) ( ) T

L

C C 6 to 7 = σ . 

When CL approaches 1 for full-scale rotors, or is perhaps as low as 0.7 for many model rotors, 

signs of aerodynamic nonlinearity are frequently seen in test data. Fig. 2-65 shows that the 

two-bladed rotor has a departure from the general trend at its highest thrust point and perhaps 

at the prior point. At the lower point, CL is on the order of 0.6 to 0.7 indicating the onset of 

separated flow along the blade span. For the untapered, untwisted blade, separated flow 

begins closer to the tip. 

 Using the test data shown in Fig. 2-66, Knight and Hefner were satisfied that their 

similarity parameters for thrust and collective pitch were correct. What appears in Fig. 2-64 

as a configuration-oriented result where solidity, planform, and twist may all be factors, is 

now less complicated because solidity is removed as Fig. 2-66 demonstrates. (The inclusion 

of separated flow effects in the airfoil Cl

 versus α assumption, rather than using the linear 

Cl

 = aα assumption, has allowed prediction of the high-thrust blade-stall-affected behavior 

seen by the two- and three-bladed data in Fig. 2-66.) 

The question might be raised as to whether Knight and Hefner’s data (vintage 1937) is 

representative today considering the overall complexity of hover testing procedures and 

theoretical aerodynamics. To allay possible suspicions, consider Fig. 2-67. I have added 

experimental data contributed by Landgrebe [246],53 Stepniewski [247], and Signor [226] to 

Knight and Hefner’s result. This data bank, when included in the substantiation of similarity 

parameters for thrust and collective pitch, simply reinforces Knight and Hefner’s suggestions 

as Fig. 2-67 shows. Their (perhaps antiquated) blade-element-momentum theoretical result is 

given by Eq. (2.78). Fig. 2-67 includes their result assuming a tip loss factor of B = 0.985 (I 

did not vary the tip loss factor with 2 C T σ or blade-aspect ratio), a representative root cutout 

of xc = 0.17, and an airfoil lift-curve slope of a = 5.73 per radian. 

 

53 Jack Landgrebe was kind enough to dig out the original tabulated data and send it to me. Now that’s a friend. 
2.3 HOVER PERFORMANCE 

157 

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.01

0 2 4 6 810 12

0.04244 (2)

0.06366 (3)

0.08488 (4)

0.10610 (5)

Thrust 

Coeff.

Nominal Collective Pitch (deg.)

Solidity (Blades)

Fig. 2-64. Knight and Hefner’s basic thrust data in 1937. 

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 2 4 6 8 10 12

0.04244 (2)

0.06366 (3)

0.08488 (4)

0.10610 (5)

Thrust 

Coeff.

Divided

By

Solidity

CT/σ

Nominal Collective Pitch (deg.)

Solidity (Blades) Probably 

Influenced By 

Blade Stall

Fig. 2-65. CT/σ is a blade-loading parameter that reflects airfoil lift coefficient 

and proximity to blade stall. 
2.3 HOVER PERFORMANCE 

158 

0

0.5

1

1.5

2

2.5

3

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

0.04244 (2)

0.06366 (3)

0.08488 (4)

0.10610 (5)

Eq. 2.78, a = 5.73, B = 0.985, xc = 0.15

Thrust 

Coeff.

Divided

By

Solidity

Squared

CT/σ2

Nominal Collective Pitch Divided By Solidity θ/σ (radians)

Solidity (Blades)

Fig. 2-66. CT/σ2 and θ/σ are similarity parameters that can remove solidity as a variable 

from the hover performance problem. 

 Before turning to the subject of power required by a single, isolated rotor to produce 

thrust, two additional points can be made. The first point deals with the lifting-surface 

theories that are evolving. Many of these codes only solve the potential flow problem. This 

generally gives a blade element airfoil the lift-curve slope of a = 2π per radian in the 

incompressible case. To better estimate actual rotors (which experimentally appear to behave 

as if a ≈ 5.73 per radian), final data of thrust coefficient at a given collective pitch can be 

scaled using the more complete similarity parameters. If, for a given θ, the rotor CT is 

obtained with a theory that basically assumes a = 2π, then the corrections would be 

(2.80) 

2

T (a 5.73) T (a 2 ) (a 5.73) (a 2 )

5.73 5.73 C C and

2 2 = = π= = π

    = θ = θ       π π   . 

 The second point deals with the elastic twist deformation which occurs even with 

perfectly balanced aerodynamic torsional moments. Simple torsion theory must still include 

the “tennis racket” term, as it is commonly called. Therefore, even for a uniformly structured 

blade 

(2.81) ( )( ) R e 2

e r

d GJ I dr

dr θ

θ = Ω θ+θ      . 
2.3 HOVER PERFORMANCE 

159 

This elementary differential equation can, of course, be solved exactly with hyperbolic 

functions. However, a useful engineering result is simply that 

(2.82) ( )

2

t

e 1 2

2 2

1 t

2

I V

GJ

x x

I V 1 GJ

θ

θ

    θ   ≈ − − θ  

+    

 . 

Both tip speed and blade torsional, structural properties play a part in the nondimensional 

parameter 2

t I V GJ θ . However, values of this parameter ranging from 0.05 for a torsionally 

“stiff” blade to 0.35 for a relatively “soft” blade are frequently representative of both model 

and full-scale rotor blades. The elastic twist is, therefore, a factor in theory versus test 

comparisons such as shown in Fig. 2-67. Suppose, for example, that a blade root was preset to 

10-degrees root collective pitch angle prior to startup. For an untwisted blade, the pitch angle 

at the 0.75 R station would also be 10 degrees. At operating speed, the blade tries to 

twist nose-down because of the torsional load created by the “tennis racket” term. The elastic 

twist between the root and the 0.75 R station could amount to a θe/θ ratio on the order 

of –0.025 for a torsionally stiff blade to as large as –0.14 for a soft blade. With a preset 

0

0.5

1

1.5

2

2.5

3

0123456

Knight & Hefner (1937) AR = 15.0, b = 2,3,4,5

Landgrebe (1971) AR = 18.2, b = 2,4,6,8

Stepniewski (1948) AR = 16.0, b = 3

Signor (et al) (1989), AR= 6.14, b = 4

Eq. 2.78, a = 5.73, B = 0.985, xc = 0.15 Thrust 

Coeff.

Divided

By

Solidity

Squared

CT/σ2

Nominal Collective Pitch Divided By Solidity θ/σ (radians)

Fig. 2-67. Knight and Hefner’s similarity parameters are quite useful when different 

rotors are compared. 
2.3 HOVER PERFORMANCE 

160 

10-degree blade angle, the 0.75 R station may, therefore, only be at 9.75 degrees and could, 

perhaps in the extreme, only be at 8.6 degrees. The agreement between blade element 

momentum theory and tests shown in Fig. 2-67 could be considerably altered if elastic twist 

were accounted for in blade element momentum theory, or any theory for that matter. 

 As more accurate lifting surface and free-wake theory is compared to experimental 

results, it seems advisable not to skip careful and detailed analysis of how thrust varies with 

blade pitch angle. 

 Knight and Hefner satisfied themselves that solidity could be removed as an 

independent parameter using the coordinates 32CT/a2σ2 and 16θ/aσ. They then turned to 

investigating the power required to produce thrust. They found that the similarity parameters 

were quite appropriate provided only the power increment above flat-pitch power was dealt 

with. The need to handle a power increment rather than the total power can be seen very 

easily. For example, one well-known classical-engineering approximation that estimates total 

hover power required is 

(2.83) 

3/2 3/2

T T do

P Po i i

C C C

CC k k

2 2 8

σ

≈+ ≈ + . 

Multiplying both sides of this equation by (32/a2σ2 )3/2 produces the thrust similarity 

parameter. That is, 

(2.84) 

3/2 3/2 3/2 3/2

d o T

2 2 P i 2 2 2 2

32 32 32 C C C k

a a 8a 2

   σ

   ≈ +    σσ σ , 

which, on simplification, becomes 

(2.85) 

3/2

P i d o T

3 3 3 2 2 2

128 2 C k 32C 16 2 C

aa a 2

  ≈ +   σσ σ   . 

Multiplying Eq. (2.85) through by 2 clears things a little more so that 

(2.86) 

3/2

P T d o

33 32 22 i

256 C 32C 32 C

K

aa a

  ≈ +   σσ σ   . 

The preceding four equations make two points. First, power divided by solidity cubed is 

dependent on thrust divided by solidity squared. Second, perhaps a much-too-unique 

nondimensional form for the power at flat pitch (i.e., zero thrust) is being introduced. After 

all, minimum profile power in the form σC 8 do is much easier to remember than 

3 2

do 32C a σ . Knight and Hefner decided to subtract CPo at the onset. That is, they restated 

the problem as 

P Po P Po T

3 3 3 2

C Min. C 16 C Min. C C g or f

a a

− −   θ   = =     σ σ σσ    

 . 
2.3 HOVER PERFORMANCE 

161 

0

0.00005

0.0001

0.00015

0.0002

0.00025

0.0003

0 0.004 0.008 0.012 0.016 0.02

Knight & Hefner

Landgrebe

Stepniewski

Sweet

Minimum 

Profile Power 

Coeff.

CPo = σCdo/8

Solidity/8

Average Cdo = 0.014

0.007

Fig. 2-68. Average airfoil drag coefficient varies considerably. 

 To effectively use Knight and Hefner’s suggested form, the power at flat pitch (i.e., 

minimum CPo ) must be accurately measured and/or calculated. Even a cursory search of test 

data shows that minimum CPo as a function of σ/8 yields a large difference in an airfoil’s 

minimum drag coefficient. Variations in blade average airfoil and minimum drag coefficients 

(Cdo) between 0.007 and 0.014 are quite common as Fig. 2-68 shows. However, Knight and 

Hefner’s scatter about a Cdo = 0.0115 is not so common. 

 Knight and Hefner’s test results for their four rotor configurations are shown in the 

most fundamental form in Fig. 2-69. They did not include this graph of total power (CP) 

versus collective pitch (θ) in their report. Fig. 2-69 shows, however, that the trend established 

by the two-, three-, and four-bladed configurations is interrupted by the five-bladed rotor set. 

It appears to me that some constant abnormality exists in the measured power required for the 

five-bladed configuration. An arbitrary power shift upwards, consistent with the minimum CPo

scatter shown in Fig. 2-68, appears appropriate. This would be an increment of about Δ CPo ≈

+0.000034. Without this increment, you might mistakenly conclude from Fig. 2-69 that there 

is little performance difference between four- and five-bladed rotors. Knight and Hefner did 

not comment on this point, presumably because they were looking closely at CP minus CPo. 
2.3 HOVER PERFORMANCE 

162 

 Knight and Hefner convinced themselves that they were on the right path by first 

plotting CP minus minimum CPo, versus collective pitch, θ. Their results are reproduced here 

in Fig. 2-70. They used the measured CP minus the test minimum CPo for each rotor 

configuration to obtain CP – CPo. As Fig. 2-70 shows, there is a clearly defined progression 

with blade number, which is in contrast to Fig. 2-69. They presumably concluded that, despite 

some inconsistency in the power at zero thrust (i.e., minimum CPo), the additional power due 

to thrust was measured accurately enough for their purposes. (By making this presumption, I 

suggest that some mechanical or aerodynamic zero shifting in the torque balance may have 

occurred with the five-bladed configuration.) 

 Knight and Hefner used blade element momentum theory to define equations for both 

induced and profile power contributions to the test (CP minus minimum CPo) trends exhibited 

in Fig. 2-70. In modern notation, their derivations leading to their suggested similarity 

parameters can be conveyed fairly easily. For induced power, they transformed 

(2.87) { } R 1

1 3 3

i (r) (r) t l(x) (x) t 2 0 0

P v dT bcRV x C v xV dx = =ρ       to 

(2.88) 

1 2

3 2 l(x) (x) 1

i t 2 2

0 t

a a 16C 16 v

P bcRV x dx

16 16 a aV

    σ σ       = ρ                σ σ   







by assuming constant chord, untwisted blades, and constant airfoil lift-curve slope. Then, 

using Eqs. (2.88), (2.73), and (2.71), they addressed the resulting induced-power integral of 

(2.89) ( )( ) c

B P i 2

3 3 x

512C

x x x 1 2x 1 2x 1 dx

a

= Θ + − + Θ + Θ−

σ  . 

Although Knight and Hefner chose the tip loss factor as B = 1 and xc = 0, the integrated result, 

including these two potential variables, is 

(2.90) ( ) ( ) ( ) ( )( )

77 55 33

Pi 22 33

33 2 2 2 c c

512C FH FH FH

Bx Bx

a 28 10 4

−−− = + − − −− −Θ

σ Θ ΘΘ

where, again, 16

a

θ Θ =

σ

 and F 1 2B and H 1 2x ≡+Θ ≡+ Θc . 

 Knight and Hefner approached the profile power due to lift by assuming a parabolic 

airfoil drag polar. They tested a rectangular wing of aspect ratio 12 in an open-throat wind 

tunnel having a jet diameter of 9 feet. Correcting this data to infinite-aspect ratio gave them 

NACA 0015 properties at a Reynolds number of 242,000, which corresponded to their model 

rotor blade-tip conditions. They concluded that, for their model rotor tests, the blade element 

airfoil drag coefficient should be on the order of 

(2.91) 22 2 2 C C 0.0115 0.75 or C C kC 0.0115 0.0228C d do d do l l ≈ +εα ≈ + α ≈ + ≈ + . 
2.3 HOVER PERFORMANCE 

163 

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01

0.04244 (2)

0.06366 (3)

0.08488 (4)

0.10610 (5)

Solidity (Blades)

Total 

Power 

Coeff.

Thrust Coeff.

Fig. 2-69. Five-bladed model does not follow trend. Measurement tare at 

zero thrust presumed in error. 

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0 2 4 6 8 10 12

0.04244 (2)

0.06366 (3)

0.08488 (4)

0.10610 (5)

Solidity (Blades)

Total 

Power 

Coeff.

Minus

Minimum 

Profile 

Power 

Coeff. 

CP - CPo

Nominal Collective Pitch (deg.)

Fig. 2-70. Knight and Hefner used delta power as the basis for their 

similarity parameter. 
2.3 HOVER PERFORMANCE 

164 

They averaged the minimum profile power measured from their two-, three-, four-, and fivebladed runs and arrived at Cdo = 0.0115, which they stated was in agreement with their wing 

test. The four configurations did have some scatter as Fig. 2-68 shows. For the incremental 

profile power due to thrust, they transformed 

(2.92) ( )( ) ( ) ( ) ( ) c

BR 2 1 2

oo l 2 r Δ = Ω Δ = Ω ρΩ P b r d D b r r cdr kC      

to 

(2.93) 

c

2 B 2 2

1 3 3 l

o t 2 2

x

a 16C P bcRV k x dx, 16 a

  σ   Δ =ρ         σ







again by assuming constant chord and constant airfoil lift-curve slope. Using Eq. (2.73), they 

obtained the incremental profile power due to blade pitch angle in the integral form of 

(2.94) ( ) ( )

c

B 2 Po

3 3 x

512 C

x 1 1 2x x dx

a ka

Δ

= Θ+− + Θ

σ



 . 

 Knight and Hefner also chose B = 1 and xc = 0 for this profile power integral. The 

result, including these two potential variables, is 

(2.95) ( ) ( ) ( ) ( ) ( ) ( ) 3 3 4 42 7 7 3 3

Po 2 2 c c

3 3 c 2 2

512 C 4B x B x F H F H

B x

a ka 3 4 14 6

Δ −Θ −Θ − −

= −+ + − +

σ Θ Θ

where, again, 16

a

θ Θ =

σ

 and F 1 2B and H 1 2x ≡+Θ ≡+ Θc . 

 With both induced and incremental profile power coefficients theoretically expressed 

as similarity parameters, Knight and Hefner immediately were able to reach the conclusion 

shown in Fig. 2-71. They made their primary theory to test comparison [dismissing the integer 

512 and a3 in both Equations (2.90) and (2.95)] simply as 

 ( ) p po Test

3

C Min. C

Exp. versus − θ

σ σ . 

Knight and Hefner’s theory-versus-test comparison is included here as Fig. 2-71. They found 

that they had underpredicted the test result as Fig. 2-71 shows. This first comparison assumed 

an airfoil lift-curve slope of a = 5.73 per radian, integration limits of B = 1 and xc = 0, and an 

airfoil drag rise with an α2 of ε = 0.75 or with a 2 Cl of k = 0.0228. They concluded that simply 

raising ε from 0.75 to 1.25, or k from 0.02284 to 0.03807, brought theory into agreement with 

test, and this result is also shown in Fig. 2-71. Most importantly, they had convincing 

evidence that solidity could be removed as an independent parameter from the power 

coefficient as well as from the thrust coefficient. 
2.3 HOVER PERFORMANCE 

165 

0

1

2

3

4

5

6

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

0.04244 (2)

0.06366 (3)

0.08488 (4)

0.10610 (5)

Solidity (Blades)

(CP - CPo)/σ3

Nominal Collective Pitch/Solidity (radians)

Eqs. 2.90 & 2.95

B = 1, xc = 0, a = 5.73

k = 0.03807

k = 0.02284

Fig. 2-71. Knight and Hefner’s delta power similarity parameter removes solidity as 

an independent variable. 

 Predicting power is a challenge given just a nominal blade angle recorded during test. 

Very few investigators care to take on this challenge today. Even fewer widely publish such a 

fundamental comparison. Today, blade angle is not generally set to the ±0.05-degree accuracy 

that Knight and Hefner demanded in their experiment. Furthermore, elastic twist is known to 

be excessive, and airfoil lift and drag coefficients, over the wide range of Reynolds and Mach 

numbers required, are rarely available. Nearly 60 years later, rotary wing aerodynamicists do 

the best they can with airfoil data, ignore elastic twist, and then adjust the theoretical 

collective pitch angle until the experimental thrust is matched. The published comparison is 

power versus thrust in some form. 

 One key conclusion to be drawn from Knight and Hefner’s application of blade 

element momentum theory to calculate induced and incremental profile power (at least up to 

blade-stall onset) is that 

( ) ( ) ( )

p po pi po

3 3 3 3 3 3

512 C Min. C should 512 C 512 C

Exp. equal Theory ka . a a a ka

  −    Δ        +     σ σ      σ   

Therefore, because induced power, profile power, and thrust depend on the collective pitch 

similarity parameter Θ= θ σ 16 a , they continued their analysis with a graph of 
2.3 HOVER PERFORMANCE 

166 

( ) p po T

3 2

C Min. C C Exp. versus Exp. . −

σ σ

Their comparison is reproduced here as Fig. 2-72. 

 Because Knight and Hefner did not use a tip loss factor (i.e., B = 1) and also ignored 

loss of lift at the blade root (i.e., xc = 0), they could only conclude that their airfoil drag polar 

was in error. Fig. 2-71 showed their theoretical results with k = 0.02284 and with k = 0.03807. 

Another possible conclusion can be drawn, however. For example, Gessow and Myers [234] 

suggested that the tip loss factor should vary with thrust coefficient as shown with Eq. (2.77), 

which is repeated here for convenience: 

1/2

T T

2

2C C2 B1 1

b AR

  =− =−   π σ  . 

Other investigators, including Prandtl and Goldstein, had suggested other semiempirical ways 

of treating blade-element lift and drag loading over the outboard region of the blade such as 

increasing the 2 to 3.25 so that 

(2.96) 

1/2

T

2

3.25 C B 1

AR

  = −   π σ  . 

 Knight and Hefner might have assumed that their airfoil drag polar was accurate. Then 

the difference between test and theory could be charged empirically to the tip loss factor. 

Fig. 2-72 shows that if the tip loss factor given by Eq. (2.96) is assumed, then correlation 

between test and theory is excellent with the airfoil drag polar described by k = 0.02284—as 

Knight and Hefner measured with their high-aspect-ratio wing test—and provided that the tip 

loss factor is increased to that given by Eq. (2.96). 

 Knight and Hefner showed that solidity could be removed as a parameter when 

comparing delta power versus thrust performance data from different rotor configurations. 

Additional data supporting their conclusion is seen in Fig. 2-73. The data summarized in 

Fig. 2-73 encompasses a wide range in blade geometry and aerodynamic parameters, 

however, all blades were untapered and untwisted. 

 The major contribution that Knight and Hefner made was showing how to remove 

solidity as an independent parameter when dealing with hovering rotor test data. Their 

suggestions appear just as valid today as they did in 1937. Their approach did not, however, 

alleviate the need to accurately predict and measure minimum profile power. Nor did it 

resolve the semiempirical trade between tip loss factor and airfoil drag polar. This trade has 

been used for decades “to make the answer come out right.” 

 There have been many discussions, some quite heated, as to what semiempirical 

factors (such as tip loss, root cutout, and airfoil aerodynamic properties) are most generally 

applicable when using blade element momentum theory to predict performance of a new 

helicopter product. So far, the rotary wing aerodynamic community has never guessed the 

right answer prior to flight test. 
2.3 HOVER PERFORMANCE 

167 

0

1

2

3

4

5

6

0 0.5 1 1.5 2 2.5 3

0.04244 (2)

0.06366 (3)

0.08488 (4)

0.10610 (5)

Solidity (Blades)

(CP - CPo)/σ3

Eqs. 2.78 & 2.90 & 2.96

B = 1, xc = 0, a = 5.73

k = 0.03807

k = 0.02284

CT/σ2

Fig. 2-72. Blade element momentum theory requires large tip loss factors to correlate 

with experiments when realistic airfoil data is used. 

0

1

2

3

4

5

6

0 0.5 1 1.5 2 2.5 3

Knight & Hefner (1937) AR = 15.0, b = 2,3,4,5

Landgrebe (1971) AR = 18.2, b = 2,4,6,8

Stepniewski (1948) AR = 16.0, b = 3

Signor (et al) (1989), AR= 6.14, b = 4

CT/σ2

(CP - CPo)/σ3

Fig. 2-73. Knight and Hefner’s similarity parameter removes solidity as a variable so 

performance differences between rotors are clearer. 
2.3 HOVER PERFORMANCE 

168 

 You should be aware that blade element momentum theory is not able to resolve 

whether, for a given solidity, a few wide-chord blades are better or worse performing than 

many narrow-chord blades. The most definitive answer to date has come from test. Landgrebe 

[246] concludes from figure 21 of his report that six aspect-ratio-13.6 blades performed as 

well as eight aspect-ratio-18.2 blades. The constant solidity of the 0.14 test was performed at 

525 and 700 feet per second, which tends to remove both Reynolds and Mach number 

considerations. A comparison of two narrow-chord versus two wide-chord blades was 

experimentally made by Sweet [248]. His results also support the conclusion that solidity is 

the primary variable as Fig. 2-73 shows. 

 Blade element momentum theory can suggest at least two twist distributions for an 

untapered blade that will minimizes induced power. The more familiar of the two twist 

distributions comes from simple, axial momentum theory. According to simple axial 

momentum theory, the induced power will be a minimum when the axial-induced velocity is 

constant over the complete actuator disc. (This conclusion has never been proven, but has 

been used ever since W. J. M. Rankine initiated momentum theory for marine propeller 

design in 1865.) When only axial-induced velocity is considered (i.e., swirl-induced velocity 

is neglected), the blade element momentum theory suggestion comes from Eq. (2.71), which 

is repeated here for a constant chord blade as 

(2.71) (x) (x)

t

16 v 16

1 2x 1

aV a

    θ

=+ −     σ σ    

. 

When the objective is uniform, axial-induced velocity, then Eq. (2.71) says that the product, 

x θ(x), of the untapered blade should be a constant. The constant is classically defined as θtip, 

and the twist distribution should be tip θ x . In Knight and Hefner’s similarity form, this twist 

distribution means that 

(2.97) tip tip

tip tip

t

16 v 16

1 2x 1 1 2 1 where

aV x a

    Θ θ

= + − = +Θ − Θ =     σ σ    

. 

Then the blade element lift coefficient, given generally by Eq. (2.73), becomes simply 

(2.98) tip tip tip tip l

2

16C 1 1 1 12

1 2x

a x xx x x

Θ Θ  Θ +− +Θ

= +− + =   σ  

. 

 The single rotor total thrust, induced power, and delta profile power due to airfoil lift 

follow directly from radial integration as was shown earlier for the untwisted blade starting 

with Eqs. (2.75), (2.88), and (2.93), respectively. The result for rotor thrust is 
2.3 HOVER PERFORMANCE 

169 

(2.99) 

( )

( )

c

c

B

B T l 2

22 2 tip tip x x

2 2

c

tip tip

32C 16C x dx 1 1 2 x dx

a a

B x 1 12

2

  = =   Θ + − + Θ

σ σ 

  − =Θ +− +Θ    





  . 

The result for induced power is 

(2.100) ( )( )

( )( )

c

c

B

Pi l(x) (x) 2

33 2

x t

B

tip tip tip x

2 2

c

tip tip tip

512C 16C 16 v

x dx

a a aV

1 1 2 1 2 1 x dx

B x 1 12 12 1

2

   =    σ σσ   

= Θ +− +Θ +Θ −

  − =Θ +− +Θ +Θ −    







 . 

The result for profile power due to airfoil lift is 

(2.101) ( ) ( )

( )

c

c

B 2

B 2 Po l 3

33 2 tip tip x x

2 2 2 c

tip tip

512 C 16C x dx 1 1 2 x dx

a ka a

B x 1 12

2

Δ   = = Θ +− +Θ   σ σ  

  − =Θ +− +Θ    





  . 

The simplicity of these rotor thrust, induced power, and delta profile power expressions easily 

permits power to be expressed in terms of thrust. This removes collective pitch from the 

performance problem. Thus, by inspection, the delta profile power due to airfoil lift becomes 

(2.102) ( )

2

Po T

3 3 2 2 2 2

c

512 C 2 32C

a ka B x a

Δ    =   σ −σ    . 

The induced power is reduced to54 

(2.103) 

3/2

Pi T

33 2 2 2 2

c

512 C 2 32C

a a B x

   =   σ σ   −    

. 

The two rotor powers given by Eqs. (2.102) and (2.103) can be added together, and the 

several integers, as well as airfoil lift curve, collected. Thus, the performance of a single, 

isolated rotor with untapered blades having a θ(x) = θtip / x twist distribution is 

 

54 The induced power squared divided by thrust cubed leads to 

( )( )

( )

( )

( )

2 2

1 12 12 1 12 1 tip tip tip tip

3 1 12 1 12 tip tip tip tip

2

Θ +− + Θ + Θ − +Θ −

= =

Θ +− + Θ Θ +− + Θ

    . 
2.3 HOVER PERFORMANCE 

170 

(2.104) 

2 3/ 2

Pi Po T T

3 22 2 2 2 2 c c

C C 4k 1 C C

B x 2B x

+ Δ     

= +     σ −σ σ      −    

. 

This result is frequently presented without using Knight and Hefner’s solidity-removing form 

so that 

(2.105) ( )

2

T T

Pi Po T 2 2 2 2

c c

C C 4k C CC

2B x B x

  σ   +Δ = +    −   − σ 

. 

 The hover performance of a single, isolated rotor having untapered blades twisted as 

θ(x) = θtip/x is occasionally advanced as an ideal rotor (expressed in coefficient form). This is 

not correct for two reasons that become clear when the previous Eq. (2.105) is expanded to 

dimensional form. In practice, minimum profile power must, at the very least, be included so 

that the total power becomes 

(2.106) ( )

( ) ( )( )

o oi

3 3/2 t 2

do 2 2 2 22 t c c

550 HP Min. P P P

bcRV 4k T C T

8 bcRV B x 2 RBx

= +Δ +

ρ

=+ +

ρ − ρπ −

. 

 Many investigators have examined the obvious question presented by Eq. (2.106), 

which is, “What configuration minimizes horsepower for a given thrust?” The minimum 

profile power term in Eq. (2.106) says, for example, that the blade area (bcR) should be zero 

and/or the rotor should not turn (i.e., Vt = 0). The delta profile power term (the second term) 

says that the blade area should be infinitely large and/or the tip speed should be infinitely 

large. The induced-power term says that the blade radius should be infinitely large. Because, 

in practice, the induced power is two to three times the sum of the two profile terms, the least 

power for a given thrust is approached with the largest diameter rotor that the overall 

rotorcraft can accept.55 Then the profile power must be minimized. 

 There is a more practical way to examine this optimization problem. If the induced 

power obtained with uniform, induced velocity is accepted as a minimum, then the minimum 

total profile power can be dealt with in terms of the airfoil lift-to-drag ratio. That is, let the 

search begin with total profile power expressed in the form 

(2.107) () () ( ) ( ) R R 2 1

o o (r) d(r) 2 0 0 P b r dD b r r c C dr = Ω = Ω ρΩ       , 

and calculate the blade-element airfoil drag coefficient from its lift-to-drag ratio as 

(2.108) ( )

l(r) l(r)

d(r)

l(r) d(r) l d max.

C C

C

C C CC ≡ = . 

 

55 The more practical design problem is how to maximize productivity per “buck.” 
2.3 HOVER PERFORMANCE 

171 

If every blade element is operated at its maximum lift-to-drag ratio and this ratio is 

independent of the radius station, then Eq. (2.108) can be substituted into Eq. (2.107), which 

gives, with some rearrangement in advance, 

(2.109) ( ) ( )

1 R 2 2 2

o (r) l(r) 0

l d max.

P bc C r r dr

C /C

ρΩ = Ω      . 

Profile power, as collected in Eq. (2.109), highlights a bracketed term within the integral that 

is proportional to total thrust. That is, rewriting Eq. (2.67) shows that 

(2.110) 2 22

(r) l(r) (r) 2 2

T 4T bc r C 8 v 8 v 8

2R R

  Ω =π =π =π =     ρπ ρ . 

This grouping of Eq. (2.67) to give Eq. (2.110), and then substituting the result into 

Eq. (2.109), reduces the total profile power to 

(2.111) ( ) ( )

1 2 R 2 2 3

o 2 0

ld ld max. max.

4T R P r dr T

C /C R C /C

ρΩ   Ω = =     ρ  . 

The induced power remains at its minimum so that the total power required to produce a 

given thrust is simply 

(2.112) ( ) ( )

2 3/2

3

o i 2

l d max.

R T 550 HP Min. P Min.P T

C /C 2 R

Ω

= += +

ρ π

. 

Because the objective is the least horsepower for a given thrust (or conversely, the most thrust 

for a given horsepower), dividing Eq. (2.112) through by thrust reduces the optimization 

problem to 

(2.113) ( ) ( ) ( ) ( )

2 2 1/2

3 3 t t

2 2

ld ld max. max.

550HP T T V V

T C /C 2 R C /C 2 R

= += +

ρ π ρ π . 

 Quite clearly, the “optimum” rotor is now seen as (1) carrying the thrust on the largest 

possible swept disc area, (2) turning with the lowest practical tip speed, and (3) using airfoils 

with the highest achievable lift-to-drag ratio. The blade planform geometry and twist 

distribution that provide this minimum power solution are given by 

(2.114) ( )

l T

(r) (x) 2

t l

4T Design C C 2

c r and

b V Design C a x

= θ = +

ρ . 

 This blade geometry is actually a relatively poor description because it is based solely 

on simple, axial momentum theory that ignores the swirl- or inplane-induced velocity. 

Furthermore, because the theory assumes an infinite number of blades, the actual loading is 

poorly described near both the blade’s tip and root. Despite these and other shortcomings, 

Eq. (2.113) does provide a first-order estimate of the least power required to produce a given 

design thrust. Of course Eq. (2.113) is not applicable to off-design conditions; rather, it is an 

envelope to the best performance of all rotors at their individual design points. 
2.3 HOVER PERFORMANCE 

172 

 The preceding, somewhat lengthy discussion of blade element momentum theory 

gives you some background about the industry’s tool used to calculate hover power required. 

This tool, or some variation, has been in use for over six decades. With the advent of digital 

computers, more sophisticated theoretical versions were programmed. In the last decade or so, 

the field of computational fluid dynamics (CFD) blossomed. CFD gave aerodynamicists the 

ability to calculate both the air flow through and about a rotor. It also allowed the prediction 

of airfoil lift, drag, and pitching moment, and tables of airfoil properties could be dispensed 

with. The insight obtained with CFD during the development of this very powerful predictive 

tool has been impressive, however the CFD rotary wing community has yet to predict 

complete helicopter hover performance, and display correlation of theory with test, in a 

comprehensive scope comparable to Kocurek [168]. 

2.3.8 Single Rotor Helicopter Summary 

 This detailed discussion about power required to hover began with Fig. 2-51 on 

page 139. The engine-power-required coefficient (CPeng) versus helicopter weight coefficient 

(CW) is shown for a number of machines. While there is a range of ±12 percent about a trend 

given previously by 

(2.41) Reqd.

3/2 C 0.0157C 1.045C P WW = + , 

the accumulated flight test data makes it possible to get a composite picture of hover power 

required by single rotor helicopter. In the following discussion, blade element momentum 

theory plays a key role in seeing just what the industry’s modern results are. 

 Consider Eq. (2.47), repeated here for convenience, as the starting point for any single 

rotor helicopter: 

(2.47) Main Rotor TailRotor

req Accessory

Main Rotor TailRotor

RHP RHP

ESHP = ++ SHP

η η . 

The main rotor power required (RHPmr) and tail rotor power required (RHPtr), along with the 

accessory horsepower (SHPacc), are the three components of the problem. Because the 

industry has tried to develop the main rotor system as close to ideal as practical, calculate the 

main rotor power required by Eq. (2.106) with an empirical, induced-power “correction” 

factor (ki) (used to make the answer come out right). Thus, 

(2.115) ( )

( )

( )

( )( )

o oi

3 3/2

t i 2

mr do 2 2 2 22 t c c

550 RHP Min. P P P

1 4k bcRV k W

RHP C W

550 8 bcRV B x 2 RBx

= +Δ +

    ρ

=+ +  

  ρ − ρπ −  

where the tip loss factor (B) I subscribe to is 

 
2.3 HOVER PERFORMANCE 

173 

(2.116) 

1/2 1/2

W T tr

2 2 tr

tr tr

3.25 C C 3.25 B 1 and B 1

AR AR

−     =− =−     πσ π σ    

, 

and the blade proper does not begin until the inboard radius station (xc). As a reminder, (ρ) is 

the air density, (b) is the blade number, (c) is blade chord, (R) is blade radius, (Vt) is tip speed, 

(Cdo) is the airfoil minimum drag coefficient, and (k) is the airfoil drag rise with the square of 

the airfoil lift coefficient. 

 You will note that in constructing Eq. (2.115) from Eq. (2.106), I have simply replaced 

hover thrust (T) with aircraft weight (W). I have done this despite the fact that every singlerotor helicopter hovers with the main rotor thrust some 2 to 5 percent greater than the 

aircraft’s weight (because of download). Neglecting this download factor (T/W) of 1.02 to 

1.05 means that the induced power “correction” factor (ki) will be artificially raised a few 

percent points as will the apparent airfoil drag rise with airfoil lift coefficient (k). Keep in 

mind that the addition of a wing adds extra download that must be accounted for. 

 To avoid excessive subscripting, let me use the subscript (tr) for the tail rotor and only 

use the subscript (mr) for the main rotor where required. 

 The tail rotor thrust required to maintain yaw equilibrium follows from the discussion 

surrounding Eq. (2.49), starting on page 142. Thus, 

(2.117) ( ) ( ) mr mr

tr

tr mr tr t mr

550RHP 550RHP T

R R 1 R RV−

= = +Ω + . 

Note here that the tail rotor moment arm (lt) has been replaced by the sum of the main rotor 

radius (Rmr) and the tail rotor radius (Rtr), which is geometrically closer to the single rotor 

helicopters under discussion. 

 A first-order approximation of the tail rotor horsepower is sufficient for this 

discussion, so assume that 

(2.118) tr o tr o tr i tr o tr tr i tr 550 RHP Min. P P P Min. P k P = +Δ + ≈ + − −− − −

and, therefore, 

(2.119) 

( ) ( )

( )

( )

( ) ( )

3 3/ 2

tr tr tr t tr tr tr

tr do tr 2 2

exit tr c tr

3 2 3

tr tr tr t tr tr mr

do tr 2 2 tr t mr exit tr c tr

1 bcRV k T

RHP C

550 8 4A B x

1 bcRV k 550 RHP C

550 8 4A B x 1 R R V

−

−

−

−

−

− −

    ρ

≈ +  

  ρ −  

    ρ  

= +     +   ρ −    

. 

You will recall from the anti-torque discussion that for an unshrouded tail rotor, Aexit equals 1 2

2 πR tr , but if the anti-torque device is a ducted fan, then Aexit = 2 πR fan . My assumption for 

ducted fans is that the tip loss factor, Eq. (2.116), is always 1.0 but that the momentum area 

reflects the large root cutout (xc) characteristic of most ducted fans. 
2.3 HOVER PERFORMANCE 

174 

 Let me stop here for a moment to examine flight test data against the nondimensional 

form suggested by Knight and Hefner. From previous discussion, these early pioneers showed 

that displaying results as 

( ) p po T

3 2

C Min. C C Exp. versus Exp. −

σ σ

should remove solidity (σ) as a primary variable. Applying their view to flight test data from 

many single rotor helicopters requires a little reformatting as follows: 

(2.120) 

mr tr

acc

mr tr W

3 23 2

t

Min.RHP Min.RHP Exp.ESHP SHP Error 550 Exp.C vs .

R V

  − − −±   η η      

σ ρπ   σ  

 

The minimum main rotor horsepower is simply 

(2.121) ( ) 3

t

mr do

1 bcRV

Min.RHP C

550 8

    ρ =  

   

. 

In like manner, the minimum tail rotor horsepower is 

(2.122) ( )

( ) ( )

3 2 3

tr tr tr t tr tr mr

tr do tr 22 2 tr t mr tr tr c tr

1 bcRV k 550Min.RHP Min.RHP C

550 8 1 R R V 2 RB x

−

−

− −

    ρ  

≈ +     +   ρπ −    

. 

The second term in the tail rotor power is induced power associated with tail rotor thrust. 

Keep in mind that when the helicopter is on the ground, friction between the landing gear and 

the ground provides anti-torque to react the main rotor’s minimum horsepower; so the tail 

rotor can be at any reasonable thrust including zero. But, off the ground (or supported by a 

frictionless bearing so that the main rotor thrust is zero), some tail rotor thrust is required for 

yaw equilibrium to balance the torque of the main rotor at minimum power. 

 Equation (2.120) includes the fact that the flight test data being examined has errors. 

The error here is that (with reasonable estimates of minimum main- and tail-rotor powers) 

when the weight coefficient is zero, the sum of all powers in Eq. (2.120) should be zero. This 

point is illustrated in Fig. 2-73. One test procedure that minimizes this error is to run the 

aircraft on the ground at zero main- and tail-rotor thrusts. Data is recorded at several engine 

RPMs. The measured main rotor and tail rotor shaft torques (not powers), when plotted versus 

their respective rotor speeds squared, should show zero torque at zero rotor speed. If they do 

not, serious questions are raised. The engine torque versus engine RPM squared will not show 

zero because of the power required by accessories. Plotting engine horsepower versus RPM 

cubed should project to a power approximating the accessory power. 
2.3 HOVER PERFORMANCE 

175 

 The results of applying Eq. (2.120) are shown in Fig. 2-74. This figure reflects modern 

results based on hover engine power required (out of ground effect) obtained with 40 single 

rotor helicopters. This group does not include results where compressibility was an obvious 

factor, such as those reported by Ritter [207]. A little statistical analysis plus educated 

guessing shows that the average constants for the 40 helicopters are: 

• Main rotor minimum airfoil drag coefficient (Cdo) = 0.008 

• Tail rotor minimum airfoil drag coefficient (Cdo-tr) = 0.016 

• Tail rotor induced-power correction factor (ktr) = 1.35 

• Main rotor transmission efficiency (ηmr) = 0.96 

• Tail rotor transmission efficiency (ηtr) = 0.95 

 Because the flight test reports give little or no information about accessory power, I 

lumped SHPacc and error into one constant horsepower for each individual helicopter. This 

lumped sum yielded 28 results with less than 5 percent error, 10 results with between 5 and 

10 percent error, and 2 results with between 10 and 15 percent error when the blade element 

results are compared to experiment. These are percentages of the lowest-recorded engine shaft 

horsepower of the respective helicopter. 

0

1

2

3

4

5

6

7

8

9

0 0.5 1 1.5 2 2.5 3 3.5 4

CW/σ2

40 Helicopters, 1450 Data points

Mean Line

Plus 5%

Minus 5%

Engine

 (CP - CPo)/σ3

Fig. 2-74. Flight test data from 40 single rotor helicopters show that Knight and Hefner’s 

similarity parameters remove solidity as a variable for engineering purposes. 
2.3 HOVER PERFORMANCE 

176 

 The 40 helicopters have a wide range in solidity and blade-aspect ratio as Fig. 2-75 

shows. The main rotor blade count varies from two, for several Bell Helicopter products, up 

to seven for the largest Sikorsky helicopter. The two helicopters with high-solidity, ductedfan, anti-torque devices (11 and 13 blades) are not shown in Fig. 2-75. 

 These very encouraging results are shown in Fig. 2-74. In 1939, Knight and Hefner 

provided a very unique, nondimensional form of blade element momentum theory. Their work 

has received far too little attention by the rotorcraft aerodynamic community. 

 The real question is, of course, how well does the semiempirically modified, blade 

element momentum theory convey the modern results of single-rotor-helicopter power 

required in hovering out of ground effect. The favorable answer is shown for the 40 

helicopters discussed in Fig. 2-76. Equations (2.47), (2.115), (2.116), and (2.119) are used 

with the main rotor airfoil drag rise with lift coefficient squared (k), and the induced-power 

“correction” factor (ki) defined. That is, along with 

• Main rotor minimum airfoil drag coefficient (Cdo) = 0.008, 

• Tail rotor minimum airfoil drag coefficient (Cdo-tr) = 0.016, 

• Tail rotor induced-power correction factor (ktr) = 1.35, 

• Main rotor transmission efficiency (ηmr) = 0.96, and 

• Tail rotor transmission efficiency (ηtr) = 0.95, 

0

5

10

15

20

25

0 0.05 0.1 0.15 0.2 0.25 0.3

Main Rotors

Tail Rotors

Blade 

Count

b = 7

6 5

b = 2 3 4

Blade 

Aspect 

Ratio

Solidity

Fig. 2-75. Flight test data from 40 single rotor helicopters covers a wide range in solidity, 

blade number, and blade-aspect ratio. 
2.3 HOVER PERFORMANCE 

177 

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

16,000

0 2,000 4,000 6,000 8,000 10,000 12,000 14,000

40 Helicopters, 1450 Data points

Perfect Prediction

Minus 5 percent

Plus 5 percent

Test 

ESHP

Estimated ESHP

Fig. 2-76. Hover engine horsepower required by 40 single rotor helicopters is estimated 

by blade element moment theory—given reasonable empirical constants. 

modern results also suggest that 

• Main rotor airfoil drag coefficient rise with 2 Cl is (k) = 0.008, and 

• Main rotor induced power correction factor (ki) = 1.12. 

 Fig. 2-77 provides two examples of the semiempirical use of blade element 

momentum theory as summarized in the preceding paragraphs. Basically, the theory predicts 

very reliable increments in power with weight increases. The primary problem in using the 

theory is accurately setting the estimated engine horsepower at “zero” weight, which only 

requires a very educated guess as to the input constants. Still, well over 40 successful 

helicopters have been developed by several companies using no better theory than what I have 

just described. 

 In 30 out of the 40 examples, the comparisons such as those shown in Fig. 2-77 

required reducing the estimated power at zero weight coefficient so that the curve passes 

through the experimental data. In that sense, I hope that the engineering equations offered in 

this summary are conservative. The reason I have chosen a measure of conservatism is that 

marketing brochures and proposals to the military have, over six decades, promised more than 

was delivered [249]. 
2.3 HOVER PERFORMANCE 

178 

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014

CH-53E

YOH-2HU

Engine 

CP

Weight Coefficient CW

Fig. 2-77. Hover power required of the smallest and largest single rotor helicopters in the 

40 examples under discussion. 

2.3.9 Twin-Rotor Helicopters 

 There is no question that the single rotor plus tail rotor configuration dominates the 

helicopter world. However, experimental, prototype, and production versions of helicopters 

using multiple main rotors are more in evidence than you might think. The culling process 

(helped by World War II) quickly discarded tri-rotors and quad-rotors, and Focke’s side-byside pioneering effort. Experimental flight of at least 40 twin-rotor machines further reduced 

the field to 3 major manufacturers. Even a quick scan of industry efforts leads to the partial 

summary of production, twin-rotor helicopters provided in Table 2-13. Within this group, 

Frank Piasecki developed the tandem configuration starting with the HRP, which grew to the 

H-21 series, and then the HUP for the U.S. Navy, and its spin-off, the H-25, for the U.S. 

Army. Charlie Kaman developed the synchropter, the H-43 series, for the U.S. Air Force. And 

Nikolai Kamov developed and produced the coaxial configuration for the then Soviet military. 

 Modern results of twin-rotor hovering performance are shown in Fig. 2-51 and 

Fig. 2-52. The trouble is you cannot see the data points because the single rotor helicopter 

points are so dominant. The two figures, with single rotor helicopter data points removed, are 
2.3 HOVER PERFORMANCE 

179 

repeated here as Fig. 2-78 and Fig. 2-79. The hover performance, expressed in engine 

CP versus CW coefficient form, is illustrated in Fig. 2-78. The solid line on this figure was 

obtained from Eq. (2.41), which is repeated here for convenience: 

(2.41) Reqd.

3/2 C 0.0157C 1.045C P WW = + . 

Table 2-13. Twin-Rotor Helicopters 

Manufacturer Type 

Power 

Plant Model Year 

Max 

TOGW 

(lb) 

Diameter 

(ft) 

Total 

Engine(s) 

(SHP) 

Piasecki tandem piston HUP/H-25 Series 1948 6,005 35.00 525 

Piasecki tandem piston H-21 Series 1954 13,233 44.00 1,425 

Boeing Vertol tandem turbine CH-46 Series 1960 21,385 50.00 2,100 

Boeing Vertol tandem turbine Model 107 1962 19,000 50.00 2,800 

Boeing Vertol tandem turbine CH-47 Series 1967 29,850 60.00 5,700 

Boeing Vertol tandem turbine Model 234 Series 1981 51,000 60.00 8,150 

Bristol tandem turbine B-173 Series 1951 14,500 48.56 1,700 

Bristol/Westland tandem turbine B-192 1958 19,995 48.67 3,300 

Yakovlev tandem piston Yak-24 Series 1957 37,479 68.92 3,400 

Kaman synchropter turbine H-43 Series 1966 9,150 47.00 1,100 

Kaman synchropter turbine K-Max 1993 10,394 42.17 1,800 

Flettner synchropter piston FL-282 1941 2,205 39.38 140 

Kamov coaxial piston Ka-15 1952 3,100 32.71 225 

Kamov coaxial piston Ka-18 1957 3,310 32.71 275 

Kamov coaxial turbine Ka-25BSh 1967 16,535 51.65 1,800 

Kamov coaxial turbine Ka-32 1982 23,148 52.17 4,410 

Kamov coaxial turbine Ka-26 1965 7,165 42.65 650 

Kamov coaxial turbine Ka-27 1974 18,500 52.17 2,500 

Kamov coaxial turbine Ka-28 1975 18,500 52.17 2,500 

Kamov coaxial turbine Ka-29 1985 27,775 52.17 4,450 

Kamov coaxial turbine Ka-32 1975 27,775 52.17 4,410 

Kamov coaxial turbine Ka-50 1985 21,550 47.58 4,450 

Kamov coaxial turbine Ka-126 1990 7,165 42.65 720 

Kamov coaxial turbine Ka-226 1995 6,835 42.67 840 

Focke side-by-side piston FA-223 1940 9,480 39.38 1,000 
2.3 HOVER PERFORMANCE 

180 

 At the present time, to the best of my knowledge, Kamov has not made detailed flight 

test performance data available to the public for any of its coaxial helicopters. As a stand-in, I 

have used published data from the Sikorsky XH-59A, their Advancing Blade Concept 

helicopter [210, 250]. 

 Twin-rotor helicopter performance in Figure of Merit form is shown in Fig. 2-79. 

Based on limited data, one would have to say that the coaxial helicopter enjoys a significant 

hover performance advantage. 

 There has been, on many occasions, rather heated technical (and marketing) 

discussions about how twin-rotor performance should be calculated and presented. For 

example, one question is, “In the calculation of total thrust, or weight, or power coefficients, 

what is the reference rotor area?” Another question is, “If Figure of Merit is the ratio of ideal 

power to actual power, what is the ideal power for twin rotors that are partially overlapped?” 

In general, the answers are quite straightforward for the coaxial helicopter because, with equal 

rotor diameter and equal blade number for the upper and lower rotors, simple momentum 

theory treats the system as one single rotor having twice the number of blades. Flight test 

reports for the Sikorsky XH-59A [210, 250] use the reference rotor area as simply πR2

 where 

(R) is the radius of one blade. The reference area for the H-43 synchropter [193] has also been 

taken as πR2

 even though there is a slight distance between the two rotor hubs. All flight test 

data for tandems has been reduced to coefficient form with a 2 πR2

 reference area. 

 The coaxial arrangement of twin rotors has received some theoretical and 

experimental study [251-253], but nowhere near as much effort as has gone into the single 

rotor configuration. Coleman’s survey [253], performed in 1997, did uncover the salient 

features of what has been done. If you want to pursue the configuration further, I would 

recommend direct discussion with the Kamov Company. 

 It is primarily with the tandem rotor helicopter, developed by Frank Piasecki [90], that 

things get a little complicated. You might not know that Frank Piasecki’s first venture was a 

small, single rotor machine, the PV-2, which was very successful. His first tandem helicopter, 

the XHRP-X, grew to become the H-21. This series had two rotors, but they were not 

overlapping. But then, in the mid-1940s, the U.S. Navy initiated a competition for a small 

helicopter to be used for airplane guard duty aboard its carriers. This helicopter was to fly 

alongside the carrier when airplanes were landing and taking off. The objective was to rescue 

pilots who went into the water. To meet the size constraints, Piasecki selected a very small, 

very overlapped, tandem rotor configuration (the XHJP-1, later to become the HUP) to 

compete against the Sikorsky conventional single rotor XHJS-1, a slightly enlarged R-5 or 

S-51. Piasecki’s HUP won the fly-off competition and entered Navy service in January 1951. 
2.3 HOVER PERFORMANCE 

181 

0

20

40

60

80

100

120

140

160

0 20 40 60 80 100 120 140

H-21B Tandem

CH-46A Tandem

CH-47D Tandem

HH-43B Synchropter

XH-59A (ABC) Coaxial

Eq. 2.41

XH-59A(ABC)

Coaxial

HH-43B

Synchropter

CH-47D

Tandem

Engine 

Power 

Coeff. 

CP×105

Weight Coeff. CW×104

Fig. 2-78. Twin-rotor helicopter performance. 

0.40

0.45

0.50

0.55

0.60

0.65

0.70

0 0.002 0.004 0.006 0.008 0.01 0.012

H-21 Tandem

CH-46A Tandem

CH-47D Tandem

H-43B Synchropter

XH-59A (ABC) Coaxial

Eq. 2.46

Figure 

of 

Merit

(Weight Coeff.)1.5/Solidity

Fig. 2-79. Coaxial helicopters appear to have the highest Figure of Merit. 
2.3 HOVER PERFORMANCE 

182 

 There is some fundamental size logic and hover performance logic for the twin-rotor 

helicopter. To illustrate this logic, consider the following contrasting views that Piasecki (with 

his XHJP-1) and Sikorsky (with his XHJS-1) must have seen. The engine of choice at that 

time was the Continental R-975-34, rated at 500 horsepower. Both helicopters, fully loaded, 

weighed about 5,300 pounds [89]. For discussion purposes, say that 250 of the 500 

horsepower was spent on ideal induced power at sea level on a standard day, where the air 

density was 0.002378 slugs per cubic foot. This would be a Figure of Merit of 0.5 and would 

ensure a power margin. For the single rotor machine, this would mean the rotor diameter 

would be 45.9 feet. That is, 

(2.123) ( ) ( )( ) ideal 2 2

4 4

W W 5,300 5,300 HP 250hp 550 550 2 D 2 0.002378 45.9 π π = = = ρ . 

The overall length of the single rotor, with both main rotor and tail rotor blades folded or 

removed, would be about 0.8 of the main rotor diameter, or about 37 feet. 

 Now think of splitting the 5,300 pounds gross weight onto two isolated rotors where 

the hubs are separated by slightly more than a diameter. This means two rotors, each having a 

diameter of 32.5 feet. That is, 

(2.124) ( ) ( ) ( ) ideal 2 22

4 44

W/2 W/2 W/2 W/2 W W/2 HP 250hp 550 550 550 2D 2D 2D π ππ = + ==

ρ ρρ . 

The overall length of this nonoverlapped (i.e., not intermeshed) tandem rotor helicopter with 

all blades removed or folded would be about 42 feet. 

 On this basis, the single rotor and tandem rotor size competition would favor the 

single rotor configuration because it is some 5 feet shorter, however, the tandem configuration 

would provide more fuselage length for cargo. But the U.S. Navy competition was not for 

cargo space. The competition was for a small-sized machine that would not occupy much 

carrier space. (Apparently, a coaxial helicopter was not in consideration—perhaps because of 

height restrictions—and blade folding must have been a given.) 

 Piasecki’s solution was to overlap the XHJP-1 rotors, which reduced the length to 

32 feet with folded blades. With refinement that included a Sperry automatic pilot, the Navy 

had the HUP-2 shown in Fig. 2-80. 

 In 1947, to support the design decision to overlap the rotors, Mr. Wieslaw Z. 

Stepniewski and a small team of enthusiasts working at Piasecki Helicopter Corporation, 

conducted a fundamental tandem-rotor hover performance test. The experiment measured 

thrust and power required by two, three-bladed, 4-foot-diameter rotors. Hover-out-of-groundeffect performance was obtained at four overlapped co-planar positions. Funding for this test 

came as part of the U.S. Navy program to develop the HUP series when this nearly 6,000- 

pound-gross-weight tandem helicopter went into production. The model thrust and power 
2.3 HOVER PERFORMANCE 

183 

Fig. 2-80. The Piasecki HUP was the world’s first overlapped tandem helicopter. Note 

that the rear rotor is considerably above the forward rotor (photo from author’s 

collection). 

data, though published [247, 254], received very limited distribution.56 Fortunately, the key 

thrust and power tabulated data from this landmark test—the only one I know of—was 

recovered along with significant background [255] and is reproduced here as Fig. 2-81. 

 The procedure Mr. Stepniewski used during his co-planar, tandem rotor overlap 

experiment was quite straightforward. The fore and aft, 4-foot-diameter rotors were first 

individually tested to baseline isolated rotor performance. Then both rotors were set to a 

nominally equal collective pitch angle. Finally, the two rotors were “slid together” starting 

from a nonoverlapped position of d/D = 1.0365, where (d) is the distance between rotor hubs 

and (D) is rotor diameter. Repositioning for each overlap required stopping the model and 

hand adjusting the movable rear rotor towards the front rotor. Data was recorded at successive 

overlaps of d/D = 1.0365, 0.8802, 0.7604, and 0.6250. This overlap sweep was repeated six 

times. The lowest collective pitch of 7 degrees was tested at 1570 and 1780 rpm, and the midcollective of 9 degrees at 1570, 1780, and 2015 rpm. The highest collective pitch, 

11.5 degrees, was tested only at 1570 rpm. The RPM range gives tip speeds of 330, 383, and 

422 feet per second. The tip Reynolds number ranges from 264,000 to 337,000. 

 

56 Mr. Wieslaw Z. Stepniewski participated in every tandem rotor helicopter developed by the now Boeing 

Helicopters Division. Mr. Stepniewski, better known worldwide as just “Steppy,” sent me an original of this very 

valuable report in 1995. I made a copy (returned the original) and put the raw data into a Microsoft® Excel®

spreadsheet. Steppy answered all my questions about the data acquisition and reduction steps. I was able to 

reaffirm the results with only minor differences. With Steppy’s encouragement and consent, the thrust and power 

data were published in tabulated and graphical form [255]. This data, which lies behind the Kov factor, should be 

of considerable value to current and future investigators. 
2.3 HOVER PERFORMANCE 

184 

0.0002

0.0003

0.0004

0.0005

0.002 0.003 0.004 0.005 0.006

CP twin

CT twin

Symbol

Open = 1,570 rpm

Shaded = 1,780 rpm

Solid = 2,015 rpm

Nominal Collective

Pitch = 7 deg.

Pitch = 9 deg.

11.5 

deg.

d/D

0.625 1.0365

0.625

0.7604

0.8802

1.0365

Fig. 2-81. Stepniewski’s 1947 co-planar, twin-rotor hover experimental results 

with varying overlap. 

 This model twin-rotor hover performance, in practical engineering coordinates of 

CP twin versus CT twin, is shown in Fig. 2-81. The secondary variable is overlap expressed as a 

ratio of distance between the hubs (d) to the rotor diameter (D). The two coefficients are 

defined as 

(2.125) ( ) ( )

1 2 1 2

P twin 2 3 T twin 2 2

t t

P P T T C and C

2R V 2R V

+ + = =

ρ π ρ π . 

The test results form visible trends in rotor system hover performance with increasing overlap 

at constant collective pitch. Approximate fairings through the data at d/D of 1.0365 and 

0.6250 are shown in Fig. 2-81. (Note that the data set at 2015 rpm and 9-degree collective 

pitch appears out of line with the lower RPM results, however, the trend with overlap is quite 

consistent.) Fig. 2-81 clearly shows that overlapping at constant collective pitch reduces 

thrust much more than it reduces power. 

 The beauty of the twin-rotor experiment Mr. Stepniewski performed lies in testing for 

the increment in performance by sliding the two rotors together while holding all other 

variables constant. This approach illuminated the 8 to 12 percent overlap influences on 

performance even though the absolute data is, perhaps, no better than ±3 percent in either 
2.3 HOVER PERFORMANCE 

185 

CP twin or CT twin. There is, of course, some experimental data scatter even with this most 

fundamental testing approach. However, Fig. 2-81 shows experimental scatter was 

substantially reduced. Mr. Stepniewski and his small group obtained the major answers to 

how overlapping affects twin-rotor hover performance with just 36 thrust-power data points! 

 As a more complete historical footnote, the first application and extrapolation of this 

meager (some might say) amount of data was on the Piasecki PV-14 tandem rotor helicopter. 

This helicopter was initially designated by the U.S. Navy as the XHJP-1, and later became the 

HUP series in production. The HUP was the first tandem rotor helicopter intermeshed (i.e., 

overlapped) to a d/D on the order of 0.62. This small, 6,000-pound-gross-weight, pistonpowered machine was followed by the CH-46 at 20,000 pounds, and then by the CH-47 with 

a gross weight approaching 50,000 pounds. The two, larger, very successful tandem rotor 

helicopters had slightly less overlapping (i.e., d/D = 0.65). 

 In Mr. Stepniewski’s original report [247], analysis of each data set was presented. 

The basic experimental trends of thrust (in pounds) and power (in horsepower) versus rotor 

overlap (1−d/D in percent) were compared to the theory that Mr. Stepniewski included in an 

appendix to the report submitted to the U.S. Navy. The conclusions of that report [247] noted 

that the theory and model test results were in agreement and that “furthermore, in flight tests 

of the XHJP-1 helicopter, good correlation was found between the predicted and measured 

performance in hovering and vertical flight.” In fact, the model test data was considered 

“slightly more conservative” than the theory, and the theory was “recommended for practical 

design.” 

 Mr. Stepniewski and his team semiempirically reduced the thrust and power data to a 

simple overlap correction factor that was designated Kov. This factor accounted for increasing 

power when two rotors are overlapped while holding total thrust constant. In its original form 

[247], the correction factor applied to the total power. Later, by subtracting a roughly 

approximated profile power from the total power, the Kov factor became a correction to just 

induced power. This semiempirical step was described in detail [237]. Steppy and Chuck 

Keys later provided a modern source that discussed this Kov factor, as well as thrust and 

power of intermeshing and overlapping rotors [238]. 

 Considerable insight about overlapped (i.e., some say intermeshed) twin-rotor power 

required can be obtained using simple blade element momentum theory discussed earlier in 

paragraph 2.3.7. The hover performance of equal solidity, twin-rotor systems (having blades 

that are untapered with a θ(x) = θtip/x pitch angle distribution along the blade, which is the 

basis of ideal rotor hover performance) is summarized in just a few equations, given some 

fundamental background. The amount of co-planar overlap is defined by the ratio of hub 

separation distance (d) to rotor diameter (D). This ratio (d/D) dictates the portions of 

geometric planform area that are either nonoverlapped (nov) or overlapped (ov). The simple 

geometry of this problem is seen in Fig. 2-82, which outlines the planform view of twin, equal 

diameter, and overlapped rotors. 
2.3 HOVER PERFORMANCE 

186 

d

Rotor

Shaft

Overlapped

Area Is Two

Segments

Rotor 1 Rotor 2 S 2 S 1

Aov = S 1 + S 2

X X

Y

Y

Fig. 2-82. Twin-rotor geometry involves the area of overlapping circles and the basic 

geometry of segments. 

 The area of one segment, or its mirror image as Fig. 2-82 shows, can be found in 

elementary science handbooks. For twin-rotor purposes, this area is defined by d/D as 

(2.126) 

2

2 1 dd d Area Segment 1 Area Segment 2 R cos 1 DD D

−

       = = −−                

. 

Johnson (page 121 of reference [235]) defines a segment area parameter (m) as 

(2.127) 

2

2 dd d 1 m cos 1

DD D

−

      

≡ −−        π       

and thus, the total nonoverlapped, planform projected, geometric area (Anov ) of both rotors is 

(2.128) ( ) 2 Twin A Rotor 1 A Rotor 2 A 2 R 1 m nov nov nov = + =π − . 

Following similar logic, the total overlapped, planform projected, geometric area (Aov ), is 

(2.129) 2

ov

m Twin A Area Segment 1 Area Segment 2 2 R 2

  =+ = π    . 

The planform projected, geometric area of a twin-rotor configuration accounting for any 

amount of overlap defined by d/D (or m) is, of course, simply 
2.3 HOVER PERFORMANCE 

187 

(2.130) 2

geo nov ov

m Twin Geometric Area A Twin A Twin A 2 R 1

2

  ≡ = + =π −    . 

Note that when the two rotor discs are just touching at their perimeters, d/D = 1 and m = 0 

from Eq. (2.130). Therefore, Ageo = 2πR2

. At the most overlapped condition of a coaxial, 

twin-rotor system, d/D = 0 and m = 1 so that Ageo = πR2

. 

 Hover thrust and power for co-planar, overlapped configurations, expressed in terms 

of tip collective pitch (θtip), are easily derived. Because the blades are untapered, solidity 

(using the blade number of one rotor) can be used to scale the tip collective pitch as Knight 

and Hefner showed [243]. Therefore, let 

(2.131) tip

tip 2

16 bcR and with both rotors of equal geometry. a R

  θ

Θ ≡   σ =

  σ π

Simplistic airfoil lift and drag aerodynamics for all blade elements are assumed as 

(2.132) 2 C a and C C kC   =α = + d do . 

Finally, the induced velocity in the nonoverlapped region is identical to the induced velocity 

of the single, isolated rotor according to blade element momentum theory. That is, assuming 

both rotors have identical geometry, 

(2.133) tip

tip

t

16 v 16

1 2x 1 1 2 1

a V ax

    θ

= + − = +Θ −     σ σ    

nov . 

 The induced velocity in the overlapped region was derived by Mr. Stepniewski who 

first published his work in 1948 [254]. Today, the somewhat revised discussion and derivation 

is contained in reference [238], starting at page 112. Following this approach, uniform 

induced velocity will also occur in the overlapped region with constant chord blades having a 

θ(x) = θtip/x twist distribution, where x is radius station (r) divided by rotor radius (R). When 

rotor 1 and rotor 2 have equal geometry, it follows that the magnitude of this uniform induced 

velocity in the overlapped region will be 

(2.134) tipR1 tipR 2 tip

t

8 1 v

1 11 1

aV 2

= + Θ +Θ − = +Θ −     σ

ov . 

With the preceding fundamentals in hand, integration of the blade element momentum 

equation yields the twin-rotor thrust coefficient, ( )

1 2

T twin 2 2

t

T T C

2R V

+ ≡ ρ π

 , as 

(2.135) ( ) ( ) ( ) ( )

2 2 2 2

T twin tip tip

a 1 1 C 1 2 1 1 m1 1 m

32 4 2

σ   ≡ +Θ − − + +   Θ −  . 
2.3 HOVER PERFORMANCE 

188 

 The twin-rotor power coefficient is defined as C P P

R V

P twin

t

≡ 1 2 +

2 3 ρ π e j 2

. The total rotor 

power required equals the sum of (a) induced power due to collective pitch, (b) minimum 

profile power, and (c) delta profile power due to collective pitch. The three elements, found 

by integrating blade element momentum equations, are 

(2.136) ( ) ( ) ( ) ( ) i

3 3 3 3

P twin tip tip

a 1 (a) C 1 2 1 1 m 1 1 m

512 4

σ   = +Θ − − + +   Θ −  , 

(2.137) d o

P o twin

C

(b) Min. C 8

σ = , and 

(2.138) (c) ( ) ( ) ( ) ( ) 3 3 2 2

Po twin tip tip tip tip

a ka m C 1 1 2 1 m 2 21

512 2

σ     Δ = Θ + − + Θ − + Θ + − +Θ        

. 

 Twin-rotor hovering performance for rotors using untapered blades having a 

θ(x) = θtip/x twist distribution can be summarized in practical engineering, CP twin versus CT twin, 

form. A useful, first-order approximation [255] for twin rotors where 2 CT twin σ lies between 

1 and 2, and d/D lies between 0 and 1, is 

(2.139) 

2 3/2

do 2 T twin

P twin T twin i

C 4k 2 d 2 d C

C C k2 1

8 2D 2 D 2

σ          ≅ + + − +−       

σ           

. 

Keep in mind that solidity is calculated using the blade number of one rotor and the reference 

area is 2πR2

. 

 The preceding simple theory confirms the experimental trends that Mr. Stepniewski 

observed in his 1947 model test, as Fig. 2-83 shows. The variation of rotor system thrust and 

power when twin rotors are overlapped is quite dependent on whether collective pitch is held 

constant, or total thrust is held constant, or total power is held constant. 

 The third term in Eq. (2.139) is the minimum induced power of hovering twin rotors 

having the assumed blade geometry. This power is multiplied by the induced power 

correction factor (ki) as you saw with single rotor configuration. If the two rotors are not 

overlapped, then d/D ≥ 1 and the bracketed term is 1.0, in which case the twin-rotor induced 

power reduces to the ideal power of two, isolated, single rotors. 

 The fully overlapped configuration, a co-planar coaxial arrangement, has d/D = 0, and 

the bracketed term is 2 . There is considerable confusion about this result in both technical 

and marketing literature. Because part of this confusion is caused by nomenclature, it is worth 

a moment to express the result without using coefficients. To begin with, 

(2.140) ( )

3/2

1 2 T twin 3/2

P twin T twin 2 3

t

P P C

Ideal induced C 2 C when d / D 0

2R V 2

+   ≡ == =  

ρ π  

. 
2.3 HOVER PERFORMANCE 

189 

0

0.0001

0.0002

0.0003

0.0004

0.0005

0 0.0001 0.0002 0.0003 0.0004 0.0005

Test 

CP twin

Theory CP twin

Fig. 2-83. Stepniewski’s twin-rotor performance shown in Fig. 2-81 is predicted using 

Eq. (2.139) with Cdo = 0.008424, k = 0.0108, and ki = 1.2023. 

Then, 

(2.141) ( ) ( )

3 2

2 3 1 2

12 t 2 2

t

T T Ideal induced power P P 2 R V when d / D 0 2R V

  +

=+= ρ π =  

  ρ π  

. 

A little bit of algebra sorts things out so that 

(2.142) ( ) ( )

( ) ( ) ( )

3 2

1 2 1 2

12 12 ideal 2 2

T T T T P P T T when d / D 0

2 R 2 R

+ +

+ = =+ =

ρ π ρ π , 

which is exactly the momentum theory for a single rotor carrying a thrust of T1 + T2 on one 

rotor having an area of π R2

. 

 As a concluding example, suppose an 8,250-pound helicopter is supported by twin 

rotors, each having a diameter of 47 feet. Each rotor has a swept disc area (πR2

) of 

1,735 square feet, a solidity of 0.03542, and a tip speed of 640 feet per second. The helicopter 

is hovering out of ground effect at sea level on a standard day where the air density is 

0.002378 slugs per cubic feet. On this basis, the twin-rotor weight coefficient would be 
2.3 HOVER PERFORMANCE 

190 

(2.143) ( ) ( )

1 2

W twin 2 2 2

t

T T 8, 250 C 0.002441

2R V 0.002378 2 1,735 640

+ = = = ρ π × . 

Now assume each rotors’ performance constants are Cdo = 0.010, k = 0.010, and ki = 1.20 and 

then, using Eq. (2.139), compute the total rotor horsepower (RHP) required by both rotors as 

the twin rotors move from a nonoverlapped arrangement (d/D = 1) to a co-planar coaxial 

position (d/D = 0). The results are presented in Fig. 2-84. 

 The lowest line (the short, dashed line) on Fig. 2-84 is the ideal, induced rotor

horsepower. (Because I have not addressed transmission efficiency and accessory power yet, 

the powers under discussion are just rotor powers.) Notice that at d/D = 1.0, the total RHP is 

about 333 horsepower. In contrast, when d/D = 0, the ideal induced power has increased to 

RHP = 475. The ratio of these two RHPs is exactly 2 . 

 The middle line on Fig. 2-84 is the ideal, induced rotor horsepower increased by the 

empirical factor, ki = 1.2. The top line on Fig. 2-84 is the total rotor horsepower, which 

includes the profile power. 

300

350

400

450

500

550

600

650

700

750

800

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Twin Rotor 

Total 

Horsepower

Overlap Ratio (d/D)

Ideal Induced RHPi

Actual Induced RHPi = ki (Ideal RHPi)

Total RHP

Fig. 2-84. An example of the effect of overlapping twin rotors at constant total thrust 

using Eq. (2.139) with Cdo = 0.010, k = 0.010, and ki = 1.20. 
2.3 HOVER PERFORMANCE 

191 

 Of course a co-planar, coaxial, twin rotor cannot be physically constructed if the rotors 

are rotating in opposite directions, however the synchropter does come very close. The 

Kaman H-43 synchropter (Fig. 2-85) has two hubs separated by 4 feet, 2.25 inches. Its rotor 

diameter is 47 feet. Therefore, d/D = 0.0891 [193]. Note that to obtain this compactness, the 

two rotor shafts are laterally inclined so that the included angle between the two shafts is 

13.0 degrees. This means that the actual rotor thrust must exceed the gross weight by a little 

more than 0.5 percent. Keep in mind that this 0.5 percent of gross weight amounts to about 

50 pounds, which could be baggage for one or two people. 

 The preceding numerical example was, in fact, a calculation of the Kaman H-43 power 

required to hover at 8,250 pounds at sea level on a standard day with 260 rpm rotor speed. 

From the flight test report [193], the engine shaft horsepower (ESHP) required is 820 hp. 

From Fig. 2-84, the rotor horsepower (RHP) required for d/D = 0.0891 is 746 hp. With a 

Fig. 2-85. The Kaman H-43 Huskie has extremely overlapped twin rotors 

(drawing from author’s collection). 
2.3 HOVER PERFORMANCE 

192 

transmission efficiency of 0.95 (a little low, I suspect) and 35 horsepower for accessories, you 

have 

(2.144) Main Rotors

Accessory

Main Rotors

RHP 746 ESHP SHP 35 820 hp 0.95

= + = +=

η . 

This H-43 calculated result, built on Mr. Stepniewski’s 1947 model rotor experiment, is rather 

satisfying in my opinion. 

 It should not come as a surprise that the former N.A.C.A. (renamed and refocused to 

NASA in 1958) continued its rotorcraft research, albeit with ever-decreasing emphasis. In 

November 1960 George Sweet reported hovering measurements for twin rotors with and 

without overlap [248]. Sweet used an improved rotor test stand used in earlier tests by 

Dingeldein [256] and others at N.A.C.A. Langley. Sweet, in his introduction, stated that 

“until recently there has been some question as to the accuracy of test results from twin-rotor 

helicopters, either because of scale effects or because of insufficiently accurate 

instrumentation. For example, the results of the twin-rotor tests of reference 1 [256]57 indicate 

a large increase in hovering performance, whereas the data of reference 2,58 for essentially the 

same configuration, show no increase in performance.” 

In the same introduction, Sweet said that “the present instrumentation is greatly improved 

over that used in the tests of reference 1, inasmuch as the performance of each rotor was 

measured individually.” It is important to note that Sweet measured the thrust and torque of 

each rotor, whether in tandem, or as the forward rotor alone, or the aft rotor alone. Sweet, 

therefore, chose to define thrust and power coefficients of each rotor individually based on the 

area of one rotor (A = πR2

). 

 Sweet was very thorough in his experiment and use of the tandem-rotor test stand. He 

had low solidity (0.0543), two-bladed rotors, and a set of higher solidity (0.0968) blades 

available to him. Before adjusting the twin rotors to the overlap separation of d/D = 0.615, he 

tested each rotor as a single rotor and then went on to test twin rotors at a separation of 

d/D = 1.015. The result of this confidence-building initial testing is shown here in Fig. 2-86 

(in Knight and Hefner’s format). Sweet could discern little CP versus CT difference between a 

rotor tested on the forward hub and a rotor tested on the aft hub of the tandem-rotor test stand, 

and there was little CP versus CT difference when the twin-rotor hubs were separated by 

slightly more than a diameter. 

 The prediction line (the solid line shown in Fig. 2-86) was computed using Knight and 

Hefner’s extended equations, (2.90) and (2.95), as discussed in section 2.3.7, Blade Element 

Momentum Theory Revisited. I used an airfoil lift-curve slope (a) of 5.73 per radian, an 

airfoil drag coefficient rise with airfoil lift coefficient ( 2

d l k dC dC = ) of 0.007, and a bladeroot cutout (xc) of 0.15, and calculated the tip loss factor (B) with Eq. (2.96). The minimum 

 

57 Sweet makes it very clear that Dingeldein’s test and conclusion [256] are suspect. 

58 Sweet refers to Stepniewski’s 1949 overlap test and the data shown in Fig. 2-83. 
2.3 HOVER PERFORMANCE 

193 

power coefficient at zero thrust (CPo = σCdo/8) was calculated with a minimum airfoil drag 

coefficient (Cdo) of 0.007. 

 The experimental results that Sweet obtained can be “predicted” with a simpler 

application of twin-rotor blade element momentum theory by modifying Eq. (2.139) to read as 

(2.145) 

( )

2 3/2

do 2 T twin

P twin T twin 2 2 2 2 c c

C 4k 1 2 d 2 d C

C FF C 2 1

8 2D 2 D B x B x 2

σ           ≅ + + − +−        

σ − −            

. 

Here the induced-power correction factor (ki) is set equal to 2 2

c 1B x − , and the tip loss 

factor (B) is given by 

1/2

Ttwin

2

3.25 C

B 1

AR

  = −   π σ   . I have introduced a fudge factor (FF) which is 

used to make the basic curve shape pass through the experimental data. When the two rotors 

are not overlapped, d/D = 1. As a reminder, the solidity (σ) is for just one rotor. My 

comparison to Sweet’s data using Eq. (2.145) is shown with the solid line in Fig. 2-86. 

The calculation was made with an airfoil drag coefficient rise with airfoil lift coefficient 

( 2

d l k dC dC = ) of 0.007, and the minimum power coefficient at zero thrust (CPo = σCdo/8) 

was calculated with a minimum airfoil drag coefficient (Cdo) of 0.007. To make the 

approximation that Eq. (2.145) offers come out “close enough,” I chose FF = 1.0. 

0.0

0.5

1.0

1.5

2.0

2.5

-0.5 0 0.5 1 1.5 2

Single Rotor, Solidity = 0.0543

Single Rotor, Solidity = 0.0968

Twin Rotors, Solidity = 0.0543, No Overlap

Twin Rotors, Solidity = 0.0968, No Overlap

(CP-CPo)/σ3

CT/σ2

Eq. 2-145

Fig. 2-86. Sweet reaffirmed Knight and Hefner’s accounting for solidity.
2.3 HOVER PERFORMANCE 

194 

 Sweet makes it very clear that blade element momentum theory provides a quite 

satisfactory comparison to his single-rotor and nonoverlapped twin-rotor experimental results. 

His data provides convincing evidence that nonoverlapped twin rotors are, to the first 

approximation, nothing more than two, isolated, single rotors. He then proceeds to the 

overlapped case. 

 For the overlapped twin rotors, Sweet chose a pair of the higher solidity blades 

(σ = 0.0968) having a diameter of 15.25 feet. The twin-rotor test stand was reconfigured to a 

hub separation of d/D = 0.615. He then ran the two rotors over the complete CP versus CT

range. His twin-rotor experimental results, which I have converted to dimensional thrust and 

horsepower at sea level on a standard day, and at a tip speed (Vt) of 500 feet per second, are 

shown in Fig. 2-87. My interpretation (Fig. 2-87) of Sweet’s experimental results uses 

Eq. (2.145) with a fudge factor to construct the three lines shown. The fudge factor is 1.03 

for the high-solidity rotor in both the single-rotor and the twin-rotor, nonoverlapped 

configurations. However, for the overlapped configuration, the fudge factor is 1.07.59 

0

10

20

30

40

50

60

70

80

90

-200 0 200 400 600 800 1000 1200

Single Rotor, Solidity = 0.0968

Twin Rotors, Solidity = 0.0968, No Overlap, d/D = 1.015

Twin Rotors, Solidity = 0.0968, Overlapped, d/D = 0.615

Twin Rotor 

Total 

Horsepower

Twin Rotor Total Thrust (lbs)

Eq. 2.145, FF = 1.03

Eq. 2.145, FF = 1.03

Eq. 2.145, FF = 1.07

Fig. 2-87. Sweet’s twin-rotor results for two overlapped separations. 

 

59 As of November 2006 there are no published results from other, more powerful theories that have tried to 

predict Sweet’s test results. The industry’s reliance on simple blade element theory shows a lack of maturity that 

is difficult to convey to upper management. 
2.3 HOVER PERFORMANCE 

195 

Fig. 2-88. The Sikorsky XH-59A has a closely spaced, coaxial rotor system because the 

nearly rigid blades do not flap. The canister between the rotors is test 

instrumentation. The helicopter is in its high-speed, auxiliary jet propulsion 

configuration (photo from author’s collection). 

 

 With this understanding of tandem and synchropter hovering performance, turn your 

attention to twin rotors arranged one above the other, which is commonly called a coaxial 

helicopter. Because the practical, coaxial helicopter cannot have co-planar, totally overlapped, 

twin rotors, the vertical gap between the upper and lower rotors must be accounted for. 

Unfortunately, within the constraint that each rotor must have equal—but opposite—torques 

to ensure yaw moment equilibrium, there is little experimental evidence that vertical spacing 

between the rotors makes a bit of difference within practical configurations [253]. By 

practical configurations, I mean those in production, and that means the products of the 

Kamov Company in Russia. The vertical spacing (h) ratioed to the diameter (D) lies in the 

narrow range of 0.088 to 0.095 for their coaxial configurations. The Kamov rotor systems are 

articulated, and careful attention is paid to rotor blade interference. Of course if the blades are 

more like propellers, the spacing can be reduced. This is the case with the Sikorsky XH-59A 

(Fig. 2-88), perhaps better known as the Sikorsky ABCTM, where h = 2.5 feet, D = 40 feet, and 

h/D = 0.0625 [257]. 

 The Sikorsky ABC helicopter finished up its concept development program in the 

early 1980s. In 2004, Burgess wrote an excellent program overview [258]. He points out that 

this program included model testing [259] and full-scale helicopter wind tunnel testing [260, 

261], as well as flight testing [210]. An assessment of the aircraft’s hovering performance was 

published in 1977 [250]. 

 The literature as summarized by Coleman [253] indicates that the coaxial, twin-rotor 

system acts, in hover, as a single rotor, and that the reference area for the thrust and power 

coefficients is based on πR2

, not 2πR2. To accommodate this approach, Eq. (2.139) with 

d/D = 0 can be converted to CP coaxial and CT coaxial form as follows. The first step is 

(2.146) ( )

3/2

1 2 do 2 T twin

P coaxial T twin i 2 3

t

P P 4k C C

C 2 C k2

R V 8 2

+     σ

= ≅+ +    

σ   ρ π    

. 
2.3 HOVER PERFORMANCE 

196 

Now, ( )

1 2

T coaxial T twin 2 2

t

T T C 2C

R V

+ = =

ρ π , 

and, therefore, 

(2.147) 

2 3 2

do Tcoaxial Tcoaxial

P coaxial i

C 4k C C

C2 k

82 2

    σ   

≅+ +        σ     

, 

which reduces to 

(2.148) ( ) ( )3 2

2 Tcoaxial do

P coaxial Tcoaxial i

C 2k C

C Ck

4 2

σ

≅+ +

σ . 

Remember for this special case of twin rotors (i.e., the coaxial configuration), the thrust and 

power coefficients are based on πR2

, but the solidity (σ) is still based on just one rotor. The 

solidity can be converted to the total number of blades for the two rotors by saying 

σ = 1⁄2 σcoaxial. Then the “standard” CP coaxial and CT coaxial form becomes 

(2.149) ( ) ( )3 2

2 Tcoaxial coaxial do

P coaxial Tcoaxial i

coaxial

C 4k C

C Ck

8 2

σ

≅+ +

σ . 

 The Sikorsky XH-59A flight test data provides the only readily available and 

published, full-scale, coaxial helicopter hovering data with which to test the first-order 

approximation of Eq. (2.149). Therefore, following the Kaman H-43 example, assume 

k = 0.010 and ki = 1.20. However, assume the minimum airfoil drag coefficient of the 

XH-59A blade is lower than that of the H-43 (say Cdo = 0.008 instead of 0.010) because of 

modern blade construction and surface condition. Because Eq. (2.149) returns just rotor 

horsepower (RHP), assume the H-43 transmission efficiency of 0.95 and accessory 

horsepower of 30 hp. 

(2.150) ( )

( )

P coaxial

P coaxial 2 3

t

Rotor C per Eq. 3.203 550 30 Engine C 0.95 R V

×

≅ +

ρ π . 

Note that my assumption here is that accessory power is constant regardless of the air density 

and engine RPM. 

 Now for some results. The XH-59A rotor diameter is 36 feet, the coaxial solidity with 

6 blades (2 rotors × 3 blades per rotor) is 0.127, and the tip speed at 100 percent rotor RPM is 

650 feet per second [250]. Continuing with the assumption that rotor thrust equals aircraft 

weight, you have the comparison shown in Fig. 2-89.60 

 

60 My first try at “correlation” was with Cdo = 0.01 and resulted in the answer being wrong. The line was parallel 

to the flight test results, but too high. So I adjusted the Cdo to 0.008 and got the right answer. Given the five 

constants to be selected, you can get “correlation” with any flight test data. Of course it is very helpful to have 

the test results first. 
2.3 HOVER PERFORMANCE 

197 

 A most illuminating result about twin rotors is that the induced-power correction 

factor (ki) is on the order of 1.2, which comes from Mr. Stepniewski’s 1947 model rotor 

overlap experiment. You saw from the single rotor discussion that this factor was more on the 

order of 1.4. That is, Eq. (2.42) for the single rotor semiempirically follows 

(2.151) do i 3 2

P W

C k Engine C C 8 2σ

= + , 

where transmission efficiency is buried in ki (equals 1.4), accessory power appears as a higher 

Cdo (say 0.01), and the tail rotor is folded into both terms. 

 In contrast, a twin-rotor helicopter semiempirically follows the slightly refined 

Eqs. (2.149) and (2.150), 

(2.152) 

2 3/2

do 2 T twin

P twin T twin i

C 4k 2 d 2 d C

C C k2 1

8 2D 2 D 2

σ          ≅ + + − +−       

σ           

0

20

40

60

80

100

120

140

160

0 20 40 60 80 100 120 140

 XH-59A (Sikorsky ABC) Coaxial 

from USAAMRDL-TN-25

Engine 

Shaft Power

Required 

Coefficient 

CP ×105

Weight Coefficient CW ×104

Eqs. 2.149 & 2.150 with:

Cdo = 0.008

k = 0.01

ki = 1.2

Xmsn eff. = 0.95

Accessory = 30 hp

Eq. 2.41

Fig. 2-89. Sikorsky’s XH-59A hover power required.
2.3 HOVER PERFORMANCE 

198 

from which it follows that 

(2.153) 

( )

2 3/2

do 2 W twin

W twin i

P twin

xmsn

accessory

2 3

t

C 4k 2 d 2 d C

C k2 1

8 2D 2 D 2

Engine C

550SHP

R V

σ          + + − +−       

σ           

≅

η

+

ρ π

where ki = 1.2. Of course a fudge factor may be used to improve the correlation after some 

real test data has arrived. 

 This result for twin-rotor helicopters versus single rotor helicopters helps quantify the 

fact that a coaxial helicopter is, in fact, capable of a 10 to maybe 15 percent hover engine 

power required improvement in nondimensional coefficient form. The configuration continues 

to receive engineering attention [262-264]. 

2.3.10 Ground Effect 

 Ground effect is the one factor that can, without question, improve hover performance. 

The favorable effect becomes increasingly influential as the distance of the main rotor plane 

to the ground (Z) becomes less than twice the main rotor diameter (D). Thus, hovering out of 

ground effect (HOGE) means that Z > 2D. The distance Z is frequently measured from the 

ground to the helicopter’s wheels or skids, plus the distance from the landing gear up to the 

main rotor hub. Therefore, even when the helicopter is on the ground, the rotor hub or plane is 

some 6 to 8 feet above the ground—at least with prudent designs that have concern for people 

walking about the aircraft when the main rotor is turning. Very few conventional helicopters 

can physically have the ratio of Z to D much less than 0.3. 

 There have, of course, been several experiments and many (actually too many to 

reference) theoretical studies of the behavior of an isolated model’s main rotor when in 

ground effect [13, 244, 265-268]. However, in 1976 it was Jim Hayden who finally conducted 

a semiempirical study of full-scale helicopters that provided usable results for the working 

engineer [268]. Hayden used the simplest performance approximation to build his ground 

effect calculation method. He started with Eq. (1.4), repeated here for convenience: 

(1.4) HOGE

3

t do

i

T T bcRV C HP k

550 2 A 8 550

  ρ = +  

ρ ×  

. 

He assumed that this fundamental equation would represent any of the 17 U.S. Armyevaluated configurations under study, whether hovering in ground effect (HIGE) or out of 

ground effect (HOGE). He replaced thrust (T) with gross weight (W) and used engine shaft 

horsepower to calculate the power coefficient (CP). Hayden approached the aircraft 

performance data analysis with Eq. (1.4) in coefficient form and added an in-ground-effect 

variable (Kge) so that 
2.4 FORWARD-FLIGHT PERFORMANCE 

213 

Oswald referred to it. (As time went on, aerodynamic performance engineers came to call (e) 

the Oswald efficiency factor.) 

 Fig. 2-97 shows the Cessna L-19A power-required curve at a gross weight of 

2,340 pounds and at 1,000-feet pressure altitude on a standard day, assuming the propeller is 

100 percent efficient. This curve is based on the lift-drag polar of the L-19A being66 

(2.165) ( )( )

2

L 2

D L

D C C 0.04 0.04 0.0605C

qS 7.448 0.7064

== + = +

π . 

Practicing aerodynamic performance engineers will immediately recognize that if CDf is 0.04, 

then the commonly used equivalent flat plate area (f being Oswald’s notation, or to others, fe) 

is fe = CDf S = Df /q = 0.04 (174) = 7 square feet. Notice that the fixed-pitch metal propeller, 

with relatively poor propeller efficiency, costs the L-19A about 20 knots in top speed. 

 There is a very interesting aspect of fixed-wing flight testing and the power required 

versus airspeed data obtained. The aspect is how to collapse data obtained at several altitudes 

(but just one weight) to a single, generalized, power-required curve. In 1928, Walter S. Diehl 

published a NACA report [285] about the reduction of observed airplane performance to 

standard conditions. His introduction and historical review are well worth reading. Diehl’s 

work was followed by Oswald’s very broad study about airplane performance [283]. By mid1951, the Air Force had generated a very comprehensive flight test engineering handbook 

[286].67 This manual was the “bible” when the U.S. Army Aviation Test Office (ATO) took up 

residence at Edwards Air Force Base in California. Keith Putnam was the Chief of the ATO at 

its inception. The first formal flight testing that the ATO did was with the L-19A, with results 

reported in ATO-TR-61-1 [281]. 

 Airplane power-required data, obtained at any pressure altitude and outside air 

temperature, collapses to a single curve if the power and airspeed are each multiplied by the 

square root of the air density ratio (ρ/ρo = σ). That is, the coordinate system is 

BHP versus V req'd. σ σ . 

It is rather easy to see this with the airplane’s lift-drag polar in dimensional form. From 

Eq. (2.164), CDf S is replaced by (fe)—the equivalent flat plate area in square feet—and lift 

(L) is set equal to the aircraft weight (W) in pounds, which gives 

(2.166) 

2

2

e 2

1 21 W D fV

2 eV b

  = ρ+   π ρ   . 

Then the engine brake horsepower required, following Eq. (2.163), becomes 

 

66 I backed this result out from TL-19D flight test data using propeller efficiency data provide by Hal Bohemen 

of the McCauley Propeller Company. 

67 This handbook was corrected and revised in January 1966. 
2.3 HOVER PERFORMANCE 

200 

 You might think that this example of modern results shows an excessive (if not 

appalling) amount of empiricism with which to predict in-ground-effect performance. 

Unfortunately, this situation from 1976 still exists today. The hover performance prediction 

problem (for either HOGE or HIGE) for a complete rotorcraft has yet to be solved. In general, 

the industry always predicts an optimistic hover performance result with each new rotorcraft 

and, so far, has always been soundly disappointed. 

2.3.11 Closing Remarks 

 This introduction to modern helicopter hover performance has shown you that the 

“bottom line” of hover performance is a decision-making chart of hover ceiling versus useful 

load (recall Fig. 2-49). To arrive at this chart, you need accurate engine horsepower available 

(from paragraph 2.1), careful bookkeeping of helicopter weight (discussed in paragraph 2.2), 

and accurate engine horsepower required as reviewed in the preceding several pages. The 

engine horsepower required to hover out of ground effect relies—initially for a new 

configuration—on prediction of a CP–CW curve where power is engine shaft horsepower. 

Today, each manufacturer has a wealth of background and prediction technology to obtain a 

CP–CW curve, and considerable progress has been made since the early pioneering days to 

ensure that a sufficient power margin is inherent in a new design. However, even as late as the 

mid-1970s, progress fell far short of customer expectations. This deficiency was made quite 

clear in the UTTAS and AAH competition. You will find the position of the U.S. Army 

pointedly stated [123-126] as follows: 

Reference [123] – Para. 185. Within the scope of these tests, the YUH-60A helicopter failed to 

meet the following commitments of the Prime Item Development Specification: 

a) The helicopter could not hover out-of-ground-effect at the primary mission gross 

weight, 4,000 feet pressure altitude, 35o C and 95 percent intermediate rated power. 

b) The aircraft could not climb vertically 550 ft/min at a pressure altitude of 4,000 feet, 

35o C, 95 percent intermediate rated power and primary mission gross weight. 

Reference [124] – Para. 195. Within the scope of these tests, the YUH-61A helicopter failed to 

meet the requirements of the following paragraphs of the Prime Item Development 

Specification: 

a) The helicopter could not hover out-of-ground-effect, nor could it climb vertically 

603 ft/min using 95 percent intermediate rated power, at primary mission gross weight 

at 4,000 feet pressure altitude, 35o C. 

Reference [125] – Para. 145. Within the space of these tests, the YAH-63 failed to meet the 

following requirements of the System Specification: 

a) The aircraft could not hover at specified conditions and, therefore, failed to meet the 

450 ft/min vertical rate of climb requirement. 

Reference [126] – Para. 150. The YAH-64 was found to be not in compliance with the following 

paragraphs of the Army System Specification against which it was evaluated. Additional 

specification non-compliances beyond the scope of this evaluation may exist. 

a) The computed vertical climb rate was 184 ft/min, 266 ft/min less than specification. 
2.3 HOVER PERFORMANCE 

201 

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

1.05

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3

YUH-60A

Kge

Z/D

Fig. 2-90. The Hayden ground effect variable.

0.0003

0.0004

0.0005

0.0006

0.0007

0.0008

0.0009

0.0003 0.0004 0.0005 0.0006 0.0007 0.0008 0.0009

Engine 

CP

CW3/2

HOGE at 100 foot 

Wheel Height

HIGE at 5 foot 

Wheel Height

Eq. 2.156

Fig. 2-91. YUH-60A hover performance HOGE and HIGE at 5-foot wheel height.
2.3 HOVER PERFORMANCE 

202 

 I have not included these four evaluations to discourage you. Rather, the U.S. Army 

evaluations point out how difficult the hover performance prediction and measuring problem 

has been—and continues to be. The industry has spent millions of dollars on improvement so 

that marketing brochures and proposals to the government are credible. However, (1) a slight 

shortfall in installed engine horsepower, (2) creeping up weight empty, and (3) a small error in 

estimated power required to hover each contribute to missed expectations. Despite the 

shortfalls in technology, once the helicopter is in flight test and the situation is clearer, engine 

manufacturers frequently can obtain a little more power, at a reasonable price, to ensure 

ultimate success [145]. 

 The most penetrating review of modern industry’s capability that I have ever read was 

provided by Charlie Crawford, a longtime friend,61 in May of 1989. He presented the 9th 

Nikolsky Lecture at the 45th Annual Forum of the American Helicopter Society (AHS). His 

Lecture was published later in the AHS Journal [249]. Charlie took the UTTAS and AAH 

competitions apart with comparisons of predictions versus results, with particular emphasis on 

optimistic weight empty and aerodynamic predictions. This paper is a must-read to gain an 

appreciation of modern helicopter development. 

 Despite the industry’s shortfalls, Charlie points out that persistency paid off, and today 

the UH-60 and AH-64 perform admirably in the field, demonstrating the success of modern 

industry. The same can be said about the many civil helicopters operating around the world. 

 These paragraphs about hover performance would be incomplete without comparing 

some measure of pioneering efforts against modern results—including my interpretation. 

Fortunately, Fred Gustafson and Al Gessow at the N.A.C.A. obtained and published [47, 48] 

flight test data (including nondimensional engine CP versus CW) for the Army YR-4B (the 

Navy’s HNS-1) in hover [48]. Their results are shown in Fig. 2-92 with large symbols 

superimposed on an enlargement of Fig. 2-51. The large, black triangle is the one test point 

obtained out of ground effect with the “original” (i.e., production) blades. The several, large, 

black circles show the performance improvement with the “alternate” blades. The two blade 

configurations are shown in planform view in Fig. 2-93. Gustafson and Gessow, in their first 

conclusion, wrote that 

 “1. An increase in thrust available for hovering at altitude [sea level, but HOGE] of more than 

300 pounds has been obtained by replacing the original set of main-rotor blades by one of 

different aerodynamic design and surface condition.” 

 The two blade configurations were significantly more different than the planform view 

suggests. The production blades (i.e., the “original” blades) were fabric covered and untwisted 

with a thrust-weighted solidity of 0.060. The airfoil was a NACA 0012 at the ribs, but left 

much to be desired aft of the 35 percent chord where the spruce leading edge “fairing” 

stopped. The trailing edge was wire. The “alternate” blades had a thrust-weighted solidity of 

0.042, were plywood covered, and had “an 8-degree twist, the pitch decreasing linearly from 

root to tip.” The alternate blade airfoil was a modified NACA 23012. Gustafson and Gessow 

 

61 Charles Crawford died in mid-August 2012, and we lost a driving force in the industry. And I lost a good 

friend. 
2.3 HOVER PERFORMANCE 

203 

10

20

30

40

50

20 30 40 50 60

YR-4B

Alternate 

Blades

YR-4B

Original Blades

Engine 

Shaft Power

Required 

Coefficient 

CP×105

Weight Coefficient CW×104

Fig. 2-92. Sikorsky YR-4B hover performance reported in 1945 suggests that modern 

results are a step backward. I do not agree with that suggestion. 

Fig. 2-93. Sikorsky YR-4B hover performance measured in 1945 with two different 

blade configurations. 
2.3 HOVER PERFORMANCE 

204 

refer to airfoil tests performed on 10 practical-construction sections by Tetervin [269]. They 

also reference the static thrust tests of six rotor blade designs on the YR-4B conducted by 

Dick Dingeldein and Ray Schaefer in the Langley full-scale tunnel [270]. Dingeldein and 

Schaefer continued tunnel testing of the full-scale YR-4B in forward flight, and this work was 

reported in 1947 [271]. The alternate blade set was studied in more detail by Gustafson and 

Gessow [272], and Gessow was able to understand the effect of blade twist and tell everyone 

in the fall of 1948. 

 These seven reports [47, 48, 269-273] written by the early helicopter pioneers at the 

N.A.C.A. are, in my estimation, worth their weight in gold. They are an absolute foundation 

to the study of early helicopter hovering performance.62 

 The concentration of the early N.A.C.A. pioneers on main rotor performance (in CPmr

versus CW or CTmr form) skipped over one facet of the hovering helicopter problem that is 

quite important, particularly to the pilot. This facet is that hover performance ultimately 

depends on the engine horsepower required to hover. To make this point, reconsider Eq. (2.47) 

repeated here for convenience: 

(2.47) Main Rotor(s) TailRotor(s)

Accessory

Main Rotor(s) TailRotor(s)

RHP RHP

ESHP SHP = ++

η η . 

Enough flight test data is provided by Gustafson and Gessow [47, 48] to show how well the 

equality matches up. Using tabulated data from these two reports, Fig. 2-94 shows that a 

linear regression analysis quantifies Eq. (2.47) for the YR-4B to 

(2.159) RHPmr RHPtr Engine BHP 12.5 0.955 1.0

= ++ . 

 This result says the main rotor transmission efficiency (ηmr) is about 0.95, the tail rotor 

drive-train efficiency (ηtr) is ideal being 1.0 (which I will explain shortly), and 

12.5 horsepower is used to drive accessories. The main rotor horsepower (RHPmr) and tail 

rotor horsepower (RHPtr) were obtained “by means of strain-gauge torque meters. The strainsensitive elements for the main rotor were mounted on the drive shaft between the gear box 

and the pylon thrust bearing. Those for the tail rotor were mounted between the tail rotor gear 

box and the rearmost shaft bearing.” This latter statement says the tail rotor torque meter 

measured both the power absorbed by the transmission as well as the tail rotor, which explains 

why ηtr = 1.0. Additionally, “the engine manifold pressure, intake-air temperature, and rpm 

values were used to calculate engine brake horsepower (BHP) by use of the calibration curve 

given in Technical Order AN-01-10 DA-1.” The main rotor efficiency is quite reasonable. The 

tail rotor efficiency should be basically 1.0 because the measurement includes the tail rotor 

 

62 The outpouring of efforts from the N.A.C.A. that followed these seven reports is phenomenal, as any literature 

search will quickly uncover. By 1951, Al Gessow and Garry Myers were able to publish their classic book [234], 

which is a true treasure. You can track down nearly all of the pre-1950 N.A.C.A. work just from the references 

provided in appendix IIA of their book. And contributions from the N.A.C.A. did not stop, as you will read in 

the 6th Nikolsky Lecture given by John Ward in 1986 at the 42nd Annual National Forum of the American 

Helicopter Society [274]. 
2.3 HOVER PERFORMANCE 

205 

gear box. Whether the engine was really performing up to spec is a matter for speculation. I 

would take issue with the accessory power. 

 While you may express some dissatisfaction with this mid-1944 YR-4B result, Bill 

Bousman at NASA Ames Research Center [213], in analyzing UH-60A flight test data some 

55 years after Gustafson and Gessow’s efforts, experienced the same dissatisfaction. 

 I have included this simple example to draw your attention to the accessory power. I 

very much doubt that the YR-4B had 12.5 horsepower used for accessories—maybe 3 or 4 

horsepower, but hardly 12.5 horsepower. A starter-generator and a battery and an oil cooler 

blower maybe, but no hydraulic system and minimal gearbox cooling. A slipping clutch would 

result in a power loss, of course, and surely heating would be a factor then. 

 What I believe is that the gains made over six decades to improve main rotor(s) and 

tail rotor performance with blade geometry—and all of the gains made to improve 

transmissions—have gone to accessory power. Modern helicopters have oil pumps, oil cooler 

blowers, power steering (i.e., hydraulic systems), interior climate control (air conditioning and 

heating), deicing for blades and other components, heavy electrical loads for computers, flyby wire, and search and rescue equipment. Accessory power loss for Bell Helicopter products 

used to support Kocurek’s paper [168] ranged from 14 horsepower for a Bell Model 206 to 

over 60 horsepower for a well-furnished Bell Model 214ST. This is just one example of 

accessory power benefiting from improved rotors and transmissions. 

110

120

130

140

150

160

170

180

190

110 120 130 140 150 160 170 180 190

Forward Flight

Hover IGE

Hover OGE

Vertical Descent

Test

Engine

BHP

Theory BHP = HPmr/ηmr + HPtr/ηtr + HPacc

Fig. 2-94. Power equality with the YR-4B in 1944 per Eq. (2.159).
206 
207 

2.4 FORWARD-FLIGHT PERFORMANCE 

 The subject of helicopter forward-flight performance is so tied to the growth of U.S. 

Army Aviation that some historical background is a prerequisite. Army Aviation, despite 

evaluation of the autogyro, really began with very light, fixed-wing aircraft. In fact, it was the 

Piper Cub—the popular J-3 model—which began it all [275]. 

 There are many who will disagree with this opening statement about Army Aviation, 

with good reason. The U.S. Army’s air force can easily be traced back to the American Civil 

War when telegraph-equipped, tethered balloons were first used as vantage points to observe 

terrain and disposition of opposing forces, and adjust artillery fire. Essentially the same 

techniques were used in the Spanish American War and, more extensively, in World War I 

when the telephone replaced the telegraph, adding voice communication capability. However, 

World War I also saw the introduction of photo reconnaissance by airplane and a new air 

observation mission, a “scouting mission,” was born. 

 A more recent point of view [276] was published by Dr. John Kitchens,63 who wrote: 

“On 6 June 1942, the secretary of war ordered the establishment of organic air observation for 

Field Artillery. Through companion memoranda sent to the commanding generals of the Army 

Air Forces (AAF) and the Army Ground Forces (AGF) the War Department issued specific 

instructions for organizing organic air observation. It also provided guidelines for relations 

between the AAF and this new air arm of the AGF.” 

With this directive from the top, the United States Army placed light airplanes under the 

command of field artillery battalions. The “scouts” functioned as aerial observation posts (Air 

OPs) for target acquisition and fire adjustment, and became an integral part of the fire 

direction system. During World War II about 5,700 L-4 Piper Cub airplanes were procured 

for this purpose. These two-place, tandem-seating, 1,220-pound-gross-weight monoplanes 

were powered by 65-horsepower reciprocating engines. The troops in Europe referred to these 

rugged and reliable airplanes as a “Maytag Messerschmitts.” The L-4 “scout” crew consisted 

of a pilot and observer, and their “mission equipment package” consisted of voice radio, 

maps, and binoculars. The application was a marked success. Artillery fire could be more 

accurately and rapidly adjusted over a wider battlefield at longer ranges. The L-4s could 

operate from unimproved airstrips, which were generally plentiful. Being simple aircraft, L-4s 

proved highly reliable and easy to maintain, even in their most forward areas. The only 

significant threat to crew survival, enemy ground fire, was largely suppressed by the highly 

responsive artillery firepower, which the crew could direct. 

 After World War II the Army’s concept of aviation broadened beyond field artillery, 

and light airplanes were placed in other service branches such as Infantry, Armor, Engineers, 

and Signal. The principal postwar airplane was the Stinson L-5, which had been used mainly 

by the Army Air Corps during World War II for liaison missions. About 900 of these Stinsons 

were made available to the Army ground forces by the then newly formed United States Air 

 

63 Dr. Kitchens is the Aviation Branch Command Historian at the U.S. Army Aviation Center located at Fort 

Rucker, Alabama. You can find the complete article on the Army Aviation Museum website. 
2.4 FORWARD-FLIGHT PERFORMANCE 

208 

Force. The L-5 was a two-place, tandem-seating, 2000-pound-gross-weight airplane powered 

by a 185-horsepower reciprocating engine. The Army’s L-5 inventory was supplemented in 

1948 by a new procurement of about 800 Aeronca L-16 airplanes. The 1,300-pound-grossweight, two-place, tandem-seating L-16, together with its 95-horsepower engine was, in many 

respects, a return to the L-4–sized aircraft of World War II. 

 The L-5 and L-16 were the core of the Army’s fleet for artillery observation, 

reconnaissance, and liaison when the Korean War began. Between December 1950 and 

October 1954, however, these airplanes were rapidly replaced by the delivery of about 2,400 

Cessna L-19 Bird Dogs. The L-19 was a two-place, tandem-seating, 2400-pound-gross-weight 

airplane powered by a 213-horsepower reciprocating engine. The new feature offered by the 

L-19 was an all-metal construction in contrast to the fabric-covered wood and metal structures 

of the L-4, L-5, and L-16. The pilot and observer’s mission equipment, however, continued to 

be voice radio, maps, and binoculars. A total of 3,400 L-19s were ultimately procured as 

production extended to 1964, and of these, about 800 were used as trainers (designated 

TL-19Ds). The L-19, redesignated the O-1 in 1962, was the last tactical light airplane 

procured by the Army for field artillery fire direction, aerial observation, reconnaissance, and 

liaison. 

 The Army began procuring light, two-place, side-by-side-seating helicopters in small 

lots in 1948. Significant quantities of both Bell H-13s and Hiller H-23s were procured during 

FY51, the first fiscal year of the Korean War. Those helicopters that were delivered in time 

were used principally in medical evacuation [277] and administrative roles (staff liaison and 

communication) rather than tactical missions. The Korean War did, however, demonstrate the 

feasibility of large-scale use of light helicopters, and these rotary wing aircraft proved more 

reliable and easier to maintain in the field than had been anticipated. While less reliable and 

less maintainable than airplanes such as the L-19, the light helicopter more than offset this 

disadvantage with its ability to hover, land virtually anywhere, and operate safely near the 

ground at low speed. 

 The Bell H-13 had a gross weight of 2,450 pounds and was powered by a 200- 

horsepower reciprocating engine. The Army had about 100 early models of the H-13 when the 

Korean War began, and nearly 1,000 were produced during the war years (1950–1953). 

Another 600 H-13s were produced for operational use through 1965. Production continued 

through 1970 with additional requirements for 400 TH-13 trainers. The Hiller H-23 had a 

gross weight of 2,700 pounds and was powered by a 250-horsepower reciprocating engine. 

Nearly 400 were produced during the Korean War with another 400 procured in the period 

from 1954 through 1958. 

 This brief, introductory bit of history shows how the U.S. Army made the transition 

from light airplanes to light helicopters during the Korean War.64 

 

64 In putting together the OH-58D story [145], I was very lucky to have Perry Craddock at Bell write the 

historical introduction. Perry was an original Maytag Messerschmitt pilot. What you have just read is a portion 

of his very authoritative history about U.S. Army scout helicopter evolution. 
2.4 FORWARD-FLIGHT PERFORMANCE 

209 

Fig. 2-95. The Cessna L-19 Bird Dog was the last tactical light airplane procured by the 

Army (photo from author’s collection). 

Fig. 2-96. The Bell H-13 (and the Hiller H-23) replaced the L-19 during the Korean War. 

Large numbers were bought beginning in fiscal year 1951 (photo from author’s 

collection). 

 The comparison between the two aircraft types is a good starting point for a discussion 

about helicopter forward-flight performance. A very interesting comparison of the Piper L-4A 

and the Cessna L-19A Bird Dog (Fig. 2-95) to the Bell H-13H (Fig. 2-96) and Hiller UH-23E 

is presented in Table 2-14. 
2.4 FORWARD-FLIGHT PERFORMANCE 

210 

Table 2-14. Early U.S. Army Aviation Aircraft 

Basic Aircraft Information

Piper 

L-4A 

Cessna 

L-19A 

Bell 

H-13H 

Hiller 

UH-12E 

References [278, 279] [280-282] [171] [192] 

Power Installed Continental Continental Lycoming Lycoming 

 Engine Model A65-8 0-470-11-C1 0-435-23 VO-540-C1A 

 Takeoff Rating at Sea Level (hp) 65 213 255 338 

 RPM for Rated Horsepower 2,300 2,600 3,400 3,200 

 Cruise Rating (hp) 60 190 200 305 

 RPM for Cruise 2,150 2,300 3,100 2,900 

Weights 

 Empty (full oil, trapped fuel) (lb) 750 1,686 1,789 1,717 

 Fuel Full (lb) 70 243 258 276 

 Two Crew (lb at 170 lb/man) 340 340 340 340 

 Two Parachutes (lb at 30 lb/man) None 70 None None 

 Baggage 10 30 60 60 

 Takeoff Weight (lb) 1,170 2,369 2,447 2,393 

 Overload Weight (lb) 1,220 n/a 2,550 2,750 

Dimensions 

 Wing or Main Rotor 

 Span or Diameter (ft) 35.21 36.00 35.125 35.333 

 Wing or Disc Area (ft2) 188.5 174.0 968.5 982.0 

 Wing or Blade Chord (ft) 5.33 4.94 0.917 0.953 

 Number of Blades n/a n/a 2 2 

 Solidity n/a n/a 0.03323 0.03428 

 Propeller or Tail Rotor 

 Manufacturer Sensenich McCauley Bell Hiller 

 Model n/a 1A200/FM9047 n/a n/a 

 Diameter (in.) 72 90 68 66 

 Blade Number 2 2 2 2 

 Blade Chord 0.81 ft n/a 0.377 ft 0.51 ft 

 Solidity 0.1875 n/a 0.0845 0.118 

 Pitch Change No No Yes Yes 

 Airfoil RAF 6 RAF 6 NACA 230xx NACA 0012 

 Airframe 

 Nose-to-Tail Length (ft) 22.375 25.8 27.333 29.8 

 Height (ft) 6.67 7.50 9.28 10.125 

 Vertical Stabilizer Area (ft2) 10.57 19.23 n/a n/a 

 Horizontal Stabilizer Area (ft2) 25.3 15.95 None None 
2.4 FORWARD-FLIGHT PERFORMANCE 

211 

0

50

100

150

200

250

0 20 40 60 80 100 120

Bell H-13H, GW = 2,370 lbs, H = 1,000 ft, AFFTC-TR-57-12, Fig. 11

Cessna L-19A, GW = 2,340 lbs, H = 1,000 ft, ATO-TR-61-1, Fig. 9

Cessna L-19A with 100% Propeller Efficiency

Engine 

BHP

True Airspeed (kts)

Prop Eff.

Fig. 2-97. Comparison of early U.S. Army aircraft performance. 

 You will recall from Volume I that Cierva compared his autogyro to the airplane and 

tried to make a convincing story that the two aircraft were nearly equal in performance. My 

more detailed comparison of the Pitcairn PA-8 Mailplane to the Pitcairn PCA-2 Autogiro did 

not support Cierva’s outlook. In this volume, Table 2-14 provides another comparison of the 

helicopter to the airplane. As a first step toward understanding helicopter forward-flight 

performance, consider the contrasting power required versus speed curves provided in 

Fig. 2-97. I have chosen to contrast the Army’s L-19A (fixed-wing airplane) [281] with the 

Army’s H-13H (rotary wing helicopter) [171]. Both aircraft were tested at nearly equal 

weights, at an altitude of 1,000 feet. From a configuration point of view, the two aircraft have 

virtually equal “wing” spans as Table 2-14 shows. 

2.4.1 Airplane 

 First let me discuss the power required versus speed data of the L-19A. This 

discussion will serve as a reminder of fixed-wing aerodynamics and provide a jumping-off 

point to helicopter forward-flight performance. As you are no doubt aware, the engine power 

required is determined by the aircraft’s propeller thrust (TP) in pounds at a given true airspeed 
2.4 FORWARD-FLIGHT PERFORMANCE 

212 

(V)65 in feet per second, and the propeller efficiency (ηP), which generally varies with 

airspeed. That is, 

(2.160) P

P

T V Engine BHP 550 = η . 

 In steady, level flight, propeller thrust is frequently taken as equal to aircraft drag (D) 

in pounds. This follows because of a small angle-of-attack assumption in Eqs. (2.161) and 

(2.162), which are simple trim equations for an airplane. (In fact, at low speeds when the 

airplane is approaching stall and the aircraft angle of attack is not small, the propeller thrust 

can contribute an appreciable amount of lift.) Thus, in steady, level flight, it is common to 

begin with the fundamental statements that 

Parallel to the flight path velocity (positive is forward)

(2.161) 

()()

( )

( )

X prop AC prop prop AC prop fuselage

wing tail AC tail interference

tail AC tail interference

F 0 Wsin T cos i H sin i D

D L sin i

D cos i

= = γ+ α + − α + −

− − α + −α

− α + −α



, 

Perpendicular to the flight path velocity (positive is down)

(2.162) 

() ()

( )

( )

Z prop AC prop prop AC prop fuselage

wing tail AC tail interference

tail AC tail interference

F 0 Wcos T sin i H cos i L

L L cos i

D sin i

= = γ− α + − α + −

− − α + −α

− α + −α



, and 

(2.163) x

req'd.

P

F V Engine BHP 550

Σ = η . 

 The basis of airplane drag is the aircraft lift-drag polar, which, following Oswald’s 

1931 fundamental report [283], is seen in coefficient form [284] as 

(2.164) 

2

L

D Df

D C C C

qS AR e

== +

π

where (CDf) is the drag coefficient at zero lift, (CL) is the lift coefficient equal to L/qS, (S) is 

the reference area normally taken as the wing area, (AR) is the wing-aspect ratio equal to 

wing span (b) squared divided by wing area (S), and (e) is the “airplane efficiency factor” as 

 

65 Considerable care is taken when referring to airspeed. Airspeed indicators are not all that accurate, particularly 

at low speed and/or high angle of attack. The indicator itself can have calibration errors, and nonlinear behavior 

is not uncommon. Because the indicator depends on a pitot-static probe, there can be indicated airspeed errors 

due to the location of the probe on the aircraft. In flight tests, the indicated airspeed is carefully calibrated with 

an absolutely believed airspeed, which allows conversion from Vindicated to Vtrue. Most flight test reports only 

present data in terms of true airspeed. True airspeed equals indicated airspeed divided by the square root of the 

density ratio. Think of true airspeed as the speed at which the aircraft follows a car on the ground, regardless of 

the altitude that the aircraft is flying at—assuming there is no wind. In that sense, true airspeed might better be 

called true ground speed. 
2.4 FORWARD-FLIGHT PERFORMANCE 

213 

Oswald referred to it. (As time went on, aerodynamic performance engineers came to call (e) 

the Oswald efficiency factor.) 

 Fig. 2-97 shows the Cessna L-19A power-required curve at a gross weight of 

2,340 pounds and at 1,000-feet pressure altitude on a standard day, assuming the propeller is 

100 percent efficient. This curve is based on the lift-drag polar of the L-19A being66 

(2.165) ( )( )

2

L 2

D L

D C C 0.04 0.04 0.0605C

qS 7.448 0.07064

== + = +

π . 

Practicing aerodynamic performance engineers will immediately recognize that if CDf is 0.04, 

then the commonly used equivalent flat plate area (f being Oswald’s notation, or to others, fe) 

is fe = CDf S = Df /q = 0.04 (174) = 7 square feet. Notice that the fixed-pitch metal propeller, 

with relatively poor propeller efficiency, costs the L-19A about 20 knots in top speed. 

 There is a very interesting aspect of fixed-wing flight testing and the power required 

versus airspeed data obtained. The aspect is how to collapse data obtained at several altitudes 

(but just one weight) to a single, generalized, power-required curve. In 1928, Walter S. Diehl 

published a NACA report [285] about the reduction of observed airplane performance to 

standard conditions. His introduction and historical review are well worth reading. Diehl’s 

work was followed by Oswald’s very broad study about airplane performance [283]. By mid1951, the Air Force had generated a very comprehensive flight test engineering handbook 

[286].67 This manual was the “bible” when the U.S. Army Aviation Test Office (ATO) took up 

residence at Edwards Air Force Base in California. Keith Putnam was the Chief of the ATO at 

its inception. The first formal flight testing that the ATO did was with the L-19A, with results 

reported in ATO-TR-61-1 [281]. 

 Airplane power-required data, obtained at any pressure altitude and outside air 

temperature, collapses to a single curve if the power and airspeed are each multiplied by the 

square root of the air density ratio (ρ/ρo = σ). That is, the coordinate system is 

BHP versus V req'd. σ σ. 

It is rather easy to see this with the airplane’s lift-drag polar in dimensional form. From 

Eq. (2.164), CDf S is replaced by (fe)—the equivalent flat plate area in square feet—and lift 

(L) is set equal to the aircraft weight (W) in pounds, which gives 

(2.166) 

2

2

e 2

1 21 W D fV

2 eV b

  = ρ+   π ρ   . 

Then the engine brake horsepower required, following Eq. (2.163), becomes 

 

66 I backed this result out from TL-19D flight test data using propeller efficiency data provide by Hal Bohemen 

of the McCauley Propeller Company. 

67 This handbook was corrected and revised in January 1966. 
2.4 FORWARD-FLIGHT PERFORMANCE 

214 

(2.167) 

2

3

req'd. e

P P

DV 1 1 2 1 W Engine BHP f V 550 550 2 e V b

    = = ρ+     η η πρ    

. 

Multiplying both sides of Eq. (2.167) by σ = ρ ρo leads, with a little algebra, to 

(2.168) ( )

2

3 o

req'd. e

PP o

DV 1 2 W 1 (Eng. BH P ) f V

550 550 2 e b V

σ ρ      σ= = σ +     

η η πρ      σ 

. 

Now the power-required curve depends on the constants o

e f

2

ρ and 

2

o

2 W

e b

    π ρ   . 

 Using the L-19A flight test data [281], you can see from Fig. 2-98 that density altitude 

has a substantial effect on power required, but by following Eq. (2.168) the data is reduced to 

one line as Fig. 2-99 shows. 

 As you saw from Fig. 2-97, propeller efficiency (ηP) might be better called propeller 

inefficiency. To illustrate this point, consider Fig. 2-100. The L-19A was tested in 1957 in a 

training configuration with a metal constant-speed propeller (i.e., a variable-pitch propeller) 

[282]. This configuration was designated as the TL-19D. The power-required comparison of 

the L-19A to the TL-19D, shown in Fig. 2-100, is really just a comparison of the fixed-pitch 

propeller versus the variable-pitch propeller, and the performance improvement is easily 

worth 10 knots. As Miller and Sawers relate [287], “The variable-pitch propeller was first 

used [commercially] in 1933 on the Boeing 247 and the Douglas DC-1 to improve the takeoff 

performance of airplanes which would otherwise have had their payload limited.” A much 

more technically oriented discussion of the evolution of the variable-pitch propeller is 

provided by George Rosen in his superb book, Thrusting Forward: A History of the Propeller 

[288].68

 The reason I have brought your attention to the propeller is twofold. First, the fixedwing branch of aerodynamics has created a wealth of experimental and theoretical work that 

rotorcraft engineers can use. Second, Volume III, which deals with other V/STOL aircraft, 

shows that aircraft such as the tiltrotor and tiltwing, and several other configurations, depend 

on propeller performance. Therefore, let me (1) provide some information about early NACA 

research into propeller performance, then (2) show how the rotorcraft engineer can look at 

propeller performance, and finally (3) show how airplane performance can be calculated in 

the rotorcraft reference frame. 

 Shortly after its inception, the N.A.C.A. initiated a very comprehensive propeller 

research program. This program included model and full-scale wind tunnel tests in 

comparison to flight tests of the VE-7 airplane (Fig. 2-101). The VE-7 was designed as an 

 

68 George Rosen’s book was published by Hamilton Standard and the British Aerospace Dynamics Group to 

commemorate the 50th anniversary of the joint efforts of these two companies. In May 1988 I gave a local AHS 

Chapter speech about propellers. The Chapter gave me a copy of Rosen’s book, which I have kept in my highly 

cherished file. 
2.4 FORWARD-FLIGHT PERFORMANCE 

215 

 

0

20

40

60

80

100

120

140

160

180

0 20 40 60 80 100 120

GW = 2,340 lbs, H = 1,000 ft, ATO-TR-61-1, Fig. 9

GW = 2,315 lbs, H = 5,000 ft.

GW = 2,305 lbs, H = 10,000 ft.

GW = 2,355 lbs, H = 15,000 ft.

Engine 

BHP

True Airspeed (kts)

Fig. 2-98. Cessna L-19A flight test data at several altitudes [281]. 

0

20

40

60

80

100

120

140

160

0 20 40 60 80 100 120

GW = 2,340 lbs, H = 1,000 ft, ATO-TR-61-1, Fig. 9

GW = 2,315 lbs, H = 5,000 ft.

GW = 2,305 lbs, H = 10,000 ft.

GW = 2,355 lbs, H = 15,000 ft.

o

Referred

Engine

BHP ρ ρ

( ) Referred True Airspeed, V kts ρ ρo

Fig. 2-99. Cessna L-19A flight test data in referred power and airspeed [281]. 
2.4 FORWARD-FLIGHT PERFORMANCE 

216 

0

20

40

60

80

100

120

140

160

180

200

0 20 40 60 80 100 120 140

Cessna L-19A, GW = 2,325 lbs,

Metal Fixed Pitch Prop

Cessna TL-19D, GW = 2,400 lbs,

Metal Constant Speed Prop

Cessna L-19A, GW = 2,400 lbs 

with 100% Prop Efficiency

o

Referred

Engine

BHP ρ ρ

( ) Referred True Airspeed, V kts ρ ρo

Fig. 2-100. Cessna L-19A flight test data shows improved performance with 

variable-pitch (i.e., constant speed) propellers. 

advanced trainer for the U.S. Army by Birdseye B. Lewis and Chance M. Vought (they 

became the Chance Vought Corp. in May 1922). The airplane was evaluated by the Army at 

McCook Field in Dayton, Ohio, in 1918. Lieutenant Alexander Klemin contributed to the 

static and flight test reports. The U.S. Navy adopted the VE-7 for training and carrier-landing 

trials. Some 129 VE-7s were built in several versions [289]; one VE-7 went to the N.A.C.A. 

Langley Memorial Aeronautical Laboratory. 

 Initial N.A.C.A. propeller research program results were authored by Durand and 

Lesley [290]. They compared model propeller performance (obtained by Durand at the 

aerodynamic laboratory of Stanford University) to flight test data. Lesley contributed VE-7 

flight test data with five propellers, which was acquired at the Langley Memorial 

Aeronautical Laboratory. Their conclusion was that “efficiencies realized in flight are close to 

those derived from model tests,” but that “both thrust developed and power absorbed in flight 

are from 6 to 10 percent greater than would be expected from the results of model tests.” 

There was, apparently, considerable concern about the flight test results reported by Lesley, 

which led to further flight testing of the VE-7 with five propellers [291]. At issue were the 

results in power-off glide tests that differed from Lesley’s findings. The situation was 

complicated by no direct measurement of either thrust or power. Around this time the 20-foot, 

open-throat wind tunnel came online at N.A.C.A. Langley [292]. Weick reported results of 

the “first complete propeller test made in the Propeller Research Tunnel” [293]. He concluded 

that 
2.4 FORWARD-FLIGHT PERFORMANCE 

217 

“1. The results obtained agree as well as can be expected with both flight tests and model wind 

tunnel tests. 

 2. The accuracy of the observations in the Propeller Research Tunnel tests, which are made 

under full-scale conditions, is apparently of about the same order as that of model propeller 

tests. 

 3. From comparison of these tests with flight tests, it seems likely that the engines used in the 

flight tests delivered somewhat less power in flight than would have been expected from 

dynamometer tests. 

 4. The effect of the tail surfaces on the propeller characteristics is negligible. 

 5. The effect of the wings on propulsive efficiency is important and deserves further 

investigation.” 

Fig. 2-101. The VE-7 test bed for early N.A.C.A. propeller research. 
2.4 FORWARD-FLIGHT PERFORMANCE 

218 

The third conclusion Weick related was, and in my opinion still is, a serious problem 

in flight tests. The engine performance was based on the engine manufacturer’s measurement 

of the output of a new engine. The performance was described with charts relating air 

conditions and engine RPM to output power. In flight testing, these charts were used to obtain 

engine power from the pilot’s notes. Weick, on the other hand, measured engine torque and 

propeller thrust directly during his wind tunnel research. Crowley and Mixson [291] carefully 

calibrated the VE-7 engine (a Wright E-2) before and after their flight testing and found 

deterioration amounting to 3 percent. 

 Weick, having evaluated the wooden fixed-pitch propeller [293], immediately tested a 

metal variable-pitch propeller [294]. The blades of the two-bladed propeller (Fig. 2-102) were 

rather standard for this between-World-Wars era, and the pitch was only ground adjustable. 

The title of Weick’s report is a little misleading today. He suggests that “a series of metal 

propellers” were tested. In fact, he tested “the 9-foot-diameter propeller” (actually 8 feet, 

11 inches in diameter) at five different pitch settings measured at the 42-inch-radius station 

(x = r/R = 42/54 = 0.778). The pitch settings were 11, 15, 19, 23, and 27 degrees. The pitch 

setting was made by inclinometer against the bottom surface of the airfoil, which, as 

Fig. 2-102 suggests, was flat. He notes that 

“since each blade as a whole was rotated in the hub to the desired setting, all of the angles 

along the blade varied the same amount, so that the pitch did not change uniformly. It is, 

however, common practice to design detachable blade metal propellers with a certain 

distribution of blade angles and then turn the blades to any pitch required for a particular 

airplane, thus facilitating production.” 

Fig. 2-102. The first variable-pitch propeller tested in Langley’s 20-foot, open-throat 

propeller research tunnel. The propeller Activity Factor was 135. 
2.4 FORWARD-FLIGHT PERFORMANCE 

219 

 Propeller designers frequently refer to a propeller’s geometry by its Activity Factor 

(AF), a measure of the integrated capacity of the blade elements to absorb power. As 

discussed by Perkins and Hage [284] for example, propeller AF is generally calculated as 

(2.169) ( ) ( ) ( ) ( ) tip 3

root

100,000 Activity Factor AF Blade No. r R b D d r R 16

  = =    

where propeller engineers use (b) as the blade chord. The helicopter designer, using Gessow 

and Myers’ book, Aerodynamics of the Helicopter [234], will recognize this AF as a form of 

power-weighted solidity because of the (r/R)3

 term multiplying the chord-to-diameter ratio 

(b/D) before integration. A power-weighted chord in the helicopter world is generally 

calculated as 

(2.170) 

1 3

1 0 3

e 1 3 0

0

c x dx

Power -Weighted Chord c 4 c x dx

x dx

== =    . 

These two views of prop-rotor geometry are related simply as 

(2.171) e

e

b c 128 AF Rotor-Power-Weighted Solidity R 100,000

≡σ = =

π π

where rotorcraft engineers use (b) as the number of blades and (c) as the chord. Both powerweighted solidity and AF are definitions that, strictly speaking, apply only to the hover or 

static thrusting regime. This is because the chord is weighted only by the cube of local 

velocity due to rotation. At the other extreme, when the prop-rotor is in forward flight but not 

rotating, the actual blade area would be numerically correct. This would be the case, for 

example, in calculating the drag of a feathered propeller during engine-out flight. Weick’s 

propeller had an AF of 135, which gives a rotor-power-weighted solidity of 0.055. 

 The output of Weick’s variable-pitch propeller test was propeller-efficiency versus 

propeller-advance ratio [294]. The raw data (provided in tabulated form) was plotted, and 

Weick created faired lines for each pitch angle, which yielded Fig. 2-103. 

 Propeller efficiency is simply the ratio of ideal power required to produce thrust 

[TPV or DV following (2.172)] to the actual power required. In equation form, 

(2.173) ( )

P

P

P oi Pr opeller

T V

TV P P η =+ +

where (Po) is the propeller’s profile power and (Pi) is the propeller’s induced power. Both of 

these propeller powers, which detract from propeller performance and lower efficiency, will 

be discussed shortly. Propeller advance ratio (J = V/nD) uses airspeed (V) in feet per second, 

divided by propeller rotational speed (n) in revolutions per second and propeller diameter (D) 

in feet. 

 You can immediately see from Fig. 2-103 why adjusting propeller pitch in flight was a 

major step forward in the fixed-wing world. For takeoff, the pilot could run the engine up to 

maximum RPM and put the propeller at a relatively low pitch. This would get the aircraft 

quickly up to speed. With increasing speed, the advance ratio would increase and the engine 
2.4 FORWARD-FLIGHT PERFORMANCE 

220 

could be set to a constant RPM, and the propeller pitch could be adjusted so that the propeller 

operated along the heavy dashed line shown in Fig. 2-103. In climb to altitude, the pilot could 

select a different pitch. Then, in cruise, another pitch could be selected. Rosen [288] referred 

to this variable-pitch feature as “giving the pilot a gear shift.” 

 The rotorcraft engineer sees propeller performance data such as those shown in 

Fig. 2-103 in a different coordinate system. The coordinate system is actual power graphed 

versus ideal power. That is, 

T V P P versus T V P oi + + ( )Propeller P . 

Rather than use propeller coefficient nomenclature, which nondimensionalizes power by 

3 5 ρ n D , let me use the rotor term of ( ) 2 3 ρ πR Vt . Then you have 

(2.174) ( )

( )

P oi Propeller

Pactual T Po Pi 2 3

t t

TV P P V Actual Power C C C C

R V V

+ +   ≡ = = ++  

ρ π  

. 

 Notice in Eq. (2.174) that where you might expect to see a propeller-advance ratio 

(J = V/nD) term, you now see a rotor-inflow ratio (i.e., V/Vt). To the rotorcraft engineer, the 

propeller is a rotor with tip path plane perpendicular to the free-stream velocity and, therefore, 

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Beta = 11 deg. at 42 inch radius

Beta = 15 deg.

Beta = 19 deg.

Beta = 23 deg.

Beta = 27 deg.

Propeller Advance Ratio, V/nD

Propeller 

Efficiency

ηP

Fig. 2-103. The first variable-pitch propeller tested in the Langley 20-foot, open-throat 

wind tunnel achieved very respectable efficiencies. 
2.4 FORWARD-FLIGHT PERFORMANCE 

221 

αtpp = – 90 degrees following Fig. 2-28 on page 63 of Volume I. Thus, from a rotorcraft point 

of view, μ = 0 and –λo = J/π.69

 Actual power versus ideal power in rotorcraft nomenclature is shown in Fig. 2-104 

using Weick’s data [294]. The long, dashed line in this figure represents the simple case 

where actual power exactly equals ideal power. The various blade-pitch angles (β) that Weick 

evaluated are each now seen breaking away from an envelope line. Fig. 2-104 shows that 

performance at a given pitch angle reaches some sort of maximum capability and then 

reverses itself. You might think that this apex and reversal is a manifestation of propeller stall. 

In general, it is not, and Fig. 2-105 shows why. Consider the lowest-pitch-setting data in 

Fig. 2-105. The propeller thrust varies nearly linearly with inflow ratio. In fact, with a slight 

-0.0005

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

0.004

-0.001 -0.0005 0 0.0005 0.001 0.0015 0.002 0.0025 0.003

Beta = 11 deg. at 42 inch radius

Beta = 15 deg.

Beta = 19 deg.

Beta = 23 deg.

Beta = 27 deg.

Ideal Power CT(V/Vt)

Actual 

Power 

CP

Fig. 2-104. Propeller performance in a rotorcraft format.

 

69 Thrust refers to the axial force in the shaft. Rotor and propeller thrust coefficients are related as 

( ) ( ) P

T 2 2 2 24 3 3 T

t

T4 4 T Rotor C Propeller C R V D 4nD == = ρ π π π ρ π .

Power implies torque times shaft rotational speed for both rotor and propeller. The power coefficients are related 

as 

( ) ( ) P 4 4 P 2 3 2 35

t

P4P 4 Rotor C Propeller C R V D 4nD == = ρπ ρπ π π .
2.4 FORWARD-FLIGHT PERFORMANCE 

222 

extrapolation, the propeller at this low blade-pitch angle could easily produce a rotor thrust 

coefficient (CT) of 0.01 at zero-inflow ratio (a takeoff condition). But with a CT of 0.01 and 

V/Vt = 0, the ideal power (CTV/Vt) must be zero. At the other extreme, where the thrust 

coefficient is zero (because inflow has overcome blade pitch), the ideal power must be zero 

again. Therefore, in between V/Vt = 0 and the V/Vt where CT goes to zero, the ideal power 

must reach a maximum. In the case where the pitch is at 11 degrees, this maximum occurs 

around V/Vt = 0.1. At the maximum pitch that Weick tested (β = 27 degrees), the maximum 

situation for ideal power occurs at V/Vt about equal to 0.25. There is, however, evidence of 

propeller stall at this higher blade-pitch angle, which is measured in rotorcraft terms by the 

parameter (CT/σ) as Eq. 2.293 (page 234 in Volume I) showed. The propeller Weick tested 

had an Activity Factor of about 135 or a rotor solidity of about 0.055. Fig. 2-105 shows that 

the 27-degree pitch angle could not produce a CT much more than 0.012. This gives a 

maximum CT/σ on the order of 0.22 and suggests that the average airfoil was operating at a 

lift coefficient of 1.3. 

 With this introduction to experimental trends of propeller performance, turn your 

attention to calculating propeller profile and induced powers as required by Eq. (2.174), 

which is repeated on the next page for convenience: 

-0.005

0

0.005

0.01

0.015

0 0.1 0.2 0.3 0.4 0.5 0.6

Inflow Ratio V/Vt

Rotor

Thrust

Coeff.

CT

-0.001

0

0.001

0.002

0.003

Ideal

Power

CT(V/Vt)

Thrust at Beta = 11 deg.

Thrust at Beta = 27 deg.

Ideal Power at Beta = 11 deg.

Ideal Power at Beta = 27 deg.

Fig. 2-105. Ideal power reaches a peak and falls, but not because the propeller stopped 

producing thrust. The ideal power must go to zero when V/Vt = 0. 
2.4 FORWARD-FLIGHT PERFORMANCE 

223 

(2.174) ( )

( )

P oi Propeller

Pactual T Po Pi 2 3

t t

TV P P V Actual Power C C C C

R V V

+ +   ≡ = = ++  

ρ π  

. 

Profile power was introduced with Eq. 2.277 (page 227 in Volume I) discussing autogyro 

performance. From this introduction, the profile power is 

(2.175) ( ) R R 3

o r rr d 0 0

b b P V dD c V C dr

2 2

ρ ρ = =  

where (ρ) is the air density in slugs per cubic feet, (b) is the number of blades, and (cr) is the 

blade chord at radius (r). The velocity at a blade element (Vr) is, to the first approximation, 

the resultant of rotational speed (Ωr) and airspeed (V), both in feet per second. Following 

Fig. 2-106 and neglecting the induced velocity (vi), the resultant velocity at a blade element is 

(2.176) ( )2 2 V rV r =Ω + . 

In coefficient form, the profile power integration then appears as 

(2.177) 

1 3

2

2

Po r d

t

0

b 1 V C c x Cdx

2 R V

      = +  

π      









. 

Suppose now, for the sake of simplicity, that the power-weighted chord defined by 

Eq. (2.170) is used so that the local blade chord (cr) can be taken outside the integral. Suppose 

also that the airfoil drag coefficient (Cd) is taken as a constant, at some average value, which 

reduces the integration to 

(2.178) 

1 3

2

e d avg. 2

Po

t

0

C V C x dx

2 V

  σ     = +        









with the result that profile power is approximately 

(2.179) 

( )

1 3

2

e davg. 2

Po

t

0

2 4

e davg.

t tt

C V C x dx

2 V

C V 93 3 V V 1 3 ln 2 ln

8 V 82 2 V V

  σ     = +        

σ           

≈ + ++ −                    







 . 

The average airfoil drag coefficient (Cd avg.) can be approximated as 

(2.180) 

2

2 T

davg. do l do

C C C CC 6  = +ε = +δ    σ
2.4 FORWARD-FLIGHT PERFORMANCE 

224 

where (Cdo) is the airfoil minimum drag coefficient and (δ) is the airfoil drag rise with lift 

coefficient squared. I have found that a reasonable value of (δ) is (Cdo) so that at Cl = 1, the 

average drag coefficient is 2Cdo. 

 Now consider the propeller’s induced power. From simple momentum theory you 

have 

(2.181) R

i i 0 P v dT =  . 

By assuming the induced velocity constant, the integration yields the result that Pi = Tvi, and 

again, from momentum theory, the induced velocity is 

(2.182) 

2

i

VT V

v

2 2A 2

  = +−     ρ . 

Therefore, the propeller’s induced power is, to the first order, 

(2.183) ( )

2

i 2

VT V P T

2 2 2 R

    =+ −       ρ π  

. 

Fig. 2-106. Propeller blade element geometry.
2.4 FORWARD-FLIGHT PERFORMANCE 

225 

Dividing Eq. (2.183) through by ( ) 2 3 ρ πR Vt puts the dimensional result into rotor power 

coefficient form. The result is 

(2.184) 

2

T

Pi T

t t

V V C C C

2V 2 2V

      = +−      

. 

 Weick’s test results for the variable-pitch propeller can be estimated with relatively 

simple theory. The results of test versus simple theory are shown in Fig. 2-107. The simple 

theory is 

(2.185) 

2

T

e do 2 4

P T

t t t t

2

T

T

t t

C C 6

V V 9 3 2 V Rotor C C 1 3 ln

V 8 V 82 V V V

V V C C

2V 2 2V

    σ +ε     σ                    = + + ++                        

      + +−      

. 

-0.001

0

0.001

0.002

0.003

0.004

-0.001 0 0.001 0.002 0.003 0.004

Beta = 11 deg. at 42 inch radius

Beta = 15 deg.

Beta = 19 deg.

Beta = 23 deg.

Beta = 27 deg.

Perfect Agreement

Experimental 

Power Coeff.

CP

Eq. 2.185 Power Coeff. 

Fig. 2-107. Propeller performance about the optimum design point can be predicted with 

relatively simple theory. 
2.4 FORWARD-FLIGHT PERFORMANCE 

226 

For the comparison in Fig. 2-107, I used Cdo = 0.02, δ = 0.02, and σ = 0.055. Because 

Weick tabulated his raw data [294], each pitch angle had data for the wind tunnel velocity, 

propeller RPM, and experimental thrust, along with the experimental engine torque. This 

gives a known inflow ratio (V/Vt) and rotor thrust coefficient (CT) required by Eq. (2.185). 

 As a final note to this propeller discussion, a more complete study of propeller 

performance as seen from a rotorcraft perspective is available in NASA Contractor Report 

196702 [295]. 

 With this background, let me return to prediction of the Cessna TL-19D powerrequired curve first seen in Fig. 2-100. The basic lift-drag polar of the TL-19D was given by 

Eq. (2.165) as 

(2.165) ( )( )

2

L 2

D L

D C C 0.04 0.04 0.0605C

qS 7.448 0.07064

== + = +

π

and, therefore, the drag—following Eq. (2.166) and with fe = CDf S = 0.04(174) = 7 square 

feet—becomes 

(2.186) ( )

2

2

2

V 0.0605 D 7.0 L

2 174 V 2

  ρ = +     ρ . 

 For this example, flight test data from steady, level flight will be used, so propeller 

thrust (TP) equals aircraft drag (D), and wing lift (L) equals weight (W). The propeller thrust 

coefficient in rotorcraft terms—so that Eq. (2.185) can be used—is simply 

(2.187) ( ) T 2 2

t

D C

R V =ρ π , 

and the propeller diameter of the TL-19D is 90 inches, which means that R = 3.75 feet and the 

propeller area is πR2

 = 44.18 square feet. According to the McCauley Propeller Company, its 

propeller number 2A36CI-U/90M-0 has an Activity Factor of 82.3, which makes the powerweighted solidity equal to 0.025. 

 This is all the geometric data needed to calculate the power required versus true 

airspeed of the TL-19D. Only a weight, an altitude, the propeller RPM, and a range of 

airspeeds are now required. The comparison of test to simple theory is shown in Fig. 2-108. 

Test results from figure 3 of reference [282] are given for the TL-19D at a weight of 

2,400 pounds and a density altitude of 1,500 feet. The pilot flew the test points with a constant 

engine/propeller speed of 1,900 rpm up to about 110 knots. Beyond 110 knots, he had to 

steadily increase RPM to get more power out of the engine. At the maximum rated engine 

speed, 2,600 rpm, he was able to record 131 knots. At this maximum speed point, the 

propeller tip was approaching the speed of sound. That is, the propeller helical tip Mach 

number of the TL-19D was 

(2.188) ( )2 2 2 2

t

s

V V 1,021 1.69 131 Helical Tip Mach No. 0.941 a 1,110+ + × == = . 
2.4 FORWARD-FLIGHT PERFORMANCE 

227 

Fortunately, this metal propeller, much like Weick’s propeller shown in Fig. 2-102, had very 

thin airfoils over the outer radius stations of the blade. This geometry minimizes propeller 

profile power rise with helical tip Mach number. 

 Fig. 2-108 shows the power components that lead to the total predicted engine brake 

horsepower versus airspeed, which is the heavy solid line on the figure. The first component 

is the basic airframe induced power, which is the power required to produce airframe lift. This 

power is calculated from Eq. (2.186) as 

(2.189) ( )

2

i d l 2

induced 2

D V dC dC V Airframe BHP W

550 SV2 550

  = =  

  ρ  

where, for the TL-19D, 2

d l dC dC 0.0605, = and wing area (S) is 174 square feet. 

 The airframe has a parasite drag that must be overcome by the propeller. The brake 

horsepower delivered to the propeller to overcome this drag is 

(2.190) 

2

para

parasite e

D V V V Airframe BHP f

550 2 550

  ρ = =    

where the equivalent parasite drag area (fe) for the TL-19D is 7 square feet. 

0

20

40

60

80

100

120

140

160

180

200

0 20 40 60 80 100 120 140

Cessna TL-19D Test Data, AFFTC-TR-57-14, Fig. 3

Airframe Induced Power

Airframe Induced + Parasite Power

Airframe Induced + Parasite Power + Propeller Profile Power

Total Predicted BHP

Engine 

BHP

True Airspeed (kts)

Prop/Engine 

RPM = 1,900

2,600

1,900

1,900

1,950

2,075

2,300

Fig. 2-108. Measured Cessna TL-19D flight test power required can be predicted with 

rotorcraft methodology (weight = 2,400 pounds and altitude = 1,500 feet). 
2.4 FORWARD-FLIGHT PERFORMANCE 

228 

 The sum of airframe-related brake horsepower [Eqs. (2.189) and (2.190)] is shown in 

Fig. 2-108 with the solid triangle symbols. 

 The propeller itself requires engine power to overcome its profile drag, and this power 

is calculated as 

(2.191) 

2 3

t e T

profile do

t

AV C V Prop BHP C 6 F 550 8 V

  ρ σ      

= +     δ            σ  

where 

(2.192) 

2 4

t t tt

V V 93 2 V F 1 3 ln

V V 8 2 VV V

                    =+ + +                 

with TL-19D propeller parameters of A = 44.18 square feet, solidity σe = σ = 0.025, Cdo = 

0.024, and δ = 0.024. The propeller thrust coefficient is calculated from the sum of airframe 

parasite and induced drags. 

 To produce thrust, the propeller creates an induced velocity that leads to the fourth 

component of power, the propeller-induced power, calculated as 

(2.193) ( )

2 3

t T

induced T

t t

AV V V C Prop BHP C 550 2V 2 2V

    ρ     = +     −

     

where the propeller thrust coefficient is calculated from the sum of airframe parasite and 

induced drags. 

 So that you will not think that the proceeding simple theory is of limited use, the 

prediction of all TL-19D flight test power-required data is shown in Fig. 2-109. The success 

of such a simple theory depends on the absence of stall and compressibility effects. And the 

prediction depends on a variable-pitch propeller, although adequate results can often be 

obtained even with a fixed-pitch propeller. 

 This brief discussion about airplane forward-flight performance does not include many 

other facets such as climb and descent performance, takeoff and landing calculation methods, 

and performance during maneuvers. There are many textbooks and handbooks available that 

delve into these details. I grew up with Perkins and Hage [284], but you will, of course, have 

your favorite. 

 Finally, as a prelude to helicopter forward-flight performance, Table 2-15 provides a 

translation of propeller and rotor notations that I have found handy. 
2.4 FORWARD-FLIGHT PERFORMANCE 

229 

0

40

80

120

160

200

0 40 80 120 160 200

Simple Theory BHP

Test 

Engine 

BHP

Fig. 2-109. Measured Cessna TL-19D flight test power required can be predicted with 

rotorcraft methodology (weight = 2,400 pounds and density altitudes range from 

1,500 to 10,000 feet). 

Table 2-15. Propeller and Rotor Nomenclature 

Parameter Helicopter Rotor Airplane Propeller 

Prop-Rotor Diameter (ft) D D 

Blade Radius (ft) R R 

Shaft Rotational Speed Ω (radians/sec) n (revolutions/sec) 

Tip Speed (ft/sec) Vt

 = Ω R Vt

 = π n D 

Disc Area (sq ft) A = π R2 A = π D2 /4 

Air Density (slug/ft3 ) ρ ρ

Flight Speed (ft/sec) V V 

Thrust (lb) T T 

Thrust Coefficient CT = T/ρAVt

2 CT = T/ρ n 2 D 4 

Power (ft-lb/sec) P P 

Power Coefficient CP = P / ρ A Vt

3 CP = P / ρ n 3 D 5 

Tip-Path-Plane Angle of Attack 

(radian) 

αtpp measured from rotor disc 

parallel to wind 

α measured from shaft 

horizontal 

Advance Ratio μ = V cos αtpp / Vt

 J = V / nD 

Inflow Ratio λo = V sin αtpp / Vt

 See Advance Ratio 

Induced Velocity (ft/sec) vi u or w 

Induced-Inflow Ratio λi

 = vi / Vt Rarely used 

Propulsive Efficiency ηP = CT λo/measured CP ηP = CT J/measured CP 
2.4 FORWARD-FLIGHT PERFORMANCE 

230 

2.4.2 Single Rotor Helicopter 

 You saw the contrast between an early U.S. Army helicopter (the H-13) and an 

airplane (the L-19A) engine brake horsepower required versus airspeed trends in 

Fig. 2-97. The contrast is, admittedly, rather startling, particularly to a fixed-wing engineer. 

After all, the airplane engineer sees that at 150 horsepower the L-19A goes 40 knots faster. 

Not only that, but at 150 horsepower, the engine is burning about 65 pounds of fuel per hour. 

Because Table 2-14 shows that both the Bell H-13H and the Cessna L-19A have about 

250 pounds of fuel to burn, both aircraft can fly for 3.75 hours, but in that time the L-19A will 

cover some 400 nautical miles at 110 knots, while the H-13H will only cover about 

250 nautical miles at 70 knots. To top it off, today’s fixed-wing engineer probably does not 

think that the 1950’s L-19A was a particularly great performing airplane, primarily because 

its maximum lift-to-drag ratio, based on engine brake horsepower and 2,400 pounds weight, 

was on the order of 

(2.194) L W 2,400 Aircraft = = = 5.4

D 550BHP 1.69V 550 150 1.69 110knots × × , 

and the H-13 helicopter was even worse at 3.4, some 2 points lower. 

 A simple photo of the H-13 (Fig. 2-110) would cause the fixed-wing engineer to make 

a long list of aerodynamic deficiencies. The list would surely include: 

1. The thing is built of tubes; all very high-drag components. 

2. Even World War I airplanes had their fuselage covered with doped canvas. 

3. Why isn’t the landing gear retractable? 

4. Does it at least have doors to cover the large cockpit openings? 

5. All that poorly shaped blade retention hardware must have high drag. 

6. Are all those bars, linkages, and pipes between the rotor hub and fuselage 

streamlined? 

7. Let’s put the fuel tanks inside. 

8. It reminds me of Bleriot’s Model XII that got across the English Channel in 1909. 

9. Propellers—okay rotors—are not suppose to go through the air edgewise. 

10. You’re lucky it can get to 80 knots. 

11. Well, it can at least hover and takeoff and land vertically. That’s something. 

12. How do you calculate the power-required curve for this helicopter anyway? 

What’s the equivalent flat-plate drag area? What’s Oswald’s efficiency factor for 

an edgewise flying rotor? 

Of course this gives the helicopter aerodynamic performance engineer an opportunity to offer 

an explanation and some insight. 
2.4 FORWARD-FLIGHT PERFORMANCE 

231 

Fig. 2-110. The H-13 lacked aerodynamic refinements (photo from author’s collection).

 The H-13 began life as the Bell Model 47 and was certificated by the CAA (now the 

FAA) on March 8, 1946. It was designed to at least hover with the then available engine. The 

rotor diameter was large to ensure a reasonable power margin at that time. Every weightempty savings that could be obtained was obtained. Hence, an uncovered fuselage, removable 

doors, and the bare necessities for a landing gear. The engine, main rotor transmission, and 

fuel tanks were placed directly under the rotor shaft. The large, bulbous “windshield” was 

selected for maximum crew visibility. The blade attachment was designed with a high margin 

of safety and very low fatigue stresses. The attachment hardware was a high-drag item as 

were the rotor shaft and control linkage. Because the Bell Model 47 was designed to use the 

installed power most efficiently in hover, the high-speed performance was simply a fallout. 

 There are a number of very aerodynamically “clean” helicopters in production today. 

One good example is the Sikorsky twin-turbine-engine Model S-76 shown in Fig. 2-111, 

which first flew in January 1975. From Jane’s All the World’s Aircraft [296], some 510 

increasingly improved models of the S-76 have been delivered since early 1979. This 

medium-sized helicopter has a crew of 2 and room for as many as 12 to 14 passengers. The 

aircraft meets Federal Aviation Regulations (FAR), Part 29 with Category A Instrument 

Flight Rules (IFR) and sold for about $6 million in 2002. Drag reduction is evident in the 

retractable, wheeled landing gear and airplane-shaped fuselage. However, the main rotor 

blade attachment hardware, the hub, is still a high-drag item. Evan Fradenburgh (a close 

friend and top-notch engineer) went to considerable effort to make the S-76 a low-drag 

helicopter [297]. 
2.4 FORWARD-FLIGHT PERFORMANCE 

232 

Fig. 2-111. The Sikorsky S-76 is one example of an aerodynamically “clean” helicopter 

(photo from author’s collection). 

 Now let me discuss the power-required curve of the H-13H shown in Fig. 2-97. This 

primary performance curve can be estimated with a simple theory that is no more complicated 

than that for the L-19A series. You learned the basics in Volume I; let me apply those basics 

to the helicopter. 

 As a starting point use Eq. (2.47), repeated here for convenience, with the notation 

change for calculating brake horsepower required: 

Eq. (2.47) mr tr

req'd. Accessory

mr tr

RHP RHP BHP BHP = ++

η η . 

Consider the main rotor horsepower (RHPmr) first. As with the L-19A, the main rotor requires 

power to overcome helicopter drag (i.e., the power associated with the equivalent flat plate 

area), the profile power (i.e., the power associated with turning the rotor against its own drag 

created by Cdo), and the induced power (i.e., the power associated with thrust and induced 

velocity). 

 The helicopter’s main rotor provides both a lift force (Fz) and a propulsive force (Fx), 

which correspond to an airplane’s propeller thrust. In steady, level flight, the resultant force 

2 2 F F z x + is adequately approximated for this example by the helicopter’s weight (W). The 

propulsive force comes by tilting the tip path plane (αtpp) nose down, which is in the negative 

direction. Thus, 

(2.195) 2

x tpp e

1 F W Df V

2

  =− α = = ρ    
2.4 FORWARD-FLIGHT PERFORMANCE 

233 

where (fe) is the equivalent flat plate area in square feet, (ρ) is the air density in slugs per 

cubic foot, and (V) is the helicopter’s true airspeed in feet per second. Then, following the 

L-19A example [Eq. (2.190)], the main rotor horsepower required for the H-13H to overcome 

parasite drag is 

(2.196) 

2

para

mr e

D V V V Parasite RHP f

550 2 550

  ρ = =    

. 

 In like manner, the main rotor requires horsepower to produce thrust, which is 

calculated as 

(2.197) i

mr

Wv Induced RHP

550 =

where the rotor induced velocity (vi) is obtained for steady, level flight (when the tip-pathplane angle is small) approximately as 

(2.198) 

1

2 2 4 2

i 2

VWV

v

4 2R 2

   

=+ −      ρπ     

so that induced power is 

(2.199) 

1

2 2 4 2

i

mr i 2

Wv WV W V Induced RHP k

550 550 4 2 R 2

   

== + −      ρπ     

. 

The inclusion of an induced power correction factor (ki) is the rotorcraft equivalent of the 

airplane’s Oswald efficiency factor, but in the numerator. Ray Prouty, on pages 125 through 

129 of his excellent and practical helicopter engineering book, Helicopter Performance, 

Stability, and Control [242], calculates that a rotor’s Oswald efficiency factor can vary 

between 0.5 and 0.8.70 A useful (but crude) approximation I use [211] is that 

(2.200) ( ) 2

i k 1.075cosh 7.5 = μ

where (μ) is the main rotor’s advance ratio (V/Vt). 

 The main rotor’s profile power calculation is much like that for a propeller. That is, 

(2.201) ( )

3

t e 2

mr do l avg. mr

AV Profile RHP C C F

550 8

  ρ σ  = +   δ  μ          

 

70 Ray Prouty’s complete paper [298] about the adverse induced drag behavior of the lifting rotor was published 

in July 1976. He originally presented the paper at the American Helicopter Society Symposium on Helicopter 

Aerodynamic Efficiency held in Connecticut in March 1975. His paper came from his thesis for a Master’s 

Degree from the California Institute of Technology in 1958. I have always thought that Ray did his best to alert 

the industry about a serious deficiency in rotor aerodynamic theory—but very few of us paid attention. 
2.4 FORWARD-FLIGHT PERFORMANCE 

234 

where the advance ratio function (Fmr) for the main rotor is, from Eq. 2.295 on page 236 in 

Volume I, 

(2.202) ( ) 2 46 F 1 4.65 4.15 mr μ = + μ + μ −μ . 

Because the rotor remains in roll equilibrium while in edgewise flight, the average airfoil lift 

coefficient (Cl avg) needed by Eq. (2.201) is calculated as 

(2.203) 

2

W

l avg 2 4

C 13 2 C 6

1 94

   + μ =      σ −μ + μ  

. 

This equation for the average airfoil lift coefficient was developed on page 44 of reference 

[211]. 

 Now consider the power required by the tail rotor. Without doing a thorough trim 

analysis that includes roll and yaw as well as pitch, some assumption about the tail rotor tippath-plane angle and thrust must be made. For this example, I will assume that the pilot has 

trimmed the aircraft so that the tail rotor is not producing any propulsive force (i.e., Fx = 0). 

Then only an estimate of tail rotor thrust is required to begin the calculation. 

 The tail rotor thrust (i.e., the anti-torque force) is calculated just as it was in hover. 

That is, 

(2.204) ( ) ( ) mr mr

tr

tr mr tr t mr

550RHP 550RHP T

R R 1 R RV−

= = +Ω + , 

and then the induced power is simply a repeat of the main rotor’s computation, but with thrust 

substituted for weight and subscripted with (tr) to indicated tail rotor. Thus, 

(2.205) 

1

2 2 4 2

tr i tr tr

tr i 2

tr

Tv T V V T Induced RHP k

550 550 4 2 R 2

   

== + −      ρπ     

. 

Of course the induced power correction factor (ki) must be based on the tail rotor advance 

ratio, which means that 

(2.206) ( ) 2 Tail rotor k 1.075cosh 7.5 i tr = μ . 

 The tail rotor profile power calculation is much like that for a propeller. That is, 

(2.207) ( )

3

tr t tr e tr 2

tr do l avg. tr tr tr

A V Profile RHP C C F

550 8

− −   ρ σ  = +δ μ             

where the tail rotor advance ratio function (Ftr) is the same as the main rotor function, 

although the tail rotor advance ratio must be used: 

(2.208) ( ) 2 46 F 1 4.65 4.15 tr tr tr tr tr μ = + μ + μ −μ . 
2.4 FORWARD-FLIGHT PERFORMANCE 

235 

Because the tail rotor also remains in roll equilibrium while in edgewise flight, the average 

airfoil lift coefficient (Cl avg.) is now based on the tail rotor thrust-coefficient-to-solidity ratio 

(CT/σ): 

(2.209) 

2

T tr

l avg. 2 4

tr tr tr

C 13 2 Tail rotor C 6

1 94

    + μ =       σ −μ + μ  

. 

 The results of applying these simple equations to the Bell H-13H are shown in 

Fig. 2-112. (The computations summarized in Table 2-17 used input from Table 2-16.) As the 

figure shows, the main-rotor brake horsepower required dominates the answer. The sharp 

reduction in induced power is simply replaced by power required to overcome the parasite 

drag, which is calculated assuming an equivalent flat plate drag area (fe) of 15 square feet. 

The profile power of the main rotor increases slightly with speed, which can be better 

appreciated with Table 2-17. I assigned the average airfoil a minimum drag coefficient (Cdo) 

of 0.01 and set (δ), the drag rise with average airfoil lift coefficient squared, equal to 0.012. 

Lacking any data, a main rotor transmission efficiency of 0.97 was assumed. 

 The difference between the main-rotor total brake horsepower required (the ×’s in 

Fig. 2-112) and the heavy, solid line without symbols accounts for the tail rotor and 

3 horsepower of accessories. The brake horsepower required by the tail rotor drops rapidly 

with speed, from 14.2 at hover to below 10 at 80 knots, as Table 2-17 shows. 

0

50

100

150

200

250

0 10 20 30 40 50 60 70 80 90

Bell H-13H, GW = 2,370 lbs, H = 1,000 ft, AFFTC-TR-57-12, Fig. 11

Predicted Total BHP

Main Rotor Induced BHP

Main Rotor Induced + Profile BHP

Main Rotor Induced + Profile + Parasite BHP

Engine 

BHP

True Airspeed (kts)

Fig. 2-112. Bell H-13H flight test power required can be closely estimated with simple 

methodology (computations in Table 2-17 using input from Table 2-16). 
2.4 FORWARD-FLIGHT PERFORMANCE 

236 

Table 2-16. H-13H Inputs to Sample Power-Required Calculation 

Parameter Main Rotor Tail Rotor 

Density 0.002309 0.002309 

Radius 17.5625 2.8385 

Tip Speed 632.67 767.59 

Solidity 0.03325 0.08465 

Airfoil Cdo 0.010 0.012 

Airfoil δ 0.010 0.012 

Transmission Efficiency 0.97 0.98 

H-13 Flat Plate Area 15 n/a 

Table 2-17. H-13H Sample Power-Required Calculation 

Forward Speed (kts) 0 16 32 48 64 80 

Parameter 

Main Rotor 

Advance Ratio 0.000 0.043 0.085 0.128 0.171 0.214 

Induced Velocity 23.02 16.68 9.65 6.51 4.89 3.92 

ki 1.075 1.075 1.077 1.083 1.101 1.139 

Induced RHP 106.6 77.3 44.8 30.4 23.2 19.2 

Average Cl 0.478 0.480 0.487 0.497 0.513 0.532 

Average Cdo 0.0123 0.0123 0.0124 0.0125 0.0126 0.0128 

F(mu) 1.000 1.009 1.034 1.078 1.139 1.221 

Profile RHP 52.6 53.1 54.7 57.5 61.6 67.1 

Parasite RHP 0.0 0.6 5.1 17.3 41.0 80.1 

Total RHP 159.2 131.0 104.6 105.2 125.8 166.4 

Total MR BHP 164.1 135.1 107.8 108.5 129.7 171.6 

Tail Rotor 

Advance Ratio 0.000 0.035 0.070 0.106 0.141 0.176 

Main Rotor Torque 2431 2000 1597 1607 1921 2541 

Thrust 119.1 98.0 78.3 78.7 94.2 124.5 

Induced Velocity 31.92 23.44 12.09 8.26 7.43 7.87 

ki 1.075 1.075 1.076 1.079 1.087 1.104 

Induced RHP 7.4 4.5 1.9 1.3 1.4 2.0 

Average Cl 0.245 0.202 0.163 0.167 0.203 0.276 

Average Cdo 0.0127 0.0125 0.0123 0.0123 0.0125 0.0129 

Ftr(μ) 1.000 1.006 1.023 1.052 1.094 1.148 

Profile RHP 6.5 6.4 6.4 6.6 7.0 7.5 

Total RHP 13.9 10.9 8.3 7.9 8.3 9.5 

Total Tail Rotor BHP 14.2 11.1 8.4 8.0 8.5 9.7 

Accessory BHP 3.0 3.0 3.0 3.0 3.0 3.0 

H-13 Total BHP 181.3 149.2 119.3 119.5 141.2 184.3 
2.4 FORWARD-FLIGHT PERFORMANCE 

237 

 The preceding numerical example shows what a simple theory, a slide rule, some 

elbow grease, and paper and pencil could do before the digital computer came along. While 

these tools were sufficient for development of early, low-speed helicopters, performance 

parameters that far exceeded the capability of a slide rule accompanied the onset of turbinepowered helicopters. Comprehensive computer codes today account for the forces and 

moments of the complete helicopter, model the airflow through and about the main and tail 

rotors and, most importantly, include nonlinear aerodynamics. The next generation of 

comprehensive codes use computational fluid dynamics (CFD), which can compute the lift, 

drag, and pitching moment of any rotor blade element. This replaces approximation of 

average airfoil lift and drag by 2 CC C d do l = +δ or more complicated means. 

 This discussion of single rotor helicopter performance would be incomplete without 

three comments about the L-19A airplane versus the H-13H helicopter. The first comment is 

self evident. The equivalent parasite drag area of the H-13H is fe = 15 square feet versus 7 

square feet for the L-19A. Thus, the helicopter’s engine horsepower required to overcome just 

airframe drag is more than twice that of the comparable airplane. The second comment is not 

so evident. The engine horsepower required to overcome induced drag is, following simple 

theory, nearly equal between helicopter and airplane if the wing spans are equally loaded. To 

see this point, first consider the induced drag for an airplane, which is calculated as 

(2.210) 

( )

( ) ( ) ( )

2

L

Di

2 2

22 2

w w

C Airplane Induced Drag qSC qS 1 AR

L 1L qS 1 1 qS b S q b

  = = +δ     π

    = +δ = +δ       π π    

where (q) is the dynamic pressure (1/2 ρV2

), (L) is airplane weight (in steady, level flight), 

(bW) is wing span, and (δ) is the correction for nonelliptical bound circulation distribution 

over the wing span. Even with a wing of poor planform shape (rectangular) and adverse twist, 

the increase of induced drag above ideal (i.e., δ = 0) is rarely greater than δ = 0.07. 

 Now for the helicopter rotor induced drag. The induced power (Pi) is simply equal to 

lift (L) times induced velocity (vi). Because drag is power divided by velocity (V), it follows 

that 

(2.211) i i

i i

P v Helicopter Induced Drag k k L V V

  = =    . 

Glauert gave the classical approximation for induced velocity as 

(2.212) 

( ) ( )( )

hp

i 2 2 2

FP hp i FP hp

T

v

2 R V sin v V cos

=

ρπ α − + α

. 

Suppose now that the hub-plane angle of attack (αhp) is virtually zero in steady, level flight 

and that the flight path velocity (VFP) is true airspeed (V) in steady, level flight. Assume that 

the rotor thrust (Thp) equals rotor lift. Then it follows that 
2.4 FORWARD-FLIGHT PERFORMANCE 

238 

(2.213) 

( ) ( ) ( )

2

i i 2 22 2 2 2

i i

L L Helicopter Induced Drag k L k

2 R Vv V 2 R V 1 vV

 

= =  

ρπ + ρπ +  

. 

Because rotor diameter (D) is twice rotor radius (R), and dynamic pressure (q) is (1/2 ρV2

), 

you have 

(2.214) 

( )

2 2

i

i i 2

i

1L 1 1L v Helicopter Induced Drag k k when is small qD qD V 1 vV

        = ≈     π π     +    

. 

You can see from Eq. (2.214) that by 32 knots (vi/V)2

 is about 0.032, so that induced drag for 

the two lifting devices depends on span loading and dynamic pressure. But note particularly 

that the correction for a non-ideal span loading (ki) has reached 1.139 by an advance ratio of 

0.214, according to Eq. (2.200). This adverse trend deserves a little more discussion (because 

it is not widely acknowledged), which you will learn later in this volume. 

 The third comment regarding the H-13H versus the TL-19D is evident by looking very 

closely at Fig. 2-108 and Fig. 2-112. While the induced power is on the same order, 

approximately 30 horsepower at 60 knots, profile power is significantly greater for the 

helicopter, about 60 horsepower at 60 knots. The difference in parasite power at 60 knots 

(i.e., 36 horsepower for the H-13H with fe = 15 square feet and 17 horsepower for the L-19A 

with fe = 7 square feet) is relatively insignificant. Of course at high speed the story changes. 

 This leads me to the conclusion that early helicopters suffered from excessive parasite 

power and excessive profile power when compared to propeller-driven airplanes. 

2.4.3 Twin-Rotor Helicopter 

 The competition between twin-rotor and single rotor helicopters really heated up in the 

1950s. In that decade, Kaman came forward with his H-43B synchropter, Piasecki perfected 

his H-21 nonoverlapped tandem, and Sikorsky offered the single rotor H-34, a militarized 

version of his commercial S-58. A great deal can be learned about twin-rotor helicopter 

performance from a comparison of these three helicopters [299]. But first a little history about 

each machine. 

 In 1951, Charles Kaman71 experimented with two 175-horsepower Boeing 505 

industrial gas turbines installed in his Navy HTK, the forerunner of his H-43 synchropter. 

With U.S. Air Force support, Kaman upgraded his synchropter with the Lycoming T-53-L-1 

engine. This turbine-powered helicopter was specially designed as a crash rescue and fire 

fighter, and was designated as the H-43B. It was found at many airfields. When an Air Force 

 

71 Kaman’s early history is well described in the book Vertical Flight—The Age of the Helicopter edited by 

Walter Boyne and Donald Lopez [300]. The forward to this book was written by Joe Mallen, then Chairman of 

the American Helicopter Society. Joe was my first boss at Vertol when I was placed in the Preliminary Design 

group after graduating from Rensselaer Polytechnic Institute in June 1956. Joe has remained a mentor and close 

friend throughout my career. 
2.4 FORWARD-FLIGHT PERFORMANCE 

239 

airplane crashed, the H-43B would scramble and fly to the downed airplane, and the pilot 

would use the helicopter’s downwash to blow the flames away from the airplane. This rescue 

mission directly parallels the Navy’s use of the Piasecki small HUP for plane guard duty 

alongside aircraft carriers. 

 Frank Piasecki’s H-21 was selected the winner (over the Sikorsky S-58 and other 

submittals) in a U.S. Air Force competition for an arctic search and rescue helicopter. The 

H-21B served the Air Force as an assault version, while the H-21C model served the U.S. 

Army as a troop transport. The H-21 series followed the development of the XHRP-X (the 

dogship) and the HRP-1, which the U.S. Navy funded. The early nickname was the Flying 

Banana, and initial operational use was as a troop carrier. 

 Igor Sikorsky’s follow-on to the S-55 was the S-58, which was developed for the 

commercial market. As the Korean War came to an end, military requirements became clearer, 

and the Army, Marine Corp, Navy, and Coast Guard all bought militarized S-58 versions 

basically designated as the H-34. 

 The Sikorsky H-34A and Piasecki H-21B/C played key roles as the services saw the 

need for bigger helicopters that could carry at least a fully armed squad of soldiers. Both 

troop-carrying helicopters and the rescue helicopter, Kaman’s H-43B, were thoroughly 

evaluated by the Air Force at Edwards Air Force Base in California. Of the three, the H-21B 

had the poorest flying qualities and the H-34A had had the best handling characteristics. The 

H-43 was evaluated as having “poor directional and lateral controllability during the approach 

and landing, often resulting in considerable pilot concern.” 

 The engine-horsepower-required variation with true airspeed for these three 

helicopters (Table 2-18) is illustrated in Fig. 2-113. This flight test data was acquired at 

1,000-feet density altitude with each helicopter operating at a disc loading (DL = W/A) of 

0

200

400

600

800

1,000

1,200

0 20 40 60 80 100 120

Engine Shaft 

Horsepower

True Airspeed (kts)

Kaman H-43B, 

Weight = 6,800 lbs

Sikorsky H-34A, 

Weight = 9,750 lbs

Piasecki H-21, 

Weight = 12,080 lbs

Fig. 2-113. Two twin-rotor helicopters and one single rotor helicopter. 
2.4 FORWARD-FLIGHT PERFORMANCE 

240 

Table 2-18. The Second Generation of Helicopters 

Basic Aircraft Information Kaman H-43B Piasecki H-21B/C Sikorsky H-34A 

References [193] [109] [108] 

Power Installed 

 Engine Model Lycoming T-53-L-1B Wright R-1820-103 Wright R-1820-84 

 Takeoff Rating at Sea Level (hp) 1,425 at 2,800 rpm 1,425 at 2,800 rpm 

 Military Rating (30 min) (hp) 860 at 6,680 rpm 1,400 at 2,700 rpm 1,400 at 2,700 rpm 

 Normal (Continuous) Rating (hp) 680 at 6,320 rpm 1,275 at 2,500 rpm 1,275 at 2,500 rpm 

Power Limits 

 Transmission (30 min) (hp) 825 at 260 rpm 

Weights 

 Empty (full oil, trapped fuel) (lb) 4,444 8,785 7,404 

 Extra Equipment (lb) 0 442 345 

 Two Crew (lb at 200 lb/man) 400 400 400 

 Minimum Operating (lb) 4,844 9,500 8,149 

 Fuel Full at 6 lb/gal (lb) 1,200 1,740 1,560 

 Design Gross Weight (lb) 6,044 13,300 11,867 

 Maximum Takeoff Weight (lb) 8,250 15,100 13,300 

Dimensions 

 Main Rotor(s) Two Two One 

 Diameter (ft) 47.0 each rotor 44.0 each rotor 56.0 

 Disc Area (ft2) 1,735 each rotor 1,520 each rotor 2,460 

 Blade Chord (in.) 15.69 16.5 16.4 

 Number of Blades 2 each rotor 3 each rotor 4 

 Solidity 0.071 each rotor 0.06 0.06215 

 Airfoil NACA 23012 NACA 0012 NACA 0012 

 Projected Disc Area (ft2) 1,931 3,040 n/a 

 Distance Between Hubs (ft) 4.1875 41.74 

 Tail Rotor None None One 

 Diameter (in.) 112 

 Blade Number 4 

 Blade Chord (in.) 7.0 

 Solidity 0.1592 

 Airfoil NACA 0012 

 Airframe 

 Nose-to-Tail Length (ft) 25.17 52.9 44.17 

 Height (ft) 12.58 15.90 15.83 

 Vertical Stabilizer Area (ft2) 

 Horizontal Stabilizer Area (ft2) 

 Center of Gravity Limits 

 Forward (in.) 3.0 rotor hub 41.0 CL between rotor 6.3 rotor hub 

 Aft (in.) 2.5 rotor hub 6.5 CL between rotor 10.4 rotor hub 
2.4 FORWARD-FLIGHT PERFORMANCE 

241 

4 pounds per square foot. The H-21B, at a gross weight of 12,080 pounds supported on two, 

nearly nonoverlapped, 44-foot-diameter rotors, has a disc loading of just under 4.0. Similarly, 

the H-34A, at 9,750-pounds gross weight supported on one 56-foot-diameter rotor, has a disc 

loading just under 4.0. And the H-43B, at 6,800 pounds with nearly coaxial 47-foot-diameter 

rotors is hovering at a disc loading of 4.0. 

 In and of themselves, the power-required trends shown in Fig. 2-113 are not startling. 

However, when rescaled to engine shaft horsepower per ton of gross weight, a very important 

facet about twin-rotor performance in level flight jumps right out at you as Fig. 2-114 shows. 

This figure shows that the tandem rotor H-21 power required does not experience as favorable 

a decrease with airspeed as its H-34 counterpart. In contrast, the H-43 with nearly a coaxial 

rotor arrangement (perhaps a very overlapped side-by-side rotor system would be more 

descriptive) behaves at low speed much like the H-34 single rotor. 

 Fig. 2-114 leads me to the major point about twin-rotor performance in steady, level 

flight. The point is that the tandem rotor machine has a significant power-required increase 

due to rotor flow field interference, particularly at low speed. The study of mutual tandem 

rotor flow interference in forward flight began with Stepniewski’s work in the early 1950s, 

which you will find in the modern literature [238]. His efforts provided initial power-required 

estimates for all tandem rotor helicopters developed by Piasecki, then Vertol, then Boeing 

Vertol, and now the Boeing Helicopter Division. Stepniewski’s approach used momentum 

theory. 

100

120

140

160

180

200

220

240

0 20 40 60 80 100 120

True Airspeed (kts)

Engine

Shaft

Horsepower

per Ton of

Gross

 Weight

Piasecki H-21, 

Weight = 12,080 

Sikorsky H-34A, 

Weight = 9,750 lbs

Kaman H-43B, 

Weight = 6,800 lbs

Fig. 2-114. The nearly nonoverlapped H-21 tandem rotor configuration does not behave 

as two isolated rotors in forward flight. 
2.4 FORWARD-FLIGHT PERFORMANCE 

242 

 The next evolutionary step beyond momentum theory to calculate induced velocity 

was made at N.A.C.A. Langley. The analytical approach, begun in 1945 by Coleman, 

Feingold, and Stempin [301], was accelerated in 1952 by Castles and De Leeuw at Georgia 

Institute of Technology (funded by the N.A.C.A.) [302] and then was refined in the early 

1960s by Harry Heyson.72 Over his career, Heyson authored some 50 NACA and NASA 

reports, most dealing with induced velocity through and about single- and twin-rotor systems. 

In June of 1978, he published a brief survey of rotary wing induced velocity theory [303], 

which is a must-read report. In this survey Heyson states that “Glauert’s formulation [ref. 

[304] and Eq. (2.198)] of the induced velocity of a rotor was merely a plausible guess.” And 

then Heyson turns right around and shows that a simple vortex theory gives Glauert’s 

formulation. 

 The “simple vortex theory” that Heyson (and his predecessors) used (Fig. 2-115) 

replaces the spiral wake trailed from a rotor blade with the mathematically tractable set of 

vortex rings bounded by a cylindrical wake. With considerable applied mathematical skill, 

Heyson solved for the velocity flow field and provided the industry with immensely valuable 

tables and charts of induced velocity. One example, figure 7 from Heyson’s NACA Report 

1319 [305], is shown here in Fig. 2-116. 

 Heyson found that a fundamental variable inherent to his “simple vortex theory” was 

the wake skew angle, the geometry being illustrated in Fig. 2-117. This fundamental angle, 

shown as 45 degrees in Fig. 2-117, is calculated simply as 

(2.215) tpp

tpp

V cos

tan

v Vsin

α

χ =

− α

Fig. 2-115. Heyson’s approximation of the vortex system created by a rotor blade. 

 

72 In my opinion, Harry Heyson, over a two-decade period, single handily carried the rotorcraft industry forward 

in its efforts to understand and calculate induced velocity. His contributions extended to understanding and 

calculating wind tunnel wall corrections used in V/STOL testing. 
2.4 FORWARD-FLIGHT PERFORMANCE 

243 

where (V) is flight path velocity, (αtpp) is the tip-path-plane angle of attack, and (v) is the 

mean induced velocity as calculated with Glauert’s “formulation.” (Heyson used the notation 

of vo for the mean induced velocity, whereas I have dropped the subscript.) Note that the wake 

skew angle, Eq. (2.215), is zero in hover and approaches the cotangent of the tip-path-plane 

angle of attack at very high speed. 

 Heyson’s work alone carried the industry until the digital computer came along. With 

that slide rule replacement, Ray Piziali and Frank DuWaldt at Cornell Aero Labs set about 

modeling a rotor blade and its vortex system with a true parallel to the fixed-wing trailed 

vortex system [306]. Their vintage 1962 vortex theory was built on visualizing the wake 

structure shown in Fig. 2-118. 

Fig. 2-116. Heyson’s induced velocity distribution along the X-axis of a rotor with 

triangular disc loading [305]. 

Fig. 2-117. The wake skew angle, χ, is a fundamental parameter. 
2.4 FORWARD-FLIGHT PERFORMANCE 

244 

Fig. 2-118. Piziali and DuWaldt modeled the vortex system trailed from rotor blades 

with straight line segments carefully placed in space. This was the beginning of 

the “prescribed wake model” [306]. 

 The encore to Piziali and DuWaldt’s digital-computer-assisted breakthrough came 

when Peter Crimi, then at Cornell Labs, freed the wake segments to find their own 

equilibrium position in space [307]. The results (Fig. 2-119) showed the rotor wake to be 

highly distorted, so much so that even today computer graphics can barely display the 

complexity. Crimi’s quantitative comparison of calculated induced velocity distributions to 

measurements that Heyson obtained [305] were impressive. In short, a foundation for the 

long-sought capability to predict induced velocity through and about rotor systems became 

fact by the mid-1960s. 

 To say that this long-sought technology advancement spread like wildfire would be an 

exaggeration. Johnson, in Chapter 13 of his invaluable book, Helicopter Theory [235], relates 

a realistic and detailed view of progress. In fact, each decade since the 1960s has seen 

engineers at universities and in industry make steady refinements. Many of the refinements 

solved mathematical instabilities, a more complete model for the complete helicopter grew, 

and now computational fluid dynamics tools are solving the problem. As I write these words, I 

am convinced that it is only the capacity and speed of the digital computer that are impeding 

the day-to-day use of a very important design tool for practicing helicopter performance 

engineers. You will find an excellent review of rotor wakes by Jim McCroskey particularly 

interesting [308]. A further discussion about calculating induced velocity and rotor-induced 

power is included in Appendix B. 
2.4 FORWARD-FLIGHT PERFORMANCE 

245 

Fig. 2-119. Crimi removed the skewed helical prescribed-wake constraint and produced 

the highly distorted, free-wake model in late 1965 [307]. 

 Now let me return to the specific problem of calculating power required for the H–21 

example shown in Fig. 2-113 and Fig. 2-114. At the time that this aircraft was developed, only 

Stepniewski’s semiempirical method [237, 238] was available. For the following discussion, 

however, I want you to see how valuable Heyson’s work was when coupled with simple blade 

element momentum theory. The tandem-rotor-helicopter power required is written as 

(2.216) front rear

acc

front rear

RHP RHP Engine SHP SHP = ++

η η . 

To save space, I will use the subscripts (f) and (r) to mean front and rear. The two rotor 

horsepowers are calculated, with simple theory, as 

(2.217) ( ) ( ) 3

f f t e 2 X

f i do l avg. f f

Tv v AV F V RHP k C C F

550 550 8 550

+ Δ   ρ σ    = + +δ μ +                 

and 

(2.218) ( ) ( ) 3

r r t e 2 X

r i do l avg. r r

Tv v AV F V RHP k C C F

550 550 8 550

+ Δ   ρ σ    =+ +       δ μ     +        . 

A detailed trim analysis would show that in steady, level flight the propulsive force (FX) 

would not, in general, be equal for the two rotors, but the sum of the two propulsive forces 

would equal the airframe parasite drag. That is, FXf + FXr = feq following Eq. (2.195) for a 

single rotor machine. A trim analysis would also show that the rotor thrusts (Tf and Tr) could

differ significantly, if for no other reason than the wide range in center of gravity allowed by 

the tandem rotor helicopter. Of course the airframe does introduce, in itself, lift, drag, and 
2.4 FORWARD-FLIGHT PERFORMANCE 

246 

pitching moments that could add differential thrusts to both rotors. To the first approximation, 

however, the sum of the two thrusts must be the helicopter’s weight (i.e., Tf + Tr = W). 

 Let me assume for this H-21 performance calculation that the two rotors are equally 

loaded. This means that each rotor carries one-half of the gross weight and each rotor 

overcomes one-half of the airframe drag. Make the practical assumption that the transmission 

efficiencies (ηf and ηr) are the same for both rotors. These simplifications allow the total rotor 

horsepower to be approximated as 

(2.219) 

( )( ) ( )( )

( )

f r

f ri i

3 2

t e 2

do l avg. r

W2 v v W2 v v

RHP RHP k k

550 550

AV V V 2 CC F f

550 8 2 550

+ Δ + Δ

+ = +

      ρ σ    ρ + +         δ μ     +           

. 

The profile power of each rotor will be equal, so calculating this power for just one rotor 

and then multiplying by two will be adequate for this example. Just so there is no 

misunderstanding, the profile power of one rotor uses the solidity (σ) of just one rotor, and the 

average airfoil lift coefficient (Cl avg,) for this one rotor is 

(2.220) ( )

2

T

l avg. T 2 4 2 2

t

C 1 3 2 W2 C 6 and C

1 94 R V

   + μ = =      σ −μ + μ   ρ π . 

 The tandem-rotor performance problem is now reduced to finding the total induced 

velocity (v + Δv) for both the front and the rear rotors as shown in Fig. 2-120. In this regard, I 

believe that the work of Bob Huston and Harry Heyson in the late 1950s and early 1960s 

offers a clear and simple method for calculating (Δvf) and (Δvr), which are the crux of the 

problem. In my mind, their work superseded Stepniewski’s original efforts and predates the 

many methods that allow the free wakes of both rotors to intermingle in what is seen today as 

a visual mess—as you can well imagine from Fig. 2-119. 

 Fig. 2-120 shows a sketch of the H-21 tandem rotor system at a negative tip-pathplane angle of attack that goes with propelling in forward flight. The subscript notation I will 

use is that (Δvr) is the increment of velocity induced on the rear rotor by the front rotor, and 

(Δvf) is the increment of velocity induced on the front rotor by the rear rotor. Huston found 

that the interference velocity (Δvf) acting on the front rotor due to the rear rotor was an 

upwash, but relatively small. In contrast, the front rotor induces a very large downwash (Δvr) 

on the rear rotor. 

 In 1958, Huston [309] tackled the tandem-rotor power required problem drawing 

heavily on Heyson’s induced velocity distribution charts [310].73 At that time, Huston and 

Heyson had access to preliminary tandem-rotor wind tunnel test results that Huston finally 

 

73 Bob Huston’s work earned him a Master of Science Degree from the University of Kansas. Harry Heyson 

suggested the thesis topic. Bob went on to N.A.C.A./NASA Langley and remains, in retirement, a strong 

rotorcraft advocate. 
2.4 FORWARD-FLIGHT PERFORMANCE 

247 

Fig. 2-120. H-21B tandem-rotor induced velocity interference diagram. 

published some 5 years later [311].74 Following Huston’s approach, I have used Heyson’s 

charts [305] to obtain the interference velocities (divided by the induced velocity of the rotor 

that created the interference) as a function of the wake skew angle. These estimates are shown 

in Fig. 2-121. Each data point shown in Fig. 2-121 was read from enlargement of charts such 

as the one shown in Fig. 2-116. The distance between the H-21 hubs is 41.875 feet, and the 

blade radius is 22 feet. This gives, in Heyson’s coordinate system, x = 41.875/22 = 1.89. From 

Fig. 2-116, for a wake skew angle of 45 degrees, the interference-velocity ratio is about 0.32. 

The interference-velocity ratio of –0.06 for the rear rotor’s interference on the front rotor is 

read at Heyson’s x = –1.89. A curve fit to the six Heyson chart values [305] gives 

(2.221) 

2

rear on front r r

r

2

front on rear f f

f

v

0.1513 0.0561

v 90 90

v

0.0165 1.2318

v 90 90

Δ   χ χ =− +    

Δ   χ χ = +    

. 

 

74 Huston’s 1963 wind tunnel test report provides the most fundamental tandem rotor results I am aware of. 

Individual rotor power data at equal thrust for two different rotor separations are shown. In 1967, Pruyn and a 

select group conducted a detailed flight test program with the Boeing CH-47 [312, 313]. The test parameters 

were so comprehensive that five volumes were required to report the results. Nothing comparable to Pruyn’s 

work was attempted until Bousman at NASA Ames Research Center led a dedicated group who, with a heavily 

instrumented Sikorsky UH-60A, conducted flight tests over a broad range in the flight envelop. This U.S 

Army/NASA Airloads Program, with testing conducted in the mid-1990s, provided a monumental data base for a 

single rotor helicopter. And, because of Bousman’s dedication, the test results reside in a computer, which allows 

nearly instantaneous access to any data channel at any test point. 
2.4 FORWARD-FLIGHT PERFORMANCE 

248 

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 10 20 30 40 50 60 70 80 90

Interference 

Velocity 

Ratio

 Δv/v

Wake Skew Angle, χ , (deg)

Front Rotor On 

Rear Rotor

Rear Rotor On 

Front Rotor

Downwash

Upwash

Fig. 2-121. Heyson’s interference velocities for an H-21 with coplanar hubs 

separated by 1.89 R. 

 The immediate next step is to calculate the wake skew angle for both rotors. This 

angle will not be the same for front and rear rotors because of the very different interference 

velocities. For the front rotor you have 

(2.222) tpp

f

f rear on front tpp

V cos

tan

v v V sin

α

χ = +Δ − α , 

and for the rear rotor you have 

(2.223) tpp

r

r front on rear tpp

V cos

tan

v v V sin

α

χ = +Δ − α . 

Note in these two preceding equations that the front-rotor wake skew angle (χf) depends on 

the velocity induced on the front rotor by the rear rotor. The converse is true for the rear rotor. 

This means that the two equations are dependent on each other, which is dealt with most 

easily by iteration. For this example of equally loaded H-21 rotors in steady, level flight, the 

primary induced velocity called for in Eqs. (2.222) and (2.223) is adequately estimated by 

(2.224) 

1

2 2 4 2

f r 2

W2 V W2 V

vvv

550 4 2 R 2

   

= == + −       ρπ  

, 
2.4 FORWARD-FLIGHT PERFORMANCE 

249 

and the forward tilting tip-path-plane angle (αtpp) of the equally loaded rotors is 

approximately 

(2.225) ( ) 1 2 e

tpp 2

Propulsive Force f V

Thrust W α ≈− =− ρ . 

 The H-21B power required as measured in flight test [109] and calculated with the 

1960’s technology just outlined (see Table 2-19 and Table 2-20) are compared in Fig. 2-122. 

Clearly, the rear rotor has excessive induced power due to the interference velocity of the 

front rotor. This rotor-rotor interference keeps the H-21 power required from decreasing 

rapidly from hover, and is a key difference when compared to the H-34 single rotor 

helicopter. 

Table 2-19. H-21 Inputs to Sample Power-Required Calculation 

Parameter Main Rotor 

Gross Weight 12,080 

Density 0.002309 

Radius 22.0 

Tip Speed 569 

Solidity 0.0597 

Airfoil Cdo 0.0085 

Airfoil δ 0.0085 

Transmission Efficiency 0.96 

H-21 Flat Plate Area 28 

0

200

400

600

800

1,000

1,200

1,400

0 20 40 60 80 100 120

H-21B Flight Test

Simple Theory

 Induced RHP

1. H-21 Rear Rotor

2. Isolated Single Rotor

3. H-21 Front Rotor

Engine

Shaft

Horsepower

True Airspeed (kts)

Fig. 2-122. H-21 performance calculated with 1960’s simple theory. 
2.4 FORWARD-FLIGHT PERFORMANCE 

250 

Table 2-20. H-21 Sample Power-Required Calculation 

Forward Speed (kts) 0 20 40 60 80 100 120 

Either Rotor 

 Thrust (lb) 6,040 6,040 6,040 6,040 6,040 6,040 6,040 

 Propulsive Force (lb) 0 19 76 171 304 475 685 

 Rotor ki 1.075 1.075 1.081 1.106 1.173 1.319 1.601 

 Tip Path Plane (deg) 0.00 –0.18 –0.72 –1.62 –2.89 –4.51 –6.49 

 Induced Velocity (fps) 29.33 21.48 12.51 8.45 6.36 5.09 4.24 

 Average Cl 0.3 0.269 0.28 0.288 0.3 0.325 0.350 

 Average Cdo 0.00911 0.00912 0.00915 0.00921 0.00929 0.00940 0.00954 

 F(mu) 1.000 1.011 1.042 1.095 1.169 1.265 1.381 

 Rotor Profile RHP 159.8 161.7 167.4 177.0 190.6 208.6 231.2 

Front Rotor 

 Δv on Front Rotor (fps) 0.00 –1.33 –1.04 –0.75 –0.58 –0.46 –0.38 

 Net Induced Velocity (fps) 29.33 20.14 11.47 7.70 5.78 4.62 3.86 

 Wake Skew Angle (deg) 0.0 59.1 79.7 84.0 84.7 83.9 82.4 

 Induced RHP 346.2 237.9 136.2 93.5 74.4 67.0 67.8 

Rear Rotor 

 Δv on Rear Rotor (fps) 0.00 11.63 12.26 9.21 7.03 5.53 4.45 

 Net Induced Velocity (fps) 29.3 33.1 24.8 17.7 13.4 10.6 8.7 

 Wake Skew Angle (deg) 0.0 45.5 69.2 78.5 81.5 81.9 81.1 

 Induced RHP 346.2 391.0 294.1 214.5 172.4 153.8 152.7 

Total Helicopter 

 Parasite RHP 0.0 2.3 18.7 63.1 149.6 292.2 504.9 

 Total RHP 1,012 955 784 725 778 930 1,188 

 Accessory BHP 30 30 30 30 30 30 30 

H-21B Total BHP 1,084 1,024 846 785 840 999 1,267 

 There is an additional facet of the tandem rotor helicopter that Fig. 2-122 shows and 

that you should know. The rotor-rotor interference mismatches the front and rear rotor 

horsepowers. Because both rotors operate at the same rotor speed, there is a net difference in 

rotor torques. The mismatched torques introduce a yawing moment about the helicopter center 

of gravity. The pilot must counter this yawing moment with a pedal input. On the H-21 

tandem helicopter, the pilot’s right pedal input puts in lateral cyclic differentially, which 

causes the front rotor to tilt to starboard and the rear rotor to tilt to port. Thus, the 

150-horsepower difference between the front and rear rotors (shown in Fig. 2-122) means that 

the pilot is dealing with a substantial directional trim problem when speed and power changes 

are made. Fortunately computer-assisted piloting, added to the CH-46 and CH-47 tandem 

helicopters that came after the H-21, has significantly lowered pilot workload. 
2.4 FORWARD-FLIGHT PERFORMANCE 

251 

2.4.4 Takeoff Following an Engine Failure 

 The preceding comparison of the H-34 and H-21 helicopters brings to light a very 

important fact about power required versus forward speed. This fact is illustrated in 

Fig. 2-114 and deals with the ability of a hovering twin-engine helicopter to reach steady, 

level flight following the loss of one engine. When you look closely at Fig. 2-114 you can see 

that minimum power required in all three examples is greater than one-half of the hover 

power required. To emphasize the point, suppose that each helicopter was powered by two 

engines, not one. And suppose each helicopter was hovering at an altitude and gross weight 

where maximum takeoff power of each engine was required. If an engine goes off-line, the 

best the pilot can hope for is a partial power glide, hopefully to a reasonable landing site. 

When safety is the primary concern—particularly in the passenger-carrying commercial 

world—the solution is, of course, to never take off using maximum power. More precisely, the 

helicopter should take off at a gross weight some 10 to 15 percent less than the machine’s 

maximum capability. But this may mean a reduced number of passengers, or less fuel, or a 

decrease in both. Of course there is an alternate. The pilot could simply burn up the remaining 

engine by exceeding specification fuel flow and operating temperature. 

 This performance problem is not unique to helicopters. It was a primary concern with 

passenger-carrying airplane design, particularly between the two world wars. A perfect 

example occurred during the development of the Donald Douglas DC-1 [314]. On March 31, 

1930, a Transcontinental & Western Air Inc. (later TWA) Fokker tri-motor crashed in a field 

near Bazaar, Kansas. Knut Rockne (the famous football coach at Notre Dame) was one of the 

eight people killed. The public outcry about commercial aviation safety—and tri-motorpowered airplanes in particular, including the Ford Tri-motor—was far reaching. All of the 

airlines wanted the new (vintage 1933) Boeing Model 247 powered by twin Pratt & Whitney 

Wasp piston engines turning fixed-pitch propellers. United Air Lines, Inc., with close business 

ties to Boeing, moved first and bought up every Model 247 Boeing could produce. TWA’s 

response was to solicit the manufacturing side of the business for an airliner that had better 

performance than the Boeing Model 247. The TWA specification called for three engines and 

demanded that the airplane “fully loaded, must make satisfactory takeoffs under good control 

at any TWA airport on any combination of two engines.” Charles Lindbergh was a stock 

holder and technical advisor to TWA at that time, and it is frequently said that he championed 

this requirement. Albuquerque New Mexico (at 5,000 feet and with temperatures above 90o

 F 

on a hot summer day) was one of the airports TWA served. Donald Douglas responded to 

TWA’s request with the twin-engine DC-1. Douglas bet that (1) the new, high-powered, 

supercharged engines being developed by both Pratt & Whitney and Wright Aeronautical, 

along with (2) the evolving NACA cowling, and (3) constant speed (i.e., variable pitch) 

propellers would satisfy the TWA requirement. On September 4, 1933, the DC-1 took off 

from Winslow, Arizona, with one engine off, and flew with one engine out to Albuquerque. 

The next day, the pilot shut down an engine during the takeoff run, continued the takeoff, 

climbed to 8,000 feet, and returned to Winslow. You know the story after that; Douglas 

quickly evolved the DC-1 into a few DC-2s, and the DC-3 went into full production. With the 

DC-3, airlines started making a profit. 
2.4 FORWARD-FLIGHT PERFORMANCE 

252 

 Given that short story as background, let me return to multi-engined helicopters and 

their takeoff performance following an engine failure. The common phrase for this situation is 

one engine inoperative (OEI). 

 With the success of the H-34 and H-21 during the Korean War, the U.S. Army and the 

Marines acquired an apparently insatiable need for more useful load (fuel plus payload) 

capability. This capability was not achievable with even the most powerful piston engines 

developed during World War II.75 The turbine engine was the solution—and not just one 

turbine engine that powered the small Army scout helicopters, but two large turbine engines. 

In fact, Sikorsky’s latest version of the CH-53, the early 1980’s E model, uses three General 

Electric T-64-GE-416 turbine engines. This engine is rated at 4,380 shaft horsepower for 

10 minutes at sea level on a standard day. That is 13,140 installed engine shaft horsepower 

lifting 69,750 pounds, which is 375 horsepower per ton of gross weight. The world’s largest 

helicopter, the Mil M-26 [95], uses two 11,400-horsepower shaft turbines to lift 

123,480 pounds gross weight, which is 370 horsepower per ton. Most recently, Augusta/ 

Westland, a subsidiary of EH Industries, Limited, flew its first production EH 101 in 

December 1999. The EH 101 has three Rolls Royce Turbomeca RTM 322-01/8 turboshaft 

engines with a takeoff rating of 2,100 shaft horsepower (but a transmission limited to 

5,580 horsepower). The maximum takeoff gross weight is 34,400 pounds giving some 

325 horsepower per ton. In direct contrast, Sikorsky’s 1942 R-4B, the U.S. Army’s first 

helicopter, barely lifted 2,450 pounds with 190 installed horsepower, which is 155 horsepower 

per ton of gross weight. The Bell H-13H, a follow-on to the R-4B, used 255 horsepower to lift 

2,850 pounds (or nearly 180 horsepower per ton of gross weight) but was still underpowered. 

 Of course tri-motor-powered helicopters have less trouble meeting a stringent TWAworded takeoff specification. However, the fundamental OEI performance of twin-enginepowered helicopters has been a thorn in the industry’s side. To examine this design and 

operating issue in more depth, let me continue using the H-34 and H-21 helicopters as an 

example. Furthermore, I will revert to rotor performance in coefficient form to generalize the 

situation. That is, power and weight coefficients will be 

(2.226) P W 3 2

t t

550 BHP W Engine C and C

AV AV = = ρ ρ . 

For the H-34 the reference rotor area (A) will be π(28)2

, and for the H-21 the area will be 

2π(22)2

 following Table 2-18. The difference between the coefficients in hover and at the 

speed (I will use advance ratio) for minimum power required is what I want you to see. 

 Flight test data for the H-34A [108] and the H-21B [109] is the basis for this 

discussion. In each report, the data acquired at various weights, rotor speeds, and altitudes 

was reduced to coefficient form. Useable power coefficient versus weight coefficient graphs 

 

75 Two notable exceptions are the Sikorsky S-56 (designated as the CH-37 by the U.S. Army), and the S-60 

crane, which evolved into the twin-turbine-powered S-64 (the CH-54 Skycrane) and, in turn, led to the U.S. 

Marine Corps CH-53 series. 
2.4 FORWARD-FLIGHT PERFORMANCE 

253 

at several advance ratios, as well as hover, are included in each report. It is from the several 

power/weight coefficient graphs that I created Fig. 2-123. 

 You can quantify the OEI problem using the H-34 data in Fig. 2-123. Imagine the 

H-34 as a twin-engine helicopter operating in hover at a power coefficient of CP ×105

 = 45. 

Assume that this is the takeoff power rating provided by two engines. According to 

Fig. 2-123, a gross weight equal to CT ×104

 = 51 could be hovered out of ground effect at this 

power. Now suppose that one engine failed, and the power available dropped by one-half to 

CP ×105

 = 22.5. The pilot, given some altitude, could transition into forward flight to the 

speed for minimum power required. For the H-34, this would be an advance ratio of μ = 0.14. 

At the reduced power of CP ×105

 = 22.5, Fig. 2-123 shows that the pilot could maintain level 

flight at a weight corresponding to CT ×104

 = 47.5. This means that the pilot should not have 

taken off (i.e., hovered) at a gross weight greater than that corresponding to CT ×104

 = 47.5. 

The helicopter would be, in effect, overloaded by about 7.4 percent. That is, the ratio of 

weight coefficients is 51/47.5 = 1.074. For takeoff, the pilot should, for safety’s sake, off-load 

useful load before takeoff. In a commercial operation, this would mean reducing the number 

of passengers—a serious revenue loss. Of course if a contingence rating for OEI was provided 

by the engine manufacturer, say of about 11 percent (i.e., 25/22.5 = 1.11) then the pilot could 

take off at the maximum helicopter capability. The H-34 could continue level flight at an 

advance ratio of 0.14 at a gross weight corresponding to CT ×104

 = 51 if one engine was 

qualified to an emergency rating of CP ×105

 = 25. Of course in twin-engine operation both 

engines could give a CP ×105

 = 50, but the pilot’s operating manual would have to be very 

15

20

25

30

35

40

45

50

55

30 35 40 45 50 55 60 65 70

H-34A, 

Hover

μ = 0.14

H-21B

Hover

μ = 0.20

Engine

Power

Coefficient

CP×105

Weight Coefficient CW×104

Fig. 2-123. H-34 and H-21 performance in hover and at speed for 

minimum power required. 
2.4 FORWARD-FLIGHT PERFORMANCE 

254 

clear that the pilot had, in effect, taken extraordinary advantage of the emergency power 

concept. An example of this extraordinary situation comes immediately to mind. The situation 

I remember is the TV images of the last helicopter lifting off from the U.S. Embassy roof in 

Saigon at the bitter end of the Vietnam War. 

 The passenger-carrying commercial business is perhaps the best example of the 

helicopter’s design problem in matching takeoff performance with OEI performance. To 

understand the performance issue, you need to review the progress that the industry has made 

in introducing helicopters into the “airline” business. Vertical takeoff and landing (VTOL) 

rotorcraft champions have never lost the belief that their aircraft can solve traveling 

congestion problems. Intercity travel could be improved with rooftop heliports. Even growing 

airport congestion would benefit because short runways, rather than building more 10,000-

foot concrete strips, would improve travel immensely. In fact, the rotorcraft industry got the 

chance to prove its point starting in the early 1950s. 

 In the early 1950s, the FAA supported certificated helicopter mail and cargo delivery, 

and passenger-carrying service. Three “airlines” were subsidized by the U.S. Government 

through the FAA in “Project Hummingbird.” They were New York Airways, Chicago 

Helicopter Airways, and Los Angeles Airways. The FAA considered the adventure an 

“experiment in the use of helicopters and evolving V/STOL aircraft in commercial transport 

service” [315]. On April 11, 1965, the FAA-subsidized experiment was over, primarily 

because no end to government subsidy requirements [316] appeared in sight. 

 A great deal was learned from the FAA’s Project Hummingbird “experiment” however. 

The economic report published in November 1960 by the Economics Branch of the FAA 

Office of Plans [315] is an invaluable source for this early history.76 For example, 

Table 2-21 shows key dates for the three airlines. Table 2-22 shows many operating 

parameters including revenue and subsidy growth over the first 7 years as the FAA 

summarized the combined operations of the three airlines. 

Table 2-21. The First Helicopter Airlines [315, 316] 

Dates 

Los Angeles 

Airways 

Chicago Helicopter

Airways 

New York 

Airways 

Certificated for: 

 Mail and Property October 1947 July 1949 March 1952 

 Passengers October 1951 August 1956 March 1952 

Service Began for: 

 Mail and Property October 1947 September 1949 October 1952 

 Passengers November 1954 November 1956 July 1953 

Subsidy Cancelled April 11, 1965 April 11, 1965 April 11, 1965 

 

76 The title of this report is The Helicopter and Other V/STOL Aircraft in Commercial Service. There is a 

secondary volume available [317] that was published in April 1961 titled A Technical Summary and Compilation 

of Characteristics and Specifications on Steep-Gradient Aircraft. This aircraft data source was prepared by the 

FAA Aircraft Branch, Air Commerce Division of the Office of Plans. The snapshot of V/STOL (i.e., steepgradient aircraft ) is as valuable a resource as the economic report. 
2.4 FORWARD-FLIGHT PERFORMANCE 

255 

Table 2-22. Economic and Operational Progress [315] 

Parameter 1953 1954 1955 1956 1957 1958 1959 

Revenue Passengers (000) 1 8 28 63 153 229 366 

Revenue Passenger Miles (000) 26 183 628 1,585 3,275 4,885 7,477 

Mail Ton Miles (000) 123 115 97 90 92 83 87 

Freight and Express Ton Miles (000) 1 16 36 42 40 38 48 

Total Revenue Ton Miles (000) n/a 150 194 282 449 594 857 

Revenue Aircraft Miles Flown (000) 1,006 1,071 1,152 1,317 1,603 1,675 1,899 

Aircraft Departures (000) 90 90 94 104 126 127 138 

Average Flight Stage (miles) 11.2 12.0 12.3 12.7 12.7 13.3 13.7 

Passenger Revenues (000) n/a n/a $208 $438 $968 $1,459 $2,309 

Federal Subsidy (000) n/a n/a $2,710 $2,834 $4,173 $4,616 $4,914 

Total Operating Revenues (000) n/a n/a $3,355 $3,711 $5,032 $6,289 $7,760 

Operating Costs Per Available Ton Mile 

 Direct n/a n/a $3.62 $3.22 $2.93 $2.47 $2.54 

 Indirect n/a n/a $3.13 $3.15 $1.89 $1.51 $1.51 

 Total n/a n/a $6.75 $6.37 $4.82 $3.98 $4.05 

Operating Costs Per Revenue Ton Mile 

 Direct n/a n/a $8.16 $6.55 $6.99 $6.22 $5.20 

 Indirect n/a n/a $7.06 $6.41 $4.51 $3.82 $3.09 

 Total n/a n/a $12.22 $12.96 $11.50 $10.04 $8.29 

 

 The 3 helicopter airlines operated 7 Bell Model 47s, 10 Sikorsky S-55s, and 2 

Sikorsky S-51s in 1955. At the end of 1959 the fleet had grown to 24 aircraft and included 6 

Sikorsky S-58s (H-34s) and 5 Vertol V-44Bs (H-21B). In summarizing the “experiment’s” 

progress through 1959, the FAA report expressed three important views: 

“1. The helicopter has achieved its greatest success in commercial transport services as a 

special purpose vehicle transferring fixed-wing air passengers between airports in the Chicago 

and New York metropolitan areas. 

2. Despite the achievement of a sizable growth in passenger traffic and improved operating 

efficiency, the three helicopter airlines have been unable to reduce their aggregate subsidy 

requirements with the single-engine, piston-powered helicopters which have been available. 

3. The inability of the helicopter airlines to achieve any significant progress toward economic 

self-sufficiency utilizing their relatively small, high unit cost helicopters has not been entirely 

unexpected. The Civil Aeronautics Board has indicated several times in certificate renewal and 

mail rate decisions that no final judgment of the helicopter experiment would be made until 

larger aircraft become available and had been placed in service.” 

 The “larger aircraft” that the budding helicopter airline industry wanted were the 

Sikorsky S-61 (a derivative of the Navy HSS-2, later to become the CH-3) and the Boeing 

Vertol Model 107 (a derivative of the Army YHC-1A, later to become the Marine CH-46). 

Basic data for both aircraft are provided in Table 2-23, which you can compare to Table 2-18. 
2.4 FORWARD-FLIGHT PERFORMANCE 

256 

I have included the Sikorsky S-62 in Table 2-23 because this single-turbine-powered 

helicopter went into service with Los Angeles Airways in late December 1960. The aircraft 

was so successful that a San Francisco bay area helicopter airline sprang up. The San 

Francisco & Oakland Helicopter Airlines (SFO) began operating June 1, 1961. And SFO was 

not subsidized. Because of this positive factor, the Civil Aviation Board gave SFO the first 

permanent operating certificate in November 1963 [316]. 

 The two Sikorsky machines had boat hulls. The S-62 was the first amphibious 

helicopter; wheels were mounted under the floats for land operations. The S-61, used by New 

York Airways, had the floats and retractable gear replaced with fixed gear. The Boeing-Vertol 

Model 107-II had a fixed gear, but was fully qualified for landing and taking off from water. 

Fig. 2-124 shows both the S-61 with its boat hull and the Model 107 landing at New York’s 

West 30th Street Heliport [316]. 

 The arrival of twin-engine helicopters led to the U.S. Civil Aeronautics Board (CAB) 

creating the transport helicopter portion (Part 7) of its Civil Air Regulations. Both the S-61 

and Model 107 were certificated to the Category A performance requirements (paragraphs 

7.110 through 7.118) of the regulation [318]. The applicant in this category was, in 1956, 

directed to select the weights, altitudes, and temperatures his aircraft would be tested at to 

show compliance. Both the S-61 and Model 107 were certificated to a takeoff gross weight of 

19,000 pounds at sea level on a standard day. At other altitudes and temperatures, the takeoff 

gross weight was lower as the flight manuals showed. The general takeoff paragraph (7.112) 

reads as follows: 

“The takeoff performance shall be determined and scheduled in such a manner that, in the 

event of one engine becoming inoperative at any point after the start of takeoff, it shall be 

possible for the rotorcraft either to return to and stop safely on the takeoff area, or to continue 

the takeoff, climb out, and attain a rotorcraft configuration and airspeed at which compliance 

with the climb requirement of paragraph 7.115 (a) (2) is met.” 

The takeoff trajectory, as you have just read, was undefined. But the requirement to climb at 

least 100 feet per minute [paragraph 7.115 (a) (1)] with one engine inoperative was very 

defined. Furthermore, paragraph 7.115 (a) (2) of the regulation required climb at 150 feet per 

minute with the critical engine out and the remaining engine(s) operating at maximum 

continuous power. Thus, a tri-engine helicopter configuration was expected. 

 When you look at the Boeing-Vertol Model 107 landing at the 30th Street heliport, 

think about the takeoff. Imagine a vertical takeoff up to, say, 100 to 150 feet. Suppose at this 

pinnacle, one engine fails. The pilot might choose a near vertical descent right back down to 

the heliport. Of course controlling and stopping the vertical descent could be a problem. The 

pilot would have the option to transition into forward flight. He would have his initial altitude 

plus maybe another 15 to 20 feet, which is the height of that heliport above the water, to make 

this transition. Given that the pilot could get to the speed for minimum power required and 

just skim the water, the helicopter would then need to climb at a minimum of 100 feet per 
2.4 FORWARD-FLIGHT PERFORMANCE 

257 

Table 2-23. The Third Generation of Helicopters 

Basic Aircraft Information Sikorsky 

HH-52 (S-62) 

Sikorsky 

CH-3C (S-61) 

Boeing Vertol 

YHC-1A (M 107) 

Type Certificate Data Sheet H8SO [319] 1H15 [320] 1H16 [321] 

References [89, 317] [206, 317] [187, 317] & [322] 

Power Installed Single Twin Twin 

Engine Model GE T-58-GE-8B GE CT58-110-1 GE CT58-110-1 

OEI (30 sec) 1,350 @ 21,275 rpm 1,350 @ 21,275 rpm 

OEI (2-1/2 min) 1,250 @ 21,275 rpm 1,250 @ 21,275 rpm 

Takeoff Rating at Sea Level (hp) 730 @ 20,960 rpm 1,250 @ 21,275 rpm 1,250 @ 21,275 rpm 

Military Rating (30 min) (hp) 

Normal (Continuous) Rating (hp) 670 @ 20,960 rpm 1,050 @ 21,275 rpm 1,050 @ 21,275 rpm 

Power Limits 

Transmission (30 min) (hp) 2,010 @ 270 rpm 

Weights 10491 10425 

Empty (full oil, trapped fuel) (lb) 5,600 11,228 12,168 

Extra Equipment (lb) 345 819 403 

Crew (lb at 200 lb/man) 200 400 400 

Minimum Operating (lb) 6,145 12,647 13,171 

Fuel Full at 6 lb/gal (lb) 1,950 2,460 2,100 

Passengers (lb at 200 lb/man) 2,400 (12) 5.600 (28) 5,000 (25) 

Category A Takeoff Weight (lb) n/a 19,000 17,900 

Category B Takeoff Weight (lb) 8,300 19,000 19,000 

Dimensions 

Main Rotor(s) One One Two 

Diameter (ft) 53.0 62.0 48.33 each rotor 

Disc Area (ft2) 2,206 3,019 1,835 each rotor 

Blade Chord (in.) 16.4 18.25 18.0 

Number of Blades 3 5 3 each rotor 

Solidity 0.06215 0.0777 0.0594 

Airfoil NACA 0012 NACA 0012 NACA 0012 

Projected disc area (ft2) n/a n/a 3,310 

Distance Between Hubs (ft) 33.33 

Tail Rotor One One None 

Diameter (in.) 106 124 

Blade Number 2 5 

Blade Chord (in.) 10.5 7.34 

Solidity 0.1261 0.1401 

Airfoil NACA 0012 NACA 0012 

Airframe 

Nose-to-Tail Length (ft) 44.17 61.42 44.57 

Height (ft) 15.83 16.08 16.83 

Vertical Stabilizer Area (ft2) 

Horizontal Stabilizer Area (ft2) 

Center of Gravity Limits 

Forward (in.) 6.3 rotor hub 6.3 rotor hub 28.0 CL between rotor 

Aft (in.) 10.4 rotor hub 10.4 rotor hub 10.0 CL between rotor 
2.4 FORWARD-FLIGHT PERFORMANCE 

258 

Fig. 2-124. The helicopter airlines bought twin, turbine-engine-powered helicopters in 

the early 1960s. The Sikorsky S-61L (top) was type certificated on November 2, 

1961 [320]. The Boeing-Vertol Model 107-II (bottom) was type certificated on 

January 26, 1962 [321]. 
2.4 FORWARD-FLIGHT PERFORMANCE 

259 

minute. This criterion is quite interesting. At a takeoff gross weight of 19,000 pounds, 

additional power available in the amount of 

(2.227) weight (lbs)×rate of climb (ft/sec) 19,000 100 / 60 ( ) Climb Power 57 hp 550 550 = = =

would be required. The climb trajectory would have to be well planned. Suppose the 

helicopter had to climb to 500 feet to clear obstacles. That would mean a climb time 

of 5 minutes (300 seconds) at, say, 60 miles per hour (88 feet per second), which is 

26,400 feet—a distance of 5 miles! Locating heliports around water or on long runways with 

plenty of clear space was certainly attractive in the early 1960s. 

 Both the S-61 and Model 107 had much better climb performance than the Federal 

Aviation Agency (FAA) required around 1960 as I will show you shortly.

 In 1991, a rather careful study of the airspace required for a one-engine-operative 

situation was prepared by Systems Control Technology, Inc. for the FAA [323]. This study 

surveyed performance data from eight helicopters and selected five helicopters77 for detailed 

study. The conclusion was that current guidance for heliport design was “inadequate to cover 

the range of helicopters and conditions that are encountered during rejected takeoff or climb 

out with one engine inoperative.” The report was critical of the FAA in that its “policy on 

takeoff and landing requirements for scheduled rotorcraft air carrier operations has been 

inconsistently applied over the years from 1952 through 1990.” 

 The FAA (previously the CAB) and the manufacturers worked diligently to improve 

the regulations. By 2006, the FAA had produced Section 29, which was much more 

quantitative in its requirements for multi-engine-powered transport category rotorcraft. The 

most stringent takeoff trajectory is shown in Fig. 2-125. The operational approach is to take 

off backwards keeping the heliport (the landing surface) in view. The takeoff can be aborted, 

following one engine failure, all the way up to the takeoff decision point (TDP), which is on 

the order of 125 feet and well aft of the emergency landing point. With one engine failure at 

the decision point, a transition into forward flight must allow the helicopter to clear an 

obstacle some 15 feet above the heliport pad. Hopefully, the pilot can reach a safe takeoff 

speed (VTOSS) and can climb to 200 feet. At that point in the trajectory, the pilot accelerates to 

the speed for best rate of climb (VY), which would be about the speed for minimum power 

required. Then the objective is to get to an altitude of 1,000 feet above the takeoff point. 

 The first question that Fig. 2-125 raises deals with the loss in height in reaching 

45 knots. Following the discussion about power-off landing starting on page 23, a relatively 

simple approximation can be made. Suppose at the 125-foot hovering decision point, one 

engine quits, and suppose the remaining engine (or engines) do nothing more than keep rotor 

speed at 100 percent. Then the height can be traded for forward speed. Simplistically, the 

requirement means that 

 

77 The helicopters were the Aerospatiale 355F and 332C, the MBB BO-105 CBS, the Sikorsky S-76A, and the 

Boeing Vertol 234 LR. 
2.4 FORWARD-FLIGHT PERFORMANCE 

260 

Fig. 2-125. The takeoff trajectory given a one-engine-out situation at the takeoff decision 

point (TDP), some 125 feet above the heliport.78

(2.228) ( ) 2 2

12 2 1

2 hh VV

g

−≥ −

where (h1) is the initial hovering height, 125 feet, and (h2) is the clearance height, 15 feet. The 

helicopter is initially at zero speed (i.e., V1 is 0), but must accelerate to (V2), which is 

45 knots or 76 feet per second. The FAA calls my V2 (VTOSS), which stands for takeoff safety 

speed. The gravity constant (g) is 32.2 feet-per-second squared. On this basis, you have 

(2.229) ( ) 2 2 2 125 15 110 76 0 89

32.2

−= ≥ − = , 

which shows that a 125-foot hovering starting point is rational because to reach 45 knots only 

requires a drop of 89 feet from the 125-foot TDP. Equation (2.229) shows that a 50-foot 

“takeoff rejection takeoff point” is perhaps a little low because it is only at 89 + 15 feet that 

the pilot will be able to get to 45 knots. Of course power from the remaining engine (or 

engines) can do more than keep rotor speed at 100 percent. On the other hand, the pilot must 

pull out of the dive and then start climbing to reach the 200-foot altitude above the helipad. 

 

78 This figure is courtesy of Tom Wood, now the Director of Preliminary Design at Bell Helicopter Textron. I 

left Boeing in mid-1976 and became Chief of Aerodynamics at Bell. Tom immediately became my right hand in 

managing the group. I know very few engineers with his outstanding grasp of fundamental helicopter technology 

and his knowledge of what it takes to develop and certificate a rotorcraft. 
2.4 FORWARD-FLIGHT PERFORMANCE 

261 

 The distances to be determined in Fig. 2-125 are not too difficult to estimate. The 

helicopter could return to the landing pad from the 125-feet TDP along, say, a 45-degree 

slope. That would mean that the TDP is 125 feet aft of the landing pad, should one engine 

quit. The pilot, by putting the nose down quickly, might get a horizontal acceleration of 0.15 g 

or about 4.8 feet-per-second squared. That acceleration would get him to 45 knots in about 

16 seconds (i.e., V = at) and requires a distance of 600 feet (i.e., S = 1⁄2 at2

) from the TDP. 

Therefore, the OEI takeoff distance would be 600 – 125 = 475 feet. At that distance from the 

landing pad, the pilot must climb at 100 feet per minute until reaching the 200-foot altitude, 

which means roughly 2 minutes at 45 knots (76 feet per second or greater) or about 9,100 feet 

(1-3/4 miles). At the 200-foot altitude, the pilot accelerates to the speed for minimum power 

required (VY), say on the order of 75 knots, which would take 10 seconds and a distance of 

some 200 feet if the horizontal acceleration is again 4.8 feet-per-second squared. The climb to 

1,000-feet altitude from 200 feet, at a minimum of 150 feet per minute, would take a little 

over 5 minutes. And at 75 knots, the aircraft would travel another 7-1/2 miles. 

 The preceding airspace that this 19,000-pound helicopter would need, therefore, 

breaks down as shown in Table 2-24. 

 Clearly, it takes about 2 to 2-1/2 minutes and some 9,000 feet to gather up a helicopter 

that just meets the minimum FAA requirements. This is really not, in my opinion, a vertical 

takeoff and landing aircraft comparable to the DC-1 that TWA paid for in the mid-1930s. 

 This example illuminates a need for considerably improved one-engine-out 

performance of a twin-engine helicopter safely taking off with a full passenger and fuel load. 

Fortunately, this need was slowly filled by the engine manufacturers. They qualified their new 

engines with power ratings above the takeoff rating. The Sikorsky S-61 was certificated to the 

then CAB one-engine-out requirement using a 30-second engine output rating of 

1,350 horsepower versus the twin-engine takeoff rating of 1,250 horsepower per engine as 

Table 2-23 shows. While only 100 more horsepower, this power increment is significant—on 

the order of 175-feet-per-minute rate of climb following Eq. (2.227). Consider, for example, 

the S-61 and Model 107 II power required versus true airspeed shown in Fig. 2-126. (In lieu 

of actual flight test data for the commercial versions of the two helicopters, I used interpolated 

flight test data for the CH-3C [206] and the YHC-1A [187] to construct Fig. 2-126. The data 

is, I believe, quite representative for this example.) 

Table 2-24. Airspace Needed by 1960’s Helicopters to Meet Minimum CAB (FAA) 

One-Engine-Out Takeoff Operation 

Flight Phase Distance (ft) Altitude (ft) Airspeed (knots) Time (sec) 

At TPD 125 aft 125 0 0 

OEI Takeoff Distance (ft) 475 15 45 16 

Climb to 200 feet 9,100 200 45 120 

Accelerate to 75 knots 200 200 75 10 

Climb to 1,000 feet 39,600 1,000 75 300 

Total Airspace 49,500 (9.4 miles) 125 to 1,000 0 to 75 knots 446 (7.5 min) 
2.4 FORWARD-FLIGHT PERFORMANCE 

262 

 Fig. 2-126 shows that both helicopters could hover at the TDP at sea level on a 

standard day at their certificated takeoff gross weight of 19,000 pounds within engine and 

transmission limits. With one engine failure at the TDP, the pilot would drop collective, move 

the cyclic pitch stick forward, and begin a controlled free fall using the loss in altitude to gain 

forward speed. To pull out, say, at about 30 knots, the pilot would pull in collective pitch and 

bring the operating engine up to its 30-second temperature limit, which provides 

1,350 horsepower. This would clear the 15-foot height above the heliport required by the FAA 

and get the helicopter to 45 knots (or faster). Clearly, the S-61 could maintain steady, level 

flight at 45 knots and would be able to accelerate to the minimum power-required speed, say 

70 knots. At 70 knots, the S-61 would have about 220 horsepower (for 30 seconds) in excess 

of the 1,130 horsepower required to maintain steady, level flight at 70 knots. This translates 

into 385-feet-per-minute rate of climb, so the 200-foot-altitude requirement would be reached 

in about 30 seconds (i.e., 200 –15 feet at 385 feet per minute is about one-half of a minute). 

Flying at 70 knots for 30 seconds, the S-61 would cover about 3,500 feet or about two-thirds 

of a mile. This is considerably less airspace than the 9,100 feet suggested in Table 2-24. 

 Getting from an engine failure at the TDP to 200-feet altitude and 70 knots would 

mean that the operating engine had given its all at the 1,350-horsepower OEI rating. The 

prudent pilot would reduce power to 1,250 horsepower and begin his climb from 200- to 

1,000-feet altitude. This would reduce the excess power to 120 horsepower (i.e., 

1,250 –1,130) and the rate of climb would drop from 385 to 210 feet per minute. Therefore, 

the 1,000-foot altitude would be reached in about 3.8 minutes, and the S-61 would cover 

27,000 feet or about 5 miles. 

1,000

1,200

1,400

1,600

1,800

2,000

2,200

2,400

2,600

0 20 40 60 80 100 120 140 160

True Airspeed (kts)

Engine

Shaft

Horsepower

Boeing Vertol YHC-1A (Model 107-II)

Sikorsky CH-3C (S-61L)

Two GE-CT58-110-1 at Sea Level, Takeoff Power

Model 107 Transmission Limit

One CT58-110-1 at S. L., OEI 30 Sec.

One CT58 at S. L., Takeoff

One CT58 at S. L., Max. Continous Power

Fig. 2-126. Engine power required and available at sea level on a standard day for the 

25- to 29-passenger helicopters certificated for passenger service in early 1960. 
2.4 FORWARD-FLIGHT PERFORMANCE 

263 

 The preceding discussion justifies Systems Control Technology’s concern [323] that 

the FAA had a mismatch between helicopter OEI performance and heliport designs, even in 

the early 1990s. 

 The Boeing Vertol Model 107 power required versus airspeed data shown in 

Fig. 2-126 raises two interesting questions. To begin with, the Model 107 tandem rotor 

helicopter hovers at 19,000 pounds using only 2,000 engine shaft horsepower. The S-61, at 

the same takeoff gross weight, requires 2,360 horsepower. The primary reason for this 

difference is, of course, the difference in disc area between the two machines, which accounts 

for about 10 percent of the difference. The S-61’s tail rotor adds to the difference. The other 

question is even more interesting: If a profitable operating airplane, say the DC-3, could take 

off from TWA’s Albuquerque airport on one engine, why shouldn’t the modern helicopter do 

the same? To meet this criteria, the Model 107, with 25 passengers and full fuel tanks, would 

need two engines rated at 2,000 horsepower for takeoff at sea level on a standard day. 

 Just to see the value of a design that can hover on one engine, consider the Model 107 

at the takeoff decision point. Both engines would be loafing at 50 percent of takeoff power. 

The loss of one engine would force the remaining engine to quite quickly pick up the slack. 

The helicopter would lose some altitude and rotor speed because of pilot and engine reaction 

time, but the pilot could confidently descend back to the heliport. Or, if warranted, he could 

continue with a relatively normal takeoff. A simplistic analysis of this relatively normal 

takeoff is rather easy to construct using the energy method of Eq. (1.31), repeated here for 

convenience (with a positive sign convention associated with climb, not descent) as 

(2.230) 

( ) ( ) ( )

f 2 2 2

1 1 1

t t h V

R 0 hV

1 1 22 22

2 1 2 2 2 1 R 2 1

550 HP dt W dh W g V dV I d

W h h Wg V V I

= Ω

Ω

= + + ΩΩ

= − + − + Ω −Ω

   . 

Suppose, following the loss of one engine, that the pilot pushes forward on the cyclic and 

quickly develops a horizontal acceleration, then forward speed, and then climbs. The 

helicopter would reach 70 knots in some final time (tf) in seconds. Now tackle the integral of 

power that Eq. (2.230) requires. To keep it simple, let the excess power available increase 

linearly with airspeed. That is, assume at time zero, when hovering, that there would be zero 

excess power available. However, at 70 knots there would be 750 excess horsepower 

available, which is the difference between minimum power required and 2,000 horsepower 

available from the operating engine. Therefore, horsepower (HP) would vary with true 

airspeed (V) as 

(2.231) ( ) 750 hp V fps HP KV 6.34 V fps 70 knots 1.69

   = =    =

   . 

The velocity (V) in feet per second is obtained by assuming some average acceleration (aavg.) 

in feet-per-second squared times time. That is, V = aavg. t. Therefore, the variation of 

horsepower with time is simply 
2.4 FORWARD-FLIGHT PERFORMANCE 

264 

(2.232) ( ) avg.

750 hp V fps HP KV 6.34 a t

70 knots 1.69

   = =    =

   . 

It follows that the horsepower integral, which is total energy, is on the order of 

(2.233) ( )( )

( )( )

f f t t

avg. 0 0

avg. 2

f

f

550 HP dt 550 (6.34a t) dt in foot pounds of energy

a

550 6.34 t

2

550 6.34 S

= −

  =    

=

 

. 

Remember that V = aavg. t so from simple calculus, horizontal distance traveled (S) equals 

1⁄2 aavg. t2

. Then, the energy solution for takeoff is simply 

(2.234) ( )( ) ( ) ( )( )( ) ( ) 1 1 22 22

f 21 2 1 R 2 1 2 2 550 6.34 S W h h W g V V I = − + − + Ω −Ω . 

Now, assume a takeoff gross weight (W) of 19,000 pounds, an initial height (h1) of 100 feet, a 

final height (h2) of 1,000 feet, an initial speed (V1) of zero, and a final speed (V2) of 70 knots 

or 118 feet per second. Furthermore, assume no change in rotor speed (i.e., Ω2 = Ω1). The 

gravitational constant (g) is 32.2 feet-per-second squared. You, therefore, have 

(2.235) 

( ) ( )

( )( )

2 2

f

19,000 19,000 1,000 100 118 0 64.4 S 6,082 feet 1.15 mile 550 6.34

−+ −

= =≈ . 

This ability to hover with one engine out at the takeoff decision point (TDP) means that 

airspace around a heliport must consider the height of objects, man-made or natural, within a 

1-mile radius of the heliport and less than 1,000 feet tall. This is a considerable reduction 

from the 9.4-mile radius arrived at in Table 2-24. (The horizontal distance to reach 45 knots 

and 200-feet altitude, using Eq. (2.234), is just a little over 1,000 feet.) 

 Now think about the average acceleration and time associated with the 6,082 feet of 

distance traveled and the final speed reached of 70 knots. Because velocity and distance are 

related to average acceleration and final time as 

(2.236) 2

f avg. f 2 avg. f

1 S a t and V a t

2 = = , 

it follows that 

(2.237) ( ) ( ) ( ) 2 2 2

avg. 2

f

1 1 a V 1.69 70 1.15 ft sec 0.036g 2S 2 6,082

= = ×= = , 

which is a relatively comfortable acceleration. The 1,000-foot/70-knot point would be reached 

in 103 seconds. The pilot would hardly have enough time to compose a simple explanation to 

the passengers for returning to the heliport! In fact, considering the very short distances that 

the three early helicopter airlines were flying (less than 30 miles), the pilot could elect to 

continue flying the scheduled route. 
2.4 FORWARD-FLIGHT PERFORMANCE 

265 

 Before leaving the discussion of the Boeing Vertol Model 107-II, you should know 

that this helicopter, which began as the YHC-1A, became the CH-46 series for the U.S. 

Marines. The Marines funded continual upgrades leading to the E model [188]. The helicopter 

has been stretched to 45 feet, 8 inches. The rotor diameter is now 25.5 feet. Most importantly, 

the transmission has been uprated to 2,800 horsepower, and the General Electric engines are 

now T-58-GE-16s with a takeoff rating of 1,870 shaft horsepower each. At 19,000 pounds, the 

helicopter can nearly hover at sea level on one engine. If the helicopter airlines had had the 

CH-46E helicopter as a commercial version 30 years ago, they and the FAA might have seen 

the need for subsidy disappear. Furthermore, the airspace needed for heliports would have 

been reduced dramatically. 

 There is no question that the industry sees the performance benefit of twin-engine 

helicopters with engines that can provide a one-engine-inoperative (OEI) rating well above 

the twin-engine takeoff rating. Perfect evidence of this fact was reported by Cole [324].79 The 

technical discussion in Cole’s paper is well worth your time to read and understand. 

 There is much more to be learned about helicopters in the commercial world as you 

will read in the purchase price, operating costs, and accident record chapters of this volume. 

2.4.5 Closing Remarks 

 Without doubt, the calculation of induced power of a rotor in steady forward flight has 

been a thorn in the side of rotorcraft engineers for decades. Glauert started the industry off 

with his well-known approximation so that the industry relied on 

(2.238) 

1

2 2 4 2

i

mr i 2

Wv WV W V Induced RHP k

550 550 4 2 R 2

   

== + −      ρπ     

. 

The inclusion of an induced power correction factor (ki) is the rotorcraft equivalent of the 

Oswald efficiency factor for airplanes. A useful, but crude, approximation [211] developed 

after free-wake calculation could routinely be made is 

(2.239) ( ) 2

i k 1.075cosh 7.5 = μ . 

 The question many of us have asked [325-327] for a long time has been, “Given that 

an elliptical lift distribution gives the minimum induced drag for a fixed wing (as Prandtl and 

Glauert found), what is the answer for a rotary wing?” We got the answer at the 2010 AHS 

Forum held in Phoenix, Arizona. Kenneth and Steven Hall [328] gave us the answer with one 

figure—Fig. 2-127. This figure says that if we could build it, our best articulated rotor would 

(at the high advance ratios typical of today’s helicopters) be anywhere between 3 and 10 times 

 

79 Jeffrey Cole first presented his paper at the American Helicopter Society 53rd Annual Forum held at Virginia 

Beach, Virginia, from April 29 through May 1, 1997. His paper was finally accepted for publishing in the AHS 

Journal in October of 2000. The final paper was published in the April 2001 issue of the AHS Journal. To me, 

this is rather slow publishing—for whatever reason—of such a good paper dealing with such an important aspect 

of the industry’s business. 
2.4 FORWARD-FLIGHT PERFORMANCE 

266 

worse than a fixed wing having a span equal to the rotor diameter. And furthermore, more 

blades than two are better. I am very glad this answer came in time to be included in this 

volume. 

Fig. 2-127. Normalized induced power of the ideal articulated rotor [328] 
267 

2.5 FUEL EFFICIENCY 

 Aircraft of all types obtain energy from burning fuel to create lift and propulsion, and 

perform. Of all the aircraft, the helicopter is the most fuel efficient hovering machine man has 

yet invented. It achieves this hovering fuel efficiency by obtaining lift and propulsion with the 

least amount of energy imparted to the air. In forward flight, on the other hand, the helicopter 

is one of the most, if not the most, fuel inefficient aircraft flying. Consider fuel efficiency in 

hover first and then fuel inefficiency in forward flight second. 

 A measure of fuel efficiency in hover is endurance, which is measured in hours. The 

hours a helicopter can hover depends on the helicopter’s engine shaft horsepower required to 

hover, the engine’s specific fuel consumption (SFC) in pounds of fuel burned per hour per 

horsepower, and the amount of fuel that the fuel tanks hold. Consider this simple approach to 

estimating endurance. The power required per pound of weight to hover (SHP/W), as 

Fig. 2-128 shows, depends—to a reasonable approximation—on Figure of Merit (FM), disc 

loading (weight divided by rotor disc area), and the density altitude at which the helicopter is 

hovering. Fig. 2-128 was created from data provided by references [108, 109, 115, 116, 118, 

121, 124, 125, 133, 170-188, 190-206] and [207-210]. 

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0 2 4 6 8 10 12 14 16

Density Weighted Disc Loading (W/σA in lbs/ft2)

Figure of Merit

0.50

0.65

0.60

0.55

Engine 0.70

Horsepower

Required

Divided

By

Weight

SHP/W

XH-59A (ABC) Coaxial

Fig. 2-128. Engine hover power required per pound of gross weight vs. density-weighted 

disc loading for 50-plus helicopters. A Figure of Merit of 0.55 is typical.
2.5 FUEL EFFICIENCY 

268 

 You will recall from Eq. (2.45) that FM is simply the ratio of ideal power to actual 

power, from which it follows that 

(2.240) Ideal Power 1 W Actual SHP W

Figure of Merit 550FM 2 A

  = =  

ρ  

and, therefore, 

(2.241) 

o o ( )

SHP 1 W 1 W 0.02637 W

W 550FM 2 A 550FM 2 A FM A

     == =     

ρ ρ ρ ρ σ      

where the ratio of engine shaft horsepower required (SHP) divided by gross weight (W) 

depends on the density ratio (σ = ρ/ρo, ρo = 0.002378 slugs-per-foot cubed) and the densityweighted disc loading (W/σA). For this example, the single (or coaxial or synchropter) rotor 

area (A) is πR2

, and the tandem rotor area is 2πR2. 

 Hover endurance also depends on the engine’s fuel consumption rate. This rate is 

generally expressed in pounds of fuel burned per hour, which, for the turbine engine, 

increases in nearly a linear fashion as Eq. (2.23) suggests. For this example, I have chosen to 

illustrate the fuel burn rate with engine SFC following Eq. (2.22). Typical results for a 

representative set of engines is shown in Fig. 2-129. 

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

0 200 400 600 800 1,000 1,200 1,400 1,600

Engine Shaft Horsepower (Installed)

Specific

Fuel

Consumption

Pound

per

hour

per

SHP

Turbomeca Arriel 1C1

Lycoming T-53-L-9

General Electric T58-GE-3

General Electric YT700-GE-700

Allison T63-A-5A

Allison 250-C30

Wright R-1820-84 at 1,000 ft & 2,500 rpm

Lycoming O-360-C2B at 260 ft & 2,500 rpm

Fig. 2-129. Engine specific fuel consumption in hover ranges between 0.50 and 0.65. 
2.5 FUEL EFFICIENCY 

269 

With these two key parameters (FM and SFC) in hand, calculate the hover endurance 

(E) in hours as follows: 

(2.242) 

final weight

initial weight

1 Endurance dw

fuel burned in pounds hour = −



 . 

Now, fuel burned per hour is simply 

(2.243) ( )( )

3/2 0.02637 W 0.02637 W lbs hr SFC SHP SFC W SFC

FM A FM A

      = =     =       σ   σ  

. 

The endurance is then calculated with the integral 

(2.244) 3

2

final weight

final weight

3/2

initial weight

initial weight

1 A FM E dW W dW

0.02637 W 0.02637 SFC SFC

FM A

σ − =− =−       σ

      

. 

Suppose the initial weight is the takeoff gross weight (W), and the final weight is 0.9 W. Then 

you have 

(2.245) FM 1 E 4.1 in hours and for fuel equal to 0.1 of takeoff gross weight. SFC W A

  =     σ

Now, from Fig. 2-128, a representative FM from the last 50 years is 0.55. And from 

Fig. 2-129 engine manufacturers can produce engines with an SFC of 0.55, which means the 

hover endurance has the first approximation of 

(2.246) 

4.1 E in hours and for fuel equal to 0.1 of takeoff gross weight. W A = σ

 Of course the FM ranges from a low of 0.5 to about 0.7, and the specific fuel 

consumption can vary from 0.5 to about 0.7, so the ratio of FM to SFC can range from a high 

of 1.40 to a low of 0.70. Nevertheless, for a given technology Fig. 2-130 shows that the lower 

the disc loading, the greater the hovering endurance. 

 Just for the fun of it, I took a moment to research the United States and world records 

that Sikorsky set with his VS-300 in 1941. From Bill Hunt’s fascinating first-person story of 

working with Sikorsky during the pioneering era [329], I read that on April 7, 1941, Sikorsky 

practiced for the records, staying up for exactly 30 minutes and using nearly all the fuel in the 

6-gallon tank located on the port side of the VS-300C-5a. Hunt notes that “there was still 

sufficient fuel left for another 6/8 min before having to take fuel from the new tank (located 

on the starboard side), which meant there would be no fuel problem for at least a full hour.” 

That statement and some photographs suggest to me that the “new tank” was quite likely 

another 6-gallon tank. At that time the VS-300C, in its -5a configuration, had a 30-footdiameter rotor and two, aft, laterally displaced rotors on outriggers, plus the tail rotor. At 

takeoff the helicopter weighed approximately 1,200 pounds, which would be a disc loading 

of about 1.7 pounds per square foot. Assuming that the port 6-gallon tank was filled with 
2.5 FUEL EFFICIENCY 

270 

6-pounds-per-gallon, 80-octane fuel, the VS-300C-5a must have been consuming fuel at the 

rate of 36 pounds per 37 minutes, or roughly 58 pounds per hour. 

 On April 15, 1941, Sikorsky captured the U.S. endurance record of 1 hour, 5 minutes, 

and 14-1/2 seconds. On that day Sikorsky benefited from a 15-mile-per-hour wind as well as 

ground effect. At 15-minute intervals Sikorsky “would return to the starting point and have 

the fuel consumption checked (from the ground by binoculars). The wind was obviously 

contributing to the noticeable amount of extra fuel remaining at each check-in, so at the third 

check-in Igor unhesitatingly said he was going for the one-hour mark.” Officials of the 

National Aeronautics Association witnessed and recorded this endurance. This little-noticed 

step to the world’s endurance record is rarely mentioned. 

 On May 6, 1941, Heinrich Focke’s F. 61 world endurance record of 1 hour, 

20 minutes, and 49 seconds established on June 25, 1937 [7], was surpassed by Sikorsky with 

a performance, according to Hunt, of 1 hour, 48 minutes, and 56.1 seconds. Apparently the 

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 2 4 6 8 10 12 14 16

Density Weighted Disc Loading

FM/SFC = 1.4

FM/SFC = 1.0

FM/SFC = 0.70

Note: Fuel to burn = 0.1 of takeoff gross weight.

Sikorsky 

VS-300

YHO-2HU

Hover

Endurance

(hrs)

Fig. 2-130. Helicopters, with their low disc loading, have the greatest hovering 

endurance of any aircraft man has developed yet (fuel = 0.1 TOGW). Note the 

Sikorsky VS-300 point shown at endurance with more fuel than used to set the 

world record of 1 hour and 32 minutes. 
2.5 FUEL EFFICIENCY 

271 

National Aeronautics Association’s witness only credited the event with 1 hour, 32 minutes, 

and 26.1 seconds, which is what history books generally quote. Hunt notes that “an elliptical 

saddle-type extension [an extra 3-1/2-gallon tank] was fitted on to the outer profile of the 

starboard tank.” He later quotes the extra fuel at 30 pounds, which is a little confusing 

because 3-1/2 gallons would weigh more like 21 pounds. Nevertheless, Sikorsky landed the 

VS-300C-5a at the 1-1/2-hour (or 1-3/4-hour) point because there was a change in engine 

noise, which the group decided was reason enough to call a halt. The noise change was caused 

by a blown exhaust gasket. 

 In a private exchange with John Kowalonek, the archivist at the Sikorsky Historical 

Archives [330], I learned that “the takeoff gross weight for this record flight was 

1,325 pounds, and included an extra fuel tank for a total fuel capacity of 14.7 gallons at 

takeoff. The amount of fuel at the end of the 1-hour-and-32-minute flight was 2.5 gallons.” 

On this basis, 12.2 gallons of fuel weighting about 73 pounds was burned, which is 

47.7 pounds per hour. 

 If you accept that 47.7 pounds per hour was the fuel consumption rate for the world 

record, Sikorsky took off at 1,325 pounds, burned about 73 pounds of fuel in 1-3/4 hours, and 

landed at about 0.95 of his takeoff weight. Following Eq. (2.244), I calculate that the ratio of 

Figure of Merit (FM) to specific fuel consumption must have been on the order of 0.962. 

Imagine now that Sikorsky had taken off at 1,325 pounds and burned 132 pounds of fuel 

(stored in larger fuel tanks), which gives a final landing weight of 0.9 of the takeoff weight. 

Then his world record would have been 2 hours and 53 minutes. I put this point in Fig. 2-130, 

just for the fun of it. 

 A more concrete example from the early 1960s is also shown in Fig. 2-130. The 

Hughes YHO-2HU [111], a very small, two-man helicopter with a 1,550-pound takeoff gross 

weight, used the Lycoming O-360-C2B engine with a fuel flow rate of about 75 pounds per 

hour at high power. This 25-foot-rotor-diameter machine had a 25-gallon fuel tank, which at 

6 pounds per gallon is 155 pounds of fuel. Assume that the helicopter hovered out of ground 

effect at sea level with no wind and landed after running the tank dry (i.e., 155 pounds of fuel 

equals 0.1 times the takeoff weight, which is the basis of Fig. 2-130.). The hover endurance 

would be about 2.1 hours at a disc loading of 3.16. In fact, the ratio of FM to specific fuel 

consumption (SFC) is about 0.9. 

 Now let me proceed to helicopter fuel efficiency in forward flight. The measure of this 

fuel efficiency is most frequently quoted by the general public in miles traveled per gallon 

when they talk about their cars. In aviation, however, the measure is more commonly quoted 

in nautical miles (nm) traveled per pound of fuel burned. The simplest calculation of nautical 

miles per pound is obtained from the Bréguet range equation [331],80 which can be easily 

 

80 My first encounter with the Bréguet range equation came from an aero course I took in 1955 at Rensselaer 

Polytechnic Institute using Perkins & Hage [284]. In October 2006 Mustafa Cavcar published a fascinating paper 

[332] tracing the origin of Bréguet’s equation back to 1918. Cavcar suggested that while “we” all quote the 

equation, “nobody” ever gives a specific reference other than Bréguet’s paper [331] and then only occasionally. 
2.5 FUEL EFFICIENCY 

272 

derived. For general use, distance traveled or range (R) in nautical miles is simply velocity 

(V) in knots times time (t) in hours. But range depends on the pounds of fuel burned. That is, 

(2.247) initial initial initial initial

final final final final

W W W t

t W W W

dt V V R V dt V dW dW dW

dW dW dt W t == = ≈ Δ Δ

         

where the initial weight (Wi) is the takeoff gross weight of the aircraft, and the final weight 

(Wf) is the landing weight. The difference in the two weights is the pounds of fuel burned. 

The rate of fuel consumption (ΔW/Δt) has the units of pounds per hour. 

 Now, fuel burn rate is specific fuel consumption (SFC) times shaft horsepower (SHP) 

so that 

(2.248) ( )( ) W SFC SHP

t

Δ = Δ

and, in forward flight, the engine power required is calculated as 

(2.249) ( ) ( )

a c fps a / c kts kts

a/c a/c

D V V D 1.69V V SHP W W W

550 550 L 550 L D 326 L D

  == = =     , 

so that 

(2.250) ( ) ( )

kts

a/c

W V SFC W

t 326 L D

Δ   =   Δ  

. 

To arrive at fuel burn rate, I have grouped the propeller efficiency with the aircraft drag (Da/c) 

to create an apparent drag in pounds. This apparent drag is divided by aircraft lift (L), which 

gives an aircraft lift-to-drag ratio [(L/D)a/c]. In steady flight, lift equals weight (W). (It is 

worth noting that 1 hp = 550 foot-pounds per second just to keep the units correct.) 

 The range equation (2.247) now becomes 

(2.251) 

( ) ( )

( )

( )

initial

initial

final

final

W

W

kts a / c

kts W

W

a/c

V L D 1 R dW 326 dW in nm

V SFC W

SFC W

326 L D

≈ =  

 

 



 

 

  

. 

The integration is performed by assuming that average values for specific fuel consumption 

(in pounds per hour per horsepower) and aircraft lift-to-drag ratio are adequate for a firstorder approximation. In fact, on a maximum range test, a pilot would slowly climb and adjust 

speed at each altitude to (1) keep maximizing the aircraft’s lift-to-drag ratio, and (2) ensure 

the lowest rate of fuel consumption. Therefore, range in nautical miles, becomes 

(2.252) ( ) ( ) initial

final

W

a / c a / c initial

W final avg. avg.

L D 1 L D W R 326 dW 326 ln

SFC W SFC W

      ≈ =            





 . 
2.5 FUEL EFFICIENCY 

273 

Range in statute miles is simply Eq. (2.252) with the constant 326 increased to 375. It is 

helpful to remember that there are 5,280 feet per statute mile and 6,076 feet per nautical mile. 

 Before converting Bréguet’s range equation into fuel efficiency, let me give you two 

interesting examples of maximum range. The first example is Charles Lindbergh’s flight from 

Long Island, New York, to Paris. An early discussion and somewhat technical analysis of the 

flight written by August Von Parseval was published in “Motorwagen” on May 31, 1927, 

translated into English by Dwight Miner, and published in the United States as NACA TM 

No. 423 [333]. In July 1927 the N.A.C.A. published the technical preparation of the Spirit of 

St. Louis (Fig. 2-131) for the flight; it was written by Donald Hall, the chief engineer of Ryan 

Airlines, Inc., who built the airplane [334]. Hall’s detailed engineering report is an absolute 

gold mine of data, if you are interested. According to Parseval’s somewhat premature article 

and Hall’s rather complete engineering data, Charles Lindbergh’s Spirit of St. Louis took off 

weighing 5,250 pounds with 450 gallons of fuel, which, at 6.12 pounds per gallon, is 

2,750 pounds. He was in the air 33 hours and 47 minutes, and traveled about 3,130 nautical 

miles (3,600 statute miles) if there was no tail wind. Hall’s data suggests that Lindbergh 

landed with about 180 pounds of fuel left, which means that 2,570 pounds of fuel was 

consumed. I will guess the initial 25 gallons of oil was down to 10 gallons at landing, so at 

7 pounds per gallon, he lost another 100 pounds. I suggest, therefore, that the landing weight 

was 2,580 to 2,700 pounds. 

 Using Bréguet’s range equation, it appears that the Spirit of St. Louis flew across the 

Atlantic at an (L/D)a/c-to-SFC average ratio of 13.5. That is, 

(2.253) ( ) [ ] ( ) a/c

avg.

avg.

L D 5,250 R 326 ln 326 13.5 .71 3,130 nautical miles SFC 2,580

    = ==         . 

In terms of miles per pound of fuel burned, that would be 3,130 nautical miles divided by 

2,570 pounds—about 1.2 nautical miles per pound or 1.4 statute miles per pound. The average 

fuel flow was near 12.5 gallons per hour. (I am sure my analysis is off a bit, but the example 

illustrates the use and first-order accuracy of Bréguet’s range equation.) 

Fig. 2-131. Charles Lindbergh’s Spirit of St. Louis (photo courtesy of Loftin Collection, 

NASA Langley Research Center). 
2.5 FUEL EFFICIENCY 

274 

The second example you should know about concerns an equally impressive nonstop, 

non-refueled, record-setting flight with a small helicopter [147]. The Hughes YOH-6A 

(Fig. 2-132), piloted by Bob Ferry, took off from Culver City, California, at 2:20 p.m. on April 

6, 1966, and landed at Ormond Beach, Florida, 15 hours and 8 minutes later. Ferry’s YOH-6A 

took off at an overload gross weight of 3,235 pounds, burned 1,850 pounds of fuel, and 

landed with about 10 pounds of fuel leftover. As fuel burned off, Ferry climbed (roughly 

linearly with time) to near 25,000-feet altitude over Jacksonville, Florida. From there he 

rapidly descended to Ormond Beach. The flight established a new, straight-line distance 

record of 2,213 statute miles (1,923 nautical miles), although the actual distance was 

2,277 statute miles. 

 Using Bréguet’s range equation, Ferry flew the YOH-6A across the United States at an 

(L/D)a/c-to-SFC average ratio of 8.2. That is, 

(2.254) ( ) [ ] ( ) a/c

avg.

avg.

L D 3,235 R 326 ln 326 8.2 0.848 2,277 nm SFC 3,235 1,850

    = =   =     −  

. 

In terms of nautical miles per pound of fuel burned, that would be 2,277 nautical miles 

divided by 1,850 pounds—about 1.23 nautical miles per pound or 1.42 statute miles per 

pound. The average fuel flow was near 20.4 gallons per hour. 

Fig. 2-132. Hughes YOH-6A set the world distance record on April 6–7, 1966 [147] 

(photo from author’s collection). 
2.5 FUEL EFFICIENCY 

275 

The contrast between the Spirit of St. Louis and the YOH-6A is noteworthy. The 1927 

airplane’s ratio of (L/D)a/c to SFC was 13.5; the 1966 helicopter’s was 8.2. Furthermore, the 

helicopter was powered by the Allison T63-A-5A, which from Fig. 2-129 had an average SFC 

during the flight on the order of 0.8. This suggests that the average lift-to-drag ratio of the 

helicopter was about 6.5. In contrast, the airplane was powered by the Wright J-5-C giving 

223 brake horsepower at 1,800 rpm. Hall’s report [334] indicates an SFC of about 0.5, which 

gives the airplane an average lift-to-drag ratio of 6.5. 

 I have three conclusions from these two examples: (1) the two aircraft had comparable 

lift-to-drag ratios, as long as you include propeller efficiency as a drag; (2) the piston engine’s 

specific fuel consumption was nearly half that of the turbine engine; and (3) nothing beats a 

tail wind, which, I am confident, was different for the two record-making flights. 

 Now let me address fuel efficiency expressed in nautical miles (nm) per pound (lb) of 

fuel burned (nm/lb). This ratio is frequently referred to as specific range (SR). Range divided 

by the fuel consumed to travel that distance is a measure of the average specific range. 

Therefore, 

(2.255) ( )a / c initial

fuel fuel initial fuel avg.

R 1 L D W SR 326 ln

W SFC W W W

     = =         −    

, 

and when the natural logarithm is expanded, you have, with some rearrangement, 

(2.256) ( ) 2

a /c fuel fuel

fuel initial initial initial avg.

R 11 1 L D W W SR 326 1

W SFC W 2 W 3 W

      

== + +                

. 

From Eq. (2.256) you can see that for a normal ratio of fuel consumed to takeoff weight—in 

the range of 0.1 to 0.15—that specific range is inversely proportional to the takeoff gross 

weight. A quite adequate approximation is simply 

(2.257) ( )a/c

fuel initial avg.

R 1 L D

SR 350 in nautical miles per pound. W SFC W

  = =    

In essence, this result says the heavier the machine (for a given aircraft and engine 

technology), the poorer the miles per gallon, which I expect you already knew. 

 The immediate value of Eq. (2.257) is the comparison of fuel efficiency for many 

helicopters. There is a wealth of data in industry literature that give takeoff weight, range, and 

fuel capacity, etc., for any given helicopter. Some of the data are “apples and oranges” of 

course. However, from a survey of some 550 helicopters,81 you will see in Fig. 2-133 that 

 

81 I have a list of over 550 helicopters in my personal collection. This unpublished list occupies a Microsoft®

Excel® spreadsheet some 590 rows deep and 50 columns wide. Not all the technical data blanks are filled in yet, 

therefore not all the sub-calculations are complete. Many of the helicopters on my list are derivatives of basic 

models, so the number of really different helicopters is much less than 550. 
2.5 FUEL EFFICIENCY 

276 

specific range does, in fact, decrease with increasing takeoff weight as Eq. (2.257) dictates. 

Furthermore, 50 years of modern helicopter history is summed up, from a fuel efficiency point 

of view, concisely with 

(2.258) [ ]avg.

fuel initial

R 1 SR 350 4.0 to 7.5 in nm/lb

W W = = . 

 Fig. 2-133 shows that with a few exceptions, the industry’s best efforts have produced 

helicopters with ( )a/c L D SFC equal to 7.5. This is the solid line that captures the top of the 

data scatter in the figure. The bottom of the scatter is captured with a long, dashed line 

calculated using Eq. (2.257) with the lift-to-drag ratio divided by engine specific fuel 

consumption equal to 4.0. 

 Cammack, the author of the paper about the YOH-6A World Record Program [147], 

closes the portion of his paper describing the cross-country flight with this key statement: 

“It is interesting to note that this distance was achieved using a turbine engine with an SFC of 

approximately 0.7. If small turbine engines with SFC’s of approximately 0.5 become available, 

distances 40 percent greater will be possible. The resulting still air range, based on the closed 

circuit distance record (Flight 7) would be 2440 miles (1740 miles × 1.4 = 2440 miles)—

virtually the West Coast to Honolulu Ferry Range that has been a goal for the past decade.” 

0.01

0.1

1

10

100 1,000 10,000 100,000

Takeoff Gross Weight (pounds)

4.0

Specific 

Range, 

nautical 

miles 

per 

pound 

of fuel 

used

(nm/lb)

( )a/c

avg.

L D

SFC

     

7.5

Fig. 2-133. Helicopter fuel efficiency after 60 years of development.
2.5 FUEL EFFICIENCY 

277 

 As of 2012, no small turbine engine with an SFC close to 0.5 has arrived. And, just as 

important, no helicopter airframe manufacturer has made a 40 percent improvement in the 

aircraft maximum lift-to-drag ratio. Furthermore, the nonstop, non-refueling helicopter flight 

from the West Coast of the United States to Honolulu has yet to be made. 

2.5.1 Helicopter Lift-to-Drag Ratio (L/D) 

 Helicopter lift-to-drag (L/D) ratio, whether average or maximum, can be a sore subject 

to bring up with members of the rotorcraft industry. Sixty years ago, helicopter pioneers 

steadfastly insisted that no real barrier existed in achieving airplane-like L/Ds. But, try as they 

might, succeeding generations have made very little progress toward this goal. The purpose of 

this section of the book is to look at helicopter L/D in the cold light of day after 60 years. 

 An aircraft’s L/D is quite easy to define given Eq. (2.47). For a helicopter in steady, 

level flight, it is simply 

(2.259) W

Main Rotor(s) TailRotor(s) P Engine

Acc.

Main Rotor(s) TailRotor(s)

L W WV C

D 550SHP / V C RHP RHP

550 SHP −

μ = = =     + +

η η  

where flight weight (W) is in pounds, and velocity (V) is in feet per second. Using anything 

other than the engine (or engines) total shaft horsepower (SHP) required to fly seems, to me, 

quite unreasonable. You have been exposed to rotor horsepower (RHP) and engine power 

used to drive accessories earlier in this discussion of modern helicopter results. 

 References [108, 109, 115, 116, 118, 121, 124, 125, 133, 170-188, 190-206] and [207-

210] provide a reasonable amount of flight test data with which to calculate L/D for these 

several helicopters. The results of this calculation are displayed in Fig. 2-134. 

 The L/D ratio for the Sikorsky UH-60A has been examined in detail in Fig. 2-135. Let 

me discuss the three upper lines in Fig. 2-135 first and then address the parasite drag of 

helicopters in a separate paragraph. 

 As you can see, the highest L/D ratio comes when the drag of only the main rotor 

blades alone is considered. You will recall (Volume I, paragraph 2.11.3, pages 225–234) that 

in 1927 Glauert held little promise that an isolated rotor would ever achieve a maximum L/D 

much greater than 8.0. For a number of reasons he did not imagine, he turned out to be right. 

The L/D of an isolated rotor in forward flight was given in Volume I, Eq. 2.289, page 232 as 

( )

R R

2 3

R R t 2

2 d min hp

FP FP

L L

D L A V C 13

2 AV 8V

= ρ σ + + μ

ρ

. 
2.5 FUEL EFFICIENCY 

278 

For the UH-60A this 1927 theory is shown as the dashed line in Fig. 2-135 using 

Cdmin = 0.008. With a better understanding of profile drag and the effect of nonuniform 

downwash [211], this favorable 1927 main-rotor-blades-alone estimate becomes more 

realistic as the estimate labeled 1980 shows. 

 The influence of accessory power, transmission efficiency, and the tail rotor cannot be 

ignored. These items decrease the maximum L/D ratio by two points! The decrement is of the 

same order as the 26 square feet of equivalent flat plate area, which I will now discuss. 

2.5.2 Equivalent Parasite Drag Flat Plate Area (fe) 

 Equation (2.259) calculates the lift-to-drag ratio of a helicopter. This ratio depends on 

the main rotor(s) horsepower required (RHPMain Rotor(s)). As discussed in Volume I, page 64, 

the autogyro era showed that this main rotor power could be calculated using the energy 

method, which says that 

(2.260) ( ) ( ) ( )

2 3

t do 2

hp hp hp hp hp FP hp

RVC

Power Q T v T sin H cos V 1 3 8

ρπ σ = Ω= − α + α + + μ , 

and that ( ) T sin H cos hp hp hp hp α+ α is just rotor drag that an autogyro’s propeller had to 

overcome. When applied to the helicopter, the rotor is both lifting and propelling so that rotor 

drag becomes a propulsive force. This propulsive force is, to the first approximation, equal to 

the parasite drag of the helicopter. The parasite drag of the helicopter, as is customary for 

airplanes, is nothing more than fe = D/q where q = 1⁄2 ρV2

. Therefore, it follows that 

(2.261) T sin H cos f q hp hp hp hp e α + α =− . 

On this basis, the main rotor or rotors require power from the engine in the amount of 

(2.262) ( ) ( )

2 3

t do 2

hp e FP hp

RVC

Power T v f qV 1 3 8

ρπ σ

=+ + + μ . 

 As I related in Volume I, pages 258 and 259, the Royal Aircraft Establishment (RAE) 

had obtained a Cierva C.30 Autogiro in 1934 to conduct an end-user evaluation. A report was 

ultimately published in March 1939 [335]. Following extensive flight testing, the RAE 

concluded that 

“the experiments do not suggest any very obvious method of improving performance of the 

aircraft [the C.30] except by reducing the parasitic drag of the fuselage. It has been estimated 

that the reduction of solidity and increase of blade angle as compared with the C.6 autogiro has 

increased the L/D ratio of the rotor at top speed from 5.9 to 8.8 and it seems unlikely that much 

further improvement in the aerodynamic performance of the rotor can be obtained.” 
2.5 FUEL EFFICIENCY 

279 

0

1

2

3

4

5

6

7

8

9

10

0 20 40 60 80 100 120 140 160 180 200 220

True Airspeed (kts)

TL-19D

 1,500 ft

10,000 ft

YR-4B

Bell Model 209

Attack Prototype

Aircraft

L/D

Sikorsky UH-60A

Utility Transport

Sikorsky S-67

Attack Prototype

Lockheed AH-56A

Attack Prototype

Fig. 2-134. Helicopter lift-to-drag ratio after 60 years of development.

0

2

4

6

8

10

12

0 20 40 60 80 100 120 140 160 180

Aircraft 

L/D

Main Rotor Blades 

Alone

(fe = zero ft2

)

1927 Theory

1980 Estimate

Main Rotor + Tail Rotor

 Blades Alone

 fe = zero ft2

 SHPacc = 100 hp

 RHPtr = 0.05 (RHPmr)

Xmsn Eff. = 0.97

Complete UH-60A

True Airspeed (kts)

Main Rotor + Tail Rotor

 Blades Alone

 fe = 26 ft2

 SHPacc = 100 hp

 RHPtr = 0.05 (RHPmr)

 Xmsn Eff. = 0.97

Fig. 2-135. Estimate of the elements that make up the L/D of a UH-60A (gross weight 

15,500 pounds, altitude 2,060 feet, and main rotor speed 244 rpm).
2.5 FUEL EFFICIENCY 

280 

Based on model wind tunnel testing, it was concluded that the 1,800-pound-gross-weight 

Cierva C.30 had a parasite drag area of fe = 7.57 square feet. The distribution of drag area by 

component is provided in Table 2-25. The reference gross weight is 1,800 pounds. 

 With the onset of World War II and the 6 years that followed, the attention of the 

rotorcraft industry was riveted on developing a helicopter. The primary effort was to just get a 

helicopter flying—never mind its aerodynamic efficiency. There was, of course, general 

agreement that the machines all had high parasite drag, but reliability, stability, control, and 

hovering performance shortcomings were of much greater importance than the inadequate 

performance in forward flight. 

 I do not mean to infer any lack of attention to parasite drag with the preceding 

paragraphs. In fact, just the opposite. Each of the pioneering companies had ongoing efforts to 

find the equivalent parasite drag area for its helicopters. As one example, consider what the 

Kellett Aircraft Corporation engineering group documented in February 1945. 

 In February 1945 the Kellett Aircraft Corporation had completed the transition from 

autogyros and was pursuing the XR-8, a synchropter (Fig. 2-136) that first flew on August 7, 

1944. The XR-8 was followed by the much larger XR-10. As part of that transition, Gordon 

Fries prepared a Kellett engineering report [336] titled A Summary of References, Methods 

and Procedures Useful in Estimating Parasite Drag. Following a thorough and careful stepby-step calculation used in parasite drag estimating at the time, Gordon established the drag 

breakdown for the Kellett YG-1B autogyro, the Kellett XR-8 helicopter, and the Sikorsky 

YR-4B.82 To construct the comparison summarized in Table 2-26, Gordon used over 20 

different references dealing with aircraft component drag estimating methods and data.83 

Table 2-25. C.30A Drag Breakdown Based on 1/8-Scale-Model Tests 

Component Drag at 

100 fps (lb) 

Parasite Area

(fe in sq ft) Percent 

Undercarriage and Its Wheels 29 2.44 32 

Engine and Exhaust Ring 17 1.43 18 

Fuselage With Vertical Fins 11 0.93 12 

Pylon 10 0.84 11 

Rotor Hub 10 0.84 11 

Tail Plane 7 0.59 8 

Windscreens 4.5 0.38 5 

Tail Wheel 1.5 0.13 2 

Total 90 7.57 100 

 

82 I count Gordon as a longtime friend. His report was checked and approved by Wayne Wiesner, another 

longtime friend. When the Kellett brothers’ (Rodney and Wallace) company failed after the XR-10 crashed in 

New Jersey in 1947, the brothers decided to manufacture frozen food containers for grocery stores. The need 

became apparent when frozen food became a new product in the United States. To stay in the rotorcraft industry, 

Gordon moved to Piasecki and Wayne moved to Hiller. Gordon started to round out my aerodynamics education 

at Rensselaer Polytechnic Institute when I moved from Preliminary Design to the Aerodynamics group in 1957. 

83 When I started doing parasite drag estimates I had Dr. Sighard Hoerner’s book [337], Fluid-Dynamic Drag

(my first-edition May 1951 copy was just titled Aerodynamic Drag), as primary reference. 
2.5 FUEL EFFICIENCY 

281 

Fig. 2-136. The Kellett XR-8 synchropter was patterned after the Flettner Fl-265, which 

had its first flight in Germany in 1938 (photo courtesy of Wayne Wiesner).

 The N.A.C.A. continued its rotorcraft research program by transitioning from an 

emphasis on autogyros to an emphasis on helicopters. In early 1945 the Bureau of Aeronautics 

and the Air Technical Service Command (the Army Air Corp) requested flight testing research 

on the Sikorsky YR-4B by the Langley Memorial Aeronautical Laboratory. The Navy 

provided an HNS-1 (its version of the Army YR-4B) and in March and April 1945, Fred 

Gustafson published two reports [47, 48]. The first report documented level flight 

performance and the second covered hovering and vertical flight performance. In analyzing 

the forward-flight performance of the YR-4B, Gustafson used initially unpublished lift, drag, 

and pitching moment data that Dick Dingeldein and Ray Schaefer obtained for a full-scale 

YR-4B in the Langley 30- by 60-foot open throat wind tunnel. The test results were later 

published [271]. This landmark data is reproduced here as Fig. 2-137. Note that with the 

camera not installed, the airframe parasite drag area varied from a minimum of (0.0172 times 

1,134) 19.6 square feet to nearly 23.8 square feet at a nose-down angle of attack of 

–16 degrees. 
2.5 FUEL EFFICIENCY 

282 

Table 2-26. Kellett Parasite Drag Area Breakdown for Three Rotorcraft 

(February 1945) 

Component YG-1B XR-8 YR-4B 

Fuselage and Pylon 5.74 5.71 5.67 

Landing Gear 1.97 9.09 5.13 

Rudder 0.05 0.15 0 

Tail Rotor Structure 0.00 0.00 0.62 

Stabilizer and Fin 0.66 1.15 

Blade Roots and Hub 1.78 4.61 5.47 

Other 0.00 1.30 2.99 

Interference Effects 0.51 0 0 

Total 10.71 22.00 19.89 

Reference Gross Weight 2,800 2,975 2,540 

Fig. 2-137. The Sikorsky YR-4B airframe aerodynamic properties with main- and tail-rotor 

blades removed. Coefficients based on the main rotor area of 1,134 square feet [271]. 
2.5 FUEL EFFICIENCY 

283 

 In using the Dingeldein data, Gustafson added 0.4 square feet of drag to account for 

the “cylindrical blade shanks.”84 Furthermore, he corrected the wind-tunnel angle of attack to 

account for the main rotor downwash, which he computed as 

(2.263) f

f 1 2 2

2

W L 57.3

V R

  + Δα =     ρ π . 

This main-rotor-interference angle of attack (Δαf) in degrees was added to the helicopter’s 

pitch attitude (in degrees), which was “determined by means of a pendulum inclinometer.” 

 The thoroughness of Fred Gustafson’s 1945 work set a high standard for those of us 

who followed. 

 By 1954 helicopter development had overcome many of the early mechanical 

deficiencies, and Robert Harrington of the N.A.C.A. Langley Memorial Aeronautical 

Laboratory published NACA TN 3234 [338]. In my opinion, his summary and introduction 

represented a call to action on reducing parasite drag. In August 1954 he wrote the following: 

“SUMMARY 

A reduction in helicopter parasite drag is possible but not profitable except in those cases 

where high speed and long range are primary requirements. For some of the factors 

causing drag, reduction in parasite-drag area may result in increased weight whereas, in 

other cases, it does not. The final design, however, must be a compromise between the 

reduction of drag and the increase in weight. 

INTRODUCTION 

In the past, there has been little consideration given to the problem of helicopter parasite 

drag. Many more serious problems such as vibration, stability, and even adequate hovering 

performance have required the full attention of the designer. In any event, parasite drag 

becomes important only in the higher speed range. 

Now, however, there are certain uses of the helicopter where high speed and long range are 

important. Wherever this is the case, it appears that significant benefits can be realized 

from reductions in parasite drag. The purpose of this paper is to indicate the order of 

magnitude of these possible benefits and to discuss a few of the ways by which parasite 

drag can be reduced.” 

To make his points, Harrington hypothesized a 10,000-pound helicopter having a parasite 

drag area of 40 square feet, which he “chose as representative of current practice for 

helicopters of this size.” He then proceeded to use several references for drag reduction from 

fixed-wing drag reduction efforts to concluded that a reduction of 25 square feet of parasite 

area could be obtained. He estimated that 20 square feet of drag reduction could be obtained 

just from applying fixed-wing lessons learned about landing gears and wheels. He explained 

his reasoning as follows: 

 

84 It is worth noting that the minimum parasite drag area of 19.6 square feet that Dingeldein obtained, plus the 

0.4 square feet Gustafson added for “blade shanks” (equaling 20.0 square feet), compares quite favorably with 

the 19.89 square feet Fries estimated as shown in Table 2-26. 
2.5 FUEL EFFICIENCY 

284 

 “Landing-gear installation. Shown in figure 2 [reproduced here as Fig. 2-138] are 

sketches of the landing-gear installations on three different helicopters in the general weight 

range which is being considered. Past experience with airplanes indicated that the landing 

gear contributed from one-third to one-half the total drag. Calculations of the parasite drag of 

helicopter landing gears such as these indicate a parasite-drag area of about 20 square feet. 

When available drag data for wheels, struts, and tubing are used, a parasite-drag area of 

15 square feet is obtained if no interference losses are considered. Experience indicates that 

the interference drag of the various strut intersections, the strut-fuselage intersection, and the 

wheel-strut intersection would probably add at least another 5 square feet and thus give a total 

area of 20 square feet. All this drag increment could be saved by use of a fully retractable 

landing gear. In some cases it may be impractical or undesirable to retract the gear fully. In 

that event, significant drag reductions, possibly equal to the sum of all these other items, may 

still be realized by proper fairing of the wheels and struts. Some data on landing-gear fairings 

are presented in references 5 [see NACA Report 485] and 6 [see NACA Report 518]. It 

should be mentioned that there will probably be some weight penalty involved in retracting or 

fairing the gear. This weight increase would somewhat reduce the estimated power saving.” 

As it turned out, smaller helicopters (e.g., the Bell H-13 and Hiller H-23) changed to skid 

gears to satisfy U.S. Army field operation requirements, but nonretractable, wheeled landing 

gear continued as standard on heavier machines until the late 1970s. 

 Harrington’s August 1954 report was quite timely because the U.S. Army began a 

search for a new Light Observation Helicopter (LOH) to replace aging Bell OH-13 and Hiller 

OH-23 first-generation helicopters. In October 1960 the U.S. Navy, acting for the Army Chief 

of Transportation, sent out a request for proposals for a four-seat, turbine-powered LOH. 

Some 25 aircraft companies were solicited. In October 1961 the contenders were narrowed 

down to the Bell YOH-4, the Hiller YOH-5, and the Hughes YOH-6. 

Fig. 2-138. Harrington’s examples of “current” landing gear installations [338].
2.5 FUEL EFFICIENCY 

285 

 One of the companies solicited for an LOH proposal was the Vertol Division of the 

Boeing Company. At that time Jack Diamond was Chief of Preliminary Design at the division. 

In July 1960 Jack had written a letter to George Dausman (Assistant Chief of Aerodynamics 

of the Airborne Support Systems, Engineering Division, Air Force) asking for helicopter drag 

data. Mr. Dausman responded with a letter [339] which read in part: 

 “A search of our old files for helicopter drag data has resulted in the attached 

tabulation of equivalent drag areas. Many of the values are estimates based upon 

preliminary drag build-ups and the remainders are calculated from Edwards flight test 

data. Generally, drag values for the H-19 and more recent machines are from test data.” 

The tabulation Dausman included is reproduced here as Table 2-27. I have added columns for 

the manufacturer and the nominal gross weight as given by Lambermont and Pirie [89]. 

 Let me stop for a moment to look at a graphical summary of the parasite drag area 

accumulated in Tables 2-25, 2-26, and 2-27. This data is summarized in Fig. 2-139. First of 

all, the somewhat limited data suggests that helicopter parasite area varies as nominal gross 

weight raised to the two-thirds power. That is, it appears that 

(2.264) ( )2/3

e f K GW /1000 = . 

Accepting this approximation, the industry decreased parasite drag by a factor of 2 in about 

15 years after the Sikorsky R-4B began flying, which is to say that K went from 8.6 to 4.2 in 

15 years. Quite interestingly to me, the helicopter drag levels appear to have overcome the 

advantage autogyros offered with their K = 5.2.

Table 2-27. Survey of Parasite Drag Area as of July 1960 

Model 

Designation Manufacturer 

Equivalent 

Drag Area (ft2

)

Nominal Gross 

Weight (lb)

R-4B Sikorsky 23.1 2,540 

H-5 Sikorsky 17.9 4,900 

H-10 Kellett 29.4 11,000 

H-12 Hiller 16.6 2,700 

H-13G Bell 10.6 2,350 

XH-15 Bell 15.4 2,777 

XH-16 Piasecki 54.0 33,577 

YH-16 Piasecki 54.0 46,750 

XH-17 Hughes 128.0 52,000 

YH-18 Sikorsky 15.3 2,100 

H-19 Sikorsky 26.0 7,200 

H-21 Piasecki 30.0 11,500 

H-26 American Helicopter 4.4 875 

H-34 Sikorsky 34.0 13,000 

H-37 Sikorsky 75.0 31,000 

XH-40 Bell 18.0 8,500 

YH-40 Bell 36.0 8,500 

YH-41 Cessna 9.0 3,000 

LZ-5 Doman 20.4 5,200 
2.5 FUEL EFFICIENCY 

286 

1

10

100

1,000

100 1,000 10,000 100,000

Equivalent

Parasite

Drag

Area

(ft2

)

Nominal Gross Weight 

Cierva

C.30

Kellett

YG-1B

Sikorsky

R-4B

American

Helicopter

XH-26

Cessna

YH-41

Bell

XH-40

Piasecki

YH-16

fe = 4.2 (GW/1000)2/3

fe = 8.6 (GW/1000)2/3

fe = 5.2 (GW/1000)2/3

Fig. 2-139. From 1945 to the late 1950s, the rotorcraft industry decreased helicopter 

parasite drag area by a factor of two.

 As part of the forthcoming LOH competition the U.S. Army wanted their own 

assessment of parasite drag. In May 1960 they assigned a research program to what was then 

the U.S. Army Transportation Research Command (USATRECOM) located at Fort Eustis, 

Virginia. A project engineer was assigned (Lt. Herbert H. Moser85) and the wind tunnel 

services of NASA Langley Research Center were enlisted. NASA obtained both a 1/5-scale 

and a full-scale model of what could be a four-place LOH, and these models were tested. 

Preliminary NASA reports [340, 341] were made available in December 1960.86 Lt. Moser 

published the results of the research program in the American Helicopter Society Journal in 

January 1961 [342], which was quite timely for the competition. 

 

85 When Herb completed his service he came to Boeing Vertol for several years. If my memory serves me 

correctly, Herb became a project engineer in Preliminary Design for Jack Diamond. The report Herb wrote is an 

absolute must-read paper. 

86 These preliminary reports, which I have copies of, were given NASA L-1469 and L-1470 numbers. They later 

were published as NASA TN D-1363 and NASA TN D-1364 in July 1962, but with slightly different titles. 
2.5 FUEL EFFICIENCY 

287 

Fig. 2-140. Parasite drag breakdown for the U.S. Army version of the Light 

Observation Helicopter [342]. 

 As Lt. Moser reported, the U.S. Army felt, based on their estimates of the LOH 

configuration, that a 2,400-pound gross weight with a parasite drag area of 6.0 square feet 

should be achievable by the industry. This meant that they expected a K of 3.35 computed 

from Eq. (2.264) as 

(2.265) ( ) ( )

e

2/3 2/3

f 6 K 3.35

GW /1,000 2, 400 /1,000 == = . 

In essence the Army was expecting industry to come up with a configuration that lowered the 

parasite drag constant (K) from 4.2 to 3.35. Lt. Moser stated the situation quite clearly in the 

introduction of his report when he wrote: 

“Subsequent to the issuing, in May 1960, of the Military Characteristics pertaining to the 

LOH, there arose a great deal of controversy with regard to the obtainability of the 

desired performance in a practical, four-place helicopter configuration with the then 

prescribed power plant [the Allison T-63 turboshaft engine rated at 250 horsepower at sea 

level standard and 206 horsepower at 4,000 ft on a 95o

 F day].” 

 Based on the NASA wind tunnel results, Lt. Moser used a summary chart showing a 

drag breakdown to convince industry that the Army target value of 6 square feet was rational. 

I have reproduced his summary chart here as Fig. 2-140. The Army configuration is illustrated 

in Fig. 2-141. The full-scale-model test report [341] gives the Run Number 28, Army 

configuration as: 
2.5 FUEL EFFICIENCY 

288 

 “Run 28: Model C with curved element pylon, three-blade articulated hub - disk plane 21 

inches above fuselage, streamlined landing skids, F.M. homer, A.D.F. sensor, F.M. 

communication, V.H.F. communication, V.O.R. split loop, door outlines, door handles, and 

rotating beacon (mounted behind hub on the pylon).” 

 The message that the U.S. Army sent to LOH competitors (via Lt. Moser87) was loud 

and clear. The parasite drag area target was 6 square feet—at least at zero fuselage angle of 

attack. Any discussion about drag increase with nose-down angle of attack, as Fig. 2-142 

shows, was quite muted. It is important to note that Lt. Moser’s drag area buildup required 

faired skid gear to make the target. While the three-blade articulated hub (plus pylon) only 

accounted for about 1.6 square feet, the difference between faired and unfaired skid gear was 

2.4 to 2.6 square feet of parasite drag area. 

Fig. 2-141. U.S. Army version of the Light Observation Helicopter [341]. 

3

4

5

6

7

8

9

10

-12 -9 -6 -3 0 3 6 9 12

Equivalent

Parasite Drag

Area (ft2

)

Fuselage Angle of Attack 

Nose Up

Base data from Run 28 of NASA L-1469

(with Faired Skid Gear)

Base data +2.2 ft2 added by Lt. Moser

for other items (see Fig. 2-161)

Addition of 2.5 ft2 if skid gear unfaired

Fig. 2-142. Parasite drag breakdown for the U.S. Army version of the Light 

Observation Helicopter. 

 

87 Lt. Moser noted at the bottom of the first page of his AHS Journal paper that “the opinions expressed in this 

paper are those of the author and do not necessarily reflect those of the Department of the Army or any other 

Government agency.” It is not often you read those kinds of words in the Journal of the American Helicopter 

Society. 
2.5 FUEL EFFICIENCY 

289 

 As you read earlier, Hughes won the LOH competition with its YOH-6. Then finally, 

in 1968, a complete full-scale helicopter (then an OH-6A) was tested in the NASA Ames 40- 

by 80-foot wind tunnel. The installation is shown in Fig. 2-143, and note that the test was 

conducted with the rotor system powered by its own turboshaft engine. The test was primarily 

directed at measuring stability and control parameters. The test results were published in a 

Hughes Tool Company Aircraft Division report in May 1970 [343]. 

 Try as I might, I have never obtained a quoted parasite drag area closer than 5.7 to 

6.4 square feet for this 2,800-pound LOH winner. Being an optimistic aerodynamicist on this 

occasion, I choose the 5.7-square-foot number because the skid gear was faired. 

Fig. 2-143. A Hughes OH-6A Light Observation Helicopter installed in the NASA Ames 

40- by 80-foot wind tunnel (photo courtesy of Bill Warmbrodt, Ames Research Center). 
2.5 FUEL EFFICIENCY 

290 

 In 1978 Bell Helicopter Textron also made use of the NASA Ames full-scale wind 

tunnel. Its Model 222, the first Bell helicopter with retractable gear, is shown installed in the 

tunnel in Fig. 2-144. A 1/5-scale model was tested in the Vought Corporation 7- by 10-foot 

wind tunnel to clarify tare and interference effects. The full-scale aircraft was not powered. 

The drag polar that was reported [344] is shown in Fig. 2-145. 

Fig. 2-144. A Bell Model 222 installed in the NASA Ames 40- by 80-foot wind tunnel 

(photo courtesy of Bill Warmbrodt, Ames Research Center). 
2.5 FUEL EFFICIENCY 

291 

10

11

12

13

14

15

16

17

18

19

20

-12 -9 -6 -3 0 3 6 9 12 15

Equivalent

 Parasite 

Drag

 Area

 (ft2

)

Fuselage Angle of Attack (deg)

Nose Up

Full Scale

NASA Ames 

40 by 80

1/5 Scale

LSWT

 7 by 10

Fig. 2-145. Bell Model 222 drag polar with gear retracted [344].

 Next the industry had a chance to apply what had been learned up to the early 1970s. 

First off the U.S. Army sought new utility and attack helicopters to replace the older Bell 

UH-1 (the Huey) and Bell AH-1 (the Cobra). The competition ultimately led to today’s 

Sikorsky UH-60 (the Black Hawk) and the Hughes AH-64 (the Apache). On the commercial 

side, Sikorsky came out with the S-76 and Bell started delivery of its Model 222. Both of 

these commercial products had retractable landing gear. Just as importantly during this 

decade, the American Helicopter Society created an Ad Hoc Committee on Helicopter 

Parasite Drag in May 1974. The committee chairman, Bob Williams, delivered the final report 

on May 14, 1975 [345]. 

 The Ad Hoc Committee report was a compilation of 15 papers authored by top 

aerodynamic engineers in the rotorcraft industry. To me this collection, plus the supplement of 

rotorcraft drag bibliography, is of such importance that I have included the key material in 

Appendix C. The bibliography itself lists over 150 references. Appendix C provides at least a 

starting point to appreciate the rotorcraft industry’s efforts in parasite drag reduction. 

 By 1990 the industry had created enough products to, in my opinion, truly summarize 

the parasite drag area progress—even to the inclusion of helicopters with retractable landing 

gear. My assessment of the progress and state of the art is shown in Fig. 2-146, which adds to 

the data shown earlier in Fig. 2-139. 
2.5 FUEL EFFICIENCY 

292 

1

10

100

1,000 10,000 100,000

Equivalent

Parasite

Drag

Area

(ft2

)

Nominal Gross Weight (lbs)

Lockheed 

XH-51

Sikorsky

S-76

Sikorsky

R-4B

Army Target 

for LOH

fe = 4.2 (GW/1000)2/3

fe = 8.6 (GW/1000)2/3

fe = 2.5 (GW/1000)2/3

Aerospatiale 

SA-341 

Sikorsky

S-67

OH-6A

Fig. 2-146. Reduction in parasite drag area from 1945 to 1980.

 As Fig. 2-146 shows, my assessment is that advanced commercial helicopters with 

retractable landing gear should be able to achieve a parasite drag area on the order of 

(2.266) ( )2/3

e f 2.5 GW /1000 = . 

By 1990 the rotorcraft industry saw that retractable gear easily paid for itself. This was a 

decision point that the fixed-wing industry encountered in the mid-1930s. They responded 

with the Boeing Model 247 and the Douglas DC-1, -2, and -3. For helicopters below 8,000- 

pounds gross weight, a retractable skid gear seems worthwhile. For heavier machines, the 

natural choice is retractable, wheeled gear. Certainly the Lockheed XH-51 (Fig. 2-147) and 

the Sikorsky S-76 (Fig. 2-148) are prime examples. Time will tell if new utility helicopters 

such as the AW 101, the NH 90, and the S-92 shown in Fig. 2-149, Fig. 2-150, and Fig. 2-151, 

respectively, have applied available knowledge. Aerodynamic knowledge abounds (see 

Appendix C) about streamlining the fuselage, improving engine inlets and exhausts, 

minimizing protuberances, and sealing gaps, etc. I suggest reading Evan Fradenburg’s paper 

[297] about the Sikorsky S-76, the superb paper about development of the Agusta A-109 

[346], and the paper about Westland Helicopter’s efforts to set a new speed record of 

216.3 knots on August 11, 1986 [347]. 

 Given that airplane lessons can now be applied to helicopters, it seems to me that 

reducing rotor hub parasite drag area is the next improvement that must be made to raise liftto-drag ratios to the maximum that industry can hope to obtain with the helicopter. 
2.5 FUEL EFFICIENCY 

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Fig. 2-147. The Lockheed XH-51 shows what can be achieved when attention is paid to 

parasite drag area (photo from author’s collection). 

Fig. 2-148. The Sikorsky S-76 shows what can be achieved when attention is paid to 

parasite drag area (photo from author’s collection). 
2.5 FUEL EFFICIENCY 

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Fig. 2-149. The Agusta Westland 101 in a civilian role (photo from author’s collection). 

Fig. 2-150. The NH Industries 90 in a military role (photo from author’s collection). 

Fig. 2-151. The Sikorsky S-92 in a flight test role (photo from author’s collection). 
2.5 FUEL EFFICIENCY 

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2.5.3 Rotor Hub Parasite Drag Area 

 Unlike the streamlined attachment of wings to a fuselage evolved by members of the 

fixed-wing world, the rotary wing industry has had to deal with a very high drag, 

mechanically complex attachment—a rotor hub. Jeffrey Jones [348] stated in the 13th 

Lanchester Memorial Lecture that “the hub is untidy.” Perhaps that is a little too simplistic. As 

you can see from Fig. 2-152, the rotary wings are indeed attached to a hub, but then the hub is 

solidly attached to a rotor mast, a rotating component. The rotor mast is an output shaft from a 

transmission. It is the transmission, finally, that is attached to the fuselage. In a converse 

sense, the fixed-system controls emerge from the fuselage and attach to the nonrotating ring 

of the swashplate. The swashplate (recall Fig. 2-44 on page 101 of Volume I) transfers the 

nonrotating control input to the rotating ring to which the bottom of each pitch link is attached 

with a rod end bearing. The top of each pitch link is attached to a pitch arm, and thus the 

pilot’s control motion finally feathers each blade. More than one fixed-wing aerodynamicists 

has said, “And you want to clean that claptrap up!” Frequently, a rotorcraft designer will 

respond with, “Maybe you could find some sort of fairing that will cut the parasite drag area 

in half ?” But then the rotorcraft champion will immediately add, “Of course the fairings must 

permit easy access to all components for a mechanic’s inspection and servicing.” 

Fig. 2-152. The Bell Model 412 rotor system with pylon fairing off 

(photo from author’s collection). 

Hub Pitch arm Blade 

Pitch link 

Collective pitch 

(fixed control 

input)

Swashplate 

assembly 

Cyclic pitch 

(fixed control 

input) 

Basic fuselage 

Pitch 

link 
2.5 FUEL EFFICIENCY 

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Fig. 2-153. The first step taken in “hub” parasite drag reduction is some sort of pylon 

fairing (photo from author’s collection). 

 A pylon fairing is a natural first step taken to shield some of the components. The Bell 

Model 412 pylon fairing is shown in Fig. 2-153. When you look at any number of helicopter 

photos in the popular press and trade magazines, you will invariably see a pylon fairing. 

 Given a pylon fairing, the question immediately comes up as to what can be done to 

further reduce the parasite drag area of the hub and control system. One immediate effort 

began with a wind tunnel test of an all-encompassing fairing around the hub and upper control 

system of the Sikorsky S-51. This was the first Sikorsky helicopter to be certificated by the 

Civil Aviation Authority. The wind tunnel test was conducted by the McCulloch Motors 

Corporation under Air Force contract. A report [349] was published in April of 1955.88 This 

effort at fairing was not promising enough to try in flight test. 

 Two additional efforts at complete fairing were carried through to flight test in the 

mid-1950s. One was the McDonnell XV-1 [350], a compound helicopter that I will discuss in 

greater deal in Volume III. The other was the Lockheed CL-475 (Fig. 2-154), which was 

developed under the inventive direction of Irv Culver at the Lockheed Skunk Works [351]. 

 

88 This report is unclassified but restricted to authorized U.S. Government agencies and their contractors. A little 

over protection I would say since rumor had it that the fairing was a large-diameter spherical enclosure. Because 

the configuration was so unsatisfactory, I have made no effort to get an unrestricted copy so that a photo could 

be included in this volume. 

Pylon fairing 

Basic fuselage 
2.5 FUEL EFFICIENCY 

297 

Fig. 2-154. The Lockheed CL-475 was used to demonstrate a bearingless rotor system in 

1955. The rotor system was quite well suited to a hub fairing on top of the pylon 

fairing (photo from author’s collection). 

The CL-475 was Lockheed’s first venture into the rotorcraft world. The primary purpose of 

this experimental helicopter was to demonstrate a bearingless hub [352, 353], which I will 

discuss in detail shortly. The rotor hub itself proved worthy of follow-on development and led 

to the Lockheed XH-51, the very low drag helicopter shown earlier in Fig. 2-147. As you can 

see, the bearingless hub was carried forward on the XH-51, but the hub fairing was not. 

 So far the several efforts at parasite drag reduction with hub fairings, including work 

done in the 1980s [354, 355], were never carried through to production helicopters. In fact, 

the pylon fairing configuration was more determined by separated flow considerations as they 

affected tail rotor and empennage vibration than by drag reduction. 

 However, one experiment that is of note was conducted by the Vertol Division of the 

Boeing Airplane Company and reported by Ed Gabriel [356] in June of 1962.89 The question 

was one of reducing the drag of the blade root ends on the HC-1B helicopter, the prototype of 

the CH-47. The situation is illustrated in Fig. 2-155. The approach was to use a series of 

elliptical cross sections. The 1/3-scale-model test was conducted in the University of 

Maryland’s 7- by 10-foot wind tunnel during the week of April 16, 1962 (Fig. 2-156). Ed used 

Scotch® tape to attach Helence nylon tufts and got some terrific flow visualization photos as 

Fig. 2-157 shows. 

 

89 I have kept this report all these years because it was a fine piece of experimental work done by Ed Gabriel. 

Unfortunately, the fairings were never flight tested, which I always thought was an oversight. Obtaining a 

practical mechanical and low-drag rotor hub aerodynamic fairing is, in my opinion, a very, very difficult 

engineering task. 

Pylon fairing 

Hub fairing 
2.5 FUEL EFFICIENCY 

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Fig. 2-155. A blade shank fairing tested in 1962 [356].

Fig. 2-156. The 1/3-scale model of a CH-47 in the University of Maryland 

wind tunnel [356].

Pylon fairing 

Basic fuselage 
2.5 FUEL EFFICIENCY 

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Fig. 2-157. Tufts showing flow angularity [356].
2.5 FUEL EFFICIENCY 

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 Searches for a fairing around the root of a blade to reduce shank drag were ongoing 

well into the late 1980s. In this decade, the U.S. Army Research and Technology Laboratories 

located at Ft. Eustis, Virginia, joined with NASA Ames Research Center to develop an 

Integrated Technology Rotor/Flight Research Rotor (ITR/FRR) [357]. As part of that effort, 

some members of the aerodynamic staff at Bell Helicopter Textron, led by Phil Alldridge, 

performed a wind tunnel test to compare potential cuff (or shank, or blade inboard radial 

section if you prefer) fairings for their ITR [358]. Phil concluded that elliptical airfoils offered 

the least drag at high speed. 

 Now let me address the hubs themselves. The first thing to know is that many, many 

different hub types have reached flight test and even production status. Many, but hardly all, 

of them are illustrated in Appendix D. This collection of hub types has been compiled from 

my own files and three other sources: 

1. Bill Bousman’s collection [359]. Bill collected photos of many hubs from several 

manufacturers. Then he had the NASA Ames graphic arts department create line 

drawings on vellum. He had the drawings framed. They were mounted on the 

second floor wall in building 215 at the NASA Ames Research Center. At my 

request, Bob Ormiston’s secretary, Pat Horn, had 8-1/2- by 11-inch copies made, 

and Pat sent the beautiful artwork to me in June 1993. They are included in 

Appendix D. 

2. Schindler and Pfisterer’s AGARD paper [360], which I consider an exceptionally 

thorough piece of work. These two men classified hub types as shown here in 

Fig. 2-158. 

3. Tom Hanson’s small, extremely valuable book titled A Designers Friendly 

Handbook of Helicopter Rotor Hubs, which he published himself [361]. 

 The paper by Schindler and Pfisterer [360] captures the major focus of rotor system 

hub designers as Fig. 2-159 shows. Schindler and Pfisterer also concluded that rotor hub 

weight as a percentage of nominal gross weight dropped from about 7 percent to about 

2 percent over three decades. A particularly important improvement along the way was the 

development and recommended application of elastomeric bearings by the Lord 

Manufacturing Company. Fig. D-2 and Fig. D-11 in Appendix D give you some idea of how 

shim stock plus rubber laminates can replace complicated roller or needle bearing assemblies 

to provide blade articulation in flap, lag, torsion, and centrifugal force reaction. Mosinskis and 

Schneider of the Vertol Division of the Boeing Company showed [362] quite specifically that 

a CH-47 hub parts count was reduced from 408 parts to 48 parts, and the need for lubrication 

relative to 233 parts was reduced to zero. The successful application of elastomeric bearings 

was a stunning breakthrough and spread throughout the rotorcraft industry rather quickly. 

 Despite their design differences, few, if any, rotor hub designers have been able to 

incorporate aerodynamic attention to parasite drag reduction. The emphasis ever since the 

demonstration of the autogyro nearly eight decades ago has been on a design philosophy “that 
2.5 FUEL EFFICIENCY 

301 

Fig. 2-158. The four basic hub configurations developed between 1936 and 2010 [360]. 

Fig. 2-159. Emphasis on reduced parts count and improved maintainability has been the 

primary focus of rotor system hub designers [360]. 
2.5 FUEL EFFICIENCY 

302 

thou shall not fail.” Beyond that, the design effort has been on improving reliability, extending 

times between overhaul, decreasing maintenance, lowering parts count, lowering cost, 

improving flying qualities, and not introducing aeroelastic instabilities. 

 The problem in achieving a low-drag hub is all wrapped up, primarily, in the 

feathering motion a hub must provide for a blade that exerts an enormous centrifugal force. A 

secondary factor is the blade-to-hub attachment joint that generally requires some provision 

for blade folding. These two features dictate the frontal area of all hubs that I know of. To 

illustrate this very important primary point, consider Fig. 2-160, which comes from Tom 

Hanson’s book [361]. Three of the five ways (b, c, and d) to provide blade feathering motion 

under centrifugal load have the frontal area set by the diameter of the pitch housing. In fact, 

the twistable straps illustrated in Fig. 2-160 (a) give the initial impression that a very low 

frontal area has been achieved. However, a close look at the Hughes OH-6 hub in 

Appendix D, Fig. D-29, shows that a large-diameter pitch housing is required to control blade 

angle. This is also true for the Hughes (then McDonnell and now Boeing) AH-64 rotor hub, 

an enlargement of the OH-6 approach. Furthermore, lead-lag motion is accommodated with a 

vertical pinned hinge, and lead-lag dampers are required. 

 The first hingeless rotor hub was developed by E. Burke Wilford and flown on his 

1932 autogyro. You read this story in Volume I, starting on page 73. An excellent photo of the 

hub was shown in Volume I, Fig. 2-35. The second hingeless hub (see Appendix D, 

Figs. D-37, 38, and 39) was developed for the then Messerschmitt-Bölkow-Blohm BO-105, 

which made its first flight in February 1967.90 

 This brings me to the bearingless main rotor (BMR) hub91 shown by Hanson in 

Fig. 2-160 (e). The illustration is also representative of several bearingless tail rotor hubs. The 

first BMR was created by Fred Doblhoff and Kurt Hohenemser, who were the core of a 

Helicopter Group within the McDonnell aircraft company. They came up with a compound 

helicopter—the XV-1 shown in Fig. 2-161. Note that both pylon and hub fairing dragreduction aerodynamic technology was applied in this early 1950’s machine. The XV-1 stiff 

inplane hub configuration is seen in Appendix D, Figs. D-42, 43, and 44. The second BMR 

was invented by Irv Culver [363] and tested on the Lockheed CL-475 (Fig. 2-154, and 

Appendix D, Fig. D-34). The follow-on was the Lockheed XH-51 bearingless hub [364], 

shown in Appendix D, Fig. D-35. Then in November 1975, the Boeing Vertol Company 

submitted a proposal to the U.S. Army Air Mobility Research and Development Laboratory 

(AVLABS) at Ft. Eustis, Virginia. This proposal was well received and a contract (DAAJ02-

76-C-0026) was awarded in June of 1976. The Boeing Vertol BMR (Appendix D, Figs. D-16 

and D-17) was designed, fabricated, and tested on a BO-105 [365-368]. 

 

90 The 5,500-pound normal gross weight BO-105 was the first light helicopter to have twin engines. A key 

engineering figure who got the BO-105 into a production run of over 1,400 helicopters was Günter Reichert. 

When we first met in Brussels for a week-long course on rotorcraft held at the Von Karman Institute in 1973, we 

cemented our relationship by exchanging sons for a few weeks in the summers of 1974 and 1975. 

91 Evan Fradenburgh, a key drag-reduction advocate during the development of the Sikorsky S-76 [297], made a 

comment to me at the 34th AHS Forum in 1978 that I have never forgotten. He said, “What’s wrong with 

bearings?” I do not think Evan was in favor of the bearingless hub. 
2.5 FUEL EFFICIENCY 

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Fig. 2-160. Five ways of accommodating blade feathering under a centrifugal load. Note 

that the actual components required to feather the blade are not shown [361]. 
2.5 FUEL EFFICIENCY 

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Fig. 2-161. The first liftoff of the XV-1 (Feb. 1954) was followed by the first official flight 

in July 1954. The XV-1 was free of aeroelastic instabilities, but aircraft drag was 

greater than predicted despite efforts during 1952 testing in the NASA Ames 

Full-Scale Wind Tunnel [350]. (Photo courtesy of David Peters from Kurt 

Hohenemser’s files.) 

 The upshot of the Lockheed and Boeing Vertol BMRs was rotor systems of marginal 

aeromechanical stability that precipitated additional experiments [369]. In short, neither 

configuration had lead-lag dampers, and the damping provided by aerodynamic and structural 

forces was insufficient for a production helicopter. The difference between the modern BMRs 

and the more successful XV-1 of the early 1950s was that the XV-1 was stiff inplane and the 

modern versions were soft inplane. The words stiff and soft refer to the natural frequency in 

the first lead-lag mode as was discussed in Volume I. 

 As the industry continued with BMR development,92 the torque tube approach to 

control blade feathering by Lockheed and Boeing Vertol was replaced with a large pitch 

housing frequently called a cuff. The cuff was designed to carry some lead-lag motion to a 

snubber/lead-lag damper. The Bell Model 680 BMR shown in Appendix D, Fig. D-15, is an 

adequate example. This inboard component is nothing more than a variation on a blade root 

end fairing. The cuff and snubber/lead-lag damper arrangement made the Hughes’ rotor from 

the Hughes’ Advanced Rotor Program (HARP) work on its Model 500E; the Bell 680 rotor 

worked on its Model 430, UH-1Y, and AH-1Z; and the Sikorsky BMR rotor [371] worked on 

its RAH-66. Huber relates this progress in his very thorough paper, Will Rotor Hubs Lose 

Their Bearings? [370]. While considerable progress was made by aeroelasticians [372-375], 

there was no hub parasite drag reduction with any of the BMRs as far as I know. In fact, I dare 

say BMRs increased hub parasite drag. 

 

92 An excellent paper recounting nearly all the industry’s BMR efforts was written by Helmut Huber [370] and 

published in 1992. He followed in Günter Reichert’s footsteps at Messerschmitt–Bölkow–Blohm (MBB), which 

then became Eurocopter Deutschland GmbH. Helmut’s paper actually uses the words “drag reduction” in a 

number of places. 
2.5 FUEL EFFICIENCY 

305 

 With the preceding synopsis of rotor hub development, let me go back to 1959. In 

February of that year, Gary Churchhill and Robert Harrington at NASA Langley published a 

report about their measurements of rotor hub drag [376]. The five hubs were tested on a long 

shaft sticking up from a very streamlined body. There was no pylon fairing, which minimized 

body-to-rotor-hub interference. Their summary results shown in Fig. 2-162 indicated that the 

primary variable was hub frontal area. 

 Churchill and Harrington’s “available to all” experiment initiated a ground swell of 

experimenting all through the 1960s and well into the 1970s. Both model and full-scale 

testing was in full swing. This led to the 1975 Ad Hoc Committee’s report [345] on rotorcraft 

drag submitted to members of the American Helicopter Society as mentioned earlier. By mid1978, the Boeing Vertol Company [377] and Sikorsky Aircraft [378] had begun to quantify 

hub drag, pylon/hub interference drag, exposed control system drag, and rotor mast (or shaft) 

drag. In March of 1978, Chuck Keys and Hal Rosenstein of Vertol published what many 

thought was a summarizing bible on hub drag. Their report [379] showed that this member of 

the rotorcraft industry had 23 internal memos about experiments conducted between 1953 

(with a full-scale H-21 hub) and 1974 (with a 1/12-scale of a heavy-lift helicopter hub). Much 

of this work was supported by NASA and the U.S. Navy and Army. Keys and Rosenstein 

included MBB’s fruitful work with an elliptical fairing on the BO-105 hingeless main rotor 

hub [380], which is shown in Fig. 2-163. 

Fig. 2-162. By 1959 the industry began to relate rotor hub drag to hub frontal area 

although the drag coefficient did appear to be dependent on hub configuration [376]. 
2.5 FUEL EFFICIENCY 

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Fig. 2-163. The BO-105 hingeless rotor hub reduced parasite hub drag by 1.1 square feet 

based on power-required measurements. No treatment of the blade root ends was 

applied (photo from author’s collection). 

 In the Sikorsky report [378] submitted by Tom Sheehy, Tom extended Churchill and 

Harrington’s summary, Fig. 2-162, and boldly suggested that the drag of unfaired hubs 

trended as 

(2.267) ( ) 2

eP P P f A 0.582 0.0349A 0.00057A =+− . 

It may be splitting hairs with Sheehy’s figure 3 data, but my review of his unfaired hub 

parasite drag (shown in Fig. 2-164) suggests that 

(2.268) ( ) 2

eP P P f A 0.4618 0.0719A 0.0024A = +− . 

This may adequately represent the majority of large, frontal area hubs presented in 

Appendix D. To this 1977 state of the art represented by Eq. (2.268), one must add 25 percent 

for all interferences and then another 15 percent for everything not accounted for. In my 

opinion, a conservative estimate of the hub drag, when operating with blades attached and 

installed on an operational helicopter, would be to just increase the hub parasite drag area 

given by Eq. (2.268) by 50 percent. 

 From the latter half of the 1970s on up to the turn of the century, the rotorcraft 

industry concentrated on incorporating bearingless main rotor hubs onto production 

helicopters and improving hingeless main rotor hubs. Helicopters such as the UH-60 and 

AH-64 were brought to production for the U.S. Army, and new commercial helicopters were 

brought to the market place. Ames Research Center continued exploration of hub fairings and 

fairings suited to bearingless and hingeless hubs. To me, it seemed like a 20-year lull in hub 

drag reduction. 
2.5 FUEL EFFICIENCY 

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y = -0.0024x3 + 0.0719x2 + 0.4618x

R2

 = 0.9897

0

2

4

6

8

10

12

14

16

18

20

0 2 4 6 8 10 12 14 16 18 20

Unfaired 

Main 

Rotor

Hub 

Parasite 

Drag 

Area (ft2

)

Hub Swept Frontal Area (ft2

)

CD = 0.50

CD = 1.0

CD = 0.75

Fig. 2-164. By 1977 rotor hub drag (before accounting for hub/pylon interference) 

suggested that the lowest drag would come when inventors and designers reduced 

hub frontal to zero! 

 In fact, there really was not a lull because Larry Young, Bob Stroub, and their small 

team at Ames Research Center kept hub and pylon drag reduction research going. In 1989 

they published results from a definitive experimental study of hub fairings [355]. In 1993 

NASA and Bell Helicopter Textron conducted a joint hub and pylon drag reduction program. 

A 1/5-scale model of the Bell 222 with the blade cuffs of a Bell 680 bearingless rotor 

(Appendix D, Fig. D-15) was tested in the NASA Ames 7- by 10-foot wind tunnel as shown 

in Fig. 2-165. The reported experimental results [381] led to the conclusion that “the total 

model drag was reduced by 20.8 % as compared to the unfaired rotor hub and mast 

configuration” shown in Fig. 2-165. Roughly speaking, hub-plus-pylon-plus-cuff parasite area 

drag could be reduced at least 1.5 to 2.0 square feet below what Bell was contemplating in full 

scale. Unfortunately, a flight research program was not conceived, but improvements did find 

their way onto the Bell Model 430 with its 680 bearingless rotor system as shown in 

Fig. 2-166. 

 This discussion about hub parasite was summarized by Evan Fradenburgh in his 1994 

Nikolsky Lecture [382]. Evan related hub fairings and pylon tailoring testing at Sikorsky. He 

included the rotor head fairing for the Sikorsky S-67, Fig. 2-167, which set a world speed 

record of 191.9 knots in December 1970. This effort, along with wind tunnel testing on an 

S-61 hub and pylon [383], led Evan to write in 1995: 
2.5 FUEL EFFICIENCY 

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Fig. 2-165. A 1/5-scale Model 222 with blade root end cuffs simulating the Model 680 

rotor system was the baseline for a NASA/Bell hub and pylon drag reduction 

effort (photo courtesy of Larry Young). 

Fig. 2-166. The Bell Model 430 used the Model 680 bearingless rotor system. Some 

aerodynamic attention was given to the pylon shape, but no hub fairing was used. 

The Bell Model 430 could be bought with retractable gear or a nonretractable 

skid gear (photo from author’s collection). 
2.5 FUEL EFFICIENCY 

309 

“Some of the more modern rotor heads for an aircraft of this size [S-61] are better, but 

not by a lot. Even the latest “bearingless” rotor head designs, while certainly simpler in 

terms of parts count, have large frontal areas and do not represent any aerodynamic 

improvement....The downside [to the S-61] concept was that it added weight, 

complexity, and made rotor head maintenance checks difficult.” 

 After 1995 through to 2009, the literature is virtually devoid of pylon and hub parasite 

drag reduction discussions.93 For that matter, I found no new data points to add to the trends 

shown in Fig. 2-168. It seems that aerodynamicists know what to do, but trying to make a 

“silk purse out of a sow’s ear” does not satisfy the rotorcraft industry. Unlike retractable 

landing gear, the tradeoff of weight, complexity, and maintenance for drag reduction by 

fairing virtually all of the large frontal area hubs in Appendix D is not a serious consideration. 

I say virtually all because there are two hubs that have the lowest frontal area that need further 

discussion. These hubs are called simply doorhinge hubs. 

Fig. 2-167. The S-67 pylon and hub fairing. This aircraft achieved 192 knots in level 

flight in 1970 and held the speed record for 8 years. Note that no fairing of the 

blade root end (or shank) was incorporated. Note also that the S-61 bifilar 

vibration absorbers were not removed [382]. 

 

93 I say virtually devoid because the one exception I found [384] was wind tunnel testing by the Fuji Heavy 

Industries company in support of the Fuji Bearingless Rotor for the Kawasaki OH-1 armed observation 

helicopter, which first flew in August of 1996. The tunnel testing was conducted with 1/4-scale models using the 

Bell Model 412 hingeless hub as the baseline. 

Vibration 

absorbers 

Blade root end 

not faired 
2.5 FUEL EFFICIENCY 

310 

1

10

100

1,000 10,000 100,000

Takeoff Gross Weight (Lbs.)

YUH-61A

S-76

SA-365N

A-109

YUH-60A

OH-6A

CH-47C (Fwd rotor)

Main 

Rotor

Hub 

Parasite 

Drag 

Area (ft2

)

YR-4B

fe = 1.20 (GW / 1000)2/3

fe = 0.85 (GW / 1000)2/3

fe = 0.50 (GW / 1000)2/3

BO-105 

(w/fairing)

Fuji

FBR

S-67

Fig. 2-168. Harris hub drag perspective in 1998. 

2.5.4 The Doorhinge Rotor Hub 

 The doorhinge rotor hub was invented by Bob Metzger in the early 1960s. Bob was a 

key member of the Bell Helicopter engineering department. The configuration is shown in 

Fig. 2-169. Bob and Jan Drees received a patent (U.S. number 3,280,918) on October 25, 

1966. Bob Lynn notes in the 37th Cierva Memorial Lecture he delivered to the Royal 

Aeronautical Society in October 1996 [385] that “the airframe of this formidable 

configuration [the UH-1B Huey gunship] was later improved to the UH-1C model [in service 

September 1965] with the introduction of the ‘doorhinge rotor.’ The new rotor was needed for 

the higher gross weight required by the machines’ new role.” Bob Lynn adds in a footnote that 

“Robert Metzger, the inventor/developer of the [doorhinge rotor] system named the design 

‘doorhinge’ much to the chagrin of the marketing people, because that is where he got the idea 

of how to increase the rotor’s inplane stiffness.” The Bell doorhinge rotor hub, Fig. 2-169, 

was designed around the teetering rotor approach. 

 The doorhinge concept found another advocate rather quickly. The advocate was the 

Lockheed Corporation. In late 1965 the U.S. Army awarded a contract to Lockheed for an 

Advanced Aerial Fire Support System (the AAFSS). In winning the competition for an 

advanced gunship to replace the Bell AH-1 fleet, Lockheed applied the doorhinge concept to a 
2.5 FUEL EFFICIENCY 

311 

stiff inplane, hingeless rotor hub for its AH-56 (Fig. 2-170). This aircraft, named the 

Cheyenne by the U.S. Army,94 flew first in September 1967. The normal gross weight of the 

AH-56 was 18,300 pounds with a maximum takeoff weight of 25,880 pounds. It demonstrated 

215 knots in level flight and reached 245 knots in a dive. 

 The AH-56 was a very promising aircraft, but the program was cancelled. There is no 

better summary of Lockheed’s venture into rotorcraft than what Ray Prouty and Al Yackle 

published in 1992 [386]. Their paper is, in my opinion, a factual account written in a very 

straightforward manner. As they recount, the aircraft experienced control-system problems 

with its initial configuration. The problems were found and ultimately fixed, but not fast 

enough to satisfy the Department of Defense and the U.S. Army. Lockheed itself was 

experiencing problems in several other major program areas. The outcome was a new start by 

the U.S. Army that yielded the Hughes AH-64 Apache95 and ultimately, in 1995, the merger of 

the Lockheed Corporation with Martin Marietta. 

 As you can see from Fig. 2-171 and Fig. 2-172 (plus other details included in 

Appendix D), the Lockheed hub was simplicity itself—and it minimized the frontal area 

because of the doorhinge concept and the compact tension-torsion arrangement necessary for 

blade retention against centrifugal force. A gyro system was mounted above the rotor hub in 

the initial AH-56 configurations. The gyro added mechanical stability augmentation 

improvement to flying qualities. 

Fig. 2-169. The Bell doorhinge rotor hub was invented and developed by Robert 

Metzger, and patented in October 1966. It was an integral part of the Bell AH-1 

Cobra fleet (photo courtesy of Burkhard Domke via Troy Gaffey). 

 

94 The Lockheed AH-56 was not a pure helicopter. It was, in fact, a compound helicopter, which I will discuss in 

more detail in Volume III. 

95 There were several lessons learned during the AH-64 program that were recorded by Ken Amer, Ray Prouty 

et al. [387]. Ken notes that the paper was written in 1987, but the DOD delayed release until 1992. 
2.5 FUEL EFFICIENCY 

312 

Fig. 2-170. The AH-56 was a compound helicopter. The gyro above the hub created 

rotor control problems in the original design. A pusher propeller and wing were 

used for forward flight. The landing gear retracted aft (photo from author’s 

collection). 

Fig. 2-171. A revised control system called the Advanced Mechanical Control System left 

a spider on top of the hub and put the gyro below the transmission [386]. All 

control rods went up through the main rotor shaft (photo courtesy of Barry 

Lakinsmith, AFDD). 
2.5 FUEL EFFICIENCY 

313 

 As I come to the end of this discussion, and with Appendix D and Fig. 2-173 in front 

of me, I am convinced that the Lockheed stiff inplane, hingeless rotor evolved in the late 

1960s gets my vote as the winner. It deserves to be resurrected, improved with advanced 

materials, redesigned perhaps, built, wind tunnel tested, and for sure, flight tested. 

Fig. 2-172. The Lockheed hingeless hub as used on the AH-56. A control gyro was 

mounted on top of the hub for mechanical flight stability (courtesy of Bill Bousman). 

Fig. 2-173. Tom Hanson’s drawing of the Lockheed hingeless hub with the gyro system 

removed [361]. The pitch horn could easily be trailing as Fig. 2-171 shows. 
2.5 FUEL EFFICIENCY 

314 

2.5.5 Closing Remarks 

 This discussion of fuel efficiency, aircraft lift-to-drag ratio, and equivalent parasite 

drag area would be incomplete if two other points were not addressed more thoroughly. 

 First reconsider Fig. 2-146 on page 292 for a moment. There are a moderate number of 

data points showing equivalent parasite drag area as a function of a nominal gross weight. A 

few of the points were obtained by drag estimating methods. A few more have come from 

scale model testing in a wind tunnel, but the majority have come from flight test. Of course 

each point can be criticized if for nothing more than being associated with the wrong gross 

weight. Beyond that, time after time scale model testing has led to an optimistic result, and a 

drag buildup by calculations based on similarity has frequently been just as optimistic. 

Finally, an equivalent parasite drag area derived from flight test is just as suspect [388], which 

leads me to a key point. 

 The aircraft parasite drag area (fe) can be obtained from flight test. That is true. 

Consider the situation where the main rotor shaft has been instrumented to measure torque. 

Then, given the rotor speed, main rotor horsepower is immediately available. Now accept for 

the moment that Eq. (2.262) is correct. It is a simple matter to solve for the parasite drag area 

as 

(2.269) 

( ) ( )

2 3

t do 2

main hp hp

e

FP

RVC

550 RHP T v 1 3

8 f

qV

ρπ σ

−− + μ

= . 

The assumption here is that the induced power (Thpv) and the profile power (the last term in 

the numerator) can be calculated accurately. This assumption is not true for any point in 

Fig. 2-146. The reason I say this is that the ability to calculate nonuniform induced velocity 

was just being developed when the helicopters shown reached flight test. Furthermore, the 

industry did not begin to calculate profile power without the use of tabulated airfoil lift, drag, 

and pitching moment (i.e., CFD) in a comprehensive “code” until the beginning of this 

century. Of course each manufacturer’s engineering department had helicopter performance 

theories to correlate with measured data [389, 390]. But calculation of accurate, main rotor 

induced and profile power was, and still is, a semiempirical art guided by correction factors. 

 Now the second point. On the horizon one can see computational fluid dynamics 

(CFD) making considerable progress. In the first decade of the 21st century, computations of 

rotor blade airloads and improving blade response were demonstrated [391-393]. Then, with 

encouragement from John Berry’s 1997 report [394] on velocity measurements behind a 

model rotor hub, the industry began applying CFD to the hub drag problem [395-397].96 It is 

my hope that a doorhinge rotor along the lines of that shown in Fig. 2-173 will have its drag 

calculated with CFD in the not too distant future. 

 

96 Virtually no quantitative data can be gleaned from these reports. Apparently hub drag values are as guarded 

by industry as weight data. Frankly, I cannot imagine any reason for this secretive behavior given Fig. 2-164, 

Fig. 2-168, and Fig. 2-173. 
315 

2.6 VIBRATION 

Vibration, caused by rotating and reciprocating components in particular, has been a thorn in 

the side of inventors, engineers, and humans in general, since the dawn of time. The rotary 

wing world has most certainly not been immune to vibration problems. You will recall from 

the discussion of vibration in Volume I that Cierva wrote in his 1935 paper [398] that 

“perhaps the most irritating of the secondary difficulties met with in the autogiro developments 

have been those of a dynamical [vibration] nature.” 

This “most irritating” of problems carried over to helicopter development. The fall 2006 issue 

of Vertiflite97 included an article by Harry Moore [399]. He wrote about his recollections from 

the early days of flying the Sikorsky R-4 (Fig. 1-2) in 1945, the first production helicopter in 

the United States. He recalled that 

“the R-4 was a very demanding aircraft to fly cross-country. It cruised at about 60 miles 

per hour and carried only enough gasoline for about an hour and a half. In addition to 

the extremely limited range, it could not be trimmed up for cruising flight, but required 

constant hands-on attention at all times. The pilot had to hold constant pressure on the 

cyclic pitch stick to keep moving in the desired direction. It had no radio and the pilot 

had to stay below 700 feet above the ground if he wore no parachute. In addition to 

these inconveniences, the noise and vibration were fierce [my italics]. This all added 

up to pretty tough navigation. The R-4 was not your ideal cross-country aircraft. In 

spite of these shortcomings, every one of us loved to fly this demanding machine. It may 

have demanded full-time attention, but it gave a bountiful return in satisfaction to the 

pilot who mastered it. It was surely precision flying at its very best.” 

As Moore stated, the vibration was “fierce,” and this situation prompted action by the Wright 

Air Development Center (WADC) located at the then Wright-Patterson Air Force Base in 

Ohio. In 1954 they contracted with Eugene Liberatore (then employed by the Prewitt Aircraft 

Company) to prepare and edit an 18-volume series on rotorcraft. Volume 7 was a Vibration 

Handbook for Helicopters written by Bob Wagner, who later moved to Hiller Aircraft 

Corporation. This volume [400] has 149 references. There is not one aspect of helicopter 

vibration that aeromechanic engineers study today that is not touched on in this handbook. 

 From 1954 on, it seems that there has been a continuing series of meetings and articles 

that restate that helicopter vibration is a problem and ask what can be done about it. Many of 

these meetings and articles describe solutions that mitigate vibration somewhat. For example, 

in 1957 the Journal of the American Helicopter Society (AHS) [401] included the article titled 

How Can Helicopter Vibrations be Minimized? Contributors to this article all gave “their 

opinions on the current state of the art, on what can be done now to improve the situation, and 

on what remains to be done towards solving the helicopter vibration problem.” By 1963, 

when the Cornell Aeronautical Laboratory and the U.S. Army Transportation Research 

Command (TRECOM) sponsored a symposium about helicopter and V/STOL dynamics loads 

[402], the situation had not improved. 

 

97 The American Helicopter Society’s Vertiflite magazine is a marvelous addition to any engineering library. The 

diversity of articles is quite amazing because each issue—almost from inception—contains some fascinating 

history, and the technical data included in the history articles is of considerable value. 
2.6 VIBRATION 

316 

 Then, in February 1974, the AHS and NASA Ames Research Center convened a 

specialists’ meeting on rotorcraft dynamics [403]. This was a milestone meeting. The general 

chairman was Ted Carter (a rotorcraft statesman in his own right) from Sikorsky. The 

technical chairman was Bob Ormiston (still a powerful voice in the aeromechanics 

community). Ted closed his opening remarks with the following statement: 

“For the next two days we’ll be assessing the state of the art and our ability to handle each of 

these problems and on Friday we will have a chance to back off and overview the whole 

situation. Bob Ormiston’s paper [see pages 284 to 302] in this final session is, as far as I 

know, unique in the comparison it makes between all of our competitive methods addressed to 

a single problem. Finally, in the panel sessions, our ultimate customers, the designers and the 

service users will be given an opportunity to tell us what we’re doing wrong.” 

The presenters and attendees at this 1974 milestone meeting reaffirmed the fact that, despite 

our best efforts, helicopter vibration was still a problem, but for the first time the detailed 

scope of the vibration problem was laid out in a quantitative manner by a large group of 

experts.98 

 Seven years later, in November 1981, an AHS Specialists’ meeting was held in 

Hartford, Connecticut. The subject of that meeting was Helicopter Vibration. At that meeting, 

Dick Gabel from Boeing gave the keynote address [404], which he titled When Helicopter 

Smooth Surpasses Jet Smooth. Dick’s address covered the full spectrum of helicopter 

vibration with about 200 slides and was, in my opinion, absolutely outstanding. In particular, 

he described vibration mitigating devices in use by every member of the rotorcraft industry. 

 Three years later, Bob Loewy was given the honor of presenting the 4th Nikolsky 

Lecture at the 40th Annual Forum of the AHS. His lecture subject was Helicopter 

Vibrations—A Technology Perspective [405]. The last sentence of Dr. Loewy’s conclusions in 

1984 reads as follows: 

“As a problem of complexity and challenge, reducing helicopter vibrations still must be 

counted in the first rank. Great progress has been made as shown in fig. 48 and much still 

remains to be done, as shown in fig. 49 (both from Ref. 2). I believe the years ahead will show 

continued progress of this kind.” 

The two figures Bob refers to are included here as Fig. 2-174.99 Whether the industry fulfilled 

the projections he and Dick Gabel hoped for in the early 1980s is still to be determined. 

 

98 This 1974 meeting report [403] contained comments from the audience. At that meeting I was a rather obscure 

but outspoken aerodynamics attendee. It was a dynamics meeting, but my impression was that the real solution 

would come when airloads could be accurately predicted. In the meantime, I thought the experts in solving the 

F = ma problem should get the “ma” side of the equation right, which the meeting showed was not in great 

shape. It was not until the first decade of the 21st century that accurate prediction of blade airloads was obtain by 

a tenacious group of aeromechanic experts using computational fluid dynamics. The technical chairman of this 

quiet group, which held its 20th get-together in February 2011, is Bob Ormiston. 

99 It seems that Dick Gabel’s keynote address was not included in the meeting proceedings. Fortunately, Bob 

Lowey had a copy, which he was able to send to me. I forwarded it to several other researchers because it 

deserved to be resurrected. 
2.6 VIBRATION 

317 

Fig. 2-174. From When Helicopter Smooth Surpasses Jet Smooth [404] by Dick Gabel. 
2.6 VIBRATION 

318 

 Then, in May of 1993, the AHS Dynamics Committee agreed to support a workshop 

on rotor dynamics analysis. Groundwork was laid during the following year, and in May 1994 

the Workshop was ready to correlate vibratory hub load predictions from eight different codes 

with data measured on a Westland Lynx helicopter. Active participants from eight 

organizations worked steadily through until June 1996. At the AHS forum that year, Bob 

Hansford and John Vorwald presented [406] the group’s results. The summary conclusion 

was not very encouraging because the workshop concluded that 

“on average, codes are not able to predict vibratory loads to an accuracy any greater than 50% 

of the Lynx measured loads.” 

So now it is March 2011, and as I write this book, vibration of a new helicopter still cannot be 

predicted. Fortunately, absolutely no one has given up trying. Furthermore, as you will read 

shortly, computational fluid dynamics (CFD) tools are being used on the blade airloads with 

considerable success. 

 The preceding hop, skip, and jump through this introduction to vibration leads me to 

Fig. 2-175. Of course, this is a very simplified presentation of the helicopter vibration 

problem. I have left out all the interconnecting lines such as aircraft response effects, blade 

airloads, and the fact that vibrating pilots can make undesirable control inputs, which starts 

another feedback loop. Still, Fig. 2-175 is a useful guide to keep in mind during the following 

discussion. Let me start with the human aspects and work backwards to blade airloads, which 

have been the unsolved source of the helicopter vibration problem. 

Fig. 2-175. The path from airfoil airloads to human and structural complaints. 

Blade 

Airloads

Blade 

Vibratory 

Response 

Humans 

Occupant Complain 

Vibration 

& 

Structural 

Fatigue 

Hub 

Vibratory 

Loads 

Aircraft 

Response 

Parts 

Break 
2.6 VIBRATION 

319 

2.6.1 Occupant Vibration, Humans Complain 

 In my mind there is no question that a human is the most sensitive “sensor” shown in 

Fig. 2-175. He or she can quite quickly describe, with any number of adjectives, any vibratory 

experience. Unfortunately, engineers do not deal very well with adjectives as design criteria. 

Low-frequency vibration, on the order of 1 cycle per second, can cause seasickness. Highfrequency vibration, upwards of 60 cycles per second, can hurt eardrums, and vision begins to 

blur. When you think of a human (Fig. 2-176) as a relatively nonrigid structure comprised of 

90 to 95 percent liquid, the vibratory response seems more like a bowl of jelly with some 

lumps. Still, the desire to quantify human response to vibration has been, and continues to be, 

a fascinating subject for human factors researchers. One example of their work is the nearly 

1,000-page Handbook of Human Vibration compiled by Griffin [407], which contains about 

1,500 references. It would not be easy to compile that many references even dealing with all 

the other helicopter vibration aspects shown in Fig. 2-175! 

Fig. 2-176. A human is not an easy component to model with classical structural 

dynamics tools [408]. 
2.6 VIBRATION 

320 

 There does, however, seem to be a general consensus among human factors 

researchers that a human has a natural frequency. This frequency appears to be around five 

cycles per second when a seated person is shaken vertically. Human factors engineers 

immediately qualify this broad, generalized opinion with statements that hands, arms, feet, 

legs, eyeballs, head, etc., can respond at other frequencies. This group does associate five 

cycles per second with “whole body response” in their shake test experiments. In this sense, a 

human is like a seismic recording instrument, which is a well-known dynamics problem. 

 Consider a human sitting on a cushioned seat that is rigidly attached to a vibrating 

floor. This would mean that underneath the seat cushion shown in Fig. 2-176 is a metal seat 

with, say, four legs extending down to the floor where the human’s feet are resting. This metal 

seat has a back to support the seat-back cushion that, in turn, supports the human in an upright 

position. Imagine that the seat cushions are “comfortable.” A design criterion would be, of 

course, an attachment of the metal seat to the floor with crash attenuation components. To a 

helicopter engineer, this would seem to be a rigid floor-to-human connection that is quite 

solid. Suppose now that the floor (subscript F) where the seat is attached vibrates up and 

down according to 

(2.270) () ( ) Z Asin t Asin 2 f t FF F = ω= π . 

This would be a sinusoidal motion of amplitude (A) in feet and a floor forcing frequency (ωF) 

in radians per second. It is quite common to express the frequency in cycles per second, which 

is called hertz (Hz) and is denoted by (f).100 That is, ω = 2πf as shown in Eq. (2.270). 

 This displacement of the floor is not a realistic measurement. Instead, engineers today 

use accelerometers that measure the second derivative of the displacement, which can then be 

integrated to give displacement. An accelerometer can be mounted to the floor under the seat. 

The output of this sensor would be 

(2.271) ( )

2

F 2 2

2 F F FF

d Z A sin t Z

dt

= − ω ω = −ω

with units of feet-per-second squared. One integration of this acceleration would be velocity 

or 

(2.272) ( ) F

F F

dZ A cos t

dt

=ω ω

with units of feet per second. Another integration of acceleration gives the displacement 

described by Eq. (2.270). 

 To humans sitting in seats (say a pilot and a copilot), the preceding engineering is of 

absolutely no interest. In fact, this engineering design and analysis is not a reasonable 

approximation at all. To illustrate this, just think of riding up and down all day in an elevator. 

 

100 The term hertz was named after Heinrich Hertz. The name was established by the International Electrotechnical Commission in 1930. The General Conference on Weights and Measures replaced cycles per second 

(cps) with Hz in 1960. Thus, 5 cycles per second equals 5 Hz in modern notation. Furthermore, 5 Hz equals 

2π(5) or about 31.4 radians per second. 
2.6 VIBRATION 

321 

This is, admittedly, a very slow vibration. Without the display showing the floor number, you 

have no reference to displacement. Furthermore, it really is only when you decelerate to stop 

at a floor (or accelerate towards a different floor) that you have a sense of velocity, and this is 

really a change in velocity, which is acceleration. 

 Using adjectives, a human feels, thinks, and expresses his perception of the 

acceleration in a vibration environment. The human’s evaluation is not in relation to the 

quantitative floor displacement. There are, of course, exceptions. For example, you hear 

comments that during an earthquake, the “building swayed.” Another example occurs when a 

pilot says, “The instruments are a blur.” I doubt, however, that that would be how a pilot 

would describe what was being experienced overall. 

 Human factor researchers [407, 408] do have a structural dynamics model of a seated 

human. Most simplistically, a human is a lump of mass (weight/32.174) in slugs, connected to 

the floor by a spring of stiffness (k) in pounds per foot and a damper (c) in pounds per foot 

per second, as Fig. 2-177 suggests. With this model, the human’s whole body displacement 

(his center of gravity) relative to the floor (zb) is governed by the simple F = ma equation of 

(2.272) () ( )

2 2

2 b b F

2 2 b FF

d z dz d Z m c kz m m Asin t

dt dt dt

+ + =− = ω ω . 

When Eq. (2.272) is divided through by mass, you have 

(2.273) () ( )

2

2 b b

2 bF F

d z dz c k z Asin t

dt m dt m

+ + =ω ω , 

which has the solution for displacement of 

Fig. 2-177. An extremely simple representation of a human flying in a helicopter that 

has a vibrating floor. 

zb

•

Floor 

Human’s 

center of 

gravity 

( )

( )

F F

F

F F

2

F 2 2

2 F F FF

Z A sin( t)

dZ A cos t

dt

d Z A sin t Z

dt

= ω

=ω ω

= − ω ω = −ω
2.6 VIBRATION 

322 

(2.274) ( ) ( ) ( )

2

F F 2

b F 2 2 F 2 2 F

2 2

F F F F

k c

m m z A sin t cos t

kc kc

mm mm

                −ω ω     = ω   ω − ω

              −ω + ω −ω + ω

          

. 

The first derivative of displacement is velocity so 

(2.275) ( ) ( ) ( )

2

F F 3 b

F FF 22 22

2 2

FF FF

k c

dz m m A cos t sin t

dt kc kc

mm mm

                − ω   ω     = ω      ω + ω

              −ω + ω −ω + ω

          

and, most importantly, the acceleration is the second derivative of displacement so 

(2.276) ( ) ( )

2

2 F F

b 4

2 FF F 22 22

2 2

F F F F

k c

d z m m A sin t cos t

dt kc kc

mm mm

                − ω   ω     = −ω      ω − ω

              −ω + ω −ω + ω

          

. 

 It is very important to remember that what the human feels is the sum of the floor 

movement, the seat movement, and the seat cushion movement, and his or her response to the 

total components’ movements. This means that the total acceleration of the seated human is 

Eq. (2.271) plus Eq. (2.276). This body total acceleration can be expressed in units of gravity, 

so that 

(2.277) 

2 2

F b

2 2

d Z d z 1 Body total acceleration in g's dt dt 32.174

 

= +    

. 

 Given the preceding discussion, let me show you three examples. To begin with, the 

human’s whole body natural frequency is b ω = k m, which, in radians per second, is 2πfb. If 

the frequency (fb) is 5 Hz, which human factors engineers say is not unreasonable, you have 

( ) b ω= =π = k m 2 5 31.4radians per second. On page 380, Griffen’s Handbook [407] states 

that vibrating humans respond as if they have a critical damping ratio (c/cc) of about 0.475. 

This means that ( ) c cm 2 km cc = , which gives c/m = 29.8. Therefore, in Eqs. (2.273) to 

(2.276), k/m equals 987 and c/m = 29.8. 

 Now suppose three floor movements are examined as defined by the following table: 

Parameter Symbol Unit Case 1 Case 2 Case 3 

Floor F 

 Vibration Frequency f Hz 1 5 20 

 Vibration Frequency ωF rad/sec 6.28 31.4 125.6 

 Amplitude A ft 0.0814977 0.00325990 0.000203744 

Human b 

 Natural Frequency ωb rad/sec 31.4 31.4 31.4 

 Damping c/m 1/sec 29.8 29.8 29.8 
2.6 VIBRATION 

323 

Note for these three cases that as the frequency of the floor vibration increases, the floor 

displacement amplitude goes down. I have chosen these proportions to ensure that the 

maximum floor acceleration remains constant at ±0.1 g (i.e., 3.2174 ft/sec2

) for each case. 

One-tenth of a g vibration can be quite uncomfortable for a human to withstand. 

 The time history of vibration expressed as acceleration in units of gravity for the three 

cases are shown in Fig. 2-178, Fig. 2-179, and Fig. 2-180. Consider the lowest frequency 

vibration case first. The human feels that he (or she) hardly moves relative to the floor. All the 

floor vibration passes nearly directly to the body. Because the body is nearly synchronized 

with the floor, the total body maximum acceleration is only slightly greater than the floor’s 

maximum acceleration. The second case, Fig. 2-179, is a case where the floor is vibrating at 

the human’s natural frequency of 5 Hz. This is the classical case of resonance. Because the 

human body acts like it has damping (internal parts do not actually slosh around too much), 

the body’s acceleration relative to the floor is not amplified excessively. The maximum total 

body acceleration is greater than the floor’s maximum acceleration by a factor of slightly 

more than 0.04 g. That is, the amplification factor (the ratio of total body to floor maximum 

accelerations) is 0.145/0.1. Note that the total body waveform is not in phase with the floor 

waveform. The third case is with the floor vibrating at 20 Hz. Now the body-relative-to-floor 

waveform is nearly completely out of phase with the floor. As the floor goes down, the body 

goes up. The two accelerations nearly cancel. The results are that the maximum total body 

acceleration is much less than the maximum floor acceleration. The amplification factor is 

about 0.0254/0.1. The human feels like his (or her) body is only being shook by a very small 

floor movement, albeit a very fast movement—something like a buzz. 

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Accelerations 

(g)

Body relative 

to floor

Total body

Floor

Time (sec)

Fig. 2-178. The floor vibrates at 1 Hz with an amplitude of 0.5 g. 
2.6 VIBRATION 

324 

-0.16

-0.14

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

Accelerations 

(g)

Body relative 

to floor

Total body

Floor

Time (sec)

Fig. 2-179. The floor vibrates at 5 Hz with an amplitude of 0.5 g. This is a case of the 

floor moving at the natural frequency of the human, which is called resonance. 

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05

Accelerations 

(g)

Body relative 

to floor

Total body

Floor

Time (sec)

Fig. 2-180. The floor vibrates at 20 Hz with an amplitude of 0.5 g. 
2.6 VIBRATION 

325 

 The preceding three cases are points along the maximum acceleration curve shown in 

Fig. 2-181. Keep in mind that at all floor vibration frequencies, the acceleration of the floor is 

given as 

(2.278) ( )()

2

F

2 F

d Z 0.10g sin t dt

=− ω . 

Note that Fig. 2-181 can be used as an amplification curve for a human for any value of 

maximum floor/seat acceleration simply by multiplying the vertical scale by 10 and then 

multiplying by the different chosen floor acceleration. Furthermore, the maximum total body 

acceleration for floor vibration frequencies beyond 20 Hz is approximated as 

(2.279) 2 2 4 F

b F F

2 2 2 2

max 2

F

c

d z dZ A m in g 's dt dt 32.174 k c

m m

        ω   ω     + =±

        −ω + ω     

. 

 It is worth remembering that vibration at 20 Hz is near the bottom of human hearing. 

An 88-key piano plays a frequency of about 27 Hz when struck on the lowest key. The highest 

key broadcasts at just under 4,200 Hz when struck. Of course, many people have “felt” 

thumps on the chest from loud notes coming from large drums. 

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Maximum

Total Body

Acceleration 

(± g)

Floor Vibration Frequency (f in Hz)

Fig. 2-181. A human feels that the floor vibration is the worst when the floor/seat 

vibrates at about 4.5 Hz (computed with a maximum floor acceleration of ±0.1 g 

at all frequencies). 
2.6 VIBRATION 

326 

 With this background, the question immediately arises as to just how much vibration a 

human can tolerate. (Keep in mind that tolerating is a far cry from accepting and that 

accepting is a further cry from not perceiving.) This is the key question that needs to be 

answered by all engineers creating products used by humans. Unfortunately, despite such 

reference material as Griffen’s Handbook [407], the design criteria are hardly definitive 

(perhaps that is a little too harsh, considering the complexity of a human and the diverse 

experiments that Griffen examines). That is not to say that helicopter design criteria for 

vibration limits are not available, re-examined, and proposed in the literature; however, there 

is an abundance of diverse opinions. 

 The rotorcraft industry has depended on military specifications for acceptable 

helicopter vibration boundaries. These specifications have depended, in turn, on the 

International Organization for Standardization (ISO),101 and specifically on ISO 2631, Guide 

for the Evaluation of Human Exposure to Whole-Body Vibration. Of course, particular 

countries still do some tailoring to serve their individual needs. In 1978, the ISO had decided 

on and published vibration criteria or boundaries at which human proficiency was decreased. 

The group quantified the boundaries in terms of acceleration in meters-per-second squared 

versus the time the vibration was endured, and they chose the frequency range of 4 to 8 Hz as 

the normalizing reference for a family of curves. Their collective view of this normalizing 

reference is shown here as Table 2-28. 

 The then current view was that vibration below 4 Hz and above 8 Hz would differ 

from the reference according to three simple equations. That is, from 4 to 1 Hz, the vibration 

tolerance would increase as K2f = . Over the frequency range from 4 to 8 Hz, K = 1, and 

for f = 8 to 80 Hz, K f8 = . Thus, the allowable (if you will) vertical vibration in units of g 

appears as shown in Fig. 2-182. Note that this figure gives three straight line segments 

because it is graphed in a log-log axis system. In a linear axis system, the 1978 ISO 2631 

appears as Fig. 2-183, which I think is more useful for this discussion.102 

 Be aware that similar logic has created similar criteria for lateral and longitudinal 

vibration. Furthermore, Griffen discusses the situation for individual parts of the body. His 

Handbook is very careful to point out that the actual situation, based on work as late as 1990, 

is far from hard lines on a graph. All humans are not the same, and tests have only been 

conducted with a very small sample of them. 

Table 2-28. Reference Acceleration for Degraded Proficiency for Vertical 

Vibrations in the Frequency Range of 4 to 8 Hz 

Time 24 hr 16 hr 8 hr 4 hr 2.5 hr 1 hr 25 min 16 min 1 min 

Acceleration (m/sec2) 0.14 0.212 0.315 0.53 0.71 1.18 1.8 2.12 2.8 

Vertical g's 0.0143 0.0216 0.0321 0.0540 0.0724 0.1203 0.1835 0.2162 0.2855

 

101 The ISO came into being through a succession of meetings that began in 1945. By April 1947 a constitution 

was hammered out and ratified by over 15 interested bodies from many countries. 

102 Griffen devotes chapter 10 to a number of vibration standards, only one of which is ISO 2631 and its growth 

from 1978 to the modern era. 
2.6 VIBRATION 

327 

0.01

0.1

1

1 10 100

24 hours

1 hour

2.5 hours

4 hours

8 hours

16 hours

25 minutes

1 minute

16 minutes

Floor Vibration Frequency (f in Hz)

Acceleration

(± g)

Fig. 2-182. Human proficiency is reduced after exposure to vertical floor vibration at 

varying accelerations and time (log-log axis). 

0

0.03

0.06

0.09

0.12

0.15

0.18

0.21

0.24

0.27

0.3

0.33

0.36

0.39

0.42

0.45

0 2 4 6 8 10 12 14 16 18 20

25 minutes

1 hour

2.5 hours

4 hours

Acceleration

(± g)

Floor Vibration Frequency (f in Hz)

MIL-H-8501A

Fig. 2-183. Human proficiency is reduced after exposure to vertical floor vibration at 

varying accelerations and time (linear axis). 
2.6 VIBRATION 

328 

 The United States military created MIL-H-8501 for helicopters in November 1952 

[409]. Shortly thereafter (September 1961) this original specification was revised to MIL-H8501A [410], which states in part in paragraph 3.7, Vibration characteristics, that 

“1. Vibration accelerations at all controls in any direction shall not exceed 0.4 g for 

frequencies up to 32 cycles per second. 

2. Vibration accelerations at the pilot, crew, passenger, and litter stations at all speeds between 

30 knots rearward and Vcruise shall not exceed 0.15 g for frequencies up to 32 cycles per 

second. From Vcruise to Vmax the maximum vibratory accelerations shall not exceed 0.2 g 

up to 36 cycles per second. 

3. Vibration characteristics at the pilot, crew, passenger, and litter stations shall not exceed 

0.3 g up to 44 cycles per second during slow and rapid linear accelerations or deceleration 

from any speed to any other speed within the flight envelope.” 

You might note in passing that Dick Gabel’s upper graph in Fig. 2-174 shows that the revised 

8501A raised acceptable vibration from 0.10 to 0.15 g for paragraph (2). A hint that the 

upward revised allowable vibration was a step in the wrong direction came in November of 

1970. In that year, Dick Gabel and two coauthors presented a paper [411] at a symposium 

dealing with environmental effects on VTOL designs. Their second conclusion is of particular 

importance because they wrote: 

“(2) The multi-harmonic nature of helicopter vibration presents a special problem. In any 

given situation, the levels at each of the component rotor harmonics can be well within 

acceptable limits and still combine to produce an unacceptable comfort level. Since the 

frequencies are harmonic, both the amplitude and phase are important and it becomes 

extremely difficult to identify the offending frequency or combination of frequencies. It is 

recommended, therefore, that comfort criteria for a generalized multi-axis, multi-frequency 

environment be developed for helicopter applications. Since the sensitivity of the hands and 

feet differ from the remainder of the body, criteria for independent stimulation of the hands 

and feet are required in addition to whole body vibration in the seated position. Modifying 

effects of noise, temperature, and humidity should also be considered.” 

 In 1977, Dan Schrage (then a Captain in the U.S. Army) presented a paper [412] that 

showed the industry’s problems with vibration on two major U.S. Army development 

programs (the UTTAS leading to the UH-60 and the AAH leading to the AH-64). The four 

helicopter companies (Bell, Boeing, Hughes, and Sikorsky) were unable to meet the Army’s 

low-vibration requirements and, furthermore, the requirements left something to be desired as 

well. A few years later, at the 37th Annual Forum of the AHS held in May 1981, Dave Kidd of 

Bell Helicopter presented an exceptionally clear story leading to an assessment of helicopter 

vibration criteria. His paper is well worth your reading time because he traces work on human 

vibration comfort criteria from 1931 up to 1981 and deals directly with words like acceptable 

and unacceptable. Finally, in March 1992, Ray Prouty (in his invaluable, clarifying style) 

wrote a 1-1/2-page article [413] for Rotor & Wing magazine that we layman could grasp. He 

illustrated his article with a figure similar to Fig. 2-183. 

 By 2006, Sam Crews (Chief of the Aeromechanics Division at the U.S. Army Aviation 

Engineering Directorate) had compiled enough knowledge to introduce a new vibration 

criteria tailored to rotorcraft. This military requirement for rotorcraft vibration specifications, 

modeling, and testing was published as an Aeronautical Design Standard [414] known as 
2.6 VIBRATION 

329 

ADS-27A-SP.103 This ADS deserves your attention because many of the issues raised by 

industry, including Dick Gabel’s second conclusion quoted previously, were addressed. 

 Let me conclude this discussion about humans with a few comments about the 

helicopters that the humans are flying in. This is, as you will see, the unfortunate side of the 

human-helicopter interface. Turn your attention to Fig. 2-184. In this figure I have shown the 

fundamental forcing frequency of many helicopters. This fundamental frequency is the onceper-revolution (1/rev) frequency computed as V Rt f

2 = π

 in Hz, where (Vt) is the rotor tip 

speed in feet per second and (R) is rotor radius in feet. The main rotors of a large number of 

helicopters fall in the 4- to 8-Hz range that ISO 2631 singles out as its reference range (as 

Fig. 2-183 shows). This immediately raises the point that if the main rotor is out of balance, or 

the blades are out of track, a 1/rev frequency will be passed from the main rotor hub to the 

airframe floor, and then to the seated human, and the human (let’s say the pilot) will 

complain. This facet of vibration was discussed in detail in Volume I. Fortunately, both the 

manufacturer and mechanics in the field can exercise considerable control of main rotor track 

and balance, which generally keeps this source of vibration well below 0.05 g. 

 On the other hand, as you learned from Volume I, main rotors pass vibration at blade 

number (b) times the fundamental 1/rev frequency, which is to say b(1/rev). Furthermore, 

main rotors pass vibration at twice the blade number times the fundamental 1/rev, which 

amounts to n[b(1/rev)] where n goes up as 1, 2, 3, 4, etc. To illustrate, Fig. 2-184 shows the 

widely used Sikorsky S-70, known as the UH-60 Black Hawk by the U.S. Army. Because it 

has four blades, the main rotor passes significant vibration at 4 times 4.3 Hz equals 17.2 Hz. 

According to ISO 2361 and MIL-H-8501A per Fig. 2-183, the pilots and passengers should 

remain proficient for 2.5 hours if the vibration at 17.2 Hz is no higher than ±0.15 g. This is a 

big if that I will address shortly. 

 Tail rotors can also be a source of vibration for single rotor helicopters. Take the 

Sikorsky UH-60 for example. It has a tail rotor that has a fundamental 1/rev frequency (see 

Fig. 2-185) of just under 20 Hz. This means that vibration caused by an unbalanced tail rotor 

might be mistaken (or added to or subtracted from) the main rotor 4/rev vibration, which is at 

17.2 Hz. 

 With the preceding background, you should be able to read and appreciate a recent 

AHS Journal paper [416]. This outstanding paper was devoted to the structural dynamics of 

helicopter seats and how vibration can be mitigated for the pilot and copilot. The research 

program was supported by the Canadian military and the Canadian National Research 

Council. The test helicopter used in the research was a Bell Model 412, which is the Canadian 

military Model CH-146. The pilot and copilot were instrumented at their helmets, shoulders, 

and thighs. Additional accelerometers were mounted on the seat frames, seat cushions, 

 

103 The U.S. Army’s intentions were conveyed to the rotorcraft industry by Sam at the 1981 AHS National 

Specialists’ Meeting on Helicopter Vibration in Hartford, Connecticut. In that paper [415], an intrusion index 

was suggested, which came to pass in ADS-27A-SP. Explaining the intrusion index, however, is beyond the 

intent of this volume. 
2.6 VIBRATION 

330 

0

2

4

6

8

10

12

0 20 40 60 80 100 120

Human's most 

sensitive frequency 

range per ISO 2631

Main Rotor Diameter (ft)

Main Rotor 

Once per Rev 

Frequency

(Hz) Sikorsky 

UH-60

Fig. 2-184. Many helicopters have their fundamental 1/rev frequency in the range where 

humans are most sensitive to vibration. 

0

10

20

30

40

50

60

0 1 2 3 4 5 6 7 8 9 10

Main Rotor Fundamental 1/rev Frequency (Hz)

Sikorsky 

UH-60

Tail Rotor 

Fundamental 

1/rev 

Frequency 

(Hz)

Fig. 2-185. Unbalanced and out-of-track tail rotors can cause vibration at their 

1/rev frequencies. 
2.6 VIBRATION 

331 

seat bases, and on the floor rails. Interestingly, the authors found that “the original in-service 

seat cushion provided effective vibration isolation at high frequencies, but the low-frequency 

vibration at 1/rev was amplified by the seat.” In laboratory tests with a mannequin, they 

showed that by using active seat-to-floor rails struts, the vibration levels could be virtually cut 

in half, which was considerably better than results obtained with nine different types of seat 

cushions. This AHS Journal paper is well worth your reading time. Finally, if you are an 

aircraft engineer you will appreciate the fact that, with Table 2-28 and Fig. 2-182, the human 

factors researchers have created a curve of allowable stress versus number of cycles (i.e., an 

S-N curve) for humans. The stress is measured in units of gravity, and the number of cycles is 

frequency (cycles per second or hertz) times time. Suppose from Table 2-28 or 

Fig. 2-182 you choose the lowest g level within the frequency range of 4 to 8 Hz, and then 

you choose the maximum human whole body response frequency of 4.5 Hz from Fig. 2-181. 

These choices let you create a “human structural fatigue S-N curve,” which I have done with 

Fig. 2-186. Note that a log scale is used for the x-axis (number of cycles). 

 A human’s proficiency is reduced when he or she is vibrated at accelerations above 

the line shown in Fig. 2-186. It appears that the vintage 1978 ISO 2631 criteria may be 

somewhat in doubt for cycles below the 16-minute point because of the rather sharp break 

leading from the 16-minute point to the 1-minute point. The inference is that below the line a 

human is more tolerant of the vibration. However, given the small sample of humans reflected 

in the data leading to the ISO 2631 criteria of 1978, you should imagine that the line shown 

on Fig. 2-186 is probably the centerline of a broad band of scattered data. 

0

0.03

0.06

0.09

0.12

0.15

0.18

0.21

0.24

0.27

0.3

100 1,000 10,000 100,000 1,000,000

Number of Cycles

Acceleration

(± g)

1 min.

8 hr.

4 hr.

2.5 hr.

1 hr.

25 min.

16 min.

24 hr. 16 hr.

Human Proficiency is 

Reduced Above This 

Line 

Fig. 2-186. An S-N curve for a human (vibration at 4.5 Hz). 
2.6 VIBRATION 

332 

2.6.2 Structural Fatigue, Parts Break104 

 Besides humans, vibration affects every part in a helicopter, and just consider how 

many parts there are in a modern helicopter such as the Sikorsky UH-60 shown in Fig. 2-187. 

It is absolutely necessary to make calculations and perform tests to establish how many cycles 

any part can absorb before the part breaks due to fatigue. Of course, design experience can be 

used for many of the parts, but there is no question that bench fatigue tests must be completed 

at the subassembly and assembly level before production begins. 

 Experimental data about material fatigue strength has been accumulating at least since 

the King of England’s coach springs kept failing. Now, after several centuries, a sufficient 

amount of data has been collected in several U.S. Department of Defense (DoD) handbooks 

[417-422] so that a designer has at least a starting point for material selection. The metals 

handbook [417] gives an explanatory example of fatigue stress versus number of cycles for a 

representative test specimen, which I have include here as Fig. 2-188. There are 50 such 

figures associated with steel alone in the 1,700-page handbook. 

 As you look at Fig. 2-188, you can see that the general trend of any one line is the 

lower the stress, the greater the number of cycles that the material can sustain before failure. 

Notice also that a log scale is used for the fatigue life, but not for the maximum stress. 

Fig. 2-187. Cutaway artist’s rendition of the Sikorsky UH-60 

(courtesy of Flight International Inc.). 

 

104 In my mind, all you can do with a part is cut it in two—or attach it to another part. By this standard, a nut and 

a bolt are two parts. When the nut is screwed onto a bolt, you have a subassembly. When a large group of 

subassemblies are put together, you have an assembly. A rotor system is an assembly to me. A large group of 

assemblies—when put together—gives you a flyable helicopter. In my experience, nothing beats a drawing tree, 

a parts list, and exploded view assembly drawings to understand a helicopter. In short, an aircraft needs to be 

understood at the part level. 
2.6 VIBRATION 

333 

Furthermore, very few of the test results in this example show data much beyond 10-million 

(107 ) cycles. The authors of MIL-HDBK-5J used data from their figure 2.3.1.2.8 (d) to create 

this presentation example, which happens to be for steel. The property of steel is such that no 

damage is found in practice for millions more cycles if the stress is below the endurance limit. 

This is called a runout and is shown on the graphs for steel with the little arrows attached to 

data points at the end of each line. (Aluminum does not exhibit this characteristic.) Notice in 

the box on Fig. 2-188 that all figures in the metals handbook include a description of the 

material (i.e., Material = A), which is 4130 steel in this example. The importance of notches in 

the test specimen is given as Kt, which can vary from Kt = 1 for no notch, up to at least 4. 

Imperfections such as notches create concentrated stresses and thus reduce fatigue strength. 

For this example, Kt = 4. The type of notch is also important, and this is defined by a few 

words in each box. Finally, the test material can be loaded by both a mean and an alternating 

force. This information is conveyed by either a value of mean stress or a stress ratio, because 

the specimen load is applied such that 

(2.279) ( ) S S S sin t (t) mean alternating =+ ω

where the time varying stress (S(t)) is defined by a mean stress (Smean) and a sinusoidal 

component of amplitude (Salternating). For the example case, it so happens that Level 1 equals a 

mean stress of 0 pounds per square inch (psi), Level 2 = 10,000 psi, Level 3 = 20,000 psi, and 

Level 4 = 30,000 psi. When the loading condition is defined by a stress ratio (SR), the 

Fig. 2-188. An S-N curve for a structural material. 
2.6 VIBRATION 

334 

handbook means 

(2.280) min

max

S SR

S

=

from which it follows that if SR = –1, the mean must be zero and the fatigue stress is simply 

Salternating. Obviously you can calculate backwards to find the mean and the alternating stresses 

given Smax and SR. 

 An important aspect of fatigue is that as the mean stress is increased, the material can 

withstand less alternating stress. To illustrate this point, imagine a part is to have a life of 105

cycles. Reading from Fig. 2-188, you have the following table: 

Mean Stress (psi) Maximum Stress (psi) Alternating Stress (psi) 

0 27,000 27,000 

10,000 34,000 24,000 

20,000 41,000 21,000 

30,000 49,000 19,000 

One example of this fatigue aspect is illustrated in the design of a rotor blade spar. This part 

has a mean load created by centrifugal force and an alternating bending moment created by 

airloads. 

 MIL-HDBK-5J makes an effort to collapse the data in Fig. 2-188 to a single line using 

an empirical formula of the form 

(2.281) ( )n

S S 1 SR eq max = − . 

The presentation example, Fig. 2-189, shows one of the better “consolidations” with n = 0.63 

in this case. Note that when the mean stress is zero (i.e., SR = –1 and Smax = Salternating), then 

the alternating stress is simply 

(2.282) eq

alternating

S

S

1.547

= . 

With this approach you see that the endurance limit for this notched specimen is on the order 

of Seq = 22,000 pounds per square inch, which means an endurance limit of about 14,000 

pounds per square inch. 

 The influence of a notch (which represents deliberate damage to a part) is serious 

because a designer must make some allowance for both manufacturing defects and field 

damage. Fatigue limits for an unnotched test specimen are shown in Fig. 2-190. This figure is 

directly comparable to Fig. 2-188. With no notch (Kt = 1.0), this steel alloy has an endurance 

limit of about 45,000 pounds per square inch if the mean stress is zero, which is more than 

three times the endurance limit of the notched specimen (Kt = 4.0) if the mean stress is zero. 

The prudent designer of a rotor blade spar made with 4130 alloy sheet (0.075-inch-thick) steel 

must “knock down” the design stress from 45,000 pounds per square inch to some lower 

value. The question has always been how much of a knock down factor should he (or she) 

use. In practice, a fatigue test would be conducted with several manufactured spars. 
2.6 VIBRATION 

335 

Fig. 2-189. An Seq-N curve for a structural material. 

Fig. 2-190. An S-N curve for a notch-free structural material. 
2.6 VIBRATION 

336 

 Appendix E contains a useful reminder about metal fatigue that crossed my desk in 

1974. I’ve referred to that article throughout my career whenever some helicopter part became 

a problem. 

 Perhaps a little more background about fatigue stresses and cycles to failure would be 

of interest. 

 A simple example about structural fatigue is a ground-air-ground cycle. Imagine that a 

military helicopter flies 600 hours a year, or a commercial helicopter flies 1,200 hour a year. 

Imagine that a typical mission is 1 hour from start to finish. That would be 600 to 1,200 

cycles per year acting on the landing gear. Whether retractable or fixed, one might expect the 

landing gear to last 30 years with minimum maintenance. That amounts to 18,000 to 36,000 

cycles.105 As another example, think of the axles and wheels and other associated parts of a 

car. If driven at 50 miles per hour for 100,000 miles, a car accumulates about 2,000 hours. 

Who knows how many cycles the springs and shock absorbers experience in 2,000 hours? But 

then think about the car’s engine turning at 2,000 revolutions per minute (i.e., about 33 Hz) at 

50 miles per hour for 100,000 miles or 2,000 hours. That means that the engine crankshaft 

accumulates 240,000,000 or 2.4×108

 cycles. An even more astounding example is the human 

heart. At a pulse rate of 60 beats per minute (1 Hz), the heart has accumulated 2.4×109

 cycles 

after 75 years. That is 10 times the life of a car engine! 

 This brings me to the subject of materials used in aircraft. The primary question, of 

course, is how many cycles can various materials such as wood, metals, and modern 

composites absorb before they break due to an alternating load. It is well known that early 

airplanes were constructed primarily of wood frames. Furthermore, George Rosen’s book 

[288] about the history of propellers describes many early wooden propellers including those 

for sale in 1910 (Fig. 2-191). According to Rosen, “The typical service life of a wooden 

propeller generally lasted no more than six months.” These early aircraft were, however, 

powered by the internal combustion engine, which the aviation pioneers borrowed from the 

budding auto industry that was rapidly encountering part failures due to metal fatigue. 

 The move to propellers made of sheet steel riveted along the edges was disappointing, 

to say the least. Caldwell [423] shows 7 figures of early efforts where the metal propellers ran 

5 minutes or less, at about 1,440 revolutions per minute, before destruction. Rosen notes that 

by the fall of 1921, Dr. Sylvanus Albert Reed had developed and successfully flight tested the 

forged duralumin (aluminum plus copper) two-bladed propellers. Reed’s success earned him 

instant fame in the aviation world and the Collier Trophy. 

 With the addition of variable pitch, the thin-tipped propeller (with any number of 

blades) that we know today came into its own. Then, as you learned in Volume I, Cierva 

developed rotor blades using a round, steel tube spar with a built-up set of ribs to achieve the 

 

105 It is more likely that a landing gear would be designed for crash landing rather than fatigue. However, you 

will remember that the British de Havilland Comet lost several commercial jets in 1954. The losses were caused 

by metal fatigue due to repeated pressurization and depressurization of the aircraft cabin. 
2.6 VIBRATION 

337 

Fig. 2-191. The first U.S. propeller manufacturer ran this ad in a 1910 issue of 

Aircraft magazine [288]. 

rotary wing. These vintage, 1930’s rotor blades had a service life of 75 hours on the Cierva 

C.30 Autogiro. The C.30 37-foot-diameter rotor operated at a nominal tip speed of 370 feet 

per second. This is a 1/rev frequency of 3.18 Hz, so 75 hours amounts to about 860,000 

cycles, slightly under 1 million or 106

 cycles. 

 World War I saw the beginning of the end of wooden airframes and the start of 

widespread use of aluminum and steel tubes and sheets. As Nelson notes in his introduction to 

his report about wooden beams used for the main structure of airplane wings [424]: 

 “The present war [WWI] has caused an unprecedented demand for selected spruce 

for airplane construction. The increased demand has necessarily caused a greatly increased 

output. However, the magnitude of the requirements and methods of construction, whereby a 

large part of the selected stock is wasted in the construction of the one-piece beams, makes 

the problem of furnishing sufficient selected stock a very serious one, even with the enlarged 

output. 

 The remedy for this condition lies either in the discovery of a perfectly satisfactory 

substitute for the spruce now used, or in the development of some method of construction 

which will conserve the present supply by utilizing more of the selected material.” 
2.6 VIBRATION 

338 

 By 1931, rather thorough experiments and analyses [425] were showing that 

aluminum and steel were viable candidates for fuselage tubular structures, about which a 

doped canvas skin could be attached. With the coming of World War II, the need for a 

substitute for wood became even more acute. This accelerated the transition from wood to 

metal; this story is well told by Eric Schatzberg [426]. Then a landmark paper establishing 

Miner’s Law for fatigue was published in September 1945. Milton Miner, a structural test 

engineer at the Douglas Aircraft Company, titled his paper Cumulative Damage in Fatigue

[427]. While modern studies have questioned some of Miner’s assumption, his “law” has been 

(and continues to be) applied to fatigue damage of many aircraft parts subjected to alternating 

loads of several magnitudes. 

 In 1950, a paper [428] was published in the Journal of the Helicopter Association of 

Great Britain.106 The paper was titled Materials and the Fatigue Aspect and presented by a 

Mr. W. E. Cooper. Mr. Cooper primarily addressed rotor systems after writing “that fuselages, 

engines and transmissions could be designed and built by established procedures.” He 

provides a very interesting table, which I have reproduced here as Table 2-29. This table 

refers first to U.T.S., which stands for ultimate tensile strength. Endurance limit refers to a 

level of vibratory stress at which the material will not be damaged with no less than the 

number of cycles listed. In fact, some materials behave as if the part will never break if the 

alternating stress never exceeds the endurance limit. This behavior is referred to as a run-out. 

The unit of tons is (I believe) a long ton, which is 2,240 pounds, not the 2,000 pounds per ton 

Table 2-29. A 1950’s View of Material Fatigue Endurance Limits

 

106 Spurred on by the founding of the American Helicopter Society in 1943, a similar body was founded in Great 

Britain. The champions were members of the Royal Air Force who met on July 10, 1945. In September of 

that year, Memorandum and Articles of the Association were signed. The first annual general meeting was held 

on March 23, 1946, and 54 members were elected. The Association’s Journal was published quarterly and 

Volume 1, Number 1, came out in September 1947. In January 1960, the Association merged with the Royal 

Aeronautical Society and became the Rotorcraft Section of the Society. There is a wealth of historically 

significant data in the Association’s Journals. 
2.6 VIBRATION 

339 

used in the United States today. Thus, the 42 long tons per square inch equates to about 

94,000 pounds per square inch. There are only a few modern steel alloys offered by MILHDBK-5J [417] that achieve this high of an endurance limit with the mean stress equal to 

zero. You will note from Volume I that Cierva used the highest strength steel listed in 

Table 2-29. 

 Because commercial autogyros and helicopters were being used in several countries 

by the early 1950s, the subject of airworthiness became a serious topic. The British Air 

Ministry created the Air Registration Board in 1936, and in 1951, Mr. J. K. Williams, a 

member of that Board, offered the Helicopter Association his views about certification 

requirements for a helicopter. He titled his paper, The Fatigue Problem With Emphasis on the 

Airworthiness Aspects [429]. In his opening remarks, Williams notes that “the designers of 

civil aeroplanes contemplate that their aircraft may be in service for at least 10,000 hours or 

so.” Then he sympathizes with helicopter designers because “when so little is still known 

about the fundamental nature of the fatigue of materials and the extreme difficulty of 

ascertaining the effect of varying external loads on a structure, the helicopter designer is 

presented with the problem of fatigue at his doorstep even at this comparatively early stage in 

helicopter development.” Nevertheless, Williams insists that “the principle must be 

established that having determined the range of stresses under all possible ground and flight 

conditions, then the service life of each critical component should be so determined as to 

ensure continuous safe operation—the service life being well below the fatigue life—of the 

component.”107 Then, after commenting on fatigue testing and explaining the concept of 

cumulative damage theory (later to become Miner’s law), Williams suggests that 

“very little research work has been carried out to date to substantiate the damage rule and 

what work has been carried out seems to indicate that the application of a number of stress 

cycles above the endurance limit lowers the life of the specimen under subsequent 

applications of a lower stress. In addition, if a number of stress cycles below the endurance 

limit is applied then the fatigue life under subsequent applications of a higher stress is 

improved. 

 Stated simply this means that the fatigue limit can be lowered by overstressing and 

raised by understressing which belies the cumulative damage rule. All these disadvantages to 

the application of the cumulative damage rule can be compensated to some extent by: 

(a) Carrying out tests on at least six specimens of each component to cover the 

scatter effect. 

(b) Introducing a multiplying factor for the magnitude of the stress cycle and this it 

is suggested should be (1.3). 

(c) Introducing a reduction factor to the fatigue life obtained on test in order to 

determine the service life. This reduction factor it is suggested should be (0.5). 

The component is to be removed from service and replaced by a new component at the 

expiration of the service life. It is suggested that the service life as obtained by the above 

method should not exceed two to three thousand hours, especially for rotor blade components. 

 

107 It continually amazes me when I see the word “all” or the words “all possible” in specifications, regulations, 

and requests for proposals. The size of “all” is absolutely mind-boggling to me; so much so that I equate “all” 

with infinity. A work statement for “all” cannot be written nor can the cost of “all” be estimated. Of course, a 

schedule for “all” cannot be laid out. In my opinion, “all” is a very dangerous word. 
2.6 VIBRATION 

340 

 If the results of the laboratory tests indicate that the most critical factored stress 

cycles are all below the endurance limit of the component, then the component should still be 

replaced at a nominally agreed period and this period it is suggested should be in the region of 

four thousand hours.” 

 Williams concludes with two key statements: 

 “Finally all that has been mentioned in this paper to date leads to the inevitable 

conclusion that for the reduction of the possibility of fatigue failure to a minimum in 

helicopters there must be: 

 First class design of component parts with special emphasis on the elimination of 

high stress concentrations which can have such a calamitous effect on the fatigue endurance 

of a structural component. These stress concentrations can be induced in various ways. 

(1) By design—Sharp angles, changes of section (re-entrant angles), screw threads. 

(2) Machine shop—Rough turning, accidental tool marks on the surface. Grinding 

cracks. Identification and inspection stamp marks. 

(3) Fabrication—Slag blowholes and cracks in welded construction. Press fits and 

shrink fits. 

(4) Heat treatment—Cracks due to hardening stresses. 

(5) Manufacture of material—Importance of surface finishing (use of shot peening 

process) because practically all fatigue failures originate at the surface. 

In addition, the workmanship and standards of maintenance and inspection on these 

components have to be of a very high order indeed. Lately we have come to realize that the 

design, manufacture and inspection of these vital component parts of the helicopter, the 

failure of anyone of which in flight may have such unfortunate consequences, must be of a 

standard even higher than that for aircraft engines. That is to say, much higher than the 

standards for the design and manufacture of fixed wing aircraft. This may yet prove to be the 

most important of all the preventatives of fatigue failure on helicopters.” 

 The helicopter industry took these 1951 airworthiness requirements to heart as it grew 

to the industry we know today. Understanding fatigue and how to avoid the pitfalls Williams 

enumerated (plus many others) has been a number-one priority of stress men, load calculating 

engineers, designers, builders, and operators, and caution has been a byword as new materials 

such as titanium and fiberglass have been introduced. 

 By 1951, the budding helicopter industry was experiencing a growing number of 

unexplained rotor blade fatigue failures. At that time, blade structural design technology was 

only able to estimate blade bending frequencies and mode shapes. Calculating actual bending 

moments and stresses was hardly attempted. The technology situation had, in fact, hardly 

improved from the autogyro era. The thought was that at and near operating rotor speed, the 

calculated natural frequencies of the vibrating beam (i.e., a rotor blade) should not be close to 

integers of rotor speed. (You learned about this aspect of blade design in Volume I, pages 139 

to 191, in relation to autogyros.) At that time, little attention was given to bending modes 

above the second flapwise mode, but with the number of blade fatigue failures growing, the 

Air Research and Development Command at the Wright Air Development Center (WADC) 

decided that action was required. The Rotary Wing branch of the Propeller Laboratory, with 

Captain Paul Simmons acting as project engineer, placed a research contract with the AeroMechanics Department of Cornell Aeronautical Laboratory. 

 
2.6 VIBRATION 

341 

 The research contract called for designing, building, whirl tower testing, and then 

flight testing three sets of blades on a Sikorsky H-5 production helicopter. The H-5 was 

designated by the U.S. Navy and the Marines as an HO3S (Fig. 2-192). The 5,500-pound 

gross weight was supported by a 48-foot-diameter rotor and powered by one Pratt and 

Whitney R-985-AN-7 450-horsepower engine. The seating was one plus three-in-a-row. 

Sikorsky sold the model commercially as an S-51. 

 The research program was named the “H-5 Variable Stiffness Blade Program.” The 

results of the program were published in six parts [430], and the principal authors were 

Harold Hirch and James Kline. The project pilot and flight engineer was Hans Weichsel, Jr.108 

The background paragraphs provided in Part 3 show just how advanced this program was and 

are of significant historical value. They read as follows: 

“Program Initiation The need for, and organization of, the so-called ‘H-5 Variable Stiffness 

Blade Program,’ from which the results presented in this paper are extracted, was conceived 

jointly by W.A.D.C. Rotary Wing Branch personnel, and engineers of the Cornell 

Aeronautical Laboratory. Approaching the problem with the limited theoretical and 

experimental data available at the time the project was conceived, it is frankly admitted that 

the existence of higher mode resonant bending was not then foreseen. In fact, at the time there 

were no proven arguments to refute the popular opinion that the role of blade bending 

stiffness in determining blade motions and stresses was of secondary importance. This 

opinion, while now proven false as a generalization, can be justified with some logic for the 

case of first mode bending, by the fact that the centrifugal stiffening effect realized with 

normal blades will be four or five times as great as that due to their structural stiffness. In 

view of this fact, and anticipating only quasi-static bending in the first bending mode, with, 

perhaps some amplification, it was felt that the differences between data, measured with 

blades possessing the limited amount of stiffness variation obtainable with conventional 

blade' construction, would be too small to be accurately determined. Design requirements 

were, therefore, established for blades which would provide a four-to-one stiffness range, yet 

possess approximately the same mass and aerodynamic characteristics [as standard H-5 

blades]. Further, the blades were to possess 1/2, 1, and 2 times the stiffness of standard H-5 

blades, and be flyable on an H-5 helicopter. With a four-to-one stiffness range, it was 

anticipated that stiffness variation effects would be sufficiently large so that they could be 

measured. 

Fiber Glass Blade Design Extensive preliminary studies (ref 5) of various blade designs 

revealed only one which met the four-to-one stiffness range requirement. The proposed design 

called for the development of three separate sets of blades, one of each stiffness, employing a 

fiber glass shell, die molded integrally to a balsa wood core. By employing the high strengthto-weight ratio of fiber glass, in conjunction with the ability to vary the elastic modulus of the 

fiber glass skin by selectively orienting the fiber direction, the required stiffness range was 

provided. Whirl test blades were first constructed to prove the fiber glass design, and, after 

they successfully passed Propeller Laboratory tests, the three sets of flight test blades were 

manufactured. Detailed information concerned with the design and manufacture of the fiber 

glass blades may be obtained from reference 6 and 7. A further description of the blades, 

together with a detailed analysis of their mass, structural, and dynamic characteristics is also 

available (ref 8). The finished appearance of the blades is shown in figure 1, p. 4.” 

 

108 Hans left Cornell Labs in 1960 and joined Bell in 1965. When I arrived at Bell in 1977, I had the good 

fortune to be influenced by him on several new product development programs. Hans was a gentleman of the old 

school, had a tremendously good intuition for practical engineering, and a feeling for the needs of the 

commercial marketplace that I thought was unmatched by anyone I had ever met. 
2.6 VIBRATION 

342 

Fig. 2-192. The H-5 served in South Korea from 1950–1953 during the Korean war 

(photo from author’s collection). 

 To me, this research into blade frequency placement to avoid resonance with periodic 

airloads was a milestone. The fact that bending in the third flapwise mode was very important, 

particularly at low speeds associated with transition, was quite an eye-opener. The Cornell 

Aeronautical Lab researchers discovered this fact using fiber glass blades in 1951. The three 

sets of blades each had one blade with flap bending strain gauges located at blade radius 

stations of 72, 108, 135, 162, 189, 216, 234, 252, and 272 inches on the 24-foot-radius blades. 

When you read this report, I am sure you will be struck by the conclusions, which were, in 

part: 

 “While the good correlation obtained, between predicted and measured results 

indicates that it should be possible to predict resonant conditions during the design stage it is 

unfortunately found that little can be done to avoid coming close to one or another resonant 

point, it appears that the best that can be done at least until the nature of the resonance is 

understood is to make provision in the design so that the natural frequencies may be shifted in 

such manner that the resonant conditions do not coincide with normal operating conditions. 

 Attention is called to the necessity of providing sufficient data stations, when 

conducting blade strain surveys so that information will be obtained at all critical blade 

stations. Equally important it is necessary that the stations be judiciously chosen, so that they 

do not fall at node points, and thereby fail to detect important higher mode contributions. 

 Finally, anticipating the probability of some higher order bending content, it is 

important that the blade designer recognize the critical role which resonant conditions may 

play in determining the fatigue life of blades. Since the blade resonant frequencies are 

harmonic multiples of the rotor speed it is important to anticipate that the load cycles applied 

to the blade will be proportional to the product of total rotor revolutions and the exited 

harmonic orders and that the peak stresses and vibratory moment amplitudes will be larger 

than predicted by current theory. 

 It is believed that this report completely substantiates the existence of the rotor blade 

higher mode bending phenomenon and that it discloses the most important manifestations of 

the problem. It is recognized that no answers are provided to many of the questions raised by 

the results presented. Such answers are not yet available. It is hoped however that the problem 

will occasion sufficient interest, and concern so that it will receive the attention which it 

merits, and that additional work aimed at providing the required answers will be undertaken.” 

The blade problem has “received the attention” as you can well imagine. 
2.6 VIBRATION 

343 

2.6.3 Hub Vibratory Loads, Aircraft Response 

 The heart of the helicopter vibration problem lies behind the five words that title this 

section. Simplistically, the problem falls in the category of forced vibration of a structural 

beam. In fact, despite some six-plus decades of intense effort, members of the rotorcraft 

community have only a general idea of the rotor system vibratory forces and moments that are 

applied to the structural beam called a helicopter. Even when given the “virtually” exact 

applied loads, the response of the beam has only been approximately estimated with an 

extremely detailed theory that relies totally on the modern computer. 

 You will find a simple analysis of the vibrating beam problem in Appendix F. It should 

help you understand the key engineering terms and concepts used by dynamists. 

 To give you more insight into the overall problem, let me first discuss some flight test 

vibration measurements for a few helicopters, then secondly, delve deeper into what are 

commonly called ground shake tests and analyses of helicopters. The progress made in 

actually calculating the hub vibratory loads will be taken up in a later paragraph. 

2.6.3.1 Some Flight Test Results 

 The pioneering efforts of the U.S. Army to select the helicopter rather than the 

autogyro for its future needs led Sikorsky to develop the R-4, R-5, R-6, and the commercial 

S-51. Then Bell developed the now familiar Bell Model 47 (Fig. 2-110). This helicopter 

received the world’s first civil certification (from the then CAA) on March 8, 1946. With the 

Korean War on the horizon, the Army began procuring light, two-place, side-by-side-seating 

helicopters in small lots in 1948. Significant quantities of both Bell H-13s (Model 47) and 

Hiller H-23s (Model 360 or UH-12) were procured during fiscal year 1951, the first year of 

the Korean War. These military helicopters were flight tested at the Air Force Flight Test 

Center located at Edwards Air Force Base in California. 

 Reported flight test results for both H-13 and H-23 helicopters included vertical 

vibration measurements on the floor between the pilot’s and passengers’ seats. The 

measurements were made with accelerometers, which give an output in feet-per-second 

squared. The general practice is to divide the accelerometer output by the gravity constant 

(32.174 feet-per-second squared) to convert vibration to units of g. 

 This first example provides vibration data for the H Model of the Bell H-13 [171]. The 

primary result is vibration versus calibrated airspeed.109 The once-per-revolution (1/rev) 

vibration for this helicopter is given in Fig. 2-193 and, because the H-13 has a two-bladed 

rotor, vibration at 2/rev is given in Fig. 2-194. The nominal main rotor speed is 344 rpm, 

which is 5.7 Hz and, therefore, 2/rev equals 11.4 Hz. Note that vibration at 1/rev is on the 

order of 0.03 g or less. Based on the 1978 ISO 2631 standards shown in Fig. 2-183, the crew 

should remain proficient for at least 4 hours. In contrast, the 2/rev vibration can reach at least 

 

109 See footnote 65 on page 212 for calibrated and true airspeeds. 
2.6 VIBRATION 

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0

0.01

0.02

0.03

0.04

0 10 20 30 40 50 60 70 80 90

GW = 2,350 lbs, Altitude = 2,000 ft, Rotor RPM = 344, CT/σ = 0.081

GW = 2,525 lbs, Altitude = 2,100 ft, Rotor RPM = 344, CT/σ = 0.087

GW = 2,510 lbs, Altitude = 2,100 ft, Rotor RPM = 322, CT/σ = 0.099

Calibrated Airspeed (knots)

Vibration 

(± g)

Fig. 2-193. Bell H-13H 1/rev vibration at the pilot’s floor [171]. 

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0 10 20 30 40 50 60 70 80 90

GW = 2,350 lbs, Altitude = 2,000 ft, Rotor RPM = 344, CT/σ = 0.081

GW = 2,525 lbs, Altitude = 2,100 ft, Rotor RPM = 344, CT/σ = 0.087

GW = 2,510 lbs, Altitude = 2,100 ft, Rotor RPM = 322, CT/σ = 0.099

Calibrated Airspeed 

Vibration 

(± g)

Fig. 2-194. Bell H-13H 2/rev vibration at the pilot’s floor [171]. 

0.2 g at 80 knots. Using ISO 2631 standards (with 0.2 g at 11.4 Hz), crew proficiency would 

begin to deteriorate within an hour or less. Of course, the pilot can drop off speed by 10 knots 

and obtain a more tolerable ride. 

 Fig. 2-194 raises a serious point about performance. If the maximum speed or, worse 

yet, the cruise speed is accompanied by quite high vibration, then the helicopter will have a 

crew-imposed speed limit. This is a very serious deficiency for any rotorcraft. It might be 

tolerated for a military mission, but this situation would never be tolerated in commercial 

operations. 

 The second helicopter of particular interest is a very small U.S. Army machine 

obtained from Hughes in the late 1950s. This helicopter began commercially as the Hughes 

Model 269 and ultimately became the Schweizer Model 300. Along the way, the initial Army 

model was designated as the YHO-2HU (Fig. 2-195), later to become the T-55 Osage. 
2.6 VIBRATION 

345 

Fig. 2-195. The Hughes Model 269 became the T-55 primary flight training helicopter 

for the U.S. Army and is now, with improvements, the Schweizer (now part of 

Sikorsky) Model 300 [111]. 

The T-55 became the standard Army training helicopter until the late 1980s. Some 60,000 

Army aviators were trained to fly in this machine. The 25-foot-diameter rotor operated 

normally at 450 rpm, which is a 1/rev of 7.5 Hz. The takeoff gross weight was 1,550 pounds, 

and the aircraft was powered by a 180-hp Lycoming HIO-360-B1A piston engine. 

 The primary vibration reported by Ken Ferrell [111] was at 3/rev or 22.5 Hz because 

of the three-bladed rotor system. The section of the report dealing with vibration spoke quite 

favorably about the vibration levels of the YHO-2HU saying: 

“The vibration characteristics in level flight are very good and compare favorably with 

the smoothest helicopters. The vibration was found to be greater for the heavy 

weight than for the light weight condition. The magnitude also increased as the 

engine speed was decreased. Vibration levels at the pilot’s seat were greater than those 

measured at the rotor mast, indicating that the cabin structure was amplifying the vibration 

in the cockpit. [My italics.] 

The vibration levels vary with airspeed and in general are at a minimum for airspeeds of 30 

to 50 knots TAS. The following illustration [see Fig. 2-196] shows a typical 

variation of vibration with airspeed: As the airspeed is increased and blade stall is 

encountered the vibration levels increase. The vertical vibration is greater than the lateral for 

both locations, with the exception of the low altitude heavy-weight conditions.” 

What is very interesting about the “illustration” shown next is that the vibration is virtually 

twice what MIL-H-8501A [410] allowed as noted in Fig. 2-183. In fact, when all the reported 

data is gathered up on one chart as I have done with Fig. 2-197, the summary “illustration” 
2.6 VIBRATION 

346 

appears rather optimistic. Furthermore, the T-55 exhibited a very substantial lateral vibration 

at the pilot’s seat as Fig. 2-198 shows. That these vibration levels (which exceed MIL-H8501A) might be considered “very good and compare favorably with the smoothest 

helicopters” can only be explained by ISO 2631 standards provided in Fig. 2-182. 

According to those standards, 0.4 g at 22.5 Hz (i.e., 3/rev) should be tolerable for somewhere 

between 25 and 60 minutes. 

Fig. 2-196. The summary opinion of the U.S. Army about the vertical vibration of the 

T-55 at the pilot’s seat and at the rotor mast [111].

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 10 20 30 40 50 60 70 80 90

GW = 1,328 lbs, Altitude = 6,440 ft, Rotor RPM = 450, CT/σ = 0.0926

GW = 1,548 lbs, Altitude = 1,150 ft, Rotor RPM = 450, CT/σ = 0.0919

GW = 1,566 lbs, Altitude = 6,940 ft, Rotor RPM = 450, CT/σ = 0.111

GW = 1,603 lbs, Altitude = 900 ft, Rotor RPM = 417, CT/σ = 0.110

GW = 1,560 lbs, Altitude = 6,950 ft, Rotor RPM = 417, CT/σ = 0.129

GW = 1,318 lbs, Altitude = 6,440 ft, Rotor RPM = 417, CT/σ = 0.107

True Airspeed (knots)

Vibration 

(± g)

Fig. 2-197. The vertical vibration data at the pilot’s seat of the T-55 for a number of 

weights, altitudes, and main rotor speeds [111].
2.6 VIBRATION 

347 

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 10 20 30 40 50 60 70 80 90

GW = 1,328 lbs, Altitude = 6,440 ft, Rotor RPM = 450, CT/σ = 0.0926

GW = 1,548 lbs, Altitude = 1,150 ft, Rotor RPM = 450, CT/σ = 0.0919

GW = 1,566 lbs, Altitude = 6,940 ft, Rotor RPM = 450, CT/σ = 0.111

GW = 1,603 lbs, Altitude = 900 ft, Rotor RPM = 417, CT/σ = 0.110

GW = 1,560 lbs, Altitude = 6,950 ft, Rotor RPM = 417, CT/σ = 0.129

GW = 1,318 lbs, Altitude = 6,440 ft, Rotor RPM = 417, CT/σ = 0.107

Vibration 

(±g)

True Airspeed (knots)

Fig. 2-198. The lateral vibration data at the pilot’s seat of the T-55 for a number of 

weights, altitudes, and main rotor speeds [111].

Fig. 2-199. The B model of the H-21 was used by the U.S. Air Force. The C model was 

the Army’s version (photo from author’s collection). 

The Piasecki H-21B shown in Fig. 2-199 is the next helicopter of particular interest. This 

tandem rotor helicopter was the result of Frank Piasecki’s first step into production. The B 

and C models had a three-bladed, 44-foot-diameter rotor with the front rotor turning 
2.6 VIBRATION 

348 

counterclockwise when viewed from above. The rotors did not intermesh. In its final grow 

version, the gross weight was 15,000 pounds. A major marketing point was that the tandem 

rotor helicopter had a much wider center-of-gravity range than a corresponding single rotor 

machine such as the Sikorsky H-34. This feature allowed greater flexibility in cargo and troop 

loading. I must tell you, however, that this marketing debate has gone on for decades. 

 An Air Force flight test report [109] written by Jim Hayden110 provided vibration data 

at three center-of-gravity positions within the gross weight to center of gravity (GW-c.g.) 

envelope111 for a gross weight of 15,000 pounds. The mid center of gravity for the test was at 

fuselage station 339 inches, which was 15 inches forward of the centerline between rotors. 

The forward center of gravity for this test was at fuselage station 328 inches, and the aft 

center of gravity was at fuselage station 347 inches. The flight test data provided in Fig. 2-200 

shows that the aft and mid center-of-gravity vertical vibration at the pilot’s floor station (along 

the main beam) was significantly lower than at the forward center-of-gravity location. At the 

test main rotor speed of 258 rpm, the 1/rev frequency was 4.3 Hz, which means that the 3/rev 

vibration shown in Fig. 2-200 was at 12.9 Hz. 

 This H-21 test report states that “every pilot who assisted in the qualitative evaluation 

commented on the low vibration of the test aircraft. Some stated that it was the smoothest 

H-21 that they had ever flown.” This statement is, of course, quite different than saying that 

“the test aircraft” was the smoothest helicopter they had ever flown. 

0

0.05

0.1

0.15

0.2

0.25

0 10 20 30 40 50 60 70 80 90 100

Vibration 

(± g)

Calibrated Airspeed (knots)

Fwd. c.g.

Mid c.g.

Aft c.g.

Fig. 2-200. Pilot 3/rev vertical vibration for the tandem rotor H-21B (gross weight 14,800 

lb, density altitude 3,000 ft, main rotor speed 258 rpm, and CT/σ = 0.106 [109]). 

 

110 When Jim left the Air Force he came to Vertol (later Boeing Vertol) and was a flying qualities expert—and a 

very good friend. 

111 The aircraft’s center of gravity ranged from about 4 inches aft of the centerline between rotors to 25 inches 

forward of the centerline for gross weights at or below 13,500 pounds. The center of gravity range decreased to 

about 15 inches at a gross weight of 15,000 pounds. 
2.6 VIBRATION 

349 

 While on the subject of tandem helicopters, I should point out that the other early 

tandem rotor helicopter that came to production with Piasecki’s leadership was the HUP (see 

Fig. 2-80). This helicopter was chosen by the N.A.C.A. for flight test and analytical study 

[431] because it “was known to have a high vibration level under certain conditions.” Tests 

were made with both wood and metal blades. The test approach was to use an in-flight shaker 

to excite coupled rotor/airframe response. Vibration at both 3/rev and 6/rev with the threebladed rotor systems was very high (approaching 0.8 g) near the forward hub in the low-speed 

range. This report is a very important piece of work that was done in 1957. 

 Using flight evaluation of the Boeing Vertol CH-47D as the measure [432], the 

vibration situation for tandem rotor helicopters since the 1957 HUP has shown only modest 

improvement over the years. From test data acquired all through 1983, the report states (from 

paragraph 94 b) that “the high level of cockpit vibration at and above cruise airspeed (about 

140 knots calibrated airspeed) is a shortcoming.112 However, attenuation of the cockpit 

vibrations is not planned due to the limited mission profile time spent above cruise airspeed, 

the weight penalty, and the complexity of attenuation systems.” This flight evaluation 

included a qualitative vibration rating scale, which I have reproduced here as Fig. 2-201. The 

crew rated the CH-47D in the 7 to 9 range at speeds above cruise. 

Fig. 2-201. The vibration rating scale frequently quoted by flight test pilots. 

 

112 In U.S. Army lingo, a shortcoming is defined as an imperfection or malfunction occurring during the life 

cycle of equipment that must be reported and that should be corrected to increase efficiency and to render the 

equipment completely serviceable. It will not cause an immediate breakdown, jeopardize safe operation, or 

materially reduce usability of the material or end product. Next comes a deficiency. A deficiency is an 

unacceptable red flag, to me, and requires immediate action by the chief engineer. 
2.6 VIBRATION 

350 

 The next helicopter of interest is the experimental model of what became the Bell 

Huey. The test report [115] deals with the Bell XH-40, which laid the foundation for the U.S. 

Army UH-1 series and Bell commercial Models 204 and 205. The first flight of this 

experimental single rotor, turbine-powered helicopter was made in late October 1956. By May 

1958, the Air Force Flight Test Center at Edwards Air Force Base was able to publish a flight 

test evaluation. The flying portion of the program was accomplished between April 30th and 

June 21st of 1957. In discussing vibration, Keith Putnam (the project engineer) and Bob Ferry 

(an Air Force Captain and the project pilot)113 had this to say: 

“As expected with a two-bladed rotor, the frequency of the predominant vibration 

harmonic was two oscillations per rotor revolution (two-per-rev). Under some flight 

conditions the four-per-rev component was also significant. Vibration was recorded in the 

lateral and vertical directions at the center of gravity, between the pilots’ seats and at the 

extreme sides of the cockpit beside pilots’ seats. Lateral vibration in the cockpit and 

vertical vibration at the cg did not exceed 0.1g in amplitude and therefore has not been 

presented in appendix I. Since vibration at the left and right sides of the cockpit was found 

to be similar, only vibration data obtained at the right side has been presented. 

Vertical vibration in the cockpit was in all cases greater than at the center of gravity. 

This indicates that the vibration input from the rotor to the airframe is being amplified 

by the cockpit structure to amplitudes that become unacceptable in the high speed 

range. Vibration at the pilots’ station was also found to increase with distance from the 

centerline of the aircraft. It is therefore suggested that the vibration experienced by the 

pilots at high speed (as induced by blade stall), at the altitudes tested, could be 

reduced considerably by changing the response characteristics of the cockpit structure. 

The helicopter was very smooth in hovering flight. Vibration under most conditions was 

less than 0.1g. The H-40 exhibited an unusually low vibration level during stabilized 

flight in the transition region (10 to 30 knots CAS), an area where many helicopters are 

quite rough. At speeds above transition, vibration decreases and remains at acceptable 

levels (less than 0.2g) until the onset of blade stall for the altitudes at which 

vibration data was gathered — 6,000 to 11,500 feet. As blade stall progresses the 

vibration level in the cockpit increases sharply with speed and quickly becomes 

unacceptable.” 

 There is no question that in terms of recorded vibration data, the XH-40 was giving 

the pilot and copilot a rough ride at the high-speed, high-altitude conditions and low mainrotor speed. While the gross weight ranged from a low of 5,290 to 5,400 pounds (nominally 

the design gross weight), the tests were conducted at three main-rotor speeds of 294, 304, and 

314 rpm. Only two nominal altitudes were flown: the low altitude was around 6,000 feet and 

the high altitude was about 11,000 feet. The blade loading coefficient (CT/σ) ranged from 

0.094 to 0.124. 

 

113 Keith and Bob took this experimental helicopter right to its limits in 30.5 hours of flying. At the design gross 

weight of 5,400 pounds, they tested up to 105 knots true airspeed at 11,500-foot-density altitude. Their 

concluding view was that “The XH-40 in the state of development tested is unacceptable for service use. 

Correction of its present deficiencies, however, will result in a helicopter with excellent performance compared 

to current helicopters.” With improvements, total production exceeded 15,000, which put this helicopter in the 

class of the Douglas DC-3 and its military equivalent, the C-47. 
2.6 VIBRATION 

351 

 The highest vibration was measured on the cockpit floor, just to the right of the pilot’s 

seat.114 This conclusion is suggested by Fig. 2-202 and Fig. 2-203. Putnam and Ferry stated 

that “at speeds above transition, vibration decreases and remains at acceptable levels (less 

than 0.2 g) [my italics] until the onset of blade stall...” This “less than 0.2 g” criteria was met 

for five of the six test data sets as Fig. 2-202 shows. From Fig. 2-203 you can see that the 

right side of the cockpit floor has about ±0.078 g more vibration than the floor between the 

crew members. This suggests that the helicopter had a lateral hub vibratory force that was 

rocking the machine about its longitudinal axis. The onset of blade stall appears to create both 

excessive 2/rev and 4/rev vertical vibration as Fig. 2-204 shows. 

 The onset of blade stall as indicated by the vibration of the Bell XH-40 was addressed 

by Putnam and Ferry in their flight evaluation report [115]. They took a very direct approach 

stating: 

“In a manner analogous to the development of the expression for stall in a fixed wing 

aircraft the following equation may be derived to express the relation between the 

variables affecting retreating blade stall in a helicopter. 

 ( ) W K V V stall rot. fwd. =σ −

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 20 40 60 80 100 120

GW = 5,280 lbs, Hd = 6,500 ft, RPM = 314, CT/σ = 0.094

GW = 5,390 lbs, Hd = 10,500 ft, RPM = 294, CT/σ = 0.124 Vibration 

(± g)

True Airspeed (knots)

Harris

Fairing

Fig. 2-202. Pilot 2/rev vertical vibration for the XH-40 [115]. 

 

114 The cockpit station for a two-man crew frequently places the pilot’s seat on the starboard side of the 

helicopter. This differs from fixed-wing practice where the pilot in command is placed on the port side of the 

aircraft. 
2.6 VIBRATION 

352 

y = 1.01x + 0.078

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

2/rev

Vibration

at

Cockpit 

Floor, 

Right 

Side of 

Pilot's 

Seat

 (± g)

2/rev Vibration at Cockpit Floor, Between Pilots Seats (± g)

GW = 5,280 lbs, Hd = 6,500 ft, RPM = 314, CT/σ = 0.094

GW = 5,390 lbs, Hd = 10,500 ft, RPM = 294, CT/σ = 0.124

Fig. 2-203. Cockpit floor 2/rev vertical vibration for the XH-40 [115]. 

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

2/rev Vibration at Cockpit Floor, Between Pilots Seats (± g)

GW = 5,280 lbs, Hd = 6,500 ft, RPM = 314, CT/σ = 0.094

4/rev 

Vibration 

at 

Cockpit 

Floor, 

Between 

Pilots 

Seats

(± g)

GW = 5,390 lbs, Hd = 10,500 ft, RPM = 294, CT/σ = 0.124

Harris

Fairings

Fig. 2-204. Cockpit vertical vibration above ±0.25 g was an indication to the flight crew 

of blade stall onset for the XH-40 [115]. 
2.6 VIBRATION 

353 

where 

 W = gross weight at which stall occurs, lb. 

σ = ratio of air density at which stall occurs to air density at sea level 

 Vrot. = tip speed of rotor due to rotational velocity, fps R

2

N R

60

π =

 NR = rotational speed of rotor, rpm 

 R = rotor radius, ft 

 Vfwd. stall = true forward speed at which stall occurs, fps. 

 K = constant determined by flight test 

As discussed in the Level Flight section of the Test Results it was very difficult for the 

pilot to distinguish between vibration due to blade stall because vibration from other 

sources was also present. In analysis of the vibration data it was observed that at high 

altitudes (6,000 to 11,000 feet) a sharp increase in vibration level occurred at certain 

airspeeds. It was reasoned that perhaps at these altitudes the only phenomena causing 

this increase in vibration level was retreating blade stall. If this were true then the 

airspeeds at which a given level of vibration occurred might correlate with the stall 

equation. A level of 0.25g was chosen since this is the beginning of the unacceptable 

vibration range and in all cases was above the airspeed at which the sharp increase in 

vibration occurred. This data correlated quite well, as may be seen in the following 

plot, considering the wide variation in density and rotor speed between the 

individual points. All stall predictions in this report were made from the line faired 

through these points.” 

The “plot” Putnam and Ferry refer to is reproduced here as Fig. 2-205. They accompanied the 

plot with a note that “each data point was taken at a vibration level of 0.25 G.” This is the first 

and only example I have of someone trying to closely relate (in a quantified manner) blade 

stall onset to increasing vibration. 

Fig. 2-205. Blade stall onset as determined by cockpit vertical vibration for 

the XH-40 [115]. 
2.6 VIBRATION 

354 

 Before proceeding to examine the final helicopter, let me stop in the mid-1970s. At the 

May 1973 Annual Forum of the American Helicopter Society, a senior flight test engineer, 

(Emmett J. Laing) of the USAASTA located at Edwards Air Force Base in California, 

presented a broad review of Army helicopter vibration. Laing’s follow-on AHS Journal paper 

[433] is a real milestone in my mind. He began the paper saying, in part: 

“It has long been suspected that the helicopter vibration environment contributes to 

instrument, avionics, and other component failure rates and degrades crew performance. 

However, accurate evaluation of the effects of helicopter vibration on components and 

crewmembers has been hampered by a lack of sufficient vibration data. To better 

understand the helicopter vibration environment, the United States Army Aviation 

Systems Test Activity (USAASTA), with the assistance of the United States Army Air 

Mobility Research and Development Laboratory, Eustis Directorate, and Northrop 

Corporation, Electronics Division, is conducting a comprehensive vibration survey on 

present United States Army helicopters. This test project was initiated to determine the 

vibration environment of Army helicopter cockpit instruments and avionics. However, it 

was rapidly expanded to include human factors and reliability and maintainability 

considerations for many other components. Testing has been conducted on the OH-58A, 

UH-1H, CH-54B, and OH-6A helicopters and will be completed on the AH-1G and 

CH-47C helicopters, hopefully in 1973.” 

Laing’s paper was just the very beginning of a massive vibration survey conducted on six U.S. 

Army helicopters. He finish the AH-1G report in 1974 and the CH-47C report in 1975, which 

completed the program.115 

 Laing’s vibration summary of the UH-1H116 (one of the several Huey models that 

followed from the XH-40) is reproduced here as Fig. 2-206. What I find so helpful from 

Laing’s several year effort is his gathering of data from what must have been miles of digital 

tapes. He was able to create a mean of the maximum of the maximums from tens of 

accelerometers to produce the worst-case situation. Then, on top of that, he reduced the data 

to a mean plus 3-sigma graph of vibration versus frequency at several stations as shown in 

Fig. 2-206. (He noted that the “mean plus 3-sigma is a statistically calculated acceleration 

below which 99.87 percent of all data falls.”) The pilot station data in Fig. 2-206 shows that 

maximum vibration from all flight conditions was at or below ±0.34 g at 2/rev, below ±0.40 g 

for 4/rev, and below ±0.36 g for 6/rev. You can get a feeling about Laing’s data analysis by 

selecting just the highest measured XH-40 vibration points from Fig. 2-202, Fig. 2-203, and 

Fig. 2-204 and quoting those points as the XH-40’s vibration. 

 In his AHS Journal paper, Laing was able to quantify (from four helicopters) the 

overall vibration that avionic components were subjected to. His assessment is reproduced 

here as Fig. 2-207. 

 Finally, it is well worth quoting Laing’s conclusions because they ultimately 

contributed to revisions in Army specifications and design standards, such as the introduction 

in 2006 of ADS 27 by Sam Crews, as I mentioned earlier. Laing’s conclusions in 1974 were: 

 

115 Laing’s six reports became a valuable source for other researchers including the Army Aeromedical Research 

Laboratory located at Fort Rucker, Alabama [434]. 

116 See Laing’s Vibration and Temperature Survey Production UH-1H Helicopter [435]. 
2.6 VIBRATION 

355 

Fig. 2-206. UH-1H maximum vibration environment [433]. 

Fig. 2-207. Avionic equipment installed in helicopters can be subjected to 

severe vibration [433]. 
2.6 VIBRATION 

356 

“This paper has presented data which describe the vibration environment of the current 

generation of Army helicopters. It has been shown that 

1. Statistical methods can be used to summarize large quantities of vibration data. 

2. Helicopter vibrations are primarily sinusoidal, with the main rotor and gunfire 

the primary instrument and avionics vibration sources. 

3. Rotating equipment such as gearboxes and shafts also cause significant 

vibrations when components are mounted close to these sources. 

4. Improved vibration isolator and seat cushion design may reduce vibrations 

transmitted to the avionics and crew. 

5. The laboratory test requirements of MIL-STD-810B present generally 

adequate acceleration limits, but present an inadequate frequency range. 

6. Consideration should be given to specifying the pilot station vibration limits of 

MIL-H-8501A as a function of frequency below 32 Hz. 

Much more data are available from USAASTA in the engineering test reports on each 

helicopter and on digital computer tape. It is anticipated that this data will increase the 

understanding of the helicopter vibration environment, and can be used to define realistic 

vibration qualification requirements for helicopter instruments, avionics, and other 

components.” 

I was particularly drawn to Laing’s sixth conclusion because in the general discussion about 

pilot station vibration data he said, “The highest vibration levels recorded were on the UH-1H 

helicopter at frequencies of 7.2 Hz and 32 Hz and the 7.2-Hz vibration was judged more 

severe than the 32-Hz vibration of equal amplitude.” The vibration at 7.2 Hz amounted to 

±0.3 g at a main rotor speed of 220 rpm during ground run-up in a 20-knot wind. The 32-Hz 

vibration (±0.5 g) at the 6/rev frequency of the main rotor was obtained during flight. 

 Now let me conclude this discussion of flight test results with the Sikorsky UH-60A as 

the example helicopter. First of all, you will recall that the then Boeing Vertol and Sikorsky 

competed in the U.S. Army competition for a new utility helicopter to replace the Bell UH-1 

Huey. Government flight test reports for both helicopters were published in November 1976 

[124, 125]. Perhaps the deciding technical issue was vibration, and this deciding issue hinged 

on the Army requirement that the new utility helicopter must be transportable in an Air Force 

C-130. Boeing took the requirement to heart (Fig. 2-208).117 Sikorsky, faced with the same 

situation, put in a shaft extension to raise the main rotor (Fig. 2-209), which significantly 

reduced its vibration problem—but significantly increased disassembly and reassembly times 

for air transportability by C-130.118 

 

117 As I recall the situation, there was disagreement between Chuck Ellis (a longtime mentor and program 

manager for the YUH-61A) and Ken Grina (chief of engineering who also corrected my design approach on the 

Boeing Vertol Bearingless Main Rotor research program). The Army had placed air transportability very high on 

the list of requirements, and Chuck felt that Boeing Vertol could win the competition with the low rotor position 

and then fix the vibration. As vibration became more of a deciding issue, the YUH-61A main rotor plane was 

raised (which did reduce vibration), but it was too little too late. 

118 Chapter 7 of Ray Leoni’s terrific book Black Hawk [162] tells a detailed story of reducing vibration after the 

early flights established that their aircraft did not meet U.S. Army vibration specifications by a country mile. 

When this occurs in a vigorous competition, it takes nerves of steel and absolute confidence in the outcome to 

watch solutions come along in time to win. 
2.6 VIBRATION 

357 

Fig. 2-208. The main rotor of the Boeing YUH-61A was mounted close to the fuselage to 

meet the requirement for air transportability in an Air Force C-130. Vibration 

was severe due to rotor-fuselage aerodynamic interference (photo from author’s 

collection). 

Fig. 2-209. On the YUH-60A, Sikorsky reduced rotor-fuselage aerodynamic interference 

by increasing the separation distance between the main rotor and fuselage. Note 

the problem of designing a fuselage with a big hole in it (photo from author’s 

collection). 

 Even after Sikorsky won the UTTAS competition on December 23, 1976, vibration 

reduction efforts continued. The Army conducted airworthiness tests on the third and fourth 

production UH-60A helicopters from October 27, 1979, to October of the following year. The 

flight test report [161] was published in September 1981. This report was approved for public 

release and showed that Sikorsky was on the way to achieving a low-vibration machine. The 

Army was, however, not satisfied, writing in the report’s abstract that “the vibrations were 

found to be quite high in several areas and were considered to be excessive for a new 

generation helicopter” [my italics]. It took the use of several vibration suppression devices, 

but early in production Fig. 2-210 shows that the pilot was getting one of the lowest vibration 

environments one might hope for at that stage in a program. Furthermore, vibration at the 

center of gravity of the aircraft was generally low as Fig. 2-211 shows. As Leoni relates on 

page 147 of Black Hawk [162], it took the “combined effects of the raised rotor, 4P absorbers, 

and airframe nose-stiffening to reduce cockpit levels to near 0.05 g.” 
2.6 VIBRATION 

358 

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0 20 40 60 80 100 120 140 160

GW = 16,360 lbs, Density Altitude = 6,180 ft, Rotor RPM = 257, CT/σ = 0.0857

GW = 16,480 lbs, Density Altitude = 6,480 ft, Rotor RPM = 258, CT/σ = 0.0859

Outside Air 

Temp.

55.7o

F

Outside Air 

Temp. 

-3.4o

F

Vibration 

(± g)

Calibrated Airspeed (knots)

Vtrue = 167 kts.

M1,90 = 0.96

Vtrue = 129 kts.

OAT = -26.1o

F

M1,90 = 0.92

Vtrue = 167 kts.

M1,90 = 0.90

Fig. 2-210. Pilot station vertical vibration was encouragingly low on the early UH-60A. 

0

0.05

0.1

0.15

0.2

0.25

0 20 40 60 80 100 120 140 160

GW = 16,360 lbs, Density Altitude = 6,180 ft, Rotor RPM = 257, CT/σ = 0.0857

GW = 16,480 lbs, Density Altitude = 6,480 ft, Rotor RPM = 258, CT/σ = 0.0859

Outside Air 

Temp.

 55.7o

F

Outside Air 

Temp. 

-3.4

o

F Vibration 

(± g)

Calibrated Airspeed (knots)

Vtrue = 167 kts.

M1,90 = 0.96

Vtrue = 129 kts.

OAT = -26.1o

F

M1,90 = 0.92

Vtrue = 167 kts.

M1,90 = 0.90

Fig. 2-211. Vertical vibration at the center of gravity showed that more work was needed 

after the flight testing of an early production UH-60A was completed. 
2.6 VIBRATION 

359 

 When you read the several paragraphs in the Vibration Characteristics section of the 

UH-60A airworthiness report [161], you will find several noteworthy sentences. For example, 

I thought these comments were quite valuable: 

1. Para. 114. “Only 4/rev vibration data test results are presented in figures 113 through 124, 

appendix E, as the other harmonics were not significant.” 

2. Para. 115. “During the test program, many modifications were made to the test aircraft by 

Sikorsky Aircraft personnel in their effort to update the aircraft to a production model. These 

changes included such items as spindle assembly, dampers and damper bolts, etc., which may 

cause a variability of vibration characteristics. Because of these changes, the aircraft exhibited 

different vibration characteristics. Therefore, throughout the test program, the vibrations 

were qualitatively assessed [with] VRS119 ratings ranging from 2 to 7. The vibration 

characteristics did not meet the requirement of paragraph 3.2.1.1.3.1.4 of the PIDS [Prime 

Item Development Specification]. Future tests should be conducted on a current 

production UH-60A in order to obtain vibration data that would be more representative 

of the aircraft.”120 

3. Para. 116. “Vibration levels at the cg of the aircraft during level flight tests are presented in 

figures 116 through 118, appendix E. At the heavy weight condition as shown in figure 

118, the vertical acceleration exceeded 0.2 g at 55 KCAS and fails to meet the 

requirements of paragraph 3.2.1.1.3.1.4 of the PIDS. The lateral and longitudinal 

accelerations were below 0.05 g at all airspeeds. At 16,480 pounds (approx primary mission 

gross weight), below 56 KCAS and above 120 KCAS the vertical acceleration exceeded 

0.1 g with a peak of 0.17 g at 148 KCAS (fig. 117). The lateral and longitudinal 

accelerations were essentially below 0.05 g at all airspeeds.” 

4. Para. 117. “The vibration characteristics of the pilot's and copilot's instrument panel were 

qualitatively evaluated throughout the test program. The pilots were able to read the instruments 

and no blurring was ever experienced.” 

5. Para. 118. “Comparing the lower rotor speed data [minimum power-on rotor speed of 

245 RPM] at heavy and primary mission gross weights to the higher rotor speed at similar 

conditions, show essentially no difference in vibration level at the pilot’s station. The 

vertical vibration levels at the aircraft cg, minimum power-on rotor speed, airspeeds below 

50 KCAS at both gross weights and above 138 KCAS at the primary mission gross weight, 

exceeds 0.15 g and does not meet the requirements of paragraph 3.2.1.1.3.1.4 of the 

PIDS.” 

6. Para. 119. “Vibration test results near primary mission gross weight and aft cg during 

maneuvering flight are presented in figures 123 and 124, appendix E. At 118 KCAS, the 

highest 4/rev vibration level was 0.24 g laterally at the pilot seat, which occurred at a bank 

angle of 45 degrees or 1.4 g normal acceleration. The 60 degree left and right maneuvering 

stability flight was difficult to perform because the airspeed fluctuated ±10 KIAS and pilot 

workload increased significantly (HQRS 6).”121 

7. Para. 120. “The vibrations were excessive during descents and translations from forward 

flight to hover, as well as in those areas previously mentioned. The excessive vibrations 

significantly increased pilot work load during certain maneuvers, and are a shortcoming.” 

 

119 The vibration rating scale (VRS) created by the flight test crew was shown in Fig. 2-201.

120 No matter how encouraging, vibration measurements on one aircraft out of a fleet can hardly be considered 

representative, but at least it is a start. 

121 The Handling Qualities Rating Scale (HQRS) also helped pilots convey their feelings to rotorcraft engineers. 
2.6 VIBRATION 

360 

 Ray Leoni points out in his terrific book Black Hawk [162] that some 25 years after 

these early UH-60A tests were reported, Sikorsky developed an active vibration control 

system for its commercial S-92. Sikorsky applied this vibration suppression system to a 

growth version of the UH-60A Model to obtain the UH-60M, which first flew in 2003 and 

began delivery in mid-2006. As Ray describes it: 

“This new system utilizes an active vibration control system (AVCS) to reduce 4/rev 

vibration throughout the airframe. The AVCS eliminates the need for the passive springmass units carried in all prior Black Hawk models, thereby significantly reducing weight. The 

AVCS further maintains consistent vibration performance when rotor speed deviates from 

its nominal 100% value and avoids the loss of effectiveness characteristic of passive 

absorbers when operating at off-design frequencies. 

The AVCS achieves lower vibration at lower weight because it is a distributed system able to 

attenuate vibration in selected zones within the airframe. Force generators of the AVCS can 

be located wherever necessary throughout the fuselage to generate forces to cancel out local 

vibrations. The heart of the system is a closed-loop algorithm that calculates the force generator 

commands required to minimize vibrations as measured by accelerometers located 

throughout the cockpit and cabin. A feedback control algorithm processes a tachometer 

signal, providing frequency and phase information, and also processes accelerometer 

signals that feed back local vibration conditions. 

The AVCS computer calculates the required force generator commands and sends them 

digitally to an electronic unit. This unit then converts the digital signals to analog signals, 

which then are sent to electric motors within the force generators. These motors drive 

counter-rotating eccentric masses to generate forces of appropriate magnitude and frequency 

to cancel fuselage vibrations. 

In the UH-60M, a force generator capable of producing 1000 lb is located in the forward 

cabin overhead, replacing a heavy spring-mass absorber. In addition, generators able to 

produce 450 lb are located one in the left landing-gear stub wing and one in the cockpit 

nose. Figures 199-201 show where the major AVCS components are located in the M 

model.” 

 What I find so interesting about efforts to reduce helicopter vibration is that there are 

(so far) two basic approaches to helicopter vibration reduction and even elimination. The first 

is to reduce the vibration at the source, which is in the rotating system. The second approach 

is to suppress and even cancel the vibratory response of the fuselage in selected regions, 

which is done in the nonrotating system. The latter approach is where the AVCS system falls 

[436]. With either approach significant weight is added, cost goes up, and more parts need 

maintenance. In 1971 and again in 1981, Dick Gabel and Bob Lowey speculated [404, 405], 

or perhaps you could say hoped, that the rotorcraft industry would produce helicopters with a 

“jet smooth ride” in the foreseeable future. We have not achieved that goal yet, but we are 

getting there. 

 As deliveries of the Sikorsky UH-60 series grew, NASA and the U.S. Army found 

another use for the machine. They initiated [437, 438] a new, and the most comprehensive, 

program the world had ever seen to measure and analyze just about everything associated 

with vibration on a UH-60A.122 This helicopter was considered modern and very much state 

 

122 I intend to use data from this program throughout the rest of this vibration discussion to illustrated points 

related to Fig. 2-175. 
2.6 VIBRATION 

361 

of the art in the mid-1980s. As the program progressed from its start in 1986, every researcher 

in the rotorcraft industry came to know about the UH-60 Airloads Program. By February 

1994, the flight test phase was completed, and experimental results began to be published 

[167]. One of the first detailed results, provided by NASA’s Karen Studebaker [439], was 

three-axis pilot vibration versus advance ratio. This data is shown in Fig. 2-212. You might 

note that data for vertical vibration at the flight crew station is considerably lower for the 

early production UH-60A (Fig. 2-210) than for the UH-60A helicopter as modified for the 

Airloads Program. Some of the difference can be explained by ground shake test and analysis 

of the fuselage response, which is the next subject to be discussed. 

Fig. 2-212. Pilot seat vibration for the UH-60A as configured for the 

UH-60 Airloads Program [439]. 
2.6 VIBRATION 

362 

2.6.3.2 Fuselage Response Given Exact Hub Vibratory Loads 

 You read in Volume I that the rotorcraft industry first encountered ground resonance 

during development of the autogyro. You also learned in Volume 1, appendix C, some basic 

dynamics of ground resonance, and the importance of aircraft pitch and roll frequencies 

required to avoid this very destructive behavior. What I did not emphasize was that, in order 

to obtain the aircraft frequencies, ground shake tests were performed as a matter of 

airworthiness qualification and safety. When it became obvious that the helicopter produced 

severe vibration in flight, the industry’s only recourse was cut-and-try fixes. By the late 

1950s, structural dynamists turned to fuselage shake tests in the laboratory to understand the 

behavior of the helicopters that designers were creating. While there was no clear ability to 

calculate the hub loads that shook the machine, structural dynamists could at least 

experimentally determine how each newly developed helicopter responded to known applied 

hub loads. These on-ground tests in a laboratory were referred to as shake tests. 

 While I have no doubt that all helicopter developers conducted (and still conduct) 

some form of shake testing with their designs, the first published experiment and analysis that 

I know of came out as a N.A.C.A. report on June 18, 1957.123 This report [431] was written 

by John Yeates, George Brooks, and John Houbolt, all of whom I came to know and respect. 

In John Yeates’ portion of the report, he captured the essence of the vibration situation. In 

1957 he wrote: 

“In some of the early designs, attempts were made to lower the vibration level by setting the 

natural frequencies of the helicopter components, such as the blades, fuselage, and engine, 

between the multiples of rotor speed. This approach to the problem was only partially 

successful. Some calculations indicated that coupling of rotor blade bending and fuselage 

bending might bring about structural resonance at frequencies where none was apparent from 

considerations of each component separately. It became apparent that the helicopter must be 

treated as a coupled system and that the effect of the interaction of the components (blades, 

fuselage, engine, etc.) is important. The problem is to design and calculate more accurately so 

that determination of the coupled response frequencies of the structure is possible before the 

prototype is built.” 

With that said, John launched first into the shake test helicopter and its setup, which is shown 

in Fig. 2-213. The location of vibration pickups and the number of components measured is 

shown in the boxed numbers in Fig. 2-214. As you can see from Fig. 2-213, the machine was 

suspended at the rotor hubs. The suspension shock cords were, in effect, very soft springs. The 

natural frequency of this setup was less than 1 Hz. A mechanical shaker was mounted on the 

front rotor transmission, just above the heads of the crew. The shaker applied a vertical 

sinusoidal vibratory force (F) with an amplitude of 0.45 (frequency in Hz squared) up to its 

limit of 75 pounds. 

 Notice immediately in the shake test setup that no rotor blades were attached. This 

promptly raises a basic question. Because the vibration solution depends on the coupled 

response of the whole helicopter (blades and fuselage), how do you represent the blades? The 

 

123 I remember that month well because it was on Saturday, June 22, 1957, that Susan Bullis and I were married 

in Center Church on the Green in New Haven, Connecticut. Suddenly, rotorcraft became my second love. 
2.6 VIBRATION 

363 

Fig. 2-213. Shake test setup for the Piasecki HUP, which had 35-foot-diameter tandem 

rotors (photo courtesy of NASA from NACA LAL 85686.1). 

Fig. 2-214. The location of vibration pickups and the number of components measured is 

shown in the boxed numbers [431]. 
2.6 VIBRATION 

364 

researchers, in chapter I of their groundbreaking report [431], replaced the blade assemblies 

with several pounds of dead weight. The blade assemblies from the flapping hinge outboard

were replaced by zero weight first, and then by 100, 175, and 250 pounds per rotor head. The 

authors did not mention the actual weight of the blade assemblies removed; however, my files 

give the weight of six blades and hinges at about 450 pounds. Therefore, the dead weight 

added per rotor station would be 225 pounds. You might think that the 250-pound additional 

dead weight would have been the most accurate representation of the missing blade 

assemblies. However, the theory available at the time said that the blade assemblies do not act 

as dead weight. Rather, the blade motion in the coupled fuselage-rotor vibration problem 

makes the blade assemblies appear to have an effective weight that is considerably less. The 

calculations at the time suggested that 100 pounds per rotor head was the more correct 

simulation. As you will see shortly, flight test results confirmed this view. The reason for this 

effective weight comes about because of the flapping and bending motion allowed by the 

flapping hinges. When the hub vibrates up, the blades tend to cone down, much like an 

umbrella closing, and when the hub vibrates down, the blades act like the umbrella is opening 

up again. Of course, the actual theory is more complicated, but that is about the best way I can 

describe the blade assemblies coupled motion in this introduction. 

 The shake test was performed by varying the shaker frequency over the range of 8 to 

17 Hz. The shaker gave a sinusoidal input at the front rotor, and the fuselage response at the 

front rotor was recorded (i.e., at the upper solid black dot from the box with a 3 in it on 

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

8 9 10 11 12 13 14 15 16 17

Maximum

Vertical 

Vibration

per

pound

of 

Shaking

Force

(± g/lb)

Shaker Frequency (Hz)

No Weight 

Added

100 lb. Added 175 lb. Added

250 lb. Added

Fig. 2-215. Shake test results as a function of dead weight added to each rotor head to 

simulate blade and hinge assemblies removed. 
2.6 VIBRATION 

365 

Fig. 2-214). For this experimental program, the fuselage response was measured in units of 

velocity in inches per second. This was a standard sensor at the time; it was later replaced by 

accelerometers in more modern times. I have taken the liberty of converting the velocity 

measurements into accelerations in units of gravity following Eqs. (2.274) to (2.276). My 

interpretation of these N.A.C.A. initial shake test results is shown in Fig. 2-215. 

 The report by Yeates, Brooks, and Houbolt [431] contains the results from the HUP 

flight test where the aircraft was shook in flight. They took data with the shaker operating and 

turned off and, in effect, subtracted the results to give the results shown in Fig. 2-216, which I 

have recast into acceleration in gravity units per pound of shaker force. Their interpretation 

was that the two peaks in the flight test results versus the one peak in the ground test indicated 

coupled motion between the fuselage and the rotor. 

 The basic message that the authors were trying to convey seems simple to me. 

Suppose the fuselage structural analysis, without considering the blades, suggests that the 

fuselage first bending mode would have maximum vibration if its frequency was at, say 

14 Hz. Then everyone would want to reduce (or increase) the fuselage stiffness to move the 

natural frequency to a lower (or higher) frequency. However, that design move could (in 

flight) land the experimental machine right on one of the twin peak vibration points of the 

coupled fuselage-rotor blade assemblies. Brooks and Houbolt were able to reinforce this point 

with their analysis, which is carried out in chapter II of their report [431]. Their theory led to 

solving eight equations in eight unknowns, which is beyond the intent of this vibration 

discussion. 

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

8 9 10 11 12 13 14 15 16 17

Maximum

Vertical 

Vibration

per

pound

of 

Shaking

Force

(± g/lb)

Shaker Frequency (Hz)

Ground Test with

100 lb. Added

Flight Test

273 RPM

55 knots

Fig. 2-216. Flight test revealed that coupled fuselage-rotor system analysis was 

absolutely required for solving helicopter vibration problems. 
2.6 VIBRATION 

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 NASA’s basic research and understanding of helicopter vibration did not stop with the 

groundbreaking effort of Yeates, Brooks, and Houbolt. The immediate follow-on was the 

construction, test, and analysis of a basic research dynamic model. The objective was to 

measure and calculate coupled frequencies and mode shapes for a 1/8-scale model. This basic 

research was reported by Milton Silveira and George Brooks in December of 1958 [440]. 

 In Volume I, you learned about natural frequencies and mode shapes of rotor blades. 

Appendix C of this volume provides an introduction to the natural frequencies and mode 

shapes of a simple beam, which has no rotor system attached. What Silveira and Brooks did 

was build an absolutely beautiful, simple dynamics model (Fig. 2-217), at small scale, where 

all the structural properties necessary for analysis were easily obtained. The four-bladed rotor 

was 66 inches in diameter and had the approximate dynamic properties (I think) of a Sikorsky 

S-58, which is the U.S. Army’s H-34. The “fuselage” was made of two welded magnesium 

angles that form a box cross section. The construction and properties of the rotor pylon and 

shaft can be found in the report [440]. The overall model, mounted on a very rigid I-beam, 

was softly attached to the I-beam so that only vertical, horizontal, and pitch degrees of 

freedom were permitted. The test was only conducted in hover outside a wind tunnel. 

 The researchers first obtained the natural frequencies and mode shapes of the 

individual components. This allowed them to construct the uncoupled natural frequencies for 

the basic model. Then, by shaking the model with the rotor operating at several different rotor 

speeds, they experimentally obtained the coupled (rotor plus fuselage plus pylon plus rotor 

shaft) system frequencies, which I have reproduced here as Fig. 2-218. The modes, called out 

by number on the figure, are as follows: 

 Mode 1 Fuselage rigid body pitching Mode 2 Fuselage horizontal translation 

 Mode 3 Blade first bending Mode 4 Shaft translation 

 Mode 5 Fuselage first elastic bending Mode 6 Blade second elastic bending 

 Mode 7 Pylon bending 

Fig. 2-217. The exploration of coupled system frequencies and mode shapes was done 

with a beautiful, simple dynamics model [440]. 
2.6 VIBRATION 

367 

 The mathematically tractable analysis used a seven-degree-of-freedom set of 

equations, and the calculated coupled system frequencies were in quite reasonable agreement 

with the experimentally obtained data as Fig. 2-218 shows. 

 The work of these N.A.C.A. researchers clearly established the need for the rotorcraft 

industry to attack helicopter vibration as a coupled system problem. It was the last conclusion 

of Silveria and Brooks’ report that set the next step for the industry. They wrote that “(t)he 

coupled natural frequencies and mode shapes can be determined by the analytical procedure 

presented herein with sufficient accuracy if the mass and stiffness distributions of the various 

helicopter components are known.” There was a big if in that conclusion. 

Fig. 2-218. Coupled mode frequencies of the simple research model [440]. 
2.6 VIBRATION 

368 

 The investigation of tandem rotor helicopter vibration did not stop with the N.A.C.A. 

research by Yeates, Brooks, and Houbolt. The idea that shake testing, both on the ground and 

in flight, was a valuable approach to basic understanding was applied at the Vertol Division of 

the Boeing Company, which was then located in Morton, Pennsylvania. This approach was 

used on the H-21B in 1961. The results were reported by Bob Ricks to the Aeronautical 

Systems Division of the Air Force Systems Command in 1962 [441]. Then, with delivery of 

the CH-46A (Boeing Model 107) to the U.S. Marines, vibration in excess of MIL-H-8501A 

was, as you might have guessed, a problem. The Model 107 had some vibration problems that 

Bob Loewy and Dick Gabel were able to solve. However, in converting the 107 to the 

CH-46A, automatic blade folding was added and vibration increased, requiring a renewed, 

2-year vibration reduction effort. 

 CH-46A vibration was tackled with the most thorough effort that the industry had 

ever, in my opinion, mounted. The author of the final report [442] was Dick Gabel who was 

then the Chief Dynamics Engineer at Vertol and was well respected throughout the industry.124

Dick opened this nearly 900-page report with a crystal clear AVID Summary. He wrote in the 

opening Background and Purpose section that 

“AVID, acronym for Advanced Vibration Development was conceived by BuWeps [Navy 

Bureau of Weapons] and the Contractor to provide a better understanding of the sources of 

helicopter rotor vibratory loads and the mechanism of the fuselage response to these loads. This 

basic knowledge type program followed two years of hardware programs on the CH-46A, which 

through fuselage stiffening and absorbers had brought vibration down to acceptable levels, and 

in fact to MIL-H-8501A requirements. AVID, was intended to provide a deeper knowledge of 

the vibration sources than was heretofore possible in the usual ‘fix’ type program. 

AVID was thus contracted to provide a step forward in the state-of-the-art as regards an in-depth 

understanding of helicopter vibration. Although it was never intended to develop or test any 

vibration reduction hardware here, it was intended to recommend those avenues which showed 

most promise for successful vibration control at least weight. Specifically, it was hoped by those 

associated with production and user activities of the CH-46A that results of AVID would lead to 

successful light weight hardware recommendations and the subsequent removal of all vibration 

absorbers.” 

The AVID program used analysis and ground and in-flight shake testing, measured structural 

loads and blade airloads, and made more than a few hardware changes to ferret out the 

sources of vibration. One of the key hardware effects was the impact of blade folding 

hardware. Testing of a Canadian CH-113A (which has no automatic blade folding hardware 

and has an 883-pound rotor hub weight) versus the CH-46A (which weighs 1,144 pounds) 

showed that the rotor longitudinal load (measured by shaft bending) was cut in half with the 

lighter hub. 

 The AVID program laid the groundwork for a broader industry program called 

DAMVIBS, which I will discuss in detail shortly. 

 

124 Dick was—and I still feel is, even in retirement—a good friend who could explain any dynamics phenomena 

so that even I understood it. Dick replaced Bob Loewy in the fall of 1962 when Bob went to the University of 

Rochester. The AVID report had rather limited distribution, but Bob Loewy, Wayne Johnson, and Bob Ormiston 

have copies. I borrowed Bob Ormiston’s copy, and Mike Scully and I spent an afternoon in May 2011 making a 

Portable Document Format (PDF) copy. 
2.6 VIBRATION 

369 

 It took several more years, plus the invention of the digital computer, before a 

structural analysis that could model a helicopter fuselage and all of its internal components 

became available.125 This analysis was called NASTRAN, which is a contraction of NASA 

Structural Analysis. It was funded by NASA under contract number NASA-10049 from June 

29, 1966, to March 2, 1970, when a final report for the project [444] was submitted by 

Computer Sciences Corporation to NASA Goddard Space Flight Center. 

 Compared to the early N.A.C.A. efforts led by George Brooks where a few 

components (as counted on Fig. 2-217) were examined with seven degrees of freedom 

(i.e., the modes), NASTRAN can have over 40,000 components and 65,000 degrees of 

freedom. This “the sky is the limit” powerhouse tool became a factor in nearly every 

engineering design from buildings to cars to space vehicles and, of course, a major tool for the 

rotorcraft industry. Finally, structural dynamists could “model” the fuselage of a helicopter, in 

a computer. An example of this NASTRAN model for the Sikorsky UH-60A primary structure 

is shown in Fig. 2-219. Notice the likeness of the NASTRAN model to the cutaway artist’s 

rendition of the Sikorsky UH-60 shown in Fig. 2-187. References [445-447] provide an 

enormous amount of detail about how such a model was constructed and how close the 

engineers came to experimental shake test results using NASTRAN. The experimental shake 

test of the UH-60A (Fig. 2-220) and its test setup (Fig. 2-221) was very carefully conducted. 

 It is worth a moment to discuss the NASTRAN model shown in Fig. 2-219. I visualize 

the model as being constructed from a Tinker Toy set. Every little stick (individual wood 

dowels of different lengths) becomes, in NASTRAN parlance, a finite element. Each stick has 

uniform stiffness and uniform mass. The sticks are joined together with the round Tinker Toy 

wooden spools having holes all around so that loads go from stick to stick through a joint. 

Each joint becomes a reference point in a NASTRAN model. With NASTRAN the whole 

assembly can be covered with a metal or composite skin to complete the basic model. Then 

other components (e.g., engine, fuel tank, rotor pylon, shafts, hubs, etc.) can build up the 

detail. At that point, the engineer can analytically apply either static or vibratory loads, such 

as vibratory hub loads. Clearly, building such a math model is not done overnight, and actual 

drawings of as many parts as possible are required. As of now, the NASTRAN model 

evaluates the helicopter’s structural properties after the designers’ drawings are done. The 

ultimate step, I believe, is to have NASTRAN create the satisfactory design and then translate 

the results to drawings to be released to manufacturing. 

 Soon after the arrival of NASTRAN, NASA Langley Research Center embarked on 

an industry-wide determination of airframe structural properties for several helicopters 

 

125 In the intervening period, the rotorcraft industry began to expand on vibration analysis of coupled modes 

with what came to be called a “comprehensive analysis.” The prototype of the comprehensive analysis was 

created by research at Bell Helicopter and, with U.S. Army support, evolved in 1967 into a computer program 

simply named C-81. This program modeled the complete helicopter with, for the time, detailed structural 

dynamics and aerodynamics of both fixed and rotating components. Of course, simpler and very informative 

studies of coupled rotor-fuselage vibration continued as Mike Rutkowski demonstrated in 1983 [443]. This 

report is well written, well illustrated with mode shapes and calculated frequencies, and can serve as a primer if 

you want to delve deeper into helicopter vibration. 
2.6 VIBRATION 

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Fig. 2-219. NASTRAN model of the primary structure of a Sikorsky UH-60A. 

Fig. 2-220. Shake test setup for experimental study of the Sikorsky UH-60A 

(photo courtesy of Ashish Bagai and Sikorsky Aircraft). 
2.6 VIBRATION 

371 

Fig. 2-221. Shake test setup for experimental study of the Sikorsky UH-60A [446]. 

manufactured by several companies. This renewed attack on vibration by NASA was 

conceived and supervised by William C. Walton, Jr., until his retirement in 1984. Technical 

guidance was provided by Eugene Naumann and Raymond Kvaternik. When Bill retired, Ray 

stepped in as program manager. Bill Walton gave the program its name, DAMVIBS, a 

contraction of Design Analysis Methods for Vibrations program. This was much stronger 

language than Cierva used in 1935. By any standard, the DAMVIBS program yielded a giant 

step forward in the rotorcraft industry’s attack on helicopter vibration. A workshop 

environment let participants freely interchange NASTRAN models and share company 

engineering data in an unprecedented manner. The key players, acknowledged by Ray in his 

final program overview [448] in April 1992, deserve much wider remembrance: 

“Acknowledgements 

John F. Ward was Manager of Rotorcraft Technology at NASA Headquarters during the 

definition of the DAMVIBS Program and provided the initial support and encouragement to get 

the program started. William C. Walton, Jr. and Eugene C. Naumann led in the definition, 

implementation, and management of the activity which resulted in the CH-47D study. Mr. 

Walton later led in the definition and implementation of the DAMVIBS Program and prepared 

coworkers to manage the program in anticipation of his retirement in June 1984. John H. Cline has 

served as the Technical Representative of the Contracting Officer for the four DAMVIBS task 

contracts since 1984. Robert J. Huston was Manager of Rotorcraft Research and 

Technology at Langley during the formative phase of the program and provided advocacy and 

support when it was needed most. James D. Cronkhite (Bell), Richard Gabel (Boeing), Mostafa 

Toossi (McDonnell Douglas), and William J. Twomey (Sikorsky) were the project engineers who 

headed up the respective industry teams.”
2.6 VIBRATION 

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 You can appreciate just how comprehensive the DAMVIBS program was from 

Fig. 2-222, which I have reproduced from Ray’s June 1989 progress report [449]. The study 

of basic airframes showed that prediction of measured frequencies “was good up to about 10 

Hz, only partly satisfactory between 10–20 Hz, and generally unsatisfactory above 20 Hz.” 

Depending on your view, these results were only a good start because these helicopters had 

three or four blades, and this meant that response to 3/rev or 4/rev (in the range of 15 to 

30 Hz) was not predicted close enough for engineering purposes. The DAMVIBS participants 

decided that much more detail about how to include engines (and drivetrain, stores, 

armament, crew, fuel, doors, avionics, instrument panels, control system access panels, 

fairings, canopy, couplings, secondary structure covers, etc.) to the primary NASTRAN 

models was going to be required. In short, virtually nothing could be left out of the model 

until it was proven to be a small effect. To mount this second phase, they tasked Jim 

Cronkhite at Bell to shake test an AH-1G in its fully assembled configuration and then 

systematically remove subassemblies, repeating shake testing at each step. Each of the eight 

steps produced new insight until Bob Domka from Bell was able to report in detail [450], at 

the 44th AHS Forum in 1986—and Jim could later summarize in 1993 [451]—that “the 

Fig. 2-222. Both metal and composite airframes were examined during the 

DAMVIBS program [449]. 
2.6 VIBRATION 

373 

natural frequency correlation at the higher frequencies was improved from 20 % error to less 

than 5 % error for frequencies up to 30 Hz (4/rev = 21.6 Hz for the AH-1G) by adding more 

detail in the tailboom and by including tightly fastening panels, doors, and secondary structure 

in the forward fuselage.” I believe that Bob Domka’s paper [450] is worth its weight in gold. 

The message as I saw it then (and still think) was that joints of any type are not rigid.126 This 

must make you wonder about how field service will cause a deterioration of a wellmanufactured, metal airframe after the helicopter is delivered. 

 With finally a rather adequate NASTRAN model of the AH-1G, the DAMVIBS 

participants went on to predict vibration measurements from flight test for this helicopter. 

Four reports came out in the 1989–1990 time frame that made the logical effort to combine 

the AH-1G NASTRAN response model with vibratory loads calculated by each of the 

DAMVIBS participants’ “comprehensive” rotor loads programs. You will read about this 

effort and its results shortly. 

 The DAMVIBS program also spun off a key ingredient for the future UH-60 Airloads 

Program that you read about earlier. The ingredient was a “much better” NASTRAN model of 

the UH-60A than was available during the DAMVIBS program. By way of background, 

during the DAMVIBS program the test configuration was a UH-60A at virtually a weight 

empty of 10,000 pounds. The DAMVIBS shake test details and results as published by 

Sikorsky’s Howland, Durno, and Twomey [446] showed that 72 accelerometers were located 

at many positions on the fuselage as Fig. 2-223 shows. 

 The vibration in g’s per pound of hub shaking force is a common output from a shake 

test. The primary independent variable is the shaker frequency. As a simple example from 

many graphs of data from Howland, Durno, and Twomey, consider just the vibration at two 

locations. I have chosen two positions on the right-hand side of the floor (see location 3 and 7 

on Fig. 2-224) to show only vertical response to vertical hub shaking force. Keep in mind that 

there can be vertical response to lateral and longitudinal hub vibratory forces as well. In fact, 

when you think about it, at any given location the full story appears more like Table 2-30 

below (and you are only being introduced here to 2 locations and 1 of the 18 data possibilities 

that are stored in Sikorsky’s files). With 72 locations and 18 possibilities, you need to be 

prepared to look at 1,296 graphs for just one helicopter in the DAMVIBS program files. 

Theory versus test adds another 1,296 curves. 

Table 2-30. Loads and Responses to be Considered in the Vibration Problem

Location Response 

Hub 

Vertical 

Force 

Hub 

Lateral 

Force 

Hub 

Longitudinal 

Force 

Hub 

Pitching 

Moment 

Hub 

Rolling 

Moment 

Hub 

Torsional 

Moment 

Vertical 

Lateral 

Longitudinal 

 

126 During the DAMVIBS program, I was deeply involved in technology at Bell. To make sure that I never lost 

my basic understanding of vibration, and appreciation for the efforts and progress Jim and his research team 

were making, I would frequently re-read NACA TN 2884, which was published in January 1953 [452]. The 

work was performed and reported to the N.A.C.A. by the National Bureau of Standards. 
2.6 VIBRATION 

374 

Fig. 2-223. During the DAMVIBS program, 72 accelerometers were placed on the 

UH-60A fuselage. The floor vibration was associated with locations 3 through 36 [446]. 

Fig. 2-224. The pilot’s and copilot’s seats are approximately above locations 7, 8 and 

9, 10 for the UH-60A DAMVIBS shake test of the primary airframe [446]. 
2.6 VIBRATION 

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0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0.0018

0.002

0 5 10 15 20 25 30 35 40 45

Cockpit Floor 

(Location 3)

Cockpit Floor 

(Location 7)

Maximum

Vertical 

Vibration

per

pound

of 

Shaking

Force

(± g/lb)

Shaker Frequency (Hz)

1/rev

4.3 Hz

8/rev

34.4 Hz

4/rev

17.2/rev

1st 

Vertical 

Bending

6.7/rev

2nd 

Vertical 

Bending

14.0 Hz

3nd 

Vertical 

Bending

19.3 Hz

Fig. 2-225. Vertical response to vertical hub shaking force at two points on the floor 

of the UH-60A127 [446]. 

 A sample of the wealth of data in the Howland, Durno, and Twomey report is shown 

here in Fig. 2-225. The basic data is frequently called a response curve, but I tend to think of 

the graph as a calibration curve. Without including the fuselage-rotor coupled result, you 

might say that a vertical hub vibratory load at 4/rev of 1,000 pounds (about one-tenth of the 

weight empty) will produce about ±0.1 g at location 3 on the cockpit floor (i.e., ±0.0001 g per 

pound times ±1,000 pounds). The primary airframe shows that there would be imperceptible 

vibration at location 7, which is along the light gray line in Fig. 2-225. 

 The first vertical bending mode of this UH-60A result appears to be right around 

6.7 Hz as Fig. 2-225 suggests. The next critical mode has a peak acceleration at 14.0 Hz, and 

the experimenters associated this frequency with the second vertical bending mode. With 

Fig. 2-225 before you, just imagine your reaction if this second mode had its peak at 4/rev. 

Then the vibration to the pilot near location 7 (the light gray line) would be, for 1,000-pounds 

hub vertical shaking force, about ±0.7 g. According to ISO 2631 criteria (Fig. 2-182), ±0.7 g 

at 17.2 Hz would cause loss of pilot proficiency in about 1 minute! 

 

127 I reproduced this graph from Howland’s report [446], page 153. The report’s summary graphs are very small, 

so I used a program called GrabIt to read points from the small graph into a Microsoft®

 Excel® spreadsheet. I 

took this approach because I was afraid to bother engineers at Sikorsky for the original artwork. After all, the 

report is over 20 years old. I felt lucky to have a good PDF file from which to make a reasonably accurate, nicesized graph for this discussion. 
2.6 VIBRATION 

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 The comparison of NASTRAN model results to each manufacturer’s helicopter during 

this 1980s time frame was, as Ray Kvaternik suggested, not too bad in the lower frequency 

range, but prediction of frequencies at which peak vibration was found was ±20 percent. The 

situation Sikorsky researchers were able to benchmark is shown here in Fig. 2-226. The 

second bending mode is predicted to be at 12.4 Hz, while test data shows 14.0 Hz. This is an 

error of about 12 percent. At these respective frequencies, the maximum acceleration was 

0.0022 g per pound of shaking force versus 0.0018 g per pound, a 22 percent error.128 

 You might argue that this example correlation between test and theory shown below is 

not good enough for detail design, and I would agree with you, but counter with this: The 

rotorcraft industry had nothing in the early 1950s. Some 30 years later, the DAMVIBS 

participants and their respective companies had a solid rock from which to make significant 

improvements. 

 Of course, just having the helicopter response, given exact shaking forces, is only half 

the battle. The accurate prediction of in-flight vibration is the objective, and this is the subject 

you will read about next. 

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0.0018

0.002

0.0022

0.0024

0.0026

0 5 10 15 20 25 30 35 40 45

Shake Test

Cockpit Floor 

(Location 3)

14.0 Hz

NASTRAN

Cockpit Floor 

(Location 3)

12.4 Hz

Maximum

Vertical 

Vibration

per

pound

of 

Shaking

Force

(± g/lb)

Shaker Frequency (Hz)

1/rev

4.3 Hz

8/rev

34.4 Hz

4/rev

17.2/rev

1st 

Vertical 

Bending

6.7/rev

2nd 

Vertical 

Bending

3nd 

Vertical 

Bending

Fig. 2-226. NASTRAN vs. shake test results for the UH-60A for vertical response to 

vertical hub shaking force at location 3. 

 

128 I remember thinking at the time that the DAMVIBS participants had achieved a miracle to just get the 

NASTRAN predictions to fall on the same graph with the shake test results. 
2.6 VIBRATION 

377 

2.6.3.3 AH-1G Vibration, Theory Versus Test 

 With this background, the DAMVIBS participants went the final step of predicting 

flight test vibration measurements for the AH-1G. This task required coupling predicted hub 

vibratory loads to the best NASTRAN model of the complete helicopter that Bell had to offer. 

Four reports came out in the 1989/1990 time frame that documented this logical effort to 

combine the AH-1G NASTRAN response model with vibratory loads calculated by each of 

the DAMVIBS participants’ “comprehensive” rotor loads programs. The four participants 

were Bell Helicopter Textron [453], Boeing Helicopters [454], McDonnell Douglas 

Helicopter Company [455], and Sikorsky Aircraft [456]. Their approach to this final theoryversus-test comparison is summarized in Fig. 2-227. 

 The effort depended heavily on two sets of data that were furnished by Bell. The first 

data set was the AH-1G NASTRAN model. This necessary data was packaged in two 

volumes totaling slightly over 1,000 pages [457]. The second data set was the flight-measured 

vibration of the AH-1G (ship number 20391) that the four companies were to correlate with 

[458]. This flight test data, taken from a loads survey done in 1976 [459], amounted to six 

points in a level flight speed sweep. The selected flight number from the loads survey was 

35A, and the counters were 610 through and including 615, which covered true airspeeds of 

67, 85, 101, 114, 128, and 142 knots. This flight was flown at a pressure altitude of 5,000 feet 

and an outside air temperature of 82.4 o

F, which is a density altitude of 2,600 feet. The main 

rotor speed was 324 rpm. The test gross weight was 8,320 pounds. 

Fig. 2-227. AH-1G theory vs. test approach at the end of the DAMVIBS program 

(example from reference [454]). 
2.6 VIBRATION 

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 Along with a great deal of aircraft geometry, structural and aerodynamic properties, 

and sensor locations, Bob Dompka and Jim Cronkhite [458] passed loads and vibration in 

harmonic coefficient form to the three other major DAMVIBS participants. This tabulated 

data of mean plus the next six harmonics was placed in appendix A of their report. This 

appendix was titled OLS129 Harmonic Data for Correlation and was grouped into: 

1. Hub Accelerations (Mast Top F/A, Mast Top Lateral, Mast Top Vertical) 

2. Fuselage Vertical Accelerations (Nose Sta. 46, Gunner Sta. 100, Pilot Sta. 146, 

Engine Deck Sta. 249, Tail Boom Sta. 297, Tail Boom Sta. 485, 90 Deg Gearbox 

Sta. 518, Tail Boom Fin Load Sta. 521, Left Wing-tip Sta. 195, and Right Wingtip Sta. 195) 

3. Fuselage Lateral Accelerations (Nose Sta. 46, Gunner Sta. 100, Pilot Sta. 146, 

Engine Deck Sta. 249, Tail Boom Sta. 297, Tail Boom Sta. 400, Tail Boom Fin 

Load Sta. 521) 

4. Main Rotor (Red Blade)—Chord Bending Moments (31%, 50%, 70% of 264 

inches) 

5. Main Rotor (Red Blade)—Beam Bending Moments (31%, 50%, 70%, 90% of 264 

inches) 

6. Main Rotor (Red Blade)—Torsion Moments (31%, 50%, 70%, 90% of 264 inches) 

7. Axial Forces (Cyclic F/A Boost Cylinder, Cyclic Lateral Boost Cylinder, 

Collective Boost Cylinder, M/R Red Pitch Link, M/R White Pitch Link, Lift Link, 

M/R Red Drag Brace) 

8. Pylon Vertical Displacements (Left Fwd, Right Fwd, Left Aft, Right Aft) 

9. Vehicle Performance Data (Hub Flapping Angle, Hub Feathering Angle, A/C Roll 

Attitude, A/C Pitch Attitude, A/C Yaw Attitude) 

This was a small, but key, sample of the nearly 60 channels of data available. Just think about 

it. The above 9 items give 46 data channels for each of 6 speeds. Each data channel has a 

mean plus 6 sine and 6 cosine amplitudes. This is a total of 46 × 6 × 14, which equals 3,864 

points on a whole bunch of graphs, and then you are ready to start correlation! 

 There are three specific areas of correlation results I want you to appreciate. The first 

is the difficulty that each of the four players had in predicting the helicopter’s trim and blade 

motions. The second is predicted versus measured vibration at the AH-1G nose, which was 

none too good. The third is the general conclusions and recommendations from the effort. 

 Each of the four reports [453-456] explained their comprehensive rotor analysis 

computer programs, and the aircraft trim and control positions that were predicted. The rotor 

analyses were known as: 

Bell—C-81 

Boeing—C-60 

McDonnell—RACAP for Rotor Airframe Comprehensive Aeroelastic Program 

Sikorsky—RDYNE for Rotorcraft Dynamics Analysis 

 

129 OLS stands for Operational Loads Survey and was the common acronym for reference [459].
2.6 VIBRATION 

379 

These computer programs were, in my mind, second-generation comprehensive analysis tools 

that tailored their program input to each company’s product line. (These tools grew out of the 

1955 groundbreaking computer program [460] developed by Alfred Gessow and Almer Crim 

of N.A.C.A. Langley, which I consider the first generation). Each company’s comprehensive 

analysis grew from a basic rotor-alone model in the mid-1960s to inclusion of elastic fuselage 

motions by the mid-1980s. However, because the AH-1G was a two-bladed Bell product 

[459, 461], the engineering staffs from the other three companies were not able to exactly 

represent the machine. One particular design aspect that Bell was quite aware of was the 

bending of the rotor mast and the underslung hub as illustrated in Fig. 2-228. This required 

work-arounds by the other three DAMVIBS participants. Nevertheless, the DAMVIBS team 

plunged ahead with openness that can only be fostered in a workshop environment. I will 

discuss these and other programs that calculate airloads and blade vibratory loads shortly. 

 The calculation of trim parameters was somewhat different for each of the four major 

DAMVIBS participants, and only three reported their results. What was reported was not very 

encouraging. In determining trim, say in the plane of symmetry, the sum of forces along and 

perpendicular to the flight path must be zero. Of course, the pitching moment about the 

aircraft center of gravity must also be zero. The AH-1G situation was not much better than the 

Cierva C.30 problem that was discussed in Volume 1. For example, the fuselage lift, drag, and 

pitching moment contributions to aircraft trim were only an educated guess. This was because 

the flow about the fuselage, including the rotor-induced velocities, was not available. Just as 

important, accurate airloads that deflected the blade, particularly in torsion, were only being 

calculated at the rudimentary level. This meant that the rotor’s contribution to aircraft trim 

was also an unknown. In short, the AH-1G trim problem was a case of having three equations 

with two very interactive unknowns and a raft of variables. 

Fig. 2-228. The AH-1G had a rather limber, main-rotor mast and an underslung rotor 

hub. This Bell design approach was not a configuration choice in the secondgeneration comprehensive analyses of other manufacturers [454]. 
2.6 VIBRATION 

380 

 The participants had the initial job of predicting the measured fuselage pitch attitude 

(θfus),130 the measured blade root feathering angle (θroot,ψ = θmean + B1s sin ψ + A1s cosψ), and 

the measured hub teetering angle (βroot,ψ = βmean + β1sin sinψ + β1cos cosψ).131 The problem was 

attacked by Bell engineers, who had the most knowledge of their own product, using an 

iteration scheme that they called full aircraft trim. Both Boeing and Sikorsky engineers chose 

to input the measured fuselage pitch attitude. Boeing engineers then chose to vary the side 

force and propulsive force until the calculated values of flapping (β1sin and β1cos) matched the 

measured values. This approach solves for the cyclic control angles (B1s and A1s). Sikorsky 

engineers chose to input measured cyclic control angles and solve for the hub teetering angles. 

Neither analyses by Boeing nor Sikorsky could obtain a trim solution for the highest speed of 

142 knots. All three groups allowed the mean root feathering angle to vary until a semblance 

of forces equal to zero was obtain. Of course, the solution process then required poetic license 

and considerable engineering judgment (and still does). 

 First, let me show you some results for fuselage pitch attitude (Fig. 2-229). Bell’s 

prediction with its iteration scheme falls within ±1 degree, which is not, in my opinion, very 

good. However, the fact that the fuselage pitches nose-down to obtain increased forward 

-6

-5

-4

-3

-2

-1

0

1

0 20 40 60 80 100 120 140 160

Aircraft 

Pitch 

Attitude

 (deg)

Nose Down

True Airspeed (knots)

Bell

Boeing,

Sikorsky

Test

Fig. 2-229. The AH-1G fuselage pitch attitude trend with forward speed was captured 

by Bell’s C-60 analysis. Boeing and Sikorsky used the measured data as input to 

their comprehensive analyses. 

 

130 Keep in mind that with mast bending, shaft angle of attack and fuselage angle of attack are not the same. 

Furthermore, fuselage angle of attack and fuselage pitch attitude are also not the same. 

131 The sign convention for the Fourier series representing blade feathering and hub teetering is not standardized 

within the industry. Some members use a carryover from the autogyro era while others use a mathematically 

pure form. In addition, the words longitudinal and lateral are represented by many different symbols and 

subscripts. Finally, plus and minus frequently can be misinterpreted. I can only suggest that you take 

extraordinary care when dealing with these aspects of helicopter trim. 
2.6 VIBRATION 

381 

speed is a fact that is captured. You should know that pilots and passengers do not like to fly 

tilted nose-down, and they will complain if the tilt is more than –2 or –3 degrees. 

 Next, consider the longitudinal (B1s) and lateral (A1s) blade feathering components in 

Fig. 2-230 and Fig. 2-231 below. Bell and Boeing predicted longitudinal cyclic to within ±1 

degree. Sikorsky chose the test data as an input to its comprehensive analysis. Keep in mind 

that all three participants used fuselage attitude as an input to their comprehensive analyses. 

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

1

0 20 40 60 80 100 120 140 160

True Airspeed (knots)

Bell

Sikorsky

Longitudinal

Cyclic

B1s

(deg)

Forward

θroot,ψ = θmean + B1s sinψ + A1s 

Test

Boeing

Fig. 2-230. Bell and Boeing predicted longitudinal cyclic to within ±1 degree. Sikorsky 

chose the test data as an input to its comprehensive analysis. 

0

1

2

3

4

5

6

0 20 40 60 80 100 120 140 160

True Airspeed (knots)

Bell

Boeing

Lateral

Cyclic

A1s

(deg)

Stick

Left

Test

Sikorsky

θroot,ψ = θmean + B1s sinψ + A1s 

Test

Fig. 2-231. Bell and Boeing underpredicted lateral cyclic. 
2.6 VIBRATION 

382 

Fig. 2-231 shows that lateral cyclic was underpredicted. Lastly, consider the hub teetering 

angle (perhaps you prefer the once-per-revolution flapping angle) provided in Fig. 2-232 and 

Fig. 2-233. 

 Prediction of trim angles is a mandatory first step in analyzing any aspect of helicopter 

behavior. The DAMVIBS participants were able to demonstrate the state of the art in the 

1980s. Their results showed that the rotorcraft industry was making progress but that the 

comprehensive analyses of the time were still falling short. 

0

0.5

1

1.5

2

2.5

3

0 20 40 60 80 100 120 140 160

Test

Sikorsky

Bell

Longitudinal

Flapping

β1cos

(deg)

βroot,ψ = βmean + β1sin sinψ + β1cos 

True Airspeed (knots)

Boeing

Up at ψ = 0 deg

Test

Fig. 2-232. Bell and Sikorsky predicted longitudinal flapping to within ±0.75 degree. 

Boeing chose the test data as an input to its comprehensive analysis. 

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 20 40 60 80 100 120 140 160

Test

Sikorsky

Bell Lateral

Flapping

β1sin

(deg)

βroot,ψ = βmean + β1sin sinψ + β1cos 

True Airspeed (knots)

Boeing

Up at ψ = 90 deg Test

Fig. 2-233. Bell and Sikorsky predicted longitudinal flapping to within ±0.5 degree. 

Boeing chose the test data as an input to its comprehensive analysis. 
2.6 VIBRATION 

383 

 The accurate prediction of vibration was the objective of the DAMVIBS participants, 

but as Fig. 2-234 and Fig. 2-235 show, this objective was not met. I have selected results from 

just one fuselage station, the AH-1G nose, to support this conclusion. However, saying that 

the objective was not met is not to say that the DAMVIBS program was a failure. It was far 

from it. Industry and NASA researchers threw every element of 1980’s advanced technology 

they had at the helicopter vibration problem. There were two major contributions that stand 

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 20 40 60 80 100 120 140 160

Nose

Vertical

2/Rev

Amplitude

± g 

True Airspeed (knots)

Boeing

Bell

McDonnell

Sikorsky

Test

Fig. 2-234. AH-1G nose vertical vibration prediction during the DAMVIBS program. 

0

0.03

0.06

0.09

0.12

0.15

0.18

0.21

0 20 40 60 80 100 120 140 160

Nose

Lateral

2/Rev

Amplitude

± g 

Bell Boeing

Sikorsky

Test McDonnell

Fig. 2-235. AH-1G nose lateral vibration prediction during the DAMVIBS program. 
2.6 VIBRATION 

384 

out. The first contribution was a giant leap forward in adapting NASTRAN to rotorcraft’s 

needs. The DAMVIBS participants established the minimum level of depth required to obtain 

the accurate natural frequencies and mode shapes of their current and future products. The 

second contribution was clear evidence that none of their comprehensive analyses could 

predict basic rotor system loads and deflections at the accuracy level required by the 

NASTRAN analysis in order to calculate vibration throughout the helicopter. 

 In January of 1993 Ray Kvaternik of the NASA Langley Research Center compiled 

and published a summary of the DAMVIBS program [462], which had been initiated in 1984. 

Ray’s summary view along with contributing papers from Bell, Boeing, McDonnell, and 

Sikorsky are included in this NASA publication. The conclusions reached by each participant 

are of immense value, and I have included several key points (in quotes, along with my 

additional thoughts without quotes) as follows: 

1. NASA—“Provided the leadership role and focal point for the type of structural dynamics 

research which was needed by the industry.” The workshop environment let the researchers 

exchange results and plan follow-on steps without compromising their competitive positions 

in the market place. 

2. Bell—“A detailed build-up FEM [NASTRAN finite element modeling] of the tail boom 

(rather than an elastic line) improved higher frequency correlations. The effects of secondary 

structure, non-structural panels, and canopy should be considered during the design phase. In 

the future, aeroelastic rotor analysis improvements are needed in the representation of rotor 

downwash and the calculation of hub loads for multi-bladed rotor systems.” In short, nothing 

can be overlooked in the NASTRAN model and that includes damping. Problems with 

calculating hub loads need to be fixed. 

3. Boeing—“A non-linear response with force was observed during shake testing. The 

frequency at the peak responses tended to decrease with increasing force level. The amplitude 

increased, but not proportionally with force level. Frequency shifts up to nearly 1 Hz and 

amplitude changes up to 35% were observed for a 2 to 1 change in force level. The changes 

were neither uniform across the spectrum nor consistent with frequency. Attachment of large 

concentrated weights or lumped masses to the airframe can be critical. The attachments must 

correctly transmit loads into the structure. Mass modeling in general has been treated rather 

superficially compared to stiffness. Considering the modal complexity of the higher order 

natural frequencies near b/rev, much more detailed modeling is needed. Modeling of a 

composite aircraft is more difficult than a comparable metal aircraft because of the need to 

determine equivalent physical properties for multi-ply structures of varying ply orientations, 

thicknesses and material types. The Stress group, as a general practice, needs to adopt 

modeling procedures which are compatible with both static and dynamic modeling 

requirements. Cost of the effort to provide a model for both static and dynamic analysis is 5 % 

of the airframe design effort. Cost of the static model alone is 4 % so the dynamic model costs 

only add an additional 1 %.” 

4. McDonnell—“The proper modeling of the mass distribution and representation of 

secondary and non structural components is essential to accurate vibration modeling. Prior to 

performing the [shake] test, magnitude and types of excitation loads should be studied using 

FEM. Excellent correlation with AH-64 shake test results was obtained at most measurement 

locations up to 13 Hz. Automated DMAP procedures enhance the analysts capabilities to do 

[NASTRAN] model checkout and verification.” The first rule of Roger’s Rules for Rangers is 

‘Don’t forget noth’en.’ This rule seems to be particularly true when building a NASTRAN 
2.6 VIBRATION 

385 

finite element model. Application of AH-1G NASTRAN modeling to the AH-64 was off to a 

good start. 

5. Sikorsky—“The development of a finite element model of the UH-60A airframe having a 

marked improvement in vibration-predicting ability has been traced. A new program, 

PAREDYM, which automatically adjusts an FEM so that its modal characteristics match test 

values, has been developed at Sikorsky. This program has shared in the improvement of the 

UH-60A model. Along with the closer look at finite element modeling, which was engendered 

by the DAMVIBS program, came also a closer look at the shake test data which were being 

used for model verification. A preliminary investigation showed important effects on the 

airframe test data of the bungee system used to suspend the test article, effects not normally 

accounted for in finite element modeling. The objective of the DAMVIBS program was to 

raise the level of the finite-element modeling of helicopter airframes to the point where it 

would be taken seriously in its ability to predict vibration and in its ability to bring low 

vibration into the airframe design process. DAMVIBS has succeeded in doing this. Although 

much improvement remains to be done, it has brought respectability to the analytical 

prediction of inflight helicopter vibration, and its stated goal of bringing low vibration into the 

design process of helicopter airframes has been seriously begun.” 

These conclusions confirm the major step forward in obtaining accurate fuselage response 

given “exact” hub vibratory loads, as in a shake test or an analytical experiment using 

NASTRAN. At the end of the DAMVIBS program, the problem of how to get accurately 

calculated hub loads was squarely on the table. 

 The data and accomplishments of the DAMVIBS program were not lost on other 

members of the rotorcraft industry. In particular, Hyeonsoo Yeo132 and Inderjit Chopra133 at 

the University of Maryland tackled AH-G vibration prediction using a comprehensive 

analysis known as UMARC, which is short for University of Maryland Advance Rotor Code. 

They took considerable care in modeling the limber main-rotor mast and an underslung rotor 

hub shown in Fig. 2-228 because, as they stated in the abstract to their Journal of Aircraft 

paper [463], “Modeling of pylon flexibility is essential in the two-bladed teetering rotor 

vibration analysis.” Furthermore, they carefully accounted for the fact that Bell’s AH-1G 

transmission is mounted to the fuselage on elastomeric springs, which allow both lateral and 

longitudinal rocking, and a degree of main rotor inplane loads isolation from the fuselage. 

 When you read Yeo and Chopra’s vintage 1999 paper you will see that prediction of 

the rotor control angles required for trim were no better than what the four DAMVIBS 

participants were able to achieve, yet they obtained predicted 2/rev vibration at the pilot’s 

seat, both vertically and laterally, well within a factor of two. Unfortunately, their success did 

not carry over to prediction of pilot vibration levels at 4/rev. 

 

132 Hyeonsoo (Dr. Yeo as I like to call him because of his many contributions at such an early age) wrote this 

paper when he was a graduate research assistant to Inderjit. After serving his apprenticeship, he became (and still 

is) a valuable member of the U.S. Aeroflightdynamics staff located at NASA Ames Research Center. 

133 When the U.S. Army and NASA began the Rotorcraft Center of Excellence program in 1985, grants were 

awarded to several universities. Because of Inderjit’s leadership, the University of Maryland received financial 

support, and the result has been a string of outstanding young men and women quite capable of improving 

rotorcraft technology well beyond the level imagined by our pioneers. The same can be said about results from 

Georgia Tech, Rensselaer Polytechnic Institute, Penn State, and other universities that have participated in the 

Centers of Excellence program. 
2.6 VIBRATION 

386 

2.6.3.4 An Introductory UH-60A Example 

 As the NASA Langley Research Center sponsored DAMVIBS program drew to a 

close, NASA Ames Research Center took up the flight testing of a heavily instrumented UH60A [167, 437]. The program, as you read about earlier, was called the UH-60A Airloads 

Program and included full-scale flight testing and full-scale, rotor-alone, wind tunnel testing. 

Bill Bousman was honored to give the 31st AHS Nikolsky lecture at the 67th Annual Forum 

of the American Helicopter Society in May of 2011. Bill traced the history of helicopter 

testing for airloads (and blade loads and deflections) from 1954 up to the conclusion of the 

UH-60A Program in 2010. Because of Bill’s excellent lecture [464], the UH-60A Program, 

and the progress made in calculating airloads using computational fluid dynamics (CFD), I 

decided to have a little fun on the side. My motivation came to a head when Ethan Romander 

(who works for Bill Warmbrodt at the Flight Vehicle Research and Technology Division of 

Ames Research Center) presented a paper at the May 2011 Forum [465]. Ethan’s paper 

showed excellent correlation of rotor-alone performance with the UH-60A airloads rotor as 

tested in the 40- by 80-Foot Wind Tunnel at Ames Research Center. The task I gave myself 

was to predict UH-60A flight-measured vertical vibration at the flight crew station due only to 

vertical hub vibratory loads over a speed range using a very limited amount of resources.134 

 The resources available for this task were relatively simple. First of all, the measured 

UH-60A vibration at the crew station had been published by Karen Studebaker as you saw in 

Fig. 2-212. To augment this data, I prevailed on Bob Kufeld (at Ames Research Center) to 

pull out the vibration waveforms that would give more depth to the overview that Karen had 

provided. Second, the UH-60A configured for the Airloads Program had been shake tested by 

Sikorsky [466], and a NASTRAN model had been created [467]. The shake test data provided 

a ballpark for cockpit vertical g response per pound of vertical hub load. Third, Ethan 

Romander had shown very encouraging prediction of power required versus wind tunnel 

speed. Given that level of correlation, I decided to bet that maybe Ethan’s calculated hub 

loads would be adequate for this simple example. Ethan was kind enough to respond to every 

one of my requests. 

 Now let me relate the fun I had. Bob gave me vertical, lateral, and longitudinal 

vibration data for the pilot and copilot at several speeds. I chose to restrict my task to 

predicting only vertical vibration for the pilot. The pilot’s location corresponds to the 

measurement point labeled 7 on Fig. 2-224. The 7 speed points Bob picked (from a total of 

23) were obtained in steady, level flight at a weight coefficient solidity ratio of CW/σ = 0.08. 

Thus, I began with Table 2-31. To get a sense of what the pilot’s vertical vibration waveform 

looked like, I chose two data points: 8515 corresponding to a true airspeed of 47 knots and 

8534 corresponding to 158 knots. The time histories for both vertical vibratory responses 

extended over a 2-second period. Fig. 2-236 and Fig. 2-237 shows this “raw” data for eight 

revolutions within the 2 seconds. On the surface, these two figures look like an oscillograph 

 

134 It is my belief that—in the not too distant future—the AVID and DAMVIBS attacks will be repeated using 

the UH-60A Airloads Program data. The improvements in hub load prediction and NASTRAN modeling will 

then be applied, and the rotorcraft industry will have a new baseline for its capability to predict helicopter 

vibration. 
2.6 VIBRATION 

387 

strip-out that I grew up with. In those days we would quickly draw horizontal lines that 

showed the approximate minimum and maximum values, and then take an average to get a 

vibration amplitude. I would estimate from these two figures that at 47 knots the pilot was 

feeling ±0.20 g. At the higher speed, it looks to me like the pilot was feeling about ±0.32 g. 

This is about what Karen showed in Fig. 2-212. It is clear that the extremes of vibration are 

not constant over the eight revolutions. 

Table 2-31. Experimental Data Points for Harris’ UH-60A Vibration Example

Data 

Point 

Boom 

Indicated 

Airspeed 

(knots) 

True 

Airspeed 

(knots) 

Advance 

Ratio 

(Vt = 726 fps)

Weight 

Coefficient 

W 2

t

W C

AV = ρ

8515 35 47.33 0.110 0.00652 

8513 55 64.97 0.151 0.00654 

8511 75 88.11 0.205 0.00656 

8526 95 111.75 0.260 0.00652 

8528 115 132.09 0.308 0.00653 

8531 127 145.89 0.340 0.00654 

8534 138 157.93 0.368 0.00651 

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0 360 720 1080 1440 1800 2160 2520 2880

Pilot

Vertical 

Vibration

(g)

Azimuth (deg)

Fig. 2-236. UH-60A pilot vertical vibration at 47 knots over 8 revolutions. 
2.6 VIBRATION 

388 

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 360 720 1080 1440 1800 2160 2520 2880

Pilot

Vertical 

Vibration

(g)

Azimuth (deg)

Fig. 2-237. UH-60A pilot vertical vibration at 158 knots over 8 revolutions. 

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0 30 60 90 120 150 180 210 240 270 300 330 360

Rev 1

Rev 2

Rev 3

Rev 4

Rev 5

Rev 6

Rev 7

Rev 8

Harmonic Analysis

Pilot

Vertical 

Vibration

(g)

Azimuth (deg)

Fig. 2-238. Eight revolutions of UH-60A pilot vertical vibration at 47 knots. 
2.6 VIBRATION 

389 

-0.45

-0.4

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 30 60 90 120 150 180 210 240 270 300 330 360

Rev 1

Rev 2

Rev 3

Rev 4

Rev 5

Rev 6

Rev 7

Rev 8

Pilot

Vertical 

Vibration

(g)

Azimuth (deg)

Fig. 2-239. Eight revolutions of UH-60A pilot vertical vibration at 158 knots. 

 It would be nice, of course, if the eight revolutions of data repeated themselves in a 

very orderly manner. In my experience, this has never been the case with experimental time 

histories. These UH-60A pilot vertical vibration time histories are certainly no exception as 

Fig. 2-238 and Fig. 2-239 show. Of course, there is a sense of a 4/rev component in both 

figures, but the higher harmonics are clearly “contaminating” the waveforms. 

 Fig. 2-238 includes a heavy black line, which is the result of a Fast Fourier Transform 

(FFT) analysis over the eight revolutions of data. An FFT analysis is a statistical averaging 

process that assumes the data is “reasonably” repetitive and, therefore, can be represented by 

a Fourier series of the form 

(2.283) () ()

N N

0 i i 0i i

i1 i1

y a a cos i b sin i a A cos(i ) = == +   ψ + ψ = + ψ − φ    

where ( ) 2 2 A a b and arctan b a i i i i ii = + φ= . You can solve backwards for the harmonic 

coefficients (ai and bi) when given the amplitude (Ai) and the phase angle (φi) using the fact 

that ii i ii i a A cos and b A sin = φ = φ . Of course, i goes from 1 to whatever you want. 

 The heavy black line on Fig. 2-238 includes harmonics up to and including the 30th. 

The line might be considered a mean curve fit to the flight point. Because the experimental 

waveforms are so unsteady, you do not get a very comforting mathematical representation. 
2.6 VIBRATION 

390 

However, Fig. 2-240 shows that vibration at 4/rev is a major contributor to the overall 

magnitude. The magnitudes of the other harmonics are caused, in part, by the dissimilar 

blades used on the UH-60A as configured for the Airloads Program. One of the four blades 

was heavily instrumented for pressure measurements; another blade had a multitude of strain 

gauges. Vibration from other components cannot be ruled out. But keep in mind that flight 

test is measuring a situation that is hardly constant from one instant in time to the next, even 

in the smoothest of air. 

 The second facet of the problem—cockpit vertical g response per pound of vertical 

hub load—came from the paper [466] authored by Durno, Howland, and Twomey from 

Sikorsky Aircraft, and presented at the 43rd AHS Forum in May of 1987. On figure 32 of 

their paper, they contrasted DAMVIBS shake test results with the UH-60A Airloads Program 

configuration. The DAMVIBS configuration was tested at a weight of 9,500 pounds. The UH60A Airloads Program configuration was shake tested at 17,800 pounds. The contrast 

between pilot vertical response to a vertical hub shaking force for the two configurations is 

provided here in Fig. 2-241. 

 The results published by Durno and his coauthors included a preliminary opinion 

about why the two configurations had different responses. They wrote that 

“in order to investigate the differences between the empty DAMVIBS and a flight 

configuration, an additional test was conducted. The configuration was chosen to simulate the 

fight test vehicle to be used for the NASA/AEFA BLACK HAWK rotor loads test program. 

The aircraft weight was 18,800 lbs [468] and was made up by distributing the weights shown 

below. 

Weight Lbs Location 

Pilot 240 Sta 253 

Co-pilot 220 Sta 253 

Instrumentation 75 Sta 264 

Instrumentation 275 Sta 389 

Cargo 4550 Sta 360 

Fuel 2300 

Figure 32 [Fig. 2-241] presents a comparison of the frequency response at the cockpit floor in 

the vertical direction due to a vertical excitation. It is evident that there is considerable 

difference in the responses. The predominant modes below 4P are labeled on the figure. The 

most significant shift is in the third vertical bending mode of the DAMVIBS configuration. 

This mode appears to have shifted down from 19.3 Hz to 13 Hz. This large shift seems 

possible due to the shape of the DAMVIBS third vertical mode which has a lot of motion in 

the cabin center. This is where the mass was placed to increase the gross weight of the AEFA 

[early identification of the Airloads Program UH-60A] configuration. 

The modal frequencies that have been abstracted from analysis are presented in figure 33 

[reproduced here as Table 2-32]. These results are actually preliminary until all of the AEFA 

data has been analyzed and mode shapes generated. Again, the largest difference between the 

empty and flight configurations is in the 13 to 19 Hz range.” 
2.6 VIBRATION 

391 

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

0.12

0.13

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

V = 47 knots. Pt. 8515

V = 158 knots. Pt. 8534

Harmonic

Amplitude 

(g)

Harmonic (per rev)

Fig. 2-240. Harmonic amplitudes for UH-60A vibration at 47 and 158 knots true 

airspeeds from 20 revolutions. 

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0.0018

0 5 10 15 20 25 30 35 40 45 50

Maximum

Pilot

Vertical 

Vibration

per

pound

of 

Hub

Vertical

Shaking

Force

(± g/lb)

Shaker Frequency (Hz)

UH-60A

DAMVIBS Configuration

at Weight = 9,500 lbs

UH-60A

Airloads Configuration

at Weight = 17,800 lbs

Fig. 2-241. The UH-60A used in the Airloads Program at 17,800 pounds had a 

substantially different shake test response than did the DAMVIBS configuration 

at 9,500 pounds [466]. 
2.6 VIBRATION 

392 

Table 2-32. Comparison of Empty vs. Flight Configuration, Modal Frequencies 

Mode Description DAMVIBS NASA/AEFA 

1st Lateral Bending 5.5 5.4 

1st Vertical Bending 6.7 6.3 

Nose Vertical n/a 8.3 

Stabilator Yaw/Roll 10.6 n/a 

Stabilator Roll/Yaw 11.9 n/a 

2nd Vertical Bending 12.3 11.6 

Transmission Roll/2nd Lateral 13.8 n/a 

Nose Vertical/Tail Vertical 14.0 14.5 

Cockpit/Cabin Roll 15.4 15.3 

Stabilator Yaw/Pylon Torsion 16.1 n/a 

3rd Vertical/Transmission Vertical 19.3 13.0 

Stabilator Bending 25.2 25.9 

In the updated shake testing of the UH-60A in its Airloads Program configuration, Goodman 

reported [468] in 1990 that 

“ground vibration testing of the NASA/AEFA configuration was conducted as a follow-on to 

testing of a lower gross weight configuration which was supported by the NASA DAMVIBS 

program (Ref(c)). Both tests were conducted with the same UH-60A helicopter (S/N 86-

24507). In preparation for shake testing, the following aircraft rotor head components and 

equipment were removed: 

Main Rotor Blades Tail Rotor Blades 

Spindles Tail Rotor Hub 

Bearings Cabin Troop Seats 

Dampers Bifilar 

Tail Gearbox Cover Intermediate Gearbox Cover 

Nose Absorber Access Cover Lower Pylon Fairing 

Fuel 

The fairings and covers were removed to provide access to measurement locations. These are 

considered to be secondary structure having little or no impact on aircraft structural dynamics. 

The main rotor and tail rotor hubs were replaced by ones modified for compatibility with the 

shake test suspension system. With the hardware listed above removed and with the test hub 

installed, the test article weight was 9500 lbs with c.g. at Station 360". A total of 640 lbs were 

then added to the rotor hub to simulate 50% of the rotor flapping mass and the bifilar mass. 

This 640 lbs was comprised of 240 lbs of shaker hardware and 400 lbs of steel plates attached 

to hub arms. With the addition of the 640 lbs the total weight reached 10,140 lbs with c.g. at 

Station 359". This was the configuration tested under the DAMVIBS contract and is 

designated as the DAMVIBS configuration. Note that the rationale behind attaching 50% 

percent of the main rotor flapping mass and the bifilar mass is that this roughly simulates the 

4/rev rotor impedance of a UH-60A, and consequently will yield modes near 4/rev with 

properties similar to the modes of an aircraft in flight which have frequencies in the vicinity 

of 4/rev. 

At the completion of DAMVIBS testing the aircraft was re-configured for NASA/AEFA 

testing. A full fuel load of 2,300 lbs was added, as well as 5,360 of miscellaneous weight 

(locations shown in Figure 1), yielding a total weight of 17,800 lb. Note that the weight 

reported in Ref (b) for the NASA/AEFA configuration was reported incorrectly as 18,800 lb. 

For both the NASA/AEFA and the DAMVIBS configurations, the nose, forward cabin, and aft 

cabin absorbers were installed, but the leaf springs were blocked, rendering the absorbers 

inactive.” [My italics] 
2.6 VIBRATION 

393 

 Then in 1993, a NASTRAN model of the UH-60A configured for the Airloads 

Program was completed by Idosor and Seible at the University of California under a NASA 

Ames Research Center contract. Their report [467] clarified many configuration details and is 

a particularly well-written piece of theoretical and related experimental work. Their 

NASTRAN analysis identified 12 modes in the 0- to 20-Hz range. However, despite the many 

improved details, comparison of test to theory showed that an accurate NASTRAN model had 

still not been achieved. 

 Now for the third facet of the vibration prediction task. This portion of the task 

required some hub loads. As I mentioned earlier, Ethan Romander’s use of computational 

fluid dynamics (CFD) (plus computational structural dynamics (CSD)) to predict performance 

of the UH-60A rotor-alone encouraged me to ask for (and receive) his calculated hub loads. 

This was “betting on the come” that maybe the calculated hub loads would be in the 

“ballpark.” But to hedge my bet, I prevailed on Tom Norman (at Ames Research Center) to 

give me his “preliminary” 40- by 80-ft wind tunnel measured hub loads (from the balance) so 

that I might have a possible range for the “real” hub loads. With these two data sets in hand, I 

made the comparison shown in Table 2-33. To be reasonably sure that 1/rev, 4/rev, and 8/rev 

loads would be adequate for this introductory example, I examined the harmonic vertical 

vibratory loads of the test data at advance ratios of 0.15 and 0.40. As you can see from Fig. 

2-242, in a more thorough analysis every harmonic up to and including 12/rev, and even up to 

30/rev, might someday become important. Because I only had pilot vertical response up to 45 

Hz (about 10/rev for 258 rpm) from Fig. 2-241, I had to forgo including the rather large 12/rev 

load at an advance ratio of 0.40. 

Table 2-33. Theory and Test Vertical Vibratory Hub Loads for UH-60A Vibration 

Example (nominal rotor speed of 258 rpm (4.3 Hz) and nominal thrust of 20,000 lb)

(A) Theory From CFD + CSD 

Advance 

Ratio 

1/Rev 

Cosine 

1/Rev 

Sine 

1/Rev 

Amp 

4/Rev 

Cosine 

4/Rev 

Sine 

4/Rev 

Amp 

8/Rev 

Cosine 

8/Rev 

Sine 

8/Rev 

Amp 

0.15 0.0 0.0 0.0 827.4 314.1 885.0 –102.8 –186.9 213.3 

0.20 0.0 0.0 0.0 580.4 36.8 581.5 –193.5 –76.4 208.0 

0.30 0.0 0.0 0.0 51.1 –217.8 223.7 –228.6 730.3 765.3 

0.37 0.0 0.0 0.0 –205.8 –552.0 589.1 –173.1 344.1 385.2 

0.40 0.0 0.0 0.0 –219.2 –468.6 517.3 –30.3 292.5 294.1 

(B) Test From Run 52 of the 40- by 80-Foot Wind Tunnel Test Number Air Force 010 

Advance 

Ratio 

1/Rev 

Cosine 

1/Rev 

Sine 

1/Rev 

Amp 

4/Rev 

Cosine 

4/Rev 

Sine 

4/Rev 

Amp 

8/Rev 

Cosine 

8/Rev 

Sine 

8/Rev 

Amp 

0.15 476.3 –6.9 476.4 634.2 26.8 634.8 373.1 178.9 413.8 

0.20 651.2 –39.8 652.5 311.6 –62.9 317.8 473.8 60.5 477.7 

0.30 1006.6 79.1 1009.7 –230.5 –502.8 553.1 –404.0 –234.7 467.2 

0.37 1328.1 636.9 1472.9 -485.0 –1052.4 1158.8 –15.5 –224.5 225.0 

0.40 1287.0 1047.9 1659.6 –152.5 –882.8 895.9 –163.3 –227.2 279.8 
2.6 VIBRATION 

394 

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Advance Ratio = 0.15

Advance Ratio = 0.40

Harmonic

Amplitude

(lbs)

Harmonic (per rev)

Fig. 2-242. Rotor-alone test of vertical vibratory hub loads up to 30/rev as measured by 

the rotor balance (note: balance not calibrated for vibration). 

 Given hub loads (Table 2-33) and pilot response to the hub loads (Fig. 2-241), the 

actual prediction was rather simple. The pilot response to a vertical hub load at 4/rev 

(i.e., 17.2 Hz at 258 rpm) is 0.00054 g per pound. At 8/rev (34.4 Hz), the pilot response is 

0.00038 g per pound. The pilot vertical vibration, therefore, becomes simply 

(2.283) ( ) () ()

( ) () ()

pilot 4cos 4sin

8cos 8sin

V 0.00054 a cos 4 b sin 4

0.00038 a cos 8 b sin 8

= ψ     + ψ

+     ψ + ψ

which, of course, neglects 1/rev vibration. The results of applying this equation with both 

theory and test values of 4/rev and 8/rev vertical hub loads is shown in Fig. 2-243. As you can 

see, I have used all of Karen Studebaker’s data from Fig. 2-212. I have bounded her UH-60A 

Airloads Program data with lower and upper lines around her points, and then added the 

results from Eq. (2.283) as the red solid circles (theory hub loads) and black solid squares 

(40- by 80-ft wind tunnel test hub loads). Frankly, I was rather pleased to obtain results that 

were only off by a factor of two, using such a woefully incomplete method. 

 Fig. 2-243 shows that at an advance ratio of 0.30, the prediction of pilot vertical 

vibration with theoretical vertical vibratory hub loads is “spot on.” This led me to examine 

comparisons of theory and test waveforms for this point at 128 knots true airspeed. The 

comparison is shown in Fig. 2-244. Note first that the harmonic analysis (the heavy black line) 

of the eight revolutions is rather representative of the flight test measurements. 
2.6 VIBRATION 

395 

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Pilot 

Vertical 

Vibration 

(± g)

Advance Ratio

Predicted With 

UH-60A Rotor Alone 

Vertical Hub Loads

Predicted With 

CFD + CSD Rotor Alone 

Vertical Hub Loads

Studebaker

Fig. 2-211

Fig. 2-243. Pilot vertical vibration predicted with calculated and measured 4/rev and 

8/rev vertical vibratory hub loads. 

-0.4

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0 30 60 90 120 150 180 210 240 270 300 330 360

Rev 1 Rev 2

Rev 3 Rev 4

Rev 5 Rev 6

Rev 7 Rev 8

Harmonic Analysis

Pilot

Vertical 

Vibration

(g)

CFD + CSD Theory

Azimuth 

(deg)

Fig. 2-244. Predicted and measured pilot vertical vibration at 132 knots true airspeed. 
2.6 VIBRATION 

396 

Admittedly, you must stare at Fig. 2-244 for a while before you believe this, but more 

importantly, note that the predicted vibration using Ethan’s CFD + CSD vertical vibratory hub 

loads (the heavy red line) is, remarkably, just as representative of the flight test data. 

 This introductory example of the UH-60A vibration in the Airloads Program 

configuration is, of course, quite incomplete. You know this because of Table 2-30 on page 

373. Furthermore, theory used by Ethan Romander did not include coupled fuselage-rotor 

dynamics because it was a rotor-alone study. Of course, an analysis that assumes all blades are 

identical precludes any prediction of harmonic loads other than 4/rev, 8/rev, 12/rev, etc. 

2.6.4 Blade Vibratory Response, Hub Vibratory Loads 

 The fixed system (i.e., nonrotating) hub vibratory loads used in the preceding analysis 

of helicopter vibration are created by rotating system, blade root, and vibratory loads. As you 

learned in Volume I, each blade element has a vertical force, an inplane force, a radial force, 

and a torsional moment. You learned early in Volume I (pages 14 and 15) that when these 

forces are summed over the blade length and averaged over a revolution you will obtain the 

primary performance of the rotor. This process of averaging over a revolution hides a great 

deal of information about any specific blade element. It is precisely because of this radial 

integration and azimuthal averaging that rotor performance and fundamental behavior has 

been obtained with considerable accuracy for so many decades. The vibration problem, 

however, requires that the loads of each blade, obtained at each azimuth, be correct. This 

means that not only must the azimuthal average be correctly predicted, but the distribution of 

blade root loads at each azimuth must be correct as well. It is a saving grace that it is just the 

radial integration at each azimuth that must be correct; that means that some of the errors at 

each blade element will be self-cancelling as the sum from blade root to blade tip is taken—

one hopes. 

 Consider, if you will, the problem presented in Fig. 2-245, which shows the loads 

from one blade acting at the coincident flapping, lagging, and feathering hinge of a UH-60A 

hub. The blade itself is not shown, but imagine it is connected to the vertical pins located at 

the end of the basic hub arm and along the spanwise root shear force vector (RSspanwise). There 

is an x, y, z coordinate system that rotates with the hub, and the z-axis is parallel to the shaft 

(vertical). The x- (spanwise) and y- (chordwise) axes lie in a plane perpendicular to the 

shaft.135 The 0, 0, 0 point of the axis system is located at the exact center of the hub. The 

blade torsional moment is reacted at the root by the pitch link, which passes a vibratory load 

(PLload) to the airframe. In the world of torsion, it is very important to remember that the blade 

torsion moment is reacted by a force couple. This means that some of the vertical root shear 

contains the reaction to the pitch link load.136 

 

135 Over the years I seem to have adopted the notion that the radial dimension of the blade is associated with x 

and that x = r/R. I am quite sure that this thinking is not universal; the sign convention is more important. 

136 I have purposely left out considering the lead-lag damper load path in this introductory discussion. As you 

can see from Fig. 245, the lag damper bridges the elastomeric bearing and contributes loads primarily in the 

spanwise direction. Comprehensive analyses such as CAMRAD II place the shears at the hub centerline. 
2.6 VIBRATION 

397 

Fig. 2-245. Rotating blade root shears and pitch link load acting on a UH-60A hub 

(basic hub picture courtesy of Bill Bousman and Bob Ormiston, AFDD). 

 The rotating root shears and pitch link load for a single blade, once you have 

calculated them, are resolved into the nonrotating hub loads as you learned in Volume I. That 

is, 

(2.284) 

Z vertical load

X spanwise chordwise

Y spanwise chordwise

Thrust Hub F RS PL

H force Hub F RS cos RS sin

Y force Hub F RS sin RS cos

==+

−= = ψ + ψ

−= = ψ − ψ

. 

 Suppose now that you want to calculate the vertical shear load (RSvertical) and the two 

inplane shear loads (RSspanwise and RSchordwise). It is a simple matter to write the basic equation 

for the vertical root shear, which you encountered in Volume I. Based on Fig. 2-84 on page 

170 in Volume I, you later came to Eqs. 2.230 and 2.231 on page 199 of that volume, which I 

have reintroduced (with some symbol changes) here as 

(2.285) 

( ) ()

( )

R R

vertical r,t r,t load b 0 0

R R 2

r,t r,t

r load b 2

0 0

RS d L d I PL w

dL z

dr m dr PL w

dr t

= − −−

    ∂ = − −−       ∂  

 

   

 

where the blade weight (wb) is 255.6 pounds for one UH-60A blade. Do not forget that a blade 

torsional moment is resisted by force couple. That is why the vertical root shear in Eq. (2.285) 

includes the PLload term. This means that the pitch link load (PLload) has an equal and opposite 

Lead-lag 

damper

Push rod

Pitch 

horn Elastomeric bearing flap 

& lead-lag “axes”

Hub

Blade attachment

Lead-lag 

damper

Push rod

Pitch 

horn Elastomeric bearing flap 

& lead-lag “axes”

Hub

Blade attachment RSspanwise

RSvertical

RSchordwise PLload

ψ = 0 

ψ

Hub 

Arm 1 

Hub 

Arm 4 

Hub 

Arm 3 

Hub 

Arm 2 
2.6 VIBRATION 

398 

Airload 

& Inertia 

PLL 

PM 

PLL 

shear force located somewhere. For the UH-60A, this shear force 

acts at the coincident flap, lag, and feathering bearing. The little 

sketch at the right reinforces this point. This a load that must be 

considered in the design of bearings. 

 Because the blade element loads are known to be periodic 

(i.e., harmonic) in simple analytical cases, Eq. (2.285) can be 

rewritten in terms of azimuth (ψ) with the substitutions 

2

2 2

1 1

t or

dt d ψ=Ω =Ω

ψ

to give 

(2.286) ( )

R R 2

r, r, 2

vertical r load b 2

0 0

dL z

RS dr m dr PL w

dr

ψ ψ     ∂

= − Ω −−       ∂ ψ  

    

 

. 

In a similar manner, equations for the inplane root shears are written as 

(2.287) 

() ()

( ) ( )

R 2

R R r, r, 2 2

chordwise r r, r 2 0 0

0

R R

R r, r, 2

spanwise r r 0

0 0

dD y RS dr m y dr m dr dr

dF y RS dr 2 m dr m r dr

dr

ψ ψ

ψ

ψ ψ

    ∂

= +Ω −Ω       ∂ ψ  

  ∂

= −Ω + Ω     ∂ ψ







     

 



, 

and the pitch link load (PLload) becomes 

(2.288) 

( ) ( )

R R 2

R r, r, 2 2

load 2 r, 0

0 0

R R

r, r,

r, r,

0 0

R 2

R 2 2 r,

r, 2 r, r, 0

0

dPM d

Pitch arm PL dr I dr I dr

dr d

dL dD

y dr z dr dr dr

d z

cg pa m dr cg pa m z dr d

ψ ψ

θ θψ

ψ ψ

ψ ψ

ψ

ψ ψψ

  θ

× = − Ω − Ωθ     ψ

− +

+ −Ω + −Ω

ψ

     

     











. 

You can delve deeper into the derivation of these first-order equations by reading pages 421 to 

429 in Wayne Johnson’s book, Helicopter Theory [235]. You might note in passing that I have 

taken considerable poetic license in using dLr,ψ/dr, dDr,ψ/dr, and dFr,ψ/dr as blade element 

forces in the z-, y-, and x-axis directions. This requires a belief that all angles are small and, 

as you will soon see, is a very poor and unnecessary assumption in the study of rotorcraft 

vibration.137 

 What I do want you to appreciate is that the blade element airloads of lift (dLr,ψ/dr), 

drag (dDr,ψ/dr), radial (dFr,ψ/dr), and moment (dMr,ψ/dr) drive the blade out-of-plane bending 

 

137 The blade element forces must be resolved into the z-, x-, and y-axis directions and then be given new 

symbols. Let me wait a bit before switching to the correct description. 
2.6 VIBRATION 

399 

(zr,ψ) and inplane bending (yr,ψ). Furthermore, out-of-plane bending and inplane bending are 

directly connected as well. Of course, elastic twisting (θr,ψ) under the blade element forces and 

pitching moments leads to the pitch link load and alters the airloads, and to top it off, inplane 

motion is quite dependent on the lead-lag damper. The solution situation appears pictorially in 

Fig. 2-246. The rotorcraft industry has had this complex, highly coupled, computational 

problem for decades and has never given up improving successive solutions. 

 The perfect circle that you see in Fig. 2-246 implies an ultimately exact computational 

solution that agrees with experiment to a level well suited to reasonably accurate rotorcraft 

design. This goal has not been achieved as I write these words, however major 

accomplishments have been made over the last several decades. One set of milestones was 

published by Wayne Johnson [469]. Wayne was given the honor of presenting the 30th 

Nikolsky Lecture at the 2010 Annual Forum of the American Helicopter Society.138 As he 

pointed out, each successive milestone he examined improved the capabilities that 

aeromechanics researchers are reaching for. In reading Wayne’s excellent summary, you will 

note that major improvements were made in CSD methods to obtain the blade elastic 

deflections (i.e., zr,ψ, yr,ψ, and θr,ψ). These CSD improvements came well before comparable 

improvements were made in calculating blade element aerodynamic forces and moments 

using CFD. 

Fig. 2-246. The rotorcraft industry has faced this vicious computational circle for 

over eight decades. 

 

138 Somehow Wayne was able to capture the history of 19 milestones using only 298 references in his lecture, 

which makes his published paper [469] a milestone in itself. 

dLr,ψ/dr 

dDr,ψ/dr 

dFr,ψ/dr 

dMr,ψ/dr 

yr,ψ zr,ψ

θr,ψ
2.6 VIBRATION 

400 

 In my opinion, the success in applying CFD to obtain the blade element airloads that 

was achieved by Frank Caradonna, Chee Tung, and Andre Desopper in 1982 [470] was like 

the door opening in a very unpleasant, dark room. The icing on the cake came 2 years later 

when Wayne Johnson succeeded in coupling CFD to CSD (his well-known CAMRAD II 

comprehensive computer program [471]). This new foundational aeromechanics tool (CFD + 

CSD) reinvigorated rotorcraft researchers [465, 472-475] to a level that I cannot ever 

remember feeling or seeing. 

 The application of the CFD + CSD comprehensive analysis to the UH-60A Airloads 

Program flight test data (and the follow-on rotor-alone wind tunnel experiment) enabled 

Ethan Romander [465] to make computations leading to Fig. 2-243, and specifically to 

Fig. 2-244. 

Now let me give you a measure of how accurate a vintage 2010 advanced theory is in 

relation to the most comprehensive, full-scale, rotor-alone wind tunnel experiment ever 

conducted. For the theory, I will use the CAMRAD II + Overflow 2 comprehensive analysis 

as reported by Romander [465]. For the test, I will use data obtained from the UH-60A 

Airloads rotor-alone as tested in the 40- by 80-Foot Wind Tunnel at Ames Research Center. 

Specifically, this was Air Force test number 10, run 52. I have selected Points 30 and 31 for 

theory-test comparison, which are for an advance ratio of 0.3. I selected this advance ratio 

because the CFD + CSD theory appeared (in Fig. 2-243) to fall within the range of measured 

pilot vibration. The performance parameters for this 0.3 advance ratio case are provide in 

Table 2-34. 

 In the first place, the full-scale UH-60A Airloads rotor was mounted on the NASA 

Large Scale Rotor Test Apparatus, commonly called the LRTA. This assembly was then 

installed in the 40- by 80-Foot Wind Tunnel as shown in Fig. 2-247. The LRTA is, indeed, a 

large-scale piece of test equipment. The body-of-revolution fairing encloses a number of very 

heavy subassemblies as you can see from Fig. 2-248. A brief description [476] states that 

“the LRTA (Figs. 1 and 3) is a special-purpose drive and support system designed to test 

helicopters and tilt rotors in the NFAC. Developed for NASA and the U.S. Army by Dynamic 

Engineering, Inc., the LRTA is capable of testing rotors at thrust levels up to 52,000 lb. Its 

primary design features include 1) a drive system powered by two 3000 HP motors, 2) a fivecomponent rotor balance to measure steady and unsteady rotor hub loads, along with an 

instrumented flex-coupling to measure rotor torque, 3) a six-component fuselage load-cell 

system to measure steady fuselage loads, 4) a complete rotor control system (including 

console) with primary and higher harmonic control, and 5) an output shaft assembly with a 

replaceable upper shaft for mating with different rotor systems.” 

 Of course, the balance is the heart of any test rig such as the LRTA. As Fig. 2-249 

shows, the balance of the LRTA is quite large in diameter, but really not very tall. Calibrating 

the balance required enormous fixtures in themselves [477], and then both a static calibration 

and a dynamic calibration had to be completed [478]. This dynamic calibration was, in effect, 

a vibration test similar to the shake testing of helicopters that you read about earlier. The 

objective was to get balance output per pound of rotor vibratory forces and moments. 
2.6 VIBRATION 

401 

Table 2-34. UH-60A Rotor Performance Parameters for Theory vs. Test Analysis at an 

Advance Ratio of 0.3. Theory Required to Closely Match Thrust, Rolling Moment, and 

Pitching Moment at Test Shaft Angle of Attack by Adjusting Controls

Parameter Symbol Unit 

Test 

Value 

Theory 

Value Notes 

Density ρ slug/ft3 0.002298 Same 

Speed of Sound aS ft/sec 1,117.0 Same temp = 519.217 oR 

Forward Speed V ft/sec 217.8 Same 129 knots 

Tip Speed Vt ft/sec 726.0 Same 

Shaft Angle of Attack αS deg –4.202 forward (physical) 

Shaft Angle of Attack αScorr deg –3.495 Same forward (includes wall correction) 

Collective Pitch θ0 deg 10.02 13.888 at coincident hinge, + nose up 

Longitudinal Cyclic θsin deg –7.55 –7.422 at coincident hinge, + nose up 

Lateral Cyclic θcos deg 1.32 0.848 at coincident hinge, + nose up 

Thrust T lb 20,466 20,458 + up 

H-force H lb –101.1 200.47 + towards ψ = 0 deg 

Y-force Y lb –530.8 125.49 + towards ψ = 90 deg 

Rolling Moment Mroll ft-lb –1,658 –1,716 + starboard side up 

Pitching Moment Mpitch ft-lb –3,010 –3,021 + nose up 

Total Horsepower RHP hp 1,786 1,757 

 Induced + Profile HPind + profile hp n/a 1,218 CFD + CSD cannot separate 

 Propulsive HPpropulsive hp n/a 539

Fig. 2-247. Tom Norman (left) and Patrick (Rick) Shinoda inspect the UH-60A Airloads 

rotor system as installed on the LRTA in the Air Force 40- by 80-Foot Wind 

Tunnel located at NASA Ames Research Center. 
2.6 VIBRATION 

402 

Fig. 2-248. The 40-foot-long NASA LRTA. Two 3,000-hp electric motors can provide up 

to 165,000 ft-lbs of torque at rotor speeds up to 320 rpm [476]. 

Fig. 2-249. The key component of the LRTA is the balance. Thrust up to 52,000 lb and 

an inplane force up to 15,000 lb can be accurately recorded. The flexure posts are 

designed for a resultant moment of 125,000 ft-lbs at the balance center [478]. The 

distance from the balance center to the hub center was 61.5 in. for the UH-60 

Airloads rotor wind tunnel test. 
2.6 VIBRATION 

403 

 Fig. 2-245 showed rotor hub forces (and, of course, moments, which are not shown) 

and pitch links, which must be transmitted to the balance. These loads follow two different 

paths as Fig. 2-250 shows. In the case of steady, vertical loads with the four-bladed UH-60 

rotor, the balance reads the sum of vertical root shears (RSvertical) from hub arms 1, 2, 3, and 4 

plus the pitch link loads (PLload) from the four blades, which follow the gray shaded parts 

noted as Path 2 on Fig. 2-250. This sum is rotor thrust, which is a force acting directly normal 

to the upper ring of the balance. 

Fig. 2-250. Hub loads and pitch link loads follow different paths to the balance of 

the LRTA [478]. 
2.6 VIBRATION 

404 

Fig. 2-251. Bob Ormiston’s and my working sketch. 
2.6 VIBRATION 

405 

 The UH-60A Airloads rotor-alone test that I am using in this discussion is noteworthy 

because of one additional measurement that has rarely been included in past experiments. 

Measurements were made of the vertical shear in each arm of the hub. Strain gauges were 

applied along the neutral axis of each hub arm. The radial location of these shear gauges was 

approximately 15 inches from the center of rotation, which is the station taken as the focal 

point of the flap, lag, pitch bearing. These gauges provide a direct measurement of vertical 

shear as given by Eq. (2.286). 

 It is worth a moment to examine in more detail the two vertical load paths to the 

balance noted in Fig. 2-250. As you study Fig. 2-251,139 you can see rather quickly that the 

vertical shear loads from the four individual hub arms find their way to the balance by way 

of the shaft. The four individual pitch links load the rotating ring of the swashplate (see 

Fig. 2-44 on page 101 in Volume I for a more detailed drawing). The rotating ring loads 

transfer through ball bearings to the nonrotating ring, which is supported by three stationary 

actuators. The three actuator loads then collectively load a plate attached to the balance. 

Numerically, the result is that the balance reads a force normal to the balance equal to 

(2.289) 

4 44 3

vertical load vertical actuator

1 11 1

Balance normal force RS PL RS F = += +    . 

The fact that during this comprehensive test the hub arms were strain gauged for vertical shear 

is a terrific additional piece of instrumentation. The reason I say this is because several checks 

on the overall system accuracy can be obtained. Just take the steady normal force that the 

balance records as an example. The balance steady normal force is rotor thrust to the 

performance engineer. This statement is obviously true because pitch link loads cannot lift the 

helicopter and, of course, inertia loads cannot lift the helicopter. All that pitch link loads and 

inertia loads can do is break parts and vibrate the machine—and make noise while doing it. 

 Now that you have some idea of the test equipment, consider experimental results for 

the rotor forces as a function of the azimuth angle of hub arm 1. These forces are in the 

nonrotating system. If the balance was mounted to the helicopter roof, they would be the 

shaking force that the airframe feels. Hub arm 1 is the master blade in the reference system 

for this test. The balance normal force is vertical and along the shaft (BZ positive up). The 

balance longitudinal force (BX) is perpendicular to the shaft and directed aft towards the tail 

rotor (if it were there). The balance lateral force (BY) is perpendicular to the shaft and directed 

towards the azimuth position of 90 degrees, which would be to starboard because the UH-60 

main rotor rotates counterclockwise when viewed from the top. The steady (i.e., mean) value 

of these forces, which vary with master blade azimuth, are the rotor’s aerodynamic thrust (T), 

and H-force and Y-force—so important to the performance engineer. 

 The primary force, the balance vertical force that supports the machine, is examined in 

Fig. 2-252. Right away you can see an important difference between flight and wind tunnel 

 

139 After trying seven times to make my version of Fig. 2-251, I gave up and called Bob Ormiston for his help. 

We spent several hours discussing his sketch, which was ten times clearer than any I had made. There are several 

subtleties involved in how each load and its reaction can be drawn, and he knew how to steer clear of any 

unnecessary complications. Finally, we arrived at a rough draft of the figure. 
2.6 VIBRATION 

406 

testing. Here 64 revolutions of vertical force data have been superimposed to create the gray, 

shaded band you see. You will recall from the UH-60 flight test data that no such repeatability 

was apparent—at least in my mind. Furthermore, the average waveform, shown with the solid 

red circles obtained from the tabulated Fourier series coefficients, does appear to be a 

reasonable base for a test-versus-theory comparison. 

 The balance longitudinal and lateral forces are provided in Fig. 2-253 and Fig. 2-254, 

respectively. You can see that the repeatability over 64 revolutions is even better than for the 

balance vertical force shown in Fig. 2-252. 

 I would be sadly remiss if I did not emphasize that no dynamic calibration corrections 

have been made to the three balance force data figures you have before you. A dynamic 

calibration of the sort performed on the LRTA’s smaller cousin—the NASA Rotor Test 

Apparatus, reported in 1996 [478]—was completed in June of 2009, and the data reduction 

and report are in work as I write this. Until then, the rotor performance data (the balance and 

rotor-alone steady forces and moments) are considered satisfactory for theory-test 

comparisons as Romander reported [465]. Despite this unfinished work, I believe that this 

“hot-off-the-press” data is such a benchmark activity that you will find it referenced many 

times in the future. Therefore, you should be quite aware of this milestone in aeromechanics 

development. 

 You will note tabulation along the bottom of each figure. These tabulations provide 

the Fourier series coefficients that reproduce the red, solid circles you see on top of the gray 

bands of experimental data for 64 revolutions. To me, it is the objective of any advanced 

comprehensive analysis to predict these vertical, longitudinal, and lateral forces. As you will 

see shortly, we cannot make an accurate prediction yet, but with the data from this 

comprehensively instrumented UH-60 Airloads rotor and the advances obtained with CFD + 

CSD analyses—and continued hard work by the rotorcraft industry—I have no doubt that we 

will. 

16,000

18,000

20,000

22,000

24,000

0 30 60 90 120 150 180 210 240 270 300 330 360

Balance 

Vertical 

(lbs)

Hub Arm 1 Azimuth (deg)

N per REV 0 123 4 567 8 9 10 11 12 13 14 15 16

COSINE 20,466 1,007 101 -40 -230 21 -7 37 -404 -26 -105 7 61 -11 -3 -6 14

SINE 0 79 93 57 -503 102 -26 39 -235 -57 -39 -53 84 39 -25 -25 -136

Fig. 2-252. Balance vertical force for 64 revolutions at an advance ratio of 0.3. 

 (Note: no dynamical calibration applied.) 
2.6 VIBRATION 

407 

-8,000

-6,000

-4,000

-2,000

0

2,000

4,000

6,000

8,000

0 30 60 90 120 150 180 210 240 270 300 330 360

Balance

Longitudinal

Force

 (lbs)

Hub Arm 1 Azimuth (deg)

N per REV 0 123 4 567 8 9 10 11 12 13 14 15 16

COSINE -101 55 -119 -30 3,830 -130 -49 -116 63 86 43 -26 -63 52 -9 -8 -17

SINE 0 -88 -60 -4 -1,399 -299 223 -12 116 -1 46 12 -74 -36 37 12 16

Positive Aft

Fig. 2-253. Balance longitudinal force for 64 revolutions at an advance ratio of 0.3. 

(Note: no dynamical calibration applied.) 

-8,000

-6,000

-4,000

-2,000

0

2,000

4,000

6,000

0 30 60 90 120 150 180 210 240 270 300 330 360

N per REV 0 123 4 567 8 9 10 11 12 13 14 15 16

COSINE -531 37 -47 131 -125 -18 -134 -19 -207 -4 49 17 220 -4 -5 -29 -2

SINE 0 91 6 -46 3,695 7 -149 -59 109 -37 36 -24 74 54 -1 -8 -6

Hub Arm 1 Azimuth (deg)

Balance

Lateral

Force 

(lbs)

Positive Starboard

Fig. 2-254. Balance lateral force for 64 revolutions at an advance ratio of 0.3. 

(Note: no dynamical calibration applied.) 
2.6 VIBRATION 

408 

2.6.4.1 Dynamic Calibration of LRTA Balance 

 You have noted, I am sure, that the three balance vibratory force measurements 

(Fig. 2-252, Fig. 2-253, and Fig. 2-254) have not been corrected for system dynamic response. 

Preliminary analysis of the dynamic calibration of the LRTA completed in June 2009 does 

show that the correction to balance vertical vibratory forces will be reasonably accurate. You 

can see this from Fig. 2-255 where amplification factors range from 0.9 to 1.4 for integer 

harmonics up to 8/rev. Unfortunately, the situation for the inplane balance vibratory forces 

presents a real challenge. Both Fig. 2-256 and Fig. 2-257 show that the primary 4/rev 

vibration characteristic of a four-bladed rotor system is severely amplified by a lack of 

stiffness within the hub to balance load path. 

 As you have learned, resonance peaks in situations where there is little damping are 

accompanied by very steep gradients on either side of the maximum. This makes obtaining 

accuracy in determining amplification factors quite difficult. In this UH-60A Airloads rotor 

test example, the 4/rev vibratory inplane forces are tabulated in Fig. 2-253 and Fig. 2-254 as 

being over ±3,500 pounds, which must be reduced by a factor of 10 for the longitudinal force 

and a factor of 5.5 for the lateral force. Roughly speaking then, the inplane vibration is not the 

±4,000 pounds shown in Fig. 2-253 and Fig. 2-254, but more on the order of ±350 to ±400 

pounds when the dynamic calibration is ultimately applied. The importance of this 

experimental situation cannot be overstated. It means that theory-versus-test comparisons for 

inplane vibratory forces are not, as I write this, very informative. Such has been the story of 

vibration for seven decades, but in this example, a great deal can be learned about vertical 

force. 

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

0 5 10 15 20 25 30 35 40

1/Rev

8/Rev 7/Rev

6/Rev

5/Rev

4/Rev

3/Rev 2/Rev

Shake Test Frequency (Hertz)

Vertical Force

Amplification 

Factor

 (lbs per lb of 

shaking force)

Per 

Rev Hertz

Amplification 

Factor

Phase 

(deg)

1 4.306 1.044 -0.24

2 8.6 0.889 -5.06

3 12.9 0.935 -3.68

4 17.2 0.993 -4.08

5 21.5 1.043 -14.43

6 25.8 1.144 -10.08

7 30.1 1.259 -17.70

8 34.4 1.419 -18.91

Fig. 2-255. Vertical force dynamic calibration (per revolutions based on 258.33 rpm). 
2.6 VIBRATION 

409 

0

2

4

6

8

10

12

0 5 10 15 20 25 30 35 40

1/Rev 8/Rev

7/Rev 6/Rev

5/Rev

4/Rev

3/Rev

2/Rev

Shake Test Frequency (Hertz)

Longitudinal 

Force

Amplification 

Factor

 (lbs per lb of 

shaking force)

Per 

Rev Hertz

Amplification 

Factor

Phase 

(deg)

1 4.306 0.836 -0.61

2 8.6 1.329 -9.90

3 12.9 1.662 -5.56

4 17.2 9.317 49.19

5 21.5 0.960 -7.50

6 25.8 0.277 -1.63

7 30.1 0.055 -5.83

8 34.4 0.539 -9.55

Fig. 2-256. Longitudinal force dynamic calibration (per revolutions based 

on 258.33 rpm). 

0

2

4

6

8

10

12

0 5 10 15 20 25 30 35 40

1/Rev

7/Rev 8/Rev 6/Rev

5/Rev

4/Rev

3/Rev

2/Rev

Shake Test Frequency (Hertz)

Lateral Force

Amplification 

Factor

 (lbs per lb of 

shaking force)

Per 

Rev Hertz

Amplification 

Factor

Phase 

(deg)

1 4.306 0.631 -3.68

2 8.6 0.917 -2.26

3 12.9 1.941 -16.66

4 17.2 5.459 37.98

5 21.5 1.312 -24.17

6 25.8 0.420 -26.83

7 30.1 0.029 19.69

8 34.4 0.082 20.22

Fig. 2-257. Lateral force dynamic calibration (per revolutions based on 258.33 rpm). 
2.6 VIBRATION 

410 

2.6.4.2 Vertical Forces 

 While an immediate correlation between theory and test cannot be made now with the 

balance data, there is a much more informative comparison to be seen. As mentioned earlier, 

data from four vertical shear strain gauges were obtained during this very comprehensive 

experiment. A comparison of theory to the measured vertical shear (RSvertical) of each hub arm 

and associated blade pitch link load (PLload) is more than fascinating.140 The reason that these 

data channels are so vital is that the contribution of each individual blade to the balance 

vertical force can be examined. This is particularly important when the research blades are 

not identical, as in this case. In this UH-60A rotor-alone test with mismatched blades due to 

instrumentation, the situation was that: 

• Hub arm 1 had a pressure blade attached, colored red 

• Hub arm 2 had a standard blade attached, colored black 

• Hub arm 3 had a strain-gauged blade attached, colored green 

• Hub arm 4 had a standard blade attached, colored blue 

 The following discussion entails graphs of data for each blade, using one page per 

blade. The four examples show theory versus test for vertical shear and pitch link load. Both 

theory and test make the vertical shear calculation according to Eq. (2.286), which is repeated 

here for convenience as 

(2.286) ( )

R R 2

r, r, 2

vertical r load b 2

0 0

dL z

RS dr m dr PL w

dr

ψ ψ     ∂

= − Ω −−       ∂ ψ  

    

 

. 

There is a little bookkeeping done with blade weight, which I will discuss after you have 

reviewed the graphs (Fig. 2-258 through Fig. 2-265) on the following several pages. 

 It is important, however, for you to realize that steady loads (also called mean loads) 

that lead to the rotor thrust are derived from Eq. (2.286) as 

(2.290) 

R

r,

vertical load b

0

dL

Rotor Thrust 1 Blade dr RS PL w

dr

  ψ = = ++    



 . 

The steady load of the inertia term in Eq. (2.286) must, by the laws of physics, be zero, and 

pitch link loads cannot lift the machine, as I pointed out earlier. 

 With these thoughts in mind, you will immediately notice in Fig. 2-258 and Fig. 2-259 

that vertical shear waveforms between theory and test are encouragingly similar. Furthermore, 

the pitch link load waveforms show primarily that the predictions have a steady load nearly 

three times more negative (nose down) than the experimental results. Fig. 2-259 shows that 

the advancing side of the blade travel is remarkably well predicted in waveform shape, but the 

retreating side (i.e., from 180 degrees back to 360 degrees azimuth) is clearly not well 

predicted at all. I would suggest that because the CFD model did not include a bent-up trailing 

edge tab, these earlier results will improve significantly in the near future. 

 

140 No similar instrumentation was included for the inplane shears, but I am sure that some future experiment 

will add this important data. 
2.6 VIBRATION 

411 

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

0 30 60 90 120 150 180 210 240 270 300 330 360

Hub 

Arm 1 

Rotating 

Vertical 

Shear

from

Pressure

Blade 

(lbs)

Hub Arm 1 Azimuth (deg)

TEST N per REV 0 1 23 4 567 8 9 10

TEST COSINE 5,487 1,259 -162 -465 165 -169 -111 137 -117 -15 -12

TEST SINE 0 199 -1,016 -28 -440 178 -11 6 24 25 44

TEST AMPLITUDE 1,274 1,029 466 470 245 112 137 119 29 46

THEORY N per REV 0 1 23 4 567 8 9 10

THEORY COSINE 6,450 910 -230 -247 25 119 6 101 -49 -10 8

THEORY SINE -620 -1,062 213 -148 243 1 23 203 12 -1

THEORY AMPLITUDE 1,101 1,086 327 150 271 6 104 209 16 8

Fig. 2-258. Pressure blade on hub arm 1. 

-2,500

-2,000

-1,500

-1,000

-500

0

500

0 30 60 90 120 150 180 210 240 270 300 330 360

Pitch 

Link 

Load

1

(lbs)

Tension

Hub Arm 1 Azimuth (deg)

TEST N per REV 0 1 23 4 567 8 9 10

TEST COSINE -502 374 38 -12 -123 91 40 -29 22 10 14

TEST SINE 0 104 199 -75 213 78 -25 12 -8 -3 -1

TEST AMPLITUDE 389 203 76 246 120 47 31 23 11 14

THEORY N per REV 0 1 23 4 567 8 9 10

THEORY COSINE -1,337 287 -42 -28 -12 -10 11 -5 -8 4 13

THEORY SINE -66 192 34 94 -38 10 11 -20 -16 -3

THEORY AMPLITUDE 294 196 45 95 39 15 12 22 17 13

Fig. 2-259. Pressure blade on hub arm 1. 
2.6 VIBRATION 

412 

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

0 30 60 90 120 150 180 210 240 270 300 330 360

Hub 

Arm 2 

Rotating 

Vertical 

Shear

from

Standard

Blade 

(lbs)

Hub Arm 1 Azimuth (deg)

TEST N per REV 0 1 23 4 567 8 9 10

TEST COSINE 5,672 -467 203 36 104 -115 85 -9 -74 -58 -19

TEST SINE 0 1,057 1,146 430 -378 -115 4 -58 51 -9 -27

TEST AMPLITUDE 1,155 1,164 432 392 163 85 59 90 58 33

THEORY N per REV 0 1 23 4 567 8 9 10

THEORY COSINE 6,450 620 230 213 25 -243 -6 23 -49 -12 -8

THEORY SINE 910 1,062 247 -148 119 -1 -101 203 -10 1

THEORY AMPLITUDE 1,101 1,086 327 150 271 6 104 209 16 8

Fig. 2-260. Standard blade on hub arm 2. 

-2,500

-2,000

-1,500

-1,000

-500

0

500

0 30 60 90 120 150 180 210 240 270 300 330 360 Pitch 

Link 

Load

2

(lbs)

Tension

Hub Arm 1 Azimuth (deg)

TEST N per REV 0 1 23 4 567 8 9 10

TEST COSINE -541 -85 -20 -40 -84 -53 -20 8 17 9 7

TEST SINE 0 385 -245 21 186 78 15 6 -15 8 4

TEST AMPLITUDE 394 246 45 204 95 25 10 22 12 8

THEORY N per REV 0 1 23 4 567 8 9 10

THEORY COSINE -1,337 66 42 34 -12 38 -11 11 -8 16 -13

THEORY SINE 287 -192 28 94 -10 -10 5 -20 4 3

THEORY AMPLITUDE 294 196 45 95 39 15 12 22 17 13

Fig. 2-261. Standard blade on hub arm 2. 
2.6 VIBRATION 

413 

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

0 30 60 90 120 150 180 210 240 270 300 330 360

Hub Arm 1 Azimuth (deg)

Hub 

Arm 3 

Rotating 

Vertical 

Shear

from

Strain 

Gaged

Blade 

(lbs)

TEST N per REV 0 1 23 4 567 8 9 10

TEST COSINE 5,786 -467 -252 351 123 144 -93 -77 -96 12 -14

TEST SINE 0 -430 -1,207 81 -316 -76 -7 -12 28 -25 30

TEST AMPLITUDE 635 1,233 360 339 163 93 78 100 28 33

THEORY N per REV 0 1 23 4 567 8 9 10

THEORY COSINE 6,450 -910 -230 247 25 -119 6 -101 -49 10 8

THEORY SINE 620 -1,062 -213 -148 -243 1 -23 203 -12 -1

THEORY AMPLITUDE 1,101 1,086 327 150 271 6 104 209 16 8

Fig. 2-262. Strain-gauged blade on hub arm 3. 

-2,500

-2,000

-1,500

-1,000

-500

0

500

0 30 60 90 120 150 180 210 240 270 300 330 360

Pitch 

Link 

Load

3

(lbs)

Tension

Hub Arm 1 Azimuth 

TEST N per REV 0 1 23 4 567 8 9 10

TEST COSINE -422 -394 14 40 -95 -54 44 6 22 -4 7

TEST SINE 0 -173 247 -4 152 -66 -17 -10 0 1 -11

TEST AMPLITUDE 431 248 40 179 85 48 12 22 4 13

THEORY N per REV 0 1 23 4 567 8 9 10

THEORY COSINE -1,337 -287 -42 28 -12 10 11 5 -8 -4 13

THEORY SINE 66 192 -34 94 38 10 -11 -20 16 -3

THEORY AMPLITUDE 294 196 45 95 39 15 12 22 17 13

Fig. 2-263. Strain-gauged blade on hub arm 3. 
2.6 VIBRATION 

414 

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

0 30 60 90 120 150 180 210 240 270 300 330 360

Hub Arm 1 Azimuth (deg)

Hub 

Arm 4 

Rotating 

Vertical 

Shear

from

Standard 

Blade

 (lbs)

TEST N per REV 0 1 23 4 567 8 9 10

TEST COSINE 5,982 544 299 6 59 198 84 -2 -71 49 -44

TEST SINE 0 -740 1,266 -321 -295 119 -9 111 65 3 -41

TEST AMPLITUDE 918 1,301 321 301 231 84 111 96 49 60

THEORY N per REV 0 1 23 4 567 8 9 10

THEORY COSINE 6,450 -620 230 -213 25 243 -6 -23 -49 13 -8

THEORY SINE -910 1,062 -247 -148 -119 -1 101 203 10 1

THEORY AMPLITUDE 1,101 1,086 327 150 271 6 104 209 16 8

Fig. 2-264. Standard blade on hub arm 4. 

-2,500

-2,000

-1,500

-1,000

-500

0

500

0 30 60 90 120 150 180 210 240 270 300 330 360

Pitch 

Link 

Load

4

(lbs)

Tension

Hub Arm 1 Azimuth (deg)

TEST N per REV 0 1 23 4 567 8 9 10

TEST COSINE -661 214 -1 69 -30 61 -19 -9 8 -10 24

TEST SINE 0 -245 -247 -22 133 -72 26 -40 -8 -21 3

TEST AMPLITUDE 325 247 72 136 95 32 41 12 24 24

THEORY N per REV 0 1 23 4 567 8 9 10

THEORY COSINE -1,337 -66 42 -34 -12 -38 -11 -11 -8 -16 -13

THEORY SINE -287 -192 -28 94 10 -10 -5 -20 -4 3

THEORY AMPLITUDE 294 196 45 95 39 15 12 22 17 13

Fig. 2-265. Standard blade on hub arm 4. 
2.6 VIBRATION 

415 

 To make the four preceding comparisons, I had to change the bookkeeping of the 

blade weight (wb), which is 255.6 pounds. Data reduction for the test placed the blade weight 

in the balance wind-off weight tares, which means that in Eq. (2.286), blade weight is 

assumed to be zero. In contrast, the CFD + CSD theory correctly accounts for blade weight 

according to Eq. (2.286), and so I added the 255.6 pounds back in (by hand). This juggling 

leads to the comparison of mean loads shown in Table 2-35. 

 In my experimental experience, I have never seen the absolute accuracy of mean 

(i.e., steady) loads that you have before you in Table 2-35. The rotor thrust has been obtained 

directly by the balance and by data from both paths shown in Fig. 2-250. The balance says 

that the rotor thrust is 20,466 pounds, and the sum of vertical shears and pitch link loads says 

that the rotor thrust is 20,801 pounds. This difference of 335 pounds out of roughly 20,000 

pounds is a difference of 1.6 percent, which I consider extraordinary and a very real 

compliment to the team that put this comprehensive UH-60A rotor test together. Note that the 

theory (20,452 lb) matches the balance (20,466 lb), which was the ground rule for this trim 

condition at an advance ratio of 0.3. 

 Now let me take a moment to compare the results from the individual blades to each 

other. It has always been the task of the manufacturing side of the rotorcraft industry to make 

blades and other key components of the rotor system assembly identical. However, the 

drawings released from engineering always include ± tolerances. The accumulation of these 

generally small tolerances has frequently led to an out-of-tolerance system and real problems 

on the delivery line. This is particularly true when matching blades, so the customer flies 

away in a machine with very low, 1/rev vibration. 

 When you look at blade-to-blade results from the vertical shear measurements in 

Fig. 2-266, you immediately see that the standard blades are, in fact, not very well matched, 

but then neither are the pressure- and strain-gauged blades. However, taken as a group, these 

experimental results are extremely encouraging. It is just the theory (the black, solid circles) 

that really stands out. I suggest that when agreement between test and theory for the pitch link 

loads (Fig. 2-267) is obtained, then the vertical shear graph comparison in Fig. 2-266 will be 

considerably more attractive. 

Table 2-35. UH-60A Steady Vertical Shear and Pitch Link Load Comparison at an 

Advance Ratio of 0.3 and a Blade Loading Coefficient (CT/σ) of 0.09

Item 

Vertical Shear 

(RSvertical in lb) 

Pitch Link Load 

(PLload in lb) 

Contribution 

to Thrust (lb) 

Test Balance Thrust n/a n/a 20,466 

 

Test Hub Arm 1 5,487 –502 4,985 

Test Hub Arm 2 5,672 –541 5,131 

Test Hub Arm 3 5,786 –422 5,364 

Test Hub Arm 4 5,982 –661 5,321 

Test Total Thrust 22,927 –2,126 20,801 

 

Theory 1 Hub Arm 6,450 –1,337 5,113 

Theory 4 Hub Arms 25,800 –5,348 20,452 
2.6 VIBRATION 

416 

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

0 30 60 90 120 150 180 210 240 270 300 330 360

Pressure Blade, Hub Arm 1

Standard Blade, Hub Arm 2

Strain Gaged Blade, Hub Arm 3

Standard Blade, Hub Arm 4

CAMRAD II + Overflow 2

Rotating 

Vertical 

Shears

(lbs)

Hub Arm Azimuth (deg)

Fig. 2-266. Blade-to-blade comparison of rotating vertical shear at an advance ratio 

of 0.3 and a blade loading coefficient (CT/σ) of 0.09. 

-2,400

-2,000

-1,600

-1,200

-800

-400

0

400

0 30 60 90 120 150 180 210 240 270 300 330 360

Pressure Blade, Hub Arm 1

Standard Blade, Hub Arm 2

Strain Gaged Blade, Hub Arm 3

Standard Blade, Hub Arm 4

CAMRAD II + Overflow 2

Hub Arm Azimuth (deg)

Pitch 

Link 

Loads

(lbs)

Fig. 2-267. Blade-to-blade comparison of pitch link load at an advance ratio of 0.3 and 

a blade loading coefficient (CT/σ) of 0.09. 
2.6 VIBRATION 

417 

 To conclude this discussion of vertical force measurements and theory, take a look, if 

you will, at the three curves shown in Fig. 2-268. The balance reading is the vertical force that 

would shake the UH-60 in flight, in my view. The summation of vertical forces from the root 

shear gauges (RSvertical) and the pitch links (PLload) appears to add some distortion in the 

comparison because of differences in higher harmonic coefficients. The theory is, clearly, far 

from adequate and contains an excessive amount of 8/rev content in its waveform. In terms of 

overall amplitude, you can see that the balance is showing ±1,550 pounds about a steady load 

of 20,446 pounds. The same load obtained by component force summation is ±1,825 pounds 

about a steady load of 20,801 pounds. Finally, the theory is only estimating ±950 pounds 

about the steady load of 20,452 pounds. 

 You might be discouraged by the concluding result given in Fig. 2-268. You should 

not be. I say this because, in my experience, just getting theory to fall on the same scale as test 

has often seemed a miracle when dealing with vibration problems, and remember, this has 

been a review of “hot-off-the-press” data from the most comprehensive test of a full-scale 

rotor in a wind tunnel. I have great confidence that the current group of aeromechanics 

researchers will scrutinize data from this experiment in detail, improve shortcomings of 

current theories, and produce far better comparisons over the complete range of speeds, 

thrusts, and shaft angles of attack that this UH-60 Airloads rotor was tested at. 

 Now consider the analysis of inplane forces, which you were introduced to with 

Fig. 2-253 and Fig. 2-254. 

18,000

18,500

19,000

19,500

20,000

20,500

21,000

21,500

22,000

22,500

23,000

0 30 60 90 120 150 180 210 240 270 300 330 360

Balance

4 4

vertical load

1 1

  RS PL +

CAMRAD II + Overflow 2

Hub Arm Azimuth (deg)

Vertical 

Vibratory 

Force

(lbs)

Fig. 2-268. Vertical vibratory force comparison between theory and test at an advance 

ratio of 0.3 and a blade loading coefficient (CT/σ) of 0.09. 
2.6 VIBRATION 

418 

2.6.4.3 Longitudinal and Lateral Inplane Forces 

 There is no doubt that rotor system vibratory inplane loads are every bit as important 

as vertical forces. You read about this in the vibration chapter in Volume I. In fact, you can 

see from Fig. 2-253 and Fig. 2-254 that the overall amplitude of inplane vibratory loads might

be nearly two to three times higher than the vertical vibratory loads shown in Fig. 2-252. 

(I say might be, because the balance inplane forces from this test have yet to be corrected for 

dynamic response.) Of course, the proportions between vertical and inplane forces vary 

considerably with flight conditions, but for this UH-60 Airloads rotor example at an 0.3 

advance ratio, inplane loads are certainly not negligible—though I really doubt they can be as 

large as I have reported in Fig. 2-253 and Fig. 2-254. 

 The longitudinal and lateral vibratory forces were obtained in two ways during this 

wind tunnel test of the full-scale UH-60A Airloads rotor system. The primary way was 

directly from the balance, which is in the nonrotating world. (Remember, the balance loads 

have yet to be corrected for dynamic response, which may, in future reports, alter the 

waveform you see in Fig. 2-253 and Fig. 2-254.) The second path comes from resolving, to 

the nonrotating world, the rotating shears created by the hub loads associated with RSlongitudinal

and RSspanwise shown in Fig. 2-245. This is done following Eq. (2.284). Somewhat indirect 

measurements of these forces were obtained by shaft-bending-moment strain gauges mounted 

to the shaft several inches below the hub center as shown in Fig. 2-251. It would be nice if the 

comparison between test and theory were in reasonable accord for the inplane vibratory 

forces. Unfortunately, at this time neither longitudinal nor lateral experimental forces are well 

predicted as Fig. 2-269 and Fig. 2-270 clearly show. 

 To help you appreciate the difficulties in measuring vibratory forces even at full scale, 

you might consider reading two reported efforts with wind tunnel models [479, 480]. The first 

effort was aimed at a Sikorsky H-37 and was the most thorough seen in the literature up to 

1967. Then, in 1982, a comprehensive attack (led by Dick Gabel at Boeing Vertol) with a 

model of a tandem rotor machine led to the following conclusions: 

“1) The rotor balances did not adequately measure vibratory loads due to poor dynamic 

response characteristics, large rotor cross coupling. 

2) The hub accelerometers provided a good qualitative assessment of vibratory loads but the 

results were sensitive to centrifugal accelerations when the accelerometers were not exactly at 

the center of rotation. 

3) The shaft bending gauges provided a good method for determining vibratory hub loads. 

They were able to measure both inplane forces and hub moments, but not vertical loads. 

4) The hub balance proved effective in measuring vertical hub loads, but large interactions 

and damaged gauges did not permit adequate measurement of inplane loads. 

5) The generalized coordinate analysis gave reliable vertical hub loads. 

6) A careful check calibration must be made on each measurement system used to insure the 

dynamic loads recorded are reliable. Even though a system has been used successfully on 

previous models, poor dynamic response characteristics can distort the true results. 

7) Vibratory hub loads were obtained that could be used to define the expected aircraft 

vibratory loads as a function of airspeed and gross weight that will prove useful in the full 

scale design process.” 
2.6 VIBRATION 

419 

-8,000

-6,000

-4,000

-2,000

0

2,000

4,000

6,000

8,000

0 30 60 90 120 150 180 210 240 270 300 330 360

Hub Arm 1 Azimuth (deg)

Longitudinal

Forces

(lbs)

From

Balance

From Shaft 

Strain Gages From Theory

CAMRAD II + Overflow 2

Fig. 2-269. Longitudinal vibratory force comparison. 

-6,000

-4,000

-2,000

0

2,000

4,000

6,000

0 30 60 90 120 150 180 210 240 270 300 330 360

Hub Arm 1 Azimuth (deg)

Lateral

Forces

(lbs)

From

Balance

From Shaft 

Strain Gages

From Theory

CAMRAD II + Overflow 2

Fig. 2-270. Lateral vibratory force comparison. 
2.6 VIBRATION 

420 

2.6.5 Blade Airloads, Blade Vibratory Response 

 You have now come to the crux of the vibration problem. Because of the most 

recently completed UH-60A Airloads rotor test [481]141 (which I am constructing this 

discussion on) you can see more clearly than ever how theory and test compare. So let me 

start with a dissection of the vertical shear (RSvertical) first. Unfortunately, a deeper look into 

inplane loads will have to wait for future analyses, and published papers and reports by others. 

2.6.5.1 Dissecting Hub Arm Vertical Shear 

 The analysis of vertical shear that you are about to review will convince you, I hope, 

that some fundamentals of vibration are, after seven decades, becoming much clearer. My 

objective here is to show you how the components of the vertical shear vary with azimuth. 

The starting point is Eq. (2.286), which is repeated here for convenience 

(2.286) ( )

R R 2

r, r, 2

vertical r load b 2

0 0

dL z

RS dr m dr PL w

dr

ψ ψ     ∂

= − Ω −−       ∂ ψ  

    

 

, 

and the data under discussion is summarized in Fig. 2-271. To begin with, the vertical shear 

comparison between test (the red, dashed line) and theory (the heavy, solid black line) shows 

that, after seven decades, aeromechanics researchers now have come close enough to start 

digging deeper. The theory (CAMRAD II + Overflow 2) waveform differs slightly in just 

where the peaks and valleys fall in azimuth, but the character and key harmonics are, indeed, 

captured. 

 With this encouragement, consider the airload,

R

r,

0

dL

dr

dr

  ψ

   





 , contribution to the 

vertical shear. This integral is available from the blade that was instrumented with pressure 

taps at eight radial stations. (The pressures at the r/R = 0.55 station are currently in question.) 

The chordwise array of the pressure taps at each radius station allowed computation of the 

airfoil’s normal force (dNpressure/dr), the chordwise force (dCpressure/dr), and the pitching 

moment—all loads due to the pressure distribution about the airfoil’s surface. As mentioned 

earlier, I have taken poetic license in referring to the blade element force as dLr,ψ/dr. When 

you look at Fig. 2-272, you can see why. I have really been referring to dT/dr. Elemental lift 

is, as you know, a force normal to the local velocity (Vlocal). In comparing theory to test, you 

must now be more exact because CAMRAD II + Overflow 2 rigorously includes all CFD 

computed terms so that 

(2.291) 

( )

( )

R

R geometric control elastic

r,

0 pressure skin friction

geometric control elastic

0

dN

cos

dT dr

Theory dr dr

dr dC dC

sin

dr dr

ψ

  θ +θ +θ  

=   − + θ +θ +θ      



 

   





. 

 

141 This paper by Tom Norman and his coauthors is an absolutely must-read document in order to appreciate the 

enormous step forward made in rotor wind tunnel testing. 
2.6 VIBRATION 

421 

-6,000

-5,000

-4,000

-3,000

-2,000

-1,000

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

10,000

0 30 60 90 120 150 180 210 240 270 300 330 360

RSvertical

Theory

Test

PLL

Hub Arm 1 

Rotating 

Vertical

Shear

from

Pressure

Blade

&

 Theory

Components 

(lbs)

Azimuth Angle (deg )

( )

R R 2

r,t r,t

vertical r 2 b

0 0

dL z RS dr m dr PLL w dr t

    ∂ = − −−       ∂  

 

   

R

r,t

0

dL dr dr

     







( )

R 2

r,t

r 2

0

z m dr

t

  ∂

  ∂  







Fig. 2-271. Theory components of vertical shear. 

Fig. 2-272. Blade element forces and angles. 

dN

dr

dCpressure

dr

dCskin friction

dr Vlocal

Shaft

dT

dr

dFchordwise

dr

r, geo cont elastic ψ θ =θ +θ +θ

αr,ψ

Plane Perpendicular to Shaft 
2.6 VIBRATION 

422 

In contrast, the preliminary integration from this “hot-off-the-press” experimental program 

computes the blade elemental thrust integral as 

(2.292) ( )

R R

r, pressure

geometric control

0 0

dT dN

Test Preliminary dr cos dr

dr dr

ψ   = θ+ θ    

      . 

Data reduction at this point in time does not include the chordwise force due to pressure nor is 

elastic twisting (θelastic) accounted for. This UH-60A rotor test had no instrumentation to 

obtain the skin friction force. 

 Despite these somewhat “apples-to-oranges” current computations, let me proceed 

anyway. You can see from Fig. 2-273 that a very encouraging result has been obtained. In 

fact, I have never seen results comparable to Fig. 2-273 in all my years in the rotorcraft 

industry. You should particularly note that the mean loads (or steady loads, if you like) are 

within 200 pounds of each other. That is, the test steady load is 5,470 pounds and the 

CAMRAD II + Overflow 2 has a mean load of 5,270 pounds. Furthermore, the first three 

harmonics dominate the waveforms as the tabulation on the figure shows. 

 Now consider the contribution of the inertia term, ( )

R 2

2 r,

r 2

0

z

m dr ψ   ∂

Ω   ∂ψ  







, to the 

vertical shear (RSvertical). Theory and test for this major force are compared in Fig. 2-274. The 

inertia load contribution shown in Fig. 2-274 is not directly measured in test or calculated 

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

0 30 60 90 120 150 180 210 240 270 300 330 360

(lbs)

CAMRAD II + Overflow 2,

Eq. 2.293

Test, Eq. 2.294

Azimuth Angle (deg )

R

r,

0

dT

dr

dr

ψ      







TEST N per REV 0 1 2 3 4 5 6 7 8 9 10

TEST COSINE 5,471 -388 668 198 116 -22 -124 -67 15 -37 -66

TEST SINE 0 1,232 79 -215 85 70 -80 -28 -60 -18 -16

TEST AMPLITUDE 1,292 673 292 143 74 147 73 62 41 67

THEORY N per REV 0 1 2 3 4 5 6 7 8 9 10

THEORY COSINE 5,267 -440 888 12 76 -22 -52 -96 -48 20 -8

THEORY SINE 0 1,041 113 -449 -215 -231 -48 -53 -159 -91 -35

THEORY AMPLITUDE 1,130 895 449 228 232 71 110 166 93 36

Fig. 2-273. Theory and test for the root thrust are in closer agreement than I 

have ever seen. 
2.6 VIBRATION 

423 

by the theory. It is derived from Eq. (2.286) for both test and theory as 

(2.293) ( )

R 2 R

2 r, r,

r vertical load b 2

0 0

z dT

m dr dr RS PL w

dr

ψ ψ   ∂   Ω = − −−       ∂ ψ  

      . 

In test, the thrust integral was found by integrating the measured pressure distributions at 

eight radial stations to give the blade element normal force as Eq. (2.292) suggests142; the hub 

arm vertical shear and the pitch link load were all measured. Thus, the residual must be the 

inertia force. This approach charges all the experimental error to the inertia term. What is so 

interesting is that the steady load in the inertia integral should theoretically be zero, not the 

489 pounds given by the tabulation. Coming this close is, to me, a remarkable achievement. 

 In backing out the inertia integral using theoretical results, you see that the steady load 

is 154 pounds, which is a measure of the theoretical error. This is a quite satisfactory result in 

my view. 

-5,000

-4,000

-3,000

-2,000

-1,000

0

1,000

2,000

3,000

4,000

5,000

0 30 60 90 120 150 180 210 240 270 300 330 360

( )

R 2

r,t

r 2

0

z m dr

t

  ∂

  ∂  







Derived 

from 

Test

CAMRAD II + Overflow 2,

Azimuth Angle (deg )

TEST N per REV 0 1 2 3 4 5 6 7 8 9 10

TEST COSINE 489 -1,949 915 837 11 200 -21 -211 137 -18 -50

TEST SINE 0 690 1,086 -353 407 -215 -134 -85 -132 -83 -94

TEST AMPLITUDE 2,068 1,420 908 407 294 135 228 191 85 107

THEORY N per REV 0 1 2 3 4 5 6 7 8 9 10

THEORY COSINE 154 -1,637 1,160 288 63 -131 -69 -191 9 26 -28

THEORY SINE 0 1,727 983 -697 -160 -437 -60 -88 -342 -87 -31

THEORY AMPLITUDE 2,379 1,521 754 172 456 92 211 342 90 42

(lbs)

Fig. 2-274. Theory and test for the inertia response of the blade to the airload 

are remarkably close. 

 

142 Randy Peterson, who works for Bill Warmbrodt at NASA Ames Research Center, performed the integration 

of Eq. (2.292) using somewhat more than 200 pressure gauges—no mean trick in my book. This means that 

airloads at only eight radial stations were available. You can read more about how Randy did it in Tom 

Norman’s paper, Full-Scale Wind Tunnel Test of the UH-60A Airloads Rotor [481]. 
2.6 VIBRATION 

424 

 The third contribution to the vertical shear (RSvertical) is the pitch link load (PLload). 

Here the disagreement between test and theory is quite significant as Fig. 2-275 shows. Not 

only is there disagreement in the steady load by nearly a factor of three, the test data clearly 

shows considerably more response at the 4/rev harmonics. This strongly suggests that not 

modeling the trim tab of the blade in the computational fluid dynamics (CFD) model is a 

situation to be rectified in the future. I would also suggest that the computational structural 

dynamics (CSD) model of the blade may be slightly off in the 4/rev frequency range. 

 The oscillation is clearly at 4/rev in the 220- to 330-degree azimuth angle, which 

might be considered the retreating blade stall region of the rotor. However, the advance ratio 

(μ = 0.3) and blade loading coefficient (CT/σ = 0.09) generally constitute a flight condition 

somewhat below blade stall onset as Romander [465] shows in his figure 14. 

2.6.5.2 Blade Airloads—Test Versus Theory 

 To conclude this vibration discussion, consider the airload measurements from the 

UH-60A Airloads pressure blade obtained during the 40- by 80-Foot Wind Tunnel testing143

and provided here in Fig. 2-276 and Fig. 2-277. Let me draw your attention first to the 

distribution along the blade of the steady blade element aerodynamic pitching moment 

-2,500

-2,000

-1,500

-1,000

-500

0

500

0 30 60 90 120 150 180 210 240 270 300 330 360

Pitch 

Link 

Load

(lbs)

Tension

Azimuth Angle (deg)

TEST N per REV 0 1 23 4 567 8 9 10

TEST COSINE -502 374 38 -12 -123 91 40 -29 22 10 14

TEST SINE 0 104 199 -75 213 78 -25 12 -8 -3 -1

TEST AMPLITUDE 389 203 76 246 120 47 31 23 11 14

THEORY N per REV 0 1 23 4 567 8 9 10

THEORY COSINE -1,337 287 -42 -28 -12 -10 11 -5 -8 4 13

THEORY SINE -66 192 34 94 -38 10 11 -20 -16 -3

THEORY AMPLITUDE 294 196 45 95 39 15 12 22 17 13

Fig. 2-275. CAMRAD II + Overflow 2 provide a very poor prediction of pitch link load 

at the present time. 

 

143 Just for future reference, the data is from Air Force test entry Number 10, Run 52, Data Point 31. 
2.6 VIBRATION 

425 

(dPM/dr) shown in Fig. 2-276. The integral from the 5-foot radius to the blade tip of the 

experimental pitching moments is a blade root aerodynamic pitching moment of about –565 

foot-pounds. The radial distribution of elemental pitching moment of the CAMRAD II + 

Overflow 2 theory is noticeably different, and the integral from root to tip is –400 footpounds. These moments are resisted by the pitch link load, which acts at a 7.2-inch moment 

arm. Thus, the pitching moment airload contributes a compressive load of some –940 and 

–500 pounds, respectively, because the pitch arm/pitch link upper rod end-bearing is leading 

the blade. You should keep in mind that the pitching moment airload is not the only steady 

load that the pitch link must react with. For instance, the blade element thrust (dT/dr) times 

inplane deflection from the torsion axis, and the blade element inplane force (dFinplane/dr) 

times an out-of-plane deflection from the torsion axis are also significant contributors 

as Eq. (2.288) reminds you. (You also learned this in Volume I, appendix D, fig. D-6 on 

page 377.)

 Now consider an example of a blade element pitching moment as the blade completes 

one revolution. I have chosen the blade element at the 20.8-foot radius station as the example. 

This radius station corresponds to the 0.775 radius station based on the UH-60A radius of 322 

inches or 26.3333 feet. I have chosen this specific radius station because so many past rotor 

studies have used the 3/4 radius station as a representative average of the whole blade. The 

example waveform of element pitching moment (dPM/dr) in foot-pounds per foot is shown in 

Fig. 2-277. 

-60

-40

-20

0

20

40

60

80

0 4 8 12 16 20 24 28

Blade 

Element 

Pitching 

Moment 

dPM/dr 

(ft-lbs/ft)

Radius (ft)

Nose Up is Positive

CAMRAD II + Overflow 2

Test

r/R = 0.195

0.225

0.920

0.400 0.675 0.775 0.865

Trim Tab

42 in. long

1.1 in. wide

0.99

0.920

Fig. 2-276. Distribution along the blade of steady blade element pitching moment. 
2.6 VIBRATION 

426 

 You should immediately notice the similarity between the elemental pitching moment 

waveform in Fig. 2-277 and the pitch link waveform shown in Fig. 2-275—particularly in the 

first half of the blade’s revolution (i.e., from 0 to 180 degrees of azimuth angle). You might 

also agree that as the blade continues its revolution to the 270-degrees azimuth angle, the 

similarity is still quite evident. However, in the final quadrant of azimuth angle, the pitch link 

load shows a marked oscillation that is only hinted at in the aerodynamic pitching moment. It 

is also clear in Fig. 2-275 that the CAMRAD II + Overflow 2 theory is at odds with test 

results in the 210- to 330-degree azimuth angle range. It is this azimuth angle range that has 

been historically [482-484] identified as the “retreating blade stall” region. In this UH-60A 

case where advance ratio equals 0.3 and the blade loading coefficient (CT/σ) equals 0.09, 

blade stall is definitely evident. However, the amount of separated flow is not sufficient to 

particularly impact the primary aerodynamic behavior of the rotor system. Were the UH-60A 

experiencing severe retreating blade stall, the pitch link load waveform shown in Fig. 2-275 

would be completely dominated by the oscillation in the 210- to 330-degree azimuth angle 

region. The domination would be so great that the alternating load (i.e., the maximum peak to 

minimum peak) would dictate the fatigue load and part life for design purposes. 

 The pitching moment behavior of this blade element at the 0.775 radius station can be 

examined in relation to the normal force (dN/dr) waveform of the element, which you see in 

Fig. 2-278. To do this, let me nondimensionalize the aerodynamic force and moment into the 

more familiar airfoil coefficient form. This requires some estimate of the local velocity 

illustrated in Fig. 2-272. I say estimate because, for a rotor blade, the actual velocity is not 

presently available in either the test pressure data or CFD theories.144 Not to be dissuaded, I 

have chosen to define the local velocity as 

Ω +r V sin ψ , 

which is the first equation you encountered in Volume I (on page 13). On this basis, it follows 

that 

(2.294) ( ) ( ) N M 2 2 1 1 2

2 2

dN / dr dPM / dr C and C

r Vsin c r Vsin c = = ρΩ+ ψ ρΩ+ ψ , 

which some more experienced aerodynamic engineers in the rotorcraft industry might take 

offense to because of my use of local velocity as Ωr + V sin ψ. However, having taken this 

step, it is possible to show you graphs of approximately correct CM and CN versus azimuth 

angle. Of course, I am using the normal force coefficient (CN) as an approximation to the 

more correct blade element lift coefficient (CL), which some readers may also take offense to 

considering Fig. 2-272.145 

 

144 This is not to say that serious attempts to deduce both local angle of attack and velocity have not been made 

[485]. Hank Tanner reported his effort in reference [486], which also included radial flow velocity measurements 

with a “boundary layer button.” 

145 I have to admit that ignoring the local induced velocity is only acceptable for radius stations well outside of 

the reverse flow region (defined by x = –μ sin ψ) and is of doubtful use for advance ratios above 0.5. Including 

the induced velocity is not currently possible because neither test nor CFD + CSD theory will tell us what this 

velocity is! You might find the tutorial about rotor-induced velocity that I wrote in 2006 [487] of some interest. 
2.6 VIBRATION 

427 

-60

-50

-40

-30

-20

-10

0

10

20

0 30 60 90 120 150 180 210 240 270 300 330 360 Blade 

Element 

Pitching 

Moment 

dPM/dr 

(ft-lbs/ft)

Azimuth Angle (deg) 

Radius Station = 20.8 ft

r/R = 0.775 

Test

Steady

-13.4 ft-lbs/ft

CAMRAD II + Overflow 2

Steady -23.4 ft-lbs/ft

Fig. 2-277. Blade element pitching moment behavior with azimuth angle. 

0

100

200

300

400

500

600

0 30 60 90 120 150 180 210 240 270 300 330 360

Blade 

Element 

Normal 

Force 

dNF/dr 

(lbs/ft)

Azimuth Angle (deg)

Radius Station = 20.8 ft

r/R = 0.775 

CAMRAD II + Overflow 2

Steady 346 lbs/ft

Test

Steady

342 lbs/ft

Fig. 2-278. Blade element normal force behavior with azimuth angle. 
2.6 VIBRATION 

428 

-0.09

-0.08

-0.07

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0 30 60 90 120 150 180 210 240 270 300 330 360

CAMRAD II + Overflow 2

Steady CM = -0.02045

Pitching

Moment 

Coefficient 

(CM)

Azimuth Angle (deg)

Test

Steady C M =-0.0277

Radius Station = 20.8 ft

r/R = 0.775 

Fig. 2-279. Pitching moment coefficient behavior with azimuth angle. 

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 30 60 90 120 150 180 210 240 270 300 330 360

Normal 

Force 

Coefficient 

(CN)

Azimuth Angle (deg)

CAMRAD II + Overflow 2

Steady CN = 0.6820

Test

Steady CN = 0.6945

Radius Station = 20.8 ft

r/R = 0.775 

Fig. 2-280. Normal force behavior with azimuth angle. 
2.6 VIBRATION 

429 

 The results of converting normal force (dN/dr) and (dPM/dr) from dimensional to 

customary airfoil coefficients (CN and CM) are shown in Fig. 2-279 and Fig. 2-280. The 

comparison between theory and test of the normal force coefficient is quite favorable; the 

comparison of pitching moment coefficients is quite unfavorable in the azimuth angle range 

from 240 to 360 degrees. This brings me to the subject of blade stall. 

 In Fig. 2-281, I have shown you how CM varies with CN. The lemniscate-shaped figure 

that the blade element traces out during a revolution has two distinct loops. The larger loop 

that lies below a normal force coefficient of 1.0 is quite typical of the behavior predicted by 

classical unsteady aerodynamics. This is the shape you saw in Volume I, appendix B. The 

smaller loop that lies in the region above CN = 1.0 exhibits the behavior that rotorcraft 

engineers have come to call “dynamic stall.” The subject of dynamic stall and rotor blade 

response, particularly in control loads growth, has been studied in so much depth and breadth 

since the late 1950s that it is beyond this introduction. I believe a book could be written just 

on this one aspect of rotorcraft design. However, a paper written by Jing Yen and Mithat Yuce 

[488] published in October 1990 will give you a particularly good starting point. These 

authors examined the effect of blade stall on pitch link loads, and Mithat Yuce included a very 

unique way to calculate the amplitude of pitch link loads when blade stall is severe. 

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

ψ = 0 deg

ψ = 270 deg

200 deg

180 deg

90 deg

300 deg

210

240

230

220

Normal Force Coefficient (CN)

Pitching

Moment 

Coefficient 

(CM)

Nose Down

Radius Station = 20.8 ft

r/R = 0.775 

CAMRAD II + Overflow 2

Test

Fig. 2-281. The UH-60A blade element at the 0.775 radius station exhibits retreating 

blade stall at about 230-degree azimuth angle. Reattached flow appears complete 

during the last 30 degrees of rotation. 
2.6 VIBRATION 

430 

0

50

100

150

200

250

300

350

400

0 4 8 12 16 20 24 28

Blade 

Element 

Normal

Force 

dN/dr 

(lbs/ft)

Radius (ft)

CAMRAD II + Overflow 2

Test

r/R = 0.195

0.675 0.775 0.865 0.920

0.400 Trim Tab

0.99

0.965

0.225

Fig. 2-282. The UH-60A blade element at the 0.775 radius station exhibits 

retreating blade. 

 I would be more than remiss if you did not have the most fundamental blade element 

test versus theory comparison to review. This fundamental comparison is, in my view, the 

steady thrust distribution versus radius station, which you now have with Fig. 2-282. 

2.6.5.3 Synthesized Airfoil Aerodynamic Characteristics 

 The general view of rotorcraft engineers using CFD is that the theory does not 

produce aerodynamic properties of rotor blade airfoils. An airfoil surface produces forces that 

can, so far, only be resolved through known geometric angles using CFD. The angle of attack 

of a blade element is not presently a known angle in the CFD world of rotor blades nor, as I 

mentioned, is the local velocity of a blade element. This is very disturbing to many 

aeromechanic researchers who have spent many years developing and applying blade element 

theory, which does calculate both angle of attack and local velocity. Given the local velocity 

and angle of attack, two-dimensional airfoil aerodynamic characteristics can then be obtained, 

and all behavior of the elastic rotor blade can be determined. The result of this progress has 

been that no direct bridge between classical blade element and CFD theories currently exists. 

 The even more practical problem is that in comprehensive computer programs today 

(such as Johnson’s CAMRAD II) 1,000 flight conditions can be analyzed during a new 

helicopter design. In contrast, with the more advanced programs, say CAMRAD II + 

Overflow 2, the chief engineer would be lucky to get 10 conditions analyzed in the same time. 
2.6 VIBRATION 

431 

Of course, with the seemingly endless development of faster computers, the industry should 

expect that advanced CSD + CFD approaches will become everyday tools within the near 

future. 

 To help bridge the gap between blade element and CFD airload estimates, let me 

suggest the following objective and approach. The objective is to obtain airfoil aerodynamic 

characteristics from CFD calculated results. That is, I want to derive the “equivalent” twodimensional airfoil angle of attack (α), lift coefficient (C), and drag coefficient (Cd) from the 

CFD computed normal force (dNpressure/dr), chordwise pressure force (dCpressure/dr), and 

chordwise skin friction force (dCskinfriction/dr). In short, I want to synthesize airfoil 

aerodynamic characteristics from CFD results after first obtaining the angle of attack of the 

blade element. 

 The basic premise to obtain angle of attack is that, according to potential flow theory, 

an airfoil has no drag regardless of its lift. This fundamental premise is illustrated by the black 

vectors in Fig. 2-283. In potential flow theory it is customary to assume the chordwise 

pressure force as positive when directed towards the leading edge of the airfoil. Thus, lift is 

made up of a normal force due to pressure (shown as the red vector) and the chordwise 

pressure force (shown as the black vector).146 On this basis, the blade element angle of attack 

(αBE) in radians can be estimated as 

(2.295) 

pressur

pressu

e pressure

re pressure

BE dN dr

dC dr

arc tangent arc tang dN

dC d

e t

r

dr

n

  

α ≈    =    

−

  

. 

Fig. 2-283. Blade element forces due to pressure distributions. 

 

146 I hope I have not confused you by leaving the blue vector for dCpressure/dr in the figure. I think of chordwise 

forces in the sense of drag, which is positive when directed towards the trailing edge. Most CFD calculators take 

all chordwise forces as positive towards the leading edge, a fact I must continually remind myself of. 

dNpressure

dr

dCpressure

dr

Vlocal

αr,ψ

dL

dr

dCpressure

dr
2.6 VIBRATION 

432 

The corollary to this premise is that the blade element lift coefficient can then be calculated as 

(2.296) ( ) ( )

( )

pressure pressu

2 2

2 1

2

re d d

C

r Vs

C dr

i c

N d

n

+ r = ρΩ+ ψ

−

 

and, therefore, lift coefficient can be plotted versus angle of attack, which follows what you 

learned in Volume I, appendix B. The results of applying this approach are illustrated in 

Fig. 2-284 and Fig. 2-285. Here I have used Ethan Romander’s CAMRAD II + Overflow 2 

computed results corresponding to the UH-60A Airloads rotor test associated with Run 52, 

Point 31, which is at an advance ratio of 0.3 and CT/σ = 0.09. The radius station is 0.775 R. 

 Fig. 2-285 shows that unsteady aerodynamics play a significant role in rotary wing 

airloads even for such a fundamental characteristic as airfoil lift coefficient. While the 

nominal lift curve slope is 0.1088 per degree, the unsteady aerodynamics create what are 

frequently called hysteresis loops. The effect, as you saw in Fig. B-10 on page 321 of Volume 

I, is that lift lags behind angle of attack when the angle of attack is decreasing. Conversely, 

lift leads angle of attack when the angle of attack is increasing. Mathematically, an airfoil in 

unsteady flow has lift coefficient behavior approximately as 

(2.297) d CA B

dt

α

 = α+ , 

and this is what you see in Fig. 2-285. 

 Suppose that now you want to synthesize the airfoil drag coefficient (Cd). Following 

the vector diagram shown on Fig. 2-272, you can see that 

(2.298) ( )

pressure skin friction

d 2 N C 1

2

dN dC dC

sin cos

dr dr dr C C sin C cos

r Vsin c

      α+ +   α     = = α + α

ρΩ+ ψ , 

which can be derived from the CAMRAD II + Overflow 2 results because both chordwise 

pressure and skin friction forces are calculated. (This is not possible with the UH-60A 

Airloads rotor because no instrumentation measuring the skin friction force was used.) 

 The influence of unsteady aerodynamics on blade element drag coefficient is 

substantially greater than on lift coefficient as Fig. 2-286 shows. You see immediately that the 

total drag coefficient is the difference between two large components that are shown with 

blue lines in Fig. 2-286. The normal force component (CN sin α)—the dashed blue line— 

is generally positive while the total chordwise component (CC cos α)—the solid blue line—is 

generally negative. Both components are roughly 10 times the magnitude of the total drag 

coefficient. This is one of those small differences in big numbers problems that engineers 

frequently have to deal with. And this is why, even in steady flow, pinning down, 

experimentally, the drag coefficient of an airfoil has historically been so difficult. Whether it 

can be done with experimental data from an instrumented blade element in a rotor blade 

remains to be seen. 
2.6 VIBRATION 

433 

-3

-2

-1

0

1

2

3

4

5

6

7

8

9

10

11

0 30 60 90 120 150 180 210 240 270 300 330 360

Local 

Angle of 

Attack

α0.775

 (deg)

Azimuth Angle (deg)

Radius Station = 20.8 ft

r/R = 0.775 

Fig. 2-284. Estimated airfoil angle of attack for the blade element located at the 

0.775 radius station for μ = 0.3 and CT/σ. 

y = 0.1088x + 0.3454

R2

 = 0.9767

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

-4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11

Local

 Lift

Coeff.

Local Angle of Attack (deg)

Radius Station = 20.8 ft

r/R = 0.775 

C

ψ = 0 deg

ψ = 270

ψ = 180

ψ = 90

Fig. 2-285. Lift coefficient vs. angle of attack reflects unsteady aerodynamic behavior. 
2.6 VIBRATION 

434 

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.01

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

Components 

of 

Local Drag 

Coeff.

Local 

Drag 

Coeff.

Cd

CN sin α

CC cos α

Local Lift Coeff.

Total Drag Coefficient

Fig. 2-286. The influence of unsteady aerodynamics on blade element drag coefficient. 

2.6.6 Closing Remarks 

 Helicopter vibration problems are a continuation of those experienced by the autogyro 

pioneers, which you read about in Volume I. As Cierva wrote in his 1935 paper [398]: 

“Perhaps the most irritating of the secondary difficulties met with in the autogiro developments 

have been those of a dynamical [vibration] nature.” 

Now you have come forward seven and one-half decades to August 2012, and the rotorcraft 

industry still has the same opinion. 

 There is no question that there has been a considerable reduction in the vibration that 

occupants of a helicopter must tolerate. However, this improved ride quality has been 

achieved, in my opinion, by cut-and-try fixes with minimal help from theory. It has, in fact, 

been the use of many different types of anti-vibration devices, added to the basic machine by 

each manufacturer, that has saved the day as the rotorcraft industry expanded. 

 You should now appreciate the tenacity of aeromechanic researchers in evolving 

improvements to theory so that calculations before first flight could be relied on. The 

importance of a coupled rotor-fuselage attack became clear in the 1950s. Comprehensive 

theory, begun with a computer program called C-81 by Bell Helicopter, spread quickly 

throughout the industry in the 1960s and 1970s. This more complex theory appeared to still be 
2.6 VIBRATION 

435 

inadequate when tested against flight test results throughout the next 40 years. Almost every 

paper during this 40-year period decried the lack of reliable aerodynamic forces and moments 

that rotor systems respond to. It has taken the development of CFD coupled to available (and 

quite satisfactory) CSD computer programs to renew industry expectations of breakthroughs 

in the foreseeable future. 

 It now appears that a very comprehensive flight and wind tunnel program [489] using 

a Sikorsky UH-60A Black Hawk helicopter has provided new foundational experimental data. 

This data, compared to one CFD + CSD theory (CAMRAD II + Overflow 2) as you have 

seen, appears to have captured prediction of vertical vibratory forces. However, the 

prediction, to the accuracy of the vertical forces, of the more difficult inplane vibratory forces 

has not been achieved yet. 

 Generally I am not one to make speculations about future progress,147 but if I were a 

betting man, I would bet that by August 2025, aeromechanic researchers—using the recently 

obtained UH-60A Airloads Program data provided by NASA Ames Research Center and its 

U.S. Army cohorts—will demonstrate quite useable correlation between test and theory for 

this widely used helicopter. Then, successful application of the newfound knowledge to a new 

helicopter design with confirmation from flight test will signify a very long awaited grasp of 

rotorcraft vibration. With luck, vibration levels at the “jet smooth level” Dick Gabel described 

in reference [404], without the current penalties in weight, cost, reliability, and maintenance 

[490], will become a reality, and then the rotorcraft industry can say that the helicopter’s 

vibration problem has been solved. 

 

147 Harry Gray, a CEO of United Technologies, placed a full-page statement in the Wall Street Journal (in the 

1970s, I think). All it said in big print was, “Don’t promise what you can’t deliver.” I keep that thought in mind. 
2.6 VIBRATION 

436 
437 

2.7 NOISE 

 People within a range of 1,500 feet of an operating helicopter frequently say that the 

noise is loud, and even intolerable, for long periods of time. They say sometimes they even 

need to put their hands over their ears. They say they do not want helicopters flying around 

their homes or places where they work, and this is just the tip of the iceberg of the list of noise 

complaints about helicopters. The situation was summed up quite well in 1955 [491]. There 

are only two exceptions to these thoughts about helicopter noise: one is in civil and military 

medevac situations and the other is in military operations such as close air support. There are

times when the noise of an approaching helicopter can be music to the ears. 

 In the discussion of helicopter noise that follows, I want you to appreciate the human 

ear and how sound is perceived, understand how noise is measured, and to be able to calculate 

helicopter noise in hover and forward flight. Finally, I want you to know about government 

efforts regulating helicopter noise levels and flight paths within the world of aviation. 

2.7.1 Sound, Noise, and Human Hearing 

 Sound and noise are words defined in the Random House Dictionary of the English 

Language [492] as follows: 

sound n. 1. the sensation produced by stimulation of the organs of hearing by vibrations 

transmitted through the air or other medium. 2. mechanical vibrations transmitted through an 

elastic medium, traveling in air at a speed of approximately 1100 feet per second at sea level. 

3. the particular auditory effect produced by a given cause: the sound of music. 4. any 

auditory effect; any audible vibrational disturbance. 

noise n. 1. sound, especially of a loud, harsh, or confused kind: deafening noises. 2. a 

nonharmonious or discordant group of sounds. 

For this discussion, it is not important for you to know much more, medically, about the 

human ear than what is conveyed by Fig. 2-287. One thing you should note in Fig. 2-287 is 

that ambient pressure on the ear drum is balanced by two sources. One source is air pressure 

acting through the ear canal onto the outer surface of the ear drum. The second source is air 

pressure acting up the Eustachian Tube onto the inner surface of the ear drum. Thus, the 

pressure difference across the ear drum is zero. To expand this point, suppose you go up from 

sea level to Denver Colorado, a mile-high city. This is a reduction in ambient pressure from 

2,116 pounds per square foot to 1,744 pounds per square foot, but because the ear drum has a 

two-sided pressure balance, the ear drum remains completely un-deflected, and the brain does 

not perceive this situation as sound. This is quite different from a balloon being blown-up at 

sea level and then carried up to Denver. In that case, the balloon would expand to reduce the 

inner pressure until it again balances the lower pressure at the higher altitude. Of course, most 

of us have experienced ear pain when the Eustachian Tube is partially blocked as with a cold 

and stuffy nose. When that happens, our ears do begin to take on the characteristics of a 

balloon because of a pressure difference between the outer and inner surfaces of the ear drum.
2.7 NOISE 

438 

 Sound and noise create a vibrational pressure having the simplest form of 

(2.299) sound pressure wave for a pure tone p p sin 2 f t == π t o ( )   . 

This constitutes the vibratory pressure that comes into the outer ear and deflects the eardrum 

in and out a very, very small amount. This type of air pressure is not balanced by the 

Eustachian Tube, therefore a vibratory auditory signal is transmitted to the brain. This 

auditory signal is transmitted from the ear drum into the middle ear, and then into the inner 

ear. The complete signal is then transmitted by nerves to the brain, which processes the signal 

into what we call sound. To me, an ear is nothing more than a microphone. 

 Equation (2.299) describes a single tone having a frequency (f) in hertz. When you hit 

a piano key you hear a note, which is a tone. The amplitude of the vibration is (po) in any one 

of several units. Using a piano key as an example, a soft touch will create a low amplitude of 

vibration pressure. Conversely, striking the key quite hard will create a large value of po. The 

most common unit of pressure in acoustics studies is newtons per square meter. One newton 

per square meter is called a pascal. When the pressure is in units of pascals, it is generally 

noted as (pa). I am still stuck in English units, so for the discussions that follow, you should 

remember that one pascal equals 0.020885434273 pounds per square foot, or if you prefer, 50 

pascals equals about 1 lb/ft2

. 

 Human factors research on hearing became quite serious in the United States shortly 

after Alexander Graham Bell was awarded a patent for the electric telephone by the United 

States Patent Office in 1876. By 1899, American Telephone & Telegraph (AT&T) Company 

was in business. AT&T had four major divisions, one of which was Bell Telephone 

Laboratories (more commonly called Bell Labs) that conducted research and development. 

Two members of Bell Labs were Harvey Fletcher and Wilden A. Munson. Fletcher was a 

physicist and director of the physical research department at Bell Labs, and Munson was an 

engineer in Fletcher’s department. In 1933, they published a landmark paper [493] in the 

Journal of the Acoustical Society of America. Their paper contained a definition of loudness, 

its measurement, and an often referenced graph showing lines of constant loudness, which 

you will see shortly. 

 A key facet of Fletcher and Munson’s work established the threshold of hearing based 

on a group of young people with very good hearing. From a helicopter engineer’s point of 

view, I think the subject of sound and noise begins with this hearing threshold that Fletcher 

and Munson set forth in 1933 and that was updated in 2003 [494]. You see from Fig. 2-288 

that this threshold of hearing for a pure tone, such as given by Eq. (2.299), is presented as a 

line on a graph of the root mean square (rms) of vibratory pressure (prms in lbs/ft2

) versus 

frequency (f) in hertz. The root mean square of pure tone vibratory pressure is calculated 

simply as 

(2.300) rms o p p2 = . 

Using Fletcher and Munson’s updated starting point (but in English units for pressure), you 

see in Fig. 2-288 that a human’s ear is rather sensitive in the frequency range from 500 to 

8,000 hertz. That is, if you are a young person with average to better-than-average hearing, 
2.7 NOISE 

439 

Fig. 2-287. A simplified schematic of a human’s hearing device. 

0.0000001

0.000001

0.00001

0.0001

0.001

0.01

0.1

1

10

1 10 100 1,000 10,000 100,000

Pure Tone 

Waveform

 rms

Amplitude

(lbs/ft2

)

Sound wave frequency, f (Hz)

Threshold of pain and then damage to ears

Mosquito

Threshold of 

hearing for a 

young person

Ref: ISO 

226:2003

Threshold of 

hearing for a 60 

year old man

o

rms

p p 2 =

Fig. 2-288. Thresholds of hearing and pain found with pure tones going into headphones 

worn by the human being tested. Converted from ISO 226:2003 [494]. 

you can easily hear a mosquito. At the other end of the frequency scale, a human’s hearing 

becomes very much less sensitive. At 10 to 20 hertz, a human may feel the sound rather than 

hear it. Hearing deteriorates with age [495], and typically by age 60 a male no longer can hear 

a mosquito or (in my case at age 77) a fly. (Apparently, young people are now taking 

advantage of this acoustical situation by using the sound of a mosquito as a ringtone for their 

cell phones. This ploy clearly obviates a great deal of adult interference in young people’s 

lives.) 

pt

To 

Brain
2.7 NOISE 

440 

2.7.2 Loudness Curves, Sound Pressure Level, and the Decibel 

 The ground work that Fletcher and Munson laid in 1933 created the first graph of 

constant loudness levels. You cannot get very far into reading about acoustics before 

encountering their often-reproduced graph, which you see here as Fig. 2-289. The ordinate 

axis is sound pressure level (SPL) in decibels, a unit that I will discuss shortly. The abscissa is 

pure tone frequencies in hertz (cycles per second). The lines represent sound at constant or 

equal loudness as determined from a group of “subjects.” Imagine you are a “subject” in a 

loudness experiment. You put on earphones and the technician turns a knob that generates a 

reasonably quiet, pure tone sound per Eq. (2.299) at, say, 1,000 hertz (cycles per second). You 

tell the technician that the sound you hear is your reference loudness and call it a loudness of 

40 (never mind the units for now). The technician will write down 40 decibels. The technician 

then turns the frequency to 100 hertz—without changing the volume. You say that the volume 

went down. The technician then says he (or she) will slowly turn up the volume until you say 

it sounds as loud as before (i.e., at 1,000 hertz). At your call, he (or she) will stop raising the 

volume and record, say, 62 decibels. 

 Following this experimental procedure, you and the technician can create one line that 

Fletcher and Munson labeled a loudness of 40. (A unit for loudness called a phon was later 

coined, and the 40 became 40 phons.) 

Fig. 2-289. Fletcher and Munson’s loudness graph of 1933 [493]. 
2.7 NOISE 

441 

 As you noticed in Fig. 2-289, the ordinate is sound pressure level (SPL) in decibels, 

which is the number the technician wrote down when you selected the reasonable volume at 

1,000 hertz (i.e., 40) as your reference. Remember he wrote down 62 at 100 hertz, the 

increased volume that you said sounded as loud as the volume at 1,000 hertz. A decibel is the 

favored unit for measuring sound pressure levels. My use of pounds per square foot as on the 

vertical axis of Fig. 2-288 will most certainly be frowned upon by many readers. I should 

have at least used pascals, you might be saying, but keep in mind that many helicopter 

engineers unfamiliar with the subject of noise think of vibratory pressure in pounds per square 

foot—and it is to those interested engineers that I am writing. 

 There is no question that using so many zeros on the vertical scale of Fig. 2-288 before 

a number appears is unwieldy—even in the engineering world. So enter the decibel. Quite 

simply, a decibel is nothing more than a re-referencing of the pressure axis on Fig. 2-288. A 

sound pressure level (SPL) in decibels is mathematically defined as 

(2.301) 

2

rms

10

reference

p SPL decibel (dB) 10 log

p

    ≡          

where, for a pure tone, the root mean square pressure (prms) is given with Eq. (2.300). You 

should notice immediately that a decibel has no units because prms is divided by a reference 

pressure (pref). The International Organization of Standardization appears to have settled on a 

value of the reference pressure as 0.00002 pascals (or 2 × 10–5 Pa, or 20 micro pascals), which 

converts to 4.17708684662×10–7 pounds per square foot. This “universal” value was 

established as the reference hearing level at a frequency of 1,000 hertz. Thus, when the root 

mean square pressure (prms) equals the reference pressure (pref) you have the log10 of 1, which 

is zero. 

 The loudness curves that Fletcher and Munson published in 1933 opened the door to a 

human factors search for refinements to their curves—and a loudness scale. After seven 

decades of human factors research,148 the International Organization for Standardization (the 

same group that was involved in vibration as you read earlier) settled on a new set of loudness 

curves, which they identified as ISO 226:2003 [494]. I have included this modern standard 

here as Fig. 2-290 for the sake of completeness. 

 The researchers’ logic and approach to creating a loudness scale appears rather straight 

forward. If “corrections” to a set of loudness curves were established that turned the curves of 

a loudness graph into straight lines parallel to the X-axis, then a human’s perception of loud 

could be quantified by a number. In fact, electronic sound meters could be developed and 

manufactured that displayed a digital readout of loudness for all to see and record. Keep in 

mind that not all humans have the same hearing ability, so efforts at standardizing by human 

factors researchers have produced results with considerable scatter. Still, the group has met 

with some success. 

 

148 A step along the way was the paper published by Robinson and Dadson [495]. They show the variation in the 

threshold of hearing from several studies. 
2.7 NOISE 

442 

-10

0

10

20

30

40

50

60

70

80

90

100

110

120

130

1 10 100 1,000 10,000 100,000

Sound 

Pressure 

Level

 (db)

Frequency (Hz)

100

30

40

50

60

70

80

90

0

10

20

Fig. 2-290. Modern equal loudness curves of 2003 published as ISO 226:2003. 

2.7.3 Weighted Loudness Curves 

 The “corrections” (i.e., weighting) that the audio industry created are called in the 

literature, A-weighted, B-weighted, and C-weighted sound pressure levels (SPLs). The game 

has been to make each curve in Fig. 2-290 flat, which is to say nearly independent of 

frequency. That means a large correction at low frequency tapering down to zero correction at 

1,000 hertz, which has been taken as the reference frequency. In fact, you can see from 

Fig. 2-290 that a “correction” curve must subtract decibels as a function of both frequency and 

loudness. This could amount to a rather complicated function. The industry was not prepared 

to tackle that complexity given electronics in the pre-digital world, so they selected only three 

loudness corrections (i.e., A, B, and C) at which to be reasonably accurate with a “correction” 

dependent only on frequency—for pure tones. 

 The creators applied some simple mathematics to arrive at the three weighting curves. 

They said, 

(2.302) [ ]

2

rms

10 2

ref

2

rms

10 10 2

ref

Unweighted Weighting factor

p Weighted SPL decibel (dB) 10 log g(f )

p

p 10 log 10 log g(f )

p

SPL W

   

≡ ×        

 

= +    

= +
2.7 NOISE 

443 

where the multiplying factor [g(f)] would 

approximately flatten the loudness curves.149 It 

was then a simple step to subtract any type of 

weighting factor (i.e., WA, WB, or WC) from a 

measured, pure-tone SPL and display a number 

that approximately quantified a human’s 

opinion of noise—in decibels. The convention 

was adopted that these weighted SPLs would be 

designated dB(A), dB(B), and dB(C). 

 They constructed the A-weighting from 

the 40-phon levels, the B-weighting from the 

70-phon levels, and the C-weighting from the 

100-phon levels. It appears that B-weighted has 

fallen into disuse and the A-weighting and 

C-weighting are applied to any measured sound 

pressure level to convert to a 1-number readout 

in decibels. Many audio equipment firms sell 

sound meters (Fig. 2-191) that display noise 

level (or sound level if you prefer) in decibels 

followed by A, B, and C. These meters 

generally include a selection between A- and 

C-weightings. 

 Let me illustrate how the three weightings are applied This calculation is important 

because so many sound meters are used to measure noise in the world, and the readouts are 

used by many government bodies to regulate noise environment. 

 The A-, B-, and C-weightings are calculated from the following equations: 

(2.303) 

( )( ) ( )( )

2 4

A 10 2 22 2 2 22 2

12, 200 f W 2.0 log

f 20.6 f 12, 200 f 107.7 f 737.9

    = +  

  ++ + +  

, 

(2.304) 

( )( ) ( )

2 3

B 10 2 22 2 2 2

12, 200 f W 0.17 20 log

f 20.6 f 12, 200 f 158.5

    = +  

  ++ +  

, and 

(2.305) ( )( )

2 2

C 10 2 22 2

12,200 f W 0.06 20log f 20.6 f 12,200

    = +  

+ +    

. 

The offsets (2.0, 0.17, and 0.06 for WA,WB, and WC, respectively) ensure that at 1,000 hertz, 

no weighting occurs. 

 

149 Do not forget that log10(x + y) does not equal log10(x) + log10(y). Rather log10(xy) = log10(x) + log10(y). 

Microphone 

Electronic circuits 

& A/C weighting 

manupulation 

Digital 

Readout 

Fig. 2-291. A modern, commercially 

available sound meter.
2.7 NOISE 

444 

 Graphically, the three weighting curves described by Eqs. (2.303), (2.304), and (2.305) 

appear as shown in Fig. 2-292. When the weightings are applied to three of the loudness 

curves, you see the results in Fig. 2-293, which may take you aback as I have often been. If 

the objective was to get three curves that were nearly flat, then by helicopter engineering 

standards the objective was not met. Nevertheless, that is today’s precision as built into many 

sound meters. A constraint has been that many sound meters still use pre-digital electronics. 

 This brief introduction to acoustics really just brings you forward from 1933 to about 

1960. After that, acoustic engineers applied their energy to the entertainment world. Hi-Fi150

became a popular source for music, then stereo, and now you have surround sound and home 

theaters—a multibillion-dollar industry. It almost seems that noise created by airplanes and 

helicopters was inconsequential—at least until after World War II. 

 The proliferation of airplanes after WWII caused an awareness of noise “pollution” 

from both propeller- and jet-driven aircraft. It was quickly found that pure tone, A-weighted 

loudness measurements did little to quantify aviation noise. Then, in 1959, a new scale that 

quantified the annoyance of aviation sounds was introduced [496] and later refined [497] by 

Karl Kryter151. He introduced Perceived Noise Level (PNL), which went on to become a 

worldwide parameter when discussing aircraft noise. I will tell you more about PNL later. 

2.7.4 Propellers and Rotors at Zero Speed 

 You might be wondering why I have included a short discussion on airplane propellers 

in this volume dealing with helicopters. First of all, a great deal of propeller noise technology 

became the foundation for helicopter rotor noise studies. Even during World War I, fighter 

and bomber aircraft were quite noisy. In fact, propeller tip speeds frequently exceeded sonic 

Mach number. Then, when United States airlines were started in the early 1920s (funded by 

the U.S. Post Office [498]), frequent complaints really began (Fig. 2-294). Secondly, several 

of the early N.A.C.A. reports illustrate some noise fundamentals quite clearly based on 

propeller static testing. Thus, I can offer you some insight about data and test procedures that 

carried over to early helicopter main-rotor-noise test results in hover. In this section, you will 

see several test results from propellers and rotors obtained in the mid-1950s through the 

1960s. Static propeller noise measurements can be considered akin to those of a hovering 

helicopter’s tail rotor. I will take up noise prediction in the next section. 

 

150 After graduating from RPI in 1956 and getting a job at Vertol, I quickly saved enough money to build my 

own hi-fidelity system from Heath kits. At that time, The Heath Company was located in Benton Harbor, 

Michigan. From their kits, I built a tube-type preamplifier, 15-watt amplifier, and an AM/FM radio, and splurged 

on a terrific turntable to play 33-1/3 records. I built two solid-mahogany cabinets, one for the electronics and the 

other for the bass reflex speaker system, which used three Altec Lansing speakers and crossover networks. Now 

that was a real home entertainment system. 

151 Kryter worked at Bolt Beranek and Newman, Inc. in Cambridge, Massachusetts. In October 2009 this wellknown and respected research organization became a wholly owned subsidiary of Raytheon. 
2.7 NOISE 

445 

-70

-60

-50

-40

-30

-20

-10

0

10

10 100 1,000 10,000 100,000

Weighting 

Curves

(db)

Frequency (Hz)

A-Weighting

B-Weighting

C-Weighting

Fig. 2-292. Weighting curves to correct measured sound pressure levels to one digital 

readout of noise. 

0

10

20

30

40

50

60

70

80

90

100

110

120

130

10 100 1,000 10,000 100,000

Sound 

Pressure 

Levels 

(db)

Frequency (Hz)

40 Phon 

curve after 

A weighting

100 Phon 

curve after 

C 

weighting

70 Phon 

curve 

after B 

weighting

Fig. 2-293. Loudness curves corrected by weighting curves. 
2.7 NOISE 

446 

Fig. 2-294. Varney Airlines, located in Boise, Idaho, later became part of United Airlines 

[316]. (Found on the Internet at Stanford.edu under noise.) 

Fig. 2-295. The joint Air Force–Navy–NACA supersonic propeller flight research vehicle 

of the 1950s. Two Westinghouse J-34-W-34 jet engines plus afterburners and one 

Allison XT-38-A-5 turboprop engine. Prop speeds of 1,700 and 3,600 rpm ground 

adjustable on gear box assembly. Conventional, maximum 10-foot-diameter prop 

shown. I believe the prop is shown stopped and feathered in this photo [499]. 
2.7 NOISE 

447 

 There is now little question that the propeller of a small, light airplane, all the way up 

to propellers on the Douglas DC-3 to -7 series and the Lockheed Constellation series, are very 

loud—no matter what the measurement scale is. This situation was a serious consideration as 

the transition from propeller-driven to jet-driven commercial transport airplanes was being 

made during the 1950s and early 1960s. Of course, the maximum speed for efficient 

propellers was a major point during very vigorous debates about the pros and cons of the two 

propulsion systems that raged on in that period. But, as airports expanded, many aspects of 

commercial airplane noise, and its effect on the nearby neighborhoods, became a serious 

concern. It was a case of wanting increased propulsive efficiency and lower noise; one of 

those cases of wanting our cake and eating it too. 

 In the 1950s, the N.A.C.A. joined with the Air Force and Navy to conduct flight 

research on propellers designed for nearly Mach 1 flight speeds. The flight research vehicle 

was the McDonnell XF-88B shown in Fig. 2-295. The program was declassified in 1958. In 

the first report about the program [499], the authors stated in their introduction that 

“several years ago the National Advisory Committee for Aeronautics realized there was a 

need for providing continuous research on propellers designed for high efficiency for 

airplanes of maximum range at speeds up to Mach number 1.0. These propellers would be 

utilized on airplanes on which range and efficiency of operation were paramount, such as 

long-range strategic bombers, tankers, long-range assault transports, maximum endurance 

tactical-fighter bombers, and passenger transports. In order to study the problem as a whole, 

including operation under installation conditions with a turbopropeller engine providing the 

driving power, a propeller flight-research program was planned. The airplane chosen for this 

study was a McDonnell XF-88 turbojet airplane. The research program is a joint Air ForceNavy-NACA effort. The airplane and continuing propeller research equipment are supplied 

by the U. S. Air Force. The Department of the Navy supplies the turbojet and turboprop 

engines. The research program and its execution are the responsibility of the NACA.” 

The program included noise measurements during ground operation of several propellers 

[500-505] designed for maximum propeller efficiency at very high advance ratios (V/nD) and 

high flight Mach number. These carefully conducted noise measurements of static propeller 

operation correspond to the helicopter operating in hover. From these tests, I have selected 

three propeller noise tests that Max Kurbjun and others reported. The first example comes 

from NACA TN 3422 in July of 1955 [500] where a “conventional” propeller (the largest at 

10-foot diameter) was tested at a tip speed of 877 feet per second. The second example [501] 

provides noise data at a tip speed of 1,319 feet per second. The third example [503] was the 

smallest diameter propeller (6.85 feet), and it was tested at a tip speed of 613 feet per second. 

 The primary data Kurbjun reported in NACA TN 3422 was overall sound pressure 

levels, which I will discuss shortly, as obtained with a microphone and a tape recorder. The 

test was a “static” propeller test. Imagine the propeller research airplane (Fig. 2-295) tied 

down (i.e., static) as if it were running up the propeller prior to beginning a takeoff. Noise was 

recorded at many azimuth points around the compass rose. The nose was taken as zero 

degrees, and the noise data was recorded at 15-degree increments in a clockwise sense. 

Basically, Kurbjun marched around the propeller hub at a 75-foot radius taking data as he 

went. Kurbjun was also very through in describing the sound recording equipment he used. 
2.7 NOISE 

448 

 Kurbjun noted in his report that “the 10-foot-diameter propeller investigated in the 

present report is typical of designs used in today’s aircraft, and the tip Mach number and 

power loading investigated are representative of those used in current operations.” He noted 

that the static propeller thrust was 2,080 pounds, the horsepower delivered to the propeller 

shaft was 1,250 at 1,675 rpm (tip Mach number of 0.79 and tip speed of 877 feet per second), 

and that the blade angle at the 0.7 radius station was 19.50 degrees. The atmospheric 

temperature was 47 degrees Fahrenheit and the barometric pressure was 30.27 inches of 

mercury (Hg). As Fig. 2-296 shows, the four propeller blades each had a constant chord of 

1 foot from the 0.4 radius station to the tip, and inboard made a transition to a 4.8-inch 

cylinder. Kurbjun did not mention the airfoil or the propeller manufacturer. 

 The measured overall sound pressure levels (OSPLs) Kurbjun recorded are reproduced 

here in Fig. 2-297 (from figure 4 of his NACA TN 3422). Notice that slightly aft of the 

propeller plane, close to 115 decibels was recorded, but for all intents and purposes of my 

discussion here, the noise is about 110 decibels all around the propeller. The predicted noise 

[506] was derived from two classic reports, both translations from foreign reports: Gutin’s 

work of 1936 [507] and Yudin’s work of 1944 [508]. 

Fig. 2-296. Four-bladed, 10-foot-diameter propeller blade geometry. Chord is b, 

thickness is h, and diameter is D. The blade twist, β – β0.7R, is nearly linear [500]. 
2.7 NOISE 

449 

Fig. 2-297. Overall sound pressure levels at a 75-foot radius from the propeller hub with 

the propeller operating at 2,080-lb thrust and absorbing 1,250 hp at 1,675 rpm. 

Tip Mach number of 0.79 [500]. 
2.7 NOISE 

450 

 The second propeller [501] was “designed for a forward flight Mach number of 0.95 at 

an altitude of 40,000 feet.” It had considerably different blade geometry from the 

“conventional” propeller as you can see by comparing Fig. 2-298 to Fig. 2-296. In this report, 

Kurbjun made a point of comparing the overall sound pressure levels between this 

“supersonic” propeller and the “subsonic” propeller as Fig. 2-299 shows. He concluded that a 

14-decibel penalty was incurred by the supersonic design, but was careful to note that that “is 

slightly high as the difference measured was between a three-bladed supersonic propeller and 

a four-blade subsonic propeller.” 

Fig. 2-298. Three-bladed, 7.2-foot-diameter propeller blade geometry. Chord is b, 

thickness is h, and diameter is D. The blade twist, β – β0.7R, is nearly linear [501]. 
2.7 NOISE 

451 

Fig. 2-299. Overall sound pressure levels at a 100-foot radius from the propeller hub 

with the propeller absorbing 1,400 hp at 3,500 rpm. Tip Mach number of 1.2 [501]. 
2.7 NOISE 

452 

 The third propeller tested [503] was referred to by Kurbjun as a transonic propeller, 

which had the blade geometry shown in Fig. 2-300. He very conveniently provided a table 

comparing the several propellers, which I have reproduced here as Table 2-36. The 

conventional propeller was not included, but he did include a “modified supersonic” type, 

which I have not included as one of my examples. From Fig. 2-301 you can see that the 

transonic propeller, designed for an advance ratio of 4.0, was the lowest static noise 

configuration and nearly on a par with the conventional propeller in Fig. 2-297. 

Table 2-36. Kurbjun’s Propeller Comparison 

Data Source 

Propeller 

Type 

Design 

Forward 

Mach 

Number 

Design 

Altitude 

(ft) 

Advance 

Ratio 

J=V/nD 

Solidity at 

0.7 R 

0.7R

Bb

2 r

σ =

π

Tip 

Airfoil 

Thickness 

Ratio 

Airfoil 

Thickness 

Ratio 

at the 

Spinner 

Tip 

Mach 

Number

NASA 

Memorandum 

4-18-59L 

Transonic 0.82 35,000 4.0 0.195 0.02 0.070 0.55 

NACA TN 

4059 Supersonic 0.95 40,000 2.2 0.154 0.02 0.042 1.20 

NACA TN 

4172 

Modified 

supersonic 0.95 40,000 3.2 0.154 0.02 0.055 0.80 

 

Fig. 2-300. Three-bladed, 6.85-foot-diameter transonic propeller blade geometry. Chord 

is b, thickness is h, and diameter is D. The blade twist, β – β0.7R, is nearly linear [503]. 
2.7 NOISE 

453 

Fig. 2-301. Overall sound pressure level of the transonic propeller nearly achieved the 

static noise level of the conventional propeller [503]. 
2.7 NOISE 

454 

 This discussion of propeller noise would not be complete without showing you some 

forward flight performance. The transonic propeller design appeared most promising with 

respect to noise at the beginning of a takeoff as Fig. 2-301 shows. This encouraged NASA 

(the follow-on to the N.A.C.A.) to obtain forward flight performance data. The flight test 

results were reported by Tom O’Bryan and Jerry Hammack in NASA Memorandum 4-19-59L 

in May of 1959 [504]. They summarized the transonic efficiency with two charts, one of 

which I have reproduce here as Fig. 2-302. This data is presented in propeller coefficient 

form, which was defined in Table 2-15, page 229. 

Fig. 2-302. Forward flight performance of the transonic propeller was not great [504]. 
2.7 NOISE 

455 

 The forward flight propulsive efficiency of the transonic propeller showed that there 

would be an appreciable reduction from conventional propeller levels at flight Mach numbers 

associated with commercial jet transports then being introduced to the airlines. While the 

noise might have been comparable to the current propeller-driven fleet, the performance 

demonstrated by the program was not good enough to continue the effort.152 I will mention 

that propeller efficiency (η = CTJ/CP) was obtained by direct measurement of shaft torque and 

RPM, but thrust was obtained from integration of propeller wake pressures measured with 

probes [511]. To me, this always made the thrust coefficient suspect because the wake 

included airframe interference effects. This, in turn, might have shortchanged the actual thrust 

leading to a lower propulsive efficiency. I note in passing that the Wright Brothers’ propellers 

achieved an estimated efficiency of 0.66 at about 20 miles per hour (i.e., Mach number of 

0.02), so getting the same efficiency at a flight Mach number of 0.84 must constitute real 

progress! 

 Lest you think that efforts to reduce propeller noise were not producing results, 

consider a solution demonstrated by the N.A.C.A laboratory at Langley in 1946 (Fig. 2-303). 

James Hanson, in his terrific history about the Langley Research Center from 1917 to 1958 

[512], included these photos with the caption: 

“Langley modified a Stinson L-5 to show that a quiet airplane could be developed. During the 

lunchtime of the NACA’s annual inspection in 1946, the modified (lower photograph) and the 

standard aircraft were flown separately over the conference building. Those who witnessed 

the demonstration were astonished by the relative quiet of the modified L-5.” 

I wonder what the berry pickers in Ada County, Idaho would have thought. 

Fig. 2-303. Noise reduction approach on a Stinson L-5 [513]. 

 

152 This is not to dismiss an earlier experiment [509]. Here a three-bladed, 9.75-foot-diameter propeller was 

tested in a wind tunnel up to a free-stream Mach number of 0.96. I found the test results particularly interesting 

[295] because of potential applications to tiltwing and tiltrotor configurations. And keep in mind that the 

concerns about the Middle East oil embargo of 1973 and national fuel consumption in the 1970s and 1980s led to 

a renewed effort to improve turboprop performance with very advanced blade geometry [510]. This program got 

off to a quick start—flight demonstrated major improvements—and the NASA Lewis Research Center and the 

entire NASA/Industry advanced turboprop team were awarded the 1987 Collier Trophy. 
2.7 NOISE 

456 

 Now let me turn your attention to helicopters and the noise their rotors make. 

 The recording of early helicopter noise followed much the same patterns and 

procedures as those used to obtain propeller noise data. In helicopter noise testing, the 

machine was hovered (generally in ground effect) and measurements were obtained around a 

compass rose with zero degrees taken off the helicopter’s nose. Now let me show you 

examples of U.S. Air Force and Army noise measurements taken during comprehensive flight 

evaluation of six helicopters that include two, small tip-driven helicopters. I have also chosen 

two NASA sets of more detailed results reported in 1973. The time frame of these 

experiments was from 1958 to 1973. 

 The ten figures that follow are sequenced according to Table 2-37. The overall soundpressure-level data for each aircraft show a range of from 75 decibels for the very light 

OH-6A (hovering out of ground effect at 15 meters, about 50 feet) at a distance of 210 feet 

from the helicopter’s center of gravity, to 140 decibels for the tip ramjet YH-32 at a distance 

of 50 feet. 

 The operating conditions for each machine is sketchy at best. In fact, I do not mind 

saying that noise measurements seemed just an afterthought when compared to cockpit 

arrangement, aircraft performance, vibration, etc. Therefore the values of parameters in 

Table 2-37 are, in too many cases, my best educated guess. In general, hover height and tip 

speeds are clearly reported. After that, I can only share your disappointment in the poor 

documentation. I have added other comments for each figure. 

 The following ten figures (Figs. 2-304 through 2-313) constitute a data bank that I will 

summarize and then use for an overall sound-pressure-level analysis including a test-versustheory graph. 
2.7 NOISE 

457 

Table 2-37. Helicopters Included in Noise Study 

Parameter Symbol Units YHO-2HU OH-6A YUH-1D YUH-1D S-62A SH-3A YH-32 Djinn

 Reference [111] [514] [133] [179] [515] [516] [517] [518] 

 Power Source Piston Turbine Turbine Turbine Turbine Turbine 

Tip 

Ramjet 

Tip Cold 

Cycle 

 Engine 

Lycoming 

0-360-C2B

Allison 

T63-A5A Lycoming 

T53-L-9

Lycoming 

T53-L-9

One 

CT58-

100-1 

Two T58-

GE-8B Hiller 

Palouste 

IV 

 Gross Weight T lbs 1,550 2,100 6,600 6,600 7,500 15,600 1,080 1,545 

 Horsepower SHPinstall hp 180 252 1,100 1,100 730 2,500 na 240 

 Main Rotor 

 Diameter D ft 25.0 26.33 44 48 53.0 62.06 23.0 36.09 

 Disc Loading T/A lbs/ft2 3.16 3.86 4.34 3.65 3.40 5.16 2.60 1.51 

 Normal RPM 450 470 324 324 228 203 545 380 

 Tip Speed Vt ft/sec 589 648 746 814 633 659 656 718 

 Tip Mach 

 Number Mt nd 0.527 0.580 0.669 0.729 0.567 0.590 0.588 0.643 

 Blades b nd 3 4 2 2 3 5 2 2 

 Chord c ft 0.5625 0.5625 1.750 1.750 1.357 1.520 0.7917 0.775 

 Airfoil 

 Thickness 

 Ratio t/c nd 0.15 0.15 0.12 0.12 0.12 0.12 0.12 0.18 

 Blade Aspect 

 Ratio R/c nd 22.22 23.40 12.57 13.71 19.53 20.34 14.53 46.45 

 Twist θt deg – 8.0 – 8.0 na na – 8.0 – 8.0 na – 4.0 

 

 Tail Rotor 

 Diameter D ft 3.33 4.25 8.50 8.5 8.75 10.0 2.67 na 

 Normal RPM 4,131 3,120 1,562 1,562 na 1,243 3,600 na 

 Tip Speed Vt fps 698 694 695 695 na 669 503 na 

 Tip Mach 

 Number Mt nd 0.625 0.623 0.623 0.623 na 0.600 0.451 na 

 Blades b nd 2 2 2 2 2 5 1 na 

 Chord c ft 0.2917 0.401 0.701 0.701 na 0.61 0.2917 na 

 Airfoil 

 Thickness 

 Ratio t/c nd 0.15 0.14 0.15 0.15 

0.165 to 

0.12 0.12 0.15 na 

 Blade Aspect 

 Ratio R/c nd 11.42 5.24 6.06 6.06 na 8.19 4.57 na 

 Twist θt deg 0.0 – 5.4 0.0 0.0 na 0.0 na na 

 

 Tethered Yes Yes 

 Wheels/Skids 

 to Rotor Plane Hr ft 7.9 7.2 11.96 11.96 14.2 15.0 7.83 8.6 
2.7 NOISE 

458 

Fig. 2-304. Noise survey of YHO-2HU in hover at 1-foot skid height. Notice that there is 

a 10-dB difference between the nose and tail noise at the 50-foot distance. The 

weight, power, pressure altitude, and outside temperature were not quoted. This 

data presentation is typical of early U.S. Air Force reports. You will find a 

dimensioned 3-view of this helicopter on page 345, Fig. 2-195 [111]. 
2.7 NOISE 

459 

Fig. 2-305. Noise survey of OH-6A in hover at 15-meters (49-foot) skid height. Note lines 

of constant decibels format; this was the data presentation format used in the 

NASA report of the OH-6A and the SH-3A. The weight, power, pressure altitude, 

and outside temperature were not quoted [514]. 
2.7 NOISE 

460 

Fig. 2-306. Noise survey of the 44-foot-diameter YUH-1D in hover at 5-foot skid height. 

The helicopter was tethered and full power was applied. The thrust and power 

given in Table 2-37 are my estimates assuming standard density. Note that the 

outside air temperature was 48oF. I will discuss the octave band analysis (the 

tabulated data) shortly, but for now note that the data only goes with one circled 

point at the 100-foot distance to the starboard side of the aircraft. The YUH-1D 

was also tested with a 48-foot-diameter rotor, which is shown in the next figure 

[133]. 
2.7 NOISE 

461 

Fig. 2-307. Noise survey of 48-foot-diameter YUH-1D at ground idle. The thrust should 

be assumed as zero. My best guess at the ground-idle-power rotor speed is from 

the pilot’s -10 manual, which says 62 percent of 324 rpm [179]. 
2.7 NOISE 

462 

Fig. 2-308. Noise survey of 48-foot-diameter YUH-1D in hover at 5-foot skid height. The 

helicopter was tethered and full power was applied. The thrust and power given 

in Table 2-37 are my estimates assuming standard density. Note that the outside 

air temperature was 48o

F. I will discuss the octave band analysis (the tabulated 

data) shortly, but for now note that the data only goes with one circled point at 

the 100-foot distance to the starboard side of the aircraft [179]. 
2.7 NOISE 

463 

Fig. 2-309. Noise survey of S-62A on the ground, maybe at ground idle, which I would 

assume is about 60 percent power turbine speed [515]. 
2.7 NOISE 

464 

Fig. 2-310. Noise survey of S-62A in hover at 5-foot skid height [515]. 
2.7 NOISE 

465 

Fig. 2-311. Noise survey of SH-3A in hover out of ground effect at 100-foot skid height. 

Note: distances in meters [516]. 

Fig. 2-312. Noise survey of YH-32 in hover at 1-foot skid height. This small helicopter 

had a one-bladed tail rotor. Note: data for XV-1 (a tip-driven compound, which I 

will discuss in Volume III) and for the French Alouette II was included for 

comparison [517]. 
2.7 NOISE 

466 

Fig. 2-313. Noise survey of Djinn in hover at 1-foot skid height. The Djinn used a cold 

cycle, tip-driven main rotor; it had no tail rotor [518]. 
2.7 NOISE 

467 

 Now that you have perused the previous ten figures, let me offer one summary shown 

with Fig. 2-314. Here, I have compared the overall sound pressure levels at the 90-degree 

compass rose azimuth versus distance from the sound source (approximately each helicopter’s 

center of gravity) for the ten examples. 

 Note that I have included noise descriptions commonly associated with what people 

can encounter in their day-to-day lives. Also be aware that ear protection at 95 decibels and 

above is required by military regulations. 

60

70

80

90

100

110

120

130

140

0 200 400 600 800 1,000 1,200

YOH-2HU

OH-6A

YUH-1D (44 feet)

YUH-1D (48 ft) Ground Idle

YUH-1D (48 ft) Full Power

S-62A Ground idle

S-62A

SH-3A

YH-42 Ramjet

Djinn Cold Cycle

Noisy Restaurant, Business Office

Alarm Clock, Hair Dryer

Heavy Truck (50 ft), City Traffic

Firecracker, Subway Train

Rock Concert, Discotheque

Jet Takeoff (200 ft)

Thunderclap. Air Raid Siren (3 ft)

Ears Damaged

Overall

Sound

Pressure

Level

(OSPL)

(dB)

Distance From Source (feet)

Ear Protecton Required per Air Force Regulation 160-3 (1948)

Fig. 2-314. Survey of noise results from several helicopters hovering in ground effect. 
2.7 NOISE 

468 

2.7.5 Overall Sound Pressure Level (OSPL) in Hover 

 Without going too far back in time, many acoustical engineers believe that the 

groundwork needed for calculating overall sound pressure level became available in the 

United States when the N.A.C.A. released translations of two reports [507, 508]. The first of 

these two reports was written by L. Ya. Gutin (a German); it came out in 1936 and was 

republished in 1948 as NACA TM 1195. The second, written by E. Ya. Yudin (a Russian), 

came out in 1944 and was republished in 1947 as NACA TM 1136. These early theories were 

put to good use at the N.A.C.A. Langley Laboratory and, in fact, throughout the aviation 

industry. 

 As a beginning, I think you will find Arthur Deming’s report [519] from 1940 quite 

helpful. His introduction defines the categories of noise clearly enough to convey with a 

simple organization chart, which you see in Fig. 2-315. Deming expands his perception, 

writing: 

“The rotation noise is due to the pressure wave enveloping each blade and moving with it; the 

vortex noise is due to pressure variations on the blade as a result of variations of circulation 

[thrust]. It may be simply stated that the rotation noise is due to the constant air force on the 

blades and that the vortex noise is due to the vortices shed in the wake.” 

In the 1940s, and for a decade or two more, Deming’s adaption [519] of Gutin’s work to 

everyday engineering was immensely valuable. Noise (at least due to torque and thrust) could 

be calculated with a slide rule. Deming and his coauthor, Stowell, also attacked vortex noise 

[520] following Strouhal’s 1878 work. You will find this report about vortex noise 

particularly simple, clear, and enjoyable because of the history the authors included. 

Fig. 2-315. The noise categories in 1940 with some modern additions. 

Propeller 

& 

Rotor 

Noise 

Rotational 

Noise 

Blade 

Thickness 

Noise 

Torque 

& 

Thrust Noise 

Other Types of Noise 

Broadband 

Impulsive 

High Speed 

Blade-Vortex 

Vortex 

Noise
2.7 NOISE 

469 

 A major theoretical step forward came in May of 1969. In that year, J. E. Ffowcs 

Williams and D. L. Hawkings published Sound Generation by Turbulence and Surfaces in 

Arbitrary Motion in the Philosophical Transactions of the Royal Society of London [521]. 

This new and firmer foundation to the basic equations needed to calculate how sound waves 

are propagated was embraced by the acoustic community. (I, however, was simply bowled 

over by the theoretical derivations because of my totally inadequate set of mathematical 

skills). Then, in 2003, an application of Williams and Hawkings’ work to helicopters by Ken 

Brentner and Feri Farassat [522] was published, which was (in my opinion) a major 

contribution. Over a decade of effort by the acoustic community is described in Brentner and 

Farassat’s paper. While the authors note in their paragraph on Preliminaries that “to learn and 

apply acoustic theory requires considerable mathematical maturity,” their inclusion of several 

theory-versus-test examples brings the whole acoustic field closer to the practicing helicopter 

engineer. In fact, a useable engineering computer program called WOPWOP was born that 

has progressed, at Pennsylvania State University under Ken Brentner’s guidance, to 

PSU-WOPWOP [523]. Then a paper that really fell within my level of “mathematical 

maturity” was published by Gaurav Gopalan in 2008 [524]. Gopalan’s paper reduced 

calculation of helicopter rotor rotational noise in hover to an introductory level where 

computations can be made with a Microsoft®

 Excel® spreadsheet. Because of Gopalan’s work, 

you have a step-by-step example in this volume of how to arrive at overall sound pressure 

levels for a helicopter rotor in hover—at least at the introductory level of rotational noise. 

 There must be several hundred papers and reports dealing with rotorcraft noise as you 

will quickly conclude from just literature searches [525, 526], conference proceedings [527, 

528], and status reports [529, 530]. Several reports having more practical engineering use 

because of the experimental data included with some theory are references [531-543]. Within 

this group, there are, in my opinion, three reports that became available between the 1940s 

and the early 1990s that you might begin with [533, 535, 541]. 

 You should also know that in 1991 Harvey Hubbard compiled and edited NASA 

Reference Publication 1258 [544], which covered (in Chapter 2) the subject of Rotor Noise 

written by Fred Schmitz [545]. At that time, Fred was Director of Aeronautics at NASA Ames 

Research Center. Fred has been an acknowledged expert in the acoustic field for decades.153

The first six pages of Fred’s contribution contain a broad discussion of rotor noise that is 

immensely valuable. The improvements in measuring equipment, Fred explains, give the 

insight you see here as Fig. 2-316, which is Fred’s third figure. Modern digital electronics 

allowed seeing the details making up OSPL. A recorded time history of noise could be 

frequency analyzed in very small frequency bands so rotor noise at each harmonic became 

quite clear [545]. Furthermore, as Fig. 2-316 shows, noises from other helicopter components 

were readily identified. 

 

153 When I retired from Bell Helicopter Textron in January 1992 (somewhat after the SuperTeam lost the LHX 

bid in April 1991), Fred extended an offer to come to NASA Ames. At that time Sue and I were living in 

Fountain Hills, Arizona. Moving to northern California turned out to be unreasonable in terms of the expensive 

housing, but the chance to extend my career was very attractive. Fred set me up to go frequently to Ames and 

make further contributions by working at home. The opportunity to concentrate again on rotorcraft technology 

was then, and is still, just plain fun. The relationship that contributed to Volume I has now led to this Volume II. 
2.7 NOISE 

470 

Fig. 2-316. The noise generated by a two-bladed Bell UH-1A [545, 546]. 

 You can see from Fig. 2-316 that helicopter overall noise is made up of many tones 

(i.e., frequencies).154 Thus, the sound pressure level (SPL) is far from the single-tone hearing 

experiments that human factors researchers have conducted and analyzed for decades. This 

multitone character seems to have led to inserting “overall”—the “O” in front of SPL. Overall 

sound pressure level is calculated with a deceptively simple equation, which is 

(2.305) ( ) 2

1

T 2

10 t 2 T

ref 2 1

1 1 OSPL 10log p dt p TT

      =         −    . 

The unit of OSPL is decibels. The reference pressure (pref) has been somewhat arbitrarily 

taken as 0.00002 pascals for decades. The sound pressure time history (pt) is measured with a 

microphone, or calculated by theory, or reported as “racket” by some people. 

 Sound pressure is displayed as a time history, but because rotor or propeller sound 

pressure is theoretically periodic, a time history of sound pressure as recorded versus time can 

be displayed as sound pressure versus an azimuth angle. The waveform may “dance” around a 

little bit as you saw in Fig. 2-258 through Fig. 2-265 starting back on page 411. This causes a 

blurring in the waveform, but the basic waveform is generally quite clear, especially in static 

and wind tunnel testing where an acoustic chamber has been created. Once you have a 

digitized sound pressure history with time, today’s computer technology makes the sky the 

limit for analysis questions. Frequently, the waveform is Fourier analyzed to give virtually 

 

154 When I was plying my trade and when it came to discussing helicopter noise, Harvey Hubbard (NACA), 

Fred Schmitz (NASA), Charles Cox (Bell), Harry Sternfeld (Boeing Vertol), Ron Schlegel (Sikorsky), 

Bob Wagner (Hughes), and John Leverton (University of Southampton, before coming to the U.S. to continue 

his career) were absolute giants in the rotorcraft industry. 
2.7 NOISE 

471 

exact amplitudes at any harmonic. Acoustic engineers generally do not demand such exact 

accounting as a Fourier series gives and are satisfied when the periodic sound pressure peaks 

are clearly visible as in Fig. 2-316. 

 As a first step, let me introduce you to the OSPL calculations in hover. In a later 

section, I will discuss the situation in forward flight. 

2.7.5.1 Thickness, Torque, and Thrust Noise From an Ideal Rotor 

 The approach to calculating rotor sound pressures that a microphone records really

became much clearer to me in January of 2008. In that year, Gopalan from the University of 

Maryland (under Fred Schmitz’s encouragement) presented a paper [524] at the AHS 

Specialists’ Conference on Aeromechanics, which was held in San Francisco. Gopalan155

arrived at a simple engineering result that I think you will find is absolutely perfect for an 

introductory calculation of overall sound pressure level due to rotational noise. 

 Gopalan, using some very creative applied mathematics, translated the fundamental 

theory Williams and Hawkings offered in 1969 [521] into very useable engineering equations. 

He restricted his work to calculating sound pressure only in the far field, which meant that the 

distance ( ) 222 S XYH = ++ from the rotor hub to the observer (obs) in Fig. 2-317 is 

considerably greater than the rotor radius (R). 

 

Fig. 2-317. The distance between the main rotor hub and the observer is considerably 

greater than the rotor radius in the prediction of noise in the far field. Note that 

θobs = arc sin (H/S). 

 

 

155 Gaurav Gopalan met with a very unfortunate death in September 2011. Fred Schmitz’ tribute to Gaurav’s life 

and accomplishments was published in the Winter 2011 issue of the AHS Vertiflite trade magazine [547]. We 

lost an exceptionally valuable contributor that I was quite ready to place in the group offered in the preceding 

footnote. 

X Y

Observer

θobs H 

S
2.7 NOISE 

472 

 To illustrate the application of Gopalan’s work, let me start with calculating thickness 

sound pressure. Thickness pressure is created because all real propeller and rotor blades have 

airfoils with thickness-to-chord ratios (t/c) varying between 0.02 and 0.18. You proceed as 

follows for this component of rotational noise: 

(2.306) Thickness p K F for one blade ψ ψ = thickness M, ( )

where the variation of thickness pressure (pψ) with the master blade’s azimuth (ψ) is also 

dependent on an “equivalent” Mach number ( ) M M cos = θ tip obs so that (FM,ψ) is computed as 

(2.306) ( )

( )

( )

2 22 24 3

M, 4 2 42 22 44

M M 40 10cos 28M cos 11M cos

F

1 Msin sin 30 10M 6M cos 35M cos 18M cos ψ

  + ψ+ ψ+ ψ =  

− ψ − ψ + + ψ + ψ − ψ  

. 

Gopalan found that he could account for an observer who was not exactly in the plane of the 

rotor by defining the (M) in Eq. (2.306) as M = Mtip cos θobs. The configuration constant (K) is 

calculated as 

(2.307) 

2

f

2

thickness s

c t S

R c K a

S 240

R

             = ρ  

      π     

where the parameters are defined by Table 2-38 on page 476. You might immediately note in 

this equation for the configuration thickness constant (Kthickness) that Gopalan put all blade 

geometry and the observer distance as ratios, and therefore everything within the [ ] of Eq. 

(2.307) is dimensionless. To me this is a sign of a good engineer. This makes the units of K 

solely dependent on the density and the speed of sound. Gopalan states in his list of symbols 

that density (on a standard day) is, in the metric system, 1.225 kilograms per cubic meter, and 

the speed of sound is 340.29 meters per second. Thus, the product ( 2

s ρa ) becomes 142,360 

newtons per square meter, which is 142,360 pascals.156

 The sound pressure created by the rotor thrust and the torque (actually just the ideal 

induced torque) was also estimated by relatively simple equations when you follow Gopalan’s 

work. Thrust sound pressure is my shorthand for what helicopter acoustic engineers call “outof-plane loading” noise. The plane these engineers refer to is the tip path plane. For thrust 

sound pressure per blade, Gaurav offered the following approximation: 

(2.308) Thrust p L D for one blade ψ ψ = thrust M, ( )

where the variation of thrust sound pressure (pψ) with the azimuth (ψ) of the master blade is 

also dependent on the equivalent Mach number (M = Mtip cos θobs), so that (DM,ψ) is computed 

as 

 

156 In the English system of units, you have 0.002378 slugs per cubic foot for density and 1116.45 feet per 

second for the speed of sound, which results in 2,962 pounds per square foot on a standard day. 
2.7 NOISE 

473 

(2.308) ( )

2 2 2

M, 3

M cos 20 20M sin 9M cos

D

1 M sin ψ

ψ   − ψ + ψ   = − ψ . 

The configuration constant (Lthrust) is calculated as 

(2.308) ( ) ( ) 2

thrust s obs 2

s

TA R L a tan

a 120 bS

   =ρ θ      ρ  

. 

For the sound pressure created by applying torque to turn the rotor (called “inplane loading” 

noise), Gopalan gave the approximation that 

(2.308) Torque p L H for one blade ψ ψ = torque M, ( )

where 

(2.308) ( )

2 2 3 2

22 42 2 33

M, 3

60 30M cos 120Msin 30M sin cos

cos

80M sin 9M sin cos 20M sin

H

1 Msin ψ

 + ψ − ψ − ψ ψ

ψ  + ψ+ ψ ψ− ψ  = − ψ . 

The configuration constant for torque (Ltorque) is calculated as 

(2.309) ( ) ( )

3/2

2

torque s obs 2

s

TA R L a cos

a 120 2 bS

   

= ρ     θ

  ρ  

. 

 There are, of course, several restrictions to the broad use of Gopalan’s equations that 

you must be aware of. The most important restrictions are: 

1. The rotor being analyzed is an ideal rotor, which is to say that the induced velocity 

is uniform over the whole rotor disc. This uniform induced velocity (v) is calculated 

as v T2A = ρ as you learned from momentum theory. A rectangular blade having a 

twist distribution of x tip θ =θ x will theoretically produce uniform induced velocity in 

hover as Gessow and Myers demonstrate on pages 57 and 58 of their classic book, 

Aerodynamics of the Helicopter [234]. 

2. The rotor blades are represented by a lifting line, not a lifting surface, in the 

calculation of thickness noise so an approximation to a real airfoil is introduced in 

Eq. (2.307) using the airfoil constant (Sf), which is equal to 0.685 for the NACA 

00xx series airfoils. 

3. The rotor blades are required to be rectangular (i.e., constant chord) and have a 

relatively high aspect ratio because of the lifting line assumption. Most helicopter 

main rotor blades fit this criteria, but this restriction tends to bring most tail rotor 

blades somewhat into question. 

4. The rotor blades are required to have a constant thickness airfoil from root to tip. 

To me, this is a small list of restrictions to a set of sound pressure estimating equations that 

can easily be solved using a simple spreadsheet calculator such as Microsoft®

 Excel®. 
2.7 NOISE 

474 

 The last point I want you to understand deals with the addition of pressures when there 

is more than one blade. The noise from, say, a three-bladed rotor is not just three times the 

noise calculated for one blade. Sound pressures are added at the observer location, not the 

source (i.e., hub) location. It takes time for the sound pressure waves to go from each blade 

(i.e., an individual sound source) to the observer (i.e., the microphone and onto a digital tape). 

While a stroboscope will show you where the blades are in azimuth, your stopwatch will be 

the real abscissa in graphing pressure versus time. This is similar to seeing a lightening flash, 

but hearing the thunder a short time later. An oscillograph recording the microphone’s 

response would show a graph of pressure versus observer time. Fortunately, observer time is 

related to blade azimuth (i.e., the source’s reference) by the following simple relationship: 

(2.310) ( )

obs

S s Ss s

S R cos S R R cos 1

t

a a aa a

   ψ ψ ψ − ψ = + +− + = +       Ω Ω . 

Here, I have taken Gopalan’s expression and made time be zero when the master blade is at 

zero azimuth, which is generally taken as over the tail boom for a single rotor helicopter. You 

might wonder about the term (cos ψ – 1). This reflects the distortion in the waveform that is 

caused by the Doppler effect. The Doppler effect creates the difference in sound tone (not just 

noise level) that you hear from a train’s horn when the train is coming towards you and when 

it is leaving your observer position. 

 Frankly, I found it much more informative to express observer time (tobs)—which 

would be digitized time in seconds with modern instrumentation—as a pseudo azimuth angle 

in degrees. That is, Eq. (2.310) can be multiplied through by rotor speed (Ω), and then you 

have 

(2.311) ( )

obs obs tip ( ) s

R cos 1

t M cos 1

a

Ω ψ− ψ =Ω = +ψ = ψ− +ψ, 

which illuminates the tip Mach number (Mtip = Vt/as) as the measure of how long it takes for 

the sound to leave its source until the digitizing microphone signal is recorded—not counting 

any instrumentation delays. An example of this difference in sending and receiving “time” 

expressed in degrees is shown in Fig. 2-318 for a rotor having a tip Mach number of 0.60. 

 Note on Fig. 2-318 that a stroboscope might show the master blade at a source azimuth 

of 150 degrees, but your ears and the instrumentation would perceive the noise coming from 

the blade when it was at 60 degrees. In short, in the time it takes for the blade’s noise, 

broadcasted at a source azimuth of 60 degrees, to reach you, the blade will already have 

passed. Of course, one revolution is one revolution. 

 The Doppler effect leads to a relatively minor scaling problem when adding noise 

from other blades. The situation, as I see it, is that it is more convenient to do the adding of 

sound pressure from all blades in a reference observer time (or azimuth, ψobs) domain, but 

Gopalan’s equations use source azimuth (ψ) as the input parameter. My approach has been to 
2.7 NOISE 

475 

0

30

60

90

120

150

180

210

240

270

300

330

360

0 30 60 90 120 150 180 210 240 270 300 330 360

Rotor Master Blade (i.e., the source) Azimuth (deg)

Observer 

"Time" 

(deg)

Doppler

 Effect

Fig. 2-318. The Doppler effect per Eq. (2.311) for a tip Mach number of 0.60. 

choose equal steps in observer time, solve for corresponding source azimuth,157 and then 

calculate the sound pressure waveform for the master blade. Given the total pressure 

waveform for the master blade, the waveform can be slid in observer azimuth for each blade 

in the rotor system. That is, for a three-blade rotor, the master blade begins its waveform at an 

observer azimuth of zero degrees. The second blade pressure from the master blade’s observer 

time of 120 degrees is placed at an observer azimuth of zero degrees. Similarly, the third 

blade sees the master blade’s observer time at 240 degrees placed at an observer azimuth of 

zero degrees. Then the pressure from the blades can be added. 

 The graphical results you will see next all came from calculations made on an Excel®

spreadsheet. 

 Let me now show you a sample of what the calculated sound pressure waveforms look 

like for a three-bladed, ideal rotor in hover, and then the overall sound pressure level 

according to Eq. (2.305) can be calculated. I have chosen the basic geometry of the 

YHO-2HU helicopter’s main rotor for this example. The inputs to Gopalan’s equations are 

provided in Table 2-38. 

 

157 To compute ψ given equal increments in ψobs requires solving Eq. (2.311) backwards. This equation is really 

a transcendental equation. My approach was to make a column of ψobs and use the goal seek tool in Excel® to 

find the corresponding input azimuth (ψ). I wrote a simple macro to perform the repetitive goal seek operation. 
2.7 NOISE 

476 

Table 2-38. Configuration Parameters Associated With Thickness Noise 

Parameter Symbol 

English 

Units 

YHO-2HU 

Geometry 

YHO-2HU 

Metric Units Notes 

Density ρ slugs/ft3 0.002378 1.225 kg/m3 Sea level, standard 

Speed of Sound as ft/sec 1,116.437 340.29 m/sec Sea level, standard 

Airfoil Shape Factor Sf na 0.685 same NACA 0015 

Chord/Radius Ratio c/R na 0.045 same 

Airfoil Thickness Ratio t/c na 0.15 same 

Tip Mach Number Mtip na 0.53 same 

Elevation Angle θobs rad. 0 same 

Observer Distance S ft 200 60.96 meters 

Blade Radius R ft 12.5 3.81 meters 

Blade Number b na 3 same 

Thrust T lb 1,600 7,117 newtons 

Disc Loading T/A lb/ft2 3.26 156.06 n/m2 

 With the parameters provided in Table 2-38, you obtain the three configurations 

constants as 

 Kthickness = 0.0024466 pascals 

 Lthrust = 0.0 pascals 

 Ltorque = 0.00063549 pascals. 

You might note that there is no noise from thrust in this example because I have placed you, 

the observer, in a plane that contains the rotor’s tip path plane. In short, you see the rotor tip 

path plane as a thin line and the elevation angle is zero. 

 The thickness sound pressure (in pascal units) calculated in this example is shown in 

Fig. 2-319. Here you have the sound pressure for each individual blade as the red, blue, and 

green curves. The total for all three blades is the heavy black line. The thickness sound 

pressure is characterized by rather narrow negative spikes as you can see. These negative 

spikes become narrower but greater in maximum negative peak value as Mach number 

increases. The peak negative value for any one blade is approximated as 

(2.312) ( )

( )

3

thickness thickness 3

3 M

Peak Negative P K M

1 M

 −  =    −   

. 

The tip Mach number for this introductory, sea-level standard YHO-2HU example is 0.53, 

which corresponds to a tip speed of 592 feet per second. (Remember that M = Mtip cos θobs

and that θobs = 0 for this example.) This is a rather low tip speed, but also typical of small, 

piston-powered helicopters of the era. At this Mach number of 0.53, the [ ] term in 

Eq. (2.312) is 3.54. If the tip speed were up at larger, turbine-powered helicopter values of, 

say, 700 feet per second, the tip Mach number would be about 0.63 and the [ ] becomes 

11.74. Whether the sound pressure level would be around three times as great would depend, 

of course, on the relative values of Kthickness. With a simple scaling up of the YHO-2HU, the 

larger machine would need to be 600 feet away from you to have the same level of sound 

pressure as the smaller machine at a distance of 200 feet. 
2.7 NOISE 

477 

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0 30 60 90 120 150 180 210 240 270 300 330 360

Thickness 

Pressure

 (pascals)

Observer 

"Time" 

(deg)

Blade 1 Blade 2

Blade 1 + Blade 2 + Blade 3

Blade 3

Fig. 2-319. Thickness sound pressure for the YHO-2HU main rotor assumed to be ideal. 

 Now consider the thrust and torque sound pressure waveforms shown in Fig. 2-320. 

Because I have chosen to place the microphone exactly inplane with the rotor disc (θobs = 0), 

the thrust contribution to the waveform is zero as you can see from Eq. (2.308). Thus, 

Fig. 2-320 gives only the torque contribution to the recorded sound pressure level. The total 

sound pressure from the three blades is clearly a three-per-rev waveform, but fortunately this 

contribution is not completely in phase with the sound pressure waveform created by 

thickness. Unfortunately, you will find from your own calculations that when the evaluation 

angle (θobs) is 10 or 20 degrees, the thrust and torque contributions are much closer in phase 

and are very additive. You might note from Eq. (2.308) that if the observer is above the rotor 

plane, then the elevation angle is negative and the thrust contribution begins to cancel the 

torque contribution to the sound pressure waveform. For the sake of completeness, you 

should note that the peak negative sound pressures for thrust and torque are, respectively, 

(2.313) ( ) thrust thrust 2

16 13.5M Peak Negative P L

1 M

  − + =    −   

 and 

(2.314) ( )

2 3

torque torque 2

60 115M 84M 28M Peak Negative P L

1 M

  −+ − + =    −   

. 
2.7 NOISE 

478 

These two components, when added together—assuming they are completely in phase, which 

is a somewhat conservative assumption—mean that the loading (i.e., thrust and torque 

contributions) is of the approximate magnitude 

(2.315) ( ) ( ) ( )

( ) ( )

2 3

2

2

loading s 2 obs

s 2

tip obs 2

60 115M 84M 28M

TA R 21 M

Peak P a cos

a 120bS 16 13.5M M sin

1 M

  −+ − +  

    −    =± ρ    θ     ρ      − +  + θ  

       − 

. 

It is worth noting that the negative peak and positive peak of loading sound pressure, which is 

the sum of torque and thrust pressures, are equal. 

 Now take the next step, which is to add thickness, thrust, and torque sound pressures 

all together. This result is shown in Fig. 2-321. This is the input required to calculate the 

overall sound pressure level (OSPL). You should know that the total pressure waveform can 

be represented by a Fourier series. A Fourier analysis of the waveform described by 

Fig. 2-321 shows that 

(2.316) 

() () () ()

() () ( ) ( )

t p 0.032742sin 3 0.042379cos 3 0.006269sin 6 0.02244cos 6

0.001114sin 9 0.009060cos 9 0.000121sin 12 0.003247 cos 12

etc.

= ψ+ ψ− ψ− ψ

+ ψ + ψ − ψ − ψ

+

. 

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0 30 60 90 120 150 180 210 240 270 300 330 360

Blade 1 Blade 2 Blade 3

Observer 

"Time" 

(deg)

Thrust

&

Torque 

Pressure

(pascals)

Blade 1 + Blade 2 + Blade 3

Fig. 2-320. Thrust and torque sound pressure for the YHO-2HU ideal rotor example. 
2.7 NOISE 

479 

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0 30 60 90 120 150 180 210 240 270 300 330 360

Acoustic 

Total

Pressure

for

3 Blades 

(pascals)

Observer 

"Time" 

(deg)

Fig. 2-321. Total sound pressure for the YHO-2HU ideal rotor example. 

 

 Now take the final step where OSPL is calculated by Eq. (2.305), which is repeated 

here for convenience as 

(2.317) ( ) ( ) 2

1

obsT 2

10 t obs 2 obsT

ref 2 1 obs

1 1 OSPL 10log p dt p TT

      =     −        . 

This step requires that the sound pressure level from Fig. 2-321 be squared and plotted versus 

observer time (in seconds). You see this graphical result here as Fig. 2-322. 

 In creating the sound pressures leading to Fig. 2-322, I used a time step of .00007374 

seconds, which corresponds to 0.2 degrees of observer azimuth, and yields 1800 ordinates 

over one rotor revolution. To perform the integration, I was satisfied with trapezoidal area 

approximations for each time step of the revolution. Thus, this YHO-2HU example, assuming 

an ideal rotor-induced velocity distribution over the disc, arrives at an overall sound pressure 

level of 66.4 decibels. 
2.7 NOISE 

480 

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Total 

Sound 

Pressure 

Squared 

(pascals2

)

Observer Time (sec)

T2 = 2π/Ω

 = 0.1328 sec

Fig. 2-322. Integrating total sound pressure squared over one rotor revolution for the 

YHO-2HU ideal rotor example yields an OSPL of 66.4 decibels (using pref of 

0.00002 pascals). 

2.7.5.2 Extending Gopalan’s Work to a Conceptual Design Tool 

 In Gopalan’s first paper [524], he examined parameters that affect maximum 

pressures. My purpose here is to extend his work to the calculation of overall sound pressure 

levels (OSPLs) for rotors having 2 to 8 blades operating at tip Mach numbers from 0.5 to 

0.75. To apply Gopalan’s work, I have provided a virtually exact equation for the total sound 

pressure level of one blade. With that result in hand, the sound pressure level for any number 

of blades up to eight is expressed in terms of the result for one blade. I have chosen to deal 

with noise created when the observer angle (θobs) is zero, which is near enough to the 

maximum noise for illustration purposes. 

 Equation (2.317) shows that the first step to obtaining OSPL for one blade with a zero 

observer angle requires evaluation of the pressure integral 

(2.318) ( ) ( ) 2

1

obsT 2

t obs obsT

2 1 obs

1 p dt T T− 
2.7 NOISE 

481 

where the sound pressure (pt) is given by Gopalan per Eqs. (2.306) and (2.307) for thickness 

pressure, and Eqs. (2.308) and (2.309) for inplane loading pressure, as 

(2.318) t thickness M, torque M, pK F L H = +ψ ψ . 

Because the pressure is for just one blade, the integration can be carried out over one 

revolution in the source azimuth (i.e., blade azimuth) coordinate system. That is, from the 

definition of observer time according to Eq. (2.310), you have 

(2.319) ( ) obs

s

dt 1R 1 sin 1 Msin

d a = − ψ = − ψ ψΩ Ω , 

and because T1 can be taken as zero for a reference and T2 equals 2π/Ω for one revolution, you 

can transform the pressure integral of Eq. (2.318) from observer time to source azimuth to 

obtain 

(2.320) ( ) ( ) ( ) 2 2 2 2

t thickness M, torque M, 0 0

1 1

p d K F L H 1 M sin d

2 2

π π

ψ = +− ψ ψ ψ ψ

π π   . 

The squared expansion of the sound pressure leads to three integrals that must be evaluated. 

Thus, 

(2.321) 

( ) ( )

( )( )

( )

2 2 2 2 2 thickness

t M, 0 0

2 thickness torque

M, M, 0

2

2 torque 2

M, 0

1 K Blade 1 p d F 1 Msin d 2 2

2K L

F H 1 Msin d

2

L

H 1 Msin d

2

π π

ψ

π

ψ ψ

π

ψ

ψ = − ψ ψ

π π

+ − ψ ψ

π

+ − ψψ

π

 





. 

Using the mathematical software called Mathematica®, I evaluated the three integrals and 

found that a quite adequate engineering result for Mach numbers up to 0.8 is 

(2.322) 

( ) ( )

( )

6 2 2 2 24 6 8

t thickness 9/2 0 2

2 24 4 4

torque 3/2 2

1 450M 22 17 59 447 Blade 1 p d K 1 M M M M

2 9 18 192 1280 1 M

1800 1 3 1 1 L 1 MM M M

3 8 16 1280 1 M

π     ψ= + − + −     π    −  

    + −−− +        −  



where, you will note, the product term thickness torque 2K L conveniently comes out exactly zero. 

To repeat, the configuration constants for one blade and zero elevation angle are 

2

f

2

thickness s

c t S

R c K a

S 240

R

             = ρ  

      π     

 and ( )

3/2

2

torque s 2

s

TA R L a

a 120 2 S

   

= ρ       ρ  

. 
2.7 NOISE 

482 

 Now for a rotor system having two or more blades, you compute the thickness and 

torque sound pressures integrals by selecting from the following pairs: 

( )

( )( )

( )( )

( )

2 2

thickness thickness b 1

22 2

torque torque b 1

2 32 2

thickness thickness b 1

2 2

torque torque

b 2, P 2 P

b 2, P 0.04091M 0.68223 M 0.13392 P

b 3, P 28.9283M 64.5194 M 47.9753M 8.8891 P

b 3, P 0.48787 M 0.12254 M 0.00879 P

=

=

=

= =

= =− + −

= = − +−

== − −

 

 

 

 ( )

( )( )

( )( )

( )( )

2

b 1

2 32 2

thickness thickness b 1

22 2

torque torque b 1

2 32 2

thickness thickness b 1

to

b 4, P 46.3691M 113.5021M 92.2180 M 20.8876 P

b 4, P 0.70555 M 0.55217 M 0.11572 P

b 5, P 6.3916 M 52.8966 M 69.3612 M 20.0193 P

b 5, P

=

=

=

=

= = − +−

== − +

= = − +−

=



 

 

 

( )( )

( )( )

( )( )

2 2 2

rque torque b 1

2 3 2 2

thickness thickness b 1

2 32 2

torque torque b 1

2

thickness

0.72823 M 0.69278 M 0.17031 P

b 6, P 117.8000 M 178.9898M 67.2027 M 5.2442 P

b 6, P 0.99622 M 1.25498 M 0.53448 M 0.07624 P

b 7, P 299.7

=

=

=

= −+

= =− + − +

== − + −

= =−

 

 

 

 ( )( )

( )( )

( )( )

3 2 2

thickness b 1

2 32 2

torque torque b 1

2 32 2

thickness thickness b 1

2

torque

618M 537.7901M 294.5375M 51.4713 P

b 7, P 1.28199 M 1.90795 M 0.96434 M 0.016495 P

b 8, P 477.9969 M 905.6624 M 538.8664 M 103.6451 P

b 8, P 1

=

=

=

+ −+

== − + −

= =− + − +

= =



 

 

 ( )( ) 3 2 2

torque b 1

.38764 M 2.21825 M 1.19569 M 0.21679 P =− +− 

Once the blade number configuration is selected, the calculation of overall sound pressure 

level is quite simple because 

(2.323) 2 2

b 10 thickness torque 2 b

ref

1 OSPL 10log P P

p

 

= +           . 
2.7 NOISE 

483 

 Let me give you an example using the YHO-2HU configuration described in 

Table 2-38. The primary variables are Mach number (M = Mtip = 0.53 because θobs = 0) and 

blade number (b = 3). Calculating the sound pressure for one blade at a tip Mach number of 

0.53 using Eq. (2.322) gives 

(2.324) ( ) [] [ ] 2 2 2 2

t thickness torque 0

1 Blade 1 p d K 71.115 L 2584.007 2

π

ψ = +

π  . 

Then the correction factor for blade number is applied using the b = 3 set on page 482 

evaluated at a Mach number of 0.53. Thus, 

(2.325) [ ]( ) [ ]( ) 22 2 2

thickness torque thickness torque b 3

2 2

thickness torque

P P K 71.115 2.721 L 2584.007 0.063306

193.5K 163.6L

=

  += +  

= +

  . 

Given that in this example 

(2.326) ( )

2

f

2

thickness s

c t S

R c K a 0.00244658

240 S R

             = ρ   =   π    

, and 

(2.327) ( ) ( )

3/2

2

torque s 2

s

TA 1 L a 0.0019051

a 120 2 S R

   

= ρ     =

  ρ  

you then have 

(2.328) ( ) b 3 10 [ ] 2 b 3

1 OSPL 10log 0.0011583 0.0005946 66.42decibels

0.00002 = =

    = +   =

   

and, therefore, the overall sound pressure level is 66.42 decibels. 

 There are, of course, many other approaches to extend Gopalan’s work and gain more 

insight to hovering rotor noise. I chose the preceding approach after spending considerable 

time in omphaloskepsis.

2.7.5.3 Insight Gained From Gopalan’s Work 

 When you look closer at Eqs. (2.325) through (2.328), you can see that the ratio of 

observer distance (S) to rotor radius (R) is common to both Kthickness and Ltorque. You will also 

note that the atmospheric condition ( 2

s ρa ) is common and so is the reference sound pressure 

(pref). This suggests that the overall sound-pressure-level equation can be rewritten to take a 

somewhat different form. Therefore, let me suggest the following: 
2.7 NOISE 

484 

(2.329) 

( )

( ) ( )

2 3/2 2

2 2

s b,M b,M

b 10 2 f 22 2 2

ref s

1 c t TA a f g OSPL 10log S

S R p R c 240 a 2 120

          ρ         = +                       πρ ×            

. 

This form illuminates an observer position parameter (S/R) and an atmospheric condition, and 

leaves the rotor itself as a constant, for a given tip Mach number, within the brackets. 

Furthermore, logarithmic properties of products and powers can be employed. For instance, 

the effect of distance for a given blade configuration and disc loading (T/A) shows you that 

overall sound pressure level should vary inversely, with distance squared, from the noise 

source. Said another way, OSPL should decrease as the log10 (S/R) increases. That is, 

(2.330) ( ) b 10 10 { } 10 ( ) 2

Constant OSPL 10log 10log Constant 20log S R

S R

    = =−      

. 

The constant, as you have noted, is 

(2.331) ( ) ( )

2 3/2 2 2 2

s b,M b,M

f 22 2 2

ref s

a c t TA f g Constant S

p R c 240 a 2 120

     ρ           = +                            πρ ×    

. 

 Now, referring back to Fig. 2-314 on page 467, you can see that OSPL does decrease 

with increasing distance from the helicopter. However, the comparisons between helicopters 

should be analyzed in terms of distance divided by radius. This insight suggests a revision of 

the horizontal axis of Fig. 2-314 to a semi-log scale, using (S/R) as the scaling parameter. You 

see the result of this rescaling and using a semi-log abscissa with Fig. 2-323. 

 There are a number of observations to be made about Fig. 2-323. First off, using 

Eq. (2.330), I have superimposed four heavy lines on top of the helicopter data to help in this 

discussion. You can immediately see at the top that the loudest machine is the Hiller YH-42 

rotor that was tip-driven by ramjets and has, apparently, a constant of 2,000×1010. The noise 

of the YH-42 clearly diminishes with distance as Eq. (2.330) prescribes. Scanning down 

Fig. 2-323, it appears that all the other helicopters (including the Djinn with its cold cycle tip 

drive) fall within a band where the constant in Eq. (2.330) is between 10×1010 and 100×1010. 

Two of the helicopters had noise data obtained while operating at ground idle, and the 

associated constant is about 1×1010. It appears that going from ground idle to hover raises the 

noise level by 10 decibels for both the YUH-1D (48 ft) and the S-62A. 

 Next, when you follow the constant’s magnitude up the OSPL scale at S/R = 10, you 

should note that a factor of ten in the constant equals just 10 decibels. This is the behavior of 

the logarithm. More importantly, it means that achieving a noticeable noise reduction requires 

substantial changes to the current fleet, which I will discuss shortly.158 

 

158 I am sorry to say that not all flight test data leading to Fig. 2-323 was quantified in enough configuration and 

flight condition detail for me to show how accurate Eq. (2.331) might be. However, in the 1970s, the Quiet 

Helicopter Program was completed, and quantified data for the Hughes OH-6A and the Sikorsky S-62A were 

obtained. I will discuss that program and its results later. 
2.7 NOISE 

485 

70

80

90

100

110

120

130

1 10 100

YOH-2HU

OH-6A

YUH-1D (44 feet)

YUH-1D (48 ft) Ground Idle

YUH-1D (48 ft) Full Power

S-62A Ground idle

S-62A

SH-3A

YH-42 Ramjet

Djinn Cold Cycle

Overall

Sound

Pressure

Level

(OSPL)

(dB)

S/R

Eq. 2.240, Constant = 1×1010

Eq. 2.240, Constant = 2,000×1010

Constant = 100×1010

Constant = 10×1010

Fig. 2-323. Comparison of noise signatures from several helicopters hovering 

in ground effect. 

 There is one very important last point that has to do with the reflections of sound 

waves off the ground and other nearby surfaces. The experimental data shown in Fig. 2-323 is 

for helicopters hovering in ground effect or at ground idle. Therefore, parts of the sound 

waves emanating from the helicopter reflect off the ground. According to Hicks and Hubbard 

[532], “In general ground reflection causes a doubling of the sound intensities at the ground 

level.” This means that the pressure squared as given by Eq. (2.329) should be multiplied by 

4. That is to say, if reflected waves are a factor, then the term 1/(S/R)2

 in Eq. (2.329) should 

be increased to 4/(S/R)2

. This is the equivalent of adding 6 decibels to a solution with no 

reflection (i.e., 10 log10 4 = 6). 

 The difficulties presented by ground reflection were brought to the industry’s attention 

again in 1973 as part of the Quiet Helicopter Program. Testing of a standard and modified 

Sikorsky SH-3A included noise measurements at four hovering heights. Bob Pegg and his 

coauthors [516] included one figure illustrating how the frequency content of the sound 

pressure level in decibels varied with frequency. I have included their figure here as 

Fig. 2-324. In their report they noted that 

“narrow-band frequency analyses (4-Hz bandwidth) from both the standard and modified 

helicopters were made from data taken while the helicopters were hovering at four heights. 

All of the narrow-band frequency data for both modified and standard aircraft showed 

evidence of a ground-plane-reflection effect. This effect became more severe with increasing 
2.7 NOISE 

486 

hover height. A typical example of ground reflection or image interference is shown in figure 

17. In this figure the increasing effects of cancellation and re-enforcement are evident in the 

narrow-band spectra in the form of peaks and valleys in the noise levels. This effect makes 

analysis of hovering data at altitude extremely difficult.” 

Fig. 2-324. SH-3A noise signatures in hover at several altitudes [516]. 
2.7 NOISE 

487 

 Although Fig. 2-324 is of poor quality, it is only at the lowest hovering altitude of 3.1 

meters that the individual harmonics of the rotor noise are clearly seen. Pegg and his 

coauthors used the data at the lowest altitude to identify the first 11 harmonic peaks of the 

main rotor and the first 2 noise peaks due to the tail rotor. I have included their detailed 

analysis here as Fig. 2-325 to illustrate how difficult it can be to find these noise source 

harmonics from hovering measurements made when ground reflections are a factor. You 

should note that the largest noise harmonic is from the tail rotor. 

Fig. 2-325. SH-3A noise signatures in hover at 3.1 meters altitude [516]. 
2.7 NOISE 

488 

2.7.5.4 Test Versus Rotational Noise Theory (Only) Using In-Ground-Effect Data 

 Now you have some test data from several helicopters in front of you (i.e., Fig. 2-323), 

and you have an introductory method of calculating main-rotor rotational noise alone due to 

thickness and torque. The natural question is, “How close does this main rotor alone noise 

theory come in predicting the total helicopter noise?” The answer is shown in Fig. 2-326. 

 Your immediate reaction to this correlation of test and theory provided by Fig. 2-326 

may well be one of disappointment, but when you look closer, you can see that the basic 

pattern for each data set is that each set lies nearly parallel to the line of perfect correlation. 

The implication of this observation is that each helicopter can be described mathematically 

with a simple constant (K) times the main-rotor-alone sound pressure. That is, following 

Eq. (2.329), assume that the total helicopter noise behaves as 

(2.332) 

( )

( ) ( )

2 3/2 2

2 2

s b,M b,M

b 10 f 2 22 2 2

ref s

K c t TA a f g OSPL 10log S

S R p R c 240 a 2 120

          ρ         = +                       πρ ×            

from which it follows from the logarithm of a product that 

(2.333) ( )

( ) ( )

{ }

2 3/2 2 2 2

s b,M b,M

b 10 f 2 22 2 2

ref s

10

1 c t TA a f g OSPL 10log S

S R p R c 240 a 2 120

10log K

          ρ         = +                       πρ ×            

+

. 

Therefore, each helicopter’s overall sound pressure level in decibels equals its main rotor 

noise (i.e., K = 1) plus some additional decibels due to a multitude of possible sound pressure 

sources. On this basis, you can see that the OSPL of the YUH-1D, with a 48-foot-diameter 

rotor, appears to be well predicted based solely on its main-rotor-alone rotational noise. That 

is, K = 1, in which case 10log10(K = 1) equals zero. At the other extreme, the YH-43 with its 

ramjet tip drive will show virtually exact correlation if K = 3,694! That is, 10log10(K = 3,694) 

= 35.6 dB. Thus, the red, open diamonds for the YH-43 move to the right on the abscissa by 

35.6 decibels, which puts the YH-43 right on the perfect correlation, green dashed line. 

 Let me draw your attention to the Hughes OH-6A shown with the blue open diamonds 

in Fig. 2-326. This helicopter’s data can be translated to the right by 15.5 decibels to achieve 

near perfect correlation. This corresponds to K = 37. According to Hicks and Hubbard [532] 

as discussed previously, ground reflection might easily double the sound pressure. This 

suggests that 6 decibels of the 15.5 decibels could be just ground reflection, and therefore 

other helicopter components might only contribute about 10 decibels. I raise this conjecture 

because during the Quiet Helicopter Program, the OH-6A was rather thoroughly examined for 

individual component noise contributors. I will discuss this aspect of the program shortly. 
2.7 NOISE 

489 

0

20

40

60

80

100

120

140

0 20 40 60 80 100 120 140

YHO-2HU

OH-6A

YUH-1D (44) Tethered at 5 ft, full power, T = 8,700 lbs

YUH-1D (48) 5 ft Hover @ W = 6,600 lbs

YUH-1D (48) Idle @ RPM = 70% , T = 0

S-62A Hover

S-62A Idle @ RPM = 70% , T = 0

SH-3A (5 ft)

YH-43 Ramjet

Djinn (Cold Cycle)

Test

Overall

Sound

Pressure

Level

(OSPL)

(db)

Main Rotor Alone Predicted OSPL (db)

Fig. 2-326. Test versus rotational noise theory (only) for helicopters hovering 

in ground effect. 

 The message from this correlation example is quite clear. The main rotor is a major 

contributor to noise emanating from a hovering helicopter. After all, for the turbine-powered 

machines such as the OH-6A, the S-62A, and the SH-3A examples, about 80 decibels out of 

100 can be attributed to the main rotor. It appears that in some cases such as the YUH-1D, the 

very simple theory provided by Gopalan may capture the whole noise signature for a 

helicopter hovering in ground effect. Of course, all the other assemblies of the machine 

(i.e., tail rotor, engine, gear boxes, engine exhaust pipe, airframe, generators, hydraulic 

pumps, auxiliary power supply, etc.) must remain as possible contributors to the noise 

signature until proven to be inconsequential by experiment or at least some predictive theory. 

2.7.5.5 UH-60 Noise Sensitivity Trade Study 

 Let me now examine how sensitive OSPL is to the first-order configuration parameters 

that Gopalan established. As a baseline, consider the main rotor of a U.S. Army UH-60A, 

more commonly known as the Black Hawk. This helicopter has a four-bladed, 53.67-footdiameter rotor. The rotor turns at 258 rpm, which gives a tip Mach number of 0.65 at sea level 

on a standard day. The rotor solidity is 0.0826, which translates to a blade chord-to-radius 

ratio (c/R) of 0.06487. The nominal airfoil thickness-to-chord ratio (t/c) is 0.10, and I have 

assumed the airfoil shape parameter (Sf) to be 0.685. At a rotor thrust of 23,400 pounds, the 
2.7 NOISE 

490 

disc loading (T/A) for this baseline example is 10.34 pounds per square foot. Because 

2

s ρa equals 2,964 pounds per square foot, it follows that 2 T/A aρ s equals 0.00349. I will 

assume that noise is to be measured at an observer distance of about 200 feet, which means 

(S/R) is on the order of 7.5. I will also assume that the UH-60 is hovering out of ground effect 

(say at a height of 100 feet) and that you, the observer, are in a 100-foot tower. This means 

you are in the rotor plane and that there is (presumably) little noise reflected from the ground. 

 Given this UH-60 input, let me now follow the calculations made for the YHO-2HU 

example. Calculating the sound pressure for one blade at a tip Mach number of 0.65 using 

Eq. (2.322) gives 

(2.334) ( ) [][ ] 2 22 2

t thickness torque 0

1 Blade 1 p d K 753.349 L 3230.101 2

π

ψ = +

π  . 

Then the correction factor for blade number is applied using the b = 4 set on page 482 

evaluated at a Mach number of 0.65. Thus, 

(2.335) [ ]( ) [ ]( ) 22 2 2

thickness torque thickness torque b 3

2 2

thickness torque

P P K 753.349 0.0394 L 3230.101 1.708

193.5K 163.6L

=

  + = +  

= +

  . 

For the UH-60 

(2.336) ( )

2

f

2

thickness s

c t S

R c K a 0.00723174

240 S R

             = ρ   =   π    

 and 

(2.337) ( ) ( )

3/2

2

torque s 2

s

TA 1 L a 0.0229791

a 120 2 S R

   

= ρ     =

  ρ  

, 

and so you have 

(2.338) ( ) b 4 10 [ ] 2 b 4

1 OSPL 10log 0.15104 0.09378 87.87decibels

0.00002 = =

    = +   =

   

. 

Note here that the relative contributions of torque loading pressure and thickness pressure are 

in the ratio of 0.09378 to 0.15104, or about 0.62. This dominance of thickness pressure over 

the inplane loading pressure is only slightly greater than what you saw for the YHO-2HU. It 

appears that the current helicopter fleet, worldwide, shares this characteristic. 

 It is helpful to see the total pressure waveform and its components, so I have included 

this data on Fig. 2-327. Here you can see that the large negative spikes due to thickness noise 

are quite dominant. When you compare this UH-60 result to the YHO-2HU result shown in 

Fig. 2-319 and Fig. 2-320, you might conclude, as I have, that helicopter noise reduction must 

first deal with thickness contributions before there is a high payoff for reducing what is 

commonly called rotational noise created by thrust and torque. 
2.7 NOISE 

491 

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0 30 60 90 120 150 180 210 240 270 300 330 360

Thickness + Loading Thickness Torque Loading

UH-60

Acoustic

Sound

Pressure 

(pascals) Observer 

"Time" 

(deg)

Fig. 2-327. UH-60 noise contributions to sound pressure at the baseline condition. 

 The overall sound pressure level is 87.87 decibels for this UH-60 example, which is 

some 20 decibels louder than the small, piston-powered YHO-2HU helicopter—at equal 

observer to helicopter distance of 200 feet. But do not be completely fooled. The YHO-2HU 

example was calculated at a distance-to-radius ratio of S/R = 16, and this UH-60 calculation 

was made at S/R = 7.5. When this UH-60 estimate is made at S/R = 16, the OSPL becomes 

81.3 decibels. Another way to look at it is this: the UH-60 would sound about like the 

YHO-2HU (at an observer distance of 200 feet) if the observer was about 2,400 feet away 

from the UH-60 at an S/R of 90. 

 It is clear that helicopter noise disappears with distance. A more pertinent question is 

what changes to the UH-60 (or YHO-2HU for that matter) could be made to lower its noise in 

hover. One change that is immediately available is to lower the rotor tip speed. High tip 

speeds were known to create noise ever since the invention of the propeller. Consider this 

analytical experiment. Suppose that the pilot of a UH-60 reduces rotor RPM while 

maintaining a steady hover 100 feet above the ground at a main rotor thrust of 23,400 pounds. 

Of course, he must increase collective pitch and probably over-torque the transmission and 

possibly over-temp an engine to do this, but assume that no restrictions are imposed during 

this experiment. Naturally, the rotor CT/σ will increase, but starting from a CT/σ of 0.10 at the 

normal 258 rpm, the rotor speed might be decreased to, say, 182 rpm (i.e., 70 percent of 

normal) before the rotor reaches a CT/σ of 0.2. That would be, I suggest, on the ragged edge 

of complete blade stall in hover. Accepting this scenario, the results of this trade study are 
2.7 NOISE 

492 

shown in Fig. 2-328, which suggests that noise would drop from 87.87 decibels to 

76.9 decibels. The sensitivity to Mach number amounts to 7.6 decibels per 0.1 M as the red 

dashed line on Fig. 2-328 shows. You can get a quick feel for the sensitivity to a change in tip 

Mach number by using the red dashed line, which behaves as 

(2.339) 

n

10 10

182rpm 182 OSPL 10log 10n log 10n ( 0.152) 258rpm 258

          Δ =      = =−            

. 

The overall sound pressure level drops from 87.87 decibels at 258 rpm (i.e., M = 0.65) to 

about 75 decibels at 182 rpm. This is a change in OSPL of roughly –13 decibels so (n) in 

Eq. (2.339) becomes about 8.6. The conservative rule of thumb, lacking a more detail 

calculation, is to use n = 6. 

 The UH-60 might be changed more extensively by increasing the number of blades 

while holding the rotor solidity (σ = bc/πR) constant at 0.0826 and the rotor thrust constant at 

23,400 pounds. By keeping rotor speed at 258 rpm, the CT/σ would remain at 0.10, which 

would at least satisfy the aerodynamic community (but probably not those interested in the 

selling price or weight empty of the redesigned machine). Still, the noise would be reduced as 

Fig. 2-329 shows. I would suggest that rotor blade aspect ratios (R/c) approaching 23 would 

70

75

80

85

90

95

100

105

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85

Tip Mach Number

Overall

Sound

Pressure

Level 

(db)

Note: Reference Pressure = 0.00002 pascals

UH-60 

Baseline

CT/σ = 0.2

CT/σ = 0.15

CT/σ = 0.075

CT/σ = 0.1 ΔOSPL/ΔM = 7.6 db per 0.1 M

Fig. 2-328. UH-60 noise reduction with reduced tip speed at a constant rotor thrust of 

23,400 pounds at sea level on a standard day. 
2.7 NOISE 

493 

present a serious challenge to rotor blade designers and aeromechanic engineers because of 

blade torsional deflections and even unsolvable instabilities. Remember that rotor blades are 

really flying wings with control at just one wing tip. 

 You might consider keeping the four-bladed rotor system as is but redesigning the 

blades with very thin airfoils. This approach would address thickness noise in an effort to 

make Kthickness smaller as Eq. (2.336) suggests. The results of this approach are shown in 

Fig. 2-330. It is interesting to note here that with a zero-thickness-ratio airfoil, only the noise 

due to torque is left, and this amounts to about 84 decibels. The meaning here is clear; if the 

thickness noise is greater than the torque noise contribution, then making Ltorque smaller with a 

reduction in disk loading will not appreciably reduce noise. 

 To emphasize this last point, consider the impact of halving the rotor thrust at several 

levels of thickness noise. You see the effect from the green line on Fig. 2-330. I bring this 

point to your attention because the noise solution that Gopalan provided is very interactive in 

the weighting between thickness and torque contributions. Clearly, thickness noise can mask 

rotational noise reductions. It is not until the thickness noise is relatively quite small that a 

simple change in thrust is perceptible. You might have guessed this from Fig. 2-319, 

Fig. 2-320, and Fig. 2-321. 

70

75

80

85

90

95

100

105

123456789

Number of Blades

Overall

Sound

Pressure

Level 

(db)

Note: Reference Pressure = 0.00002 pascals

UH-60 

Baseline

ΔOSPL/Δb = - 3.2 db per blade

Blade Aspect 

Ratio = 7.7 

Blade Aspect 

Ratio = 30.8 

Blade Aspect 

Ratio = 23.1 Blade Aspect 

Ratio = 15.4 

Fig. 2-329. UH-60 noise reduction with increased blade number at constant solidity, tip 

Mach number, and constant rotor thrust of 23,400 pounds at sea level on a 

standard day. 
2.7 NOISE 

494 

70

75

80

85

90

95

100

105

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

Overall

Sound

Pressure

Level 

(db)

Airfoil Thickness Ratio (t/c)

UH-60 

Baseline

Note: Reference Pressure = 0.00002 pascals

ΔOSPL/Δ(t/c) = 1 db per 0.02 t/c

Rotor Thrust = 23,400 lbs

Rotor Thrust = 11,700 lbs

Fig. 2-330. UH-60 noise reduction with decreasing airfoil thickness ratio alone for two 

main rotor thrusts. Thickness noise is zero when t/c is zero. 

2.7.5.6 Thickness and Torque Noise From a Real UH-60 Rotor 

 Using the ideal rotor in the preceding UH-60 example should, I hope, please helicopter 

performance engineers. After all, that has been their goal (perhaps dream would be a better 

word) for decades. However, practically speaking, the majority of helicopter main rotors that 

are flying have simple linear twist and rectangular blades. Tail rotors for the single-main-rotor 

machines are even further from ideal because they generally have zero twist and rectangular 

blades. For other than the ideal rotor, which you will recall has a twist distribution of 

θx = θtip/x, the nice closed-form equations for the torque and thrust sound pressure comparable 

to what Gopalan obtained for the ideal rotor have yet to be published. As a result, I will begin 

one step back from the integrated equations Gopalan gave to recalculate the sound pressure of 

the UH-60 main rotor taking account of its production blade geometry. 

 Geometric twist does not change the thickness sound pressure—at least within the first 

order of magnitude being addressed in this introduction—but the rotational noise charged to 

torque and thrust sound pressure is influential. To illustrate just how large this influence might 

be, consider just the torque sound pressure calculation. This sound pressure is obtained from 

the more fundamental, pre-integrated equation Gopalan gave. I have rearranged his result 

slightly to read 
2.7 NOISE 

495 

(2.340) ( )

( )

1

tip

torque 3

0 per blade

M dD cos

p dx 4 S dr 1 M x sin

     ψ−φ  =    

π       − ψ−φ   





 . 

It is from this equation that Gopalan obtained the closed form integrations for the ideal rotor. 

He was able to do this for the ideal rotor because the blade element inplane drag (dD/dr) is 

constant and can be taken outside the integral. If you work in English units as I do, then for 

Eq. (2.340) the rotor speed (Ω) is in radians per second, the speed of sound (as) is in feet per 

second, and the distance between observer and the rotor hub (S) is in feet. You will have to 

divide the final result by 0.02088 to convert from pounds per square foot to pascals. The 

complexity of Eq. (2.340) increases because the phase angle (φ) must be included. This angle 

accounts for the Doppler effect and is found from 

(2.341) ( )

( )

1 x cos

M

1 M xsin

  − ψ φ=−     − ψ . 

 Suppose now that the blade element drag (dD/dr) in pounds per foot is not constant for 

the blade under consideration. Then a more complicated representation must remain a part of 

the integrand. The immediate task is to define blade element drag. To obtain a calculated 

distribution of blade element thrust and drag, I turned to Wayne Johnson who used his 

CAMRAD II comprehensive program to produce Fig. 2-331. My intention here is to calculate 

the torque noise with a real blade element drag distribution and compare the results to the 

ideal UH-60 case that you have just finished reading. 

0

10

20

30

40

50

60

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

100

200

300

400

500

600

Blade 

Element 

Drag 

(lbs/ft)

Blade 

Element 

Thrust 

(lbs/ft)

Total drag Thrust

Blade Radius Station (x = r/R)

Induced 

drag

Ideal drag

Fig. 2-331. UH-60 blade element forces (23,400-lb thrust, 258 rpm, sea level, 

standard day). 
2.7 NOISE 

496 

 It is worth a moment to calculated the ideal blade element drag per foot to provide a 

comparison to the CAMRAD result shown in Fig. 2-331. Assuming small angles, 

(2.341) ( ) ( )

3/2

ideal 2 3

per blade per blade

dD v dT 1 v 4 4 T 4 rv v

dr r dr b r b b 2 A

     πρ πρ  

= =π   ρ= =         Ω Ω ΩΩ      ρ . 

The blade element thrust (dT/bdr) given by momentum theory is rotated through the blade 

element induced velocity angle (v/Ωr) to create an induced blade element drag (dD/dr). For 

this UH-60 example, the rotor thrust is 23,400 pounds at sea-level standard. This is a disc 

loading (T/A) of 10.345 pound per square foot. The rotor speed, 258 rpm, corresponds to 

Ω = 27.04 radians per second. Therefore, the ideal induced blade element drag is slightly over 

28 pounds per foot. This drag level is shown as the horizontal line on Fig. 2-331. It is also 

worth comparing the induced velocity distribution along the blade span, which you see in 

Fig. 2-332. 

 To continue then, Fig. 2-333 shows the comparison of the inplane torque loading 

pressure when the blade element drag distribution is a constant (i.e., ideal) and when the drag 

distribution reflects a comprehensive code (i.e., CAMRAD II) best estimate. The small 

change in loading pressure due to a practical, twisted blade has virtually no effect on the noise 

because the thickness noise is so dominant. The calculated OSPL for the UH-60, assuming an 

ideal blade element drag distribution, is 87.87 decibels; for what I would call a production 

blade, the OSPL is 88.34 decibels! 

0

10

20

30

40

50

60

70

80

90

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Blade Radius Station (x = r/R)

Induced 

Velocity 

(ft/sec) Ideal induced velocity

CAMRAD II

Fig. 2-332. Induced velocity at UH-60 blade elements (23,400-lb thrust, 258 rpm, 

sea level, standard day). 
2.7 NOISE 

497 

 That is not quite the whole story though. The blade elements of a real rotor have both 

pressure drag and skin friction drag.159 However, my few UH-60 calculations of inplane 

torque pressure, and then the overall sound pressure level, showed that the UH-60 OSPL 

would increase to only about 89 decibels when the total blade element drag distribution shown 

in Fig. 2-331 is used in the calculation. 

 In closing this discussion of how to get 90 percent of the right estimate of rotor 

rotational noise in 10 percent of the time, I have come to the conclusion that helicopter mainrotor noise broadcasted radially to an observer nearly in the main rotor plane is dominated by 

thickness sound pressure. It appears that for many of today’s helicopters, thickness sound 

pressure is so dominant that loading sound pressure is a minor factor. Thus, rotor blade 

parameters of radial chord and airfoil distributions offer the greater potential for helicopter 

noise reduction—at least noise created by nearly inplane sound pressure. Unfortunately, I 

have only touched briefly on noise that reaches an observer when the helicopter is hovering 

well above the observer. Still, when you look back at Fig. 2-303, you can see that blade 

planform, number of blades, and tip Mach number are worth several more rotary wing 

experiments. Of course, cost, maintenance, weight, and performance trade-offs must be made 

before a significant departure from what is flying can be sold to the industry. 

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0 30 60 90 120 150 180 210 240 270 300 330 360

Torque Loading, Ideal

Torque Loading CAMRAD, Ideal dD/dr Distribution Only

UH-60

Acoustic

Sound

Pressure 

(pascals)

Observer 

"Time" 

(deg)

Fig. 2-333. Differences between ideal and realistic blade element drag distributions do 

not appear to be a major factor in inplane loading sound pressure. 

 

159 In discussing this skin friction aspect of noise with Ken Brentner in mid-January of 2012, he pointed out that 

skin friction does add noise, but it is generally neglected because it is small. 
2.7 NOISE 

498 

2.7.6 The Quiet Helicopter Program 

 “The high noise level of the present-day helicopter reduces its tactical effectiveness. 

The element of surprise made possible by the mobility of helicopter-supported operations is 

negated to a large extent by early aural detection. The possibility of a helicopter-quieting 

program was the subject of a May 1968 meeting at the Institute for Defense Analyses in 

Washington, D. C. As a result of this meeting, a research and development program was 

initiated by the Advanced Research Projects Agency under the direction of Dr. C. J. Wang 

and technically administered by Mr. R. C. Dumond, Eustis Directorate, USAAMRDL. 

 In 1969, three helicopters – the Sikorsky SH-3A, Kaman HH-43B, and Hughes OH6A – were modified for low-noise operation. The NASA Langley Acoustics Branch 

conducted acoustics measurements of the noise characteristics of the three helicopters. The 

OH-6A achieved the greatest overall noise reduction of the three helicopters tested. 

 The approach for the Phase I program was to concentrate on quieting the major noise 

producer in the OH-6A helicopter – the tail rotor. By incorporating a four-bladed tail rotor (in 

lieu of a two-blader) and a low-speed tail rotor gearbox, the aircraft was safely operated at 

70 percent N2 with minimum gross weight (1450 pounds nominal), thus attaining overall 

sound pressure level reduction of 11 decibels in hover and 11.5 decibels in forward flight. 

This achievement represents a sound pressure decrease of approximately 73 percent. 

 In April 1970, a contract was awarded for a Phase II program to obtain a maximum 

reduction of the sound pressure level (SPL) of all noise sources on the OH-6A helicopter. 

Descriptions of the modifications, the test programs, and the results obtained are included in 

this report.” 

 The above quotation was the introduction that began a report by William Barlow and 

his coauthors concerning the OH-6 Phase II Quiet Helicopter Program [548]. This report came 

out in September of 1972. About a year later, the NASA Langley Acoustic Branch released 

unclassified noise measurement data for the Sikorsky SH-3A [516] and the Hughes OH-6A 

[514]. A report of the Kaman HH-43B results was released with a NASA Confidential 

restriction in February of 1971 [549]. The SH-3A and OH-6A reports were declassified by the 

end of 1973, but for some reason the HH-43B report still remains classified—perhaps because 

the modified configuration showed very little noise reduction and/or no request for 

declassification has been made. All three reports note that the activity was a joint project of 

the Eustis Directorate, U.S. Army Air Mobility Research and Development Laboratory 

(USAAMRDL), the Advanced Research Projects Agency (established in 1958; became 

DARPA in 1972 with the addition of the D), and the NASA Langley Research Center. 

 In the initial selection process, ARPA wanted a Bell UH-1 helicopter based on Bell’s 

milestone work reported in 1962 [546], but with the production requirements for the Vietnam 

War, Bell could not be responsive to the desired schedule. This led to the inclusion of the 

Hughes OH-6A modified helicopter. It is the Hughes OH-6A modifications to the standard 

machine, and the results obtained, that I want to convey in this discussion of the Quiet 

Helicopter Program. The primary emphasis of this discussion is on hover. 
2.7 NOISE 

499 

 But first I should mention that a limited edition of the highly modified OH-6A allowed 

a very covert, secret mission to be conducted on December 5 and 6, 1972. The story came to 

light when James Chiles published an article in the Smithsonian Air & Space Magazine dated 

March 1, 1980 [550], which you can read on the Internet. The limited edition OH-6A became 

known as the Hughes 500P and carried the name “The Quiet One.” What I found interesting 

was that Barlow’s report [548] contains not only the highly modified configuration 

description, but also the equivalent of a mini-flight program suited to a flight safety release. 

The mini-flight program was conducted from April 1970 to April 1971, and apparently testing 

was also conducted at the now well-known Area 51. Chiles reports that “Hughes shipped two 

500P helicopters to Taiwan in October 1971 and flight training was completed in June 1972.” 

And then Air America and the CIA really went to town. Chiles’ article really is quite 

interesting and well worth your reading time. 

 While all this Black program was going on, Hughes was carrying out its basic Quiet 

Helicopter Program. They provided a standard OH-6A and three modified configurations as 

reported in the NASA unclassified reported [514] authored by Henderson, Pegg, and Hilton. 

A summary of the modifications tested in 1969 as part of the Phase I program, and another, 

more highly modified configuration that arrived during Phase II and was tested in 1971, are 

shown in Table 2-39 below, which I have reproduced directly from Henderson’s report. 

Table 2-39. Three Modifications to the Standard OH-6A Were Tested by NASA Langley 

in Two Phases of the Hughes Quiet Helicopter Program [514] 
2.7 NOISE 

500 

 The preliminary work that the Hughes team accomplished during Phase I of the 

program identified the usual culprits associated with helicopter noise. These culprits are the 

tail and main rotors, which demand a much slower tip speed than that found when minimum 

weight empty is the performance objective. The Phase I program leading to the 1969 

modifications was limited to those that could easily be made to a standard helicopter. One tail 

rotor issue that was settled was that at equal solidity (σ = 0.24) and tip speed (Vt = 363 fps), 

four narrow-chord blades (Fig. 2-335) were quieter than two wide-chord blades (Fig. 2-336). 

Furthermore, scissoring the four-bladed tail rotor to a 60-degree acute angle rather than the 

common 90-degree orthogonal arrangement offered a measurable improvement. There was no 

question that the reduced rotor speeds were required to achieve the lower noise signature. 

Henderson and his coauthors concluded that 

“a field noise measurement program has been conducted on a standard OH-6A helicopter 

[Fig. 2-334] and two OH-6A helicopters modified to reduce the external noise levels. The 

purpose of this study was to document the noise characteristics of each helicopter during 

flyover, hover, landing, and take-off operations. The 1969 modifications were limited to those 

which could easily be made to a standard helicopter. The 1971 modifications consisted of 

extensive modifications of an OH-6A helicopter to have low external noise characteristics. 

Based on the analysis of the measured results, the average noise levels associated with the 

final modified helicopter (configuration E) are 14 dB lower than the standard helicopter 

(configuration D) while operating at an altitude of 30 meters with an airspeed of 70 knots in 

level flight. 

Narrow-band spectra data of the hovering helicopters show that there was a general reduction 

of harmonic content with the modified aircraft. Noise reductions at frequencies below 80 Hz 

are associated with main rotor modifications, those between 80 Hz and 630 Hz with tail rotor 

modifications, and those above about 630 Hz with engine and gearing modifications.” 

What I found rather interesting about these conclusions is that comparative OSPL data from 

the 1969 results were not even mentioned in the conclusions. It is as if enthusiasm was 

brimming over to get to the next step, which was Configuration E shown in Fig. 2-337. 

Fig. 2-334. Standard Hughes OH-6A. Configurations A and D (courtesy of Bill 

Warmbrodt and NASA Langley Research Center). 
2.7 NOISE 

501 

Fig. 2-335. Configuration B modification to the OH-6A. Four-bladed, scissor-tail rotor 

(courtesy of Bill Warmbrodt and NASA Langley Research Center). 

Fig. 2-336. Configuration C modification to the OH-6A. Two-bladed, wide-chord tail 

rotor (courtesy of Bill Warmbrodt and NASA Langley Research Center). 

Fig. 2-337. Configuration E modification to the OH-6A, which was called The Quiet One 

and later identified as the Hughes Model 500P. The “P” stood for Penetrator 

(courtesy of Bill Warmbrodt and NASA Langley Research Center). 
2.7 NOISE 

502 

 I have chosen just one chart from Henderson’s report [514] to summarized the noise 

signature from the OH-6A and its several modified configurations. As you can see from 

Fig. 2-338, detection time is reduced considerably. Think of it this way: if a standard OH-6A 

is first heard at –20 seconds, then a person would hear the machine (traveling at 40 knots or 

67.5 feet per second) when it is about 1,400 feet away—about a quarter of a mile. In contrast, 

The Quiet One (configuration E) becomes audible (assuming the same OSPL level in 

decibels) at about 3 seconds before arrival when it is about 200 feet (or two-thirds of a 

football field) away. It is easy to see why the Hughes Model 500P was selected for the covert 

operation carried out in early December of 1972. 

 To fully appreciate how The Quiet One came about, you would do well to review two 

reports. The first is William Barlow’s report titled OH-6A Phase II Quiet Helicopter Program

[548]. This report’s abstract, with my notes in [ ], is quite informative: 

“This report presents the results of the Phase II Quiet Helicopter Program. A Hughes OH-6A 

Light Observation Helicopter (LOH) was extensively modified to obtain a maximum of 

quieting. The purpose was to apply the latest known sound-suppression techniques available 

to industry to an actual helicopter and then to measure the results. An acoustic goal was set 

which required a balanced treatment of each noise-producing source throughout the full 

frequency range. Noise reductions ranged from 14 to 20 dB depending on the flight 

conditions. 

Fig. 2-338. The Quiet One (configuration E) offered a dramatic reduction in noise when 

compared to the Standard OH-6A (configuration D). Measurement made as 

helicopter approaches, passes directly overhead, and departs. Flight at 1,600 

pounds, speed of 40 knots, altitude of 100 feet [514]. 
2.7 NOISE 

503 

The report describes the detailed configuration changes, the test and development programs, 

and the final sound level measurements compared to the standard OH-6A. 

The concept involved the adding of main and tail rotor thrust capacity [4 to 5 blades on main 

rotor and 2 to 4 blades on tail rotor] to permit operation at reduced RPM and propulsion 

system quieting to match the overall sound level goals. The additional rotor capacity at full 

RPM permitted a large net gain in payload and forward speed. Two flight modes were 

developed: a very quiet low-RPM mode [0.67 times 645 fps main rotor tip speed and 

1,600 pounds gross weight] and a quiet high-performance mode [0.78 times 645 fps and 

2,400 pounds gross weight]. The pilot changes modes, in a few seconds, by trimming RPM 

in flight.” 

 The natural question to ask is what was the weight-empty penalty paid to achieve this 

very significant reduction in noise signature. In discussing the weight and balance of The 

Quiet One, Barlow reported that 

“the basic weight of the helicopter was increased 192 pounds with the incorporation of the 

quieting features. This represents a 15 percent loss in useful load for the standard OH-6A, 

which has a maximum Army-approved gross weight of 2400 pounds. However, the added 

rotor capability at 100 percent N2 will permit increasing the gross weight to 3150 pounds – a 

payload increase of more than 85 percent. 

The permissible longitudinal center-of-gravity range for the Quiet Helicopter is from 4 inches 

forward to 7 inches aft of the main-rotor centerline (stations 97 to 107). Since most of the 

weight was added aft of the main-rotor centerline, the center of gravity of the aircraft moved 

from station 109 to station 114.9, making it necessary to carry forward ballast when operating 

at 1600 pounds to remain within the aft limit. Ballast is not required, however, when 

operating the aircraft at heavier gross weights with the usual avionics equipment installed in 

the forward areas.” 

The basic weight of the OH-6A is given [117] as 1,145.5 pounds, the primary mission weight 

is 2,163 pounds, an alternate mission weight is 2,400 pounds, and the structural limit is 

2,700 pounds. Barlow states that the modifications to the OH-6A amounted to 192 pounds, of 

which 71 pounds went to engine and engine compartment treatment. Thus, the basic weight 

increased to 1,337 pounds, a 17 percent increase. To offset that penalty, Hughes was prepared 

to increase the maximum takeoff gross weight from 2,400 to 3,150 pounds. You might think 

that was rather aggressive, but keep in mind that Hughes proceeded to grow the Model 500 

series rather quickly to the five-bladed 500 D, which was FAA certified in early December of 

1976 with a weight empty of 1,414 pounds and a maximum gross weight of 3,000 pounds. I 

believe any competent helicopter manufacture could duplicate Hughes’ efforts at quieting 

their products. It only requires management of weight empty and selling price. Clearly the 

technology existed in the early 1970s. 

 The second report to read was written by Frank Robinson and titled Component Noise 

Variables of a Light Observation Helicopter [541]. This NASA-sponsored effort was a ground 

test of an OH-6A and several individual components. In this experiment, first a standard OH6A and then the evolving Quiet One were attached to a test rig as shown in Fig. 2-339. 

Robinson’s report includes only data measured at just the one microphone location shown. 

Some 255 runs were made covering such variables as rotor speed, thrust, engine and engine 
2.7 NOISE 

504 

compartment muffling, and many sub-configurations. Frank Robinson’s report is, in my 

opinion, a gold mine.160

 The test setup included several unique features and components as Robinson points 

out. Four key points I selected for you are: 

“1. At the rear of the [test rig] unit is the dynamometer which can be connected to the 

aircraft's power plant by means of a drive shaft with universal joints at each end. The Allison 

T-63 engine has provisions for driving from either end which allows the dynamometer drive 

shaft to be connected without disturbing the aircraft's regular drive system. The dynamometer 

cooling system consists of three automotive radiators, with electrically driven automotive 

fans, a cooling water reservoir, and an electrically driven circulating pump. The dynamometer 

was able to absorb full engine power. There was, however, a noise frequency recorded which 

corresponded to the RPM of the dynamometer drive shaft. 

2. A separate large tank muffler, or [engine] silencer, was also fabricated and can be seen at 

the extreme right of figure 2. For those test runs requiring the engine to be silenced, this tank 

muffler was connected to the engine exhaust with a long insulated duct, also visible in fig. 2. 

3. When mounted on the test rig, the helicopter could be run with any combination of its 

major components either removed or silenced. The tail rotor could be removed and the engine 

silenced so only the main rotor could be heard. The main rotor could be removed and the 

engine silenced so only the tail rotor could be heard. Both the main and tail rotors could be 

removed with the dynamometer absorbing the power so only the engine could be heard. 

4. The test aircraft was equipped with precision visual instrumentation for reading engine 

torque, tail rotor torque, tail rotor thrust, collective pitch and tail rotor pitch. The aircraft was 

flown in free hover at a 6-foot skid height and a variety of gross weights and rotor speeds to 

obtain calibrated readings. This enabled the pilot to duplicate the various rotor thrust and 

power conditions with the helicopter mounted on the test rig by setting-up the same values for 

collective pitch, etc., as those recorded during free hover.” 

 Now let me show you what I think was the starting point for what led to The Quiet 

One. Following point 4 above, an overall sound pressure level of 87.0 decibels in free hover 

was measured. The aircraft was at a gross weight of 2,400 pounds, the main rotor tip speed 

was 666 feet per second, and the tail rotor tip speed was 692 feet per second. These tip speeds 

correspond to 103 percent of design engine operating speed. When mounted to the test rig at 

the same control settings, the measured OSPL was 88.5 decibels. For reference then, the 

narrow band frequency content of noise for this base case is shown in Fig. 2-340. Note that I 

have added a red line, to the right of which a human is likely to hear the OH-6A. Thus, the 

first noise peak at about 31 Hz—a 4 per rev from the main rotor—should be readily heard. 

 

160 Frank Robinson was not able to interest any of his employers (Cessna, McCulloch, Kaman, Bell, and finally 

Hughes) in his concept for a small, low-cost helicopter, so he resigned from Hughes and in June of 1973 founded 

Robinson Helicopter Company in his Palos Verdes home. The first R22 prototype was built in a tin hangar at the 

nearby Torrance Airport, and in August of 1975, Robinson flew the R22 on its first flight. In 1979, after 3-1/2 

years of testing and technical analysis, the R22 received its FAA Type Certificate. The first R22 was delivered in 

late 1979 and soon became the world’s top selling civil helicopter. His four-seat R44 was FAA certified in late 

1992. His R66, a turbine-powered machine, was certified in October 2010. In June 2010, with FAA certification 

of the R66 eminent, Frank Robinson retired at the age of 80. The company publicly announced his resignation as 

President and Chairman in August 2010. Now that is a story that easily matches those of our pioneers. 
2.7 NOISE 

505 

Fig. 2-339. Tie-down test rig used during OH-6A component noise measurement 

program placed the main rotor plane 14.2 feet above ground level [541]. 

40

45

50

55

60

65

70

75

80

85

90

0 50 100 150 200 250 300 350 400 450 500

Overall 

Sound 

Pressure 

Level 

(db)

Frequency (Hz)

OH-6A in Free Hover

Threshold of 

hearing a single 

tone

Fig. 2-340. Narrow band frequency content of OSPL for the OH-6A in free hover at an 

altitude of 6 feet (gross weight 2,400 lb, 103 percent engine rpm). The helicopter’s 

OSPL was 87.0 decibels [541]. 
2.7 NOISE 

506 

 Now consider the three major components and their individual contribution to the 

OH-6A noise signature that you see in Fig. 2-341, Fig. 2-342, and Fig. 2-343. The testing of 

the engine alone (Fig. 2-341) required the dynamometer to absorb 215 horsepower at 

103 percent N2 because both the main and tail rotors were not installed. No acoustic treatment 

of the engine or the engine compartment was applied at this point, nor was the low-noise 

exhaust pipe installed. This was just the noise of a production Allison T63-A-5A as installed 

in a production OH-6A. Well, that is not quite right because the drivetrain was still operating 

as if the rotors were installed. However, drivetrain noise signatures only became obvious 

above 1,000 hertz as you will see when you read Barlow’s report [548]. 

 The main rotor’s contribution to the OH-6A noise signature (Fig. 2-342) at a thrust of 

2,400 pounds (206 hp) and tip speed of 666 feet per second shows that it was only very 

apparent at the 4 and 8 per revolutions of the main rotor. Beyond that, the engine and tail rotor 

noises are dominant and mask all higher harmonics. Notice the orderly progression of the 

noise spikes at multiples of 1×4/rev, 2×4/rev, 3×4/rev, etc.; this follows fundamental acoustic 

theory. 

 Finally, the tail rotor’s contribution to the OH-6A noise signature (Fig. 2-343) at a 

thrust of 130 pounds (18.9 hp) and 692 feet per second tip speed shows that it was very 

apparent at its fundamental two-bladed frequency and for several multiples of 2/rev, even 

above the 500-hertz range I have chosen to examine in this introduction. 

30

40

50

60

70

80

90

0 50 100 150 200 250 300 350 400 450 500

Overall 

Sound 

Pressure 

Level 

(db)

Frequency (Hz)

OH-6A in free hover

OH-6A on test rig,

Engine alone

Fig. 2-341. Engine-alone frequency content of OSPL for the OH-6A. The OSPL of just 

the engine alone was 83.5 decibels [541]. 
2.7 NOISE 

507 

30

40

50

60

70

80

90

0 50 100 150 200 250 300 350 400 450 500

Overall 

Sound 

Pressure 

Level 

(db)

Frequency (Hz)

OH-6A in free hover

OH-6A on test rig,

Main Rotor Alone

Engine Muffled

Fig. 2-342. Main-rotor-alone frequency content of SPL for the OH-6A. The OSPL of just 

the main rotor alone was 86.0 decibels [541]. 

30

40

50

60

70

80

90

0 50 100 150 200 250 300 350 400 450 500

Overall 

Sound 

Pressure 

Level 

(db)

Frequency (Hz)

OH-6A in free hover

OH-6A on test rig,

Tail Rotor Alone

Engine Muffled

Fig. 2-343. Tail-rotor-alone frequency content of SPL for the OH-6A. The OSPL of just 

the tail rotor alone was 86.0 decibels [541]. 
2.7 NOISE 

508 

 As you can quickly appreciate from the three preceding figures, the attack on OH-6A 

noise had to include silencing of the engine and its compartment, and many of the drivetrain 

components (to be able to operate the aircraft at a low RPM), and then tackling the noise 

spikes that became apparent. I find it very interesting that the body of Barlow’s report [548] 

was a very packed 54 pages, 23 pages of which were devoted to engine and drivetrain details. 

Five pages were used to discuss the tail rotor, and only 4 pages covered the main rotor. Two 

charts in Barlow’s report stand out, in my opinion, as summarizing the comparison of The 

Quiet One versus the standard OH-6A before the aircraft were shipped to NASA Langley. 

Most impressive is the reduction in aural detection distance by a factor 6, which is shown in 

Fig. 2-344. The noise reduction demonstrated in hover is shown here as Fig. 2-345. 

 Taking Barlow’s and Robinson’s work to heart, it seems clear to me that there is no 

assembly in any helicopter now flying, or that is yet to be conceived and put into production, 

that can be overlooked if the objective is to significantly reduce noise. Furthermore, I would 

suggest that the place to start is with the engine and drivetrain areas, which may be less 

glamorous than studies of main and tail rotor noise, but offer high payoff for considerably less 

time and money spent. And in closing, I think that Hughes’ accomplishments equal what 

NASA showed could be done with a Stinson L-5, which you saw earlier in Fig. 2-303. 

Fig. 2-344. Reduction in OH-6A aural detection distance achieved by Hughes during 

Phase II of the Quiet Helicopter Program [548]. 
2.7 NOISE 

509 

Fig. 2-345. Reduction in standard OH-6A hover noise achieved by Hughes during Phase 

II of the Quiet Helicopter Program [548]. 

2.7.7 Government Noise Regulations for Helicopters 

 Shortly after the completion of The Quiet Helicopter Program, the war in Vietnam 

came to an end.161 The number of helicopters then being sold in the world was climbing by 

leaps and bounds. In the United States alone, The Federal Aviation Administration (FAA) was 

(a) experiencing an overwhelming number of applications for airworthiness certificates, and 

(b) providing helicopter registrations at the rate of 500 per year as Fig. 2-346 shows. But then, 

in the late 1970s, the general public started to have enough helicopters flitting about that 

people began noticing them—and the noise they produced. It was simply a repeat of what 

happened when the airplane came on the scene in the mid-1920s, only now there were more 

people complaining than just berry pickers near Boise, Idaho. National authorities of several 

nations, including the U.S., began to prepare draft regulations that would restrict operations of 

helicopters in highly populated areas—just the areas that the helicopter was designed to 

service. In fact, the FAA issued a Notice of Proposed Rulemaking on July 19, 1979, outlining 

proposed noise certification procedures and limits [551]. 

 About this time, the International Civil Aviation Organization (ICAO), supported by 

the FAA and most European nations, established a working group to develop helicopter noise 

certification standards. Faced with the certainty of some ill-conceived regulations, the 

industry, and the Helicopter Association International (HAI) in particular, offered a different 

approach. At this point, let me quote directly from the HAI Fly Neighborly Guide [552]: 

 

161 Saigon fell on April 30, 1975. 
2.7 NOISE 

510 

“The industry, and HAI in particular, felt that a better approach would be for the industry to 

develop voluntary guidelines to control the noise impact by operational means. After a 

number of FAA/industry meetings, the FAA, in the fall of 1981, agreed to withdraw its initial 

NPRM related to helicopter noise certification while additional technical data were 

acquired.162 This was done with the understanding that the helicopter industry would develop 

new technology—creating quieter, more advanced equipment, and implement a voluntary 

noise abatement program. This resulted in the establishment of the HAI Fly Neighborly 

Program based on an earlier program developed by Bell Helicopter Textron [553-555]. 

ICAO initially issued international noise standards in 1981, as a part of the International 

Standards and Recommended Practices, Environmental Protection, Annex 16 to the 

Convention on International Civil Aviation. These were not adopted by many nations before 

they were relaxed in 1985. Since that time, the standards have been amended a number of 

times. The FAA subsequently issued helicopter noise certification standards in 1988. These 

have been revised over the years. They are defined in 14 CFR Part 36.” 

You can download the HAI Fly Neighborly Guide [552] (only 28 pages, all for free) and I am 

sure you will have no trouble grasping its content. The reason I say that is because the 

technical content has been obtained from key rotorcraft engineers reinterpreting much of their 

noise measurements so that even laymen get the points. In stark contrast, the ICAO’s set of 

aircraft noise standards is slightly over 200 pages [556] and costs $180 with shipping, and 

then you have the FAA’s regulations about rotorcraft noise [557, 558], which spell out the 

certification procedure in nearly infinite detail. For example, precise microphone placement 

and noise measurements for three flight profiles must be obtained. The profiles cover takeoff 

(Fig. 2-347), flyover (Fig. 2-348), and landing (Fig. 2-349). Then the recorded data is reduced 

to a pass/fail grade using a most detailed set of equations [558]. (Further discussion of ICAO 

and FAA requirements relative to noise is definitely beyond the scope of this discussion.) 

 The HAI Fly Neighborly Guide gets to the heart of the helicopter noise problem. If 

you will take a moment to review Fig. 2-315 on page 468, you will note that listed under 

Other Types of Noise are High-Speed Impulsive noise and Blade-Vortex Impulsive noise. The 

combination of basic research and operational experience during the late 1970s and early 

1980s disclosed that some airfoils along a rotor blade could experience transonic flow at 

certain operating conditions. At high speed, severe noise became quite clear to an observer on 

the ground as the tip of an advancing blade began to exceed a critical Mach number. It was as 

if the blade tip was breaking the “sound barrier.” You will recall that when an airplane breaks 

the sound barrier, people hear only one loud bang or crack, and then the airplane is gone. 

Low-speed helicopters take considerably longer to pass the observer, but the observer hears 

many rotor revolutions before the helicopter is out of sight, and each revolution produces mini 

sonic booms from every blade. Rotorcraft aero-acousticians have labeled this high-advancingtip Mach number noise as high-speed impulsive noise. 

 

162 The initial proposed regulation would have required retrofitting all helicopters in the fleet. This would have 

required an enormous amount of research, time, and money. In essence, the helicopter industry would have had 

to ground virtually every machine. The revised regulations basically grandfathered what was flying, which gave 

industry the time to meet the new regulations with much quieter machines. 
2.7 NOISE 

511 

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000

Registered

Rotorcraft

Fleet

Size

End of year

Total

rotorcraft

fleet

Commercial

helicopter

manufacturers

only

All

other

types

Fig. 2-346. Growth in the U.S. rotorcraft fleet. 

Fig. 2-347. FAA takeoff flight profile for noise certification [557]. 
2.7 NOISE 

512 

 The other very annoying noise came when a helicopter was descending at relatively 

low speed as in an approach to landing. The magnitude of this noise was on par with highspeed impulsive noise that came with transonic Mach numbers of rotor blade tips, but was, 

upon research, associated with the wake from an upstream blade impinging on a following 

blade. Testing and analysis led to calling this wake-blade interaction situation Blade-Vortex 

Interaction and adopted the shorthand notation of BVI. The HAI Fly Neighborly Guide had 

Fig. 2-348. FAA flyover flight profile for noise certification [557]. 

Fig. 2-349. FAA landing flight profile for noise certification [557]. 
2.7 NOISE 

513 

this to say about the operating noise characteristics: 

“For a typical small/light helicopter, the most annoying noise mechanism impulsive noise 

(BVI) occurs during partial power descents and in sharp/high-rate turns. For a typical medium 

or large/heavy helicopter, they can occur in low-speed level flight, during partial power 

descents, and in sharp/high-rate turns. Figures 1, 2 and 3 show the flight conditions under 

which you can expect main rotor impulsive noise to occur. 

The impulsive noise boundary for your particular helicopter may be somewhat larger than that 

shown in Figures 1 and 2 because the main rotor may generate impulsiveness intermittently 

when it encounters wind gusts, or during a rapid transition from one flight condition to 

another. Although the sound produced at these descent rates is not extremely loud to 

crewmembers inside the helicopter, they can, in most cases, recognize it and, thereby, define 

the impulsive noise boundaries for their particular helicopter. However, in some cases, the 

impulsive BVI noise cannot be detected in the cockpit. Of course, people on the ground hear 

impulsive noise grow more intense as the helicopter descends.” 

I have included here as Fig. 2-350, the first two of the three figures that the Fly Neighborly 

Guide refers to. 

Fig. 2-350. Regions of high blade-vortex interaction (BVI) to be avoided [552]. 
2.7 NOISE 

514 

 The HAI Fly Neighborly Guide goes on with a discussion about how to make the 

approach to landing so as to fly around the blade-vortex interaction region. Because the BVI 

region is less pronounced for small and light helicopters, the Fly Neighborly Guide suggests 

two ways around the BVI region, but for medium and heavy helicopters the guide suggests 

skirting around the BVI region so the approach would be made at a rate of descent of about 

900 to 1,000 feet per minute. I have added the FAA’s 6-degree required approach for 

certification to both figures (Fig. 2-351 and Fig. 2-352). Personally, it appears to me that 

lower noise will be produced using an approach glide slope more like 12 degrees. In fact, the 

guide makes this very point with its figure 7, which you see here as Fig. 2-353. 

2.7.8 Noise in Forward Flight 

 At this point in the discussion,163 it would be nice to write that understanding and 

prediction of helicopter noise in forward flight is complete, but even after nearly four decades 

of research, noise created by blade-vortex interaction (BVI) and/or transonic advancing blade 

tip speeds has only recently become predictable. You may wonder then how the HAI could 

publish such clear advice in graphical form as shown in Fig. 2-351 and Fig. 2-352. The 

answer is rather simple: the HAI suggestions are based on a collection and simplification of a 

large body of experimental data. This is not to infer that no theoretical progress has been 

made. In fact, quite the opposite is true as I will now summarize. 

Fig. 2-351. The HAI Fly Neighborly Guide for noise abatement with small/light 

helicopters [552]. 

 

163 As of February 14, 2012. 

FAA 6-deg 

approach slope 
2.7 NOISE 

515 

Fig. 2-352. The HAI Fly Neighborly Guide for noise abatement with larger 

helicopters [552]. 

Fig. 2-353. The HAI Fly Neighborly Guide suggests that a lower noise footprint can be 

achieved operationally with steeper approaches than the 6 degrees specified by 

the FAA for certification purposes [552]. 

FAA 6-deg 

approach slope
2.7 NOISE 

516 

 The research that has gone on since 1970 has not concentrated on what a person on the 

ground hears. That is the task that regulatory bodies have concentrated on. Rather, noise 

research has concentrated on the sound pressure levels emanating from the sources on the 

helicopter. While regulatory bodies have worked to quantify annoying noise in terms of a 

decibel,164 researchers have been deciphering particular noise signatures from pressure 

waveforms plotted as a time history (with pressure being in pascals or sometimes in dynes per 

square centimeter; note that 10 dynes/cm2

 equals one pascal). And the research that has gone 

on has been, rather specifically, on the most annoying rotor noises, which are high speed and 

blade-vortex impulsive and broadband. To guide this summary, let me refer you to the 

classifications of rotor noise you saw earlier, which I have repeated here as Fig. 2-354. 

 To provide you with some insight into progress in noise research, I intend to draw the 

story primarily from four papers and two status reports. These publications were compiled by 

very knowledgeable researchers: 

1. Fred Schmitz and Don Boxwell’s 1976 landmark AHS Journal paper [559]. 

2. Fred Schmitz and Yung Yu’s 1979 follow-on AHS Journal Paper [560]. 

3. Fred Schmitz’s Chapter 2 in Volume 1 of Harvey Hubbard’s two volumes, which 

came out in 1991 [545]. 

4. Ken Brentner and Feri Farassat’s two papers, one from 1994 [561] and the other 

from 2003 [522]. 

5. Mike Watt’s Chapter 3 from the September 2009 NASA status report compiled by 

Gloria Yamauchi and Larry Young [530]. 

 By the late 1960s, engineers had a good handle on rotational noise. This progress 

came about primarily because of research on fixed-wing propeller noise. Then in the early 

1970s, research on helicopter noise began in earnest despite little industry interest or serious 

requests from either the military or civil marketplaces. The motivation came from the 

theoretical work published by Ffowcs Williams and Hawkings [521] in 1969 and the germ of 

an idea to record in-flight helicopter noise, which came to Fred Schmitz in 1974.165 

 In my opinion, experimental noise research took a giant step forward when Fred 

Schmitz and Don Boxwell published [559] the first results of helicopter in-flight noise 

measured by a very quiet fixed-wing aircraft flying in formation with the helicopter under 

investigation. This first-of-its-kind experiment used a U.S. Army UH-1H helicopter trailing 

 

164 I myself would suggest that the units of annoying noise should be the number of kids and/or grandkids 

awaken from an afternoon nap. 

165 As Fred related the story to me, he was in Europe training pilots of Hueys to fly quietly when operating near 

their airbases, which were generally close to cities. He happen to see an icing rig used to spray ice in flight onto 

a following aircraft. He asked Dick Lewis (then working at Edwards), “Why can't we mount a microphone on a 

OV-1 and record helicopter noise?” Dick thought it could be done. Despite several naysayers (including Fred’s 

boss, Irv Statler) Fred made it happen. Later, Fred used his persuasive powers to obtain an FBI YO-3 airplane for 

extensive testing of many other helicopters at NASA Ames Research Center. Much of the data is still classified. 
2.7 NOISE 

517 

Fig. 2-354. The noise categories in 1940 with some modern additions. 

Fig. 2-355. The first in-flight measurements of helicopter noise must be credited to a 

team led by Fred Schmitz and Don Boxwell [559]. 

Propeller 

& 

Rotor 

Noise 

Rotational 

Noise 

Blade 

Thickness 

Noise 

Torque 

& 

Thrust Noise 

Other Types of Noise 

Broadband 

Impulsive 

High Speed 

Blade-Vortex 

Vortex 

Noise
2.7 NOISE 

518 

Fig. 2-356. UH-1H sound pressure waveforms with the helicopter at 80 knots indicated 

airspeed and at a rate of descent of 400 feet per minute. Time scale is for one 

revolution [559]. 
2.7 NOISE 

519 

behind a U.S. Air Force OV-1C. The geometry of the test procedure is illustrated in 

Fig. 2-355, and results are shown in two forms. The first form is shown here in Fig. 2-356. By 

maneuvering the OV-1C carefully around the UH-1H, sound pressure levels and characteristic 

waveforms were obtained at several radiating angles. To the searching eye, distinct pressure 

impulses were quite evident, and this began identification of blade-vortex interaction and 

high-speed, impulsive noise waveform signatures. 

 

Fig. 2-357. UH-1H sound pressure waveforms for a small matrix of indicated airspeeds 

and rates of descent. Time scale is one-half of a revolution [559]. 
2.7 NOISE 

520 

The second form provide by Fred and Don’s paper [559] is a sparse airspeed and rateof-descent matrix of sound pressure waveforms. This data is shown here in Fig. 2-357. Now 

you see the influence of advancing tip Mach number, which clearly dominates the pressure 

waveform. Given that the UH-1H tip speed is about 814 feet per second, the advancing tip 

Mach number is calculated as o at FP t s ( ) M M V V a, x 1, 90 = ψ=

== + and so it follows that 80 knots 

equates to an advancing tip Mach number of about 0.85, 100 knots to 0.88, and 115 knots to 

0.90, assuming that the speed of sound (as) is 1116.4 feet per second. You can see that the 

noise impulse creates a very large pressure spike approaching 3,000 to 4,000 dynes per square 

centimeter at 115 knots. That is equivalent to 300 to 400 pascals. 

 It is worth a moment to crudely estimate the overall sound pressure level produced by 

such massive impulses as Fig. 2-357 shows. Suppose I make use of the fundamental equation 

that calculates overall sound pressure level (OSPL) in decibels that you encountered earlier. 

That is, let me apply 

(2.305) ( ) 2

1

T 2

10 t 2 T

ref 2 1

1 1 OSPL 10log p dt p TT

      =         −   

to the time history of sound pressure (pt) shown in Fig. 2-358. Here I have assumed a 

UH-1H two-bladed main rotor having a tip speed of about 814 feet per second. A tip speed of 

814 feet per second corresponds to nearly 5.4 revolutions per second or, more usefully, one 

revolution in 0.186 seconds. The two-bladed UH-1H will have two sound pressure impulses 

for every revolution. As Fig. 2-358 shows, the two impulses will occur over a very short time 

increment of T3 –T1 and T6 –T4. I will assume that between the two spikes the sound pressure 

is zero. On this basis, the OSPL equation is used in this example as follows: 

(2.341) ( ) () () ()

1 2 3

2 1 0

T T T 2 22

10 0 1 1 2 2 3 2 T T ref 7 0 T

1 OSPL 10log p dt p dt p dt etc. p TT → →→

     

= + ++       −    

  

   . 

 Now suppose the pressure drop is linear with time. That is, from T1 to T2 the time 

history behaves simply as a straight line so that pt = At+B = pmax(t–T1)/(T2-T1). Note that the 

pressure drop occurs during the first half of the impulse time so that T2 = T1+(T3–T1)/2. 

Assume the rise in pressure from T2 to T3 is a mirror image of the pressure drop. Thus, a 

pressure impulse is modeled as two right-triangles placed back to back on the long side. 

Finally, assume the second pressure impulse is a duplicate of the first. This makes four righttriangles to be accounted for with a two-bladed rotor. 

 With this two-bladed impulse model, you have, in effect, four pressure segments (the 

left and the right hands of two spikes, if you will) and the OSPL calculation is reduced to 

(2.342) ( ) ( ) ( )

3 1 2

1

T T T 2 2

max

10 1 2

ref 7 0 2 1 T

4 p OSPL 10log t T dt p TT TT

+    =        = −       − −          







and the integration result is simply 
2.7 NOISE 

521 

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

T0

pmax

Impulse Width (T3 - T1) 

(sec)

Sound 

Pressure

Pt 

(pascal)

One rev (T7 - T0) 

(sec)

pmax

T6

T5

T T4 3

T2

T1 T7

Fig. 2-358. UH-1H sound pressure waveforms for a small matrix of indicated airspeeds. 

(2.343) 

2

max

10 2

ref

2 impulse time p OSPL 10log 3 p time of 1 rev

      =           . 

 Now consider a numerical result using the UH-1H data at 115 knots in level flight as 

provided in Fig. 2-357. Here the peak sound pressure (pmax) is on the order of 3,000 dynes per 

square centimeter (or 300 pascals). The reference pressure (pref) is the industry standard of 

0.0002 dynes per square centimeter, so the ratio (pmax/pref) is about 15×106

. The time of one 

rotor revolution at 814-feet-per-second tip speed is 0.186 seconds. Suppose for simplicity’s 

sake that the impulse time is 1.86 milliseconds, which is 0.00186 seconds. Then the ratio of 

impulse time to the time of 1 rotor revolution is about 0.01. With these approximate values, 

you will calculate that the overall sound pressure level (OSPL) is 122 decibels. 

 Do not forget that in this experiment, the 122 decibels just arrived at is associated with 

a microphone mounted on the vertical tail of the OV-1C, which was about 100 feet away from 

the noise source. The UH-1H has a radius of 24 feet, which means the distance-to-radius ratio 

(S/R) is about 4. Making use of Eq. (2.330), which gives the influence of distance on OSPL, 

you can see that the UH-1H at 115 knots creates an OSPL about in accordance with 

(2.344) ( ) { } ( )

13

13

b 10 10 10 2

2.4 10 OSPL 10log 10log 2.4 10 20log 4 122

S R

    ×

= =×   − =

   

. 

Suppose now that a person was 1,000 feet from the UH-1H. Then Eq. (2.344) estimates that 

that person would experience an OSPL of 102 decibels. Even at a distance of one statute mile, 

the OSPL would be 87 decibels, which is still quite annoying. 
2.7 NOISE 

522 

 Here is an interesting point. Suppose a UH-1H is coming to save you and you are in 

the open (say the middle of the desert), and suppose the pilot is going flat out at 115 knots 

(130 miles per hour or 11,646 feet per minute) with a rate of descent of 800 feet per minute. 

This is a flight path angle to the ground of just under 4 degrees. Say you first hear him 

2 minutes before he is right there with you. Two minutes means the UH-1H is about 2 miles 

away when you first hear it. The closing distance (S) in Eq. (2.344) would be 

(2.345) Closing distance S S 11,646 t == − t 2= ( ), 

and your time (t) starts at zero when you become aware of the helicopter. The question I am 

leading up to is this: “How does the noise increase as you wait?” The answer comes by using 

Eq. (2.344) and plotting OSPL versus time since awareness, which you see in Fig. 2-359. You 

might note in passing that this figure is quite similar to Fig. 2-338 on page 502. Only the 

noise created as the machine slows down and comes to hover is lacking. 

 Now let me go back to a key speculation that Fred and Don made in their 1976 paper. 

They took a hard look at the pressure waveform that you see in box 9 of Fig. 2-357, which 

you can associate with an airspeed of 115 knots and a rate of descent of 800 feet per minute. 

60

70

80

90

100

110

120

130

0 5 10 15 20 25 30 35 40 45 50 55 60

Overall

Sound

Pressure

Level

(db)

Time From First Awareness (sec)

About 2 

miles away

One mile 

away

250 ft

away

500 ft

away

1,000 ft

away

One-half 

mile away

Based on 115 knots flight speed

Fig. 2-359. UH-1H overall sound pressure level as a function of distance from 

the observer. 
2.7 NOISE 

523 

They took representative data and made what they called a composite illustration, which I 

have reproduced here as Fig. 2-360. You might first notice that here the negative pressure is 

plotted in the opposite direction from what you probably use. They made the point that “the 

convention established by early high-tip-speed propeller researchers is adhered to: a pressure 

decrease (negative pressure) is indicated upward and a pressure increase (positive pressure) 

downward.” I thought that that little bit of history was rather interesting because in all 

subsequent reports and papers, pressure data was plotted the “right” way. But back to the key 

speculation. Their speculation in 1976 was that 

“the composite waveform model illustrates three predominant pressure disturbances observed 

in the data. They are shown in the same relative sequence and approximate pulse width that 

were characteristic of the measured data. Typically, the sequence began with one or two 

successive increases in positive pressure of "triangular" pulse shape (fig. 4, no. 1). These 

positive pressure peaks were followed by a large near-triangular negative pressure pulse. At 

high advance ratios, the negative pressure rise (fig. 4, no. 2) increased in amplitude slightly 

slower than its subsequent rapid decrease (fig. 4, no. 3) and the waveform is represented more 

by a saw-tooth or half-triangular pulse. Finally, when it was observed to occur, an extremely 

narrow positive pressure spike followed immediately after or as a result of the extremely rapid 

increase in pressure. Although it is not the intent of this paper to relate in detail the potential 

Fig. 2-360. Dissecting a sound pressure waveform [559]. 
2.7 NOISE 

524 

design causes of the radiated noise to the acoustic time history, some discussion and general 

observations are in order. It is the authors’ hypotheses that the initial series of positive pulses 

(fig. 4, no. 1) is a direct result of blade-tip vortex interaction and that the remainder of the 

impulsive noise waveform features are associated with high advancing-tip Mach numbers. 

The large rise in negative pressure (fig. 4, no. 2) is thought to be attributable to “thickness” 

effects, while the following sharp increase in pressure (fig. 4, no. 3) is related to a radiated 

shock wave being shed from the advancing rotor blade. No attempt at theoretical justification 

of these hypotheses is attempted in this work; the primary intent is to furnish a consistent set 

of acoustic impulsive noise data.” 

 You will note on the right axis of Fig. 2-360 a translation of 512 dynes per square 

centimeter into a sound pressure level. The pressure waveform is shown as a dashed line 

conveying two cycles of sine wave. The message here is that if the sound wave went on 

forever with an amplitude of 512 dynes per square centimeter, you would hear a continuous 

noise of 124 decibels. (In the 1979 paper by Fred and Yung Yu, the 512 was corrected to 

448). The sound pressure level in decibels of a pure tone is calculated according to 

Eq. (2.301), so you have 

(2.346) 

2 2

rms

10 10

reference

p 448 2 SPL decibel (db) 10 log 10 log 124 p 0.0002

        ≡= =                    

. 

 By 1979, Fred and Yung Yu concluded that the earlier speculation was correct and, in 

the intervening period, the OV-1/UH-1H test done at Edwards was repeated using a YO-3A 

(borrowed from the FBI!) and a UH-1H. This follow-on testing was conducted at NASA 

Ames Research Center. This effort was reported through an AHS Journal paper [560] and 

included a graph of peak negative pressure versus advancing tip Mach number, which you can 

see here as Fig. 2-361. As you can see, test data from the two different sites and recording 

airplanes was in close enough agreement for engineering purposes. The cause for concern was 

that theory and test data did not agree—at all. 

 This disagreement between theory and test (hardly an uncommon situation) sent noise 

researchers off in three directions. The first direction was to obtain in-flight noise data for a 

Bell AH-1S attack helicopter and later a multitude of other machines. The second direction 

was to step back from full-scale testing in flight and obtain data for model rotors in hover. 

The third direction was, of course, to start improving the theory, which was, at that time, quite 

embryonic. Let me briefly discuss each of the three directions in turn. 

2.7.8.1 In-Flight Noise Measurements 

The step that incorporated the AH-1S into a growing noise database allows me to show you 

the comparison in Fig. 2-362. Here you have both full-scale AH-1S and 1/7-model-scale 

AH-1S data [562] compared to the full-scale UH-1H. Fred notes [545] that “the model-scale 

acoustic data were taken in the DNW (Deutsch–Niederländischer Windkanal) anechoic wind 

tunnel and are of very high quality.” In a 1983 report [563] by Fred and Yung Yu, the authors 
2.7 NOISE 

525 

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

0.8 0.85 0.9 0.95

OV-1S Data, Fig. 14, Schmitz & Yu, AHS Vol.24, No.1, January 1979

YO-3A Data, Fig. 14, Schmitz & Yu, AHS Vol.24, No.1, January 1979

Schmitz & Yu Theory AHS Vol. 24, No.1, January 1979

Peak 

Pressure 

(Corrected to sea 

level standard)

dynes/cm2

Advancing Tip Mach Number, UH-1H Helicopter

112 db

128 db

126 db

124 db

122 db

118 db

-500 106 db

OSPL 

75 feet 

away

Fig. 2-361. 1979 theory did not predict UH-1H peak negative pressure-spike increases 

with advancing tip Mach numbers. I have added the red decibel scale following 

the discussion surrounding Fig. 2-358. 

-700

-600

-500

-400

-300

-200

-100

0

0.8 0.825 0.85 0.875 0.9 0.925 0.95

OV-1 + UH-1H

YO-3 + UH-1H

YO-3 + AH-1S Data Set 1

YO-3 + AH-1S Data Set 2

1/7 Scale Model of AH-1S

Schmitz & Yu Linear Theory AHS Vol. 24,

No.1, January 1979

Peak 

Negative

Pressure 

(pascals)

Advancing Tip Mach 

112 db

128 db

126 db

124 db

122 db

118 db

OSPL 75 

feet away

Fig. 2-362. In-flight noise test data for full-scale UH-1H and AH-1S helicopters plus 

1/7-scale model of the AH-1S clearly show that low tip Mach numbers reduce 

high-speed impulsive noise. 
2.7 NOISE 

526 

note that testing of a scale model UH-1H showed that the “dominant” parameter for highspeed impulsive noise is advancing tip Mach number and that advance ratio was a minor 

player—at least over an advance ratio range of 0.091 to 0.264. They also became aware of a 

significant difference in pressure waveform as the advancing tip Mach number was increasing 

(Fig. 2-363). They reported as follows: 

“Perhaps the most interesting aspect of high-speed helicopter noise is the development of the 

saw-toothed waveform at high advancing-tip Mach numbers. This is shown in figure 36 

[reproduced here as Fig. 2-363] together with a plot of the peak pressure versus advancing-tip 

Mach number (MH is constant and μ is varying) (ref. 13). In case A (MAT = 0.867), a nearsymmetrical pulse is observed; the subjective qualities could be described as a loud thumping. 

As the advancing-tip Mach number is increased, the symmetrical pulse becomes saw-tooth in 

character (case B, MAT = 0.90); the waveform consists of a large decrease in pressure 

followed by an extremely sharp increase in pressure (ΔP/Δt ≅ 4×106

 dynes/cm2/sec). 

Crispness (many harmonics) and intensity of the acoustic signature are its dominant features. 

At still higher advancing-tip Mach numbers (case C, MAT = 0.925), the peak negative pressure 

becomes very large, and the sudden rise in pressure becomes nearly instantaneous (ΔP/Δt ≅

1×107

 dynes/cm2/sec). Some overshoot can be seen, part of which is real and part of which is 

due to instrumentation bandwidth limitations. The noise generated by this latter waveform is 

rich in higher harmonics and can be subjectively classified as harsh and extremely intense. 

It is known that this rapid increase in pressure (case C) is a radiating shock wave. Early 

indications of its formulation can be seen in case B at the lower advancing-tip Mach number. 

Of course we know that local shock waves do exist near the tip of the rotor blade throughout 

this Mach number range. However, this acoustic plot suggests that these local shock waves 

‘delocalize’ at a certain ‘delocalization Mach number’ and propagate to the acoustic far-field. 

Below the delocalization Mach number (-0.9 for the NACA 0012 airfoil), all shock waves are 

confined to the blade. Above the delocalization Mach number, shock waves on the surface of 

the blade radiate as shock waves to the acoustic far-field (see refs. 20 and 22).” 

 In-flight measurements were gathered on many helicopters as part of the NASA 

In-Flight Rotorcraft Acoustic Program, and the YO-3 airplane was put to very productive use. 

Most of the data obtained with military helicopters is still classified. However, one 

investigation of blade tip geometry effects on noise was published in the appendix of 

reference [564]. The blade geometry testing was accomplished with the YO-3/AH-1S 

combination. On the civil side, you will find some very interesting reports. For example, a 

Sikorsky S-76 helicopter was tested behind a YO-3 to obtain data that could be compared to 

test results obtained with an isolated main rotor in the 80- by 120-foot wind tunnel at NASA 

Ames Research Center [565]. This work was directed at learning more about blade-vortex 

interaction noise. While only a small range in thrust, rate of descent, and advance ratios was 

covered, this in-flight test provided a very clear picture of the sound pressure created by 

blade-vortex intersections on a four-blade rotor system as Fig. 2-364 shows. This particular 

data is associated with a helicopter rotor thrust coefficient (CT) of 0.00778, an advance ratio 

(μ) of 0.167, a true airspeed of 65.8 knots, and a rate of descent of 748 feet per minute. This 

figure shows the clear difference between the blade-vortex signature and the signature due to 

high advancing tip Mach number (Fig. 2-363). Watch the scales here and remember that a 

pascal is 10 dynes per square centimeter. Incidentally, the overall sound pressure level for this 

data point was 106.2 decibels. Other recorded data showed OSPLs ranging from 99.9 to 

109.6 decibels. These measured waveforms gave the small band of noise researchers even 

more food for thought. 
2.7 NOISE 

527 

Fig. 2-363. Compressibility creates severe sound pressure spikes [563]. 

Fig. 2-364. Blade-vortex interaction sound pressure waveform for the 

Sikorsky S-76. Time period is one revolution [565]. 
2.7 NOISE 

528 

 An even more comprehensive test program was conducted with an MBB BO-105 and 

reported in 1994 [566]. However, the authors reported some rather discouraging findings in 

the abstract to their paper, saying in part that 

 “acoustic measurements of a Messerschmitt-Bölkow-Blohm (MBB) BO-105 helicopter in 

flight are compared with acoustic measurements of a full-scale BO-105 rotor tested in the 

40- by 80-Foot Wind Tunnel at NASA Ames Research Center and with acoustic 

measurements of a small-scale BO-105 rotor tested in the Deutsch–Niederländischer 

Windkanal (DNW). 

Significant differences are seen in both the magnitude and shape of the blade-vortex 

interaction (BVI) events in the 40- by 80-Foot Wind Tunnel data and DNW data, as compared 

to the flight data. The rotor wakes in the 40-by 80-Foot Wind Tunnel and DNW are concluded 

to be different from the rotor wake occurring in flight. The differences in the respective wakes 

are primarily attributed to different trim conditions, wind tunnel wall effects, different shaped 

bodies underneath the rotors, and wind tunnel turbulence levels. The free-wake calculation 

results are generally consistent with the measured flight test acoustic data, and provide 

valuable insight into the kinematics of blade-vortex interactions.” 

The rotor model was a 0.4 scale of the BO-105. 

 One important action item that got closed in 1984 was how to scale model-noise data 

to full-scale data and vice versa. This task was reported in reference [567]. 

 Then in 1986, noise researchers got probably the highest-quality model database 

obtained up to the end of the 1980s [568]. The introduction to this paper (authored by Russ 

Zinner, Don Boxwell, and Bob Spencer) could hardly contain the enthusiasm of the noise 

researchers’ community. It read in part: 

“Helicopter noise was recognized as a problem as early as 1954 when Hubbard and Lassiter 

wrote their paper entitled ‘Some Aspects of the Helicopter Noise Problem.’ Although 

Hubbard and Lassiter were primarily describing engine and transmission noise, external noise 

is of even greater concern with today’s helicopters. Helicopter noise was officially addressed 

in 1979 when the International Civil Aviation Organization (ICAO) Committee on Aircraft 

Noise established limits on the amount of external noise a helicopter could produce under 

different flight conditions. This new set of standards required manufacturers to produce 

helicopters that reduced noise below the levels established by the ICAO. 

One way to ensure that new helicopters produce noise below the ICAO limits is to use 

accurate acoustic prediction codes in the early design stages. The confidence level of these 

prediction codes needs to be high to keep the acoustician an integral part of the design team. 

One of the most important steps in code development is code validation, for which a highquality rotor acoustic data base is essential. Unfortunately, only limited high-quality acoustic 

data have been available for use in validation, often consisting of merely a single point or a 

single flight condition. This dearth of acoustic data is one of the factors limiting the rapid 

progress of acoustic prediction codes. 

A new rotor acoustic data base is now available to the aeroacoustic research community in a 

25-volume, 11-report set. This data base, inspired by a joint agreement between the U.S. 

Army Aeroflightdynamics Directorate and Boeing Helicopters (BH), was collected in the 

Duits-Nederlandse Windtunnel (DNW) in 1986. This experimental test was one in a series of 

tests under the Army’s Aerodynamic and Acoustic Testing of Model Rotors (AATMR) 

program and used a dynamically scaled, blade-pressure-instrumented -of the forward rotor on 

the BH 360 helicopter. 
2.7 NOISE 

529 

This paper collates and summarizes the validated acoustic data base in an order that gives 

careful attention to four areas of current rotor acoustic research: I) high-speed impulsive 

(HSI) noise, 2) blade-vortex interaction (BVI) noise, 3) low-frequency noise, and 

4) broadband noise (BBN). Each of these basic rotor-noise sources was identified in 

validating the BH 360 data base, and the data for each are presented and arranged in terms of 

trends using critical scaling parameters. These scaling parameters are the same as those 

already reported in the literature. Also to be discussed is the extent to which distinct features 

of each source exist in this data base, including some known anomalies and deficiencies of 

which users should be aware when including this data base in specific areas of their rotor 

acoustic predictive work.” 

The first sentence of the authors’ conclusions was italicized and said, “High-quality data 

necessary for acoustic code validation are now available.” You definitely want to read this 

report. Then if you want to go into all the data that was recorded, you will need to tackle the 

25-volume data contained in the 11 reports, which are available but only on a limited basis. 

 The value and quality of noise data obtained in the DNW wind tunnel quickly spread 

throughout the industry. For example, the Army’s Aerodynamic and Acoustic Testing of 

Model Rotors (AATMR) program included testing of a dynamically similar model of the 

McDonnell Douglas HARP composite bearingless main rotor and a Model 369 tail rotor [569]. 

Sikorsky obtained data for an S-76 model rotor that was reported in 1990 [570], also under the 

AATMR program. Then in 2001, a follow-on BO-105 model rotor was tested at the DNW. 

Results from this second entry, referred to as HART II, with a more extensive objective were 

reported [571] by Yung Yu and his nine coauthors. In the abstract to their paper, the authors 

state: 

“In a major cooperative program within the existing US-German and US-French Memoranda 

of Understanding/Agreements (MOU/MOA), researchers from German DLR, French 

ONERA, NASA Langley, and the US Army Aeroflightdynamics Directorate (AFDD) 

conducted a comprehensive experimental program in October 2001 with a 40% geometrically 

and aeroelastically scaled model of a B0-105 main rotor in the open-jet anechoic test section 

of the German-Dutch Windtunnel (DNW). This international cooperative program carries the 

acronym HART-II (Higher harmonic control Aeroacoustics Rotor Test). 

The main objective of the program is to improve the basic understanding and the analytical 

modeling capabilities of rotor blade-vortex interaction noise with and without higher 

harmonic pitch control (HHC) inputs, particularly the effect of rotor wakes on rotor noise and 

vibration [My italics]. Comprehensive acoustic, rotor wakes, aerodynamic, and blade 

deformation data were obtained with pressure-instrumented blades. The test plan has been 

concentrated on measuring extensive rotor wakes with a 3 component Particle Image 

Velocimetry (PIV) technique, along with measurements of acoustics, blade surface pressures, 

and blade deformations. 

The prediction team with researchers from DLR, ONERA, NASA-Langley and AFDD was 

actively involved with the pre-test activities to formulate a test plan and measurement areas of 

the PIV technique. The prediction team predicted all the test results in advance before 

performing the wind tunnel test. This was done to obtain the best quality of test data, to 

improve the speed of measurements, and to determine the necessary measurement information 

for code validation. In this paper, an overview of the HART-II program and some 

representative measured and predicted results are presented.” 
2.7 NOISE 

530 

 As you may be sensing by now, after the original in-flight noise testing opened the 

book on helicopter rotor noise research, the database has been continually expanded and the 

data quality has been continually improved. Much of the data has found its way into the open 

literature as you read this. You can also appreciate that the small band of very knowledgeable 

noise researchers has grown—not enough in my opinion, but grown. This group has decided 

that high-speed impulsive noise (i.e., the advancing blade tip Mach number noise) needs to be 

studied, understood, and predicted in hover before dealing again with forward flight. On the 

other hand, they have concluded (a) that blade vortex interaction (BVI) noise is clearly a rate 

of descent at low speed problem, and (b) comprehensive free-wake theories are required to 

provide airloads leading to BVI analytical noise calculations and numerical results useful to 

the working engineer. It is interesting to me that rotor blade airloads are even more important 

to the prediction of noise than to vibration predictions. It appears that computational fluid 

dynamics (CFD) is the fundamental tool required for helicopter design work. 

2.7.8.2 More Study of Noise in Hover and Forward Flight 

 The second direction taken (to deal with high-speed impulsive noise) was to step back 

from full-scale testing in flight and obtain data for model rotors in hover. The attack was 

led by the Aeromechanics Laboratories, a part of the U.S. Army R & T Laboratories 

(AVRADCOM) located at NASA Ames Research Center. The first step was to turn the test 

cell used to measure hovering rotor performance into an Anechoic Hover Chamber. This 

facility improvement was accomplished under the leadership of Andy Morse.166 The 

transformation is illustrated here in Fig. 2-365. The more detailed description of the 

transformation [572] stated: 

“The data presented in this paper were gathered in a unique anechoic hover test facility which 

was designed primarily to gather acoustic and aerodynamic data on hovering rotors. The test 

chamber has been lined with polyurethane foam and has been designed to be anechoic 

(without acoustic reflections) down to 110 Hz. As illustrated in figure 1, aerodynamic 

recirculation is avoided by allowing quiescent air to be drawn into the room through 

acoustically lined ducts, collecting the wake of the hovering rotor through an annular diffuser, 

and exhausting the wake to the outside. In its current configuration, the test chamber can 

accommodate rotors from 1.5 to 2.4 m in diameter.” 

The early testing in the improved hover chamber was done with 1/7-scale rotor models of the 

UH-1H. As Fig. 2-366 shows, this model was tested first with blades having the full scale 

twist (θt) of –10.9 degrees. Fred and Yung Yu noted [563] then that 

“one of the same rotors used in the scaling tests (a 1/7 scale of a UH-1H main rotor) was run 

for these high-speed hover tests (ref. 15). The geometrically scaled rotor has a NACA 0012 

airfoil section with a root-to-tip washout of 10.9°. Because thrust appeared to be unimportant 

in the high-speed noise generation process, a second set of untwisted but geometrically scaled 

rotor blades was run at near-zero net thrust. Some small positive net thrust was required to 

avoid shed-wake interference effects. The data were taken with a microphone located within 

the tip-path-plane of the rotor at a distance of 1.5 rotor diameters (r/D = 1.5) from the hub. 

This in-plane microphone position is consistent with that used in previous in-flight and wind 

tunnel tests and is in a position to measure the most intense high-speed impulsive signature.” 

 

166 During this period, Irv Statler was the “chief” of the laboratory and Andy Morse reported to him. 
2.7 NOISE 

531 

Fig. 2-365. The Anechoic Hover Chamber located at the U.S. Army Laboratory at NASA 

Ames Research Center [572]. 
2.7 NOISE 

532 

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

0.8 0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1 1.02

1/7 Scale UH-1H

1/7 Scale UH-1H with Untwisted Blades

Peak 

Negative 

Pressure 

(pascals)

Hover Tip Mach 

1979 Schmitz & Yu

Ffowecs-Hawkings

Theory (monopole only)

1991 Baeder

 Ffowecs-Hawkings

Theory (monopole, dipole 

and quadrupole)

1991 Baeder

Application of CFD

Euler Theory

Fig. 2-366. Theory (versus test) has improved in the prediction of impulsive noise due to 

high tip Mach number. 

0

200

400

600

800

1,000

1,200

1,400

1,600

0.8 0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1 1.02

Peak 

Negative 

Pressure 

(pascals)

Hover or Advancing Tip Mach Number

1/7 Scale UH-1H in Hover

1/7 Scale UH-1H in Forward 

Flight. Hover Mtip = 0.732

Fig. 2-367. Blades with the NACA 0012 airfoil probably should not be flown above an 

advancing tip Mach number of 0.80—if noise is a consideration. 
2.7 NOISE 

533 

 After the 1/7-scale UH-1H testing was completed in hover, the model was tested in the 

NASA Ames 7- by 10-foot wind tunnel [553] located next to the Anechoic Hover facility. 

The test section of the tunnel was lined to a depth of 3 inches with “Scottfelt” (a polyurethane 

foam) to provide a measure of acoustic isolation. The model was tested at a hover tip Mach 

number of 0.732, and the advance ratio varied from 0.093 to 0.264 so that data over a 

reasonable range in advancing tip Mach number was obtained. The rotor thrust coefficient 

(CT) to solidity (σ) ratio was maintained at 0.064, and the angle of the tip path plane (αtpp) was 

trimmed to a –2 degrees forward. This simulated flight test data. The comparison of noise in 

hover versus noise in forward flight is, I think, quite interesting as Fig. 2-367 shows. 

Apparently, serious impulsive noise will be broadcasted above an advancing tip Mach number 

of 0.80 for blades having the NACA 0012 airfoil over the outer portion of the blade. 

2.7.8.3 Theory is Improving 

 The first payoff for the growing and broadening attack on predicting rotor noise at its 

source was in the area of high-speed impulsive noise. Two perfect examples are the results 

Jim Baeder achieved in 1991 with direct calculation of noise using CFD [573] and the 

extension of the Ffowcs Williams–Hawkings theory (by adding a quadrupole167) to the 

WOPWOP analysis as Ken Brentner and Feri Farassat review in reference [522]. You will 

note in Fig. 2-366 that I have include the predictions of these two tools compared to hover 

noise measurements of a model UH-1H [563]. (I cannot yet, however, show you a theoryversus-test comparison of the UH-1H data you saw in Fig. 2-362.) In discussing the two 

approaches with several engineers familiar with high-speed impulsive noise, I came to three 

conclusions as of this writing. The first conclusion is that it is a very encouraging step forward 

that impulsive noise can now be predicted at least up to Mach numbers in the transonic range. 

The second conclusion is that taking the propeller approach of thin tips, reducing the design 

tip speed, sweeping the blade tip, and giving the helicopter operator a low-tip-speed option as 

Hughes did with The Quiet One is the only way to deal with such an undesirable noise 

signature. The implication of this second conclusion is that not only does advancing tip Mach 

number pose some limitations on desirable performance, it also poses an operating restriction 

for quiet as Fig. 2-368 suggests. The third conclusion is that this is going to still be a very 

hard sell to customers (and upper management) considering (a) the implied increases in 

weight empty, (b) a potential loss in useful load, (c) selection of a more powerful engine, and 

(d) an unfavorable increment in selling price. As I write this, it is not clear how to have our 

cake and eat it too, but it is clear that very innovative engineering, marketing, and pricing will 

be required. 

 The second payoff from this 25-plus-year effort has come in predicting blade vortex 

interaction (BVI) and broadband noise. Here the progress is also quite impressive despite the 

very detailed knowledge required about rotor wake geometry and the individual blade elastic

 

167 The Ffowcs Williams–Hawkings theory calculates noise using monopoles, dipoles, and quadrupoles to model 

the pressure waves emanating from the rotor blade airfoils. The clearest discussion I found about these pulsating 

pressure “devices” was on the Internet at http://www.acs.psu.edu/drussell/Demos/rad2/mdq.html. The author is 

Daniel A. Russell. I never studied these mathematical techniques in sufficient depth to adequately discuss them, 

so you are better off reading what a person with a Ph.D. has to say on this topic. 
2.7 NOISE 

534 

0

50

100

150

200

250

300

350

400 500 600 700 800 900 1000

Ft F t

1,90

s

o

VVV V M

a 1116.45

459.67 OATin F

518.67

+ θ+ θ = =

+ θ =

Flight

Path

Velocity

(kts)

Rotor Tip Speed (fps)

Compressiblity Becomes a Performance 

Factor Above M1,90 = 0.93

High Speed Impulsive Noise Becomes a 

Factor Above M1,90 = 0.80

VF

θ

Vt

θ

Fig. 2-368. Advancing tip Mach number should be both a performance and impulsive 

noise design consideration. 

deflections. In the April 2000 Journal of the American Helicopter Society, Thomas Brooks 

and his coauthors [574] developed a connected group of tools, which they named TRAC (Tilt 

Rotor Aeroacoustic Codes—even though it can do helicopters too). Their block diagram 

describing the code is reproduced here as Fig. 2-369. You can see that CAMRAD is used to 

obtain the rotor trim and then a computational fluid dynamics (CFD) code derives the rotor 

blade loading. An alternate loading can be obtained from the HIRES code. At this point there 

is enough information to give WOPWOP details to compute noise, which is the final pressure 

waves and magnitude in pascals. 

 Brooks and his coauthors compared their TRAC program to BO-105 data obtained 

during the HART II program and a sample of their achievement is shown here with 

Fig. 2-370. While many refinements can be expected, these sample results published in April 

2000 are, in my opinion, quite impressive. The group followed up with more progress, which 

you can read about in references [575, 576]. 
2.7 NOISE 

535 

Fig. 2-369. The TRAC analysis created by a NASA Langley team [574]. 

Fig. 2-370. Sound pressure waveforms in low speed are predictable [574]. 

2.7.9 Closing Remarks 

In closing, I must first apologize for not including all of the noise reduction efforts that 

have been made in England and Europe. Those efforts have easily been on par with what I 

have related to you here in this limited discussion. 

 Helicopter noise comes from many sources as Fig. 2-371 suggests. What you have just 

finished reading has only dealt with external noise (and just rotor noise at that), which 

earthbound people and animals find very annoying. Space limitations have kept me from 
2.7 NOISE 

536 

discussing interior noise in detail, but you can read a very good summary in Mike Watt’s 

chapter on noise that Gloria Yamauchi and Larry Young included in reference [530]. Also, I 

found the report [577] describing how interior noise in a Sikorsky CH-53A was reduced from 

115 dB in its untreated military configuration (!) to 87 dB, after the cabin was acoustically 

treated, quite instructive. The authors closed their summary with the statement that 

“Specifically, a reduction of 12 dB from the first-stage planetary gear clash in the main gear 

could result in an interior environment which is only slightly higher than that in current 

narrow-body jet transports.” This work was done in 1977. 

 There is no question that a quarter century of research by a relatively small core of 

very talented and dedicated individuals has provided the rotorcraft industry with foundational 

tools that can help design less annoying helicopters. In my opinion, the next step is to be able 

to calculate, during the preliminary design phase, the machine’s noise levels relative to 

regulations required by certificating bodies (such as the FAA in the United States). As you 

saw from Fig. 2-347, Fig. 2-348, and Fig. 2-349, the noise during takeoff, flyover, and landing 

must be calculated in advance of a commitment to production. Currently the FAA has defined 

“not to exceed” noise levels as a function of rotorcraft gross weight. These limits are shown in 

Fig. 2-372 with the solid lines. Wayne Johnson prepared168 this figure from two references 

[578, 579]. You will note that the noise unit for FAA certification is EPNdb, which is 

shorthand for Effective Perceived Noise in decibels. As you read earlier, this parameter is 

spelled out by the FAA in considerable detail [557, 558]. 

Fig. 2-371. The many sources of both external and interior noise created by a helicopter. 

 

 

168 Wayne prepared this figure for inclusion in his soon-to-be-published book titled Rotorcraft Aeromechanics. 

He kindly gave me permission to include the figure in advance of his publication. 
2.7 NOISE 

537 

 Finally, the question I think a chief engineer needs answered during preliminary 

design of a new rotorcraft is, “Where does the design team’s configuration fall on 

Fig. 2-372?” There is, in fact, test data that noise researchers can use to compare analysis, 

when it is created, to test. You can begin to address this need by reviewing the paper that 

David Conner, Casey Burley, and Charles Smith presented at the 2006 American Helicopter 

Society Annual Forum [580]. 

Fig. 2-372. The FAA’s not-to-exceed noise levels if aircraft is to be certificated in the U.S. 

(courtesy of Wayne Johnson).
538 
539 

2.8 PURCHASE PRICE 

 Consumers, in the course of shopping, frequently look at an item and wonder, “How 

much does this cost?” With a little effort they search and find a price tag, or maybe a clerk 

comes forward with a computer scan showing the price. Now think about the use of those two 

words: cost and price. The consumer is really asking about how much he or she must pay to 

purchase the item. The consumer is not asking how much the manufacturer has spent to put 

the item before the consumer, and therein lies the reason for titling this chapter Purchase 

Price. 

 In this chapter you will be reading primarily about the list price of helicopters and 

very little about manufacturing costs. The reason for this is that manufacturers do not readily 

divulge their costs. In fact, cost data is not even spread around the company—in my 

experience. However, in military procurement situations manufacturers do provide financial 

data as requested by the government (at least in the United States). And, frankly, my 

experience has been to often wonder if the larger helicopter manufacturing companies really 

even know the accurate cost of producing any given aircraft they are delivering to a customer. 

The situation may be different for companies dealing only in the civil marketplace. They may 

know their product costs quite accurately, as would smaller cost centers that pursue pure 

research and development. Very productive groups such as the Lockheed Skunk Works [581] 

clearly demonstrate they know their costs. Of course, the difference between cost and price 

reflects some measure of profit, depending on how the books are kept. 

 In 1984 I bought the second edition of Augustine’s Laws [582], which introduced me 

to a number of Department of Defense (DoD) trends that I had never thought too much about. 

One of the trends, and Norm Augustine’s caption for it, caught my eye, and I have included it 

here as Fig. 2-373.169 This one book inspired me to delve into (a) the selling price of 

helicopters in the civil marketplace, and (b) military procurement of helicopters. The next 

several pages discuss these two topics. 

2.8.1 Civil Marketplace 

 The marketplace for civil helicopters is worldwide as you can easily imagine. The “list 

price” of helicopters in this marketplace is quite variable as you can also easily imagine. But 

there is one source that captures prices for almost all civil helicopters that have been sold over 

several decades. That source is HeliValue$, Inc. [583] located in Wauconda, Illinois. For years 

this company has published The Official Helicopter Blue Book®, and this collection is truly a 

gold mine of data used in the buying and selling of new and used machines.170

 

169 You will find Augustine’s Laws very thought provoking. Norm Augustine has been accorded many honors 

and has been a major figure serving this country both in the government and as a leader in industry as you can 

read from articles on the Internet. Incidentally, his Law XVI (in the 1984 edition) states that “In the year 2054, 

the entire defense budget will purchase just one aircraft.” 

170 Mike Scully and I used data from this source and some others to write a paper [584] which we titled 

Rotorcraft Cost Too Much. In this paper, we offered a helicopter price estimating equation. 
2.8 PURCHASE PRICE 

540 

Fig. 2-373. Norm Augustine captioned his figure 11 with: “The slope of the unit cost vs. 

time curve for rotary wing aircraft is the same as for fixed-wing aircraft, albeit 

getting off to a somewhat belated start” [582]. 

 When you study the trend of civil helicopter prices you will be immediately struck by 

the fact that one of Augustine’s Laws, shown here as Fig. 2-373, is just as applicable to the 

increase (over several years) in the selling price—perhaps list price would be a better term—

for any one specific helicopter model. One thing you should be aware of is that almost all 

civil helicopters contain engine, drivetrain, and rotor subassemblies developed, at least in 

part, with government money. An exception is the Robinson Helicopter Company’s 

R-22, R-44, and R-66 lines. Bell Helicopter’s Model 206B Jet Ranger is a more typical 

example. 

 You will recall that Bell participated in the U.S. Army Light Observation Helicopter 

competition with Hughes and Hiller, which Hughes won in the prototype fly-off because of a 

very competitive machine and very aggressive per-unit pricing. Bell’s submittal, shown in 

Fig. 2-374, lost. Bell immediately turned their design into a civilian machine shown in 

Fig. 2-375, and proceeded to sell over 7,300 206B-II and 206B-III, and U.S. Army OH-58A 

and OH-C versions over nearly four decades. 
2.8 PURCHASE PRICE 

541 

Fig. 2-374. Bell Helicopter’s YOH-4 prototype for the Light Observation Helicopter 

competition during the 1960s. First flight was December 8, 1962 (photo from 

author’s collection). 

Fig. 2-375. Bell Helicopter capitalized on the YOH-4 engine, drivetrain, and rotor 

systems with a civil marketplace fuselage. This began the Model 206 Jet Ranger 

series. FAA certificated October 20, 1966; first sale January 13, 1967 (photo from 

author’s collection). 

 The primary difference between the 206B II and 206B III (or OH-58A and OH-58C) is 

a slightly increased takeoff rating of the Allison (now Rolls Royce) Model 250 C-20 gas 

turbine engine. A secondary difference is that the growth versions had a slightly larger 

diameter tail rotor (5.2 feet increased to 5.42 feet). It is very hard to pinpoint any other 

significant changes in the basic configuration of this helicopter over its production life of four 

decades. What did improve was the time between overhaul (TBO) of many of the helicopter’s 

expensive parts. 
2.8 PURCHASE PRICE 

542 

 The Bell Model 206B was introduced to the civil marketplace in 1967 at a factory list 

price of $89,500 in its base configuration. 171 Of course, you could have it factory equipped 

with VHF, VOR, ADF, transponder, flight instruments, dual controls, and heater, but then 

your purchase price was $105,500.172 Bell delivered 115 Jet Rangers in 1967, which, I am 

sure, was a very positive indication that the civil marketplace was ready for small gas-turbinepowered helicopters even though they cost more than the piston-powered versions. 

 As the number of Bell Jet Rangers produced grew (Fig. 2-376), the list price also kept 

growing (Fig. 2-377). This fact may fly in the face of many cost estimators who swear by the 

relatively well-known “learning curve,” which I will discuss in more detail later. The point to 

grasp here is that there is a large group, at least in the United States, that claims some skill in 

estimating cost. However, as I have pointed out, price is different than cost, and the group that 

sets the selling price of helicopters is very, very small indeed. 

 In my opinion, the single most critical decision required from the president of a civil 

helicopter manufacturing company is illustrated by Fig. 2-376. As you can see from this 

figure, Bell did not produce a constant number of the Model 206Bs each year. This is a 

significant difference between military and civil production rates. Fulfilling a military 

contract generally entails producing a large quantity over several years, at so many a year and 

even so many a month. With this kind of assurance, a very stable production line can be set 

up, and production costs can be lowered as everyone learns the job. But when the number of 

machines to be produced each year varies as much as Fig. 2-376 shows, production proceeds 

in a jerky manner, the manufacturing staff is not constant from year to year, and learned skills 

can disappear—only to be required all over again next year. 

 Now assume you are the president of, let’s say, Bell Helicopter, and you must make 

the critical decision about how many Model 206Bs are to be produced next year. Keep in 

mind that if you release more for production than can be sold, the number of aircraft sitting 

outside the final assembly line building becomes unsold inventory, and you may not even 

cover the cost of production for that year. If you release too few for production and the 

marketplace demand for your product is particularly high, you will be sold out before the end 

of the year, and with helicopter production you cannot get additional machines to sell just at 

the snap of your fingers, even if you are the president. In fact, the lead time between your 

decision about how many aircraft are to be produced and the resulting first additional finished 

helicopter is about 18 months. Just think about the cost implications of Fig. 2-376, and then 

think about how you would set the average selling price for each year’s production batch. 

 If you let your imagination search for the many other factors involved in the difference 

between cost and price, you may conclude, as I have, that a chief engineer has a relatively 

easy job. All the engineering department has to do is release drawings (to manufacturing) for 

a world-class design that beats the competition at every turn. Let me examine this point with 

Fig. 2-378. 

 

171 The Official Helicopter Blue Book® provides factory list prices for helicopters in both base and equipped 

configurations. Sharon Desfor, the president of this company, is a delight to talk to, and she has all kinds of 

sources that could be tapped should you want to delve more deeply into the civil marketplace. 

172 This is the kind of experience you have when buying a new car! 
2.8 PURCHASE PRICE 

543 

0

50

100

150

200

250

300

350

400

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

Deliveries 

per Year

Year

Fig. 2-376. Per-year production of the Bell Model 206B was hardly constant over its 

four-decade life. 

$0

$200,000

$400,000

$600,000

$800,000

$1,000,000

$1,200,000

$1,400,000

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015

Bell 

Model 

206 B

FOB

List 

Price

($$)

Year

Fig. 2-377. Base configuration factory list price of the Bell Model 206B Jet Ranger has 

increased over the years, primarily due to inflation. (Excerpted from The Official 

Helicopter Blue Book®, with permission from HeliValue$, Inc.) 
2.8 PURCHASE PRICE 

544 

 The accumulating income to Bell for selling about 5,000 Model 206B Jet Rangers is 

shown in Fig. 2-378. The 5,000 aircraft constitute serial numbers 1 through 2,283 of the -II 

model, the rest being the -III model. In essence, this is the cumulative number of Jet Rangers 

listed in The Official Helicopter Blue Book®, which you see distributed by year in Fig. 2-376. 

I took the product of each year’s batch times the list price for that year (Fig. 2-377), and then 

summed it to arrived at Fig. 2-378. This does not include income from U.S. military sales of 

about 2,300 OH-58 helicopters. 

 You can see that from an initial investment of, say, $60 million over the 4-year span 

(from first flight of the YOH-4 and first sale of the 206B), Bell had a cumulative income of 

$1.4 billion. Of course, when the cost of producing the 5,000 aircraft is subtracted (say $1.3 

billion) and income tax on the $0.1 billion is paid, Bell might have had $600 million available 

to invest in a new product or even to do more research and development for, say, a V-22 

tiltrotor.173 From the chief engineer’s point of view, he must use the initial $60 million to 

manage the program that gets the product line to that first sale. In the early 1960s, $60 million 

was a lot of money and, with inflation, is about $600 million today. Also keep in mind that the 

YOH-4 research and development to first flight was funded by the U.S. Army, so Bell had a 

running start on its commercial derivative of the engine, drivetrain, and rotor systems. 

$0

$200,000,000

$400,000,000

$600,000,000

$800,000,000

$1,000,000,000

$1,200,000,000

$1,400,000,000

$1,600,000,000

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015

Cum

Income

from

Bell

Model

206B

Sales

Year

Fig. 2-378. Cumulative income to Bell Helicopter as Model 206B sales were made over a 

four-decade production life. 

 

173 In Bell’s case, they had to return some money to their parent corporation, Textron, so that Textron could pay 

stockholders a dividend and have some money left over for other investments in any of their many other 

companies like E-Z-GO golf carts. Of course, Textron also had to advance Bell some more money so that Bell 

could develop the Bell Model 206 L, which became the 206 Long Ranger. 
2.8 PURCHASE PRICE 

545 

2.8.1.1 Estimating Purchase Price 

 During the mid-1990s, Mike Scully and I worked very intensely to develop an 

equation that reasonably predicted factory list price. Our work came to a conclusion when 

reference [584] was published in January of 1998. One motivation for our effort was a joint 

feeling that pricing (or costing) a helicopter on the basis of dollars per pound of weight empty 

was quite questionable,174 so we began to accumulate an Excel® file of selling prices. From 

that file, we established an average curve of inflation for helicopters, and then we indexed 

the price of all the listed helicopters to 1994. Of course, it was then quite easy to create 

Fig. 2-379, which showed us just how inaccurate estimating factory list price by weight 

empty alone was. 

 As we continued to expand [585] and refine and correct our database, we began a 

year-long search for an equation that would reduce the scatter in any price estimating 

relationship. Early efforts showed that a regression analysis using up to 13 parameters was not 

producing major improvements. The problem was that with 13 parameters, the regression 

analysis had statistical confidence in only a few parameters. This led us to selecting weight 

empty (WE) in pounds, total engine(s) rated horsepower (THP) in horsepower, and number of 

blades (b) per rotor as the primary variables. We relegated other influential parameters to a 

constant (H). 

$100,000

$1,000,000

$10,000,000

$100,000,000

100 1,000 10,000 100,000

27 Small Piston

6 Large Piston

6 Conversions to Turbine

31 Small Turbine

33 Light Twin Turbine

9 Medium Twin Turbine

4 Large Twin Turbine +1 Tri Turbine

Base 

Configuration

List Price

in 1994 

Dollars

Weight Empty (lbs)

$1,000

per

pound

$100/lb

$200/lb

Fig. 2-379. List prices are not accurately estimated by weight empty alone [584]. 

 

174 Mike and I are of the same mind-set. We do not like to base a quantitative number on feelings. 
2.8 PURCHASE PRICE 

546 

 The final price-estimating relationship was keyed to 1994 U.S. dollars. With slightly 

abbreviated nomenclature, you now have 

(2.347) 0.4638 0.5945 0.1643 Base List Price $269(H)(WE) (THP) (b) = 

where H is the product of five factors and is computed as: 

(2.348) H = Engine Type × Engine No. × Country × Rotors × Landing Gear. 

The factors (found by regression analysis) used in computing H are: 

Engine Type Engine Number Country 

Piston 1.000 Single 1.000 U.S. Commercial 1.000 

Piston (geared supercharged) 1.398 Multi 1.344 Russia 0.362 

Piston (converted to turbine) 1.202 France/Germany 0.891 

Gas Turbine 1.794 Italy 1.056 

 U.S. Military 0.883 

Number of Main Rotors Landing Gear 

Single 1.000 Fixed 1.000 

Twin 1.031 Retractable 1.115 

 The predictive accuracy of Eqs. (2.347) and (2.348) is shown in Fig. 2-380. If the 

relationship were 100 percent accurate, every symbol in this figure would fall precisely on the 

diagonal line. Many data symbols nearly touch the diagonal line indicating this estimating 

relationship has very high assurance that it can at least come within 20 percent of the “actual” 

price 106 out of 121 times, or about 88 percent of the time. Quotations are used around the 

word “Actual” on the y-axis label on Fig. 2-380 for two reasons. First, purchase price 

(whether base or equipped) frequently was negotiable in the year the helicopter was bought. 

Secondly, we assumed the same inflation regardless of country, manufacturer, or helicopter 

model. 

 Try as we might, Mike Scully and I could do no better than what you see in 

Fig. 2-380. We had reasonable engineering confidence (a) that helicopters powered with a gas 

turbine engine were clearly more expensive than those powered with a piston engine—at 

equal total rated power, (b) that twin engines were more expensive than a single-engine 

configuration—at equal total rated power, (c) that the economic situation in Russia made their 

product very attractive from a selling point of view, and (d) that the U.S. military got a price 

break if they purchased large numbers in multi-year lots. 

 Let me leave you with one additional thought. The increase in list price when the base 

helicopter is equipped with modern avionics can easily amount to 20 percent, as we showed in 

the published paper. When you think about it, pricing avionics on a dollar-per-pound basis 

seems quite unreasonable. On a dollar-per-pound basis, a diamond, for example, just does not 

fit on Fig. 2-379. The trend over the last two decades seems (to me) to be to equip a basic air 

vehicle (i.e., the platform) with a growing suite of avionics that does not weigh very much—

and the avionics price is disproportional to the air vehicle price. Therefore, some additional 

effort that identifies how many avionics’ dollars are included in the “base” factory list price 

may well alter the price estimating relationship we offered in January of 1998. 
2.8 PURCHASE PRICE 

547 

$100,000

$1,000,000

$10,000,000

$100,000,000

$100,000 $1,000,000 $10,000,000 $100,000,000

Predicted Base Price In 1994 Dollars

27 Small Piston

 6 Large Piston(s)

 6 Turbine Conversions

31 Small Turbine

33 Light Twin

10 Medium Twin

 5 Large Twin + 2 Tri

"Actual"

FOB

List

 Price

in 1994

Dollars

Line O f

Perfect

Prediction

R-22

Sikorsky

S-51

Wood Blades

Bell

47G-2

BO 105 LS

MD 500E

206 B

SA 365 N-2

S-76C

EH 101

Mil-6

234 LR

S-61 N/L

AS 332 L-1

CH-53E

Fig. 2-380. Out of 121 helicopters, 106 are price predicted to within ±20 percent [584]. 

2.8.1.2 Productivity Per “Buck” 

 You will recall reading about productivity starting on page 115 in the discussion of 

weight. On page 116 you read that the industry frequently used an assumption that 

Payload Speed PV Productivity Per Dollar Weight Empty WE× ∝ =

and that weight empty could be used as a stand-in for cost. The basic assumptions were that 

(1) helicopter manufacturing costs, (2) the purchase price, (3) the user or operator’s costs, and 

(4) the end benefactor cost (say a passenger’s ticket price) ALL are proportional to the 

helicopter’s weight empty. In footnote 42 I pointed out that saying I am not in favor of these 

assumptions would be an understatement! On more than one occasion I have seen the focus 

placed solely on reducing weight empty regardless of the manufacturing or material costs. 

Sidestepping the issue of rotorcraft costs is not something I recommend. 

 Given some reasonably concrete list price data now available to you, it is possible to 

redefine productivity in terms of list price rather than weight empty. Of course, a customer 

would most certainly want to know what other financial considerations there are (such as 

operating costs). In fact, total life cycle costs passed on to the paying customer would be an 

even more comprehensive parameter to replace weight empty. For now, let me show you the 
2.8 PURCHASE PRICE 

548 

trend of productivity per “buck.” For the numerator, productivity, I choose useful load 

(i.e., the difference between takeoff gross weight and weight empty) times economical cruise 

speed. This product has the units of pound-knots or ton-knots. For the denominator, let me use 

factory list price for the equipped configuration in 1,000 dollars. Thus, 

(2.349) Useful Load Cruise Speed Productivity Per Dollar Equipped List Price in $1,000

× ≡

The trend of productivity in ton-knots per $1,000 is shown in Fig. 2-381. As you can see, I 

have added my suggestion of the boundary that few helicopters have exceeded. 

Notwithstanding my interpretation, however, it does appear that increased speed over the 

decades has not increased productivity per “buck” with edgewise flying rotors. The move 

from piston-powered helicopters (i.e., the black open circles) to turbine-engine-powered 

machines (i.e., the green open squares, the red solid triangles, the black x’s, and the solid 

black circles) raised useful load and cruise speed—but not enough to offset the accompanying 

increase in list price. Fig. 2-381 does, of course, raise the basic question of the value of speed. 

This question is not answered by the productivity per “buck” parameter chosen here. 

 To conclude this discussion of productivity, let me show you a figure that compares 

helicopters to fixed-wing aircraft. This comparison, shown in Fig. 2-382, is a somewhat 

different view than what Mike Scully and I offered in reference [584]. I must mention that 

Evan Fradenburgh175 was a great help to us when he read a draft of our work and initial 

thoughts about productivity per “buck.” In Fig. 2-382 you see that the fixed-wing aircraft 

have increased productivity per dollar by increasing speed. In quite sharp contrast, the 

helicopter industry has not achieved a similar result. You will note that the Type B Wright 

Flyer of 1911–1912, the Douglas DC-3, and The Lockheed Electra (the turboprop one) are 

convincing evidence that this segment of the transportation industry has capitalized on speed. 

 The reason that the helicopter has the adverse trend shown in Fig. 2-382 was explained 

in reference [584] as follows: 

 “The helicopter industry offers users increased productivity if they will pay more as 

figure 2 shows. The productivity that a 1994 dollar will buy is described by the simple, 

empirical equation 

( )0.75 PRODUCTIVITY (ton-knots) 0.00425 1994 Dollars =

This equation is the dark solid line near the top of the open and solid circle symbols on 

figure 2 and represents current technology and business pricing offered by the rotorcraft 

industry. The helicopter’s starting technology is measured by the dotted line lying below most 

of the circle symbols on figure 2 and approximated by the equation 

( )0.75 PRODUCTIVITY (ton-knots) 0.00215 1994 Dollars = 

 

175 Evan Fradenburgh was a superb engineer at Sikorsky whom I could turn to for advise on any rotorcraft 

subject. I thought his aerodynamic cleanup of the Sikorsky S-76 was quite a remarkable feat. His Nikolsky 

Lecture [382] was a very well deserved honor, and the paper is well worth your reading time. I felt the loss of a 

good friend when he died in May 2006. 
2.8 PURCHASE PRICE 

549 

0

0.05

0.1

0.15

0.2

0.25

0 20 40 60 80 100 120 140 160 180 200 220

27 Small Piston

6 Large Piston

6 Conversion to Turbine

31 Small Turbine

33 Light Twin Turbine

9 Medium Twin Turbine

4 Large Twin Turbine +1 Tri Turbine

Economical Cruise Speed (kts)

Productivity 

per $1,000

(ton-kts

per

$1,000)

Fig. 2-381. Increasing size and speed, and adding features, has not increased 

productivity per “buck.” Just the opposite has happened. 

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0 40 80 120 160 200 240 280 320 360 400

Productivity 

per $1,000

(ton-kts

per

$1,000)

Economical Cruise Speed (kts)

Fixed 

Wing

Helicopter

Wright Flyer 

Type B DC-3

Lockheed

Electra

Fig. 2-382. I really do not have an adequate explanation for the helicopter’s 

disappointing trend (but edgewise flying rotors may be at the heart of the matter). 
2.8 PURCHASE PRICE 

550 

These measures of the equipped helicopter’s place in the transportation world show that our 

industry has doubled productivity per 1994 dollar since our start with the Bell 47 and 

Sikorsky S-51. This progress is reflected by the constant 0.00215 increasing to 0.00425 in the 

above equations. The S-51 offered 1,500 pounds of useful load and 70 to 80 knot cruise speed 

for about $114,000 in 1953. Escalating 1953 dollars to 1994 dollars, following Figure 1, 

would make the S-51’s price today approximately $1.0 million. Today’s helicopter has almost 

twice the cruise speed for the same useful load which accounts in large measure for the 

increased productivity. 

 The rotorcraft industry justifiably takes pride in maturing the helicopter over the last 

five decades. However, a fixed wing advocate might point out that today’s modern gas turbine 

helicopter is about on par with such pre World War II airliners as the Ford Tri−motor and the 

legendary Douglas DC-3. Of course, this simple measure of productivity ignores (1) the 

helicopter’s unique ability to operate from very small vertiports and (2) the airliner’s need for 

long runways and dedicated terminal area airspace. 

 The downside to our efforts in maturing the helicopter is that productivity per “buck” 

has gone down as we have offered larger and more sophisticated products. This fact is 

demonstrated with a little simple math as follows: 

( )

( ) ( )

0.75

14 14

Productivity 0.00425 1 0.00425 1994 Dollars

1994 Dollar 1994 Dollar 1994 Dollar Size& Features = =∝

This formula says that the productivity per “buck” of a $1,000,000 equipped helicopter is 

about 134 ton-knots per $1M. However, for a $10,000,000 equipped helicopter, the 

productivity per “buck” goes down to 76 ton-knots per $1M. This adverse trend may well 

explain the slow sales of large, sophisticated, fully equipped helicopters.” 

2.8.2 Military Procurement 

 There is little question that selling helicopters in the civil marketplace is very, very 

different from fulfilling a military procurement request. After all, a commercial customer is 

buying off-the-shelf, so to speak. In contrast, the military most frequently asks for a 

replacement of an aging helicopter model in its fleet. Thus, satisfying the military frequently 

requires starting with a clean sheet of paper, and this requires application of research, new 

technology, and extensive development, all in a very competitive environment.176 

 In his book titled Stephen Morris [586], Nevil Shute (Norway)177 added an additional 

thought about the difference between the two purchasers. He has his fictional character (in 

England, just after World War I) saying: 

 “Two days later Morris started work in the design office of the Rawdon Aircraft 

Company (1919) Ltd. He did not find the work very difficult after the first few days. The 

whole business of designing an aeroplane he found to run on certain very definite lines. First 

 

176 I suggest again that you read Augustine’s Laws [582] to get a more complete view. It is more than a tonguein-cheek story of what must be considered in Department of Defense procurement.

177 Nevil Shute (Norway) is, by far, my favorite author. He was an aeronautical engineer by day and an author 

by night until his worldwide popularity became so great that he gave up the aviation industry to write full time. 

He used his full name in his engineering career and “Nevil Shute’ as his pen name in order to protect his 

engineering reputation. 
2.8 PURCHASE PRICE 

551 

of all, certain broad considerations governing the design of the machine came to the designer. 

Thus if it were a passenger machine for an air line, the air line had certain definite ideas as to 

what they wanted; the carrying capacity, the speed, the landing speed, and the “ceiling” or 

maximum height that it was possible for the machine to attain. Such considerations as these 

would be settled in conference with the designer, who would indicate tactfully where they 

were asking for technical impossibilities. If the machine were a military one for the Air Force 

the procedure was, in general, much the same, with the difference that the purchaser had a 

habit of asking for technical impossibilities and refusing to discuss the matter. This made the 

design of military machines a very specialized business.” 

 As president of a publically held company that only sells commercial helicopters, you 

are responsible for your employees while answering to your customers, your board of 

directors, and your stockholders. Now think about who you also answer to if you are the 

president of a company that designs and manufactures helicopters for, say, the United States 

Army. Now you are faced with several layers of authority, which I am suggesting in 

Fig. 2-383. As the military contractor, you face three immediate constraints: namely cost, 

schedule, and performance. Cost as used here means the price that the Army will pay for the 

sum of development, production, operation, and support; in effect, life cycle cost to the 

taxpayers. Schedule includes such meaningful points as first flight date and when the 

helicopter is introduced into service. Performance as used here is not just helicopter 

aerodynamic performance. Rather, performance may also include kill probability, system 

reliability, and many other parameters found in a system specification. 

 A military contractor takes several risks (over and above normal business risks) when 

doing business with the U.S. Government. Before discussing a number of these risks, you 

should be aware that there are two very common contractual arrangements that the 

U.S. Government

Senate

House

Supreme Court

DoD

Schedule

Cost

Performance

Military

Contractor

President

Fig. 2-383. Military contractors must meet the specification, stay within budget, and 

deliver on schedule. Unfortunately, it is a very rare occurrence when this 

happens. The reasons for this rarity are enumerated by Norm Augustine in 

Augustine’s Laws [582]. 
2.8 PURCHASE PRICE 

552 

Department of Defense enters into. The most risky for a military contractor is a fixed-price 

contract.178 The less risky type is a cost-plus-fee contract (the sum equals price). In the 

former, you, as president, may really be “betting your company” that your team can deliver 

what you promise within the time, and for the price, you quoted. If you underrun your quoted 

price, you will make a handsome profit. If you overrun your quoted price, your company may 

be deep in debt when the dust settles. 

 With a cost-plus-fee contract the U.S. Army (in my example) can expand the work 

statement by demanding many specification changes not originally envisioned, and the 

government pays the increased cost. Your company is financially protected (but maybe not 

your reputation), and you still receive the negotiated fee, but the program may be cancelled 

before you get the chance to make good on the finished product because of “requirements 

creep,” technical problems, cost growth, and schedule slippage.179 

 A number of risks that a military contractor must take when entering either type of 

contract were discussed in the Boeing Company 2011 Annual Report to stockholders [589]. 

With my paraphrasing, you must, as president, be prepared for at least the following: 

1. Your funding is subject to congressional appropriations and the government may 

modify, curtail, or terminate your contract(s) without prior notice and at its 

convenience. 

2. Your contract costs are subject to government audits. If the audit results are not 

satisfactory to any particular audit agency, you have the start of trouble. 

3. Your business is also open to potential government inquires and investigations, any 

one of which could result in fines or even prevent you from a future military 

business opportunity. 

4. All of your government work is subject to a raft of procurement regulations. 

5. You may well be overly dependent on subcontractors and suppliers, as well as on 

the availability of raw materials and components. 

6. Your risk assessment and cost and schedule estimates may be somewhat in error, or 

even just plain wrong. 

7. You have no assurance that you can successfully compete against current or future 

competitors. 

The above list is, of course, incomplete. One program that was successful, despite the odds, 

created the U.S. Army UH-1 series, which was produced by Bell Helicopter. 

 

178 Bell Helicopter entered into this contract type with the Army Helicopter Improvement Program (AHIP), 

which fielded the OH-58D [145]. Incidentally, the unpublished full-length copy of this conference paper [145] is 

available from the author. 

179 This is what happened to the RAH-66 Comanche program. You will find more detail about lessons learned 

from the Comanche program on the 12 CDs compiled by Bill Harper and Mike Richey [587]. Also, a case 

history about the LHX/RAH-66 program was published as a master thesis by Jason Galindo while at the Naval 

Postgraduate School in Monterey, California [588]. His review stops just before the RAH-66 development 

program was cancelled. 
2.8 PURCHASE PRICE 

553 

2.8.2.1 The Bell Helicopter UH-1 Program 

 In February 1955, shortly after the Korean War ended in July 1953 with an armistice, 

the U.S. Army announced the selection of the Bell Helicopter Corporation180 to develop a 

helicopter suitable for front-line casualty evacuation, utility missions, and instrument training. 

The Army’s requirement was for a turbine-engine- or piston-engine-powered helicopter. 

Twenty-one design proposals were received from nine contractors in October of 1954. (Note 

that the Army made its decision in less than 5 months.). Bell’s designation for its winning 

configuration was Model 204, which led to the commercial variant of early models of the 

Army’s “Huey.” 

 The Huey is almost universally accepted as the most successful helicopter ever 

produced (Fig. 2-384).181 To me, the parallel between the development and production of the 

Bell UH-1 and the Douglas DC-3 is uncanny. Like the DC-3, the UH-1 was initially available 

just before a major war. One hundred and seventy-three UH-1As were delivered by the end of 

1961 as U.S. involvement in Vietnam escalated, and both aircraft had a total production run of 

about 10,000 machines, counting both commercial and military versions. 

Fig. 2-384. About 2,500 D Model Hueys were produced. 

 

180 The Corporation started by Larry Bell later became a subsidiary of Textron, Inc., and it has been known 

informally as just Bell ever since. 

181 You should keep in mind that the Sikorsky UH-60 Black Hawks now number over 3,500 and production—

Ray Leoni [162] and I both believe—will continue for many more years. 
2.8 PURCHASE PRICE 

554 

191

45

8

27

3,187

205

2,674

1,769

173

0 500 1,000 1,500 2,000 2,500 3,000 3,500

UH-1N

TH-1L

UH-1L

HH-1K

UH-1H

UH-1E

UH-1D

UH-1B

UH-1A

Number Produced Through Fiscal Year 1970

Fig. 2-385. Nearly 8,300 Hueys were produced through fiscal year 1970. 

$0

$50,000

$100,000

$150,000

$200,000

$250,000

$300,000

0 500 1,000 1,500 2,000 2,500 3,000 3,500

Number Produced Through Fiscal Year 1970

UH-1A

UH-1D

UH-1B

UH-1N

UH-1H

UH-1E

HH-1K

UH-1L

TH-1L

Average 

Unit 

"Cost"

Fig. 2-386. Bell could agree to lower its average unit cost (maybe price?) when the U.S. 

Army ordered large quantities of Hueys, as they did during the Vietnam War. 
2.8 PURCHASE PRICE 

555 

 It is not often that an engineer stumbles across financial data of significant value, but 

during the later part of my career I did [590]. This report dealt primarily with weight-empty 

growth for several helicopters, which was my particular interest at the time, but, can you 

imagine, it included Huey development and production cost data by contract number. The 

report has no distribution list or notes about why it was created, and I can find no reference to 

it so I suspect it was not widely distributed. The authors did note, however, that 

“in a request for cost history of the UH-1, the AVSCOM procurement directorate provided an 

itemized list of 33 procurement contracts from FY 1955 through FY 1970.” 

Because of the inclusion of this data in reference [590], you can appreciate some quantified 

dollars and cents historical information that is quite interesting. 

 For example, it was pointed out that the U.S. Air Force was the contracting service for 

the Army’s start of the Huey development. The table included in the report [590] is 

reproduced here as Table 2-40 and lists not only Huey models but also the YAH-1G attack 

helicopter, popularly known as the Cobra. What you should particularly note is getting from 

the XH-40 (three experimental aircraft) through to nine preproduction HU-1As consumed just 

over 29 million dollars of Department of Defense (DoD) money. This research and 

development investment, plus another $20 million for 16 more models, allowed the Army to 

procure the nearly 8,300 Hueys shown in Fig. 2-385. For this production quantity, the DoD 

paid Bell $1,176 billion. Just think about these numbers for a minute or two. A production line 

amounting to $1,176 billion for a very successful helicopter was established, and the initial 

Research and Development investment was $49 million, which is 4.2 percent of the total cost. 

 Do not forget, however, that this is an example during a wartime situation. The 

Vietnam War led to a very large requirement for several models of Hueys, which, in turn, led 

to Bell learning how to produce in quantity more and more efficiently. This learning allowed 

Bell to reduce the average cost of a Huey, as I have illustrated in Fig. 2-386. Here I have just 

graphed the tabulated data provided by reference [590]. This is a parallel example to how the 

United States dealt with production during World War II. Certainly, it is a parallel to how 

Douglas Aircraft learned to produce DC-3s [314]. 

 This brings me to the subject of a “learning curve.” 

Table 2-40. R&D Contracts Leading to Huey Production 

Contract No. Type Model Qty Unit Price Total Contract Price 

 AF33(600)30229 CPFF R&D XH-40 3 4,418,460.00 13,255,382.00 

 AF33(600)33710 CPFF R&D YH-40 6 1,681,614.00 10,089,684.00 

 AF33(657)34920 CPFF R&D HU-1A 9 643,393.11 5,790,538.00 

 AF33(600)39616 CPFF R&D HU-1B 5 1,350,285.20 6,751,426.00 

 AF33(600)41636 CPFF R&D YUH-1D 7 1,707,137.14 11,949,960.00 

 AF33(657)9777 CPFF R&D UH-1E 4 423,007.25 1,692,029.00 

 DA23-204-AMC-04075 CPIF Supply YAH-1G 2 3,795,000.00 7,590,000.00 
2.8 PURCHASE PRICE 

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2.8.2.2 The Learning Curve 

 You can see from Fig. 2-386 that as the number of helicopters produced increases, it 

appears that the cost per unit decreases. An observation of this sort was publically stated in 

February 1936 by Mr. T. P. Wright.182 His paper, which you will find in the Journal of the 

Aeronautical Sciences (now the A.I.A.A.) [591], is fascinating for two reasons. I suppose the 

first reason is that his paper must be referenced in every follow-on discussion of aircraft costs 

and cost estimating that has ever been published. More importantly, his compilation of factors 

affecting the cost of airplanes has stood the test of time. Wright provided evidence that, 

among other factors, quantity affects airplane costs. While he never uses the words “learning 

curve” in his 1936 paper, those are the descriptive words used by every author who studied 

this particular factor. 

 Wright says in his introduction that 

 “the effect of quantity production on cost, particularly, requires study as in this 

respect more than in others, there exists a lack of appreciation of the variation which occurs. 

Recently the matter became of increasing interest and importance because of the program 

sponsored by the Bureau of Air Commerce for the development of a small two-place airplane 

which, it was hoped, could be marketed at $700 assuming a quantity of ten thousand units 

could be released for construction. 

 The present writer started his studies of the variation of cost with quantity in 1922. A 

curve depicting such variation was worked up empirically from the two or three points which 

previous production experience of the same model in differing quantities made possible. 

Through the succeeding years, this original curve, which at first showed the variation in labor 

only, was used for estimating purposes and was corrected as more data became available. The 

form which this curve takes when plotted on plain cross-section paper is shown in fig. 1 

[shown here as Fig. 2-387]. On this figure there is also shown the variation of the ratio of 

labor to raw material as quantity varies. The correcting of curves of this type by new points of 

actual experience resulted in data which permitted other curves to be plotted, showing the 

variation of raw material, purchased material, and finally, of the whole airplane, against 

quantity.” 

After discussing the influence of design factors, tooling, changes, and size, he notes that 

 “in developing the curve which shows variation of labor cost with production 

quantity, it became evident that its form was of the type depicted by the formula F = Nx

.” 

and the formula became known as the Wright’s Learning Curve. 

 The cost sum of labor, material, and tools gave Wright the dashed line shown in 

Fig. 2-387, which he elected to approximate with his F = Nx formula. More specifically, 

Wright points out with his dashed line that his experience strongly suggests that the behavior 

is calculated as 

(2.350) x

Approximate Cost of the Last Machine of a Series 1

Cost of the First Machine N =

 

182 At the time, Theodore Paul Wright was Chief Engineer and Manager of the Curtiss–Wright plant in Buffalo, 

New York. Wright was head of the Civil Aeronautics Administration from 1944 to 1948. He died in August of 

1970. 
2.8 PURCHASE PRICE 

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Fig. 2-387. T. P. Wright’s starting point for the “learning curve.” 

where (N) is the number of the last machine in the production lot, and (x) is some number that 

fits a manufacturer’s experience, or perhaps hope, or perhaps a military negotiated 

expectation. The dashed line in Fig. 2-387 that Wright uses as an example assumes x = 0.322. 

Thus, if N = 40, then the approximate cost of the 40th machine, as fraction of the cost of the 

first machine, will be 1/400.322, which equals 0.305. 

 As Wright’s observations became apparent to other manufactures, particularly during 

World War II, a number of other ways to mathematically say the same thing came into the 

economic literature. Personally, I prefer stating Wright’s observation as 

(2.351) ( ) [ ]

log N

log 2 Cost of Aircraft N First Aircraft Cost LCF N 1

      = =

where [LCF] stands for learning curve factor. This factor ranges from perhaps as low as 0.70 

to hopefully no more than 1.0. In this form, the dashed line in Fig. 2-387 has an LCF = 0.8. 

You will frequently hear cost estimators say, “Let’s assume a learning curve of 80 percent as 

part of our cost estimate.” You should keep in mind that while Eq. (2.351) uses the word 

“Cost,” the learning curve can apply to labor hours, or price, or many other units. Wright 

made his initial observation from labor hours as Fig. 2-387 shows. 

 As you read Wright’s milestone paper, you will begin to realize that he is about to 

debunk the Bureau of Air Commerce’s objectives for its Small Plane program. The Bureau 

was saying that the total number of airplanes to be built was to be 10,000 and that anyone 
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could buy one for $700 (i.e., the price). As Wright’s reasoning unfolds, he tackles (at the end 

of his paper) the $700 airplane Small Plane program that the Bureau of Air Commerce was 

proposing. He first suggests that the general specifications for a “small two-place airplane” 

would be: 

Useful Load 700 lb 

Weight Empty 1,100 lb 

Gross Weight 1,800 lb 

Structural Weight 800 lb 

Engine 100 to 125 h.p. 

High Speed 125 to 150 m.p.h. 

Speed Range 3 [This is the ratio of maximum speed to stall speed] 

Material All metal 

Then, to make his point, he assumes that the price estimate in a small production lot of 25 

would be on the order of: 

Cost (1,100 lb weight empty @ $6/lb) $6,600.00 

Profit (manufacturing, at 10%) $660.00 

Sales Discount (20%) $1,815.00

 Price $9,075.00 

which he rounds off to $9,000 by expecting to get a break on the engine cost. Then, pricing 

production in several lot sizes assuming the price for the first article is $16,356 and a constant 

LCF of 0.83, he tabulates (with my editing)183

Quantity 25 100 500 1,000 10,000 

Selling Price by Lot Size $9,000 $6,372 $4,184 $3,481 $1,880 

Total Income (P×Q) $225,000 $637,200 $2,092,00 $3,480,500 $18,797,000

With these financial figures on the table, Wright concludes: 

“We thus see that for a plane of these specifications and in the original quantity cited by the 

Bureau of Air Commerce when commencing its $700 Small Plane program, [the airplane] 

would have to be priced at about three hundred percent more than was hoped. Perhaps some 

reductions from the estimate could be effected by altering construction, design, and reducing 

sales discounts and profits (although by so doing the ten thousand units would probably never 

be sold) but in the quantity of ten thousand units which is under consideration, it is doubtful 

whether a price of less than $1,750 could possibly be attained.” 

You should note that the total cost (or total income in this case) is computed simply as 

(2.352) 

( ) ( ) ( ) { }

N

1

st log2 log2 log3 log2 log N log2

Cost of N Aircraft P Q Cost of Aircraft N

Cost1 Aircraft 1 LCF LCF ... LCF

=× =

= + + ++



and that the selling price for each aircraft in a given lot (i.e., P) can be closely approximated 

with 

 

183 Wright appears to have obtained his approximate figures with graphs and a slide rule. I used Excel®. 
2.8 PURCHASE PRICE 

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(2.352) ( ) { } st 2 3 1.573 log N 0.693(log N) 0.0692(log N) P Cost 1 Aircraft LCF + − = . 

 When I first became interested in the “learning curve,” I came across an article in the 

November 1952 copy of Aero Digest written by a Mr. W. A. Raborg, then employed by 

Northrop Aircraft, Inc. Several paragraphs from his paper stuck with me and you may also 

find them interesting (because a few hundred thousand papers and reports have been 

published trying to extend, refine, make more complex, and apply Wright’s original work). 

For example, Raborg wrote [592] in 1952 (with my editing and additions in brackets) that 

“by the end of World War II, the major aircraft companies had rather generally recognized the 

value of the [learning] curve by its application to their own particular production data. The 

smaller companies, however, comprising most of the sub-contractors, had little knowledge of 

its use. The United States Government had also come to recognize the importance of the 

learning curve. In order to strengthen the aircraft industry for future military requirements, the 

Government distributed World War II aircraft production data to all contributing companies

[my italics]. In addition, the Government sponsored several research projects with private 

organizations to develop further the application of the theory. Probably the best known of 

these was the work done by the Stanford Research Institute which was later made available to 

the various Aircraft companies.” 

The World War II aircraft production data that Raborg mentions was published with the title 

Source Book of World War II Basic Data: Airframe Industry, Volume I—Direct Man-Hours –

Progress Curves [593]. No date shows on this 200-page document, but data is included from 

January 1940 through December 1945, so for reference purposes I have used 1946. This 

Source Book is the foundation for nearly all studies applying and extending Wright’s 

Learning Curve. The Source Book tabulates labor man-hours for the Boeing B-29 through to 

Sikorsky’s R-4, R-5, and R-6. One thing I have found absolutely fascinating (over and above 

the four massive tables) is the Direct Labor Progress Curves (i.e., learning curves) that show 

actual data for direct man-hours per airframe unit weight plotted versus cumulative plane 

number. Table 3 of the Source Book states that 

“airframe Unit Weight is the airplane weight empty minus the total weight of the following 

items: 

engine (dry weight); 

propeller hubs, blades, power control and governor; 

wheels, brakes, tires, and tubes; 

auxiliary power plant; 

turbo-superchargers; 

radio receivers, transmitters, radar and removable units, but not installation parts and wiring; 

starter; 

battery; 

generator, turrets and power-operated gun mounts. 

The source of these data is the Airframe Unit Weight reports which were issued periodically 

by predecessors of the Air Materiel Command. Changes in Airframe Unit Weight from one 

month to the next may indicate a change in the basic model. Where variations of the same 

basic model with different airframe unit weights (such as A-20G and A-20H at Douglas—

Santa Monica) were accepted in the same month, a weighted average airframe unit weight 

figure was calculated, weighted by the number of acceptances. The data from the Airframe 

Unit Weight Reports are rounded to the nearest hundred; the weighted average data are not 

rounded off.” 
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 On each figure you have the facility, the aircraft model, and the airframe unit weight 

noted. The accumulated data from bombers, fighters, transports, light planes, helicopters, etc., 

really does not support the use of man-hours per pound as a fundamental parameter as you 

will conclude, as I have, after thumbing through the 129 figures. But because the unit airframe 

weight varies so much with aircraft type, and to a lesser extent with what factory was building 

that type,184 the parameter is useful in keeping the same scales for all types. 

 Let me give you an example of learning curve data from two aircraft that you will find 

in table 4 of the Source Book, with associated graphs in the Source Book’s appendix. Keep in 

mind that it is World War II production data that is under discussion. First of all, you can see 

from Fig. 2-388 that learning curve data is almost always plotted on a log-log axis system, 

which Wright pointed out in his original work is preferable. This axis system is particularly 

handy because the basic hypothesis given by Eq. (2.351) becomes an intercept and a slope. 

You see this when you take the logarithm of both sides of Eq. (2.351) 

(2.353) ( ) ( ) [ ]

log N

log 2 N 1 log Cost of Aircraft N log First Aircraft Cost LCF

      =

  =    

, 

which gives you 

(2.354) ( ) ( ) ( ) ( )

( )( )

N 1 log First Aircraft Cost log LCF log Cost of Aircraft N log N log10 log 2 log10

A Blog N

=  

= +  

 

= +

. 

 You will note on Fig. 2-388 that I have “eyeballed” linear lines that I think best fit the 

learning curves for these two aircraft. From the lines, I calculated the learning curve factor 

(LCF) quite simply as 

(2.355) 

log2

Cost of Aircraft N log N

LCF

First Aircraft Cost

      

=     . 

Using the Boeing B-29 as an example, you have 

(2.356) 

log 2 0.301

0.27 mh/lb log10,000 0.27 4

LCF 0.705 for B 29

28 mh/lb 28 

              

= == −       , 

and for the Sikorsky R-6 (built in quantity by Nash–Kelvinator in Detroit, Michigan) you 

obtain an LCF of 0.715. 

 It should be clear that estimating cost (in any units) of the Nth aircraft a priori can be 

simply an educated guess, but given some previous actual data, the guess may, with 

considerable luck, not be in error by more than ±25 percent [594]. 

 

184 For example, the Boeing B-29 was built by Boeing in Renton, Washington, and Wichita, Kansas; by Bell 

Aircraft Corporation in Marietta, Georgia; and by the Glenn L. Martin Company in Omaha, Nebraska. Clearly 

the factories were quite dispersed and not always near what we would call headquarters. 
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10000, 0.27

1, 28

1, 42

1000, 1.5

0

1

10

100

1 10 100 1,000 10,000

Manhours

per

Unit 

Weight

(hr/lbs)

Cumulative Aircraft Number

Boeing B-29 Built at Boeing's Wichita, Kansas Plant

Airframe Unit Weight = 48,100 to 49,700 lbs

Feb. 1943

Sept. 1945

Sikorsky R-6 Built at Nash Kelvinator Corp. Plant in Detroit, Michigan

Airframe Unit Weight = 1,450 lbs

Oct. 1944

Aug. 1945

0.1

Fig. 2-388. T. P. Wright’s observations about how quantity affects cost were reaffirmed 

based on data gathered during World War II [593]. 

 In view of what you have read, let me now reexamine the Bell Huey data provided in 

Fig. 2-386. The points shown in this figure came from the following tabulated information 

(Table 2-41) [590]. There are a few points to be made about this data. First of all, this is data 

for a cost-plus-fee type of contract. What the actual numbers at contract completion were are 

probably available—in some file somewhere. Second, I do not know if the engine (and other 

assemblies) were furnished to Bell, and therefore they may not be included in the unit price.185

Table 2-41. Some Production Contracts for Hueys [590] 

Fiscal 

Year Contract No. Model Qty Unit Price 

Total Contract 

Price 

Cum 

Qty 

Cum 

Dollars 

 AF33(600)36024 HU-1A 47 414,342 19,474,100 47 19,474,100 

 AF33(600)38615 HU-1A 110 217,726 23,949,921 157 43,424,021 

 AF33(600)40447 HU-1A 16 197,360 3,157,764 173 46,581,785 

 AF33(600)40447 HU-1B 74 270,553 20,020,947 247 66,602,732 

 AF33(600)41900 HU-1B 118 246,178 29,048,958 365 95,651,690 

 AF33(657)7001 UH-1B 315 183,379 57,764,490 680 153,416,180 

 AF33(657)10000 UH-1B 289 254,707 73,610,237 969 227,026,417 

 AF33(657)11111 UH-1B 272 135,771 36,929,712 1241 263,956,129 

 AF33(657)11111 UH-1B 18 132,701 2,388,629 1259 266,344,758 

 AF33(657)7001 UH-1B(MAP) 8 183,394 1,467,150 1267 267,811,908 

 AF33(657)11111 UH-1B(RAN) 3 171,902 515,706 1270 268,327,614 

1965 DA 230204-AMC-02805(Y) UH-1B 149 125,833 18,749,117 1419 287,076,731 

 

185 Webb Joiner, whose first job at Bell was assistant to then Bell CFO Jim Atkins, mentioned in private 

correspondence [595] that “The early contracts, that covered the major part of the aircraft deliveries, were fixed 

price target incentive contracts. At the beginning of the contract we negotiated a target cost and a target profit 

along with a sharing factor (rate) for overruns on cost and normally a different sharing factor for underruns. As 

we worked the contract we filed quarterly estimates to adjust interim cash flow to Bell and at the end of the 

contract we had a second contract negotiation to determine final cost and contract price. The final price of each 

contract was different from the original price. This final price was incorporated into the contract by an 

amendment. I also want to remember that some of the later contracts were pure fixed price.” Webb also told me 

that “The engines, I believe in every contract, were Government Furnished Equipment (GFE) to Bell; also 

avionics, small dollar amounts—primarily radio equipment, was also GFE to Bell. So the cost of these items was 

not in Bell's contract values.” Jim Atkins, then Jack Hoerner, and then Webb Joiner later became presidents of 

Bell, and it was my good luck to have worked at Bell during the period of their outstanding leadership. 
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Table 2-41. (continued) 

Fiscal 

Year Contract No. Model Qty Unit Price 

Total Contract 

Price 

Cum 

Qty 

Cum 

Dollars 

1965 DA 230204-AMC-02805(Y) UH-1B 8 130,976 1,047,808 1427 288,124,539 

1965 DA 230204-AMC-02805(Y) UH-1B 6 145,419 872,514 1433 288,997,053 

1965 DA 230204-AMC-02805(Y) UH-1B 1 133,342 133,342 1434 289,130,395 

1965 DA 230204-AMC-02805(Y) UH-1B 4 129,294 517,176 1438 289,647,571 

1965 DA 230204-AMC-02805(Y) UH-1B 1 160,024 160,024 1439 289,807,595 

1966 DA 23-204-AMC-03501(T) UH-1B 500 127,498 63,749,000 1939 353,556,595 

1966 DA 23-204-AMC-03501(T) UH-1B 1 119,835 119,835 1940 353,676,430 

1967 DAAJ01-67-C-0025(B) UH-1B 2 167,694 335,388 1942 354,011,818 

 AF33(657)7001 UH-1D 30 436,764 13,102,930 1972 367,114,748 

 AF33(657)11111 UH-1D 410 172,952 70,910,320 2382 438,025,068 

1965 DA 230204-AMC-02805(Y) UH-1D 571 136,711 78,061,981 2953 516,087,049 

1965 DA 230204-AMC-02805(Y) UH-1D 4 133,302 533,208 2957 516,620,257 

1965 DA 230204-AMC-02805(Y) UH-1D 45 121,590 5,471,550 3002 522,091,807 

1966 DA 23-204-AMC-03501(T) UH-1D 1613 114,599 184,848,187 4615 706,939,994 

1966 DA 23-204-AMC-03501(T) UH-1D 1 122,003 122,003 4616 707,061,997 

 AF33(657)9779 UH-1E 29 265,097 7,687,805 4645 714,749,802 

 AF33(657)11112 UH-1E 48 156,361 7,505,328 4693 722,255,130 

1964 DA 23-204-AMC-02897(X) UH-1E 24 137,574 3,301,776 4717 725,556,906 

1964 DA 23-204-AMC-02897(X) UH-1E 28 142,755 3,997,140 4745 729,554,046 

1966 DA 23-204-AMC-04011 UH-1E 31 144,042 4,465,302 4776 734,019,348 

1966 DA 23-204-AMC-04011 UH-1E 27 145,433 3,926,691 4803 737,946,039 

1967 DAAJO1-67-C-0030(B) UH-1E 18 171,259 3,382,500 4821 741,328,539 

1967 DAAJ01-67-C-0025(B) UH-1H 769 130,401 100,278,369 5590 841,606,908 

1967 DAAJ01-67-C-0025(B) UH-1H 1 141,745 141,745 5591 841,748,653 

1967 DAAJ01-67-C-0025(B) UH-1H 3 138,223 414,669 5594 842,163,322 

1967 DAAJ01-67-C-0025(B) UH-1H 9 156,345 1,407,105 5603 843,570,427 

1967 DAAJ01-67-C-0025(B) UH-1H 2 133,317 266,634 5605 843,837,061 

1967 DAAJ01-67-C-0025(B) UH-1H 3 133,346 400,338 5608 844,237,399 

1967 DAAJ01-67-C-0025(B) UH-1H 4 138,060 552,240 5612 844,789,639 

1967 DAAJ01-67-C-0025(B) UH-1H 10 141,605 1,416,050 5622 846,205,689 

1968 DAAJO1-67-C-0566 UH-1H 528 125,952 66,502,656 6150 912,708,345 

1968 DAAJO1-67-C-0566 UH-1H 1 132,242 132,242 6151 912,840,587 

1968 DAAJO1-67-C-0566 UH-1H 4 130,691 522,764 6155 913,363,351 

1968 DAAJO1-67-C-0566 UH-1H 1 133,710 133,710 6156 913,497,061 

1968 DAAJO1-67-C-0566 UH-1H 2 131,333 262,666 6158 913,759,727 

1968 DAAJO1-67-C-0566 UH-1H 6 125,952 755,712 6164 914,515,439 

1968 DAAJO1-67-C-0566 UH-1H 16 148,117 2,369,872 6180 916,885,311 

1968 DAAJO1-67-C-0566 UH-1H 3 125,952 377,856 6183 917,263,167 

1968 DAAJO1-67-C-0566 UH-1H 1 131,326 131,326 6184 917,394,493 

1968 DAAJO1-67-C-0566 UH-1H 11 129,202 1,421,222 6195 918,815,715 

1968 DAAJO1-67-C-0566 UH-1H 4 125,952 503,808 6199 919,319,523 

1968 DAAJO1-67-C-0566 UH-1H 8 125,952 1,007,616 6207 920,327,139 

1968 DAAJO1-67-C-0566 UH-1H 546 125,952 68,769,792 6753 989,096,931 

1968 DAAJO1-67-C-0566 UH-1H 6 125,592 755,712 6759 989,852,643 

1968 DAAJO1-67-C-0566 UH-1H 12 125,592 1,511,424 6771 991,364,067 

1968 DAAJO1-67-C-0566 UH-1H 11 125,592 1,385,472 6782 992,749,539 

1969 DAAJ01-69-C-0028(2B) UH-1H 1226 130,409 159,881,730 8008 1,152,631,269 

1968 DAAJ01-68-C-1911(B) HH-1K 27 209,688 5,661,563 8035 1,158,292,832 

1968 DAAJ01-68-C-1911(B) UH-1L 8 209,698 1,677,500 8043 1,159,970,332 

1968 DAAJ01-68-C-1911(B) TH-1L 45 209,688 9,435,938 8088 1,169,406,269 

1969 DAAJ01-69-C-0085(2B) UH-1N 79 265,000 20,935,000 8167 1,190,341,269 

1970 DAAJ01-70-C-0205 (Navy) UH-1N 62 302,112 18,731,000 8229 1,209,072,269 

1970 

DAAJ01-70-C-0234 

(Canadian) UH-1N 50 265,000 13,250,000 8279 1,222,322,269 
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 Notwithstanding some reservations about data contained in reference [590], let me 

proceed with a simple analysis. In Fig. 2-389 you see the accumulating contract awards to 

Bell (in millions of dollars) plotted versus aircraft numbers to be delivered. Excel’s regression 

analysis (i.e., the trendline tool) of this data offered the opinion that 

(2.357) ( )0.80632 2 Cum Dollars $809,600 N R 0.9988 = = . 

I chose to round off the price of the first aircraft (i.e., N = 1) at $800,000. Then I applied 

Eq. (2.352), adjusting the LCF until the resulting line on Fig. 2-389 looked “close enough.” 

This process gave an LCF of 0.857. On this basis, you have the opinion that the learning 

curve for Bell, while producing the Huey over the fiscal years 1960 to 1970, was 

(2.358) [ ]

log N

Price of Huey N $800, 000 0.857 log 2

    =   . 

 It is quite important for you to appreciate that the analysis arriving at Eq. (2.358) 

includes the influence of inflation. During World War II, prices were fixed, but during the 

decade of the 1960s, helicopter selling prices slightly exceeded the U.S. Consumer Price 

Index as figure 1 of reference [584] illustrates. Using a value of unity in 1950, this reference 

arrived at an inflation factor of 1.292 in 1960 and 1.855 in 1970. This means that the price of 

the 8,000th Huey of about $108,180 reflected about a 43 percent increase over the 10-year 

period. That is, the price of the 8,000th Huey should have been, without inflation, only about 

$61,660. This means that the LCF was actually closer to 0.815, which is considerably better 

that the LFC of 0.857 you see with Eq. (2.358). 

$0

$200

$400

$600

$800

$1,000

$1,200

$1,400

0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000

HU-1A

UH-1B

UH-1D

UH-1E

UH-1H

HH-1K, UH-1L, TH-1L

UH-1N

From Learning Curve With

Price First Aircraft = $800,000

Learning Curve Factor = 0.857

Cum 

Income 

From 

Huey 

Military

Sales

(Millions)

Numbers Sold (N)

Fig. 2-389. Bell Helicopter’s approximate income from military sales of the Huey. 
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 Let me conclude this discussion with other paragraphs Mr. Raborg [592] included in 

his 1952 Aero Digest article: 

 “The staff organizations of the aircraft companies, which had become familiar with 

the applications of the learning curve during World War II, however, dwindled to skeleton 

forces during the post war period of reduced production. Now, as the industry is expanding its 

production again, much of the experience gained in World War II must be repeated for, or at 

least brought to the attention of, the newer employees. Relatively few persons understand the 

application of the learning curve, and there are few accurate references on the subject. 

 The problem is even more serious now than before. During the growth of airplane 

manufacture from 1940 to 1945, the learning curve was used almost exclusively by 

management and its staff groups, and little interest in its use appeared anywhere in the line 

organization. Today, however, the general acceptance of the curve by management and by the 

Government has led to its recognition by the shop as well. Production departments, that is, 

personnel on the line, knowing that it is a tool which they are expected to use, are now 

accepting the theory and asking for technical assistance in its use. Probably the most versed 

persons on the subject arc still among management, and certainly one of the prerequisites for 

production management positions is a thorough understanding of its application. 

 Some idea of the importance of the learning curve may be seen from the fact that: 

(1) Military planners use the learning curve to estimate the nation’s 

aircraft mobilization expansion potential. Air Force equipment, pilots, 

ground crews and supporting personnel, training schools, etc., are all 

closely coordinated with aircraft production, and therefore reflect the 

reliability of the learning curve theory; 

(2) The Government uses the learning curve to measure [an] aircraft 

manufacturer for efficiency and production; 

(3) The Government checks [an] aircraft manufacturer’s bids for 

accuracy and reasonableness. This examination is largely based upon 

statistical analysis of the manufacturer’s own record with respect to 

general industry production performance; 

(4) Aircraft manufacturers use the learning curve in preparing bids for 

new business; 

(5) Aircraft manufacturers use the learning curve in developing labor 

loads, area and equipment requirements, shop efficiency measures, 

budgets, and often standards; and 

(6) Aircraft manufacturers use the learning curve to measure the 

progress of active contracts. This is often the basis for contract 

payments and loans.” 

The statements Mr. Raborg made seem to me to be every bit as applicable today as they were 

in 1952. In fact, his statement that “relatively few persons understand the application of the 

learning curve, and there are few accurate references on the subject” may be even more 

correct today. It is absolutely amazing to me how successive investigators have cast Wright’s 

simple observation [596, 597] into many different (and more complex) forms. However, there 

is, I think, one noteworthy exception published in 1959 by John Nichols of Hiller Aircraft 

Corporation [598]. 
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2.8.2.3 Design to Cost 

 T. P. Wright’s paper can certainly be classified as a milestone because it introduced the 

learning curve, but stop for a moment. His application was, in fact, to the Bureau of 

Commerce plan to create a market for a $700 small plane in 1936. To me, this was a very 

early example where designing to meet a price was the objective. The whole concept of 

designing to meet a selling price was finally put into a major Department of Defense policy 

statement and labeled Design to Cost. This policy [599] was released in October 1977 with 

the title Joint Design-to-Cost Guide, Life Cycle Cost as a Design Parameter. This guide starts 

with a one-page foreword (dated 9 January 1976) signed by three generals and one admiral186

who said: 

“We approve this revised ‘Guide on Design to Cost’ for use within our commands. It provides 

information and guidance for application of the Design to Cost concept. 

Since the first edition of this Guide in October 1973, there have been numerous applications 

of Design to Cost in both major and non-major system, sub-system and component 

developments. The great majority of these applications have been limited to ‘unit production 

cost.’ Although no Design to Cost program has yet matured to the point at which "lessons 

learned" can be garnered from factual cost data, we are convinced from evidence in hand that 

the concept works and will be of great benefit. 

However, the concept can and must be expanded beyond unit production cost to include 

operating and support costs. Approaches which concentrate on those operating and support 

costs which are design sensitive are currently available even in the absence of a uniform, 

useable and historical data base for all operating and support costs. 

We seek a favorable balance among the elements of life cycle cost, (development, production, 

operating and support costs) and the performance of every system. 

There are no easy steps in designing a complex weapon system to established cost goals. The 

DOD and contractors must be committed, effectively communicate and maintain essential 

effort toward achieving the established Design to Cost goals. 

Supplemental instructions may be issued by the individual commands.” 

The guide further notes that “several cost effective weapon systems have recently been 

developed which, because of their cost, were not affordable in adequate numbers to satisfy 

mission requirements, necessitating additional lower cost developments.” The purpose of the 

guide (to solve this problem) was, and still is, “to establish life cycle as a design parameter 

during a system’s design and development phase and provide a cost discipline to be used 

throughout the acquisition of a system.” The trend Augustine provided earlier (Fig. 2-373) 

sums up the whole situation quite clearly—as far as I am concerned in this introductory 

volume. 

 The guide also introduced the Work Breakdown System (WBS) in its appendix A. The 

purpose of the WBS was to ensure that performance, cost, and schedule (see Fig. 2-383) of 

future system acquisitions would be more carefully monitored. By 2011, appendix A of the 

 

186 General John R. Deane, Jr. as Commander of the U.S. Army Material Command; General William J. Evans 

as Commander of the Air Force System Command; General F. W. Rogers as Commander of the Air Force 

Logistics Command; and Admiral F. H. Michaelis for the Naval Material Command. 
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guide had grown to a 251-page document and had become a military standard now known as 

MIL-STD-811C [600]. 

 On a personal note: The guide has been the “bible” for over four decades, yet I have 

not found any quantitative evidence that the DoD and its contractors’ basic problem has been 

solved by using the Design-to-Cost Guide (but then, I have hardly made a thorough search). 

My view is that the guide does not address human frailties, misbehaving hardware (be it 

mechanical or electronic), or computer software that has gone off course. In being a part of 

the team that fielded the OH-58D [145], I rarely viewed the WBS as anything more than data 

for economic historians. To me, successful development is only accomplished by a small team 

lead by a great designer like Kelly Johnson [581] or Ed Heinemann [601], and only then if 

they are unencumbered by monitors, accountants, watchers, calendars, and WBS computer 

printouts. To me, successful production is only accomplished by a company having very 

strong engineering and manufacturing voices, and led by someone like Donald Douglas [314] 

or William M. Allen, who was president of Boeing from September 1945 to April 1968, and 

later chairman of the board. I am convinced that creating a guide and a system that models 

men like the ones I have acknowledged cannot be done. 

 In the 1970s, a number of papers and reports were published that (a) aimed at more 

accurate cost estimating [602], (b) suggested how to establish a designer’s cost target [603], 

(c) described planning a product [604], and (d) dealt with tradeoffs between cost and 

performance [605], etc. Much of this information was derived from commercial practices 

even for general aviation products [604], which is the category where the FAA places 

commercial helicopters. 

 In the papers and reports just referenced, you will read comments that the product’s 

price is nearly set in concrete during the conceptual design phase. I firmly believe this to be 

absolutely true. Consider this upfront decision: when a military or commercial customer 

chooses a helicopter instead of a fixed-wing aircraft for his mission, he has already accepted a 

50 percent surcharge for the vertical takeoff and landing capability—according to reference 

[584]. 

 But let me proceed, given the decision by military planners that a new helicopter is 

required. The next two major cost decisions are whether to use a piston or a gas turbine 

engine and whether to have one or two engines. By making state-of-the-art decisions of twin

gas turbines, you increase the lowest cost configuration by factors of 1.344 and 1.794, 

respectively, as Eq. (2.348) shows. The expectation from these two decisions is, of course, 

that life cycle cost savings over, let’s say, 30 years, will easily cover the higher unit cost. 

 With these three major cost-driving decisions made, put yourself in a very high-level 

position and you must give U.S. Army go-ahead approval for development and production of 

a new helicopter. For example, say you are in Mr. James Ambrose’s shoes187 and wrestling 

with the new Light Helicopter (LHX) that the Army Training and Doctrine Command 

 

187 James Ambrose was the Under Secretary of the Army (from October 1981 to February 1988) who approved 

the LHX go-ahead. 
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(TRADOC) says is required in the near future. This was, in fact, exactly what happened 

during the birth of the LHX program that led to the RAH-66 Comanche. At that time the 

configuration was presented as having a weight empty of 7,500 pounds, powered with two gas 

turbines each rated at 1,300 horsepower, and the average price (perhaps you would prefer 

cost) of $5.3 million (capped by Congress) in a fielding of up to 7,000 machines.188 The 7,000 

LHXs were to replace Hueys, OH-58s, OH-6s, and the AH-1 Cobras. The total development 

and production program (including the yet to be developed engine!) was estimated at $37 

billion [606]. 

 Now take a minute to reflect on the baseline that 7,000 LHXs are to be delivered at an 

average price of $5.3 million each, for a total of $37.1 billion. Given Bell Helicopter’s 

performance in delivering over 8,000 Hueys, let me assume an LCF of 0.857, which includes 

some inflation. Working backwards using Eq. (2.352), you will find that the price of the first 

production RAH-66 is $29.6 million and that the price estimate of the Nth RAH-66 will be as 

follows: 

(2.359) [ ]

log N th Price of the N RAH-66 $29,593,000 0.857 log 2

    =   . 

 It is quite interesting to compare the first Huey aircraft price of $0.8 million obtained 

with Eq. (2.358) to the first RAH-66 aircraft price of $29.6 million arrived at with 

Eq. (2.359). This is a first-aircraft price ratio of 37 to 1. No doubt many readers will be simply 

taken aback and left wondering if the RAH-66 would have provided the military with a 

correspondingly better machine (if the program not been cancelled). However, at least four 

major design-to-cost factors created this price ratio. I believe the major design-to-cost factors 

are: 

 1. General inflation of helicopter prices (quite apparent in the commercial world), 

 2. Significant basic helicopter configuration changes, 

 3. Addition of major advancements in mission equipment, and 

 4. Procurement quantities. 

Let me discuss each design-to-cost factor in turn. 

 First of all, inflation, from the early 1960s when Hueys became available to the U.S. 

Army to the mid-1990s when the RAH-66s were to have arrived on the scene, amounted to 

about a factor of 9 [584]. This would mean that the $0.8 million would realistically become 

$7.2 million 35 years later. Thus, inflation becomes a factor in applying past performance to 

current cost estimates. In this Huey-based example, the first aircraft ratio should be thought of 

as more like 29.6/7.2, which is 4.1. 

 

188 As I remember it, in the early 1980s Secretary Ambrose legislated that the LHX go-ahead was based on a 

weight empty of 7,500 pounds, a unit cost of $7.5 million, and replacement of all the aging utility, 

reconnaissance, and attack helicopters then in the Army’s fleet. I do not recall the Secretary’s numbers being 

supported by any significant industry input. I thought at the time that all his numbers did was set the goal in 

concrete and hold the Army’s and industry’s feet to the fire. The Secretary never wavered in his position much 

like Nevil Shute had his character, Stephen Morris, saying: “If the machine were a military one for the Air Force 

the procedure was, in general, much the same, with the difference that the purchaser had a habit of asking for 

technical impossibilities and refusing to discuss the matter.” 
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 Secondly, the Huey was the first turbine-powered helicopter to enter U.S. Army 

service, and it was powered with a single engine. The RAH-66 was powered by twin turbines 

incorporating state-of-the-art technology. The effect of this and other basic configuration 

differences can be estimated using the price estimating relationships provided by Eqs. (2.347) 

and (2.348). As applied to the RAH-66 program, you first obtain the factor (H), which is 

based on the major decisions made before any real designing has begun. Thus, 

(2.360) ( )( )( )( )( )

 RAH-66 H factor Engine Type Engine No. Country Rotors Landing Gear

= 1.794 1.344 0.883 1.000 1.115 2.374

= × × ××

= . 

The same major decisions for the Huey were quite different. For the Huey you calculate an H 

factor of 

(2.361) ( )( )( )( )( )

 Huey H factor Engine Type Engine No. Country Rotors Landing Gear

= 1.794 1.000 0.883 1.000 1.000 1.584

= × × ××

= . 

Then there is the difference in weight empty of the two aircraft, the difference in installed 

power, and the difference in number of blades to consider. A designer can, within the bounds 

of fundamental physics, control the outcome here. However, a design constraint of air 

transportability in an Air Force C-130, or requiring the machine to fit in a space allocated on 

some U.S. Navy ship, is very limiting. Looking at the complete story and using reference [116] 

for HU-1A data, you see that the basic configuration differences create an air vehicle (i.e., the 

platform) first aircraft factor of 

(2.362) 

( )

( )

0.4638 0.5945 0.1643

1stA/C

RAH 66 7,500 2 1,300 5 $269 2.374 = Huey $269 1.794 3,900 1 860 2

4.02

  − ×                            ×     

=

 . 

On this basis, the inflated Huey first aircraft price of $7.2 million becomes $28.8 million, 

which I believe can be compared to the RAH-66 first aircraft price of $29.6 million. 

 The third item of mission equipment package differences between the Huey and the 

RAH-66 must, therefore, amount to $800,000. Commercially, in 1994, Bell sold the Model 

412EP for $4,400,000 in its base configuration [583]. If you wanted the machine with factory 

installed equipment, the price jumped to $4,800,000 [583]. The inference here is that the 

military-equipped RAH-66 had all the standard items such as autopilot, flight instruments, 

copilot package and heater, plus special avionics, radios, self-protection devices, weapon, etc., 

all for a total price of about $800,000. 

 The fourth design-to-cost factor has more to do with total program price. If this is the 

design constraint, the number of aircraft becomes the major program price-driving factor. You 

can appreciate this factor from Table 2-42. The original selling point to the Army itself and to 

Congress was that up to 7,000 LHXs were going to be bought—some in utility configuration, 

some in reconnaissance configuration, and some in an attack helicopter configuration. As the 

program marched on to an RAH-66 development contract award on April 1, 1991, things 

started going south during development—much like Augustine recounts [582]. By May of 
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2001, the weight empty had grown to over 9,500 pounds (Fig. 2-390 [587]), the airframe had 

run out of space—within its stealth-dictated outer mold lines—for mission equipment 

additions, and the LHTEC team of Allison and Garrett was being asked to uprate its T800 

engines from 1,300 to 1,563 horsepower. Any thought of a $5.3 million price per RAH-66 

ceased to be real, and the total program price of $37 billion began to fall into the unaffordable 

range as development dragged on. What the final outcome would have been had the program 

not been cancelled on February 23, 2004, will, of course, never be known.189

Fig. 2-390. RAH-66 weight-empty growth over 10 years of development [587]. 

Table 2-42. Effect of Lot Size on Program Price 

Lot Size 

Average Price 

($ millions) 

Total Production 

Price ($ billions) 

7,000 5.300 37.10 

3,500 6.088 22.83 

1,750 7.208 12.62 

1,000 8.159 8.16 

500 9.054 4.75 

250 11.061 2.77 

100 13.481 1.35 

25 17.971 0.45 

 

189 More than enough has been written about the LHX/RAH-66 program and lessons learned abound [587, 588, 

606-617]. 
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2.8.3 Concluding Remarks 

 On one occasion190 after Mike Scully and I had published our Rotorcraft Cost Too 

Much paper [584], I was approached by Marat Tishchenko, the very prominent Russian chief 

engineer.191 He said that he was quite disappointed that Mike and I had not separated out 

engine costs before doing the regression analyses leading to Eqs. (2.347) and (2.348). Of 

course, I had to agree with him, but I also explained that engine manufacturers were even 

more reluctant to divulge cost data than the prime U.S. helicopter manufacturers were. Marat 

simply smiled. But it does raise the point for future study—a study that I hope someone will 

tackle. In 2003, Marat published a paper [618] that examined the effect of disc loading on 

preliminary design of transport helicopters using methodology developed by the Mil Design 

Bureau. He notes his concerns about Eqs. (2.347) and (2.348) writing: 

 “It should be noted that the above formula [Eqs. (2.347) and (2.348)] is based on the sale 

price of helicopters and includes a (variable) profit element that is not the same for all helicopters. 

A factor of 1.16 is included to account for an annual inflation rate of 2.5% (from 1994 to 2000). 

The coefficient H is equal to 2.40576 for helicopters with payloads of 4, 10 and 20 metric tons 

(single rotor). Figure 4 shows the price (in current dollars) vs. disk loading for different payloads 

and number of blades. The price increases with disk loading for all the values of payload 

considered. This indicates that the lowest practical disk loading should be selected in order to keep 

the purchase price low. However, in Eq. (31) [Eqs. (2.347) and (2.348)], a key factor that 

influences the price is total engine power, which in turn increases rapidly with increase in disk 

loading. Such a sharp growth of the price due to a change of power seems to be an overestimation 

of this effect and requires modifications to the formula for the price. One possible reason for this 

could be that Eq. (31) reflects the prices of helicopters for which parameters are already 

optimized and vary gradually within limits.” [My italics] 

When a chief engineer of Marat’s stature and successful track record (he was the leader for 

the MIL-26 program!) has some misgivings, you better take notice. 

 In late 2011, as I was thumbing through Jane’s All the Worlds Aircraft for 2011-2012

[619], I came across the price of Sikorsky’s new S-92 quoted at $21.333 million for the 

“typically equipped” helicopter. Out of curiosity, I calculated what the S-92 would have sold 

for in 1994 using the price estimating relationship that Mike and I devised as follows: 

(2.363) ( )( )( )( )( )

 S-92 H factor Engine Type Engine No. Country Rotors Landing Gear

= 1.794 1.344 1.000 1.000 1.115 2.688

= × × ××

= , 

and then in 1994, the unequipped price would be 

(2.364) ( )

0.4638 0.5945 0.1643

0.4638 0.5945 0.1643

S-92 Base List Price $269(H)(WE) (THP) (b)

$269 2.688 (16,752) (2 2,520) (4)

$13.13million

=

= ×

=

 . 

 

190 I cannot remember specifically, but would guess it was at an AHS Forum in 1998 or 1999. 

191 At age 39 Marat Tishchenko became the head of the Mil Moscow Helicopter Plant when the founder, 

Mikhail Mil, passed away January 31, 1970. He remained as plant manager and chief engineer until retiring in 

1991. Through the auspices of Inder Chopra and the Alfred Gessow Rotorcraft Center, Marat became a Minta 

Martin Visiting Research Scholar, which led to his many contributions here in the United States. 
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100

110

120

130

140

150

160

1994 1996 1998 2000 2002 2004 2006 2008 2010 2012

Inflation

(Percent)

Consumer 

Price 

Department 

of Defense

(Production 

Programs)

Fig. 2-391. Two views of inflation since 1994. 

Following figure 10 of reference [584], the most that equipping adds (i.e., top of scatter) to 

the price is 20 percent, which yields the estimate for an equipped S-92 of $15.75 million in 

1994 dollars. A recent study by Wayne Johnson using two sources [620, 621] has yielded the 

inflation from 1994 through 2011 data shown here as Fig. 2-391. You can see that the 

consumer price index suggests that an inflation factor of 1.4 to 1.5 is not unreasonable. 

Therefore, the $15.75 million should escalate to around, say at most, $23.6 million. This 

suggests to me that Sikorsky might be selling its new S-92 at a bargain! 

 Looking at the military side of helicopter procurement over the last 50 years, I would 

say that the U.S. Army and industry did not acquit themselves at all well on the LHX/RAH-66 

and, to a lesser extent, the AH-56 programs. This is in distinct contrast to the CH-47, OH-6, 

OH-58, UH-60, AH-64, and OH-58D development and production programs. Harper and 

Richey, in their 12-lesson, roughly 1,500-slide PowerPoint® presentation [587], make the 

statement that “we did everything right and still we failed,” which can be summarized here 

with just one of their charts, Fig. 2-392. Personally, I would disagree with their statement. My 

view is that the LHX/RAH-66 program did everything “by the book” and this caused the U.S. 

Army and industry to fail. That says to me that the “book” should be thrown away. 

 The book came into being because of the long period between the early 1970’s start on 

UH-60 and AH-64 developments, and the LHX/RAH-66 program, which had its competition 

decided on April 1, 1991. You may figure the gap differently, but in that period system 
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engineering came into its own. The corollary to system engineering was Integrated Product 

Teams (IPTs—occasionally referred to as silos). Before long the people writing about how to 

develop and produce helicopters had never designed, developed, and/or produced anything. 

The product of these system engineering proponents was nothing more than guidelines, work 

management schemes, DoD directives, MIL standards, and a ton of ancillary conceptual 

flowcharts, none of which deserve to be referenced in this volume.192 

 Frankly, even the discipline labeled as system engineering is incomprehensible to me 

because the “discipline” is too far removed from words like designing, releasing drawings, 

preparing subassembly specifications, and then building, flight testing, qualifying, and 

delivering. I believe that the rise of system engineering destroyed the practice of having a 

chief designer (I prefer chief engineer) and a director of manufacturing, and giving them the 

power, resources, and any additional support needed to do the job. Regardless of the 

complexity of the ultimate product, I believe that for a development program an organization 

need be no more unrecognizable than what you see here as Fig. 2-393. Then you select these 

leaders based on their skill breadth and track record, and then you trust them. 

 When a helicopter worth producing is obtained from development, the organization 

for development must be altered to emphasize the director of manufacturing, and the 

emphasis on engineering should be substantially reduced. 

Historical Helicopter SD&D Expenditure Profiles

(Normalized to constant 2004$)

$0

$100

$200

$300

$400

$500

$600

$700

$800

$900

$1,000

0 2 4 6 8 10 12 14 16 18 20

Contract Years

Millions of Constant 2004$

UH-60A/L

SH-60B

AH-1Z/1Y

MH-60R

CH-53E

RAH-66A

Source: U.S. Military Aircraft Data Book, 

1995,2004, Data Search Associates

Requirement creep

Terminated

Reprogramming 

Funding Shortfall

Nine Years

Fig. 2-392. The LHX/RAH-66 program was in trouble almost from the start [587]. 

 

192 I have strong opinions about system engineering. 
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Fig. 2-393. On a development program, system engineering is no substitute for a team 

made up of a chief engineer, a chief of air vehicle (i.e., the platform), and a chief 

of mission equipment—no matter how complex the product is. 

 A little earlier you read that I do not think much of the Work Breakdown System 

(WBS). It was hardly in vogue during the UH-60 and AH-64 programs (as I remember them) 

and those programs can hardly be called failures. On the other hand, the WBS definitely was a 

burden placed on the AHIP/OH-58D program, which I had the privilege to be a part of in the 

position of chief engineer. When you review the WBS [600], you will see that cost is 

measured by time. Money spent is presumed to equate to tasks completed. Tracking can be 

made, to pick an extreme, at the pennies and seconds level thanks to data entries made into a 

computer on a weekly basis. But, as the OH-58D chief engineer during development, after a 

month or so I found that the WBS could not tell me what was happening on any given day. 

Nor could it tell me what the problem of the day (or even of the week) was, and it offered no 

insight about a coming crisis. In fact, the WBS very much inhibited me from walking around 

and talking to the men (and a few women) at drawing boards and computer screens, or 

making parts on the shop floor, or struggling with subcontractors—all the people who were 

actually doing work and producing something. 

 As related in the more complete, unpublished version of reference [145], I described 

the Milestone Done-Done (MD2

) method of tracking what was going on (at least in 

engineering) during the AHIP/OH-58D development program. With some of my additional 

thoughts in brackets, this is what I wrote: 

Company 

President

Program 

Manager 

Chief 

Engineer 

Chief 

Air Vehicle 

Chief 

Mission 

Equipment 

Director of 

Manufacturing 

Everyone 

Else 
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 “The Bell AHIP Engineering team [leaders, Mike Kawa for Air Vehicle, Jack Floyd 

for Mission Equipment, and myself] actually managed their business on a day-to-day and 

week-to-week basis using primarily the Milestone Done-Done (MD2

) method rather than 

relying very much on the MCS [Bell’s government-approved WBS version] cost and schedule 

variance weekly report or the monthly historical report. This statement of fact may come as a 

disappointment to the originators and proponents of the WBS. The MD2

 engineering business 

management method was introduced to AHIP by the author, based on some success with an 

earlier program that is reported in reference 24. Doing business by the MD2

 method follows 

from the primary management chart shown in figure 53 [seen here as Fig. 2-394] and focuses 

almost entirely on “what is and isn't getting done.” Comparatively little engineering attention 

is given—in the MD2

 management method—to gathering man-hours-spent data or the time of 

day since this information is readily supplied by an overabundance of accountants, calendars 

and watches. 

 The MD2

 method requires Engineering to completely define and vigorously manage 

the accomplishment of a meaningful set of detailed milestones. For AHIP there were 669 

detailed milestones and the what, who, how much and when for each was completely 

described. With this tabulated plan [and a drawing tree], the more commonly used graphs of 

(1) milestones done versus time and (2) man-hours spent versus time become quite secondary. 

The primary management view (of the plan and tracking to the plan) is graphically presented 

in the form shown by figure 53. Three reasons for choosing the format of figure 53 are: 

Engineers generally prefer graphs to tables. A good plan or line will require Engineering to 

define quite a few milestones or the graph will plot as a series of large step functions which 

engineers do not like. If milestones are not getting done and man-hours are being spent, the 

line of actual performance goes straight up which is graphically disturbing to any engineer. 

 The MD2

 management method has only one corollary and that is to set the standard 

for being done. This is an important point because no credit is given for partial completion of 

a milestone (i.e., Engineering's “percent complete” is formed by the ratio of the two whole 

numbers of milestones done divided by total milestones). The standard, given a plan with 

many milestones, is very simple: a milestone is not done if words like “...... is done except” 

are used. Thus, the standard says that “done” and “except” cannot be used together. The 

standard replaces “except” with “done” and that is why the method is referred to as 

Milestones Done-Done, or MD2

. 

 The actual performance of the Bell Engineering Department is shown on Figure 53. 

All engineering relating to the contractual milestones shown by figure 53 is done except 

(notice that “all” and “except” do not go well together either) FSED [Full Scale Engineering 

Development] is not done-done. As of March 14, 1986, even with the DD250 (i.e., the 

Government Acceptance form) of several production aircraft, there were three milestones still 

left undone and expenditures stood at 637,232 man-hours.193 In fact, FSED activity is at the 

trickle level, but getting the last few milestones done-done is like pulling teeth.” 

 

193 The department’s budget, as allocated by Program Management, was 528,700 man-hours. As an aside, this 

budget was the proverbial “success-oriented budget” and, in Engineering’s view, only addressed the knownknown tasks in the AHIP program. Following suggestions from Augustine’s Laws [582], Engineering had 

prepared a broader view that included known-unknown tasks (620,000 man-hours) and an even broader view 

that included unknown-unknown tasks. This latter estimate was made with the thought that if Bell Engineering 

exceeded 800,000 man-hours to complete their portion of AHIP, there was a disaster in the making.
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Fig. 2-394. The Work Breakdown System should be thrown away on development 

programs and replaced with the MD2

 system. 

 Please keep in mind that the AHIP/OH-58D program was a relatively simple program 

(compared to LHX/RAH-66 and, say, the V-22 tiltrotor) because all the major assemblies of 

the air vehicle had been demonstrated to be ready—through flight testing. In contrast, the 

mission equipment package was all new from the ground up. Had a mockup in which to locate 

the many electronic subassemblies (and associated wiring bundles) and a mission equipment 

system integration laboratory not been in place in a timely manner, I believe there would have 

been real trouble on the program. 

 This, in my estimation, was one of several major factors causing the LHX/RAH-66 

program to get off to a less than satisfactory start. The U.S. Army overall approach was to 

have the first several aircraft be virtual prototypes of the full-up production product. Thus, allnew air vehicle technology, an all-new engine, and an all-new mission equipment architecture 

were on the table at the same time for two competitors, and then selection of a winner from 

the two competitors was based primarily on paper designs. The whole past lesson of “try (or is 

it fly) before you buy” was dismissed because of a misguided perception that all the design 

and analysis tools were infallible. Following a system engineering organization, the concept of 

Integrated Product Teams (ITPs) and relying on WBS accounting for program status just 

ensured failure. 
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 I think one real lesson is that a bare bones air vehicle must be demonstrated by flight 

testing as a satisfactory platform. Then the machine can be stuffed with mission equipment 

that meets the mission needs. All of the mission equipment can be demonstrated in a system 

integration laboratory while the basic air vehicle is being debugged in flight testing. Then, and 

only then, should the mission equipment installation in the air vehicle be completed. After 

installation, the system can be debugged and made ready for customer acceptance. 

 There are many who think the reason why the AHIP/OH-58D development program 

was reasonably successful was because it was a fixed-price contract. In my opinion, they are 

all wrong. The key factor was that the specification and work statement were fixed so adding 

all manner of emerging mission equipment after contract award could not be done on anyone’s 

whim or an even stronger urging. Furthermore, increasing the number of fatigue specimens or 

some other airworthiness activity was not allowed. During the AHIP/OH-58D program, the 

word no by Army and Bell program management (Colonel Bud Forster, who later became a 

Lieutenant General, and Teddy Hoffman, respectively) meant no with a period. 

 There are two additional thoughts that came my way. Both thoughts deal with some 

UTTAS history. The first was offered to me by Colonel Clarence (Bud) Patnode, retired,194

and I am very glad to include it in these concluding remarks. After reading this chapter, Bud 

wrote me an e-mail [623] saying in part: 

 “Based on my six years in the UTTAS program (three years as the Department of the 

Army Systems Staff Officer (DASSO) and three years in the PM shop leading up to the fly off) 

and my four years in the AAH PM shop as the PM for TADS/PNVS I will offer some 

comments. 

 Single vs. twin engine. The UTTAS was the only system of the Army’s Big Five 

(UTTAS, AAH, XM-1 Tank, Bradley Armed Personnel Carrier, Patriot Air Defense System) to 

be approved by the Defense Systems Acquisition Review Council on its first attempt. During 

that formal DSARC review, the USAF and some DOD folks challenged the need for twin 

engines. Although the requirement for twin engines had been well substantiated in the extensive 

analysis done in Concept Formulation, it became a potential show stopper during this final 

review to approve program start. LTG Robert Williams set those analysis aside and in an 

eloquent way stated to the effect that it sometimes comes down to trying to answer the parents 

of a soldier lost in an accident as to why the Army did not value their lives enough to provide 

the added safety of twin engines. Much to the surprise and pleasure of many of us in attendance, 

LTG Williams replaced hundreds of pages of analysis with a brief convincing statement. 

Certainly, the UTTAS twin engine configuration was a major cost driver and decision. 

 Fixed Price and Fixed Requirements. Throughout the UTTAS Concept Formulation 

and Development, the army medical corps continued to try to force a major change in the 

dimensions of the fuselage to accommodate their belief of a better way to transport patients. 

During Concept Formulation LTG Williams made it very clear to the medics that they would be 

flying Hueys for a very long time if they in some way caused a change in the UTTAS 

requirements. He had to stomp their butts to keep them from causing a major change to the 

requirements. During the early years of development, BG Leo Turner, PM UTTAS continued 

 

194 Bud and I became friends around the start of the AHIP/OH-58D days. His wise council has kept me out of 

more trouble than I care to admit. Bud’s story [622] about how the army and then DOD reached a decision to 

develop the UTTAS is fascinating. 
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holding off the medics who would have killed the program had they prevailed. A great example 

of fixed requirements. BG Turner was one tough Texan who continued to block changes to the 

requirements. 

 The concept of design to cost does not address the up-front decisions that the customer 

already has made his mind up about. For example, a chief designer is not likely to be able to 

convince U.S. Army aviation leaders or a commercial customer that an airplane or autogyro 

will do the job and cost him less than a helicopter, or that maybe a piston engine might do, or 

that a single gas turbine saves purchase price when compared to a twin-engine choice. Of 

course, overrunning a legislated budget and delivering late to a prescribed schedule with an 

underperforming product does not enhance a reputation. However, in my view, after over 55 

years, performance, cost, and schedules have always finally been negotiated without including 

known-unknowns and unknown-unknowns. The differences between plan and reality created 

by executive amnesia are still quite amazing to me. 

 It is a setup for continued failure when you do not include known-unknowns and 

unknown-unknowns when selling a program. 

 Now as to the second thought that came my way. There is one question that has been 

on my mind for several years. It deals with designing to cost, or, as the military prefers, 

Design to Unit Production Cost (DTUPC). If cost data is held so close to the vest by top 

management, how does engineering get concrete dollar numbers and targets to do its detailed 

design work? In struggling with this question relative to the military, I turned to Bud Forster 

(retire Lieutenant General, U.S. Army, and a friend) and asked if the 1970’s Department of 

Defense design-to-cost policy [599] helped improve performance on military procurements. 

With Bud’s permission, here is his reply (with a little of my editing): 

 “DTUPC worked well in the 1980s when we had Program Managers, and 

subsequently Program Executive Officers, as well as TRADOC195 System Managers and 

School Commandants with a fair degree of operational experience. We had lived through the 

early days of Vietnam with equipment designed for use against the USSR in Europe. We no 

longer could accept the point solution—nor could we intentionally set out to design 

lightweight, but lethal tanks for the jungle nor helicopters that could only survive against crew 

served machine guns. Key to DTUPC were some enlightened School Commandants, like Don 

Parker and Lou Wagner, who would listen to Program Managers explain why [a] AHIP could 

not afford the weight of a cargo hook, [b] why Apache was barely affordable and 

manufacturable while barely meeting its performance requirements, and [c] they would ban 

the trade of fuel tankers to enhance the Ml tank. To these School Commandants, maintaining 

schedule and unit production costs were key because of the pressure on the Army budget 

following Vietnam and the competition for peacetime dollars with a Navy and Air Force that 

appeared to be much more favored in the Office of the Secretary of Defense. So any changes 

to the approved requirement had to be assessed in light of DTUPC impact and few changes 

were approved by the School Commandants. 

 The tight link between TRADOC School Commandants, TRADOC System 

Managers, and Program Managers was weakened with the advent of the Acquisition Corps. 

Program Managers no longer had the operational experience, and therefore rapport, with 

 

195 U.S. Army Training and Doctrine Command 
2.8 PURCHASE PRICE 

578 

School Commandants. Also School Commandants, for reasons I don’t understand fully, 

became less and less involved in acquisition decisions. Perhaps this was because of pressures 

to train and retrain for Desert Storm, Iraqi Freedom, and Enduring Freedom. The fact that 

TRADOC System Managers became part of the Acquisition Corps and became more and 

more civilianized may have contributed to less rigor in enforcing requirements stability. 

 During the Army Acquisition Review of late 2010/early 2011 almost every example 

of success we used was from the 1980s. The exception I remember was the Block 2 upgrade 

of the Apache AH-64D, which seemed to have recreated the Program Manager and TRADOC 

System Manager link to operational experiences. This Apache program was managed to a 

dollar level that kept it out of the spotlight and was executed quickly enough to avoid death by 

“good ideas” and “help from higher up.” 

Bud’s short note says to me that when the tight links between the war fighter and the rest of us 

are broken, thing go to “hell in a hand basket” very quickly. I think that replacing excellent 

leadership traits and skills learned by experience with some directive or handbook just never 

seems to work. 

 Let me add, perhaps, a less philosophical note. A most recent paper [624] that derived 

list price estimating methodology for fixed-wing aircraft was brought to my attention by 

Wayne Johnson. The authors of this paper are all affiliated with the Institute of Aeronautics 

and Astronautics located in Aachen, Germany. Their paper is titled Aircraft Cost Model for 

Preliminary Design Synthesis. These authors were able to examine list price at the airframe 

component level. The work is an example of what I believe needs to be done in the rotorcraft 

industry. I hope somebody takes up the challenge. 

 Finally, you should be aware that there are many “cost estimating methods” that try to 

estimate purchase price, operating costs, and even life cycle costs. For helicopters currently 

operating in the commercial fleet, you have Conklin & de Decker, Inc. that offers very 

popular software products, one of which I will introduce you to shortly. For military 

helicopters you have no place to turn. Of course, each major manufacturer has its own ability 

to estimate purchase price, operating costs, and life cycle costs in response to a military 

request. And, of course, the U.S. Department of Defense has the ability in all service branches 

to make a reasonable estimate of what something “should cost” just to keep suppliers from 

straying too far from reality. I can, however, suggest one paper that may be of interest to you. 

Although it deals only with fixed-wing aircraft, J. Wayne Burns’ paper [625] gives you a 

feeling of the breadth and detail you need just to become familiar with the world of cost 

estimating. 
579 

2.9 OPERATING COSTS 

 One of the major factors in the mind of a potential buyer of a transportation product is 

the cost (to the buyer) of operating the machine. In the United States today, for example, an 

automobile buyer is most certainly concerned about what fuel mileage the car that he (or she) 

wants is going to get. The same is most certainly true in the world of rotorcraft. But beyond 

the question of fuel efficiency, a potential helicopter buyer must also consider total operating 

costs for each future year. Total operating cost is frequently broken down into fixed costs 

(like hanger rental for a year) and variable costs, which are costs that are incurred every time 

the helicopter is flown. Before discussing helicopter operating costs in detail, and then 

reviewing two examples of maintenance, it helps to have some background about fixed-wing 

and rotary wing airlines. 

2.9.1 Airplanes 

 To begin with, let me quote from one of my favorite books about how the airline 

business got started and the aircraft that made it possible. This book, written by Peter W. 

Brooks who captured many details about autogyros [4] that you read about in Volume I, is 

titled simply The Modern Airliner [626].196 He wrote on page 43: 

 “During the first 10 years after the end of the First World War the centre of gravity of 

transport aircraft development remained in Europe, where all the major countries were soon 

engaged in the creation and expansion of passenger-carrying scheduled air services. During the 

greater part of this period, U.S. transport aircraft remained inferior to European designs, although 

the Americans produced two notable series of radial air-cooled engines, the Wright Whirlwind and 

Pratt & Whitney Wasp. Not until the Ford Tri-Motor appeared in 1926 did American transport 

aircraft begin to be competitive with those in Europe. The United States’ most important 

contributions to the first 10 years of air transport’s development were in the operational field. 

Because their operations were confined to mail carriage, they had a powerful incentive to 

undertake bad-weather and night flying as soon as possible—night flying was introduced in 

1923—and to achieve the highest possible standards of regularity and punctuality, even at the 

expense of safety. As a result, instrument and night flying and the development of navigational 

aids made more rapid progress in the United States than it did in Europe. An exception to this was 

ground-to-air radio communication, which was in general use in Europe for several years before it 

was adopted in the United States. The Americans’ lead in most of these fields was to have 

important repercussions later, when the all-weather capabilities of passenger carrying aircraft 

increased rapidly in the early 1930s. It was, in fact, one of the factors which helped to create the 

ascendency which the Americans were to win in the 1930s and which they retain to this day.” 

The ascendency in air transport that Brooks refers to is traced with great clarity by R. E. G. 

Davies in his classic book titled Airlines of the United States Since 1914 [316]. This story and 

two other more technical classics [628, 629] all make the point that the Ford Tri-Motor 

(Fig. 2-395 and Fig. 2-396) exposed the public to air travel for business and pleasure. 

However, this 1926 airplane did not make any airline operationally feasible without 

government subsidies. That freedom came 10 years later with the Douglas DC-3 (Fig. 2-397 

and Fig. 2-398). 

 

196 This 176-page book came out in 1961, and Brook’s followed it in 1962 with an absolutely superb, technicalfact-filled 585-page book dealing with both fixed-wing and rotary wing aircraft in use by the airline industry 

[627]. Peter Brooks was an Englishman; he died January 17, 1996, at the age of 76. 
2.9 OPERATING COSTS 

580 

Fig. 2-395. Vibration and noise were just barely tolerable in the Ford Tri-Motor 

(Internet photo). 

Fig. 2-396. The Ford Tri-Motor could maintain flight on two engines when operating 

near sea level (photo from author’s collection). 
2.9 OPERATING COSTS 

581 

Fig. 2-397. The Douglas DC-3 provided the minimum level of comfort passengers have 

come to expect (photo courtesy of Ben Wang). 

Fig. 2-398. The Douglas DC-3 could maintain flight on one engine, even at altitude 

(photo from author’s collection). 
2.9 OPERATING COSTS 

582 

 Edward Pearson Warner197 was a prominent (and unbiased) figure in aviation as the 

airlines and aircraft manufacturers were reaching their first plateau. In 1938, while a member 

of the National Advisory Committee for Aeronautics (N.A.C.A), he delivered five lectures at 

Norwich University located in Northfield, Vermont. In his third lecture he spoke about 

airliner technical development and its effect on air transportation [630]. The lecture was 

published by the university as a small book, and it became a classic reference for later authors 

and historians. What is so interesting to me about this 42-page book is that Warner laid out 

operating cost data in a few major categories. Warner’s discussion (about six early aircraft 

used by airlines) is an invaluable starting point to learn about operating cost. 

2.9.1.1 E. P. Warner’s Direct Operating Cost (DOC) Analysis 

 To begin with, imagine it is the late 1930s and you have decided to start an airline—

just a small one to start with, of course. Say you are guessing that you can make a handsome 

profit with three Douglas DC-3s and charging very reasonable fares. You have decided that a 

route from Washington D.C. to Huntsville, Alabama, with several intermediate stops, is an 

ideal niche to fill because American, TWA, Eastern, and United (Fig. 2-399) are not 

interested (perhaps because they want to expand their transcontinental route structures). You 

figure the D.C.–Huntsville route is about 900 miles outbound and 900 miles retracing your 

steps, including some margin (Table 2-43). What you want to know now is how much it will 

cost to operate your company each year and, more specifically, how much it will cost to 

operate each of the three DC-3 aircraft for one year. Then you can contemplate what your fare 

structure will be. You have read E. P. Warner’s thin book [630] cover to cover and are going 

to make your estimates based on his bookkeeping.198 You are particularly interested in the 

comparison that Warner made between the Ford Tri-Motor and the Douglas DC-3 aircraft. 

However, based on what you have heard about the new Douglas machine, you are fairly 

certain that you will not make a profit with the Ford Tri-Motor. The deciding factor appears to 

be a 10-seat machine priced at $6,800 per seat versus the Douglas DC-3 aircraft priced at 

$5,240 per seat. Still, you have decided to let the operating cost comparison make up your 

mind. Of course, Warner has made it clear that his numbers are primarily for making a 

comparison and may not apply to the route and airline you are planning; still it is a start. 

 There is, of course, a great deal of preliminary input data you need to have before 

starting your accounting calculations. With some help from the Douglas Company, you 

summarize your basic information about their DC-3 as shown here in Table 2-44. 

 

197 Edward Pearson Warner (November 9, 1894–July 11, 1958) was an American pioneer in aviation and an 

aeronautical engineering teacher. He became a member of the U.S. Civil Aeronautics Board at its founding 

in 1938, a delegate to the 1944 Chicago Conference for the Convention on International Civil Aviation, and 

an international civil servant. Edward Warner's achievements are commemorated in the world’s civil aviation 

community by the international award that bears his name. 

198 In offering this example, I recreated Warner’s example from pages 33 to 42 of his little book. It took some 

fill-in estimates on my part because his details are left to the reader’s imagination in several categories. Warner 

was making the point that technical progress made between the Ford Tri-Motor and the Douglas DC-3 provided 

a way for airlines to become profitable without subsidies from the Postal Department for carrying mail. His story 

and analysis support that view quite well. 
2.9 OPERATING COSTS 

583 

Fig. 2-399. How United, Eastern, TWA, and American came into being [316]. 

Table 2-43. Planned Route Structure for Your Startup Airline 

Segment 

No. Leave Arrive 

Statute 

Miles 

Minimum On-Ground 

Time 

1 Washington, D.C. Norfolk, VA 143 4 at Norfolk 

2 Norfolk, VA Elizabeth City, NC 44 4 at Elizabeth City 

3 Elizabeth City, NC Rocky Mount, NC 91 4 at Rocky Mount 

4 Rocky Mount, NC Raleigh–Durham, NC 57 4 at Raleigh–Durham 

5 Raleigh–Durham, NC Greensboro, NC 66 4 at Greensboro 

6 Greensboro, NC Winston–Salem, NC 16 30 at Winston–Salem 

 (refuel) 

7 Winston–Salem, NC Charlotte, NC 75 4 at Charlotte 

8 Charlotte, NC Ashville, NC 89 4 at Ashville 

9 Ashville, NC Knoxville, TN 88 4 at Knoxville 

10 Knoxville, TN Chattanooga, NC 87 4 at Chattanooga 

11 Chattanooga, NC Huntsville, AL 83 Overnight at Huntsville 

Total 840 
2.9 OPERATING COSTS 

584 

Table 2-44. Input Data for Operating Cost Analysis 

Input Units Ford Douglas Notes 

 Model 5-AT Tri-Motor DC-3A 

 Engine 3 P&W Wasp C 2 P&W R-1830-S1C3G 

 Total installed horsepower hp 1,260 2,400 Pratt & Whitney spec 

 Max takeoff gross weight lbs 13,250 25,200 Douglas spec 

 Weight empty lbs 7,576 16,860 Your requirement 

 Number of passenger seats number 10 to 15 21 to 28 Your requirement 

 Horsepower at cruise (HPcr) hp 750 1080 Douglas flight test 

 Cruise speed (Vcr) mph 125 180 Douglas flight test 

 Payload tons 1.6 2.5 Your requirement 

 Range miles 625 900 Your requirement 

 Cruise time hrs 5.00 5.00 Your requirement 

 Fuel flow (SFC) lbs/hr per hp 0.50 0.44 Pratt & Whitney spec 

 Fuel price cents/gallon 11.0 12.5 Current price 

 Fuel density lb/gallon 6.0 6.0 Aviation gas spec 

 Pilot number Yes Yes Your requirement 

 Co-pilot number Yes Yes Your requirement 

 Price of complete airplane dollars $68,000 $110,000 Douglas list price 

 Price of airframe dollars $50,000 $90,000 Douglas list price 

 Depreciation rate for airframe years 5 5 Your requirement 

 Price of engines dollars $18,000 $20,000 Pratt & Whitney list price 

 Engine life hrs 3,500 5,000 Pratt & Whitney spec 

 Engine life in miles flown miles 437,500 900,000 (engine life) × Vcr 

 Flying time per year hrs 2,000 2,000 Your requirement 

 Miles flown per year miles 250,000 360,000 (yearly hours)(cruise speed) 

 Miles per crash number 3,500,000 7,000,000 Your safety plan 

Table 2-45. Fuel Cost for the 900-Mile Trip Equals $53.10 for the DC-3 

Fuel Cost Units Ford Douglas Notes

 Fuel burn rate in cruise gallons/hr 62.5 79.2 (SFC × HPcr)/(fuel density) 

 Gallons used in cruise gallons 313 396 (gallons per hour)(cruise time) 

 Other gallons used gallons 34 29 about 10% of cruise fuel 

 Fuel used for 5 hours gallons 347 425 sum all gallons 

 Fuel cost per 5 hours cents 3,813 5,310 (gallons used)(fuel price) 

 Fuel cost per mile cents/mile 6.10 5.90 (fuel cost)/(miles traveled in 5 hours) 

 Cost per ton-mile cents/ton-mile 3.81 2.36 (cents per mile)/(payload in tons) 

 Cost per hour dollars/hr $7.63 $10.62 (cents per mile)(Vcr)/100 

 Cost per available seat-mile cents/seat-mile 0.61 0.28 (cents per mile)/(no. of seats) 

 Fuel cost per 900 miles dollars $54.90 $53.10 (cents per mile)(900 miles)/100 
2.9 OPERATING COSTS 

585 

You immediately see from Table 2-44 that three DC-3A aircraft are going to cost you 

$330,000. No spares are included, and the Douglas price is F.O.B. Santa Monica, California, 

which means it will cost another $20,000 to get them back to Washington National Airport 

(now Reagan National), which is scheduled to be completed in June of 1941. 

 Warner’s approach to estimating the cost to operate one aircraft requires a detailed 

accounting in five cost categories: namely fuel, crew, maintenance, depreciation, and 

insurance plus crash reserve. In each category, you want data about cost per mile, cost per 

payload miles in ton-miles, cost per hour, cost per available seat-mile, and cost for one 900-

mile trip. So you start with the fuel cost estimate. For this item Warner wrote that 

 “the first of the major cost items is fuel, and fuel involves three variables. The improving 

aerodynamic efficiency of the airplane has yielded a steady increase in speed for a given 

power loading, which in turn has meant the accomplishment of more ton-miles of work per 

horsepower-hour. Improvement in engine design and improvement in fuel have reduced 

specific consumption. But improvement in fuel has also increased the price per gallon at 

which fuel must be bought.” 

The step-by-step calculations appearing in Table 2-45 show that fuel cost per the 900-mile 

trip favors the DC-3 slightly, but on a per-seat basis, the Ford costs $5.49 per seat while the 

DC-3 costs just $2.53 per seat. It makes you begin to wonder though if all the seats that are 

available on each aircraft will always be filled with paying passengers. If the DC-3 is making 

trips with only one-half of the available seats filled, then it may be a losing proposition 

compared to the Ford machine flying with all seats filled on every trip. 

 The cost of manning the two aircraft with both a pilot and a copilot is shown in 

Table 2-46. On this cost element, Warner says that 

“the rate of pilot compensation is now fixed by a formula established by the National Labor 

Board in 1934, and subsequently given the force of law by specific reference in the Air Mail 

Act of 1934. Under that ruling, pilots receive a base pay plus an additional sum for each hour 

of flight, the rate of accumulation of this supplementary portion being dependent on the speed 

of the airplane. Until that provision was adopted, they were paid either a flat sum per mile or a 

flat sum per hour in addition to their base pay. In the first case, assuming the number in the 

crew always to be the same, the personnel cost per mile would be substantially the same for 

every airplane. Under the second alternative, the cost per mile would be inversely 

proportional to the speed of the plane. The Labor Board ruling establishes in effect a 

compromise between the two, the cost per mile going down with increasing speed but not so 

rapidly as the speed goes up.” 

Table 2-46. Crew Cost for the 900-Mile Trip Equals $64.80 for the DC-3 

Crew Salaries Units Ford Douglas Notes

 Crew cost per mile cents/mile 9.3 7.2 Warner's numbers 

 Cost per ton-mile cents/ton-mile 5.8 2.9 (cents per mile)/(payload in tons) 

 Cost per hour dollars/hr $11.63 $12.96 (cents per mile)(cruise speed)/100 

 Cost per available seat-mile cents/seat-mile 0.93 0.34 (cents per mile)/(no. of seats) 

 Crew cost per 900 miles dollars $83.70 $64.80 (cents per mile)(900 miles)/100 
2.9 OPERATING COSTS 

586 

Warner also makes a point about stewardesses saying they are “a passenger service, rather 

than a direct operating cost. Present-day transports could be operated without stewardesses, 

were it felt that passengers were more interested in a little additional economy than in 

personal service; and conversely, stewardesses could at any time have been put onto any 

airplanes large enough to have an aisle along which they could move.” 

 Warner also makes a further comment about crew size saying that 

“there is, of course, another factor which has played some part in the economic history; that of 

the size of the crew. Even after passengers began to be carried, the single pilot remained for 

some time the common rule; and when a co-pilot was taken it was more as a safety measure, 

in the event of sudden illness of the pilot, than because he had any definite duties to perform. 

Not until about 1934 did the functions of the cockpit become so multifarious and so 

elaborately organized that they had to be distributed between two men and kept them both 

forever busy. On Pan-American oceanic flying boats the operating crew numbers four or even 

five, and it is likely to grow to three on the domestic airlines with the introduction of fourengine planes such as the DC-4 or the Boeing 307; but for the purposes of this analysis the 

DH-4, the Boeing 40, and the Lockheed Vega will be treated as single-pilot craft, while the 

other three parties to the comparison will each be charged with a co-pilot.” 

 The third category is maintenance cost provided here in Table 2-47. Here Warner 

offers a warning saying that 

“maintenance is much less determinate. We find ourselves limited to very general speculation 

based on the required frequency of overhaul of various engines, the complexity of the rigging 

of the various airplane structures, and the relative rapidity of deterioration of the materials of 

which they were composed. Engine overhaul periods have increased from about 120 flying 

hours of the Liberty [which powered the DH-4], as used by the Post Office in 1924, to about 

500 hours at present [1938]. The internally braced metallic structures of the present day 

require much less routine rigging attention than did the wire-braced biplanes that preceded 

them; and the metal is inherently less likely to deteriorate than was the wooden structure of 

the past, and especially plywood wing covering, though the difference in that respect in 

temperate climates is much less than is commonly supposed. Maintenance costs were kept 

low on the Liberty engines by the availability of large stocks of parts from the Army’s 

wartime accumulation at a nominal charge; but that was an abnormal factor dependent on a 

special and temporary situation [World War I] and in no way inherent in the nature of the 

equipment, and I have excluded it from the accounting. I have assumed costs on the Liberty 

engine and the DH-4 planes, both in figuring maintenance and in estimating a depreciation 

allowance, as they would have been if the equipment had been built up especially for 

commercial use and purchased directly from a manufacturer. It must be emphasized once 

more that the values so tabulated assume modern maintenance organization, in every case, 

and an equal degree of managerial competence throughout.” 

Table 2-47. Maintenance Cost for the 900-Mile Trip Equals $45.00 for the DC-3 

Maintenance Units Ford Douglas Notes

 Airplane and engine cents/mile 8.70 5.00 Warner's numbers 

 Cost per ton-mile cents/ton-mile 5.44 2.00 (cents per mile)/(payload in tons) 

 Cost per hour dollars/hr $10.88 $9.00 (cents per mile)(cruise speed)/100 

 Cost per available seat-mile cents/seat-mile 0.87 0.27 (cents per mile)/(no. of seats) 

 Maintenance cost per 900 miles dollars $78.30 $45.00 (cents per mile)(900 miles)/100 
2.9 OPERATING COSTS 

587 

 Let me interject here that maintenance costs for helicopters are frequently provided by 

the helicopter manufacturer. In my experience, the operators rarely seem to achieve the 

manufacturer’s claims. Later, you will read in some detail just what the maintenance manual 

for a Robinson R-22 has to say. 

 The fourth operating category is depreciation (Table 2-48) about which Warner said 

“involves assumptions on equipment life, number of hours flown per year, and first cost. Life 

is dependent principally on the rate at which technical progress crowds existing equipment 

over the edge of obsolescence; but that is one of the variables that it is hard to project into the 

present day, and it can hardly be regarded as inherent in the particular piece of equipment 

under analysis. It seems fair then to take a uniform life of five years for the airplane, a length 

of time well within the sheer physical survival capacity of any of them; but for the engines, 

for which life is determined primarily by actual wear and so is measured in operating hours, a 

reasonable total of time has risen from 1,200 hours with the Liberty to 3,500 with the early 

air-cooled types, and to 5,000 at the present time. The hours of flying per year were 

extravagantly low in the days of the government-operated mail service, when each pilot had 

his own machine permanently assigned. They probably did not average above 600; but if the 

same equipment were being operated now, the standards of its employment would be less 

prodigal, and the hours would be limited by the time that schedules required on the ground 

between trips and by the time necessary for mechanical servicing. Projecting all types into the 

present, I would take 1,200 hours a year as reasonable for the DH-4, 1,700 for the Boeing 

Model 40, and 2,000 for each of the other types. First costs on a commercial basis, at present 

price levels, should be about as tabulated.” 

This price data, as well as cruise speed, is tabulated in Table 2-44. 

 The fifth and last operating cost category is insurance and reserving money in a crash 

account (Table 2-49). Warner decided to assume a self-insured choice and made it clear that 

by 

“assuming self-insurance, no factor of insurance company operating expense or profit enters 

into the calculation. The approximating of insurance and crash reserve again involves a 

difficult projection. The DH-4 flew without even a radio receiver; and the [Lockheed] Vega, 

the Ford, and the early Boeing Model 247 all operated in a period when the radio beam was 

unknown or virtually unused, and when contact flying in bad weather had to remain the rule. 

Faithful to my oft-repeated purpose of restricting these cost variations to the factors inherent 

Table 2-48. Depreciation Cost for the 900-Mile Trip Equals $65.00 for the DC-3 

Depreciation Units Ford Douglas Notes

 Airframe loss per year dollars $10,000 $18,000 (purchase price)/number of years 

 Airplane cents/mile 4.00 5.00 (airframe loss price)/(miles flown per year)

 Engine cents/mile 4.11 2.22 (engine price)/(miles flown per engine life)

 Depreciation per mile cents/mile 8.11 7.22 Warner's numbers 

 Cost per ton-mile cents/ton-mile 5.1 2.9 (cents per mile)/(payload in tons) 

 Cost per hour dollars/hr $10.14 $13.00 (cents per mile)(cruise speed)/100 

 Cost per available seat-mile cents/seat-mile 0.81 0.34 (cents per mile)/(no. of seats) 

 Depreciation cost per trip dollars $73.03 $65.00 (cents per mile)(900 miles)/100 
2.9 OPERATING COSTS 

588 

in the equipment, I have assumed that each of the six [aircraft] types being compared is being 

operated at the present time and fitted with as much instrumental and communication 

equipment as it could reasonably hold. Obviously it would be impossible, both because of 

space limitations and because of the concentration of all the responsibility in a single pilot, to 

put as many navigational devices and radio sets into a Boeing Model 40 as are being planned 

for the DC-4, for example; but I have supposed that even the DH-4, if reincarnated and set to 

prove itself economically, would have the benefit of two-way communication and beam 

reception.” 

 Warner goes on to say that “the principal differentials of hazard, in addition to the 

difference in the amount of equipment to be carried, would then lie in the number and 

reliability of the power-plants and in the ability to get down into bad fields without the 

likelihood of damage to the airplane. Making what seems to be due and reasonable allowance 

on those accounts, I set the probability at a loss of the total value of one DH-4 airplane by 

crash (whether in a single complete washout or in a larger number of accidents of less 

individual destructiveness) for every 800,000 miles; for the Boeing Model 40, at one every 

2,000,000 miles; for the Ford, 3,500,000; for the Vega, 1,500,000; and for the Boeing 247 and 

the DC-3, 7,000,000.” 

Table 2-49. Insurance and Reserve Cost for the 900-Mile Trip Equals $12.60 for the DC-3 

Insurance + Crash Reserve Units Ford Douglas Notes 

 Insurance cost per mile cents/mile 1.90 1.40 Warner's numbers 

 Cost per ton-mile cents/ton-mile 1.19 0.56 (cents per mile)/(payload in tons)

 Cost per hour dollars/hr $2.38 $2.52 (cents per mile)(cruise speed)/100

 Cost per available seat-mile cents/seat-mile 0.19 0.07 (cents per mile)/(no. of seats) 

 Insurance and reserve cost per trip dollars $17.10 $12.60 (cents per mile)(900 miles)/100 

 It is only necessary now to show the total of the five categories to get Warner’s 

comparative estimates of direct operating cost (DOC) for the Ford Tri-Motor and the Douglas 

DC-3A. The sum, reproduced here as Table 2-50, shows that the most common DOC 

benchmark, cost per available seat-mile, was reduced from 3.41 to 1.27 cents per available 

seat-mile. This is more than a 50 percent reduction because of Douglas’ technology. 

Table 2-50. DOCs used by E. P. Warner to Show the Role Technology Played in Making 

Air Transportation Profitable Without Government Subsidies 

DOC Parameters Units 

Ford 

Tri-Motor 

Douglas 

DC-3A 

 Cost per mile cents/mile 34.11 26.72 

 Cost per ton-mile cents/ton-mile 21.32 10.69 

 Cost per hour dollars/hr $42.64 $48.10 

 Cost per available seat-mile cents/seat-mile 3.41 1.27 

 Cost per 900-mile trip dollars per trip $307.03 $240.50 
2.9 OPERATING COSTS 

589 

 In 1970 Ronald Miller and David Sawers’199 superb research about aircraft and 

airlines was published in the United States [628]. It is probably coincidental that the title of 

their book, The Technical Development of Modern Aviation, somewhat mirrors Edward 

Warner’s 1938 lecture titled Technical Development and its Effect on Air Transportation

[630]. Be that as it may be, the depth of research from airline files, the number of aircraft 

manufacturers contacted, and the list of contributors they acknowledge, allowed them to 

gather an enormous amount of technical data and DOC data. For example, in appendix I, they 

provide detailed DOCs in the standard form (CAB Form 41) for over 18 aircraft in airline use 

up to 1966. Fig. 2-400 is my summary of their work. It is clear that the Douglas Aircraft 

Company produced aircraft with the lowest DOC from just before the start of World War II 

until turbojet fixed-wing aircraft came on the scene and proved themselves, say by 1963. 

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

1926 1931 1936 1941 1946 1951 1956 1961 1966

Boeing 247D (piston)

Douglas DC-3 (piston)

Douglas DC-4 (piston)

Douglas DC-6 (piston)

Douglas DC-6B (piston)

Douglas DC-7 (piston)

Douglas DC-7C (piston)

Convair CV-240 (piston)

Convair CV-343/440 (piston)

Lockheed L-18 (piston)

Lockheed L-049 (piston)

Lockheed L-749 (piston)

Lockheed L-1049G (piston)

Lockheed L-1649 (piston)

Viscount 700 (turboprop)

Lockheed L-188 (turboprop)

Friendship F-27 (turboprop)

Boeing 707 (turbojet)

Douglas DC-8 (turbojet)

Then

Year

DOC

(Cents

per

Available

SeatMile)

Year

DC-3

DC-6

Boeing 707

DC-4

( )0.8526

40.6 DOC

Year 1903 = −

Douglas DC-8

Fig. 2-400. Historical view of direct operating costs (DOCs) in then year dollars for 

airlines. (Note: includes the effect of inflation.) 

 

199 The book’s jacket states that “Ronald Miller spent his undergraduate years at Harvard and went on to obtain 

his doctorate at Princeton after writing a dissertation on the application of modern mathematical techniques to 

airline scheduling (published as Domestic Airline Efficiency by MIT Press in 1963). He is now an associate 

professor at the University of Pennsylvania. 

 David Sawers spent three years at Oxford, then became research assistant to Professor John Jewkes, helping 

him in the writing of The Sources of Invention. From 1959 to 1964, he was a member of the editorial staff of The 

Economist. He then spent eighteen months at Princeton, as a visiting fellow in the Department of Economics, 

working on this book.”
2.9 OPERATING COSTS 

590 

 As I have noted on Fig. 2-400, this direct operating cost summary compiled by Miller 

and Sawers includes the effect of inflation. The authors, in appendix III of their book, 

provided an interesting data set about inflation. They wrote: 

“To be able to make allowances for changes in the prices of various goods and services used 

in operating an airplane, a composite Index of Input Prices has been constructed. Deflating the 

unit operating cost series of various aircraft by this index will thus remove the purely 

monetary effects of changing prices. The four items for which reasonably useful price 

material is available are: flying personnel, fuel and oil, mechanics and the aircraft themselves. 

(a) Flying personnel. This series reflects the trend in salaries of pilots, co-pilots and other 

flight personnel. Wage rate data, rather than annual earnings, would be preferable; because of 

the complexities of individual airline contracts with their pilots, this ideal was not feasible. 

Instead, the numbers of people in the Federal Aviation Agency’s classifications: pilots and copilots, and other flight personnel, for each of the years, were divided into the total annual 

payrolls for these two groups. 

(b) Fuel and oil. The total annual expenditure on fuel consumed by domestic carriers is 

divided by a composite figure—total gallons of gasoline and oil (and jet fuel, from 1955 

onward)—to produce an average annual cost of fuel-and-oil per gallon. 

(c) Mechanics. The trend in average annual earnings of mechanics is used as a measure of 

changes in the costs of performing aircraft (airframe and engine) maintenance. The same 

reservations regarding the use of annual earnings instead of a wage rate apply here as with 

flying personnel. 

(d) Aircraft. The index of aircraft prices which was used is explained in detail in section B of 

this appendix. 

In order to combine these separate series into one composite index, weightings were adopted 

based on the total annual expenditures by scheduled domestic air carriers on the different 

items. In the case of aircraft, the weighting employed was the annual expenditure on 

depreciation. In so far as the quality of each of these items has been improved over the years, 

this index probably rises too rapidly. In the case of human resources, both flying personnel 

and mechanics, such changes are extremely difficult to measure. The octane rating does 

provide an index of quality improvement for gasoline, but it has not been possible to 

incorporate it in the fuel and oil series. The aircraft index does attempt to remove the 

influence on prices of newer model airplanes, concentrating on changes in the price of an 

‘unchanged type’ over the years. (See below, section B.) The composite index and its 

component parts are shown in table 1, below.” 

The table Miller and Sawers are referring to is reproduced here as Table 2-51. 

 You might notice that if Fig. 2-400 was corrected for inflation, then the rise in DOC 

each year exhibited by some aircraft would not be very apparent. In fact, when the Boeing 

707 was introduced in 1959, its DOC was 1.77 cents per available seat-mile. But in 1948 

dollars, Miller and Sawers’ data suggest that the Boeing 707’s DOC would have been about 

1.07 cents per available seat-mile versus 1.87 for the Douglas DC-3. This suggests that if the 

Douglas DC-3 achieved one-half of the DOC of the Ford Tri-Motor and that made the airlines 

profitable, then the turbojet-driven, swept-wing aircraft—having 5 to 10 times the number of 

available seats (and nearly three times the cruise speed!)—should have really lowered air 

transportation fares. That, of course, is exactly what has happened. In the summer of 2008, I 
2.9 OPERATING COSTS 

591 

presented a seminar [631] about aviation history to several interns working for Bill 

Warmbrodt at NASA Ames Research Center. An introductory slide that seemed to go over 

well is shown here as Fig. 2-401. When I asked if any of the interns had come to NASA by 

cross-country flying, two interns said they had paid about $450 and made the trip in less than 

6 hours flying time—by modern jet aircraft. 

Table 2-51. Trends in Inflation [628] 

Year Flying Personnel Fuel and Oil Mechanics Aircraft Composite Index 

1939 65 77 42 74 65 

1940 63 76 41 68 63 

1941 67 78 45 70 66 

 

1948 100 100 100 100 100 

1949 102 107 109 111 107 

1950 106 108 118 127 114 

1951 115 106 124 129 118 

1952 124 109 130 137 124 

1953 137 114 132 144 130 

1954 144 120 144 147 137 

1955 144 115 142 151 136 

1956 148 113 145 160 139 

1957 153 117 144 176 145 

1958 167 117 154 187 152 

1959 185 99 176 217 166 

1960 198 85 172 225 168 

1961 211 79 189 225 173 

1962 223 74 191 236 177 

1963 234 70 197 258 187 

Fig. 2-401. It was the successive introduction of faster aircraft with more seats that led to 

the growth of airlines [631]. 

 

 

 

 18 hours with 3 stops. 21 passengers. 

$149.95 + $4.00 for swivel seats 

 + $8.00 for sleeper berth 

$149.95 in 1936 = $2,220 in 2008 

8 hours with no stops. 

 66 seats at 41-inch pitch 

 92 seats at 38-inch pitch 

$158.85 in 1955 = $1,210 in 2008

Three Major Steps in Transcontinental Passenger Air Service

 Ford Tri-Motor, 1929 Douglas DC-3, 1936 Lockheed L-1049G, 1955 

48 hours with 10 stops. 10 passengers. 

2,000 miles by air at 90 mph and 

 1,000 miles by train at 50 mph 

$351.94 in 1929 = $4,220 in 2008 
2.9 OPERATING COSTS 

592 

 Now let me conclude this discussion about direct operating costs. 

 The preceding tables and discussion show you the bare-bones bookkeeping of what is 

generally called direct operating costs or DOC, a common acronym you hear more than 

occasionally. Warner is careful to point out that “these, of course, are the totals for the direct 

costs alone, and indeed only for a selected group of the major items among them. To give an 

idea of the scale of charges or of Government assistance at which an airline could cover 

expenses, a total for all costs of operation, including the overhead, is required.” This second 

grouping has been called indirect operating costs. 

2.9.1.2 E. P. Warner’s Indirect Operating Cost Analysis 

 Your airline will require ground crews, main office staff (from president to janitor), 

and all other costs that support the flying operations. Warner called this major cost category 

Indirect Operating Costs, saying that “of the items not so far individually taken into account, 

some are roughly proportional to the totals tabulated above being the minor direct costs that 

may be expected to vary on much the same scale as the major ones. Some are proportional to 

the total mileage flown, and largely independent of the characteristics of the airplane. Some 

are proportional to the product of mileage by size, or to the total volume of traffic handled. 

Some examination of the manner of variation of individual elements of indirect cost and of 

traffic-handling cost has led me to the rough rule that total [operating] cost can be taken as 1.2 

times the total just tabulated [i.e., the five line items associated with direct aircraft operating 

cost leading to Table 2-50] plus 14 cents a mile, plus 9 cents a ton-mile (of payload) times 

payload.” Warner’s estimate means that the indirect operating cost is 

(2.366) 

( )

( )

Indirect Operating Costs 0.2 DOC in cents per mile

cents cents 14 9 useful load in tons

mile ton mile

=

  + +     −

 . 

Accepting Warner’s estimates of your airline’s probable indirect operating costs, you would 

find for the Ford Tri-Motor that 

( ) ( ) cents cents Indirect Operating Costs 0.2 34.11 14 9 1.6 mile ton mile

35.22 cents mile

  = ++     −

=

, 

and for the Douglas DC-3A, that 

( ) ( ) cents cents Indirect Operating Costs 0.2 26.72 14 9 2.5 mile ton mile

41.84 cents mile

  = ++     −

=

. 

2.9.1.3 Summary Results of E. P. Warner’s Total Operating Cost Analysis 

 Now having both direct and indirect operating costs, you can draw a comparison of 

total operating costs between a Ford Tri-Motor and a Douglas DC-3A. Your results, shown 

here in Table 2-52, immediately tell you the minimum what-to-charge story. Both aircraft 
2.9 OPERATING COSTS 

593 

Table 2-52. Operating Cost Summary 

Item Units Ford Tri-Motor Douglas DC-3A 

Direct operating cost cents/mile 34.11 26.72 

Indirect operating cost cents/mile 35.22 41.84 

Total cents/mile 69.33 68.56 

 

Other measures 

 Cost per ton-mile cents/ton-mile 43.3 27.4 

 Cost per hour dollars/hr $86.67 $123.41

 Cost per available seat-mile cents/seat-mile 6.93 3.26 

 Cost per 900-mile trip dollars per trip $624.01 $617.06

can fly your 900-mile trip at a virtually identical cost of about $620. If you use the Ford with 

only 10 seats, you will have to charge a fare of $62 per passenger. The 21-seat Douglas 

DC-3A lets you charge only $30 per passenger. Of course, these are just-break-even numbers; 

too many empty seats on the trip probably mean you will not make payroll that week! How 

you factor in (a) flying a trip at less than a 100 percent load factor, or (b) what weather might 

do, or (c) what happens if your aircraft is forced down in a farmer’s field thus creating some 

unscheduled maintenance are just a few of the decisions that you must make as president. 

 Now let me complete this example considering the fact that you have three DC-3As in 

your fleet. Suppose you want to provide 365-days-a-year service. You want to have one 

aircraft leaving Washington, D. C. in the morning, West bound for Huntsville, and a second 

aircraft leaving Huntsville in the morning at the same time, but East bound for Washington, 

D. C. That leaves you one aircraft in reserve at all times. Thus, one aircraft is always flying 

5 hours per day times 365 days per year, which equals 1,825 hours a year. This is well within 

the 5,000-hour life of the Pratt & Whitney engine that Warner used in his direct operating cost 

analysis. This would also be somewhat less than the 2,000-hours-per-year utilization Warner 

suggests as typical. Based on the $617 dollars per 900-miles-one-way trip from Table 2-52, 

your cost could be as high as two aircraft times $617 per day times 365 days per year, or 

about $450,000. The third aircraft might be available for some charter work but otherwise it is 

a “hanger queen” that, let me guess, only costs you 300 hours per year at $123 per hour, or 

about $50,000 per year. Your cost for the first year is, therefore, $500,000, even if nobody 

bought a ticket all year! 

 Just think about these costs for your first year. If you go to a bank and borrow the 

$350,000 to pay the Douglas Aircraft Company, you might get a loan of $250,000, provided 

the bank loan officer is convinced that you and your backers have a very feasible business 

plan. He would, I imagine, take the three new DC-3As as collateral and also insist that real 

insurance (not the self insurance you used in your DOC computations) be obtained. Say the 

loan officer offers you a 7-year loan at 4.5 percent interest (compounded annually). This deal 

means a monthly payment of 

( ) ( )7 12

0.045 0.045 12 Monthly payment $250,000 $3,900 12 1 0.045 12 1 ×

 

=+ =  

+ −  

, 
2.9 OPERATING COSTS 

594 

and this means that your fare structure must provide for another $46,800 per year. This is just 

one example of the “extra” costs that you must consider to get your airline up and running. 

 To close this discussion about direct and indirect operating costs (i.e., total operating 

costs) of running an airline, you should be aware that more than a few papers and reports have 

been published about how to estimate operating costs [632-635]. Fortunately, an accounting 

structure, negotiated between the Department of Commerce’s Civil Aeronautics Board (CAB) 

and the airlines in the 1940s, was refined over the years. In 1999, I tried my hand at creating 

an economic model for certificated airlines [636] using CAB/FAA Form 41 data that came 

from the Department of Commerce through Data Base Products200. The Form 41 has several 

schedules that provide you with detailed data. (Form 41 and its schedules are very much like 

the Internal Revenue Service Form 1040 and its schedules that the IRS requires each year.) 

The major accounting line items are shown in Fig. 2-402. You can see here that 

E. P. Warner’s bookkeeping of direct operating costs (DOCs) has been slightly rearranged and 

relabeled as “Total Aircraft Operating Expenses,” and that his indirect costs have been 

carefully expanded. I gave indirect operating costs a label of “All Other Operating Expenses” 

in reference [636] because Form 41 did not seem to have one. 

Fig. 2-402. Accounting tree for total operating expenses [636]. 

 

200 My contact at Data Base Products is Lucretia Frederich. I believe she knows more about Form 41 and Data 

Base’s manual and CD products [637] than anyone. She was unbelievably helpful as I worked to produce 

reference [636]. 
2.9 OPERATING COSTS 

595 

2.9.2 Helicopters 

 The founders and the leaders of our rotorcraft industry who followed, from Cierva to 

today, have always had a dream. Many early proponents believed that there could be a 

helicopter in every garage.201 The more practically minded believed that some sort of 

helicopter shuttle service around cities would be the ideal use of the helicopter. And today 

many believe that a helicopter operating between two nearby congested areas (such as 

between New York City and Boston in the United States, or between Tokyo and Osaka in 

Japan) will best serve national transportation needs. There are, of course, others who believe 

that high-speed rail is the most cost-effective solution for congestion. 

 An example of the high-speed rail view was offered by none other than Ronald 

Edwards George (R. E. G.) Davies, an Englishman born on July 3, 1921, who “wrote the 

book” on airline history in the United States [316]. His view [638] is very definitely worth 

your reading time because Davies was a lifelong aviation enthusiast right up until the day he 

died (July 30, 2011). He adapted his contribution to Aviation Week’s Handbook of Airline 

Economics from a lecture he gave before the Wings Club in New York City in May of 2000. 

At that time, he was the Curator of Air Transport at the National Air and Space Museum in 

Washington D.C. Davies “emphasize[d] four main criteria for long-range planning: 

1. 650-seat airliners will be in service 

2. Supersonic airliners will not 

3. Airport planning for 2020 must start now [in 2000] 

4. Major airports must incorporate high-speed rail.” 

Davies’ chapter in the Aviation Week Handbook is 25 pages long, and he makes a very strong 

argument for his view based on projections in population growth. He does not suggest that 

scheduled airline service with helicopters, or any other rotorcraft, is just around the corner. 

Davies was right on his first two points and may yet be right on the last two points. 

 You might think that R. E. G. Davies was unaware of helicopters and what they 

offered the transportation system. You would be wrong. He did, in fact, devote nearly 12 

pages out of 678 pages of his most referenced book [316] to a section he titled “Helicopter 

Experiments.” The primary experiment he describes concerned the CAB’s subsidy of Los 

Angeles Airways, Chicago Airways, and New York Airways from their certificated inception 

(May 1947, August 1949, and December 1951, respectively) to when the subsidy was 

“formally terminated on 11 April 1965.” One bright spot in this era was the start of San 

Francisco and Oakland Helicopter Airlines that began service in June of 1962. Davies makes 

the point that “a striking initial feature of the San Francisco helicopter operation was its 

independence of subsidy and, because of this demonstrated viability, it received in November 

1963 from the C.A.B. the first permanent C.A.B. certificate to be awarded to any helicopter 

carrier.” As Davies comes to the end of his story, he writes: 

 

201 Can you imagine a couple of hundred Saturday morning grocery shoppers coming by helicopter to land at a 

Walmart? 
2.9 OPERATING COSTS 

596 

 “After twelve years of passenger operations, therefore, the Helicopter Carriers had 

been given a good chance to prove the efficiency of rotor-driven aircraft, but had failed to 

make their case. When the subsidy was withdrawn, they had to seek other artificial support. 

There was no great wave of protest from the American public as a whole, and very few 

sympathizers from the airline world itself, except from the interested sponsors like Pan 

American, United, TWA, and American. 

 Senator T. H. Kuchel, the Californian Republican, wrote to the C.A.B. Chairman in 

April 1965 (when the subsidy was cut off) suggesting that Los Angeles Airways should be reclassified as a Local Service airline, and thus qualify for subsidy and a share of the 

$60,000,000 which was allocated annually to those carriers. But nothing came of this. 

Possibly the C.A.B. did not regard the type of service provided by LAA as a true social 

amenity, benefiting as it did only a minority of privileged citizens who wished to save a little 

time on the congested freeway system in the vast Southern Californian metropolis. 

 The Board had held serious doubts about helicopters for several years. On 17 May, 

1960, simultaneously with the renewal of New York Airways’ certificate for seven years, it 

affirmed that the type of equipment offered by helicopter operators need not be confined to 

rotary-winged aircraft in the true sense of the word. This was interpreted as permitting the use 

of VTOL (Vertical Take-off and Landing), STOL (Short Take-Off and Landing), and other 

direct-lift aircraft.” 

Despite what I think was a heroic effort, Los Angeles Airways had to give up in July of 1971, 

Chicago Helicopter Airways ceased operations December 31, 1965, and New York Airways, 

though carried on by Pan American for a while, closed its doors in 1972. By then, each of 

these pioneering efforts had experience with twin-turbine helicopters—the Boeing Vertol 

Model 107 II, the Sikorsky S-62, and then the Sikorsky S-61N. This step forward in 

helicopter progress by the manufacturers was still not great enough to make the helicopter 

airlines profitable without government subsidy. The helicopter industry just could not make 

the giant step that Donald Douglas provided with the DC-3. 

 There is, of course, still more to this story, which I will get to shortly, but first let me 

discuss the Federal Aviation Agency’s (FAA’s) view of helicopter airlines up to 1960 and 

what they forecasted for the future. 

2.9.2.1 Project Hummingbird 

The “Helicopter Experiment” that R. E. G. Davies referred to was named Project 

Hummingbird by the FAA [315]. The experiment began in October 1947 when Los Angeles 

Airways (LAA) was given a temporary certificate to carry mail and property. LAA began 

service almost immediately, and their small fleet started to accumulate aircraft miles rather 

quickly as Fig. 2-403 shows. Chicago Helicopter Airways (CHA), the next helicopter airline 

to carry mail, quickly added their helicopters to the budding experiment. Three years later, 

New York Airways (NYA) came online as the last mail carrier to participate in Project 

Hummingbird. In Appendix G you will find a copy of the FAA’s report about the experiment 

that gives results through 1959.202 This report provides enormous insight into how the FAA 

 

202 You would think such a milestone report would have received wide distribution, but when I checked to see if 

you could get a copy easily, I found it so buried away that I thought it was better to include it herein. 
2.9 OPERATING COSTS 

597 

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960

End of Year

Los Angeles

(mail)

Oct. 1947 

Chicago

(pass. & mail)

Nov. 1956 

Los Angeles

(pass. & mail)

Nov. 1954 

New York

(mail)

Oct. 1952 Chicago

(mail)

Sept. 1949 

New York

(pass. & mail)

July. 1953 

Revenue 

Aircraft 

Miles 

Flown

Each

Year

(1,000)

Fig. 2-403. Helicopter airlines steadily increased miles flown [315]. 

followed the same path that was taken in the creation of the fixed-wing airline industry. That 

is, build a route structure using helicopters to carry mail, and subsidize the adventure until the 

industry can stand on its own two feet and make a profit carrying passengers without 

government assistance. 

 The three helicopter carriers began with five different helicopter models: the Sikorsky 

S-51, S-55, and S-58; the Bell Model 47, and the Vertol Model 44. During the one year of 

1959, the three airlines, each with a very small fleet, had expanded to the point that they put 

nearly two million aircraft miles on their combined fleet. Because each successive helicopter 

came with more seats, the three airlines quickly found themselves transporting an ever 

increasing number of passengers each year. In fact, being well subsidized so fares would be 

competitive with ground transportation, the growth in paying customers was exponential 

(Fig. 2-404), and the trend suggested even better things to come in the 1960s. Of course, the 

trip miles each passenger was transported was rather short—the average trip distance being 

only about 20 miles in 1959. This was, in part, due to the FAA restricting the helicopter 

airlines to a radius of 50 to 60 miles about their respective cities. The FAA made it very clear 

that they did not want the helicopters encroaching on the routes of trunk-line and short-haul 

carriers that they were already subsidizing to the tune of $60,000,000 a year (Fig. 2-405). 
2.9 OPERATING COSTS 

598 

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

1952 1954 1956 1958 1960 1962 1964 1966

Passengers

Carried

Each

Year

(1,000)

Year End

Fig. 2-404. The helicopter airlines got off to a very good start, and the projections 

through 1965 looked rosy [315].

-$1,000,000

$0

$1,000,000

$2,000,000

$3,000,000

$4,000,000

$5,000,000

$6,000,000

$7,000,000

$8,000,000

$9,000,000

1955 1956 1957 1958 1959 1960

Total 

Operating 

Revenue

For Year Ending

Mail & Freight

Passengers

Subsidy

Fig. 2-405. CAB/FAA subsidy amounted to over 60 percent of what the three helicopter 

airlines needed to break even [315].
2.9 OPERATING COSTS 

599 

 The revenue from carrying passengers quickly exceeded that coming from carrying 

mail and other property. Unfortunately, the direct and indirect costs (i.e., the total operating 

costs) far exceeded the revenue coming in from fares and mail carrying operations. The 

situation—as I interpret it from reading the report on Project Hummingbird included here in 

Appendix G—is shown in Fig. 2-406. It appears that the total operating costs for each of the 

first 5 years was running at $14.61 for every passenger carried. This is the slope of the line 

shown in Fig. 2-406 going through the solid green boxes. The data points are from table 13 of 

the Project Hummingbird report and the abscissa, of passengers carried each year, is from 

table 4. The trip distance is on the order of 20 miles, as an average. Therefore, the 

approximate cost per paying passenger seat-mile is 73 cents (i.e., 1461/20), which is a more 

pessimistic way of looking at the 5-year period than the several tables in Appendix G show. 

 Of the total $14.61 per passenger required to just break even, the helicopter airlines 

were only charging their passengers $6.67 per average trip. You might note in reading 

Appendix G that the actual operating costs were coming down (see table 15 in Appendix G), 

and the helicopters finally reached a point in 1959 where half of the seats were filled on an 

average trip (see table 7 in Appendix G). However, weather-related problems kept the fleet 

grounded about 12 percent of the time the aircraft were scheduled to fly. Still, everyone 

thought that progress was being made. 

$ = 14.61P + $2.86 million

$0

$3,000,000

$6,000,000

$9,000,000

$12,000,000

$15,000,000

0 300,000 600,000 900,000 1,200,000 1,500,000 1,800,000

Projected 

Funding

Passengers Carried Each Year (end of year)

1960

1964

1963

1962

1961

1965

1959

Total

Income 

Required

to Break 

Even

Congress Caps 

Subsidy at $6 

million

Congress Cuts Subsidy to $4.3 million, Dec. 1964

Congress

Terminates

Program

April 11, 1965

Airlines only Charging

 $ 6.67 per Passenger

Fig. 2-406. The helicopter airlines had total operating costs far in excess of what they were 

charging their customers [315]. 
2.9 OPERATING COSTS 

600 

 What seems to be of great concern was the out-year projection of how many 

passengers might be expected. If the subsidy stayed at $7.94 per passenger and the number of 

passengers transported continued to climb, then there would be a considerable drain on the 

U.S. Treasury. In essence, if the helicopter airlines continued to attract the traveling public as 

the projections were suggesting, the helicopter airlines would break the bank. 

 As you read the Project Hummingbird report [315] included here in Appendix G, you 

will see that the CAB thought that helicopter operating costs were the problem. The statement 

is repeated several times and, most discouragingly, they did not see a helicopter currently in 

development that would alter the outlook. The suggestion was also made by the CAB that the 

helicopter airlines might raise their fares so the subsidy could be reduced. However, the 

airlines felt that the current levels were “in the judgment of airline management” at just the 

right level “to produce the maximum gross revenues while meeting requirements to be 

competitive with limousine and cab fares and to contribute to traffic development.” 

 The helicopter airline management pointed at the soon-to-be-available Boeing Vertol 

107 and Sikorsky S-61 as twin-turbine helicopters that would reduce direct operating costs 

when compared to the then current fleet. The problem, as summarized by the CAB in table 16 

of their report, is included here as Table 2-53. To explain the helicopter situation to fixedwing advocates, the report (see table 14 in Appendix G) shows that domestic trunk and localservice airlines had total operating costs in 1959 of $0.28 and $0.51, respectively, per 

available ton-mile, as compared to total operating costs of $4.05 per available ton-mile for the 

helicopter airlines as a group in 1959. This comparison was startling to some and showed just 

what a tall mountain the helicopter airline advocates had to climb. 

 The CAB was careful to point out that the problem was not just direct operating cost. 

Their report included table 15, provided here as Table 2-54, which must have, I am guessing, 

sealed the fate of those pioneers of helicopter airlines. As you can see, even if the direct 

operating costs of all of the helicopters in operation were reduced to zero, the indirect 

operating costs were still way out of line with comparable fixed-wing trunk and short-haul 

carriers. 

Table 2-53. Direct Operating Cost of Helicopters Operating in Certificated Airline 

Service for Years Ending June 30, 1958, and September 30, 1959 

Helicopter Type 

Year Entered 

Service 

DOC Per Hour 

Flown ($) 

DOC Per Available 

Ton-Mile ($) 

DOC Per Available 

Seat-Mile ($) 

Sikorsky S-51* 1947 – – – 

Bell B-47 1949 54.37 to 54.75 4.95 to 5.33 – 

Sikorsky S-55 1952 77.97 to 142.10 2.38 to 7.35 0.28 to 0.35 

Sikorsky S-58 1956 208.05 to 260.92 1.67 to 3.02 0.20 to 0.33 

Vertol V-44B 1958 256.28 to 260.35 3.35 to 3.47 0.36 to 0.40 

*The S-51 was flown too few hours for any meaningful cost experience. 
2.9 OPERATING COSTS 

601 

 While the Postal Department was quite willing to subsidize fixed-wing airline 

development for nearly three decades,203 the CAB was not going to recommend nurturing 

helicopter airlines for any more than the 18 years between 1947 and 1965. I had two feelings 

from the Project Hummingbird report: (1) they did not foresee a step comparable to the 

replacement of the Ford Tri-Motor with the Douglas DC-3 even by 1970, and (2) mass transit 

was not ever going to be the helicopter’s (the report mentions V/STOL configurations204) 

strong suit. 

 It is interesting that the helicopter airlines were carried for several more years after the 

Hummingbird report came out, but I think that this was just a gesture to the proponents who 

felt that the operational data from the new twin-turbine helicopters might cast a whole new 

light on the economic situation. You get this feeling from the first paragraph in the Unit Costs 

and Fares section (page 914 of Appendix G), which says: 

 “In addition to greatly improved performance characteristics, the new twin-turbine 

helicopters ordered by the three certificated operators are also expected to provide important 

reductions in unit costs. Actual operating experience with the new turbocopters is lacking, of 

course, but available estimates show a range of about 10 cents to 16 cents for direct operating 

costs per available seat mile. Comparatively, direct operating costs of the piston-powered 

S-58 are 20 cents per seat mile. If these unit cost estimates are realized, they will therefore 

represent a substantial improvement over current levels which suggest the possibility of lower 

fares as a factor which will promote traffic growth.” 

I read the FAA report as saying that they did not want to call a halt to the “helicopter 

experiment” until the next-generation helicopter was given a chance to demonstrate that it 

would cut direct operating costs by as much as 50 percent. The helicopter that the helicopter 

airline pioneers were pinning their hopes on was the Sikorsky S-61. 

 I hope you read the full Project Hummingbird report included in Appendix G of this 

volume. 

Table 2-54. Direct and Indirect Operating Costs of Certificated Helicopter Airlines 

From 1955 to 1959

Dollars Per Available Ton-Mile Dollars Per Revenue Ton-Mile

Year Total Direct Indirect Total Direct Indirect

1955 6.75 3.62 3.13 15.22 8.16 7.06

1956 6.37 3.22 3.15 12.96 6.55 6.41

1957 4.82 2.93 1.89 11.50 6.99 4.51

1958 3.98 2.47 1.51 10.04 6.22 3.82

1959 4.05 2.54 1.51 8.29 5.20 3.09

 

203 The story is well told by F. Robert van der Linden [498]. 

204 The Project Hummingbird report makes reference to compound helicopters and short takeoff and landing 

aircraft, which are configurations I will discuss in Volume III: Other V/STOL Aircraft. 
2.9 OPERATING COSTS 

602 

2.9.3 A Direct Operating Cost (DOC) Calculator 

 You have just read that the three helicopter airlines, LAA, CHA, and NYA, needed a 

helicopter that would cut their direct operating costs by at least 25 percent, and hopefully even 

in half. You can appreciate the giant step that was being taken just by looking at LAA’s effort 

from starting with the 4-passenger-seat Sikorsky S-51 in 1947 (Fig. 2-407), to 15 years later 

when the 26-passenger-seat (in a full airline interior) Sikorsky S-61 (Fig. 2-408) came online. 

As I read the history, I began to wonder if, in fact, the S-61 did lower DOCs. My searching 

(as of this writing) has not turned up an answer, though I imagine that archives somewhere 

have the answer. So I thought it would be fun to see if a reasonable estimate might be 

obtained. That is the purpose of the following: to use a DOC calculating method of that time 

to estimate the DOC for a Sikorsky S-55 and compare it to an S-61, both operating in 1967. 

 One of the earliest methods for estimating helicopter operating expense, that I am 

aware of, was published by Bob Stoessel and Jack (John E.) Gallagher205 in October of 1967 

[639]. They were offering a more realistic approach to estimating DOC for Vertical Takeoff 

and Landing (VTOL) aircraft. Their paper briefly traces development of the Air Transport 

Association of America’s (ATA’s)206 DOC calculation method from its beginnings in 1944. 

What Stoessel and Gallagher proposed was a tailoring of the ATA method for use in 

comparing and estimating DOC of VTOL aircraft. At that time, exploration of many VTOL 

types was in full swing. Jack Gallagher, as President of New York Airways, was able to 

contribute “accurate maintenance data [for the Sikorsky S-61 and Boeing V-107] in sufficient 

detail to be useable as a base or anchor points.” The major distinction between fixed-wing and 

rotary wing aircraft that was addressed was maintenance costs. Stoessel and Gallagher 

proposed adding to the then current ATA method consideration in more depth of “costs 

incurred per flight cycle and costs incurred per engine shutdown.” 

 I will use the Stoessel and Gallagher DOC estimating method of 1967 to compare the 

Sikorsky S-55 (10 passenger, piston powered) to the Sikorsky S-61 (26 passenger, turboshaft 

powered). In deference to Jack Gallagher, this example will use the New York Airways interairport shuttle flight path route (Fig. 2-409), schedule (Fig. 2-410), and fares (Fig. 2-411) as 

the operation for each helicopter to complete. Of course, any scenario could be studied. The 

three primary cost categories (and their next-level breakdown) that contribute to DOC will be 

those addressed by Stoessel and Gallagher. They are: 

• Flying operations (flight crew, fuel and oil, insurance) 

• Direct maintenance of flight equipment (accounting for per rotor hour, per flight 

cycle, and per engine shutdown) 

• Depreciation of flight equipment (including spares) 

 

205 Jack Gallagher was an instrumental figure in New York Airways. I was put in touch with Jack Gallagher Sr. 

by his son (also named Jack Gallagher) who worked in program management at Bell Helicopter Textron while I 

was there. 

206 The ATA was the first, and remains the only, trade organization of the principal U.S. airlines.
2.9 OPERATING COSTS 

603 

Fig. 2-407. LAA, the first helicopter airline, began airmail carrying operations with the 

Sikorsky S-51 on October 1, 1947 (photo from author’s collection). 

Fig. 2-408. LAA was the first to use the Sikorsky S-61; it was introduced into service on 

March 1, 1962 (photo courtesy of Ed Coates).
2.9 OPERATING COSTS 

604 

Fig. 2-409. NYA route map during its early startup years (author’s collection).

Fig. 2-410. NYA hourly schedules for inter-airport show how short the in-flight travel 

times were using the Sikorsky S-55 (author’s collection). 
2.9 OPERATING COSTS 

605 

Fig. 2-411. NYA fare structure using the Sikorsky S-55 was thought to be competitive 

with ground transportation in August of 1957 (author’s collection).

 You will see that I have based all costs on one trip. This takes some poetic license 

with Stoessel and Gallagher’s published work, but you will see results in terms of DOC per 

hour and DOC per seat-mile in the summary. 

2.9.3.1 Flight Profile 

 The example flight profile I have constructed envisions leaving New York 

International Airport (now John F. Kennedy Airport) for LaGuardia Airport, and then 

continuing on to Newark Airport. Then a return trip is made by retracing the outbound route. 

You have, therefore, the following flight profile scenario: 

 Start rotors turning at 7:45 a.m. 

 Lv. N.Y. Int’l at 8:00 a.m. after 15 minutes of ground operation with rotors turning 

 Ar. LaGuardia at 8:10 a.m. after 10 minutes at cruise 

 Lv. LaGuardia at 8:15 a.m. after 5 minutes of rotor-turning ground operation 

 Ar. Newark at 8:35 a.m. after 20 minutes at cruise 

 Lv. Newark at 9:00 a.m. after 25 minutes of ground operation (5 minutes of ground 

 operation with rotors turning + 20 minutes in shutdown and restart) 

 Ar. LaGuardia at 9:20 a.m. after 20 minutes at cruise 

 Lv. LaGuardia at 9:25 a.m. after 5 minutes of rotor-turning ground operation 

 Ar. N.Y. Int’l at 9:35 a.m. after 10 minutes at cruise. 

 Shutdown for 15 minutes, refuel, and be ready to take the 10:00 a.m. trip with a rotor 

 startup at 9:50 a.m. 
2.9 OPERATING COSTS 

606 

 This postulated flight profile provides several important parameters necessary for 

calculating the DOC. These parameters are: 

 1. Time spent at cruise is 10 + 20 + 20 + 10 minutes = 1.0 hour 

 2. Time spent in rotor-turning ground operation is 15 + 5 + 5 + 5 minutes = 0.50 hour 

 3. Total rotor-turning time per trip = 1.5 hour/trip 

 4. Number of flight cycles (i.e., ground-air-ground) per trip = 4 

 5. Number of engine startup and shutdown cycles = 2 

 6. Total round-trip time (leave at 8:00 a.m. and return at 9:35 a.m.) = 1.58 hours 

 7. Total round-trip distance traveled = 85 statute miles 

While the S-61 cruises faster than the S-55 on paper, I have chosen to assume that both 

helicopters fly the same schedule. This may potentially penalize the S-61 in fuel used, but the 

distances are so short, and the possibility of traffic control holdups so real in this example, I 

doubt that the S-61’s cruise speed benefit would be seen in the final numbers. 

 The question of how many trips are made in a year is particularly important to 

distributing yearly costs of insurance and depreciation. When you look at the inter-airport 

shuttle service that New York Airways offered (Fig. 2-410), you can count about 16 roundtrips scheduled for each day. The schedule offers this service 6 days a week for 52 weeks, 

skipping Sundays and holidays. This means that rotor-on time each day could be on the order 

of 16 trips times 1.5 hours per trip or 24 hours! Clearly, this would leave no time for 

scheduled maintenance (never mind unscheduled maintenance), and this means the fleet must 

consist of more than one helicopter. Therefore, let me assume that one helicopter makes 3 

round trips per day, in which case the number of trips in 1 year is calculated as 3 trips/day × 6 

days/week × 52 weeks/year or 936 trips per year. This assumption means the rotor-on time is 

about 1,400 hour per year, which is, in fact, a very high utilization rate for helicopters. On the 

other hand, there are 8,760 hours in a year, and this leaves about 6.25 maintenance hours for 

every rotor-turning hour. 

 With the above background in place, let me proceed with the DOC calculation. 

2.9.3.2 Flight Crew Costs 

 In discussing the cost of a flight crew, Stoessel and Gallagher did not reference a year, 

but let me assume it is 1967. Because this example is a comparison in the same year, the 

actual year is relatively unimportant. They said in their paper that 

“the formulas for flight crew represent an average for the U. S. helicopter air carriers. They account for 

the following factors: 

 Size of crew 

 Crew pay differential 

 Average crew utilization 

 Credit (or duty) hour increment 

 Travel and incidental expense 

 Check pilots’ pay increment 

 Retirement, payroll tax, and insurance contribution increment” 
2.9 OPERATING COSTS 

607 

and proceeded to use the estimating formula as: 

(2.365) $ GW Rotor time Vcr $45 0.03 2.00

Trip 1,000 100 Trip

       

=+ +                

where GW is the maximum certificated gross weight in pounds, and Vcr is the average cruise 

speed in miles per hour. For the S-55, you have GW = 7,200 pounds and an economical cruise 

speed of 75 miles per hour. For the S-61, you have GW = 20,500 pounds and an economical 

cruise speed of 115 miles per hour. Therefore, the flight crew costs for the two helicopters 

amount to: 

 S-55 equals $70.07 per trip for flight crew 

 S-61 equals $71.87 per trip for flight crew. 

2.9.3.3 Fuel and Oil Costs 

 To approximate fuel and oil costs, Stoessel and Gallagher showed computations for 

both U.S. domestic and international cases. Here, I will only deal with the U.S. domestic case 

where Jet A fuel was being bought by the airlines for $0.11 per gallon, and oil was 

considerably more at $7.50 per gallon.207 Following their proposed method, fuel and oil costs 

are calculated as 

(2.365) 

( )

$ Fuel used in lbs 1 $

Trip Trip lbs gal. gal. Avgas

1 $ Rotor time in hours 0.13 No. of engines lbs gal. gal. oil Trip

    =        

    

+          

. 

Stoessel and Gallagher noted that Jet A fuel had a density of 6.7 pounds per gallon and that oil 

for turbine engines was 8.1 pounds per gallon. They did not suggest prices and densities for 

piston engines. Therefore, I will use approximate values of Avgas at 6.1 pounds per gallon 

and oil for piston engines at 8.1 pounds per gallon. For 100-octane Avgas, I will guess the 

price at about $0.13 per gal and oil at $7.50 per gallon. 

 An accurate estimate of fuel burned per trip requires, of course, a thorough 

understanding of the performance of both helicopters, but as representative values, let me use: 

Helicopter 

Fuel Flow at 

Cruise (gal./hr) 

Economical Cruise

Speed (mph) 

Fuel Flow at 

Flight Idle (gal./hr) 

S-55 40 75 5 

S-61 160 115 20 

From the flight profile, 1 hour is spent at cruise and 1/2 hour is spent at ground idle. 

Therefore, the S-55 uses 40 + 2.5 or 42.5 gallons, or 260 pounds, in one round-trip; the S-61 

uses 160 + 10 or 170 gallons, or 1,139 pounds in one round-trip. This information shows the 

fuel and oil costs for the two helicopters being compared as: 

 

207 In early 2012, Jet A fuel was selling for $5.63/gal. and Avgas for $6.04/gal. The respective engine oils were 

selling for $57.18/gal. and piston engine oil for $64.42/gal. 
2.9 OPERATING COSTS 

608 

 S-55 equals $5.71 per trip for fuel and oil 

 S-61 equals $19.06 per trip for fuel and oil. 

2.9.3.4 Insurance 

 Stoessel and Gallagher’s view on insurance was that 

 “the annual rate of insurance is usually high for the initial service period of a new ‘family’ of 

aircraft where there are major innovations in technology or state of the art. The initial rate for 

a new type of aircraft similar to one already operational is also somewhat higher, but not as 

high as for a new family. The following are representative variations in insurance rates with 

service experience: 

When VTOL transport aircraft become widely used for short-haul operation, the insurance 

rates will become equivalent to those for conventional fixed-wing or [conventional takeoff 

and landing] CTOL aircraft. Therefore, a stabilized rate of 2 percent, which would be 

attained by the third year of operation, is used. Using this recommended rate, the insurance 

cost after the third year of operation is: 

(2.365) $ 0.02 (Cost of complete aircraft in dollars)

Trip Trips per year = .

”

According to HeliValue$, Inc. [132] data, in 1967 an S-55 sold for about $350,000, and an 

S-61N sold for about $1,200,000 (both being in the equipped configuration). Accepting the 

estimate that one helicopter in the fleet does 936 trips per year, you arrive at: 

 S-55 equals $7.27 per trip for insurance 

 S-61 equals $24.92 per trip for insurance. 

2.9.3.5 Direct Maintenance 

 Stoessel and Gallagher believed that considerably more detailed estimating was 

required in the area of direct maintenance cost of flight equipment. They offered the opinion 

that both labor man-hours and repair parts’ costs must be accounted for on a per-rotor-hour 

basis, a per-flight-cycle basis, and a per-engine shutdown and restart basis. They wrote in their 

introduction (with some condensing and editing on my part): 

“Introduction. The basic philosophy employed in the derivation of maintenance labor and 

materials formulas is that (1) it is valid to project VTOL aircraft maintenance costs from data 

on existing rotary wing aircraft provided that rational adjustment factors are introduced and 
2.9 OPERATING COSTS 

609 

(2) the best base from which to project such costs is the experience of commercial helicopter 

airlines, particularly those with comprehensive detailed records of maintenance. 

 New York Airways uses the Air Transport Association’s Specification 100 System 

for segregating and recording maintenance labor and material cost. As sufficient statistical 

information becomes available, the following grouping is recommended for comparative 

maintenance cost analyses: 

 1. Airframe 

 Aircraft (less engines, rotors & controls and drive system) 

 Rotors & Controls 

 Drive System (transmissions & shafts) 

 2. Engines 

 However, when analyses are made for initial concepts and for parametric studies, 

just the two major groupings—of airframe and of engines—are recommended. This is the 

case, also, when brochure and other descriptive data are utilized to supply input for such 

studies, because these seldom provide information in sufficient detail to warrant separation of 

the airframe into its major components. 

 When the VTOL aircraft now in commercial air carrier service are compared with 

their CTOL or fixed wing counterparts from the standpoint of maintainability characteristics, 

it is apparent that the time element is of greater significance than the cyclic one. Two reasons 

for this appear to be: 

 1. The greater amount of vibration—even with rotors operating in ground-idle. 

 2. Decreased maintenance requirements for landing gear structure, wheels, tires and 

 brakes (a function of flight cycles, or wheels-off to wheels-on). 

 Rotor time (the total time of rotor operation) has been selected as a measurement of 

the "time" factor because (1) most of the systems are functioning completely when rotors are 

engaged (this includes a greater amount of engine power than for ground idle with CTOL 

aircraft) and (2) there is such a wide variation in the ratio of rotor hours to flight hours, from a 

low of 1.09 for one of the helicopter operations analyzed to a high of 1.78 for another. 

 As for measurement of maintenance cost as a function of engine shutdowns (engine 

start, operation at some temperature or temperatures, and shutdown), there are generally only 

four elements of the aircraft so affected. These are (1) engine, (2) engine starting system, 

(3) engine exhaust system and (4) rotor brake.” 

2.9.3.5.1 Airframe Maintenance Costs 

 Stoessel and Gallagher prefaced their equations for estimating airframe maintenance 

with a brief discussion of the parameters involved. They wrote: 

“Parameters. The basic parameters considered desirable for comparative analyses of VTOL airframes 

are: 

a. Cost and weight of 

 Basic Airframe (less rotors & controls, and drive system) 

 Rotors & Controls 

 Drive System (transmissions & shafts) 

b. Cabin area (for determination of maintenance costs for ‘payload accommodations’) 

For analyses involving initial concepts and parametric studies, the foregoing requirements are reduced 

to: 
2.9 OPERATING COSTS 

610 

a. Weight of aircraft, less engines 

b. Cost of aircraft, less engines 

 A maintenance burden ratio of 1.8 times direct labor is now recommended for general 

operating expense comparisons of CTOL [Conventional Takeoff and Landing] aircraft. Nevertheless, 

the ratio recommended for VTOL aircraft is 1.3, because this is more in line with current averages for 

helicopter and for local service carriers. As for direct labor rates, an hourly rate of $4.00 per manhour is 

recommended. This is identical to the rate used in the forthcoming ATA method for CTOL aircraft.” 

I have regrouped Stoessel and Gallagher’s equations into one equation so that you now have 

the following for the estimate of airframe maintenance labor man-hours per trip: 

(2.365) 

1 1

2 2

af af

1

2

af

Man-hours Rotor hours Flt. cycles W W 3.0 2.0 0.2 0.2

Trip 1,000 Trip 1,000 Trip

W Engine shutdowns 0.1 0.1

1,000 Trip

       

=+ ++                

     

+ +            

. 

And for airframe materials per trip, Stoessel and Gallagher offered: 

(2.366) 

af af

6 6

af

6

Dollars Cost Rotor hours Cost Flt. cycles 4.0 4.0 0.6 0.6

Trip 10 Trip 10 Trip

Cost Engine shutdowns 0.3 0.3

10 Trip

          = +    + +                 

     

+ +            

. 

 Of course, the man-hours per trip, Eq. (2.365), needs to be expressed in dollars per 

trip. This conversion introduces one of the most widely sought numbers in any evaluation of a 

new aircraft’s maintenance program. This parameter is maintenance man-hours per flight hour 

(MMH/FH). You see its importance because 

(2.367) 

( )

( )

Dollars FH Direct Labor Rate Overhead rate

Trip trip mh

MMH Direct Labor Rate Overhead rate

trip m

M H

FH

h

M    =      

 

     

 =      

. 

Maintenance man-hours per flight hour for the helicopters flying today range from a low of 

0.5 to as much as 6 MMH/FH, although a few of the most recent, larger helicopter models are 

below 5 MMH/FH as you will see shortly. Please take note that Stoessel and Gallagher 

addressed the parameter not as man-hours per flight hours, but rather as man-hours per rotorturning hours. 

 Now let me introduce some specific numbers to make a comparison between the 

S-55 and the S-61. First of all, you have the flight profile information that there are 1.5 rotor 

hours per trip, four flight cycles per trip, and two engine shutdowns per trip. Furthermore, 

Stoessel and Gallagher observe that the direct labor rate in 1967 is $4.00 per hour, and they 

recommend the overhead rate (i.e., the maintenance burden ratio) of 1.3. On this basis, only 

the airframe weight (Waf), which is the weight empty less the engine weight and the airframe 
2.9 OPERATING COSTS 

611 

cost (Costaf), again not including the engine, are required before the calculation can be 

completed. The weights, of course, are available from many sources (though not many 

sources agree). The airframe and engine cost-split making up the selling list price is not so 

easy to come by, as I have mentioned before. For this example, I have assumed the total 

power plant(s) cost is one-fourth of the selling list price. It is useful to have the numbers in a 

small table, which I have included here as Table 2-55. 

 From here on out, the calculations are straightforward arithmetic, and you will find 

that “airframe” direct maintenance costs for one trip amount to: 

 S-55 equals $53.31 per trip for airframe direct maintenance ($41.95 labor; $11.36 materials) 

 S-61 equals $68.27 per trip for airframe direct maintenance ($51.17 labor; $17.10 materials). 

Table 2-55. S-55 and S-61 Data for DOC Calculations

Type 

No. of 

Engines 

Weight 

Empty (lb) 

List Price 

($) 

Airframe 

Weight (lb) 

One Engine 

Weight (lb) 

Airframe 

Cost ($) 

One Engine 

Cost ($) 

S-55 1 5,250 0.35 mil 4,400 850 0.2625 mil 0.0875 mil 

S-61 2 12,460 1.20 mil 11,700 340 0.90 mil 0.150 mil 

2.9.3.5.2 Engine Maintenance Costs 

 Here again Stoessel and Gallagher preface their equations for estimating engine 

maintenance with a brief discussion of the parameters involved. They wrote: 

“Parameters. The engine parameters considered satisfactory for use in evaluation of operating 

expenses of VTOL aircraft are basic parameters considered desirable for comparative 

analyses of VTOL airframes: 

a. Number of engines 

b. Equivalent shaft horsepower per engine [at rated takeoff power, sea level on a 

 standard day] 

c. Cost per engine 

As in the case of VTOL airframes, the following assumptions can be used for engine 

maintenance: 

a. Labor rate—$4.00 per manhour 

b. Maintenance burden—30 percent of direct labor” 

and suggested that for engines without gearboxes the estimating equation would be: 

(2.368) 

TOrated

eng eng

TO

eng eng

1

2

TOrated

eng eng

Man-hours Rotor hours SHP

0.5N 0.02N

Trip 1,000 Trip

SHP rated Flt. cycles 0.2N 0.02N

1,000 Trip

SHP Engine sh 0.1N 0.01N

1,000

     

= +            

     

+ +            

   

+ +        

utdowns

Trip

     

. 

Quite interestingly, they differentiate between engine drivetrains where there is an engine 

gearbox attached to the engine. I suspect this reflects the difference between a Boeing Vertol 
2.9 OPERATING COSTS 

612 

107 and a Sikorsky S-61 as Gallagher experienced at New York Airways in 1967. To account 

for “engines with gearboxes” they only changed one number in Eq. (2.368), which had to do 

with the man-hours per rotor hours. They suggested that the configuration differences should 

increase 

TO rated TO rated

eng eng eng eng

SHP SHP

from N 0.02N to N 0.02N

1, 000 1, 000

0.50 0.55

          + +              

. 

 Stoessel and Gallagher then gave their equation for engine materials per trip offering: 

(2.369) 

eng eng

eng 5 5 eng

eng

eng 5

Dollars Cost Rotor hours Cost Flt. cycles 2.1N 1.3N

Trip 10 Trip 10 Trip

Cost Engine shutdowns 0.7N

10 Trip

         

= +                    

     

+            

. 

 The configuration description provided in Table 2-55 only needs the added 

information that the S-55 had only one engine (Neng = 1), a Pratt & Whitney Wasp R-1340-57, 

rated at a SHPTO rated of 600 horsepower takeoff at sea level on a standard day. The S-61 was a 

twin-turboshaft-powered machine (Neng = 2). One engine was rated at SHPTO rated equal 1,400 

horsepower. Neither helicopter had engines delivered with gearboxes, so Eqs. (2.368) and 

(2.369) apply in this comparison. 

 Again, from here on out the calculations are straightforward arithmetic, and you will 

find that “engine” direct maintenance costs for one trip amount to: 

 S-55 equals $18.04 per trip for engine direct maintenance ($9.51 labor; $8.53 materials) 

 S-61 equals $49.34 per trip for engine direct maintenance ($20.09 labor; $29.25 materials).

2.9.3.5.3 Total of Direct Maintenance Costs 

 The contributions of airframe and engine maintenance costs can be summarized as you 

see here in Table 2-56. 

 This summary would, of course, be incomplete without highlighting what many 

perceive as the key parameter of man-hours per flight hour. You no doubt realize that Stoessel 

and Gallagher chose instead man-hours per rotor-turning hour based, I would assume, on New 

York Airways’ operational data. They apparently felt that it made little difference to 

maintenance costs whether the rotor was turning in flight or running at ground idle. 

Table 2-56. S-55 and S-61 Direct Maintenance, $/Trip Data for DOC Calculations

Helicopter Total 

Airframe

Total 

Airframe

Labor 

Airframe

Material 

Engine

Total 

Engine 

Labor 

Engine 

Material 

S-55 71.35 53.31 41.95 11.36 18.04 9.51 8.53 

S-61 117.62 68.27 51.17 17.10 49.34 20.09 29.25 
2.9 OPERATING COSTS 

613 

 To emphasis what I believe was their main point, they included two graphs showing 

how maintenance man-hours could accumulate when flight cycles, and engine shutdowns and 

restarts, are added to man-hours required because of rotor-turning time. These two pieces of 

information are included here as Fig. 2-412 and Fig. 2-413. These two figures show that using 

a helicopter (or any other VTOL machine, for that matter) on very short-haul trips, like a bus 

or perhaps even commuter trains, can require as many labor man-hours due to stopping and 

starting as are required because of cruising. 

 Before going on to depreciation, the last operating cost line item, there is one thing I 

might add. It bothers me that the curves shown in Fig. 2-412 and Fig. 2-413 do not go through 

zero-zero. In fact, the dominant man-hour cost in the airframe group says that even if the 

Fig. 2-412. Airframe maintenance labor man-hours are a function of airframe weight 

(i.e., weight empty less engine(s) dry weight) [639]. 

Fig. 2-413. Engine maintenance labor man-hours are a function of the engine’s sea-level 

standard takeoff rating [639]. 
2.9 OPERATING COSTS 

614 

airframe weight (which includes the rotor systems) is zero, it still takes 3 man-hours per rotorturning hour. This assumption implies that small, 2- or 3-seat helicopters will be severely 

penalized. Therefore, I would suggest that Stoessel and Gallagher’s curves deserve some 

attention. The curves may be quite satisfactory for the Boeing Vertol 107- and Sikorsky 

S-61-size machines of the 1960s, and even for larger VTOL configurations. However, an 

extrapolation to helicopters of twice the size must surely be open to question. Frankly, the 

situation today is that the rotorcraft industry is still having considerable trouble establishing 

believable maintenance man-hours per flight hour even after detail design is completed. 

2.9.3.6 Depreciation of Flight Equipment 

 In approaching direct operating costs due to depreciation, Stoessel and Gallagher took 

the position that “there seems to be no reason for VTOL aircraft to have shorter useful lives 

than comparable CTOL aircraft. Therefore, a 12-year depreciation period is used herein for 

VTOL aircraft, with a zero residual value. This is the equivalent of: 9 years to 25 percent 

residual value or 10 years to 16-2/3 percent residual.” 

 Stoessel and Gallagher also noted that “larger fleets require less spares than smaller 

fleets, if other factors such as the degree of spares pooling and the number of enroute (or 

through) and turnaround stops remain substantially unchanged. For analyses involving a 

single-based shuttle service, and also for a multi-base inter-city operation, the following 

spares provisioning allowances are recommended: (1) airframe spares, as a percent of aircraft 

cost, less engines [should be] 10 percent and (2) engine spares, as a percent of engine costs 

[should be] 40 percent.” 

 With those thoughts in mind, they offered the following equation for estimating 

depreciation including spares 

(2.370) ( )( ) af spares af engspares eng eng Dollars 1 K Cost 1 K N Cost

Year Depreciation period

+ ++ =

and recommend that the airframe spares constant (Kaf spares) be 0.10, and the engine spares 

constant (Keng spares) be 0.40. They seemed quite comfortable (in 1967) with a depreciation 

period of 12 years. 

 On this basis, you have the comparable depreciation (including spares) yearly 

expenses of $117,500 per year for the S-61 and $34,270 per year for the S-55. Fortunately, 

these yearly costs can be spread over 936 trips per year. You might note in passing that you 

are, in effect, buying the helicopters and spares all over again every 12 years. This is a cost 

line item that CPAs probably understand better that I do. At any rate, you have: 

 S-55 equals $36.61 per trip for depreciation (including spares) 

 S-61 equals $125.53 per trip for depreciation (including spares). 
2.9 OPERATING COSTS 

615 

2.9.3.7 DOC Calculation Summary 

 Looking at a summary table obtained with the Stoessel and Gallagher DOC calculator 

lets you draw some very interesting conclusions. As you see here in Table 2-57, the direct 

operating cost to fly the S-61 on one trip is just about 1.9 times the cost of flying the S-55 on 

one trip. This is hardly unexpected because the S-61 is powered by twin-turboshaft engines 

and has 26 seats available. The piston-powered S-55 has only 10 seats available. 

 The more common parameter for decision making is DOC per available seat-mile. 

Because the flight profile has been done for a route that totals 85 miles, you can quickly see 

that the S-61, with 16 additional seats, does offer an economical improvement over the S-55. 

That is, for the S-55 you will estimate 

$191.22 S 55 22.5 cents per available seat-mile 10 seats 85 miles −= = × , 

and for the S-61 you see hope because 

$359.73 S 61 16.3 cents per available seat-mile 26seats 85 miles −= = × . 

This comparison certainly provides a basis for going to the Project Hummingbird program 

managers and pleading for an extension of temporary certification (along with its subsidy) to 

Los Angeles Airways, Chicago Helicopter Airways, and New York Airways. 

 However, the extensions ultimately were not granted, and this first voyage by 

rotorcraft into the airline business came to an end in April of 1965. 

Table 2-57. S-55 and S-61 Direct Operating Costs, $/Trip Data Comparison

DOC Line Item ($/Trip) S-55 S-61 

DOC total 191.22 359.73 

 Flying operation 83.26 116.57 

 Flight crew 70.07 71.87 

 Fuel and oil 5.71 19.06 

 Insurance 7.48 25.64 

 Maintenance 71.35 117.62 

 Airframe 53.31 68.27 

 Engine 18.04 49.34 

 Depreciation (including spares) 36.61 125.53 
2.9 OPERATING COSTS 

616 

2.9.4 S-61 Direct Operating Costs in 2011 

 You might be interested in seeing what time has done to the direct operating costs of 

flying a Sikorsky S-61 in 2011. This updating will change your perspective about what cost 

items are the big drivers. You have seen in Table 2-57 that direct operating costs for the S-61 

amounted to $359.73 per trip. The situation in 2011 is somewhat different, primarily because 

of inflation. 

 To build the direct operating cost story in 2011, let me introduce you to a very refined 

source that you should be aware of. This commercially available source arose from work 

started by Alan Conklin and Bill de Decker in the mid-1970s. Their efforts created a company 

(Conklin & de Decker Associates, Inc.) that has grown into an industry source of aviation 

information. They have a software product available today that evaluates aircraft operating 

costs. I purchased the computer program Aircraft Cost Evaluator (ACE) [640] because it 

includes variable operating costs, fixed operating costs, and total operating costs208 of nearly 

100 helicopters currently in operation. The company has not added a capability to predict 

costs of an aircraft in design and development, but with all their current insight, I imagine 

they could. 

 The Sikorsky S-61N is one of the helicopters in the Aircraft Cost Evaluator data bank. 

The cost line items in this evaluation tool are not directly comparable to the classic DOCs 

used in the world of fixed-wing aircraft operating in today’s airlines. (I will discuss the cost 

line items preferred in the world of helicopter operations in more detail later.) However, all 

the data required to make a nearly apples-to-apples comparison to what you have learned so 

far is there. You will recall that I expressed DOC in dollars per trip and that a trip was 85 

statute miles, not nautical miles, which is the preferred unit today. The 1967 versus 2011 

comparison shown in Table 2-58 is quite interesting. Notice immediately that the proportions 

of the three major line items (i.e., flying operations, maintenance, and depreciation) do not 

appear to have changed significantly. But within flying operations, fuel has become nearly

one-half of the cost versus being less than one-fifth of the cost in 1967. Notice also that 

maintenance costs per trip have increased by a factor of 12. (Let me discuss maintenance in 

Table 2-58. S-61 DOC, $/Trip Cost Comparison Between 1967 and 2011

DOC Line Item ($/85-Statute-Mile Trip) S-61 in 1967 S-61 in 2011 

DOC total $359.73 $3,443.57 

 Flying operation 116.57 1,438.53 

 Flight crew 71.87 315.77 

 Fuel and oil 19.06 887.47 

 Insurance 25.64 235.29 

 Maintenance 117.62 1,482.18 

 Depreciation (including spares) 125.53 522.86 

 

208 The bookkeeping of operating cost line items is somewhat different from that used by Stoessel and Gallagher 

who patterned their line items on the Air Transport Association’s Report 100. 
2.9 OPERATING COSTS 

617 

more detail shortly.) Finally, you can see that depreciation has increased by a factor of 5, 

primarily because in 1967 the S-61 had a list price of $1,200,000, which translates to a list 

price of $3,187,500 in 2011. Overall, there appears to be a growth factor of 10 in total DOCs 

over the 45-year period. It is worth noting that when configured in an airliner interior with 26 

seats for passengers, the calculated DOC per available seat-mile is 16 cents (i.e., $359.73 

divided by 85 and 26) when the S-61 was operating for New York Airways in 1967. Today 

that cost is estimated to be $1.56. When comparing helicopter DOCs in 1967 per available 

seat-mile of 16 cents to fixed-wing aircraft as shown on Fig. 2-400, even I get a little 

discouraged about ever seeing large fleets of helicopters carrying millions of passengers from 

city center to city center. 

2.9.5 Fuel and Maintenance DOCs in 2011 

 Because Table 2-58 shows that, today, fuel and maintenance costs are big-ticket items 

within flying operations, they deserve more detailed discussion. I have chosen to address 

these two cost line items in the paragraphs that follow. The discussion will draw on the data 

bank embedded in the Aircraft Cost Evaluator by Conklin & de Decker Associates, Inc., 

because the data bank has been created from broad surveys of many helicopter operators. 

 Today you will encounter direct operating costs expressed in dollars per hour, 

particularly when comparing a number of different helicopters. You will also find that the 

dollars-per-flight-hour convention is used by the Aircraft Cost Evaluator, so let me discuss 

fuel and maintenance direct operating costs in those units. 

2.9.5.1 Fuel and Oil Operating Costs in 2011 

 Consider fuel (and oil) costs first. This line item cost per flight hour depends, to the 

first approximation, on only two parameters. Simplistically, you can state that 

(2.371) ( ) Fuel DOC Gallons of fuel used Fuel price Fuel price Fuel Flow

Hour Flight hour Gallon Gallon

   = =      . 

It is true that books have been written about aviation fuel. However, for my purposes here in 

August of 2012, it is sufficient to say that Jet A gas used for turbine engines costs about $6.67 

per gallon and has a density of 6.7 pounds per gallon. For piston engines, you have AvGas at 

$7.29 per gallon with a density of 6.1 pounds per gallon. 

 A helicopter operator (and the chief engineer, as well) are at the mercy of the world’s 

commodities markets for the price of fuel on any given day (see Fig. 2-414). Furthermore, 

both interested parties must accept what chemical engineers have achieved in extracting 

energy per gallon of fuel. The only thing left that will lower fuel costs is to burn less fuel for 

any given job. To the user this means buying helicopters that are the most fuel efficient.209 

 

209 To the practicing helicopter engineer, this means increasing specific range, which is the name these engineers 

give to pounds of fuel burned per nautical mile flown. You encountered this very important parameter earlier in 

the discussion about fuel efficiency in Section 2.5, starting on page 267 of this volume. 
2.9 OPERATING COSTS 

618 

Fig. 2-414. You are probably well aware of this dollars-per-gallon trend because the cost 

of gasoline for a car simply parallels this data for Jet A fuel used by gas turbine 

engines (courtesy of Conklin & de Decker Associates, Inc.). 

 The gallons per hour (i.e., fuel flow) that a helicopter uses in a given job depends, of 

course, on the job. Hovering for an hour can be very expensive as opposed to cruising at the 

most economical speed for an hour. To examine fuel and oil contributions to DOC in this 

discussion, let me assume a passenger-carrying job between two cities that are 50 nautical 

miles apart. Imagine the trip begins with a taxi, takeoff, and climb, and then cruises 50 

nautical miles. The trip ends with a descent, landing, and taxiing to where the passengers can 

get out. I will assume that when in cruise, the speed is, say for an S-61, 110 knots, which 

means in-flight time is about three-quarters of an hour. The actual time the rotor is turning 

adds, to keep things simple, about 15 percent of the cruise time for such a short-distance 

flight. The passengers think the trip is just under an hour, and they would compute the 

average speed at about 100 knots. The S-61 pilot would read from his instruments that this 

helicopter was burning fuel at roughly 175 gallons per hour. With Jet A fuel selling for $6.67 

per gallon, that 1-hour trip incurs fuel expenses amounting to $1,167. Within the accuracy of 

the numbers, I will say that oil is included in the $1,167 at about 3 percent, or roughly $35. 
2.9 OPERATING COSTS 

619 

 You can see that fuel flow (i.e., gallons of fuel burned per hour) is a very influential 

parameter. Fortunately, the Aircraft Cost Evaluator has nominal fuel-flow data for nearly 100 

helicopters in its data bank. This practical operational data, when graphed as shown here in 

Fig. 2-415, gives you a very good idea of what today’s current civil helicopter fleet 

experience is. The lowest line on Fig. 2-415 represents, in my opinion, helicopters with 1990s 

technology doing 150- to 200-nautical-mile trips, such as offshore oil rig support [641]. The 

middle line is a regression analysis result for all turbine-powered helicopters. I see this line as 

representing all helicopters in a general utility role. The highest line is my view of what the 

first generation of turbine-powered helicopters achieved. The combination of improved 

turbine engine technology and attention to helicopter parasite drag has improved fuel 

efficiency from a coefficient of 0.036 to 0.023, which, by my calculation, is a 37 percent 

improvement (i.e., 0.023/0.036 = 0.63). On the other hand, all the progress that engineers can 

make to helicopter fuel efficiency (and thus lower fuel DOC) in a decade or two gets wiped 

out when the price of a gallon of Jet A fuel jumps by a factor of two or three, as Fig. 2-414 

shows can happen. This makes fuel efficiency even more important. 

 It is, of course, possible to get into a discussion that splits hairs about (a) not 

accurately accounting for all segments of a flight profile, or (b) not following FAA rules for 

fuel reserves, or (c) simply lumping oil used as a percentage of fuel used. In my opinion, if 

selling a new helicopter to a potential civil customer requires this kind of discussion, the 

design is most certainly too marginal. Most importantly, as demonstrated so far, the helicopter 

lacks the fuel efficiency that operators of fixed-wing aircraft have come to expect. This fact 

was even clear during the autogyro era as Fig. 2-125 on page 261 of Volume I shows. 

0

50

100

150

200

250

300

0 5,000 10,000 15,000 20,000 25,000 30,000 35,000

Small Piston

Single Turbine

Light Twin Turbine

Medium Twin Turbine

Heavy Twin Turbine

Bell 214B

AS/SA 330J

Fuel 

Flow 

(gallons

per

hour)

Certificated Takeoff Gross Weight (lbs)

Turbine Powered

FF = 0.027(GW)0.88

FF = 0.036(GW)0.88

FF = 0.023(GW)0.88

AW 101

S-92

K-Max AW 109 K2

S-76C

Piston Powered

FF = 0.026(GW)0.82

S-61

Fig. 2-415. Fuel efficiency of today’s civil helicopter fleet [640]. 
2.9 OPERATING COSTS 

620 

 In dealing with direct operating costs, I prefer to express the costs as dollars per 

available seat-mile (however, you should remember that dollars per flight hour is a very 

popular metric.) Because dollars per available seat-mile has been a well-used parameter 

within the transportation world, I find it less confusing; once you have the dollars per mile (be 

it statute or nautical) it is a simple step to see how the helicopter’s interior might be 

configured for the lowest DOC. Of course, a helicopter configured with a limited-seating 

executive interior will always show a higher DOC per available seat-mile than a helicopter 

configured for a commercial or utility job. 

 The fuel flow data in Fig. 2-415 can be transposed to fuel cost per nautical mile quite 

easily just by dividing fuel DOC per hour by cruise speed. That is, 

(2.372) 

( )

cr

Fuel price Fuel flow Fuel DOC Fuel DOC Hour Gallon

Nautical mile Cruise speed in nautical miles per hour V in knots

      = = . 

An additional step can be taken to show the fuel efficiency parameter that helicopter 

performance engineers are most accustomed to using. This parameter is called specific range 

and has the units of nautical miles traveled per pound of fuel burned. Thus, 

(2.373) ( )( )

Nautical mile Vcr Specific Range Pound of fuel used Fuel flow Fuel density = = . 

Specific range for the current civil helicopter fleet is shown in Fig. 2-416. This is the 

helicopter engineer’s way of seeing the fuel flow data shown in Fig. 2-415. Unfortunately, it 

is quite rare to see engineering fuel efficiency results that include the price of fuel. 

 You can see in Fig. 2-416 that quite a few turbine-powered helicopters define the top 

of scatter in this important parameter. This top of scatter line is, in my mind, the fuel 

efficiency that all future helicopters should meet or exceed. On the undesirable side, you see 

several helicopters are performing rather poorly in the field. [As an aside, I would suggest that 

the goal of a new design should be at the top of scatter; but to marketing (and the customer) I 

would base fuel and oil costs derived by using the bottom of scatter. This would give a better 

than 50-50 chance of delivering what is promised, keep engineering’s focus on what is 

possible, and offer hope that the new helicopter would perform above the mean of scatter. Of 

course, this approach to quoting fuel efficiency should not be kept a secret; everybody should 

be aware of it.] 

 Specific range can be calculated rather accurately for any helicopter design as it 

progresses from concept to completion of qualification testing. However, the Aircraft Cost 

Evaluator accounts for all aspects of any given job, but only with a first-order approximation. 

This means that idle, taxiing, hold for traffic, takeoff, climb, and begin cruise, etc., are lumped 

into an overall specific range value. The data bank does allow a benchmark for a nominal, 

average specific range of helicopters currently in operation. This benchmark, shown here as 

Fig. 2-416, is quite valuable when bridging the gap between an engineer and an operator 

because it tells the engineer to allow for the difference between theory and real-life operator 

experience. 
2.9 OPERATING COSTS 

621 

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 5,000 10,000 15,000 20,000 25,000 30,000 35,000

Single Turbine

Light Twin Turbine

Medium Twin Turbine

Heavy Twin Turbine Specific 

Range 

(SR)

(Nautical 

Miles per 

Pound of 

Fuel)

Certificated Takeoff Gross Weight (lbs)

Turbine Powered

SR = 280/GW0.79

SR = 220/GW0.79

SR = 350/GW0.79

Fig. 2-416. Specific range in cruise flight of operational, turbine-powered civil 

helicopters. Derived from Conklin & de Decker’s Aircraft Cost Evaluator data 

bank. Includes 30 percent for reserve and 3 percent for oil. 

 There is a fundamental about fuel efficiency that you should be aware of. In helicopter 

performance calculations for any given helicopter and its engine (or engines), specific range 

varies (a) with speed at a given weight and altitude, (b) with weight in flight at a given 

altitude, and (c) with altitude for a given weight. Let me illustrate this important fundamental 

with Fig. 2-417, which shows specific range varying with speed. Because the S-61 has been 

used as an example earlier, pretend that Fig. 2-417 is for an S-61 at sea level on a standard 

day and at its certificated maximum flight weight of 20,500 pounds. 

 Two views of fuel efficiency are shown in Fig. 2-417. First take a look at what the 

helicopter performance engineer might present for the efficiency in nautical miles per pound 

of fuel used—after the calculation is reduced by about 25 to 30 percent to approximate an 

operator’s real-life usage. Performance engineers most frequently want to state nautical miles 

per pound at a high cruise speed, a practice that comes from dealing with military 

requirements. Generally, military requirements are weight driven. To find this cruise speed, 

the maximum nautical mile per pound is multiplied by 0.99, and a horizontal, dashed line is 

drawn as shown on the figure. This line intersects the specific range curve at two speed 

points, which, in this example, are at 99 and 113 knots. The engineer will only quote the 

cruise speed at the 113-knot point. In my experience, it is rare that an engineer will add that 

the specific range of 0.085 equates to 0.57 nautical miles per gallon given that Jet A fuel 
2.9 OPERATING COSTS 

622 

weighs 6.7 pounds per gallon. Only once in my career have I heard an engineer throw in an 

“oh, and by the way, Jet A fuel is selling for $6.67 per gallon so our design spends $11.67 per 

nautical mile at 113 knots!” 

 Now, look at Fig. 2-417 from an operator’s point of view. The lower line (in green) is 

fuel DOC in dollars per hour, which you read on the right-hand scale. According to the 

Aircraft Cost Evaluator data bank, the typical S-61 operator cruises the machine at about 100 

to 115 knots, but generally closer to 100 knots. This speed range is precisely where the fuel 

DOC per nautical mile is a minimum. The geometry of these statements is illustrated by the 

straight, dashed line in Fig. 2-417. You can see that this line is just tangent to the fuel-DOCper-hour curve at about 105 knots. (Keep in mind that dollars per hour divided by cruise speed 

in knots is dollars per nautical mile.) Furthermore, an operator is likely to choose the lower 

speed because the fuel DOC per hour is lower. 

 In short, the civil operator chooses to fly a helicopter at slightly lower speed than a 

military operator because he does not value speed quite as much as his military counterpart. 

And, of course, other line items that contribute to DOC benefit by flying a helicopter at 

reduced power. 

 This brings me to a discussion about maintenance direct operating costs. 

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0 20 40 60 80 100 120 140 160

0

250

500

750

1,000

1,250

1,500

1,750

2,000

2,250

2,500

Fuel 

DOC 

per 

Hour

Speed (knots)

Specific 

Range 

(SR)

(Nautical 

Miles per 

Pound of 

Fuel)

Vcr = 113 

0.99 SRmax

Engineer's 

View

Operator's 

View

FF = 175 gal/hr

Fuel DOC per hr = $1,167 

FF = 198 gal/hr

Fuel DOC per hr = $1,324 

FF = 157 gal/hr

Fuel DO C per hr = 

Best Fuel DOC 

per nautical mile

is $11.60

Fig. 2-417. Engineers and operators frequently see fuel efficiency in quite different ways. 

Furthermore, the military operator values speed and weight above hourly costs.
2.9 OPERATING COSTS 

623 

2.9.5.2 Maintenance Costs in 2011 

 The 2011 maintenance cost of the S-61 is estimated in my example at $1,482 per 

85-statute-mile trip as Table 2-58 records. In more conventional terms, this equates to $17.44 

per statute mile (i.e., 1,482/85). In fact, the Aircraft Cost Evaluator obtains its estimate of 

variable costs in terms of dollars per cruise flight hour and uses 100 knots or 115 miles per 

hour as the average cruise speed for the S-61. (It calculates fixed costs in dollars per year.) 

This means that a conversion from my DOC example using dollars per 85-statute-mile trip 

requires division by 85 to get dollars per statute mile and then multiplying by a cruise speed 

of 115 miles per hour to get maintenance dollars per cruise flight hour. The conversion of 

total maintenance costs from my 85-statute-mile-trip example to the more often quoted dollars 

per flight hour, along with some notes, is shown in Table 2-59. All estimates in this example 

are based on surveys of helicopter operators flying the S-61, and include considerable 

research and analysis on the part of the Conklin & de Decker group. 

 Estimating maintenance costs per flight hour before the helicopter has even flown is a 

relatively new concept to the helicopter industry. It is, of course, not new to the fixed-wing 

manufacturing industry because they, and the several airlines operating in the United States, 

have been at it for about nine decades. The airlines, as certificated by the FAA, have a very 

well developed accounting tree (see Fig. 2-402) and any number of Form 41 financial and 

economic reports [636] that you could refer to and perhaps follow. They also have the Air 

Transport Association (ATA), that has acted as a spokesman for the whole airline service 

industry [642] for just over 75 years. The corresponding organization for helicopters is the 

Helicopter Association International (HAI) that has, since 1948, been dedicated to promoting 

the helicopter as a safe and efficient method of transportation, and championing the 

advancement of the civil helicopter at every opportunity. 

 Unfortunately, the FAA classifies helicopters as part of the much larger General 

Aviation group that they keep track of. As such, financial and economic data for helicopters is 

nowhere near airline data in depth and accuracy. Fortunately, the HAI’s Economic Committee 

has continually improved its Guide for the Presentation of Helicopter Operating Cost 

Estimates, the latest revision being dated October 2010 [643]. The industry has struggled with 

a number of questions since the The Guide first came out in 1981. The effort to obtain some 

uniformity in just defining terms and establishing common accounting practices has not been 

easy. The effort is difficult because of three primary reasons. First, helicopters come in so 

Table 2-59. S-61 Estimated Maintenance Cost Breakdown

Maintenance Total 

$1,482 Per 

85 Statute

Miles 

$2,008 

Per Flight 

Hour Notes 

 Labor $402.16 $514.82 5.47 man-hours per flight hour; $94 per labor hour 

 Parts airframe/engine/avionics $216.92 $293.87 Referred to as just “materials” by some 

 Engine restoration $341.52 $462.66 Often called engine overhaul 

 Major periodic maintenance $476.86 $646.01 Daily, 100 hours, 250 hours, etc. 

 Refurbishing (interior) $44.72 $60.58 10 man-hours per seat per year; labor rate of $94 

 per hour 
2.9 OPERATING COSTS 

624 

many different types and sizes. Second, many variables can affect the operating costs, even 

for a given type helicopter. Third, published operating costs from a variety of sources can 

represent a variety of assumptions. The HAI envisions that it can ultimately serve as a 

repository for the developing knowledge of operating cost estimates. Despite the fact that an 

individual operator considers its operating costs quite proprietary, there has been a great deal 

of progress as you will see by reading a copy of The Guide [643]. Now, let me show you the 

current civil helicopter fleet’s maintenance cost, line item by line item, using the Conklin & 

de Decker Aircraft Cost Evaluator data bank as the most representative and reliable source. 

2.9.5.2.1 Direct Maintenance Labor Costs in 2011 

 Invariably, the first line item is the direct operating cost of maintenance labor, which 

depends on two components and is calculated as 

(2.374) Labor DOC Labor hours Labor Dollars MMH Labor Dollars

Flight hour Flight hour Labor hours FH Labor hours

      = =            . 

It is here that one of the most (if not the most) difficult parameters to estimate in the whole set 

of DOC accounting line items is found. This parameter is maintenance man-hours per flight 

hour (MMH/FH) and, to this day, accurately pinning down MMH/FH in advance of operating 

experience seems nearly impossible. This, of course, is a minor difficulty for the military who 

are very careful to require a potential helicopter contractor to include “design to” values in a 

system specification. For example, paragraph 3.2.4 of the OH-58D specification (Fig. 2-418) 

[644] specifically states: 

Fig. 2-418. MMH/FH “design to” requirements for the U.S. Army OH-58D [644].
2.9 OPERATING COSTS 

625 

You might note that this requirement has a parenthetical note in paragraph 3.2.4.1 to “see 

6.3.11.” When you turn to that system specification paragraph, you will find that it is titled 

Minimum Performance and says: 

“The performance values referenced in these paragraphs [3.2.4.1 and others] are predicted 

values to which the contractor [Bell Helicopter] shall design, test and qualify. In the event that 

demonstrated values fail to confirm the predicted values, the following are the minimum 

demonstrated values which shall be considered to fulfill the requirements of this 

specification.” 

And in a subparagraph, 6.3.11e, you will read that minimum maintenance values were: 

“(1) Allocation of subsystem values for each of the above paragraphs will be incorporated at 

 the final configuration audit. 

 (2) OH-58D system maintenance manhours to flight hour ratio of 1.8.” 

In short, the “design to” requirement for the OH-58D system total was an MMH/FH ratio of 

1.475. Furthermore, if the OH-58D overall system MMH/FH was at or below 1.8 in operation, 

Bell was not to be penalized. In my opinion, the U.S. Army’s need was clearly stated, and the 

latitude they would accept was equally clear.210 

The military requirement to pay attention to MMH/FH in design is just as important to 

manufacturers and operators of civil helicopters. The industry’s success is shown in 

Fig. 2-419. The data is graphed versus weight empty, but it should be clear that MMH/FH 

0

2

4

6

8

10

12

0 5,000 10,000 15,000 20,000 25,000

Piston

Single Turbine

Light Twin Turbine

Medium Twin Turbine

Heavy Twin Turbine

Heavy Tri Turbine

Labor 

Manhours 

per

Flight 

Hours

(MMH/FH)

Weight Empty (lbs)

MMH/FH = 0.0017(WE)0.78

MMH/FH = 0.0037(WE)0.78

All Types

MMH/FH = 0.0027(WE)0.78

S-61

S-92

AW 101

Fig. 2-419. Direct maintenance labor hours per flight hour (derived from Conklin & 

de Decker’s Aircraft Cost Evaluator data bank). 

 

210 The Advanced Helicopter Improvement Program (AHIP) team is quite proud (and happy, as well) that the 

OH-58D and its several upgrades are still performing well in the field even as I write this volume about 

helicopters [145]. 
2.9 OPERATING COSTS 

626 

depends on many variables besides weight empty. You know this because there is so much 

scatter in the data. I found from regression analysis that no combination of typical design and 

configuration data reduced the scatter. Therefore, the use of weight empty as the abscissa in 

Fig. 2-419 is only a convenient way to summarize the available data. Nevertheless, let me 

suggest that the lower curve in Fig. 2-419 would be the starting point for a conceptual design. 

 The only other parameter you need to estimate maintenance labor’s contribution to 

DOC is, following Eq. (2.374), the hourly labor pay rate. As you might guess, the Aircraft 

Cost Evaluator data bank has the trend of this parameter with years, and it is available here as 

Fig. 2-420. It interesting to me to wonder just how would a chief engineer, and other members 

of the company, guess maintenance labor costs for a configuration that is just beginning to 

come together in preliminary design and is probably 3-plus years away from the first delivery 

to a customer. 

Fig. 2-420. The trend in labor rates over the past three decades 

(courtesy of Conklin & de Decker, Inc.). 
2.9 OPERATING COSTS 

627 

 You should know that each of the major helicopter manufacturers keep track of their 

products’ performance in the field. Bell Helicopter, for example, has published a quarterly 

newsletter called Rotor Breeze211for many years. Each year, they pick one issue and include 

an article titled Direct Maintenance Cost Projection for that year. An example for 2012 is 

shown here in Fig. 2-421 [645]. If you look just below the label “Labor Sub-Total” in bold 

print you see a line labeled “MMH/FH.” This is the company’s estimate of maintenance manhours per flight hour based on the operators they have surveyed. It probably will not surprise 

you to learn that these Bell Helicopter estimates do not agree with MMH/FH estimates 

embedded in Conklin & de Decker’s Aircraft Cost Evaluator. Here is the comparison: 

Fig. 2-421. Direct maintenance costs per hour for four Bell helicopters in the first 

quarter of 2012 [645]. 

 

211 Bell has published this newsletter for, I think, about 60 years. Today you can see recent copies by going to 

http:/www.bellhelicopter.com/en_US/SupportServices/TechPublications/RotorBreeze.html 
2.9 OPERATING COSTS 

628 

Estimator 206L4 407 412 429 

Bell Helicopter 0.73 1.05 1.00 1.81 

Conklin & de Decker 1.19 1.17 2.31 2.54 

It is entirely unproductive to enter a debate about who has the correct values because neither 

estimate is the definitive estimate, and both estimates fall within the bounds shown in 

Fig. 2-419. The reason I say this is because I seriously doubt that any two surveys captured all 

the same operators, and quite probably the jobs each helicopter type is doing vary even for the 

same operator, as you will see shortly. 

 Sikorsky is another helicopter manufacturer who keeps in daily contact with operators 

who fly their products. They publish Sikorsky Commercial Links [641]. The July 2005 issue 

was particularly interesting to me because the focus was on the then newly fielded S-92. One 

article in the newsletter struck me because it stated operational data obtained by Norsk 

Helikopter, which service offshore oil rigs in the North Sea. The article is included here as 

Fig. 2-422. 

An accompanying article about Norsk Helikopter in the Sikorsky Commercial Links of July 

2005 provided some key maintenance data stating that 

“from a maintenance perspective, the design of the S-92 is autonomous in the field for ease of 

maintenance. [Two hundred and fifty] and 500 hour inspections have been performed in the 

field and were carried out without any noted discrepancies. Reports indicate that the 

inspections took a total of 5 men and 100 man-hours to complete, approximately 2 days less 

than the industry standard.” 

 In my experience, the working (and soon-to-be-working) helicopter engineer does not 

get enough close looks at the operator’s side of the rotorcraft industry. Newsletters such as 

Bell’s RotorBreeze and Sikorsky Commercial Links are quite valuable and can fill a gap. 

These newsletters deserve more attention by the engineering community, and I believe each 

issue should be delivered to their desks and be required reading. 

Fig. 2-422. Sikorsky’s S-92 was a hit right from the start (photo courtesy of 

Sikorsky Aircraft Corporation).
2.9 OPERATING COSTS 

629 

 When you have questions about the civil helicopter fleet, the best place to turn, in my 

opinion, is the Helicopter Annual [646] that is published by the Helicopter Association 

International (HAI). Their membership numbers over 2,500. The Helicopter Annual issue is 

just packed full of facts and figures. Using this source, consider two very important questions 

that companies face when doing a survey of operating costs. The first question deals with how 

many operators are operating how many helicopters. The answer, for the year 2009, is shown 

here in Fig. 2-423. You can see at the extremes that there are 219 operators who have just a 

single helicopter in their fleet. At the other end of the spectrum, there are 14 operators who 

have 51 or more helicopters in their fleet. Frankly, it is hard for me to imagine that all 622 

operators (in 2009) have the same bookkeeping of operating cost line items. On top of that, it 

is just as hard to imagine that all their helicopters are doing nearly the same job. This is in 

sharp contrast to certificated airlines whose fixed-wing airliners provide basically one service 

—transporting people. A broad spectrum in operator fleet size such as Fig. 2-423 enumerates, 

surely contributes to the wide scatter shown in Fig. 2-419. 

 The second question that bears on helicopter direct maintenance costs and contributes 

to the scatter shown in Fig. 2-419 is, “What jobs do all these operators tackle?” Again, HAI’s 

Helicopter Annual [646] has the answer, and it is shown here in Fig. 2-424 for the 2009 

snapshot. By my count there are 28 different roles that helicopters play in the transportation 

world. There are, you might note in passing, several operators whose fleets provide the 

equivalent of airline passenger service. Certainly Air Taxi/Charter (Part 135), Commuter/ 

Scheduled, Corporate/Not for Hire (Part 91), Executive Transport, and Offshore fall in this 

airline-like business category. Now let me proceed to the next maintenance cost line item. 

Fig. 2-423. The number of helicopters that each HAI-member operator has in its fleet 

(courtesy of the Helicopter Association International). 
2.9 OPERATING COSTS 

630 

Fig. 2-424. The number of helicopters used in each of 28 job categories in 2009 

(courtesy of Helicopter Association International).

2.9.5.2.2 Parts Airframe/Engine/Avionics 

 The DOC line item of what was frequently referred to just as “materials” in earlier 

years is illustrated in Fig. 2-425. These are the parts and pieces that mechanics use to maintain 

a helicopter on a daily basis. To collect the Aircraft Cost Evaluator (ACE) data of parts’ cost 

per hour, I arbitrarily chose the listed base price of helicopters in 2011. Of course, many 

helicopters were not sold new in 2011. This meant that helicopters sold new in some past year 

needed their price inflated to 2011. Therefore, purchase price data from The Official 

Helicopter Blue Book® [583] that led to prices in 1994 (as discussed in Chapter 2.8, Purchase 

Price) had to be further inflated to 2011 using a factor of 1.52 (see Fig. 2-391). Then, from 

this hodgepodge of The Official Helicopter Blue Book®, ACE, and other data, I selected the 

2011 “list” base prices for Fig. 2-425. I am sorry that I could not come up with a more 

accurate estimate. 

 You will no doubt notice in Fig. 2-425 that the Bell Helicopter Model 222 series sticks 

out like a sore thumb. The A model of this series was near its first flight date (August 13, 

1976) when I joined Bell in July of 1976 as chief of aerodynamics.212 The basic helicopter 

showed great promise, but the Lycoming LTS 101-650 engine was nowhere near mature 

 

212 I left Boeing Vertol after 20 years because I wanted to work in the civil helicopter world for awhile. It was, in 

retrospect, a rather short-term prospect because Mr. Jim Atkins suggested that I become chief engineer on the 

AHIP/OH-58D program [145], which was soon to begin with a competition (between Hughes and Bell) for a 

new scout helicopter. Mr. Atkins was then President of Bell, and because I had (and still have) so much respect 

for this man, I put my military helicopter hat on again. 
2.9 OPERATING COSTS 

631 

0

100

200

300

400

500

600

700

800

900

1,000

0 5 10 15 20 25 30 35

Piston

Single Turbine

Light Twin Turbine

Medium Twin Turbine

Heavy Twin Turbine

Heavy Tri Turbine

S-92

S-61

AW 101

Base Price in 2011 ($ million)

Cost = 34(Price)0.68

AS 332L1

Parts

Cost 

(Airframe 

+

Engine

+

Avionics) 

($/hr)

Cost = 56(Price)0.68

Cost = 79(Price)0.68

Bell 222

Series

Bell 430

Fig. 2-425. Costs per flight hour of parts and pieces required in daily maintenance 

(derived from Conklin & de Decker’s Aircraft Cost Evaluator data bank).

enough for production. The engine problems soon became widely apparent in the civil 

helicopter world, and this stymied sales despite all efforts by the Bell marketing group. 

Reduced pricing and improvements made by Lycoming yielded the -750 engine. This engine 

and several airframe improvements creating the B Model 222 did not turn the helicopter’s 

sales prospects around. Nor did the introduction of a skid gear version (the Model 222U) 

recoup the situation. Replacing the two Lycoming LTS 101 engines with two Allison (now 

Rolls Royce) 250-C30 engines led to the Model 230 and a more realistic, break-even price in 

the early 1990s, but it was too little too late. Then a switch, from the two-blade rotor system 

of the Model 230 to a four-blade rotor system and uprating the Rolls Royce 250-C30 engines 

to 250-C40 engines, created the Model 430 (first flight in 1994). This helicopter was 

introduced and the civil helicopter market regained confidence in Bell. It was an expensive 

lesson. 

2.9.5.2.3 Engine Restoration (i.e., Overhaul) 

 Engine restoration, or overhaul as it is frequently referred to, is also a major 

maintenance DOC line item. Fortunately, turbine engine manufacturers have improved their 

product’s time between overhaul (TBO). What started out as 500 to 1,000 hours TBO is now 

approaching 3,500 hours and, in a few examples, turbine engine manufacturers have adopted 

a policy called “on condition” inspections before determining that a complete overhaul is 

required. 
2.9 OPERATING COSTS 

632 

 Fig. 2-426 shows my summary of the range in DOCs for engine restoration. Engines 

offered by General Electric, Rolls Royce, and Pratt & Whitney completely dominate the 

helicopters surveyed here. Both the General Electric CT7 series and the Rolls Royce 250 

series use the “on condition” criteria before a decision to overhaul is made. When you think 

about it, a 3,000- to 4,000-hour TBO means that new turbine engines do not need a complete 

overhaul for 5 to 7 years when helicopters are only flying 600 hours a year. This is quite 

remarkable when you consider that the best high-powered piston engines of World War II 

required a complete overhaul every 500 to 1,000 hours. 

 Let me turn your attention to Frank Robinson’s recent certification of his R66. The 

growth from the piston-powered R44 to the turbine-powered, five-passenger R66 shows, in 

my view, just how wise a man Robinson is. The turbine engine he selected was the Rolls 

Royce RR300 shown in Fig. 2-427. This engine is almost a relic in some engineers’ minds 

because it is a resurrected (but improved, primarily with fewer parts and modern technology) 

Allison 250-C18, which was the engine the U.S. Army chose in the 1960s to fill their Light 

Observation Helicopter requirement. The RR300 is a low-cost alternative to piston engines in 

the 240- to 300-horsepower class. This means that small fixed-wing and rotary wing aircraft 

finally have an entrance-level step to all the benefits of gas turbine engine technology. The 

price of the RR300 engine still requires a call to Rolls Royce by “serious buyers only,” but 

with general aviation encompassing such a worldwide market, you have to believe that this 

engine is going to be a winner. Now let me proceed to the next DOC line item. 

0

100

200

300

400

500

600

700

0 1,000 2,000 3,000 4,000 5,000 6,000 7,000

Piston

Single Turbine

Light Twin Turbine

Medium Twin Turbine

Heavy Twin Turbine

Heavy Tri Turbine

Bell 214B

LycT55-08D

AW 139

PT6C-67C

AS/SA 330J

Turmo IVC

Engine 

Restoration

Cost

($/hr)

Total Takeoff Power of All Engines (SHP)

S-70A/C

GE CT7-2C

AW 101

GE CT7-6

S-92

GE CT7-8A

R-66

RR 300

S-61

GE CT58-140

Cost = 1.74(SHP)0.67

Cost = 2.27(SHP)0.67

Cost = 1.45(SHP)0.67

Fig. 2-426. Engine overhaul costs per flight hour (derived from Conklin & de Decker’s 

Aircraft Cost Evaluator data bank).
2.9 OPERATING COSTS 

633 

Fig. 2-427. Frank Robinson worked with Rolls Royce for nearly 3 years to get a good fit 

of the RR300 with his R66, 5-passenger helicopter. At the February 2012 Heli 

Expo held in Dallas, Texas, Rolls Royce announced that the R66/RR300 had over 

10,000 flight hours and that support for the engine was growing globally (photo 

from author’s collection). 

2.9.5.2.4 Major Periodic Maintenance 

 There is no question, at least in my mind, that engine manufacturers have done their 

job in reducing maintenance direct operating costs and, from the airframe side of the coin, 

there is also no question that the cost per hour of major periodic maintenance has been 

significantly reduced over time. You see this in Fig. 2-428 where I have concluded that major 

periodic maintenance cost per hour is a fraction of the list base price (in millions of dollars). 

This DOC line item has gone from a factor of 50, with some of the earliest helicopters, to 

about 18 for what can be considered the state of the art in the first decade of the twenty-first 

century. This represents a reduction of nearly 60 percent. The engine manufacturers, 

according to Fig. 2-426, went from a factor of 2.27 to 1.45, which suggests a reduction of 

about 36 percent. 

 There are several noteworthy points made by Fig. 2-428. To begin with, it is quite 

clear that virtually all of the early helicopters were very difficult to maintain. Statements such 

as, “It’s a nightmare compared to a Piper Cub,” or “I have to work 2 or 3 hours for every hour 

that thing flies” were commonly overheard. Every helicopter to the near or to the left of the 

red dashed line in Fig. 2-428 falls in this unsatisfactory group. Starting with the A model, the 

Sikorsky S-76 series had a disproportionately expensive major periodic maintenance cost. 

What is unique about the S-76 series is that as successive price changes with corresponding 

 
2.9 OPERATING COSTS 

634 

0

100

200

300

400

500

600

700

0 5 10 15 20 25 30

Piston

Single Turbine

Light Twin Turbine

Medium Twin Turbine

Heavy Twin Turbine

Heavy Tri Turbine

Base Price in 2011 ($ million)

Major 

Periodic 

Maint.

Cost

($/hr) K-Max

Bell

SA 214B

315B & 

Bell 

222 

S-76A S-76D

Bell 

Bell 430

AW 101

EC 155B1

 SS-61

S-70A/C

S-92

EC 225 AS 332L1

Bell 214ST

AS/SA 330J

AW 139

AS 332L2

Cost = 18(Price)

Cost = 28(Price)

Cost = 50(Price)

Fig. 2-428. Major periodic maintenance costs per flight hour (derived from Conklin & 

de Decker’s Aircraft Cost Evaluator data bank).

model changes drove the purchase price up, the periodic maintenance costs did not rise. 

Today the S-76D, with all the field experience and the improvements that followed, falls 

somewhat below the regression analysis result of “Cost equals 28 times Base Price in 2011.” 

 The Bell Model 222 series presents another interesting example. Here the rather 

limited field experience was incorporated into the Model 230. Then the change from a twobladed, classical Bell product to a “modern” four-bladed hingeless rotor system finally created 

a successful machine, the Bell Model 430. 

2.9.5.2.5 Refurbishing (Interior) 

 The last DOC line item embedded in Conklin & de Decker’s Aircraft Cost Evaluator

data bank is refurbishing, principally of the passenger compartment. The Conklin & 

de Decker survey for 2011 suggests that this DOC item has a yearly cost of 10 maintenance 

man-hours per passenger seat per year. Accepting this rule of thumb means that 

(2.375) 

MMH Seats Labor Dollars

Refurbishing DOC Seat Year Labor hour

Flight hour Flight hours/Year

            = . 
2.9 OPERATING COSTS 

635 

 As a numerical example, consider again the Sikorsky S-61, which has 26 seats in its 

New York Airways’ configuration. This results in 10 times 26 seats, which equals 260 manhours per year for passenger compartment refurbishing. In 2011, the Aircraft Cost Evaluator

default labor rate is $94.00, so the yearly cost is $24,440 per year. Assuming about 400 hours 

per year of flight operations, you have $60.58 per flight hour. This repair for wear-and-tear 

expense might be more that 10 man-hours per seat if the flight hours per year were 800 hours. 

Therefore, this refurbishment could, in fact, be a rather fluid expense. 

2.9.5.2.6 A Maintenance DOC Near-Term Goal 

 It is worth a moment to construct a maintenance DOC target for helicopters 

contemplated in the near future. For example, this future helicopter should minimize the costs 

in all five maintenance line items just discussed. Using this criterion, the Maintenance DOC 

in dollars per flight hour would be at or below the following value: 

(2.376) 

( )

( )

0.78

0.68

6

0.67

Takeoff

Maint. DOC Labor dollars 0.0017 WE for Labor

Flight hour Labor hour

Helicopter list Base Price +34 for Parts

10

+1.45 TotalSHP for Engine Restoration

Helicopter list Base +18

  =      

     

( )

6

 Price for Major Periodic Maint. 10

Labor dollars

Labor hour +10 No. of seats for Refurbishing Flt.hours/year

     

   

 

   

It should be obvious that I have simply taken the equation bounding the bottom of scatter 

from Fig. 2-419, Fig. 2-425, Fig. 2-426, and Fig. 2-428 to create this near-term goal (or target, 

or design objective, if you prefer). 

 This near-term goal is hardly out of reach because several helicopters included in 

Conklin & de Decker’s Aircraft Cost Evaluator have reached this goal. You can see this 

conclusion from Fig. 2-429 on the next page. The abscissa on this graph is Eq. (2.376) 

computed for each helicopter in the Aircraft Cost Evaluator data base. The ordinate is the 

actual survey maintenance DOC for that associated helicopter. Because I have taken bottom 

of scatter, virtually all data points for helicopters in the current civil fleet lie above the solid, 

green, diagonal line. A simple linear regression analysis shows that the current civil fleet, as a 

group, is some 40 percent above the goal. This fact is captured with the red dashed line. 

 As you look at Fig. 2-429 you can immediately see that the medium twin-turbine 

helicopter class (the green, open diamonds) has no machine in the current civil fleet even 

approaching the goal. It appears to me that the reason for this situation is that many of the 

helicopters in this class are simply re-engined versions of 1980’s machines. 
2.9 OPERATING COSTS 

636 

 In the heavy twin-turbine class (the round, solid brown circles) you have the Augusta 

Westland 139 (AW 139), which was designed as a replacement for the Bell Model 212. The 

first flight of the AW 139 was February 3, 2001. The Eurocopter 225 (EC 225) is a growth 

version of the 1970’s Aerospatiale 332 Puma and was designed to compete with Sikorsky’s 

S-92, which is truly an example of 1990’s technology. The Agusta Westland 101 has three 

turbine engines and was conceived in the early 1980s, but did not enter service until June of 

2000. 

 Considerable progress toward lower maintenance DOCs has been made by 

manufacturers of light twin-turbine and single-turbine helicopters as Fig. 2-429 suggests. 

 There are a few things to keep in mind if you use Eq. (2.376). The most important 

point is that the prediction is very inflation sensitive. Since the time between when a decision 

is made to offer an all-new helicopter and when the first customer takes delivery can be a 

decade, a mechanic’s pay (with benefits) can increase by a factor of 3 to 3.5 as past history 

shows (Fig. 2-420). This statement about inflation is just as true for the list base price of the 

all-new helicopter, and if the selling price inflates, you can be sure that the price of spare parts 

will escalate as well. On the flip side of the coin, you should at least hope for reductions in 

maintenance man-hours per flight hour as the A model gives feedback to the manufacturer 

that can initiate improvements in the B and C models. A good example of this is the increase 

in time between overhaul—particularly for transmission and rotor hub subsystems. Finally, I 

expect that continued research and development by the rotary wing industry will introduce 

technology to all future new machines that will make Eq. (2.376) obsolete. 

Current Fleet = 1.40(Goal)

R2

 = 0.8336

0

500

1,000

1,500

2,000

2,500

0 500 1,000 1,500 2,000

Piston

Single Turbine

Light Twin Turbine

Medium Twin Turbine

Heavy Twin Turbine

Heavy Tri Turbine

Current

Fleet

Maint.

DOC 

($/Flt. hr)

Suggested Near Term Goal for Maint. DOC as Given by Eq. 2.376 ($/Flt. Hr)

Design Objective for Future Helicopters is less than Eq. 2.376 Predicts

AW 101

S-92

EC 225

AW 139

S-61

Fig. 2-429. There is nothing to suggest that maintenance DOC cannot be further reduced 

as the helicopter continues to mature. 
2.9 OPERATING COSTS 

637 

2.9.6 Parts and Prices, Limited-Life Parts, and Scheduled Maintenance 

 In Volume I: Overview and Autogyros, you were introduced to autogyro maintenance. 

Appendix K of Volume I included a maintenance manual used by the Royal Air Force for the 

Cierva C-30, which was identified as the ROTA Gyroplane by the British Air Ministry. I 

included that maintenance manual for two reasons: the first reason was because of its 

historical significance, and the second reason was to give you a reference point to which 

helicopter maintenance could be compared. 

 It really is not possible to discuss helicopter maintenance, and such key factors as 

maintenance man-hours per flight hour, without studying maintenance manuals and parts 

catalogs in detail. Therefore, I have selected one helicopter, the Robinson R22, to discuss in 

more detail. It seems to me that the Robinson R22 is an ideal candidate because it is a welldeveloped, two-seat helicopter that parallels the two-seat Cierva C-30 autogyro, both useable 

in general utility operation. The choice of the Bell 206B Jet Ranger would be a natural choice 

because it was one of the first turbine-powered machines and because so many have been 

produced. Perhaps you also sense that the progression is from a piston-powered autogyro 

to a piston-powered helicopter to a turbine-powered helicopter. Both helicopters have 

maintenance and parts catalogs available, which I bought or was given. My study of the rather 

thick books suggests a few major observations that will let you appreciate the tasks operators 

must complete to keep their helicopters in safe, ready-to-fly condition. 

2.9.6.1 Parts Count and Spare Part Prices 

 The Cierva C-30 parts count was 3,241 as you learned in Volume I. The question that 

occurred to me was, “How many parts does it take to make a comparable, state-of-the-art 

helicopter (i.e. the Robinson R22)?” Or, if you care to pursue it, “How many parts are in the 

most popular, entry-level turbine-powered helicopter (i.e., the Bell Model 206B)?” Both of 

these helicopters have enjoyed long-term sales, both have well above 100,000 fleet hours, and 

both have had their initial shortcomings corrected. 

 It is not hard to get a reasonably accurate parts count for helicopters that are in the 

civil fleet—simply buy a parts catalog from the helicopter manufacturer. For example, the 

parts catalog for the R22 comes in a nice blue binder containing approximately 250 pages 

separated into 16 sections [647]. Each section deals with a major assembly installed on the 

helicopter such as airframe, power plant, rotor system, etc. Each section has excellent 

exploded views (illustrations), and the subsystem parts are all numbered.213 

 The Bell 206 series’ Illustrated Parts Breakdown Manual that I have [648] is about 

1 foot thick (versus 3 inches for the R22 catalog) and has 67 chapters (versus 13 sections for 

the equivalent R22 document). One reason the Bell document is larger than the Robinson 

document is because the Bell document includes five major revisions that update the basic 

 

213 The parts catalog exploded views are just like the one or two sheets Sears Roebuck and Co. gives you with a 

lawn mower or like a Black & Decker® power tool parts breakdown sheet. All of these types of documents give 

you some idea about how the machine is assembled. 
2.9 OPERATING COSTS 

638 

May 1996 copy to include the B and B3 versions of the Model 206A. This makes my copy up 

to date as of November 1, 2001. 

 Let me restrict the detailed analysis of parts count and the price of spare parts to just 

the Robinson R22. I have had to do this because it took me a month to analyze this 

manufacturer’s illustrated parts catalog in sufficient detail to reach meaningful conclusions. 

Let me emphasize here that real and accurate configuration control and management can only 

be done at the parts level. There is no getting around this fact of real engineering. 

Configuration management is generally a task included in military contracts for the 

development of a new machine. It is a task that frequently falls in the “ilities” group that 

members of the maintainability and reliability profession expect a potential contractor to treat 

very seriously—particularly during the development phase. Unfortunately, I am sorry to say 

that in my experience younger engineers seem to scoff at this configuration management task. 

This is too bad. While it may seem a rather mundane task compared to preliminary and 

detailed design, and then manufacturing, a chief engineer needs to know his aircraft at the 

parts level (not some system engineering level) if an outstanding machine is to be produced. 

 The Robinson R22, Fig. 2-430, is a two-place, piston-powered helicopter. It is built 

from about 9,000 parts categorized in 11 major assemblies, which you see summarized in 

Fig. 2-431 and presented with expanded detail in Table 2-60 and Fig. 2-432. All the data that 

you have before you is for the R22 Beta II and is for an effective date of January 15, 2007. 

Fig. 2-430. The Robinson R22 Beta II is powered by a Lycoming O-360-J2A 

reciprocating engine. In 2007, a well-equipped configuration, delivered fully 

assembled, had a list price of $220,000 [583] (photo from author’s collection). 
2.9 OPERATING COSTS 

639 

0 300 600 900 1,200 1,500 1,800 2,100 2,400

Airframe

Landing Gear

Power Plant

Drive Train

Flight Controls

Rotor Systems

Heating & Ventilation

Fuel System

Instruments

Electrical & Avionics

Furnishings

1,982 & $51,000 

433 & $8,400 

321 & $55,900 

937 & $31,900 

794 & $66,500 

1,428 & $72,900 

123 & $6,600 

366 & $6,800 

1,574 & $39,200 

518 & $14,700 

529 & $9,500 

Number of Parts

Fig. 2-431. The Robinson R22 Beta II, in a well-equipped configuration, has just over 

9,000 parts. If built out of spare parts (rather than bought assembled), the price 

of parts alone would be about $360,000 in 2007 [647]. 

Table 2-60. Robinson R22 Parts Count and Prices at the Subassembly Level in 2007 [647]

Major Assembly Subassembly Description 

Parts 

Count 

Spare 

Part List 

Price 

AIRFRAME CABIN - WINDSHIELDS, COWLING 566 $9,734 

CABIN - ROOF, WINDSHIELD SUPPORT AND DOOR 106 $3,712 

CABIN - SKIRT ASSEMBLY 49 $432 

CABIN - FLOOR, SEAT SUPPORTS 138 $9,059 

CABIN - BELLY, LOWER EXTERIOR 96 $1,439 

 HORIZONTAL FIREWALL 148 $1,246 

 DOOR ASSEMBLY 120 $5,160 

 MAST FAIRING 207 $985 

 WELDED FRAME 217 $9,819 

 TAILCONE 202 $4,620 

 EMPENNAGE 57 $3,057 

 HARDPOINT/TIE-DOWN INSTALLATION 39 $1,417 

BAGGAGE COMPARTMENT COVERS 36 $273 

LANDING GEAR LANDING GEAR 90 $5,656 

 TIE-DOWN INSTALLATION 33 $973 

POWER PLANT ENGINE INSTALLATION 128 $41,935 

 COOLING SYSTEM 606 $11,472 
2.9 OPERATING COSTS 

640 

Table 2-60 (continued) 

Major Assembly Subassembly Description 

Parts 

Count 

Spare 

Part List 

Price 

POWER PLANT AIR INDUCTION SYSTEM 122 $6,090 

(cont) OIL SYSTEM 84 $2,578 

 OIL FILTER INSTALLATION 29 $1,705 

 ENGINE CONTROLS 244 $6,597 

CARB HEAT ASSIST AND MIXTURE CONTROL 95 $647 

CARB HEAT ASSIST BELLCRANK ASSEMBLY 41 $469 

 MUFFLER 77 $1,391 

DRIVETRAIN MAIN ROTOR GEARBOX AND MAST 125 $19,210 

MAIN ROTOR GEARBOX INSTALLATION 56 $1,227 

 DRIVE SYSTEM 235 $23,456 

 A041-12 DAMPER 40 $469 

 CLUTCH ASSEMBLY 65 $7,974 

B021 TAIL ROTOR GEARBOX 50 $5,628 

BELT TENSION ACTUATOR 86 $4,801 

 ROTOR BRAKE 136 $3,745 

FLIGHT CYCLIC CONTROL SYSTEM 246 $8,047 

CONTROLS ADJUSTABLE CYCLIC SPRING ASSEMBLY 51 $807 

CYCLIC FRICTION ASSEMBLY 69 $1,010 

 COLLECTIVE CONTROL SYSTEM 203 $8,889 

 SWASHPLATE ASSEMBLY 65 $5,349 

SWASHPLATE BALL INSTALLATION 60 $2,090 

TAIL ROTOR CONTROL SYSTEM 242 $5,720 

ROTOR SYSTEMS MAIN ROTOR BLADE ASSEMBLY 85 $32,572 

MAIN ROTOR HUB 51 $6,970 

 TAIL ROTOR 97 $11,037 

HUB ASSEMBLY - ELASTOMERIC BEARING 9 $674 

A029-2 TAIL ROTOR BLADE INSTALLATION (ROUND TIP 

BLADES) 79 $4,677 

HEATING & CABIN HEAT SYSTEM - AFT OUTLET 185 $3,798 

VENTILATION CABIN HEAT SYSTEM - FORWARD OUTLET 199 $4,115 

CABIN HEAT SYSTEM - DUAL FORWARD OUTLET 38 $461 

 CABIN VENTILATION 11 $55 

FUEL SYSTEM FUEL SYSTEM 163 $4,742 

 AUXILIARY FUEL SYSTEM 124 $2,809 

AUXILIARY FUEL COWLING ASSEMBLY 156 $988 

FUEL PRIMER AND LINES INSTALLATION 86 $982 

INSTRUMENTS UPPER CONSOLE - SEVEN-INSTRUMENT 167 $7,057 

LOWER PANEL - SEVEN INSTRUMENT 156 $4,804 

LOWER CONSOLE AND RADIO INSTALLATION 91 $930 

 PITOT/STATIC LINES INSTALLATION 104 $1,885 

ELECTRICAL & POSITION AND LANDING LIGHTS INSTALLATION 117 $1,829 

AVIONICS ELECTRICAL COMPONENTS INSTALLATION 153 $4,080 

 ALTERNATOR AND STARTER INSTALLATION 88 $3,691 

ELECTRICAL CIRCUIT BREAKER PANEL 80 $1,101 

ENGINE INSTRUMENT SENDERS AND TEST SWITCHES 53 $1,011 

TACHOMETER AND LOW RPM WARNING UNIT 68 $4,021 

NOSE BATTERY INSTALLATION 101 $1,088 

AFT BATTERY INSTALLATION 99 $1,503 
2.9 OPERATING COSTS 

641 

Table 2-60 (continued) 

Major Assembly Subassembly Description 

Parts 

Count 

Spare 

Part List 

Price 

ELECTRICAL & TRANSPONDER AND BLIND ENCODER INSTALLATION 76 $343 

AVIONICS (cont) BELLY ANTENNAS 41 $1,752 

 FM/DME/TRANSPONDER ANTENNAS 22 $66 

 ADF/MARKER BEACON ANTENNAS 42 $157 

NAV ANTENNA INSTALLATION 28 $798 

 FORWARD TAILCONE ANTENNAS 18 $1,004 

AFT TAILCONE ANTENNAS 21 $1,120 

GPS ANTENNAS (COWL MOUNT) 37 $307 

 LORAN ANTENNAS 42 $57 

VHF COM ANTENNA 23 $183 

 RPM GOVERNOR INSTALLATION 128 $11,329 

ELECTRICAL WIRE HARNESS 31 $1,594 

 DIGITAL CLOCK INSTALLATION 14 $295 

 ELT INSTALLATION (POINTER) 81 $1,131 

 DME INSTALLATION 64 $222 

FLOOR TRANSMIT SWITCH INSTALLATION 21 $254 

PICTORIAL NAVIGATION SYSTEM (HSI) 69 $133 

FLUX GATE INSTALLATIONS 54 $153 

FURNISHINGS INTERIOR FURNISHINGS 335 $6,599 

 FIRE EXTINGUISHER INSTALLATION 31 $160 

GRAND TOTAL 9,005 $363,400

0

50,000

100,000

150,000

200,000

250,000

300,000

350,000

400,000

1 10 100 1,000 10,000

Spare 

Parts 

List 

Price 

($)

Number of Parts

One Engine - Textron Lycoming 0-360-J2A = $40,260

Two Main Rotor Blade and Spindle Assemblies = $32,400

Main Rotor Gearbox and Mast Assembly = $16,900

Swashplate Assembly = $5,250

Tail Rotor Gearbox Assembly = $5,530 

Clutch Assembly = $7,600 

Tail Rotor Assembly = $9,200 

First 185 Subassemblies/Parts 

Account for

80 Percent of $360,00 Total Price 

9 Assemblies Account 

for

32 Percent of $360,00 

Total Price 

Fig. 2-432. Twenty percent of the assemblies/subassemblies/parts account for 80 percent 

of the spare parts list price in 2007. 
2.9 OPERATING COSTS 

642 

Naturally the preceding parts count and spare part list prices have to be considered 

rather approximate. It would, of course, be quite accurate if prepared by a member of the parts 

department at Robinson Helicopter Company, but I felt that would be too much to ask because 

their real business is customer service. Despite these thoughts, I believe that the tabulations 

provided here are the right orders of magnitude. 

 One thing worth repeating is that the list price of an assembled R22 is $220,000 [583]. 

If the helicopter was built up out of spare parts, just the assemblies/parts would cost about 

$360,000, and the labor would be an additional cost. The ratio of $360,000 to $220,000 is 

1.64. 

 The comparison of the Robinson R22 Beta II to the Cierva C-30 autogyro shows that 

the R22 is comprised of about 9,000 assemblies/parts and the C-30 contains only about 3,200 

assemblies/parts (as you read in Volume I, page 276, table 2-22). The difference is dominated 

by (a) the instruments plus electrical and avionics major assemblies, which account for nearly 

2,000 assemblies/parts, and (b) the airframe itself. This is not quite an apples-to-apples 

comparison as the 1930’s C-30 autogyro certainly did not have the elegant interior furnishings 

of the R22, its welded tubular fuselage frame was canvas covered versus the R22’s all metal 

skin, and the pilot’s C-30 instrument panel was a far cry from what Robinson offers in their 

seven-instrument panel arrangement shown in Fig. 2-433. You might note in passing that 

what many buyers would consider as reasonable instruments, avionics, and associated 

electrical equipment total just under $54,000 at spares list price. On this basis, and then 

adding in the Lycoming engine at around $40,000 (bringing the total to $94,000 out of 

$360,000) roughly one-fourth of the helicopter’s $220,000 list price is spent before you have 

anything to install the assemblies/parts in. This could be an exaggeration on my part.214

2.9.6.2 Limited-Life Parts 

 The Robinson R22 contains about 9,000 parts, and you can see from Fig. 2-432 that 

some 185 assemblies/parts account for $290,000 out of the total spares price of $360,000. Not 

many of the parts wear out or need to be replace in the 10 to perhaps 20 (or maybe even 

longer) years of useful life the machine provides. However, a select few are life limited to 

5,000 (up to even 10,000) rotor-turning hours, and even fewer parts are life limited to 2,200 

hours in certain critical part cases. Unfortunately for the helicopter operator, these life-limited 

parts always seem to be the most expensive ones. The result is, of course, that scheduled 

maintenance becomes more expensive when subassemblies like rotor blades must be retired

 

214 Do not forget that each decal, screw, washer, nut, bolt, etc., is given a part number. The Robinson Helicopter 

Company’s illustrated parts catalog [647] includes a file that occupies about 2,500 rows and 3 columns of a 

Microsoft®

 Excel® spreadsheet. The file that I created gives the part number, a description, and the unit price. 

The bulk of the catalog contains exploded views of a subassembly and attaches an index number for each part in 

the subassembly. Separate pages list the index numbers, the corresponding part numbers, and the quantity of 

each part number needed. This allows you to find the spare part price for any one of those particular parts. Then 

quantity times unit price gives the total price for that particular part. 
2.9 OPERATING COSTS 

643 

Fig. 2-433. Robinson offers a quite reasonable package of instruments, avionics, and 

necessary electrical equipment (photo from author’s collection).

after, say for example, 2,200 hours. For the Robinson R22, this would mean that a set of two 

main rotor blades (they must be replaced in pairs) and their spindles (see Fig. 2-434 and 

Fig. 2-435) priced as spares cost the helicopter owner $32,400 in parts alone in 2007. (This 

price has gone up to about $39,000 as of June 2012, and the price is “subject to change.”) 

 Stop and think about these numbers for a moment. Suppose you, as an operator, buy 

your R22 new in June of 2007 and fly it rather casually at 300 hours per year. The blade life 

of 2,200 hours would be used up in 7 years, in mid-2012. You must start saving for new 

blades at the rate (guessing inflation) of $39,000 divided by 2,200 hours, which works out to 

$18 per hour. This is just a simple example of what you, as the helicopter owner, must charge 

any customer who might ask, “How much for an hour flight?” 
2.9 OPERATING COSTS 

644 

Fig. 2-434. Exploded view of a Robinson R22 main rotor blade assembly [647].
2.9 OPERATING COSTS 

645 

Fig. 2-435. Tracking index number to part number [647] for the R22.
2.9 OPERATING COSTS 

646 

 In fact, the Robinson R22 (like so many helicopters currently flying) has a number of 

parts that are identified as “fatigue life limited.” When these parts are identified during the 

development program, they become subject to Airworthiness Limitations and require FAA 

attention. A section of the maintenance manual [649] generally contains one page (hopefully) 

certifying FAA approval for continued flight airworthiness as long as the operator/owner 

replaces the helicopter parts in question at the stated times. Fig. 2-436 shows you this very 

important page for the Robinson R22 [649]. 

 You can immediately see in Fig. 2-436 that 19 subassemblies/parts contained in an 

R22 are limited to between 2,200 and 6,260 hours of engine run (or flight) time. Because the 

Bell Model 206B has been in service since the mid-1960s, its maintenance manual [650] has a 

much more detailed (and longer) list of individual parts that must be retired (i.e., replaced) in 

order to maintain the machine’s airworthiness. In either example, it may be that only one 

single ball bearing in a subassembly needs to be replaced, so it is not as if a complete gearbox 

is replaced. It might interest you to know that main rotor blades for the Bell 206B series are 

life limited to 5,000 hours, and each blade is list priced at $47,530 (per blade) as of March 15, 

2010 [583]. You will recall from Volume I that C-30 blades had a service life of 75 hours. 

 There is a short list of fatigue life-limited parts for many helicopters currently in 

service in the United States. This data is included in The Official Helicopter Blue Book®

published by HeliValue$, Inc. [583]. You will find major subassemblies (such as a main rotor 

blade or a complete tail rotor gearbox) tabulated in this source. A second column states the 

quantity required for that helicopter, and a third column provides the factory list price for a 

new replacement part. For example, the Sikorsky S-76 series’ main rotor blade is life limited 

to 28,000 hours; then each blade must be replaced at a cost to you, the owner/operator, of 

$162,390 (per blade). With respect to blades, significant progress has been made with the 

transition to fiberglass blades. For example, the Bell Model 412 series’ blades do not have a 

fatigue life limit. Rather the Bell 412 main rotor blade replacement is based on “on 

condition,” which is, I will admit, somewhat vague but hopefully means at least 10,000 hours 

barring unusual in-service deterioration. The per-blade cost is $180,440 (as of January 2009) 

for a Bell 412 blade, and you need four of them. 

 I suspect you are getting my drift here. The fatigue life-limited parts and 

subassemblies are major operating cost drivers. Even with a short list of the more expensive 

components, you can derive an impression of a minimum cost per flight hour that you must 

expect just from the costs of parts to be replaced. Of course you must also include the hours of 

labor required to make the replacement. 

 Let me add a closing thought. The Robinson Helicopter Company offers an R22 

Factory Overhaul at 2,200 hours for $140,000 (plus upgrades). This works out to $64 per 

flight hour, and includes parts and labor. In effect, after buying your new R22 for $220,000 in 

2005, you need to save (accounting for inflation) about $140,000 over 7 years to put it back 

into top-notch condition in 2012. Roughly speaking then, you are buying about 64 percent of 

the helicopter every 7 years assuming 300 hours flying every year. Unfortunately, your 

original investment is probably depreciating—just like your new car. 
2.9 OPERATING COSTS 

647 

Fig. 2-436. The FAA-approved airworthiness page for the R22 listing assemblies and 

parts that must be replaced after a certain amount of operating time [649].
2.9 OPERATING COSTS 

648 

2.9.6.3 Scheduled Maintenance 

 You will recall from Volume I that the Cierva C-30 autogyro maintenance schedule 

called for “inspection between flights, and inspections (a) daily, (b) every 10 hours, (c) every 

20 hours, (d) every 40 hours, and (e) every 120 hours.” The Civet I engine and its “airscrew” 

required inspection as well, of course. The engine and propeller inspection intervals were 

identical to the airframe. Furthermore, the aircraft required lubrication at 39 different points 

on nearly a daily schedule. 

 The Robinson R22 has a similar list of tasks, albeit with a more liberal schedule. 

Paragraph 1.101 of the maintenance manual [649] states (with some of my editing) that 

“1.101 Scheduled Maintenance. Some helicopters require further maintenance and inspections 

in addition to the following minimum requirements for new helicopters. Consult aircraft 

maintenance records, Service Bulletins (SB), aviation regulations, Airworthiness Limitations, 

and Airworthiness Directives (AD) for specific applicability. Publications listed are subject to 

revision. 

Flight Time

First 29 hours: Change engine oil and filter and inspect oil suction screen and filter per 

Lycoming SB480E. Check alternator belt tension per Lycoming Service 

Instruction (SI)1 129B. Verify track and balance of drive system. Verify 

sheave alignment. 

Every 50 hours: Change engine oil and filter and inspect oil suction screen and filter per 

Lycoming SB480E. Inspect and service engine per Lycoming Operator's 

Manual and SI1080B. 

First 100 hours: Drain and flush main rotor gearbox (section 1.120) and tail rotor gearbox 

(section 1.130). Check engine exhaust valve guide clearance per Lycoming 

SB388C. 

Every 100 hours: Inspect per section 2.400. Inspect and service engine per Lycoming 

Operator's Manual, SB366, SI1080B, and SI1129B. Inspect and service 

engine ignition components per TCM SB636, SB643B, SB653, SB658, and 

SB663A. 

Every 300 hours: Lubricate the clutch actuator’s upper and lower bearings (see A181-4 Rev K, 

Rev L, and Rev M bearings per section 2.502). Lubricate A184 bearing per 

section 2.503. Inspect valves and check engine exhaust valve guide clearance 

per Lycoming SB301 B, SB388C, and Operator’s Manual. 

Every 500 hours: Drain and flush main rotor gearbox (section 1.120) and tail rotor gearbox 

(section 1.130). Inspect main rotor blade spindles per FAA AD 88-26-01 R2. 

Every 800 hours: Lubricate the clutch actuator’s upper and lower bearings (see A181-4 Rev N 

bearing per section 2.502). 

Every 2,200 hours: Overhaul helicopter per section 2.7000. 

Calendar

Every 4 months: Change engine oil and filter and inspect oil suction screen and filter per 

Lycoming SB480E. 

Every 12 months: Inspect per section 2.400. Lubricate clutch actuator’s upper and lower 

bearings (see A181-4 Rev K, Rev L, and Rev M bearings per section 2.502.). 

Lubricate A184 bearing per section 2.503. Inspect emergency locator 

transmitter (ELT) per FAR 91.207. Clean main rotor gearbox and tail rotor 

gearbox chip detectors per section 1.115. 
2.9 OPERATING COSTS 

649 

Every 24 months: Test and inspect transponder per FAR 91.413. 

Every 4 years: Lubricate clutch actuator’s bearings (see A181-4 Rev N bearing per section 

2.502). Overhaul the engine magnetos per TCM SB643B. 

Every 12 years: Perform 12-year inspection and limited overhaul per section 2.600, or 

overhaul per section 2.700.” 

 You will see in most maintenance manuals that the first few introductory pages 

provide when to do and what to do instructions. The R22 manual follows this vitally 

important information with a section 2. This section 2, composed of 66 pages, provides more 

detail about what to do and how to do it. The rest of the R22 manual (some 400 pages) tells 

you how to do maintenance on each of the major subassemblies listed in Fig. 2-431. The R22 

maintenance manual states, in no uncertain terms, that “the helicopter must be inspected 

periodically to verify it is in airworthy condition. Required inspection intervals are [a] 

maximum [of] 100 hours time in service or 12 calendar months (annually), whichever occurs 

first. Fluid leaks, discoloration, dents, scratches, nicks, cracks, galling, chafing, fretting, and 

corrosion all warrant further investigation. Unairworthy items must be replaced or repaired as 

allowed by Robinson Helicopter Company. This section contains procedures for performing 

the required periodic airframe inspections.” 

 It should be apparent now that the schedule for R22 maintenance according to section 

1, and the Periodic Maintenance how to according to section 2, require many man-hours of 

time for a qualified technician and/or a mechanic. After taking delivery of your new R22, you 

must plan your flying so that after the first 29 hours of operation the helicopter power plant 

(i.e., the Lycoming O-360) and the drivetrain get some attention. After that you get 21 more 

hours of flying before the first 50-hour servicing must be done. Then flying can continue for 

another 50 hours at which time the first 100-hour periodic maintenance must be performed. 

When you graph maintenance man-hours versus flight hours (read the note on Fig. 2-436), 

you get the accumulating labor hours versus accumulating flight hours shown in Fig. 2-437. 

0

100

200

300

400

500

600

700

0 200 400 600 800 1,000 1,200 1,400 1,600 1,800 2,000 2,200 2,400

Maint.

Labor

(MMH

in

hours)

Flight Time (FH in hours)

MMH/FH = 0.19

MMH/FH = 0.27

Complete 

Overhaul at 

2,200 hours

Fig. 2-437. The ratio of R22 maintenance labor hours to flight hours is about 0.27 when 

the overhaul task at 2,200 flight hours is included (per the Robinson Helicopter Co.).
2.9 OPERATING COSTS 

650 

 Data for this figure was arrived at by talking directly to Daniel Huesca, a member of 

Robinson Helicopter Company’s technical representative staff. He kindly quoted labor hours 

for each of the scheduled maintenance tasks as follows: 

R22 Scheduled Maintenance at Maintenance Man-Hours (hr) 

50 hours 2 to 3 

100 hours 12 to 16 

300 hours 13 to 17 

500 hours 14 to 18 

800 hours 12 to 16 

2,200 hours 180 

In constructing Fig. 2-437, I took the upper limit figures that Huesca quoted. 

 Fig. 2-437 shows that, approximately speaking, the average maintenance man-hours 

per flight hour prior to the 2,200-flight-hours point215 (when your brand new R22 must be 

completely overhauled) is just over 0.19. When the 2,200-hour overhaul is included, you have 

the blue solid line, which says that you should plan on an MMH/FH ratio of 0.27. 

Additionally, the Robinson Helicopter Company assumes unscheduled labor hours at 0.074 

per flight hour, which means the total MMH/FH ratio is on the order of 0.344. 

 There appears to be a difference between maintenance labor hours published by many 

helicopter manufacturers, and what operators and owners experience in the field. It probably 

comes as no surprise that the manufacturer-quoted scheduled and unscheduled maintenance 

hours can be considerably lower than actual field experience. As one example, the Conklin & 

de Decker’s Aircraft Cost Evaluator (ACE) [640] bases its maintenance direct operating cost 

data on an MMH/FH ratio of 0.452 for the R22, which includes both scheduled and 

unscheduled labor. The explanation for the difference, according to Bill de Decker, the 

inventor of ACE, is primarily due to a simple, scheduled maintenance task frequently 

revealing additional repairs or some other corrective action that may not be included in all 

manufacturers’ estimates of maintenance labor. These additional, unforeseen tasks can easily 

increase unscheduled maintenance labor and add parts above manufacturers’ allocation. 

 Because Conklin & de Decker have been so successful in gathering and analyzing 

helicopter maintenance data and specifically MMH/FH, I prevailed on Bill de Decker to share 

some of his knowledge. (As you will see, the Conklin & deDecker approach requires a 

manufacturer to provide its MMH/FH for scheduled maintenance, and this becomes the 

baseline.) In response, Bill wrote the following: 

 “To estimate realistic maintenance labor manhours per flight hour requires the 

inclusion of a number of factors. The Conklin & de Decker approach includes the following 

elements: 

 

215 You might keep in mind that today’s new cars easily reach 2,000 operating hours after traveling 100,000 

miles at, say, 50 miles per hour. A complete overhaul of the car at this time is, in my experience, hardly required. 
2.9 OPERATING COSTS 

651 

Schedule Maintenance (Airframe and Systems)

 This is the maintenance associated with all scheduled inspections and is the labor 

required to accomplish the scheduled portion of each inspection. This consists usually of 

removing/replacing access panels, a visual inspection, and often measuring pressure, volts, 

ohms, flow rate, etc., for specific functions or components. Almost all manufacturers can 

provide a quite accurate estimate of the typical number of labor hours expended for the 

scheduled portion of each inspection. 

Unscheduled Maintenance (Airframe and Systems)

 There are two types of unscheduled maintenance. The first is the unscheduled labor 

required to repair/replace and retest whatever was found during the scheduled inspection to be 

worn, damaged, or out of specification. The second is the maintenance that is required as a 

result of “squawks” and maintenance actions that arise in between scheduled maintenance 

actions. Typically these are the result of a pilot maintenance write-up at the end of a flight. 

 Some manufacturers can provide an estimate for the required labor that is typically 

required to accomplish this. In general, a ratio of one hour of unscheduled labor for each hour 

of scheduled time has proven to be a good rule of thumb. 

Troubleshooting

 Troubleshooting is an integral part of aircraft maintenance, particularly maintenance 

associated with fixing a “squawk” or pilot write-up. Sometimes the problem is not well 

described and sometimes it cannot be duplicated on the ground. In addition, the maintenance 

technician may not be very familiar with the system or component experiencing the stated 

problem. Conklin & de Decker’s approach, based on experience, is to add a factor that is 

based directly on the size and complexity of the helicopter, as shown in the following table. 

As can be expected, the amount of labor expended in troubleshooting is a direct function of 

the complexity of the systems on the helicopter. 

 Troubleshooting Labor Hours Per Flight Hour 

Helicopter 

Weight Class Engine Type Engine Number MMH/FH 

Light Piston 1 0.30 

Light Turbine 1 0.40 

Light Turbine 2 0.60 

Medium Turbine 1 0.50 

Medium Turbine 2 0.70 

Heavy Turbine 2 0.80 

Engine Maintenance (on Aircraft)

 Engines require both scheduled and unscheduled maintenance in between overhauls 

and other major maintenance actions. This includes the scheduled 25 or 50 hour oil and filter 

changes as well as unscheduled maintenance on fuel injectors, fuel controllers, igniter boxes, 

etc. It also includes the removal and installation of engines sent out for heavy maintenance. 

As with estimating troubleshooting labor, Conklin & de Decker approaches this cost element 

by using factors associated with the type, size (SHP) and number of engines, as shown in the 

following table: 
2.9 OPERATING COSTS 

652 

Engine On-Aircraft Labor Hours Per Flight Hour

Helicopter 

Weight Class Engine Type Engine Number 

MMH/FH 

Per Engine 

Total 

MMH/FH 

Light Piston 1 0.15 0.15 

Light Turbine 1 0.15 0.15 

Light Turbine 2 0.15 0.30 

Medium Turbine 1 0.20 0.20 

Medium Turbine 2 0.20 0.40 

Heavy Turbine 2 0.30 0.60 

Heavy Turbine 3 0.30 0.90 

Avionics Maintenance (on Aircraft)

 Avionics also require maintenance. However, this maintenance is almost all of the 

unscheduled variety. And while most radios, navigation receivers and instruments are not 

repaired on site, they still require removal and installation as well as repairs on associated 

wiring. Conklin & de Decker uses the same approach as for the engines to estimate the 

required labor hours per flight hour for this maintenance element. For the avionics the factors 

that determine the labor effort are the weight class of the helicopter, whether it is a VFR or 

IFR installation, and whether the helicopter is flown by a single pilot or two pilots, as shown 

in the following table. 

Avionics On-Aircraft Labor Hours Per Flight Hour

Helicopter 

Weight Class Engine Type VFR or IFR 

Number 

of Pilots MMH/FH 

Light Piston VFR 1 0.10 

Light Turbine VFR 1 0.15 

Light Turbine IFR 1 0.20 

Medium Turbine VFR 1 0.20 

Medium Turbine IFR 1 0.20 

Heavy Turbine IFR 2 0.30 

Heavy Turbine IFR 2 0.30 

Example of Applying These Additive Labor Hours Per Flight Hour

 Adding these several additional labor hour per flight hour elements for a particular 

make and model helicopter yields a total labor hours per flight hour MMH/FH for a particular 

make and model of helicopter and is quite straightforward. It requires only to obtain the 

scheduled MMH/FH for that particular make and model, which almost all manufacturers can 

provide. For example, a typical, popular single engine turbine helicopter equipped for VFR 

operations would have the following total MMH/FH using this analysis: 

Scheduled Maintenance 0.33 MMH/FH 

Unscheduled Maintenance 0.33 

Troubleshooting 0.40 

Engine 0.15 

Avionics 0.15 

Total 1.36 MMH/FH 

Actual survey data based on over 200 data points for the Bell 206B and 206L family that 

Conklin & de Decker has collected over the last 20 years shows that the actual MMH/FH for 

this popular helicopter averages 1.31 MMH/FH. This is within 5% of the estimated number 

shown above.”
2.9 OPERATING COSTS 

653 

 You must also keep in mind that the final maintenance labor cost depends on the cost 

of one labor hour, which can range from $60 to $90 per hour (currently in 2012). Using the 

R22 as the example means, therefore, this direct operating cost line item could range from a 

low of $60 per hour times an MMH/FH ratio of 0.19 (i.e., $11.40 per flight hour) to as high as 

$90 per hour times an MMH/FH ratio of 0.452 (i.e., $40.70 per flight hour)! 

 Finally, there is another source for total maintenance cost per flight hour (i.e., both 

labor hours and replacement parts’ cost); this source is The Official Helicopter Blue Book®

[583]. The Blue Book has purchase price data, specifications, other very useful data, and 

maintenance costs for “running the helicopter for one hour.” The Blue Book now comes on a 

CD, which I purchased from HeliValue$, Inc. The compilers of The Blue Book use the 

acronym HMC for the hourly maintenance cost and state the ground rules for the numbers 

they publish quite clearly. They say that 

 

 “to determine HMCs, it was necessary to make certain assumptions such as: 

1. The helicopter will be subjected to no more than two start cycles per flight hour. 

2. The average take-offs and landings will not exceed three per flight hour. 

3. Other than during take-off and landing, the helicopter will be operated at 75% or less of its 

maximum continuous power rating. 

4. Rotor blades without a scheduled removal interval have been assigned a useful life of 

10,000 hours. 

5. Mechanical and hydraulic components which do not have a scheduled removal interval are 

assigned an overhaul interval of 5,000 hours. 

6. Operations which increase the number of engine starts, add the higher than average takeoffs and landings, or require the helicopter to operate at more than 75% of its maximum 

power, will increase the HMC. 

7. Different components which alter the model number of an aircraft within a series have had 

their HMCs determined by using an average of the possible variations.” 

The Blue Book also provides an itemized list of what is not included in their quoted HMC. 

This line item list basically makes clear that no other cost line items associated with direct 

operating costs (DOCs) or indirect operating costs are included. Finally, the HMC is quoted 

as a range rather than one specific number. 

2.9.7 Total Operating Cost (TOC) 

 Operating costs that vary with helicopter utilization (say, per flight hour) constitute 

one major group of accounting line items. The other major group of accounting line items 

gathers up costs that are not dependent on utilization (e.g., hanger rental fees) and are 

generally recorded annually. The sum of Variable Costs plus Fixed Costs equals Total 

Operating Cost (TOC). Giving a cost line item a name has not been, historically, a difficult 

problem in the helicopter industry. What has been difficult has been to associate the particular 

cost item as a Variable Cost per flight hour item or as a Fixed Cost per year item. To help 

standardized assignment to the flight hour group or to the annual group, both operators and 

manufacturers have turned to their trade organization, Helicopter Association International 
2.9 OPERATING COSTS 

654 

(HAI). Over the years, HAI has been able to guide and improve how cost accounting is done 

by operators, and airframe and engine manufacturers. Since 1981, HAI has depended on their 

Economics Committee to periodically improve what is commonly called The Yellow Book or 

The Guide. 

 In 1987, the HAI Economics Committee, reinforced by the Aerospace Industries 

Association of America, produced the 1987 Guide for the Presentation of Helicopter 

Operating Cost Estimates. This very helpful document, the 1987 Guide, sufficed until early in 

the first decade of the twenty-first century. By that time the need for improvements became 

quite clear and, in October 2010, a revised document, still called The Guide, was published 

[643]. The preface of this 2010 edition begins with: 

“What does it cost to operate and maintain a helicopter? Upon first read, this is a simple 

question, but it is one that has created a great deal of debate and confusion for the industry.” 

This edition shows particular concern for operators by spelling out some pitfalls that might 

lead to an operator underestimating TOC. The result of underestimating TOC can, of course, 

easily cause an operator to undercharge a customer for the use of the helicopter. 

 When you read The Guide for 2010 you will see that (1) operators have a long list of 

cost items to incorporate when doing their accounting work, and (2) both airframe and engine 

manufacturers are given guidance in reporting cost estimates for numbers that they are experts 

in deriving. For example, who is better than the operator to estimate most of the fixed-cost 

line items, and who is most qualified to define and price, say, the life-limited parts. A key 

section of The Guide deals with defining most of the operating cost categories that have arisen 

over 30 years. The accounting items, with some editing by me, read as follow: 

II. Operating Cost Categories 

 A. Fuel and Lubricants 

 B. Maintenance 

 1. Life-Limited Parts

 2. Major Overhauls (airframe and engine) 

 3. Periodic Inspections 

 4. On-Condition Components 

 5. Service Bulletins and Air Worthiness Directives (ADs) 

 6. Unscheduled Maintenance 

 7. Optional Equipment 

 8. Sources of Maintenance Cost Estimates 

 C. Insurance 

 1. Hull 

 2. Aviation General Liability 

 3. Workers’ Compensation 

 D. Personnel 

 1. Flight Crew 

 2. Mechanics and Technicians 

 3. Office Staff 

 4. Management Salaries 

 5. Benefits 

 E. Training 

 F. Depreciation 

 G. Taxes 
2.9 OPERATING COSTS 

655 

 H. Finance 

 I. Overhead 

 1. Rental or Lease Fees (hangar, vehicle, office, storage, etc.) 

 2. Utilities (telephone, electricity, water, etc.) 

 As you can quickly appreciate, The Guide is constructing a primer for a small business 

that operates at least one or two helicopters, which, by the way, require a great deal of “tender 

loving care.” Furthermore, each line item (i.e., A, B, C, etc.) is addressed in detail. 

The Guide makes a considerable effort to suggest which cost line items are variable 

costs and which are more typically fixed costs. In Fig. 2-438, you have one possible 

assignment of the many cost line items to either the variable- or the fixed-cost groups. 

Fig. 2-438. Total operating costs for a year can be divided into two groups: (1) variable 

(with flight hour) and (2) fixed (typically for a 1-year period).

FIXED COSTS Flight Crew 

 Salaries 

 Benefits 

Other Personnel 

 Salaries 

 Benefits 

Service Bulletins & ADs 

Insurance 

 Hull 

 Liability 

 Workers’ Comp 

Recurrent Training 

Navigation Chart Service 

Refurbishing 

Weather Service 

Depreciation 

Overhead 

 Rentals 

 Utilities 

$/Yr.

$/FH × FH/Yr.

VARIABLE COSTS

Fuel & Lubricants 

Scheduled Maintenance 

 MMH/FH 

 $/labor hr 

 Parts (Airframe, Eng, Avionics) 

Unscheduled Mainteance 

 MMH/FH 

 $/labor hr 

 Parts 

Overhaul of Airframe 

Overhaul of Engine 

Landing & Parking 

Supplies & Catering 

Flight Hours 

$ 

per 

Yr. 

1 Yr.
2.9 OPERATING COSTS 

656 

0

200

400

600

800

1,000

1,200

0 5,000 10,000 15,000 20,000 25,000 30,000

Small Piston

Single Turbine

Light Twin Turbine

Medium Twin Turbine

Heavy Twin Turbine

Heavy Tri Turbine

Fixed

Operating

Costs

per

Year

($1,000)

List Price ($1,000)

Dollars Price 175,000 29.8 Yr. 1,000

  = +    

Fig. 2-439. Fixed operating costs per year for newer helicopters (2011 dollars).

$0

$500

$1,000

$1,500

$2,000

$2,500

$3,000

$3,500

$4,000

0 5,000 10,000 15,000 20,000 25,000 30,000

Small Piston

Single Turbine

Light Twin Turbine

Medium Twin Turbine

Heavy Twin Turbine

Heavy Tri Turbine

Variable

Operating

Costs

per

Flight

Hour

List Price ($1,000)

0.57 Dollars Price 8.92

FH 1,000

  =    

AW 101

Fig. 2-440. Variable operating costs per flight hour for newer helicopters (2011 dollars).
2.9 OPERATING COSTS 

657 

 It is becoming more common in the helicopter industry to define total operating costs 

as the sum of variable and fixed costs rather than direct and indirect costs.216 Fig. 2-438 

follows this trend, which states, in equation form, that 

(2.377) TOC Fixed Costs Variable Costs Flight Hour

Year Year Flight Hour Year

   = +       . 

This relationship is of the form of a straight line (i.e., y = a + mx). That is, it has an intercept 

(a), which is fixed costs per year. The slope (m) is variable costs per flight hour, which you 

also see pictorially in Fig. 2-438. 

. 

 To give you a rough order of magnitude for the two key parameters (intercept and 

slope), let me draw upon the data bank embedded in Conklin & de Decker’s Aircraft Cost 

Evaluator (ACE). I selected only equipped helicopters introduced into the civil fleet from the 

year 2000 to 2011 as being representative of “today’s state of the art.” Beyond that, I accepted 

factory list price as the primary variable to plot the results. Of course, using list price as the 

abscissa is absolutely not the only parameter that drives operating costs. For example, you 

might add number of seats as a variable. Still, for illustration purposes here, it appears 

adequate. You see the results for fixed costs per year in Fig. 2-439 and variable costs per 

flight hour with Fig. 2-440. 

 There is a line and an equation on both Fig. 2-439 and Fig. 2-440. These represent a 

regression analysis result of just newer turbine-powered helicopters. Using these two 

approximations, the total operating costs per year can be estimated to the first order simply by 

substituting the two equations from Fig. 2-439 and Fig. 2-440 into Eq. (2.377), which yields 

an equation for total operating costs per year. Thus, you have 

(2.378) 

0.57 TOC Price Price Flight Hour 175,000 29.8 8.92

Year 1,000 1,000 Year

        =+ +                 

. 

The underlying assumption here is that the owner/operator has one turbine-powered helicopter 

in his (or her) company. 

 The 2010 edition of The Guide is very careful to point out that an operator must be 

aware that TOC per flight hour is very dependent on flight hours flown per year. Ignoring this 

fact could mean that bidding on a job by using so much per flight hour—based on an incorrect 

flight-hours-per-year expectation—could mean a substantial loss on a particular job. You can 

see why The Guide’s caution is well-founded by looking at Fig. 2-438. Imagine you had a 

$5,000,000 helicopter and planned (perhaps hoped would be better) that you would get 400 

flight hours worth of business during the forthcoming year. You bid a 1-week job fairly 

confident that it will take 40 flight hours at $2,000 per hour, or $80,000 plus some profit. All 

 

216 Another way for operators to categorize costs is based upon their attachability or traceability to an activity, 

product, or department within an organization. Two categories are used. The first category is direct costs, which 

can be traced directly to, say, how much fuel one helicopter uses. The second category is indirect costs, which 

requires proportioning some yearly fixed cost, say a mechanic’s yearly salary, to the time he spends working on 

that same helicopter. 
2.9 OPERATING COSTS 

658 

you need is 10 jobs like this to meet your goal and make a profit for the year, but then the 

feast turns to a famine and you only fly 300 hours by the end of the year. In essence, you 

should have (if you had been clairvoyant) bid the 40-hour job at $2,300 per hour or $92,000. 

You just lost about $12,000 on that 40-hour job. Naturally, you will bid differently on future 

jobs and perhaps break even at the end of the year. 

 You no doubt noticed in Fig. 2-439 that operators with one or two small pistonpowered helicopters have fixed costs per year that are about one-half of those for operators of 

turbine-powered machines. For example, suppose you buy just one Robinson R22 Beta II new 

on January 1, 2011 for $258,000. You are likely to have fixed costs of around $86,000 by the 

time the year is out—according to the Aircraft Cost Evaluator [640]. The same source 

suggests that the variable cost per flight hour for this modern, two-place helicopter is, on 

average, just under $200 per flight hour. Now imagine you accumulate 500 flight hours 

during the course of the year. That means your total operating costs for 2011 will be $186,000 

(i.e., $86,000 + 500 × $200).217 While these dollar figures may strike you as rather expensive, 

you should keep in mind that the Robinson Helicopter Company started out selling 7 of the 

original R22s in 1979 and, by the end of 2009, the company had sold about 4,500 R22s in 

several versions with no end in sight. It seems to me that when Bell Helicopter stopped 

$0

$1,000

$2,000

$3,000

$4,000

$5,000

0 200 400 600 800 1,000 1,200

$250,000 

$25 million

$20 million

$15 million

$10 million

$5 million

$1 million 

Total

Operating

Costs

per

Flight

Hour

Planned Flight Hours per Year

0

Helicopter 

List Price

Fig. 2-441. TOC per flight hour is quite sensitive to the flight hours planned for a year. 

 

217 With all deference to our pioneers, this is not the dollar outlay that puts a helicopter in every garage! 
2.9 OPERATING COSTS 

659 

producing its ground-breaking Model 47 in the mid-1970s, Frank Robinson picked up the ball 

with his R22.218 There should be no question that the R22 is the helicopter of choice as an 

entry into the world of helicopter operations. 

 As a final note, the Robinson R22 total operating costs per year of $186,000 

(assuming 500 hours per year flying) means that you are buying about 72 percent of a new 

machine each year. This made me wonder about the detailed numbers that Conklin & de 

Decker found in averaging their survey of many users. Just for the fun of it, I built a TOC cost 

breakdown to see just what an operator of one R22 should be planning for. My TOC estimate 

was built upon the estimate dated 15 January 2012 that the Robinson Helicopter company 

provides on its website [651]. The additional line-item costs used my variation on ACE data. I 

assumed I was both the pilot ($96/hr) and the mechanic ($64/hr), albeit a slow one. Table 

2-61 gives you my impression of operating costs for an R22. 

Table 2-61. Total Operating Costs for a Robinson Helicopter Company R22 Beta II 

Bought New for $274,000 and Flown 500 Hours Per Year

Cost Line Item 

Harris’ 

Estimate Notes and Assumptions 

VARIABLE COSTS Per Year $82,690 

Fuel $21,400 8 gal./hour, $5.35/gal. and 500 hours (RHC input) 

Lubricants and Fluids $430 2% of fuel (RHC input) 

Scheduled Maintenance $7,680 MMH/FH × $64 × 500 hrs 

 MMH/FH 0.24 Fig. 2-437, but slower by 25%. No overhaul included 

Unscheduled Maintenance $3,840 

 MMH/FH 0.12 0.5 times scheduled MMH/FH 

Parts (Airframe/Eng/Avionics) $10,000 $20 per flight hour for periodic maintenance parts. ACE input 

Engine Restoration $6,140 $12.27/FH (RHC $27,000 engine exchange program) 

Airframe Overhaul $31,800 $140,000/2,200 hr × 500 hr (RHC factory overhaul program) 

Landing and Parking $750 $1.50 per hour. No RHC input 

Misc $650 $1.30 per hour for catering and misc supplies. No RHC input 

FIXED COSTS Per Year $85,610 

Crew Salaries 

 Base $48,000 Harris at $96/hr. No RHC input 

 Benefits $14,400 Harris at 30% of Base. No RHC input 

Aircraft Modernization $1,300 ACE input. No RHC input 

Hanger $2,400 ACE input. No RHC input 

Hull Insurance $13,700 5% of $274,000 (I know a guy, and I am a great pilot) 

Liability Insurance $1,900 1.25% of $274,000 (I know a guy, and I am a great pilot) 

Recurrent Training $1,500 ACE input. No RHC input 

Navigation Chart Service $430 ACE input. No RHC input 

Refurbishing $1,280 ACE input at 10 labor hours per year per seat × 2 seats 

Weather Service $700 ACE input. No RHC input 

Depreciation Negligible RHC input 

Total Operating Costs Per 

Year $168,300 

 

218 He added the R44 series in 1993 and now has the turbine-powered R66 in production. 
2.9 OPERATING COSTS 

660 

2.9.8 Concluding Remarks 

 Helicopters have become the aircraft of choice for more than two dozen different jobs, 

as Fig. 2-424 shows, in spite of total operating costs (TOCs) considerably higher than 

comparative fixed-wing aircraft. Of course, in many, many cases, the job requirements simply 

exclude fixed-wing aircraft because they cannot hover. Helicopter operators have found that 

air taxi, charter, offshore oil rig support, and executive transport, for example, are profitable 

tasks. Where helicopter operators have found that high operating costs simply exclude them 

from virtually any business is in a head-to-head competition with commercial airlines. The 

operators have been shut out of even short-haul routes where airports exist, and they have 

been shut out of city-center-to-city-center routes (even with heliports available) because the 

unsubsidized ticket price is just too high. 

 Several generations of helicopter proponents have carried the banner saying that their 

machines offer just the right addition to the present overall transportation system. The banner 

states that helicopters now, and future rotorcraft to come, will save the public’s time by 

avoiding growing highway congestion. The more enthusiastic proponents maintain that the 

whole air traffic system will benefit (and may even avoid collapsing) if the helicopter is 

introduced. I’m beginning to find the arguments for the helicopter’s expanded role rather 

annoying. I say this because so little reality about operating costs is brought to the table. 

Project Hummingbird offered the helicopter industry its first try at creating unsubsidized 

airlines. This first try showed just how small a percentage of the total traveling public would 

benefit. This first try also showed just what the ticket price would have to be for a helicopter 

airline to just break even. 

 Even as late as the mid-1960s, it was not clear to me that helicopter proponents were 

facing up to their economic obstacles. In December 1963, United Research Inc. prepared a 

report [652] titled Outlook for Vertical-Lift Aircraft in Scheduled Commercial Transportation

for the Sikorsky Division of the United Aircraft Corporation, the Vertol Division of the 

Boeing Company, and for the Small Aircraft Engine Department of the General Electric 

Company. Let me quote several sentences from the summary of what I consider today to be 

(1) the best in-depth report ever published studying key aspects of our transportation system 

and how VTOL aircraft will fit in, and (2) an over-glowing view that keeps being repeated: 

“5. As is true in air transport, the subsidy requirements of the helicopter carriers have been 

related closely to the economic characteristics of their flight equipment. Until the recent 

introduction of twin-turbine helicopters, the break-even requirements remained well above 

100 percent of aircraft capacity. The introduction of twin-turbine equipment has already cut 

unit operating costs in half and unit costs for turbine operators continue to decline as traffic 

volume grows. Despite the recent progress which has been made with turbine operations, 

however, the industry is still heavily dependent upon subsidy support. Subsidy accounts for 

roughly 50 percent of total operating revenues. Until unit costs are lowered further with an 

increased scale of operation and load factors raised with higher traffic levels, any substantial 

reduction in subsidy would cripple the operations of the subsidized carriers at the present 

time. (Chapter III, pages III-10 through III-27.) 
2.9 OPERATING COSTS 

661 

6. The prospects of carriers achieving economic self-sufficiency in the future are good. The 

nation’s intercity and international air travel will continue to expand, and a major part of this 

travel will be funneled through the airports serving our large metropolitan areas. The 

pressures which account for severe surface traffic congestion in these urban areas will 

continue to grow. No technological improvements in surface transportation offering an 

alternative expedited service are in sight for the near future. Further unit cost reductions can 

be expected as increasing traffic demand and pending certification of all weather operations 

increase the utilization of existing facilities, flight equipment and personnel. Although the 

achievement of economic self-sufficiency is by no means certain, the characteristics of 

aircraft now available provide the potential for a drastic reduction or possible elimination of 

subsidy toward the end of a five-year period. (Chapter III, pages III-40 through III-60. )” 

This 1963 report has facts and figures in abundance. Unfortunately, if this research were 

repeated today, I do not believe you would find much has changed. Despite periodic 

workshops [118], no new argument (in over 35 years) for VTOL airlines came to my attention 

until the tiltrotor arrived. Then in 1995, at the prodding of Congress, the U.S. Department of 

Transportation “evaluated the technical feasibility and economic viability of developing civil 

tiltrotor (CTR) aircraft and a national system of infrastructure to support incorporation of 

tiltrotor technology into the national transportation system.” [653, 654]. I am not aware of any 

progress, beyond a recommendation for more studying and more research, that came from the 

DOT report. The negative views again prevailed. 

 You may think I have lost all hope of VTOL airlines ever becoming a reality. Nothing 

could be further from the truth. Keep in mind that commercial airlines sell transportation (seat 

miles per year) not time in the air (flight hours per year) like General Aviation. Therefore, 

productivity of V/STOL aircraft (tiltrotor, etc.) may have a significant payoff when compared 

to a helicopter. While I am disappointed in progress that substantially reduces the purchase 

price and operating costs of helicopters, the rotorcraft industry has opened a door with the 

tiltrotor. This VTOL configuration may, in fact, demonstrate the improvement that the 

Douglas DC-3 gave to the fixed-wing side of the business. At least this gives the rotorcraft 

industry another chance. 

 And there is another reason I am always hopeful. It is a quote that I ran across in a 

report by the American Society of Planning Officials about helicopters in May 1965 [655]. 

(This group frequently deals with planning for helicopter use in cities.) The short paragraph 

reads as follows: 

 “This new vehicle costs too much for everyone. One estimate of initial and 

maintenance cost for six months is $5,500. It is unsafe, has no utility, is difficult to operate 

and expensive to run. There are no adequate service facilities, the insurance costs are 

extremely high, and there is a most undesirable noise factor. It is practically useless at night 

and cannot be used in bad weather. Moreover, it compares miserably with the relative 

cheapness of existing methods of transportation.” 

This statement came from a 1907 newspaper article about the automobile. It is not too hard to 

imagine nearly the exact same words being used to describe the Wright Brothers’ invention. 
662 
663 

2.10 ACCIDENT RECORD 

 It seems that accidents have been a part of aviation since the dawn of time. First there 

were tower jumpers, with or without makeshift wings, who were not successful. Then came 

very rudimentary aircraft of all types that were unstable, uncontrollable, and structurally 

unsound, not to mention underpowered. Balloons and dirigibles did better, which provided 

some encouragement until the Hindenburg airship disaster on May 6, 1937, when nearly 100 

people were killed. Otto Lilienthal, the German aviation pioneer, was killed on August 10, 

1896, after many successful hang glider flights. And in the United States, Wilbur and Orville 

Wright appeared immune until Orville’s crash at Fort Myer on September 17, 1908. The 

passenger, Lieutenant Thomas E. Selfridge, was killed in that accident. Orville suffered a 

fractured left leg, four broken ribs, a fractured and dislocated hip, and a back injury. This was 

the first accident with a powered, heavier-than-air aircraft in which a person died. Orville’s 

accident report to Wilbur by letter on November 14, 1908, traced the initial accident cause to 

propeller failure. Wilbur wrote a more detailed accident report to Octave Chanute on June 6, 

1909, and thus began the practice of accident reporting, all with the purpose of learning how 

to avoid future accidents. 

 In this chapter, you will first read some historical background after World War I 

(WWI) leading up to the last five decades of rotorcraft accidents. These opening remarks 

include an examination of helicopter accidents per 100,000 flight hours and point out a 

serious flaw with this commonly quoted accident rate. The second part of this chapter 

examines 11,426 rotorcraft accidents that the National Transportation Safety Board (NTSB) 

has reported from January 1, 1964, through 2011. The third part provides a detailed analysis 

of 8,436 accidents from January 1, 1964, through 1997, and gives a clearer picture of the 

major human and aircraft deficiencies facing the rotorcraft industry. The concluding remarks 

offer some specific suggestions that, if taken, will reduce the number of rotorcraft accidents 

per year by more than half, even as the fleet continues to grow. 

2.10.1 History, Accident Rate, and Predictions 

 As WWI drew to a close in late 1918, the major European combatants turned their 

attention to civil air transportation. Experimental air routes were established in 1919, most 

with postal service, and passenger acceptance of air travel appeared in 1920. In 1921, the 

number of passengers significantly increased [656], and traveling by air became an 

established, but subsidized, industry. France took the lead because of massive government 

subsidies to its budding airline industry. Great Britain’s Government offered little help to its 

industry until mid-1921. Germany, despite some terms of the armistice, began passenger 

service as well. In the United States, little national interest beyond air postal service appeared 

until Charles Lindbergh’s nonstop, solo flight across the Atlantic on May 20–21, 1927. 

 In November 1921, France hosted the Premier Congrés International de la Navigation 

Aérienne. Two important papers from this conference were translated into English and 

published in the U.S. by the newly formed National Advisory Committee for Aeronautics, 

(N.A.C.A.) [657, 658]. The first paper, titled Organization and Exploitation of Regular Aerial 
2.10 ACCIDENT RECORD 

664 

Transportation Lines, was presented by Tete [657]. Tete comprehensively described 

commercial aviation growth in France from September 1918 through September 1921. Initial 

“aerial lines” experimenting began with mail delivery. These experiments quickly showed 

that “for the regular functioning of aerial transportation lines, it was first necessary to lay out 

air routes, i.e., to establish airdromes and emergency landing fields, a suitable meteorology 

service, and a system of communications.” The cooperation of several bureaus within the 

French Government quickly provided infrastructure, and “at the end of 1919, four French 

companies were engaged in the regular transportation of passengers and freight” over three 

major routes. This expansion, illustrated in Fig. 2-442 using tabulated data from Tete’s paper, 

shows that by the end of 1921, the French airline industry was growing by leaps and bounds. 

Unfortunately, France’s airlines were covering only about 18 percent of their total operating 

costs with ticket sales—and this was typical of the world’s air transportation system. 

 A second paper titled Aviation and Insurance [658] was presented by Mayo at the 

November 1921 conference. Mayo took the position that both France’s and England’s 

commercial aviation seemed “to be enjoying a considerable degree of prosperity.” But he 

immediately goes on to say that “in reality the air services in both countries are in a very 

unsatisfactory condition” because “the air traffic companies of both countries do not pay 

0

50

100

150

200

250

300

1917 1918 1919 1920 1921

The

"Great War"

Ends

6,387 Passengers

Carried Thru Sept. 

1921

527 Passengers

Carried During

1919

982 Passengers

Carried During

1920

Operating

Airplanes

End of Year

Fig. 2-442. France led the world in developing air transportation. 
2.10 ACCIDENT RECORD 

665 

expenses without aid and will probably not be able to do so for many years to come.” Mayo 

suggests “many and complex” reasons for this “state of affairs” and then continues saying that 

“there is, however, one aspect of the question [i.e., the unsatisfactory financial condition] 

which is all important for the future development of commercial aviation, to wit, aviation 

insurance.” He makes it very clear that the “existence of satisfactory insurance conditions is 

indispensable to the commercial prosperity of any enterprise whose capital is invested in 

anything susceptible of being damaged or destroyed.” 

 Mayo’s view (just as true today as in 1921) was that if accidents continued at such a 

high rate, insurance costs would remain high, or go higher, and civil aviation, without 

continued subsidies, would cease. His “analysis of the statistics of accidents that have 

happened in civil aviation since the armistice, shows that the number of accidents in which 

the pilot and passengers were killed or even injured, has been remarkably small. It is 

doubtless due to this fact that civil aviation has prospered as it has and that the number of 

passengers carried has risen so rapidly and constantly. The number of airplane accidents, 

however, has been lamentably high.” Mayo makes it clear that “the [airline] companies must, 

in their own interest, frankly face the situation and make a determined effort to reduce the 

number of accidents.”219 

 Mayo alerts the several aviation companies that the insurance industry is well aware of 

the accident rate and that “several large [underwriters] have been obligated to stop taking 

aviation risks.” He then points out the “causes of the many accidents which account for the 

high insurance rates,” stating: 

“The frequent accidents to airplanes employed on air routes have been due to widely divergent 

causes. Probably 90 % of them were due to carelessness and could have been avoided, had the 

necessary precautions been taken. The principal causes of accidents may be enumerated as 

follows: 

1. Poor piloting; 

2. Engine trouble; 

3. Lack of system [i.e., not employing top-notch people]; 

4. Poorly adapted airplanes; 

5. Poor airdromes; 

6. Unfavorable meteorological conditions.” 

In concluding this discussion of civil aviation history up to the end of 1921, I suggest that, 

with only minor changes, R. H. Mayo’s paper could be presented today at any helicopter (or, 

for that matter, even general aviation) safety symposium. 

 Now take a 10-year step forward to aviation and its accident situation in the U.S. The 

birth of commercial aviation in the U.S. is traced back to 1914 by Davies in Airlines of the 

United States [316] and by van der Linden in his superb book, Airlines and Air Mail—The 

Post Office and the Birth of the Commercial Aviation Industry [498]. As is well known, the 

 

219 It is quite clear that the airline companies of the world have made the “determined effort” Mayo spoke about 

(as you will no doubt agree)—and they have been remarkably successful. Unfortunately, the results achieved by 

the rotorcraft industry are not so clear. 
2.10 ACCIDENT RECORD 

666 

post office played a key role in starting commercial aviation in this country. In many ways, 

the U.S. simply followed France’s startup model. What is not so well known is that the 

growing number of airplane accidents up to the late 1920s became a great concern to several 

departments of the U.S. Government. Army, Navy, and civilian aircraft pilots were 

experiencing stalls followed by spins, forced landings following engine failure were all too 

common and, even with power, landings frequently ended as crashes. By 1928 the situation 

was serious enough to warrant attention from the Assistant Secretaries for Aeronautics in the 

Departments of War, Navy, and Commerce. 

 These departments called upon the N.A.C.A. to establish a special commission that 

would “prepare a basis for the classification and comparison of aircraft accidents, both civil 

and military.” The commission was formed, and the first meeting was held on March 1, 1928. 

Finally, after 16 meetings, the committee’s work was published on August 15, 1928, as NACA 

Report No. 308 [659]. This report defined 13 classes of accidents, 4 classes of injuries, and 6 

classes of damage to material. Categories of immediate and underlying accident causes were 

established, and an accident form was adopted. This classification basis was used to analyze 

1,432 military and 1,400 civilian accidents that occurred before January 1929. The resulting 

analysis and associated tabulated data were published one year later in NACA Report No. 357 

[660]. 

 In June 1936, a further refinement to definitions and methods of analysis was 

established with NACA Report No. 576 [661]. This report, titled simply Aircraft Accidents,

became the standard U.S. reference on the subject and formed the foundation for current 

NTSB aviation accident reporting. The accident form (Fig. 2-443) had evolved, and it proved 

to be of immense value. Notice that the “immediate causes of the accident” were divided into 

four subcategories and the “underlying causes of accident” into only two subcategories. 

Furthermore, it was not enough to just record pilot error or material failure. The form 

demanded much more in-depth investigation and reporting. 

 The form, plus analysis of some 2,800 accidents, led to a table of summary 

conclusions [660], which is displayed here using the bar chart in Fig. 2-444. There was an 

immediate payoff for the efforts of the N.A.C.A.-led committee. Analysis of the data revealed 

major shortcomings in aircraft design and pilot training (e.g., deficiencies in aircraft stability, 

and control and spin recognition and recovery by pilots) for which corrective actions were 

developed and implemented. It should be noted that solving these problems did not require 

computing accidents per flight hour or other ratios that are considered important measures of 

transportation safety today. The priority then, as now, was to put an end to accidents. 

 Of course, World War II (WWII) disrupted the orderly and documented study of 

accidents. However, in October 1944, the U.S. Civil Aeronautics Administration (CAA), the 

predecessor to the Federal Aviation Administration (FAA), published the first Statistical 

Handbook of Civil Aviation [662]. This first of many CAA (and then FAA) handbooks 

pointed out that reported accident statistics were based on definitions and classifications 
2.10 ACCIDENT RECORD 

667 

Fig. 2-443. By mid-1936 the U.S. had an accident reporting form [661]. 
2.10 ACCIDENT RECORD 

668 

0% 5% 10% 15% 20% 25%

Taxying accidents

Collisions in full flight with

objects other than aircraft

Take-off accidents

Spins or stalls without engine

failure

Forced landings

Landing accidents

Army & Navy 1,432 Accidents

Civil 1,400 Accidents

Total Analyzed 2,832

Accidents (% of 2,832)

 Classification . 

Fig. 2-444. Accident classification uncovered pilot and airplane deficiencies that 

needed fixing. 

established by NACA Report No. 576 (although the Statistical Handbook incorrectly 

referenced the NACA Report as No. 567). This document summarized aviation statistics 

dating back to 1926, including air carrier and private flying accident statistics compiled by the 

U.S. Civil Aeronautics Board (CAB), the predecessor to the NTSB. In the introduction, the 

CAA acknowledged that “There are some gaps in the early statistics [about private flying] 

because fact-gathering machinery had not been fully organized and it also was extremely 

difficult to obtain reliable figures from an industry still inchoate.” With respect to private 

flying, the CAA noted that “because of the dislocation caused by the war, statistics on the 

amount of private flying during the war years [1942 and 1943] are incomplete.” Despite these 

reservations, the 1944 CAA handbook provided early examples of detailed tables regarding 

aircraft operating statistics for both air carriers and private flying. A composite of statistical 

data from several tables in the 1944 CAA handbook is provided here in Table 2-62. 

 Historically, Table 2-62 reflects three major events in aviation progress. The first event 

came with the depression in the early 1930s, which caused the drop in aircraft sold and the 

demise of several manufacturers. The second event was the rapid rise in air carrier miles 

flown with fewer aircraft, which came with the transition from Ford Tri-Motors to the Boeing 
2.10 ACCIDENT RECORD 

669 

Model 247 and the Douglas DC-3. The third event was the United State’s entry into WWII 

and the rapid conversion of commercial aircraft to military configurations, which affected 

statistics in 1942 and 1943. 

 Despite the upheaving events that are reflected in Table 2-62, the primary aviation 

safety statistic of the era showed that air transportation safety was improving. The 1944 CAA 

handbook illustrated this fact with tabulations of statute miles flown per accident, and this 

historical data is shown in Fig. 2-445. The contrasting trends between air carrier and private 

flying are quite remarkable. The fare paying public was reading fewer blaring newspaper 

headlines about fatal airliner crashes and seeing more people boarding airplanes in the 

movies. Of course, during WWII service men and women in great numbers were exposed to 

flying in many forms. When these servicemen and women came home, aviation really began 

the upward trend to become what we know today. As an aside, the New York Yankee baseball 

team started traveling by airplane in May 1946. 

 Now jump ahead to today, July 2012, and look back at what has happened in the world 

of commercial (and amateur) rotorcraft. The modern era of U.S. civil rotorcraft operations 

officially began on March 8, 1946, with the CAA’s certification of the Bell Model 47. In that 

year, Bell began a first lot production run of 10 helicopters. The two-place Model 47 was 

followed by the four-place Sikorsky S-51, certificated on April 17, 1947. The S-51 was 

developed from Sikorsky’s R-5 military helicopter and benefited from experience gained with 

the smaller R-4 and R-6 military models. On October 14, 1948, the CAA certificated the 

Hiller Model 360, the beginning of the UH-12 series. By the end of 1957, the CAA’s 

Statistical Study of U.S. Civil Aircraft reported 540 registered helicopters in the civil fleet 

(Table 2-63). 

Table 2-62. Early Aviation Statistical Data in the United States [662] 

Year 

Air Carrier 

Aircraft in 

Service 

Air Carrier 

Revenue Miles 

Flown 

(all services)

Air Carrier 

Accidents

Private 

Flying 

Aircraft in 

Service

Private 

Flying 

Miles Flown 

Private 

Flying 

Accidents

1926 n/a 4,258,771 n/a 1,300 18,746,640 n/a 

1927 n/a 5,779,863 25 2,612 30,000,000 253 

1928 268 10,400,239 85 4,779 60,000,000 1,036 

1929 442 22,380,020 124 9,315 110,000,000 1,586 

1930 497 31,992,634 88 9,218 108,269,760 2,033 

1931 490 42,755,417 117 10,090 94,343,115 2,205 

1932 456 45,606,354 108 9,760 78,178,700 1,951 

1933 406 48,771,553 100 8,780 71,222,845 1,603 

1934 417 40,955,396 71 7,752 75,602,152 1,504 

1935 356 55,380,353 58 8,613 84,755,630 1,517 

1936 272 63,777,226 65 8,849 93,320,375 1,698 

1937 282 66,071,507 42 10,446 103,198,355 1,917 

1938 253 69,668,827 33 10,718 129,359,095 1,882 

1939 265 82,571,523 33 13,217 177,868,157 2,175 

1940 358 108,800,436 42 17,253 264,000,000 3,446 

1941 359 133,022,679 33 24,124 346,303,400 4,312 

1942 179 110,102,860 31 22,329 293,592,580 3,176 

1943 194 103,601,443 24 22,323 TBD 3,762 
2.10 ACCIDENT RECORD 

670 

Fig. 2-445. Early aviation safety statistics in the United States. 

 As Table 2-63 shows, the CAA segregated aircraft by “active” and “inactive” based on 

the following definitions: Active aircraft were those that held a valid certificate of 

airworthiness, and that had an approved inspection during the previous 12 months and were 

eligible to fly. Aircraft classified as inactive “need not necessarily be in unairworthy condition 

and may hold a valid airworthiness certificate, but they have not met the periodic inspection 

requirement.” With only minor variations, these definitions have remained the same for nearly 

seven decades. 

Table 2-63. The CAA Registered Helicopter Census at the End of 1957

Manufacturer Model Active Inactive Total 

Bell Aircraft Corp. 47 246 49 295 

Hiller Helicopters UH-12 29 20 49 

Sikorsky R-4, R-6, S-51, S-52 14 25 39 

S-55 27 12 39 

S-58 21 0 21 

All others Various 33 64 97 

Total 370 170 540 
2.10 ACCIDENT RECORD 

671 

 The size of the helicopter fleet grew substantially after WWII ended, as Fig. 2-446 

shows. The FAA made a minor bookkeeping correction to this growth trend in 1970. The 

growth continued until the early 1980s when the market for new piston- and turbine-powered 

rotorcraft virtually collapsed. The market began recovering in the early 1990s. At the end of 

2005, the FAA Civil Aviation Registry showed a computer listing of nearly 19,000 rotorcraft 

(mostly helicopters, some autogyros, a couple of compound research helicopters, and two 

tiltrotors), each with an assigned FAA registry number, or N number as it is commonly 

referred to. My detailed review of the registry found a significant number of rotorcraft in 

museums or simply stored. Therefore, a somewhat lower count of active plus inactive 

rotorcraft is shown in Fig. 2-446 as the Harris count. 

 Fig. 2-446 raises an interesting point about which there has been growing 

disagreement for the past two decades. The immediate impression created by Fig. 2-446 is 

that while more and more rotorcraft have been registered (i.e., bought and N number 

assigned), the number of rotorcraft actually in use and flying does not seem to have changed 

appreciably since 1980 or 1981—according to FAA reporting. For example, in the 1980 

census, which reported statistics for 1979, the realistic count would be 9,000 active plus 

inactive rotorcraft. However, the FAA statistically found that only 6,000 flew (at least 1 hour) 

in 1979. In contrast, by the end of 2003, the active plus inactive count was on the order of 

15,000 rotorcraft, but the FAA statistically found only 6,500 were “active.” I find it 

unimaginable to think that the FAA’s count of active rotorcraft is remotely correct after 1980, 

particularly because spare parts’ sales have done nothing but increase. 

 Apparently, even the NTSB began to have some serious misgivings about the FAA 

civil aviation statistics as well—so much so that they formally expressed themselves in 2005 

[663]. Shortly thereafter (July 20, 2010), the FAA decided to address the problem with a new 

set of rules and regulations [664]. In this Federal Register (vol. 75, no. 138) final rule, starting 

October 1, 2010, and over the next 3 years, all aircraft owners would have to reregister their 

aircraft, forcing (hopefully) the FAA Master Registry List220 to become up to date. In the 

executive summary, the FAA states: 

 “The FAA estimates that approximately one-third of the 357,000 registered aircraft 

records it maintains are inaccurate and that many aircraft associated with those records are 

likely ineligible for United States registration. The inaccuracies result from failures in the 

voluntary compliance based system. Although aircraft owners are required to report the sale 

of an aircraft, death of an owner, scrapping or destruction of an aircraft, and changes in 

mailing address; many have not. Without owner initiated action, there has been no means to 

correct those records. The FAA has been asked by government and law enforcement agencies 

to provide more accurate and up-to-date aircraft registration information. [Other interested 

parties have asked, too.] This rule is intended to support the needs of our system users.” 

Time will tell if FAA statistical data accuracy will improve after this new ruling is fully 

implemented. 

 

220 The FAA Civil Aviation Registry (called the Master List) is maintained at the FAA Mike Monroney 

Aeronautical Center, 6500 South MacArthur Boulevard, Oklahoma City, OK 73169. The telephone number is 

(405) 954-4331. The Master List is now available online. This FAA center is about 30 miles away from 

Piedmont, Oklahoma where Sue and I now live. 
2.10 ACCIDENT RECORD 

672 

Fig. 2-446. The FAA-registered rotorcraft fleet has grown, but not all are flying. 

 At issue, of course, are the FAA statistics for just how many rotorcraft are “active.” 

The reason the issue is so important is that the number of flight hours flown by the active 

aircraft falls in the denominator of the most-quoted safety statistic, which is 

accidents

100,000 flight hours

.

The numerator, accidents per year, is well documented by the NTSB. The denominator, flight 

hours per year, is provided by the FAA Statistics and Forecast Branch based on their count of 

active rotorcraft. By way of background, each year this FAA branch publishes a “Census of 

U.S. Civil Aircraft.” (Rotorcraft fall in the General Aviation category, which was referred to as 

Private Flying by the CAA.) The census provides details about the number and types of 

aircraft currently operating in the U.S. civil aviation fleet, along with other relevant data such 

as flight hours. Fleet size and flight hour data for General Aviation are obtained by 

extrapolating data from a survey questionnaire mailed to a sample of registered owners. The 

validity of this database, to say nothing about the extrapolation, has been questioned 

occasionally. In fact, the rotorcraft industry requested and received a “one time only” survey. 

The results [665] did virtually nothing to allay industry concerns about the FAA’s estimate of 

hours flown per year by the rotorcraft fleet. 
2.10 ACCIDENT RECORD 

673 

 The “one time only” rotorcraft activity survey for 1989 [665] chose 10,469 owners 

from the Registration Master File to mail the standard questionnaire to. There were 1,883 

postal returns, which “reflect a seriously out-of-date rotorcraft file.” After three mailings and 

some culling, the data bank was reduced to 6,724 responses. The survey extrapolation 

methodology determined that there were 7,488 active rotorcraft in the fleet. Furthermore, the 

“estimate of total hours flown” by the active aircraft in 1989 was published as 2,828,697—

give or take a few minutes. The NTSB recorded 213 rotorcraft accidents in 1989, which 

means that 

Rotorcraft accidents 213 7.53 for 1989

100,000 flight hours 28.28697 = = .

The official, published rate for 1989 was 8.39 based upon the larger survey of General 

Aviation for 1989. As an aside, the special rotorcraft survey [665] noted in its table 3.4 that 

Arizona-based rotorcraft made 113,332 landings on offshore platforms, which at first 

impression seems ridiculous. 

 The 47-year trend of accidents per year and active rotorcraft flight hours per year is 

provided in Fig. 2-447. There has been a noticeable, favorable, and well-documented decline 

in accidents according to NTSB records. And, according to FAA statistics, fleet flight hours 

steadily climbed each year from 1964 to 1979; then abruptly began to decline from 1980 

onwards to 2002, whereupon a marked increasing trend began to emerge. The abrupt decline 

in active rotorcraft count (Fig. 2-446) and flight hours (Fig. 2-447) occurred when the FAA 

changed their survey methodology. A more complete discussion of this methodology change 

is provided in appendix B of reference [666], U.S. Civil Rotorcraft Accidents, 1963 through 

1997. Laying aside the FAA’s active aircraft and flight hour dilemma for the moment, the 

47-year accident rate (accidents per 100,000 flight hours) history is shown graphically in 

Fig. 2-448. 

 Fig. 2-448 gives the impression that the rotorcraft accident rate steadily improved 

from 1964 to 1979. After 1979, the rotorcraft accident rate remained constant at about 10 

accidents per 100,000 flight hours, give or take some randomness. In contrast to the overall 

fleet statistics, at least two corporations have shown that the national rotorcraft fleet statistics 

do not apply to them. In an article [667] in the February 1999 issue of Rotor & Wing, writer 

John Persinos explains that Mrs. Carroll Suggs, head of Petroleum Helicopters, Inc., instituted 

a new and aggressive safety program in 1992. The result of this program was that her 

company’s “accident rate averaged fewer than one accident per 100,000 flight hours, 

compared to the national average of more than seven per 100,000 flight hour.” The second 

company with a published accident rate is CHC Helicopters, Inc. Sylvain Allard, President 

and CEO of CHC, presented a paper at the September 2005 International Helicopter Safety 

Symposium [668] where he said that “all accidents are preventable” and that “accidents are a 

failure of management.” With this forceful commitment from the top, CHC’s accident rate 

was 0.47 using a 5-year rolling average ending in 2003, which Allard notes is comparable to 

the average of major airlines. 
2.10 ACCIDENT RECORD 

674 

0

500,000

1,000,000

1,500,000

2,000,000

2,500,000

3,000,000

3,500,000

4,000,000

1960 1970 1980 1990 2000 2010 2020

0

100

200

300

400

500

600

700

800

Hours

Flown

per

Year

(FAA 

Estimate,

Active

Rotorcraft

Only)

Rotorcraft

Accidents

per

Year

Accidents

Hours

End of Year

Fig. 2-447. Hours flown and accidents per year used in the accident rate calculation 

(the FAA’s hour-flown data is questionable; the NTSB data is not). 

0.1

1

10

100

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015

Rotorcraft

Accidents

per

100,000

Flight Hours

NTSB & FAA View Using 

Questionable FAA Activity Data

7.5

12.9

64.6

Petroleum Helicopter, Inc. at 0.9

CHC Helicopters at 0.47

End of Year

4.4

Fig. 2-448. No accidents is the real goal. 
2.10 ACCIDENT RECORD 

675 

 The favorable downward trend in rotorcraft accidents per 100,000 flight hours that you 

see in Fig. 2-448 after 2005 has come about, I believe, because of the formation of the 

International Helicopter Safety Team (IHST). You should become aware of this worldwide 

team, and the rotorcraft industry should be grateful for their efforts as well. Dave Downey, 

Vice President of Flight Safety at Bell Helicopter, wrote some history about the team in 

Heliprops magazine [669], saying: 

 “The IHST came to life in a meeting at the American Helicopter Society 

International headquarters in early 2004 with participants from the Helicopter Association 

International, the FAA, helicopter manufacturers, and others interested in the reduction of 

helicopter accidents. In order to get the movement going, the first International Helicopter 

Safety Symposium was held scheduled for everyone to meet in Montreal, Canada in 

September 2005. Industry interest and attendance was overwhelming.” 

He further explains that “the goal of the IHST is to reduce the helicopter accident rate 

80 percent by 2016. It is not a complicated goal, however, it is an ambitious one!” The goal 

was set in September 2005. Accepting a value of 10 accidents per 100,000 hours flown as the 

reference point according to Fig. 2-448 means, to me, that by 2016 the accident rate should be 

below 2.0. By my analysis of FAA and NTSB U.S. statistics, the U.S. civil fleet is at 4.4 

accidents per 100,000 hours flown at the end of 2011, and a trend has been established. You 

can read about the IHST in more detail by visiting their website at http://ihst.org. 

 The fact that accident rate is a questionable metric (because the hours flown 

denominator values available from the FAA are questionable) with which to measure 

rotorcraft safety is not the lesson to be learned from my historical discussion. The real lesson 

is that correcting human and aircraft deficiencies based on in-depth accident investigation and 

analysis is where real progress is made. It is the numerator in accident rate that is important. I 

believe the only real objective is no accidents at all.

2.10.2 In All, 11,426 Accidents From 1964 Through 2011 

 As an overview to detailed accident analysis, consider our accidents-per-year track 

record over the last 47 years, as shown in Fig. 2-449. NTSB records show that there has been 

a broadly defined improvement trend. In fact, a very positive spin can be obtained from this 

data. In 1964, there were 2,196 rotorcraft in the FAA Registry according to the Harris count in 

Fig. 2-446. The NTSB records count 264 accidents in that year. That works out to about 120 

accidents per 1,000 registered rotorcraft in 1964. In 2005, the Harris fleet count was 15,650 

rotorcraft and there were only 205 accidents, which is 12 accidents per 1,000 registered 

rotorcraft. And in 2011, there were 148 accidents in a fleet size of 19,764 rotorcraft, which is 

7.5 accidents per 1,000 registered rotorcraft. Thus, the rotorcraft industry, portrayed in this 

light, has reduced accidents by more than a factor of 10 from 1964 to 2011—even as the 

registered fleet increased nearly tenfold. 

 A closer examination of accidents during the 47 years discloses, however, two very 

serious facts that paint the industry in a poor light. The first fact is that the introduction of the 

single-turbine-powered helicopter was accompanied by a very high yearly accident count, 

which peaked in 1980. The second fact is that rotorcraft attrition, caused by accidents, has 

been unacceptably high compared to the commercial airline business. 
2.10 ACCIDENT RECORD 

676 

 A more careful examination of Fig. 2-449 shows that between 1972 and 1986 

accidents per year did not follow the linear trend shown by the dashed line, which is labeled 

as the Harris trend. I have put a label to this rise and fall of accidents per year from 1972 to 

1986 and called it an “accident bubble.” The accident bubble occurred when single-turbinepowered helicopters were introduced. To see this fact, consider first the fleet growth by 

rotorcraft type shown in Fig. 2-450. The major growth in single-turbine-powered helicopters 

clearly occurred between the years 1970 and 1985. The impact of introducing single-turbinepowered helicopters becomes abundantly clear in Fig. 2-451, which documents the accidents 

per year for helicopters powered with piston or turbine engines. Observe from Fig. 2-451 that 

accidents per year for single-turbine-powered helicopters increased nearly in proportion to the 

fleet growth shown in Fig. 2-450. 

 An even more distressing trend becomes apparent when accumulating accidents are 

plotted versus fleet growth, as shown in Fig. 2-452. For all intents and purposes, the industry 

added, in a given year, four helicopters to the FAA Registry and crashed one. And, most 

distressing, Fig. 2-452 shows no evidence that twin-turbine helicopters are faring better than 

single turbine-powered helicopters. One hopes that the introduction of future rotorcraft such 

as tiltrotors will not follow such a disturbing and unacceptable trend. 

 To complete this overview, it is important to quantify just how costly this accident 

track record has been over 47 years. In terms of people affected, 3,027 people have been 

killed in 11,426 accidents, and 2,362 people have been seriously injured. Thankfully, 17,590 

0

50

100

150

200

250

300

350

1960 1970 1980 1990 2000 2010 2020

Rotorcraft

Accidents

Each

Year

(NTSB

Records)

Harris

Trend

Assumes

Bubbles

Accident

"bubble"

Probably

Another

Bubble

End of Year

Fig. 2-449. Accidents per year for the last 47 years (we are doing better, but the 

goal is no accidents). 
2.10 ACCIDENT RECORD 

677 

0

3,000

6,000

9,000

12,000

15,000

18,000

21,000

1950 1960 1970 1980 1990 2000 2010 2020

Rotorcraft

Fleet

(Harris

 Count)

Single Piston

(Commercial Only)

Single Turbine

Twin Turbine

Commercial 

Total

Fleet Total

Amateur

End of Year

Fig. 2-450. Rotorcraft fleet growth by rotorcraft type. 

0

50

100

150

200

250

300

350

1960 1970 1980 1990 2000 2010 2020

Rotorcraft

Accidents

Each

Year

Single Piston

(Commercial + Amatuer)

Single Turbine

Twin Turbine

End of Year

All Rotorcraft

Fig. 2-451. An excessive number of accidents accompanied the introduction of single 

turbine-powered helicopters. 
2.10 ACCIDENT RECORD 

678 

Fig. 2-452. Accumulating accidents vs. fleet growth (what a trend—sell four 

and crash one)! 

people escaped relatively unharmed. Of lesser importance, 2,905 rotorcraft have been 

destroyed, 8,223 aircraft have been substantially damaged, and only 298 rotorcraft crashed 

and received minor or no damage. 

 You might be wondering just how much this track record has cost the rotorcraft 

industry in cold, hard cash. Let me offer one estimate. The cost of one accident was put at 

slightly over one million U.S. dollars by the HAI Safety Committee in the spring of 1991 

[670]. Walt Lamon, the chairman of the committee, estimated this cost in 1991 as follows: 

 Operator $194,000 

 (Loss of business, Increase in premiums, 

 Loss of pilot services, Legal expenses, 

 Lost time, etc.) 

 Insurance $775,000 

 (Repair or replacement, Claims paid 

 Admin costs, Legal fees, etc.) 

 Passengers’ Company $90,000 

 (Loss of business, 

 Loss of employees’ service, 

 Corporate legal, Lost time, etc.) 

 Cost of One (1) Accident $1,059,000 
2.10 ACCIDENT RECORD 

679 

On this basis, the 11,426 accidents since 1964 have siphoned off $12 billon, which is, to me, a 

staggering amount of lost money for such a relatively small industry—and this estimate does 

not even consider inflation! 

 Now let me conclude this overview of rotorcraft accidents investigated and recorded 

by the National Transportation Safety Board (NTSB) between January 1, 1994, and December 

31, 2011, with a summary shown in Fig. 2-453 and Table 2-64. 

 The NTSB has divided the classification of rotorcraft accidents into 1 of about 21 

different groups. One classification, for example, is loss of engine power. You can sense right 

away that a classification might be called a cause of the accident, but that immediately begs 

the question, “What caused the loss of power?” The accident investigator might find, for 

example, that the engine was starved for fuel, but then that leads to the question, “Why wasn’t 

the fuel getting to the engine?” Of course, an answer here leads to another question, and the 

answer to that question precipitates another question until, finally, reaching a satisfactory root 

cause (like maybe the fuel tank was empty). But then someone might ask, “Why was the fuel 

tank empty?” Just stop a moment and think about the answer to that question. I am sure you 

can appreciate that the simple act of assigning an accident into a classification is really just 

the starting point for an NTSB investigator. 

 To emphasize this one example (i.e., loss of engine power), consider the abbreviated 

NTSB investigator’s report that follows: 221 

11012 Report Status: Factual NASDAC Database Entry: None 

NTSB Identification: ERA11CA166

14 CFR Part 91: General Aviation 

Accident occurred Saturday, February 26, 2011 in Fort Pierce, FL 

Aircraft: ENSTROM F-28C, registration: N5689B 

Injuries: 2 Minor, 1 Uninjured. 

Full narrative available

ERA11CA166 

The pilot of the helicopter stated that the fuel gauge indicated “one-eighth to one-quarter” full 

on takeoff. At an altitude of approximately 200 feet, the low fuel pressure light illuminated, 

followed by a total loss of engine power. The pilot performed a 180-degree autorotation to a 

parking lot, and the helicopter landed hard, resulting in substantial damage to the left skid and 

tail boom. During post accident examination, a Federal Aviation Administration inspector 

drained approximately 3 ounces of fuel from the gascolator. The pilot stated that there were 

no mechanical malfunctions or anomalies with the helicopter, and that he “ran it out of fuel” 

by “trusting the gauge.” 

 

221 The NTSB religiously posts their accident reports on their website and you can download the reports. 

Generally, a preliminary report is available first and is followed later by the final report with a full narrative. 
2.10 ACCIDENT RECORD 

680 

0 500 1,000 1,500 2,000 2,500 3,000 3,500

Loss of engine power

Loss of control

In flight collision with object

Airframe/component/system failure/malfunction

Hard landing

In flight collision with terrain/water

Rollover/noseover

Weather

Stall/settling with power

Propeller/rotor contact to person

Midair collision

On ground/water collision with object

Commercial Amateur

Number of Accidents

3,041/26.6%

78/0.7%

76/0.7%

85/0.7

97/0.8

254/2.2%

541/4.7

880/7.7

927/8.1%

1,458/12.8%

1,685/14.76

1,754/15.4%

Fig. 2-453. Ninety-five percent of accidents fall into one of twelve classifications. 

 I selected this particular NTSB report (ERA11CA166) because the pilot makes the 

point that he trusted the fuel gauge. It seems to me that the accident might easily have been 

traced back to the chief engineer of the company that manufactures the fuel gauge. Of course, 

if the pilot had some misgivings about the gauge, you might argue that some sort of dip stick 

could have been used. Perhaps the fuel tank designer might have added a sight gauge. Or you 

could even argue that the takeoff was made with less than the minimum fuel reserve that the 

FAA requires. 

 The classification of 11,426 rotorcraft accidents is shown in Fig. 2-453 for the civil 

rotorcraft fleet. Here you have the top 95 percent of the 11,426 accidents that have been under 

study by a small group over the last 18 years.222 You might notice rather quickly that 

 

222 You may be curious about how this chapter on safety came to be. During the summer of 1994, I began to 

wonder about the statement that “virtually all accidents are caused by human error.” To satisfy my curiosity 

about this often quoted statement, I called the NTSB and asked for a copy of all rotorcraft accident reports going 

as far back as they cared to give me. The young lady sent me a stack of floppy discs almost in the blink of an 

eye. That data bank went into a massive Microsoft® Word file and I started reading. Shortly thereafter, Gene 

Kasper and Laura Iseler at NASA Ames Research Center expressed an interest in this matter. So the three of us 

took on the task of transferring the Word documents into an Excel® spreadsheet that contained what we thought 

were key summary data about 8,436 rotorcraft accidents that occurred from late 1963 through 1997. It was a 

daunting task, frequently accompanied with some very depressing thoughts as the repetition became clear. We 
2.10 ACCIDENT RECORD 

681 

loss of engine power (i.e., a forced landing) accounts for 3,041 accidents, or 26.6 percent of 

the 11,426 accidents under discussion. That is virtually identical to what airplanes were 

experiencing in the 1920s and 1930s as you learned from Fig. 2-444. I find the similarity in 

several classifications (or categories) to what was learned by studying the 2,832 early airplane 

accidents very interesting. 

 To begin with, accidents can be grouped by a first-occurrence category. The original 

accident form (Fig. 2-443) identified these “immediate cause” categories for airplane 

accidents. Today the NTSB has expanded the number of first-occurrence categories and 

included categories most associated with rotorcraft. Rotorcraft accidents grouped by the 12 

most common first-occurrence categories are shown in Fig. 2-453. Helicopters, with their 

ability to be flown “low and slow,” experience many more in-flight collisions with objects 

when compared to airplanes. Interestingly, loss of control is just as prevalent with helicopters 

as stall-and-spin airplane accidents were in the 1920s. Despite the helicopter’s mechanical 

complexity, accidents caused by some failure or malfunction of the airframe, or some airframe 

system, have caused less than 13 percent of accidents. In-flight collisions with terrain and/or 

water are just as common with helicopters today as with airplanes in the 1920s. 

 An interesting difference between helicopters and airplanes of the 1920s and 1930s is 

accidents categorized as hard landings. Fig. 2-444 shows that airplane landing accidents (with 

power on) were quite prevalent back then, while helicopters—in approximately the same state 

of development and use—appear one-third as prone to this category of accident. Roll-over 

and nose-over accidents caused principally by taking off with a skid tied down is, of course, a 

helicopter trait given its vertical takeoff capability. Finally, weather-related accidents appear 

about equal for helicopters (Fig. 2-453) and airplanes [660]. 

 Now turn your attention to Table 2-64, which sorts the 11,426 accidents into the 

commercial (10,540 accidents) and amateur (886 accidents) activities of the industry. 

 

published our detailed analysis and opinions in December of 2000 [666]. Then, in May of 2006, I was given the 

honor of presenting the 26th Nikolsky Lecture, and I chose to speak about rotorcraft accidents [671]. (This was 

probably not the subject my peers thought I should address; perhaps this book will be some sort of 

compensation.) The Nikolsky Lecture gave me the chance to update the files to 10,416 rotorcraft accidents, 

which I could not have done without Gene Kasper’s carefully kept records. And so you come to this last chapter 

in Volume II, and again, with Gene Kasper’s continued data gathering, you have some insight about 11,426 

accidents as of the end of 2011. Gene Kasper is still at Ames Research Center on the U.S. Army side, and he 

continues to keep the NTSB accident record file in Excel® format current by downloading accident reports from 

the NTSB website. 
2.10 ACCIDENT RECORD 

682 

Table 2-64. Classification and Number of Rotorcraft Accidents, 1964 Through 2011

Major Category for No. 1 Occurrence 

Helicopter 

Commercial

Piston 

Helicopter 

Commercial 

Single 

Turbine 

Helicopter 

Commercial 

Twin Turbine 

Autogyro 

Commercial

Piston 

Amateur 

Helicopter

Piston 

Amateur 

Helicopter

Single 

Turbine 

Amateur 

Autogyro 

Piston 

Loss of engine power 1,778 996 65 5 83 4 110 In-flight collision with object 1,092 458 83 5 10 0 37 Loss of control 897 481 69 23 83 2 199 Airframe/component/system failure/malfunction 747 431 134 12 58 0 76 Hard landing 634 219 18 5 18 0 33 In-flight collision with terrain/water 541 225 36 6 16 2 54 Roll-over/nose-over 353 146 7 2 17 0 16 Weather 85 131 28 3 1 0 6 Stall/settling with power 77 4 2 2 1 0 11 Propeller/rotor contact to person 33 38 11 1 0 0 2 Midair collision 21 44 9 0 0 0 2 On ground/water collision with object 34 28 12 0 0 0 4 Fire/explosion 30 17 6 0 2 0 0 Abrupt maneuver 13 11 2 1 1 0 9 Gear collapsed 16 3 6 1 0 0 1 Undershoot/overshoot 17 5 3 1 0 0 2 Dragged wing, rotor, pod, float or  tail/skid 20 4 2 0 1 0 0 On ground/water encounter with  terrain/water 8 13 0 0 0 0 3 All Others (undetermined, missing,  not reported) 131 158 38 3 2 0 20 Grand total 6,527 3,412 531 70 293 8 585 

 2.10 ACCIDENT RECORD 

682 
2.10 ACCIDENT RECORD 

683 

2.10.3 Detailed Accident Analysis 

 The compilation of data summarized in Fig. 2-453, and examined in more detail in 

Table 2-64, is the accident record over 47 years. In fact, the distribution of accidents in the 

several categories (as a percentage) has been changing over the last 47 years. This important 

fact about rotorcraft accidents is shown in Fig. 2-454. In this figure I have focused on the top 

four categories or classifications that you see in Table 2-64. These four categories account for 

70 percent of all rotorcraft accidents. I have treated the remaining 30 percent as just one 

group, beginning with hard landings. 

 Fig. 2-454 is read from the bottom up. That is, the single grouping of accident 

categories that accounts for 30 percent of accidents each year becomes the base. This group 

has accounted for virtually a constant 30 percent of yearly accidents for the past 47 years. 

Accidents caused by some failure or malfunction of the airframe, or some airframe system, 

add slightly over 12 percent to the base. Fig. 2-454 shows that loss-of-control accidents have 

more than doubled, as a percentage, since 1964. This is a serious and adverse trend. 

Helicopters are thought to require a special piloting talent to fly. However, Fig. 2-454 

suggests that the basic handling qualities of the aircraft really are poor. Our rotorcraft pioneers 

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1960 1964 1968 1972 1976 1980 1984 1988 1992 1996 2000 2004 2008 2012 2016

Distribution 

of

Rotorcraft

Accidents

Each

Year

+Airframe

All Other Categories

Form a 30% Base

+Loss of engine power

+In flight collisions with objects

+ Loss of control

End of Year

Fig. 2-454. Loss-of-control accidents are a growing problem. 
2.10 ACCIDENT RECORD 

684 

dreamed of a helicopter in every garage, and they imagined that a trip to market by helicopter 

would soon be an everyday occurrence. Frankly, seeing several hundred helicopters flitting in 

and out of a mall parking lot does not paint a pretty picture to me—given this trend in loss-ofcontrol accidents. 

 On the positive side, in-flight collision with objects appears to be considerably 

reduced since 1964, as the shrinking wedge on Fig. 2-454 suggests. Moreover, while not so 

dramatic, accidents associated with loss of engine power show clear signs of decline. 

 In the next several paragraphs, I will show you details of just the four accident 

categories singled out in Fig. 2-454. Details of these four categories, and all the other 

categories making up the 30 percent base, were first studied and reported in reference [666], 

which was published in December of 2000. This report dealt with accident analysis up to 

1997 and included a study of 8,436 accidents. As Gene Kasper and I read NTSB accident 

briefs for the period beyond 1997 up through early 2012, we generally agreed that very few 

new causes of accidents in the four major categories could be highlighted. And so for this 

chapter, I have “stolen” data, with some updating, from our December 2000 report [666] to 

bring this Volume II about helicopters to a close. At the risk of repeating myself, it may be 

disquieting, but the last 47 years of helicopter accidents bear considerable similarities to 

airplanes in their early stage of development. 

2.10.3.1 Loss-of-Engine-Power Analysis 

 So, what causes loss-of-engine-power accidents? More precisely, why did so many 

engines lose power? NTSB investigators have been able to backtrack toward a root cause for 

this failure in most of the accidents that began with a loss of power. A simple, first-step 

analysis of the NTSB accident reports turns up one startling and very disturbing, fact. The fact 

is that pilots of single turbine-powered helicopters are just as prone to loss of engine power as 

pilots of single piston-powered helicopters. 

 Consider the results of this first-step analysis by looking at Table 2-65, which is data 

from reference [666]. From 1964 through 1997, there were 8,436 accidents recorded by the 

NTSB as the rotorcraft fleet expanded. Some 2,408 accidents, about 29 percent of the 8,436 

total, were charged to loss of engine power. The accidents are distributed by engine type and 

divided into commercial and amateur types. This data shows immediately that single turbinepowered helicopters did not improve the loss-of-power accident situation relative to single 

piston-powered helicopters. That is, single piston-powered helicopters experienced 1,554 

loss-of-power accidents out of their total 5,371 accidents. This amounts to 29 percent. And, 

though it may come as a shock, single turbine-powered helicopters fared no better at 31 

percent (i.e., 704 out of 2,247 accidents). On the positive side, twin turbine-powered 

helicopters are showing the promise that many thought would come when single turbinepowered helicopters were introduced. After all, the turbine engine is almost universally 

thought to be much more reliable than the piston engine. 
2.10 ACCIDENT RECORD 

685 

Table 2-65. Loss-of-Engine-Power Accident Data, 1964 Through 1997

Accident Count (1964–1997) Single Piston Single Turbine Twin Turbine Amateur 

8,436 Total 5,371 2,247 302 516 

 

2,408 Loss of Engine Power 1,554 (29 %) 704 (31 %) 39 (13 %) 111 (15 %) 

 Table 2-65 does not, of course, suggest why engines are losing power. It takes the next 

analysis step to begin the explanation, and the results of this step are shown in Table 2-66. 

These results have been taken directly from reference [666] and, therefore, only include 

analysis of the 8,436 accidents that occurred from January 1, 1964, up to 1997. 

 To begin with, Table 2-66 shows that actual engine structural failure only caused 495 

of the 2,408 loss-of-engine-power accidents, which is one fifth of the loss-of-engine-power 

accidents. Unfortunately, NTSB data shows that turbine engine structural failure accounts for 

a larger percentage of failures than piston engines. Perhaps even more worrisome is the 

number of engine(s) structural failures in the small fleet of twin turbine-powered helicopters. 

 The primary reason for loss of engine power is fuel/air mixture related. Slightly over 

1,000 loss-of-engine-power accidents (some 43 percent of the total 2,408) were traced to 

incorrect fuel/air mixture. NTSB data shows that pilots of each helicopter class clearly share 

this fundamental problem. And, believe it or not, fuel exhaustion, which is a polite way of 

saying that the aircraft ran out of gas, is the culprit. There may be some deeper reason, some 

root cause, for a forced landing because of fuel exhaustion, but my discussion with many, 

many fixed-wing and rotary wing pilots did not uncover it. (Running out of gas is an awkward 

subject to bring up.) 

 A nearly typical fuel exhaustion accident is illustrated by the experience of a 45-yearold instrument-rated pilot with 2,335 rotorcraft flying hours who was forced to land 

a Bell 206L-1 on a hazy night after losing power in cruise. NTSB Docket Number 

0059/CHI82DA034 reads as follows: 

 THE ENGINE LOST POWER IN CRUISE DURING A NIGHT FLIGHT 

WHILE ENROUTE TO OBTAIN FUEL. THE LOW RPM AUDIO AND WARNING 

LIGHT WERE NOTED WHEN THE LOSS OF POWER OCCURRED. THE PILOT 

ENTERED AN AUTOROTATIVE DESCENT AND TURNED TO LAND ON AN 

INTERSTATE HIGHWAY. AS HE STARTED TO DECELERATE FOR LANDING, 

POWER LINES BECAME VISIBLE IN HIS FLIGHT PATH. HE DUMPED THE 

NOSE AND DOVE UNDER THE POWER LINES, THEN FLARED AND TOUCHED 

DOWN AT ABOUT 25 TO 30 MPH. DURING THE LAST PART OF A GROUND 

SLIDE, THE MAIN ROTOR STRUCK A POLE FOR AN OVERHEAD SIGN AND 

A SPEED LIMIT SIGN. NO PRE-ACCIDENT ENGINE FAILURES WERE FOUND. 

One might guess that the accident investigation uncovered some reason for the loss of engine 

power. However, no explanation was offered, and this particular accident was counted as one 

of the 609 in the Undetermined/Other category on Table 2-66. Virtually every one of the 

2,408 loss-of-engine-power accidents recorded by the NTSB from the end of 1963 to the end 

of 1997 resulted in a substantially damaged or destroyed helicopter. Therefore, the fact that 

power-off landing proficiency is not required by the FAA in order to obtain a helicopter pilot’s 
2.10 ACCIDENT RECORD 

686 

certification appears inconsistent with the number of accidents. It also appears that helicopters 

currently in the civil fleet provide marginal to inadequate autorotational capability for the 

average pilot to successfully complete the final flare and touchdown to a generally unsuitable 

landing site. This is, to me, a very large step backward from the capability designed into 

autogyros. Furthermore, it appears that training in full autorotation landings all the way to 

touchdown, even to a prepared landing site, is avoided because of both real and perceived 

risks. 

 I would say that low rotor inertia of helicopter rotor systems is a serious shortcoming 

in the current civil fleet. The design issue of trading increased rotor inertia at the expense of 

increased weight empty, and perhaps aircraft selling price, has been controlled by military 

designs. I say this because so many civil helicopters have come to the commercial 

marketplace as derivatives of military machines. It is not that autorotation capability is 

downplayed as a serious requirement in military designs—far from it. It is just that the 

requirement to meet a weight-empty goal has overridden, in my opinion, the improvement in 

safety that comes with a design that the average pilot can successfully land with zero forward 

ground speed after engine power failure. 

 This issue of how much autorotational safety can or should be provided in a new 

helicopter design became particularly important when the gas turbine engine arrived on the 

Table 2-66. Loss-of-Engine-Power Accident Data, 1994 Through 1997 [666].

Accident Count (1964–1997) Single Piston Single Turbine Twin Turbine Amateur 

2,408 Loss of Engine Power 1,554 704 39 111 

 495 Engine Structure 263 (17 %) 189 (27 %) 15 (38 %) 28 (25 %) 

1,042 Fuel/Air Mixture Related 686 (44 %) 299 (42 %) 17 (44 %) 40 (36 %) 

 Fuel exhaustion 326 82 1 8 

 Fuel contamination 97 43 1 4 

 Fuel starvation 72 26 5 4 

 Carburetor heat 70 0 0 6 

 Fuel system 67 92 3 10 

 Fuel control 42 27 3 7 

 Fuel improper 6 3 0 1 

 Induction air system 6 26 4 0 

 135 Other Systems 101 (6 %) 17 (2 %) 1 (3 %) 16 (14 %) 

 Ignition system 69 0 0 13 

 Lubricating system 24 15 1 3 

 Accessory drive assembly 8 2 0 0 

 62 Rotor Drive System 53 (3 %) 7 (1 %) 0 (0 %) 2 (2 %) 

 Clutch assembly 33 1 0 1 

 Transmission to main rotor 14 1 0 0 

 Engine to transmission drive 4 4 0 1 

 Freewheeling unit 2 1 0 0 

 65 Other Subcategories 54 (3 %) 11 (2 %) 0 (0 %) 0 (0 %) 

 Simulated power failure 36 8 0 0 

 Rotor RPM not maintained 18 3 0 0 

 609 Undetermined/Other 397 (26 %) 181 (26 %) 6 (15 %) 25 (23 %) 
2.10 ACCIDENT RECORD 

687 

scene. With that step forward, low disc loading design approaches almost inherent with 

piston-engine-powered helicopters were discarded in favor of reduced weight-empty 

approaches that virtually doubled disc loading. Furthermore, no increase in rotor inertia was 

made to offset the disc loading increase. The basic issue became important to the military by 

the mid-1970s as many of their helicopter missions required nap-of-the-earth flying. The loss 

of engine power while flying very low and slow (just the opposite of what is preached by 

fixed-wing advocates) became of serious concern with single engine military helicopters. This 

precipitated a flight test program [75] that clearly established the overall benefits of storing 

energy for power-off landings in higher rotor inertia. The message, delivered by Tom Wood of 

Bell Helicopter at the May 1976 American Helicopter 32nd Annual Forum [672], was ignored 

by both the military and commercial branches of the rotorcraft industry. Instead, a move to 

twin engines began. 

 The debates about multi-engine helicopter safety over single-engine machines are 

almost legendary. Even fixed-wing advocates were demanding three- and four-engine aircraft 

in the early days. And you will recall that the initial specification for what led to the Douglas 

DC-3 stated a requirement for three engines. The airline industry and the FAA have finally 

satisfied themselves that twin-engine-powered aircraft are good enough even for transoceanic 

passenger-carrying service as witnessed by the Boeing 777. 

 Part of the multi-engine safety debates has been mathematical probability 

computations223 that champion the thought that, with multi-engine redundancy, no one need 

ever worry about loss of power causing an accident again. Of course, you can see from Table 

2-66 that (mathematics be damned) twin-engine helicopters have virtually the same 

percentage of loss-of-engine-power accidents caused by fuel/air mixture problems as do 

single-engine helicopters! You might wish that this was not the case, but NTSB data do not 

support your wish. 

 The basic argument for multi-engine designs centers on the ability to continue flight 

with one engine out. Why just one of the engines going off-line is the criteria is not at all clear 

to me, but most studies start with this criteria. A recent example came up during a 2005 

NASA study about heavy lift rotor systems [674]. The NASA investigation somewhat 

paralleled the U.S. Army search for a heavy lift helicopter capable of lifting 20 to 30 tons of 

payload. The NASA study was, of course, aimed at the technology requirements of a notional, 

large civil airliner—something in the 120-passenger size and a VTOL aircraft that might 

enjoy the same commercial success as the Boeing 737. 

 A portion of this 2005 NASA investigation was carried out by Bell Helicopter and 

Sikorsky Aircraft who “prepared expositions on autorotation and one-engine-inoperative 

requirements for heavy lift.” The Sikorsky report by Mark Scott [675] and the Bell report by 

Tom Wood [676] are two very concise, well-written documents that deserve your undivided 

attention. 

 

223 Mr. H. L. Price delivered a lecture titled Safety in Numbers before The University of Leeds in West 

Yorkshire, United Kingdom, in November 1966. I was given a copy of the lecture [673] by Dick Carlson during 

a discussion we were having on probability as it relates to twin-engine safety. 
2.10 ACCIDENT RECORD 

688 

 The reports by Wood and Scott focus on two very important points. First of all, it is 

the FAA who is going to certify any heavy lift vertical takeoff and landing (VTOL) concept. 

And, between the two authors, you will read that current Part 29 and CAT A requirements 

may well be made more stringent for any future VTOL configurations of the type under study 

by NASA and the U.S. Army in 2005. Secondly, heavy lift twin-engine VTOL performance 

following a loss of one engine is particularly sensitive to the ratio of what horsepower the 

remaining engine can produce and how long that operating engine can produce that power. 

Both authors suggest that the emergency rating of the operating engine should be at least 0.9 

times the power required to hover. That means that the ratio of an engine’s emergency rating 

should be upwards of 1.8 of the standard takeoff rated power. Again, I recommend both 

reports for even more detailed discussion. 

 You should also be aware that the Russian Mil Moscow Helicopter Plant certificated 

its heavy lift Mi-26 helicopter in mid-1980 for complete twin-engine power failure. The 

requirement for this 120,000-pound helicopter was to complete autorotational landings to 

touchdown and to a final stopping of all motion. The paper [677] by Gourgen Karapetyan, 

Chief Test Pilot for Mil, is quite practical in all the details about meeting this certification 

requirement. I do not know of a better paper to read on the subject. 

 As a final note, consider the loss-of-engine-power accident trend shown in 

Fig. 2-455. The adverse trend that came with the single turbine-powered helicopter was 

reversed after 1981when the industry showed what vigorous attention could achieve, but then 

it appears as if compliancy set in, and the industry failed to follow up. 

0

20

40

60

80

100

120

1960 1970 1980 1990 2000 2010 2020

Loss of

Engine 

Power

Accidents

Each

Year

It is not clear why the slope changed.

This slope shows what can be done.

Introducing single turbines

End of Year

Fig. 2-455. The introduction of the single turbine-powered helicopter came with a 

serious increase in loss-of-engine-power accidents. 
2.10 ACCIDENT RECORD 

689 

2.10.3.2 In-Flight Collision With Objects 

 The preceding NTSB accident synopsis recounting a loss-of-power accident says, in 

part, that the pilot, as he started to decelerate for landing, saw power lines in his flight path, so 

he dumped the nose and dove under the wires. He was one of the lucky ones. Unfortunately, 

in-flight collisions with wires, wires/poles, and trees are a major cause of accidents. The 

statistics are quite clear as Fig. 2-456 and Table 2-67 show. Unfortunately wires have been, 

and continue to be, a major threat to helicopter activities, which you learn immediately from 

Fig. 2-456. 

 Table 2-67 shows that the major contributor to these in-flight collisions with objects 

was the single piston-powered helicopter fleet, most frequently during crop dusting. Quite 

often “crop dusters” appeared to know where the obstacles were relative to a field, but for 

some reason (e.g., fatigue, sun glare, misjudging distance, etc.) still collided with them. This 

helicopter type had about equal numbers of main- and tail-rotor strikes. 

 Unlike piston-powered helicopters, single turbine-powered helicopters were engaged 

in general utility and passenger service when most of the objects were struck. The single 

turbine-powered helicopter class, which does relatively little crop dusting, experienced four 

tail-rotor strikes for every three main-rotor strikes. 

Fig. 2-456. In-Flight Collision With Objects, 1994 Through 1997 (Pilots Cannot See 

Wires, Poles, and Trees Well Enough) [666]. 
2.10 ACCIDENT RECORD 

690 

 Table 2-67 shows that pilots of twin turbine-powered helicopters were, on a 

percentage basis, nearly as prone to hitting wires and trees as pilots of single engine 

helicopters. What stands out is that 12 of the 43 collisions were with airport/helipad facilities. 

In fact, 9 objects hit were protuberances around the heliport (6 on offshore oil rig platforms, 

1 stairwell at a hospital, 1 crane at a building site, and 1 jetway gate). A tail rotor was swung 

into a hanger, and a barge rising and falling was an inadequate heliport. Twin-turbine 

helicopters had more than twice as many tail-rotor strikes as main-rotor strikes. 

 NTSB accident investigators most frequently cite the pilot for failing to see and avoid 

the object as the cause of the accident. That failure statement is all well and good, but it 

hardly gets to the root of the problem. Commercially manufactured helicopters are sold 

primarily because they perform well flying low and slow. Unfortunately, this flight regime 

places the helicopter pilot in a very hostile environment, populated by many natural and manmade objects. The average pilot’s situational awareness of objects that must be avoided is, in 

fact, significantly impaired because most of the objects are not readily visible. Wires, in 

particular, are well-known threats to low flying for all aircraft types. It would be very helpful 

if all man-made objects higher than 500 feet were marked, mapped, and included in electronic 

databases, such as used in Global Positioning System (GPS) equipment. Perhaps, more 

practically, a low-price proximity spherical sensor should be developed and certified; a sensor 

sphere of some large radius should, in effect, cocoon the helicopter and provide the pilot with 

sufficient warning time to avoid obstacles. 

 An important reference point is that fuel-/air-mixture-related accidents caused at least 

1,042 loss-of-engine-power accidents as Table 2-66 shows. This one area, leading to loss of 

engine power, equals more than the total amount of accidents caused by rotorcraft pilots 

running into wires (441), wires/poles (226), and trees (211). 

Table 2-67. In-Flight Collision With Objects Accident Data, 1994 Through 1997 [666]

Accident Count (1964–1997) Single Piston Single Turbine Twin Turbine Amateur 

8,436 Total 5,371 2,247 302 516 

2,408 Loss of engine power 1,554 (29 %) 704 (31 %) 39 (13 %) 111 (15 %) 

 

1,322 In-flight collision with objects 953 (18 %) 298 (13 %) 43 (14 %) 28 (5 %) 

 441 Wire 310 108 13 10 

 226 Wire/pole 197 24 0 5 

 211 Tree(s) 148 50 7 6 

 68 Pole/pipe 47 19 2 0 

 64 Airport/helipad facility 32 20 12 0 

 312 All other objects 219 77 9 7 
2.10 ACCIDENT RECORD 

691 

2.10.3.3 Loss of Control 

 The upward trend in loss-of-control accidents is a very serious concern. In one sense 

the trend, shown in Fig. 2-457, has been obscured because loss-of-engine-power accidents 

have had a favorable decline in recent years as has been the case for the total civil fleet. As 

Fig. 2-453 shows, pilots of the commercial fleet lost control of their helicopters—regardless 

of their certification level—and this caused 949 of the 7,920 accidents. Pilots of amateur 

rotorcraft lost control nearly three times as often (on a percentage basis). 

 Table 2-68 shows that taking off and hovering clearly tax piloting skill. Fig. 2-458 

indicates that controlling anti-torque in all flight phases is a root problem with the singlemain-rotor helicopter configuration. This is particularly true with the single piston-powered 

helicopter, where fluctuations in engine RPM occur because of the reciprocating engine’s 

RPM governing system. The turbine engine RPM governing system virtually removed this 

cause of accidents. However, on a percentage basis, pilots of single turbine-powered 

helicopters lost directional control twice as often as pilots of single piston-powered 

helicopters did, which suggests a design deficiency. Equipping some single engine and 

virtually all twin turbine-powered helicopters with an automatic stability and control system 

has generally improved the overall loss-of-control situation. 

0

10

20

30

40

50

60

70

1960 1970 1980 1990 2000 2010 2020

Loss of

Control

Accidents

Each

Year

End of Year

This is a very 

disturbing 

trend.

Fig. 2-457. The trend of loss-of-control accidents presents a very serious situation, 

1964 through 2011. 

 
2.10 ACCIDENT RECORD 

692 

 Perhaps the most misunderstood phase of helicopter flight is taking off, hovering, and 

landing. These phases rarely (if ever) are flown in a no-wind situation. Fixed-wing aircraft, as 

you probably know, are particularly sensitive to crosswinds during these critical flight phases, 

Table 2-68. Loss-of-Control Accident Data

Accident Count (1964–1997) Single Piston Single Turbine Twin Turbine Amateur 

8,436 Total 5,371 2,247 302 516 

2,408 Loss of engine power 1,554 (29 %) 704 (31 %) 39 (13 %) 111 (15 %) 

1,322 In-flight collision with objects 953 (18 %) 298 (13 %) 43 (14 %) 28 (5 %) 

 

1,114 Loss of control 625 (12 %) 284 (12 %) 40 (13 %) 165 (32 %) 

 271 Takeoff 148 74 6 43 

 233 Hover 150 61 5 17 

 178 Maneuvering 96 39 8 35 

 122 Landing 79 30 2 11 

 104 Cruise 43 34 6 21 

 81 Approach 37 20 8 16 

 125 All other phases 72 26 5 22 

0% 10% 20% 30% 40% 50% 60%

Pitch

Roll

Vertical

Yaw

Loss Of Control Accidents

Single Piston (Commercial Only)

Single Turbine

Twin Turbine

Complicated by

Low Rotor RPM

for Single Piston

 Type Accidents

Single Piston 338

Single Turbine 137

Twin Turbine 20

Amateur 78

Axis Not Reported 541

 Total 1,114

Fig. 2-458. Controlling yaw is a BIG problem. 

Loss-of-Control Accidents, Percent 
2.10 ACCIDENT RECORD 

693 

and the single rotor helicopter is, if anything, even more sensitive. The reason is that 

crosswinds can create unanticipated aircraft yawing because the tail rotor experiences variable 

climb and descent conditions. It appears that the tail rotor authority of many aircraft in service 

is inadequate for many of these flight conditions, which can create excessive yaw rates. 

Certainly this was a serious concern with the Bell Model 206 series. The concern became 

quite clear after U.S. Army testing of an OH-58 (the military version of the Bell Model 206) 

revealed the occurrence of an unanticipated right yaw under certain low-speed flight 

conditions. The army referred to the right yaw characteristic as “loss of tail rotor 

effectiveness.” This concern was also addressed by Bell Helicopter Textron in a special 

RotorBreeze newsletter article in the May/June 1991 issue [678].224 In this excellent, twopage article (which might have been saved in the pilot’s fight manual), wind direction from 

several azimuth angles can place the tail rotor in the wake of the main rotor. This adverse 

situation can add to or reduce the weather cocking behavior of the single rotor machine. In 

fact, the main rotor wake can put the tail rotor in a vortex ring condition, which reduces tail 

rotor control to at least zero or, even worse, gives the helicopter negative weather cocking 

behavior. This “swapping ends” in a split second is severely disorientating, even to an 

experienced pilot. 

 Current single piston-powered helicopters (and turbine-powered helicopters to a 

somewhat lesser extent) appear inordinately difficult to fly particularly when the average pilot 

has to devote attention to another task, or has a real or imagined emergency. Cross coupling 

between the vertical/power/RPM and yaw axes is clearly excessive. The handling qualities 

design standards applicable to the current helicopter fleet date back to the 1950s. Although 

generally tolerated, the resulting helicopter stability and control characteristics now appear 

quite unsatisfactory. This point is driven home in spades by Dugan and Delamer in their 

excellent paper titled The Implications of Handling Qualities in Civil Helicopter Accidents 

Involving Hover and Low Speed Flight [679]. Handling quality and certification standards for 

all future helicopters should immediately be raised to levels consistent with what modern 

technology can provide. 

 Today there are many radio control model helicopters flying. Many of these models 

are equipped with Young’s Bell bar or a version of the Hiller servo paddle stabilizing system, 

which adds stability to the Bell Model 47 and Hiller UH-12 helicopters, respectively. And just 

as many models are flown with miniature gyro systems to augment stability and control. 

Furthermore, the number of larger Unmanned Air Vehicles (UAVs) flying under complete 

autopilot control is impressive. Why this level of stability and control is not a part of every 

aircraft in the rotorcraft fleet is, quite frankly, very disappointing to me. Surely, it cannot be a 

cost issue. 

 One last point concerns the introduction of a new design into the civil fleet. When 

Frank Robinson got his R22 type certificate (TC H10WE dated March 16, 1979) [680] and 

sales began to take off, pilots began to experience a rash of “loss-of-control” accidents as the 

1980s wore on. Early experience with the R44 began to suggest that both helicopters might 

 

224 The article initially appeared as Bell information letters nos. 206-84-41 and 206L-84-27, dated July 6, 1987. 

These letters were followed by RotorBreeze articles in July/August 1984 and 1987, and as handouts at various 

safety seminars. 
2.10 ACCIDENT RECORD 

694 

have serious design flaws. The news media, always on the alert for aviation problems, picked 

up on the increasing number of R22 crashes in July of 1991. In Arizona in that month, KTAR 

radio traffic reporter Mike Nuetzman was killed when his Robinson R22 helicopter crashed 

through the roof of a northeast Phoenix house. Then several months later, in the Sunday, 

November 15, 1992, publication of The Arizona Republic [681], I read the special report titled 

DANGER in the SKY, which covered several pages. By 1996, the NTSB had completed its 

Special Investigation Report [682] of the R22’s loss-of-main-rotor-control accidents, an 

investigation that had backtracked to the early 1980s. Robinson made some design changes to 

deal with the mast bumping problem that caused the main rotor shaft to be severed, followed 

by complete loss of the main rotor. Even more important were improvements he made to the 

flight training program. The R22 and R44 are very low inertia helicopters and, as such, are 

very sensitive to control inputs, which was not fully realized by many pilots. The NTSB’s 

special report is well worth your reading time because there is much more to this story. 

 Not to belabor the point, but fuel-/air-mixture-related accidents caused at least 1,042 

accidents as Table 2-66 shows. Thus, this one area—leading to loss of engine power—about 

equals all of the accidents caused by loss of control. 

2.10.3.4 Airframe-Related Failure 

 Accidents caused by some failure or malfunction of an airframe component or part, or 

some airframe system, caused 1,083 of the 8,436 accidents (about 12 percent) that occurred 

from 1964 through 1997. Thus, all of the airframe-related failures virtually equal the 1,042 

fuel-/air-mixture-related loss-of-engine-power accidents seen in Table 2-66. Table 2-69 shows 

that main- and tail-rotor systems, which include the rotor itself plus the rotor drivetrain plus 

the rotor control system, account for over 80 percent of the 1,083 airframe-related failures. 

Only 182 accidents, less than 20 percent, were caused by failures of other airframe-related 

components. 

 Table 2-69 shows that, on a percentage basis, there is little difference between single 

piston-powered and single turbine-powered helicopter accidents caused by airframe-related 

failures. That is, both aircraft have contributed about 12 percent (i.e., 639 out of 5,371 

accidents) of airframe-related failures to their respective totals. However, early data for twin 

turbine-powered helicopters suggests that this rotorcraft configuration is experiencing over 

twice this percentage (about 29 percent) relative to its single engine configuration. This is a 

disturbing fact coming from NTSB data. 

 When viewed as subtotals in percent, Table 2-69 shows that there is no significant 

difference between single engine (piston or turbine) and twin engine helicopters with respect 

to main- and tail-rotor system failures. Of course, the vast majority of helicopters in the civil 

fleet are simply outgrowths of military configurations from the 1960s and 1970s. The 

manufacturers of these helicopters have continually improved successive models, but initial 

design decisions associated with 30-year-old military design standards are not easily, quickly, 

or inexpensively changed for civil application. For example, drivetrain components designed 

for 1,200- to 2,400-hour life for the military help maximize rotorcraft performance in that 

application. However, that same drivetrain used in a civil helicopter is a contributor to 

excessive operating costs and, in many civil applications, woefully under designed. 
2.10 ACCIDENT RECORD 

695 

 Data from reference [666] provides considerable insight as to the failure modes the 

NTSB determined for nearly all airframe-related accidents. As might be expected, failures 

caused by fatigue top the list, followed closely by improper assembly, installation, or 

maintenance. In the drive system, every component from engine output to transmission 

(particularly clutch assemblies, free-wheeling units, and tail-rotor drive shafts) has been a 

constant source of failure. Fatigue failure of rotor blades and hubs (particularly tail rotor 

components) is still much too prevalent. And, somewhat surprisingly, nonrotating control 

components (i.e., the so-called lower control systems) failed twice as often as components in 

the rotating system. Of the 1,083 airframe-related failures, 249 failures were finally traced to 

fatigue. Another 273 failures were attributed to NTSB descriptions such as material failure, 

failed, or separated. While these descriptions are less precise than fatigue, the specific 

component (and even part) are identified and analyzed in reference [666], U.S. Civil 

Rotorcraft Accidents, 1963 through 1997. 

 Commercial rotorcraft manufacturers have made considerable progress in reducing 

airframe-related accidents over the past 40 years as Fig. 2-459 shows. Of course, the 

introduction of single turbine-powered helicopters with their increased performance did 

require solving new problems and implementing many fixes based on field experience. 

However, the rotorcraft fleet is approaching 10 times the fleet size of 47 years ago, and 

airframe-related accidents per year are still declining, albeit slightly, even over the last few 

decades. 

Table 2-69. Airframe Failure Accident Data, 1964 Through 1997

Accident Count (1964–1997) Single Piston Single Turbine Twin Turbine Amateur 

8,436 Total 5,371 2,247 302 516 

2,408 Loss of engine power 1,554 (29 %) 704 (31 %) 39 (13 %) 111 (15 %) 

1,322 In-flight collision with objects 953 (18 %) 298 (13 %) 43 (14 %) 28 (5 %) 

1,114 Loss of control 625 (12 %) 284 (12 %) 40 (13 %) 165 (32 %) 

 

1,083 Airframe-related failure 639 (12 %) 282 (12 %) 89 (29 %) 73 (14 %) 

 192 Tail rotor itself 124 52 10 6 

 197 Tail rotor drivetrain 119 54 19 5 

 56 Tail rotor control system 38 11 7 0 

 445 Tail rotor systems subtotal 281 (44 %) 117 (42 %) 36 (41 %) 11 (15 %) 

 145 Main rotor itself 57 36 19 33 

 197 Main rotor drivetrain 127 49 13 8 

 114 Main rotor control system 63 29 11 11 

 456 Main rotor systems subtotal 247 (39 %) 114 (42 %) 43 (41 %) 52 (71 %) 

 118 Airframe 64 41 8 5 

 32 Landing gear 24 2 2 4 

 10 Engine* 7 3 0 0 

 22 Undetermined/other 16 5 0 1 

 182 Other systems subtotal 111 (17 %) 51 (18 %) 10 (11 %) 10 (14 %) 

* Do not forget the 495 engine structural failures listed in Table 2-66. 
2.10 ACCIDENT RECORD 

696 

Fig. 2-459. The introduction of the single turbine-powered helicopter was accompanied 

by too many accidents. 

2.10.4 Concluding Remarks 

 You read at the beginning of this chapter that fixed-wing aircraft suffered from stall 

and spin accidents.225 The accident rate was so alarming that several branches of the U.S. 

Government sprang into action. This action led to the National Transportation Safety Board 

being established as part of the Civil Aeronautics Act of 1938. The NTSB began as the Civil 

Aeronautics Board’s Bureau of Safety and became an independent agency within the 

Department of Transportation in 1967. In 1974, U.S. Congress made the NTSB a completely 

independent agency from the Department of Transportation (DOT) (and thus from the FAA, 

as well). As one study authored by the Rand Corporation [684] reported in December of 1999, 

 “The National Transportation Safety Board (NTSB) is pivotal to the safety of the 

traveling public in the United States and throughout the world. While it is not a regulatory 

agency and does not command significant enforcement powers, the NTSB exerts enormous 

influence based on the independence and accuracy of its accident investigations and the 

authority of its recommendations. The NTSB is charged with the responsibility of 

investigating and establishing the facts, circumstances, and probable cause of transportation 

accidents, and with making safety recommendations to governmental agencies to prevent 

similar accidents from happening in the future. Fundamentally, the safety board provides a 

quality assurance function vital to the ongoing safety of all modes of transportation. The 

 

225 The stall and spin characteristics of even modern day general aviation fixed-wing aircraft have shown to be 

a very, very difficult problem. The historical overview that Seth Anderson of NASA Ames Research Center 

published in July of 1979 [683] provides real insight should you care to delve into the subject. 
2.10 ACCIDENT RECORD 

697 

NTSB's unique role in transportation safety is contingent on the ability of the board members 

and the professional staff to conduct independent investigations of accidents and major 

incidences and, in so doing, to assure public confidence in the safety of our national 

transportation systems.” 

You might not know that the whole NTSB is staffed by less than 500 full-time people and has 

a yearly budget of around $120 million. If there is a more efficient and cost-effective 

government agency then the NTSB, I am not aware of it. I believe accident investigators are 

the most dedicated people in the transportation industry, and I take my hat off to each and 

every one of them. As a member of the rotorcraft industry, I am very sorry that rotorcraft 

accidents have just added to their workload. 

 The rotorcraft industry, a relative newcomer to aviation, does not enjoy a particularly 

good safety record. The record is frequently quoted in terms of rotorcraft accidents per 

100,000 flight hours flown by the commercial and amateur fleet. Because the denominator, 

hours flown, is quite questionable, I have tried to draw your attention to accidents per year 

and the growing size of the rotorcraft fleet. 

 The NTSB has recorded 11,426 rotorcraft accidents from January 1, 1964, through 

December 31, 2011, as the FAA-registered fleet size increased from about 2,200 to virtually 

20,000 machines. The study of these accidents that you have read about shows that: 

1. The industry’s track record is to sell four turbine-powered helicopters and 

then crash one. This trend applies to twin- as well as single-engine-powered 

configurations. 

2. Accidents classified as loss of control have continually increased at an alarming 

rate for 47 years. 

3. Loss of engine power causes 30 percent of all single-engine-powered helicopter 

accidents. This is true for both piston and turbine engine configurations. The most 

frequent reason for the engine’s loss of power is not engine structural failure, but an 

incorrect fuel/air mixture, which accounts for nearly one-half of the 30 percent. The 

primary cause of incorrect fuel/air mixture is simply running out of gas! 

You will recall from Volume I that Henrich Focke [45], when designing the world’s first truly 

successful helicopter, set the number-one design requirement to provide for the “possibility of 

a forced landing in case of engine failure.” In my view, we have a civil helicopter fleet that 

does not come even close to providing the autorotational landing capability of the Cierva, 

Pitcairn, and Kellett autogyros. Power-off, run-on landings may demonstrate to the FAA that 

any given design meets their requirement, but I submit that this is nowhere near good enough. 

I believe that we should not design and produce a new single-engine civil rotorcraft with such 

marginal autorotational capability. The average pilot needs twice as much rotor inertia per 

helicopter as the current fleet has. Touchdown with virtually zero forward speed should be the 

minimum design requirement. Doubling current levels of rotor inertia can completely remove 

the “dead man’s curve” (i.e., the height-velocity curve) restriction from flight manuals as Tom 

Wood reported in 1976 [672]. The impact on a helicopter’s weight empty and purchase price 

appears small enough that this improvement could reasonably be incorporated in growth 

models of many helicopters in the current commercial fleet. 
2.10 ACCIDENT RECORD 

698 

 In 2005 the rotorcraft industry, recognizing that its track record was not improving, 

began to mount a worldwide, unified attack on accidents associated with their products. The 

International Helicopter Safety Team (IHST) was formed with the goal of reducing accidents 

by 80 percent. I have interpreted this goal as reducing accidents from 10 per 100,000 hours 

flown at the end of 2005 to 2 accidents per 100,000 hours flown by the beginning of 2016. 

The IHST has already shown that their efforts are paying off, because the trend in accidents 

per year is clearly downward as Fig. 2-447 shows. There is a wealth of studies about 

rotorcraft accidents, both military [685, 686] and civil [687-692] that can be reread and the 

lessons applied. This background, along with the IHST’s ongoing investigations, says to me 

that the industry goal will be met. It seems plausible to look forward to a time where only a 

few accidents occur in a year—and then maybe we can go a whole year without one accident. 

That should be our next goal. 

 This chapter began with a question about the oft-quoted statement that “virtually all 

accidents are caused by human error.” After reading 11,426 NTSB rotorcraft accident reports, 

I am forced to agree. Nevil Shute (an aeronautical engineer by day and world famous author 

by night) wrote in his autobiography Slide Rule [693] that 

“Aircraft do not crash of themselves. They come to grief because men are foolish, or vain, or 

lazy, or irresolute, or reckless.* One crash in a thousand may be unavoidable because God 

wills it so—not more than that.” 

*Now I would add: or tired, late, pushed by management, sick, broke, distracted, hungover, or 

overwhelmed, or they just guessed wrong or “just weren’t thinking.” 
699 

3 CONCLUDING REMARKS 

 The rotorcraft industry completed the transition from autogyros to a helicopter product 

line by the end of 1945. The helicopter then demonstrated its value during the Korean War 

(June 1950–July 1953) after which the industry turned to civilian applications. By the end of 

1956, the Federal Aviation Agency (FAA) had 540 helicopters in its U.S. registry, although 

only 370 were actively being flown. This miniscule fleet is lumped into the FAA’s General 

Aviation category, in a subcategory named rotorcraft with a designation of Code 6. The 

General Aviation category includes virtually all aircraft over and above those being used in 

the airline business. As I write these concluding remarks during August of 2012, the FAA’s 

rotorcraft count is nearly 20,000. The U.S. Department of Defense fleet adds another 6,500 

helicopters. 

 You should be aware that military needs for helicopters have paid for much of the 

research, development, and field experience that the industry needed to establish its 

commercial product lines. You can also well imagine that the industry, in producing this 

growing military and civilian fleet, has had to overcome a multitude of engineering, 

manufacturing, marketing, product support, and community acceptance problems. 

 This introduction to helicopters has focused your attention on the major shortcomings 

of today’s helicopters—at least as I see them. Now let me offer some thoughts about how to 

overcome these shortcomings. I will discuss these major shortcomings in my order of 

importance, starting with the accident record and concluding with engines. 

 If you talk to manufacturers about helping to substantially reduce accidents by 

modifying their helicopters, it may seem like a dead end. In fact, I have frequently 

encountered individuals who say, “Safety doesn’t sell.” The next reason you may hear is that 

“the cost of complete re-certificating to FAA standards is sobering.” Nevertheless, these same 

manufacturers continue to make major product improvements such as Bell Helicopter’s move 

from two-bladed rotor systems to multi-bladed (i.e., four) rotor systems. Why some 

improvements for safety are not included in these product refinements is beyond me. For 

example, increased rotor inertia can be accomplished along with an increase in engine takeoff 

ratings. Yes, some of the increase in useful load sought may have to be forfeited, and a portion 

of re-certificating expense will be incurred, but just imagine the marketing advantage a 

manufacturer would get by being the first to remove the height-velocity restriction from the 

flight manual. 

 Loss-of-control accidents are increasing at an alarming rate as Fig. 2-457 showed. The 

installation of a low-authority stability augmentation system (SAS) (with, at most, 15 percent 

authority) seems entirely in order, certainly for the next product improvement of single engine 

helicopters. I suggest that this can also be done as an aftermarket product for helicopters in the 

current civil fleet. As a bare minimum, pilots need help with directional control, which hardly 

seems like a tall order. 
3. CONCLUDING REMARKS 

700 

 Operating costs of helicopters are, to be blunt, unreasonably high. I believe this 

situation has come about because military requirements have spilled over on to commercial 

helicopters. The military only requires components with time between overhauls (TBOs) on 

the order of 2,000 hours because (I guess) in war the attrition rate can be very high, and in 

peacetime, relatively little flying goes on. Of course, there can be a weight-empty saving with 

low TBOs, but operating costs go up. The use of these same military helicopter components 

(say transmissions, for example) in the civil fleet, which can put 1,000 hours or more per year 

on a machine, immediately raises operating costs. Anything less than TBOs of 10,000 hours 

for civil helicopters seems to me to be, as the British say, “penny-wise and pound-foolish.” 

Another interesting example concerns the use of advanced materials. Rotor blades made with 

composites have a number of attractive features over metal spar blades, but I am not 

convinced that their TBO of 10,000 hours (or even “on condition”) justifies the price that 

manufacturers are charging for spares. In fact, I suggest that graphs of purchase price and 

operating cost versus TBO would be very, very interesting. 

 Operating costs are significantly driven by airframe maintenance overhaul prices. The 

small number of components involved in an overhaul (about 25 to 75), which account for 

about one-third of yearly maintenance costs, should be redesigned and requalified (if 

necessary) whenever a model upgrade is considered. A simple weeding-out process over a 

decade of operational experience should do wonders for this shortcoming. Maybe new designs 

that are not derived from military components and design requirements, but really are driven 

by what commercial helicopter users so desperately need (even before performance), can 

produce rotorcraft that would attract major airlines and the short-haul service they could 

initiate. 

 Helicopters are just plain too expensive to buy. The 50 percent premium for VTOL 

over a fixed-wing aircraft is excessive, which seems to keep relegating the machine to niche 

markets. If it is true that purchase price is driven almost entirely by weight empty and 

installed power as Eqs. (2.347) and (2.348) on page 546 suggest, then there may be very little 

that can be done, other than reducing profit margins. On the other hand, it may well be that 

manufacturing labor hours per pound, or per part count, are too high when compared to the 

fixed-wing industry—and that might be because rotary wing engineers have learned very little 

from fixed-wing engineers. Let me suggest, therefore, that a more in-depth examination be 

done to find out why helicopter prices are so much higher than comparable fixed-wing prices. 

I would think that an answer to this question would immediately help the rotorcraft industry. 

Furthermore, an in-depth study could help NASA and the U.S. Army direct their rotorcraft 

Research and Development (R&D) programs to elements having a much higher return for 

their dollars. 

 Noisy helicopters continue to be less and less accepted by an ever-growing number of 

communities. A small group of researchers now have a reasonable understanding of the many 

sources of helicopter noise. However, only one helicopter manufacturer (Hughes, in 1972 

with The Quite One) has demonstrated a practical design approach that really lowered 

helicopter noise [548] and that raised useful load at the same time. Hughes’ design approach 

could be applied today if the rotorcraft industry cared to. Frankly, I would bet (my company, 
3. CONCLUDING REMARKS 

701 

if I had one) that there would be a significant increase in helicopter sales if the industry 

offered low-noise products across the board. 

 The fact that helicopter sales remain relatively strong, despite the machine’s reputation 

for vibration, is quite interesting. The way I see it, there is a big gap between what researchers 

have learned and how much of this knowledge is incorporated into each manufacturer’s 

newest product. For example, tuning both the rotor system and the fuselage to avoid 

amplification of rotor hub loads, before these vibratory loads reach every occupants’ seat, is 

the most fundamental approach to reducing helicopter vibration with today’s rotor systems. 

This is the primary approach I favor. That means fuselage design tools such as NASTRAN 

[444-446, 457, 466, 467] must be used not only for early stress analysis during preliminary 

design, but for early vibration analysis as well, which is hardly current engineering practice. 

 Helicopter performance—including fuel efficiency, and engine and weight-empty 

subjects—is the most mature technology of all, in my opinion. After seven decades of clearly 

defining and demonstrating the helicopter’s fundamental capabilities, the industry knows 

where this VTOL aircraft sits in the world of transportation. We know (a) that we can make 

very large helicopters (like a Russian Mi-26), (b) what ratio of useful load to takeoff gross 

weight we can offer (with reasonable accuracy), and (c) that we have rather discouraging 

insight about what we can offer for an economical cruise speed. On virtually every new 

design, we pick the installed engine takeoff power based on hover performance requirements 

and then we just accept whatever forward flight performance comes out. Quite frankly, I am 

tired of spending so much money to raise hovering Figure of Merit. I think the real effort 

should be to increase cruise and maximum speeds at engine takeoff power by reducing 

parasite drag of the airframe (including the rotor hub and landing gear). This is the tried and 

true, aerodynamic approached used by fixed-wing designers for a century. It is time rotary 

wing designers followed this advice. 

 It seems to me that we are flogging a dead horse trying to optimize rotor system 

hovering performance, which can, I admit, be just plain theoretical fun. I believe engine 

manufacturers can match any hover performance increase obtained by complicated blade 

geometry at one-tenth of the cost of rotor system “Figure-of-Merit improvements” by 

airframe manufacturers. Instead, I see research dollars going to hubs designed for low drag 

(like the AH-56 doorhinge hub) and configurations where landing gears are retracted and fuel 

is carried internally (like the Sikorsky S-76, to single out just one example). 

 My perception is that innovation in the helicopter industry has stagnated. We have 

lived off of civil helicopter derivatives of military designs and components for seven decades. 

But now (in 2012) we are faced with the likelihood that the military’s requirements, and its 

money, are drying up. Even if the military did want, and could afford, a “new machine,” the 

industry would probably just adapt 1970s and 1980s technology to its need, give or take a 

modern “glass” cockpit and fuselage shaping for stealth. That is what we did for the 

LHX/RH-66 Comanche program. This may be good enough for the military, but it is hardly 

good enough if we really want to increase civil helicopter usage. 

 
3. CONCLUDING REMARKS 

702 

 For the civil marketplace, we cannot continue to coast along perpetuating a 

commercial fleet with the major shortcomings that I have brought to your attention. If we do 

continue to coast, I believe the marketplace and our pioneers—Cierva, Pitcairn, Kellett, 

Focke, Sikorsky, Bell’s Young and Kelley, Piasecki, Hiller, and Kaman—to name just a 

few—will be very, very disappointed in us. 

1

10

100

1,000

10,000

1 10 100 1,000 10,000

4 Min. Mile

HP per

Ton of

Gross

Weight

Speed (mph)

129 Autogyros

Helicopters

Airplane

Up To 1950s

Ships

Tiltrotors

MV-22

XV-15

High Speed Helicopters

Westland Lynx

Boeing 360

What Price Speed

 by Gabrielli and

 Von Karman

Oct. 1950

Russian

Tu-142

Lockheed

Electra

Concorde

Trains

Cars

&

Trucks

50 200 500

Rotorcraft enjoy a unique position in the transportation industry. 
703 

4 REFERENCES 

1. Liberatore, E. K.: Helicopters Before Helicopters. Malabar, Fla.: Krieger Publishing 

Co., 1998. 

2. Boulet, J.: History of the Helicopter as Told By Its Pioneers, 1907–1956. Paris, 

France: Editions France-Empire, 1982. 

3. Gablehouse, C.: Helicopters and Autogiros: A History of Rotating-Wing and V/STOL 

Aviation. Philadelphia, Pa.: J.B. Lippincott & Co., 1967. 

4. Brooks, P. W.: Cierva Autogiros: The Development of Rotary-Wing Flight. 

Washington, D.C.: Smithsonian Institution Press, 1988. 

5. Gibbs-Smith, C. H.: The Aeroplane. London, England: Her Majesty’s Stationery 

Office, 1960. 

6. Apostolo, G.: The Illustrated Encyclopedia of Helicopters. New York, N.Y.: Bonanza 

Books, 1984. 

7. Coates, S.; and Carbonel, J.-C.: Helicopters of the Third Reich. Surrey, England: 

Classic Publications, 2003. 

8. Anderson, J. D., Jr.: A History of Aerodynamics. Cambridge, United Kingdom: 

Cambridge University Press, 1997. 

9. Pritchard, J. L.: The Dawn of Aerodynamics. The Royal Aeronautical Society, vol. 

LXI, 1957. 

10. Durand, W. F.: Aerodynamic Theory, A General Review of Progress. Mineola, N.Y.: 

Dover Publications, 1976. 

11. Timoshenko, S. P.: History of Strength of Materials. Mineola, N.Y.: Dover 

Publications, 1983. 

12. Dugas, R.: A History of Mechanics. Mineola, N.Y.: Dover Publications, 1988. 

13. Betz, A.: The Ground Effect on Lifting Propellers. NACA TM 836, Apr. 1937. 

14. Drees, J.: Blade Twist, Droop Snoot, and Forward Spars. Vertflite, Sept./Oct. 1976. 

15. Gessow, A.: Standard Symbols for Helicopters. NACA TN 1604, June 1948. 

16. Gregory, H. F.: Anything a Horse Can Do: The Story of the Helicopter. New York, 

N.Y.: Reynal & Hitchcock, 1944. 

17. Crocco, G. A.: Inherent Stability of Helicopters. NACA TM 234, 1923. 

18. Hohenemser, K.: Dynamic Stability of a Helicopter With Hinged Rotor Blades. 

NACA TM 907, 1939. 

19. Morris, C. L.: Pioneering the Helicopter. New York, N.Y.: McGraw-Hill Book Co., 

Inc., 1945. 

20. Sikorsky, I. I.: The Story of the Winged-S: Late Developments and Recent 

Photographs of the Helicopter. New York, N.Y.: Dodd, Mead & Co., 1967. 

21. Young, A. M.: A New Parameter of Lifting Rotors. Proc. Second Annual Rotating 

Wing Aircraft mtg. sponsored by the Philadelphia Chapter of the Institute of the 

Aeronautical Sciences, Philadelphia, Pa., 1939. 

22. Young, A.: The Helicopter and Stability. American Helicopter, Mar. 1948. 

23. Klemin, A.: Helicopter Engineering: Two-Bladed Rotor by Young. Aero Digest, Apr. 

1946.
4. REFERENCES 

704 

24. Putnam, V. K.; and Ferry, R. G.: Stability With a Stabilizing Bar. AFFTC-TR-58-4 

(see also AD-124128), Air Force Flight Test Center, Edwards Air Force Base, Calif., 

1958. 

25. Tipton, R. S.: They Filled the Skies. Ft. Worth, Tex.: Bell Helicopter Textron, Inc., 

1983. 

26. Kelley, B.: Helicopter Stability With Young’s Lifting Rotor. Society of Automotive 

Engineers (SAE) J., vol. 53, no. 12, Dec. 1945 (see also SAE TP 450232, 1945). 

27. Kelley, B.: Response of Helicopter Rotors to Periodic Forces. NACA Advance 

Restricted Report 5A09, Mar. 1945. 

28. Anon.: The Bell Rotor System. Report No. 30-929-123, Bell Aircraft Corp., Ft. Worth, 

Tex., 1954. 

29. Spenser, J. P.: Vertical Challenge, The Hiller Aircraft Story. Seattle, Washington: 

University of Washington Press, 1992. 

30. Stuart, J., III: The Helicopter Control Rotor. Proc. 16th Annual Mtg. of the Institute of 

Aeronautical Sciences, New York, N.Y., Jan. 26–29, 1948. 

31. Stuart, J., III: The Helicopter Control Rotor. Report No. 150.1, United Helicopters, 

Inc., Palo Alto, Calif., Mar. 19, 1947. 

32. Stuart, J., III: Analysis of Effect of Lowering a Lifting Rotor Mounted Control Rotor 

Relative to the Teetering Axis. Report No. 150.2, United Helicopters, Inc., Palo Alto, 

Calif., 1947. 

33. Jacoby, D. R.: Analysis of the Hovering Stability and Control of the UH-12 

Helicopter. Report No. 150.3, United Helicopters, Inc., Palo Alto, Calif., Mar. 22, 

1948. 

34. Klemin, A.: New Ideas in Helicopter Control. Aero Digest, vol. 56, no. 4, Apr. 1948. 

35. Miller, R.: Helicopter Control and Stability in Hovering Flight. J. Aeronautical 

Sciences, Aug. 1948. 

36. Sissingh, G. J.: Automatic Stabilization of Helicopters. J. Helicopter Association of 

Great Britain, vol. 2, no. 3, 1948. 

37. Sissingh, G. J.: The Frequency Response of the Ordinary Rotor Blade, the Hiller 

Servo-Blade, and the Young-Bell Stabilizer. Aeronautical Research Committee R&M 

No. 2860, 1950. 

38. Prewitt, R. H.: Report on Helicopter Developments in Germany. Society of 

Automotive Engineers (SAE), May 1945. 

39. Liptrot, R. N.: Rotating Wing Activities in Germany During the Period 1939–1945. 

British Intelligence Objectives Sub-Committee Overall Report, vol. 8, Her Majesty’s 

Stationary Office, London, England, 1948. 

40. Sissingh, G. J.: Contributions to the Dynamic Stability of Rotary-Wing Aircraft With 

Articulated Blades, Part I—General Principles. Translation No. F-TS-690-RE, 

Headquarters Air Material Command, Wright Field, Dayton, Ohio, Aug. 1946. 

41. Sissingh, G. J.: The Dynamic Stability of Helicopters With Articulated Rotors. 

Translation No. F-TS-1002-RE, Headquarters Air Material Command, Wright Field, 

Dayton, Ohio, Sept., 1946. 

42. Guarino, L. S.: Automatic Control and Stabilization of Helicopters. Mid-Eastern Proc. 

American Helicopter Society, Feb. 19, 1953. 
4. REFERENCES 

705 

43. Anon.: Automatic Control for Helicopter. InterAvia, vol. 6, no. 3, 1951. 

44. Burkham, J.: Penni Helicopter. American Aircraft Modeler. Jan., 1970. 

45. Focke, H.: The Focke Helicopter. NACA TM 858, Apr. 1938. 

46. Focke, H.: German Thinking on Rotary-Wing Development. J. Royal Aeronautical 

Society, vol. 69, no. 653, May 1965, pp. 293–305. 

47. Gustafson, F. B.: Flight Tests of the Sikorsky HNS-1 (Army YR-4B) Helicopter. 1—

Experimental Data on Level-Flight Performance with Original Rotor Blades. NACA 

WR-L-595, 1945. 

48. Gustafson, F. B.; and Gessow, A.: Flight Tests of the Sikorsky HNS-1 (Army YR-4B) 

Helicopter. 2—Hovering and Verical-Flight Performance With the Original and an 

Alternate Set of Main-Rotor Blades, Including a Comparison With Hovering 

Performance Theory. NACA WR-L-596, 1945. 

49. Dingeldien, R. C.; and Schaefer, R. F.: Static-Thrust Tests of Six Rotor-Blade Designs 

on a Helicopter in the Langley Full-Scale Tunnel. NACA WR-L-101, 1945. 

50. Dingeldien, R. C.; and Schaefer, R. F.: Full-Scale Investigation of Aerodynamic 

Characteristics of a Typical Single-Rotor Helicopter in Forward Flight. NACA Report 

No. 905, 1948. 

51. Cheeseman, I. C.; and Bennett, W. E.: The Effect of the Ground on a Helicopter Rotor 

in Forward Flight. Report No. A.A.E.E./Res/288, Aeroplane and Armament 

Experimental Establishment, Minister of Supply, Boscombe Down, July 11, 1955. 

52. Heyson, H. H.: Theoretical Study of the Effect of Ground Proximity on the Induced 

Efficiency of Helicopter Rotors. NASA TM-X-71951, May 1977. 

53. Mashman, J.: To Fly Like a Bird. Potomac, Md.: Phillips Publishing, Inc., 1992. 

54. Glauert, H.: The Theory of the Autogyro. J. Royal Aeronautical Society, vol. 31, 

no. 198, 1927, pp. 483–508. 

55. Lock, C. N. H.; and Bateman, H.: Some Experiments on Airscrews at Zero Torque, 

with Applications to a Helicopter Descending with Engine “Off,” and to the Design of 

Windmills. Aeronautical Research Committee R&M No. 885, Sept. 1923. 

56. Lock, C. N. H.; Bateman, H.; and Townend, H. C. H.: An Extension of the Vortex 

Theory of Airscrews with Applications to Airscrews of Small Pitch, Including 

Experimental Results. Aeronautical Research Committee R&M No. 1014, June 1926. 

57. Lock, C. N. H.; and Townend, H. C. H.: Wind Tunnel Experiments on a Symmetrical 

Aerofoil (Gottingen 429 Section). Aeronautical Research Committee R&M No. 1066, 

Nov. 1926. 

58. Glauert, H.: The Analysis of Experimental Results in the Windmill Brake and Vortex 

Ring States of an Airscrew. Aeronautical Research Committee R&M No. 1026, Feb. 

1926. 

59. Lock, C. N. H.; and Townend, H. C. H.: Photographs of the Flow Round a Model 

Screw Working in Water, Especially in the “Vortex Ring State.” Aeronautical 

Research Committee R&M No. 1043, May 1926. 

60. Caygill, L. E.; and Nutt, A. E. W.: Wind Tunnel and Dropping Test of Autogyro 

Models. Aeronautical Research Committee R&M No. 1116, Nov. 1926. 

61. Wheatley, J. B.: Lift and Drag Characteristics and Gliding Performance of an Autogiro 

as Determined in Flight. NACA TR 434, 1933. 
4. REFERENCES 

706 

62. Castles, W.; and Gray, R. B.: Empirical Relation Between Induced Velocity, Thrust, 

and Rate of Descent of a Helicopter Rotor as Determined by Wind Tunnel Tests on 

Four Model Rotors. NACA TN No. 2474, Oct. 1951. 

63. Fitzwilliams, O. L. L.: Engine-Off Landings. Flight Magazine, Nov. 13, 1947. 

64. Nikolsky, A. A.; and Seckel, E.: An Analytical Study of the Steady Vertical Descent 

in Autorotation of Single-Rotor Helicopters. NACA TN 1906, June 1949. 

65. Nikolsky, A. A.; and Seckel, E.: An Analysis of the Transition of a Helicopter From 

Hovering to Steady Autorotative Vertical Descent. NACA TN 1907, June 1949. 

66. Slaymaker, S. E.; Lynn, R. R.; and Gray, R. B.: Experimental Investigation of 

Transition of a Model Helicopter Rotor From Hovering to Vertical Autorotation. 

NACA TN 2648, Mar. 1952. 

67. Slaymaker, S. E.; and Grey, R. B.: Power-Off Flare-Up Tests of a Model Helicopter 

Rotor in Vertical Autorotation. NACA TN 2870, Jan. 1953. 

68. Katzenberger, E. F.; and Rich, M. J.: An Investigation of Helicopter Descent and 

Landing Characteristics Following Power Failure. J. Aeronautical Sciences, vol. 23, 

no. 4, 1956, pp. 345–356. 

69. Fradenburgh, E. A.: A Simple Autorotative Flare Index. J. American Helicopter 

Society, vol. 29, no. 3, 1984. 

70. Hanley, W. J.; and DeVore, G.: An Analysis of the Helicopter Height Velocity 

Diagram Including a Practical Method for Its Determination. Federal Aviation 

Administration Report No. NA-67-1, Feb. 1968. 

71. Hanley, W. J.; and DeVore, G.: An Evaluation of the Effects of Altitude on the Height 

Velocity Diagram of a Single Engine Helicopter. Federal Aviation Agency Report 

ADS-1, Feb. 1964. 

72. Hanley, W. J.; and DeVore, G.: An Evaluation of the Effects of Altitude on the Height 

Velocity Diagram of a Lightweight, Low Rotor Inertia, Single Engine Helicopter. 

Federal Aviation Agency Report ADS-46, July, 1965. 

73. Hanley, W. J.; DeVore, G.; and Martin, S.: An Evaluation of the Effects of Altitude on 

the Height Velocity Diagram of a Lightweight, High Rotor Inertia, Single Engine 

Helicopter. Federal Aviation Agency Report ADS-84, Nov. 1966. 

74. Pegg, R. J.: An Investigation of the Helicopter Height-Velocity Diagram Showing 

Effects of Density Altitude and Gross Weight. NASA TN D-4536, May 1968. 

75. Dooley, L. W.; and Yeary, R. D.: Flight Test Evaluation of the High Inertia Rotor 

System. USARTL TR 79-9, U.S. Army Research and Technical Laboratories, Ft. 

Eustis, Va., June 1979. 

76. Butler, H. K.: Army Air Corps Airplanes and Observation (1935–1941). Saint Louis, 

Mo.: Historical Office, U.S. Army Aviation Systems, Feb. 1990. 

77. Butler, H. K.: A History of Army Aviation Logistics (1935–1961), Rotary-Winged 

Aircraft and the Army (1939–1943). Saint Louis, Mo.: Historical Office, U.S. Army 

Aviation Systems Command, Feb. 1990. 

78. McClarren, R. H. (Ed.). Proc. Rotating Wing Mtg., Franklin Institute, Philadelphia, 

Pa., Oct. 28–29, 1938. 

79. Ralph McClarren (Ed.): Proc. Second Annual Rotating Wing Aircraft Mtg., Franklin 

Institute, Philadelphia, Pa., Nov. 30–Dec. 1, 1939. 
4. REFERENCES 

707 

80. McClarren, R. H.: Personal letter to F. D. Harris; Early Helicopter Meetings at the 

Franklin Institute Mar. 21, 1993. 

81. Klemin, A.: Rotary Aircraft. Aero Digest, Dec. 1938, 

82. Hardy, C. W.: History of Air Force Development of Rotary-Wing Aircraft. J. 

American Helicopter Society, vol. 1, no. 1, 1956. 

83. Gessor, A. J. (Ed.): American Helicopter Society, vol. 1, no. 1, 1956. 

84. Wiesner, W.: Performance Analysis of U.S. Army Air Force Model XO-60 Rotor 

Aircraft Equipped With a Jacobs I-6MB-A Engine Rated at 300 H.P. and a Hamilton 

Constant Speed Propeller. Report No. 130.8, Kellett Autogiro Corp., Upper Darby, 

Pa., May 1943. 

85. Klemin, A.: An Introduction to the Helicopter. NACA TM 340, J. Mechanical 

Engineering, Nov. 1924. 

86. Alex, R. P.: Helicopters From “A to Z”—Part I. American Helicopter Society 

Newsletter, vol. 7, no. 10, Oct. 1961 

87. Alex, R. P.: Helicopters From “A to Z”—Part II. American Helicopter Society 

Newsletter, vol. 7, no. 11, Nov. 1961. 

88. Alex, R. P.: Helicopters From “A to Z”—Part III. American Helicopter Society 

Newsletter, vol. 7, no. 12, Dec. 1961. 

89. Lambermont, P. M.; and Pirie, A.: Helicopters and Autogyros of the World. New 

York, N.Y.: A.S. Barnes and Co., 1970. 

90. Spenser, J. P.: Whirlybirds: A History of the U.S. Helicopter Pioneers. Seattle, Wash.: 

University of Washington Press, Oct. 1998. 

91. Nowarra, H. J.: German Helicopters, 1928–1945. West Chester, Pa.: Schiffer 

Publishing Ltd., 1991. 

92. Cobey, W. E.: Evaluation and Tests of the Flettner-282 German Helicopter. Technical 

Report ATI No. 20283, Headquarters Air Material Command, Wright-Patterson Air 

Force Base, Dayton Ohio, Sept. 1948. 

93. von Gersdorff, K.; and Knobling, K.: Hubschrauber und Tragschrauber. Munchen, 

Germany: Bernard & SeitGraefe Verlag, 1982. 

94. Everett-Heath, J.: Soviet Helicopters. Surrey, United Kingdom: Jane’s Information 

Group, 1988. 

95. Gordon, Y.; Komissarov, D.; and Komissarov, S.: Mil’s Heavylift Helicopters: Mi6/Mi-10/V-12/Mi-26. Hinckley, England: Midland Publishing, 2005. 

96. Gordon, Y.; and Komissarov, D.: Mil Mi-8/Mi-17: Rotary-Wing Workhorse and 

Warhorse. Hinckley, England: Midland Publishing, 2004. 

97. Marshall, C. (Ed.): The World’s Great Military Helicopters. New York, N.Y.: 

Aerospace Publishing, 1990. 

98. McGuire, F. G.; and McKinnis, M. F.: Helicopters 1948–1998, A Contemporary 

History. Alexandria, Va.: Frank L. Jensen, Helicopter Association International, 1998. 

99. Ludvigsen, K.: The Mercedes-Benz Racing Cars. Newport Beach, Calif.: Bond/ 

Parkhurst Books, 1971. 

100. Scott-Moncrieff, D.: The Three-Pointed Star, the Story of Mercedes-Benz. London, 

England: Gentry Books, Nov. 1979. 
4. REFERENCES 

708 

101. Marks, L. S. (Ed.): Mechanical Engineers’ Handbook, 2nd Ed. New York, N.Y.: 

McGraw-Hill Book Co., Inc., 1924. 

102. Taylor, C. F.: Aircraft Propulsion. Washington, D. C.: Smithsonian Institution Press, 

1971. 

103. Setright, L. J. K.: The Power to Fly: The Development of the Piston Engine in 

Aviation. London, England: George Allen & Unwin, Ltd., 1971. 

104. Anon.: Power Progress. Aero Digest, July 1953. 

105. Tryckare, T.: The Lore of Flight. Gothenburg, Sweden: Trychare, Cagner & Co., 

1970. 

106. Anon.: U.S. Standard Atmosphere, 1962. NASA 63N13176 (see also NACA TR 

1235), Dec. 1962. 

107. Anon.: Aviation Week & Space Technology, Mar. 12, 1979; Mar. 14, 1983; and Mar. 

18, 1991. 

108. Chabot, W. J.; and Ferry, R. G.: H-34A Phase IV Performance Test. AFFTC-TR-56-8, 

Air Force Flight Test Center, Edwards Air Force Base, Calif., 1956. 

109. Hayden, J. S.; and Eggert, W. W.: H-21 Phase IV Performance and Stability Tests. 

AFFTC-TR-57-4, Air Force Flight Test Center, Edwards Air Force Base, Calif., 1957. 

110. Odgers, P. W., Major General: The Air Force Test Center—Cradle of Postwar 

Aviation. The Society of Experimental Test Pilots 27th Annual Symposium, Beverly 

Hills, Calif., Sept. 28–Oct. 1, 1983, pp. 260–268. 

111. Ferrell, K. R.: YHO-2HU Air Force Flight Evaluation. AFFTC-TR-60-2, Air Force 

Flight Test Center, Edwards Air Force Base, Calif., 1960. 

112. Anon.: MIL-E-5007. Engines, Aircraft, Turbojet and Turbofan, General Specification 

for. Department of Defense, Washington, D.C., 1949. 

113. Anon.: SAE ARP-681B. Society of Automotive Engineers, 1950. 

114. Smith, L. K. (Ed.): AHS Vertiflite, vol. 39, no. 5, 1993. 

115. Putnam, V. K.; and Ferry, R. G.: XH-40 Air Force Flight Evaluation. AFFTC-TR-58-

15, Air Force Flight Test Center, Edwards Air Force Base, Calif., 1958. 

116. Macpherson, D. F.; and Balfe, P. J.: HU-1 Performance Evaluation, Addendum I to 

AFFTC-TR-59-33. Air Force Flight Test Center, Edwards Air Force Base, Calif., 

1960. 

117. Nagata, J. I.; and Shapley, J. J.: Engineering Flight Test of the OH-6A Helicopter 

(Cayuse) Phase D, Final Report. USAASTA Project No. 65–37, U.S. Army Aviation 

Systems Test Activity, Edwards Air Force Base, Calif., 1969. 

118. Schroers, L. G.; and Nelson, E. E.: Engineering Flight Test (Performance Phase) of the 

OH-5A Helicopter. USATECOM Project No. 4-3-0250-31/32/33, Edwards Air Force 

Base, Calif., 1969. 

119. Melton, J. R.; and Watts, J. C.: Engineering Flight Test (Performance Phase) of the 

OH-4A Helicopter. USATECOM Project No. 4-3-0250-11/12/13, Edwards Air Force 

Base, Calif., 1969. 

120. Ashley, T. (Ed.): Flight Magazine—14th Annual Helicopter Edition, vol. 55, no. 1, 

1966. 
4. REFERENCES 

709 

121. Benson, T. P.; Buckanin, R. M.; Mittag, C. F.; and Jenks, J. E.: Evaluation of an OH58A Helicopter With an Allison 250-C20B Engine. USAAEFA Project No. 74-48, 

U.S. Army Aviation Engineering Flight Activity, Edwards Air Force Base, Calif., 

1975. 

122. Congress, U. S.: Review of Army Procurement of Light Observation Helicopters. 

Hearings Before the Subcommittee for Special Investigations of the Committee on 

Armed Services, House of Representatives, 19th Congress, 1st Session, 1967. 

123. Nagata, J. I. et al.: Government Competitive Test, Utility Tactical Transport Aircraft 

System (UTTAS), Sikorsky YUH-60A Helicopter. USAAEFA Project No. 74-06-1, 

U.S. Army Aviation Engineering Flight Activity, Edwards Air Force Base, Calif., 

1976. 

124. Winn, A. L., et al.: Government Competitive Test, Utility Tactical Transport Aircraft 

System (UTTAS), Boeing-Vertol YUH-61A Helicopter. USAAEFA Project No. 74-

06-2, U.S. Army Aviation Engineering Flight Activity, Edwards Air Force Base, 

Calif., 1976. 

125. Bender, G. L. et al.: Development Test I, Advanced Attack Helicopter Competitive 

Evaluation, Bell YAH-63 Helicopter. USAAEFA Project No. 74-07-1, U.S. Army 

Aviation Engineering Flight Activity, Edwards Air Force Base, Calif., 1976. 

126. Steward, R. L. et al.: Development Test I, Advanced Attack Helicopter Competitive 

Evaluation, Hughes YAH-64 Helicopter. USAAEFA Project No. 74-07-2, U.S. Army 

Aviation Engineering Flight Activity, Edwards Air Force Base, Calif., 1976. 

127. Anon.: Boeing Sikorsky’s LH, Now the Army’s Commanche. Rotor & Wing, vol. 25, 

no. 5, 1991. 

128. Morrocco, J. D.: R & D Shortfall Forces Comanche Changes. Aviation Week & Space 

Technology, Oct. 25, 1993, p. 26. 

129. Schrader, E. (Los Angeles Times): Pentagon Scraps Plan for Copter. San Jose 

Mercury News, Feb. 24, 2004. 

130. Berger, A.-Y.; and Burr, N.: Ultralight and Microlight Aircraft of the World. 

Somerset, England: Haynes Publishing Group, 1983/84. 

131. Carlson, R. M.: The Future of Aerospace. Proc. Symposium in Honor of Alexander H. 

Flax, National Academy of Engineering, National Academy Press, Washington, D.C., 

1993, pp. 45–63. 

132. Anon.: The Official Helicopter Blue Book®, HeliValue$, Inc., Wauconda, Ill., various 

years. 

133. Reschak, R. J.; and Baldwin, R. L.: Category II Performance and Limited Handling 

Characteristics Tests of the YUH-1D With a 44-Foot Rotor. AFFTC Report No. 63-

43, Air Force Flight Test Center, Edwards Air Force Base, Calif., 1964. 

134. Anon.: MIL-STD-1374A. Weight and Balance Data Reporting Forms for Aircraft 

(Including Rotorcraft). Department of Defense, Washington, D.C., Sept. 30, 1977. 

135. Anon.: MIL-W-25140B. Weight and Balance Control System (for Aircraft and 

Rotorcraft). Department of Defense, Washington, D.C., Oct. 31, 1977. 

136. Prewitt, R. H.: Detailed Specification for Model XR-2 Rotorcraft. Report No. 120.19, 

Kellett Autogyro Corp., Philadelphia, Pa., Feb. 27, 1941. 
4. REFERENCES 

710 

137. Prewitt, R. H.: Detailed Specification for Model XR-3 Rotorcraft. Report No. 120.20, 

Kellett Autogyro Corp., Philadelphia, Pa., Apr. 22, 1941. 

138. Anon.: Model Specification, Helicopter, XR-4 (Vought-Sikorsky Model VS-316). 

Report No. 5536, Vought-Sikorsky Aircraft Div., United Aircraft Corp., Stratford, 

Conn., Jan. 1, 1942. 

139. Anon.: Model Specification, Helicopter, YR-4A and YR-4B (supercedes Report No. 

5922 dated May 4, 1942). Report No. 5922A, United Aircraft Corp., Vought-Sikorsky 

Aircraft Div., Stratford, Conn., Nov. 1, 1944. 

140. Anon.: Model Specification, XR-6 (VS-316B). Report No. 5922, Vought-Sikorsky 

Aircraft Div., United Aircraft Corp., Stratford, Conn., Oct. 20, 1942. 

141. Anon.: Model Specification, Helicopter, R-4B. Report No. SER-400B (supercedes 

SER-400A dated Oct. 10, 1944). Vought-Sikorsky Aircraft Div., United Aircraft 

Corp., Stratford, Conn., Mar. 10, 1945. 

142. Anon.: Model Specification, Helicopter, XR-5. Report No. 5930A, Vought-Sikorsky 

Aircraft, Div. of United Aircraft Corp., Stratford, Conn., June 1, 1942. 

143. Anon.: Model Specification, Helicopter, R-5A. Report No. SER-406, Sikorsky 

Aircraft, Div. of United Aircraft Corp., Stratford, Conn., Feb. 1, 1944. 

144. LePage, L.: Model Specification for Army Air Forces Helicopter Model YR-1A. 

Engineering Dept. Spec. No. S-144, Platt-LePage Aircraft Co., Eddystone, Pa., Jan. 

17, 1944. 

145. Harris, F. D.: AHIP: The OH-58D From Conception to Production. Proc. 42nd Annual 

Forum of the American Helicopter Society, Washington, D.C., June 1986. 

146. Kawa, M. M.; and Van Kirk, J. M.: Kiowa Warrior—A Bridge to the Future. Proc. 

American Helicopter Society 53rd Annual Forum, Virginia Beach, Va., Apr. 29–May 

1, 1997. 

147. Cammack, S. P.: YOH-6A World Record Program. Proc. 23rd Annual National Forum 

of the American Helicopter Society, Washington, D.C., May, 1967. 

148. Ulisnik, H.: Private correspondance to F. D. Harris, Nov. 1992. 

149. Davis, S. J.; and Wisniewski, J. S.: User’s Manual for HESCOMP—The Helicopter 

Sizing and Performance Computer Program. Report No. D210-10699-1, Boeing 

Vertol Co., Philadelphia, Pa., Sept. 1973. 

150. Schoen, A., H.; and Wisniewski, J. S.: User’s Manual for VASCOMP II—The 

V/STOL Aircraft Sizing and Performance Computer Program. Report No. D8-0375, 

Vol. VI, Boeing Vertol Co., Philadelphia, Pa., Mar. 1973. 

151. Johnson, W.: NDARC-NASA Design and Analysis of Rotorcraft. NASA/TP-2009-

215402, Dec. 2009. 

152. Crabtree, J. A.; and Amer, K. B.: Helicopter Configuration and Propulsion Systems 

Study, Part 1. Statistical Weight Analysis. Hughes Tool Co., Aircraft Div., Culver 

City, Calif., Nov. 1957. 

153. Stepniewski, W. Z.: Rotorcraft Weight Trends in Light of Structural Material 

Characteristics. U.S. Army Aviation Systems Command Technical Report No. TR-87-

A-10 (also AD-A186 576), Apr. 1987. 
4. REFERENCES 

711 

154. Wisniewski, J. S.: The Boeing Model 360 Advanced Technology Demonstrator 

Helicopter. Proc. 51st Annual Conference of the Society of Allied Weight Engineers, 

Hartford, Conn., May 18–20, 1992. 

155. Stepniewski, W. Z.: A Comparative Study of Soviet vs. Western Helicopters, Part 1: 

General Comparison of Designs. NASA-CR-3579 (see also AVRADCOM-TR-82-A9), Mar. 1983. 

156. Stepniewski, W. Z.; and Shinn, R. A.: A Comparative Study of Soviet vs. Western 

Helicopters, Part 2: Evaluation of Weight, Maintainability, and Design Aspects of 

Major Components. NASA-CR-3580 (see also AVRADCOM-TR-82-A-10), Mar., 

1983. 

157. Klemin, Lt. A.: Aeronautical Engineering and Airplane Design. New York, N.Y.: The 

Gardner-Moffat Co., Inc., 1918. 

158. Bréguet, L.: The Gyroplane. J. Royal Aeronautical Society, vol. 36, no. 8, Sept. 1937. 

159. Ferrell, K. R.; Frederick, A. C.; and Kishe, J. S.: Flight Evaluation, Compliance Test 

Techniques for Army Hot Day Hover Criteria. USAASTA Project No. 68-55, U.S. 

Army Aviation Systems Test Activity, Edwards Air Force Base, Calif., Apr. 1974. 

160. Nagata, J. I. et al.: Government Competitive Test, Utility Tactical Transport Aircraft 

System (UTTAS), Sikorsky YUH-60A Helicopter. USAAEFA Project No. 74-06-1, 

U.S. Army Aviation Engineering Flight Activity, Edwards Air Force Base, Calif. 

1976. 

161. Nagata, J. I. et al.: Airworthiness and Flight Characterists Evaluation, UH-60A (Black 

Hawk) Helicopter. USAAEFA Project No. 77-17, U.S. Army Aviation Engineering 

Flight Activity, Edwards Air Force Base, Calif., Sept. 1981. 

162. Leoni, R. D.: Black Hawk: The Story of a World Class Helicopter. American Institute 

of Aeronautics and Astronautics, Inc., Reston, Va., 2007. 

163. Anon.: UH-60A Weight Report. Sikorsky Aircraft, Stratford, Conn., 1979. 

164. Anon.: YUH-60A Weight Report. Sikorsky Aircraft, Stratford, Conn., 1976. 

165. Gould, W., et al.: Rotor System Evaluation. AEFA Project No. 85-15, Edwards Air 

Force Base, Calif., Mar. 1988. 

166. Bousman, W.; and Kufeld, R. M.: UH-60A Airloads Catalog. NASA/TM-2005-

212827 (see also AFDD-TR-05-003), Aug. 2005. 

167. Kufeld, R. M., et al.: Flight Testing the UH-60A Airloads Aircraft. Proc. American 

Helicopter Society 50th Annual Forum, Washington, D.C., May 11–13, 1994. 

168. Kocurek, J. D.; Berkowitz, L. F.; and Harris, F. D.: Hover Performance Methodology 

at Bell Helicopter Textron. Proc. 36th Annual Forum of the American Helicopter 

Society, Washington, D.C., May 1980. 

169. Lewis, R. B.: Army Helicopter Performance Trends. J. American Helicopter Society, 

vol. 17, no. 2, 1972. 

170. Lyle, J. A. et al.: Technology Flight Evaluation of the Aerospatiale SA 365 N-1, 

Dauphin 2, Helicopter. USAAEFA Project No. 85-06, U.S. Army Aviation 

Engineering Flight Activity, Edwards Air Force Base, Calif., 1990. 

171. Johnson, J. N.; and Ferry, R. G.: H-13H Phase IV Performance Test. AFFTC-TR-57-

12 plus Addendum No. 1, Air Force Flight Test Center, Edwards Air Force Base, 

Calif., 1957. 
4. REFERENCES 

712 

172. Melton, J. R.; and Watts, J. C.: Engineering Flight Test, Performance Phase of the 

OH-4A Helicopter. USATECOM Project No. 4-3-0250-11/12/1, U.S. Army Aviation 

Test and Evaluation Command, Edwards Air Force Base, Calif., Aug. 1964. 

173. Yamakawa, G. M.; and Watts, J. C.: Airworthiness and Flight Characteristics Test, 

Production OH-58A Helicopter, Unarmed and Armed with XM27E1 Weapon System. 

USAASTA Project No. 68-30, U.S. Army Aviation Systems Test Activity, Edwards 

Air Force Base, Calif., Sept. 1970. 

174. Laing, E. J.; Benson, T. P.; Werner, A. W.; and Broahurst, D. G.: Evaluation of the 

OH-58A Helicopter With an Allison 250-C20 Engine. USAASTA Project No. 71-24, 

U.S. Army Aviation Systems Test Activity, Edwards Air Force Base, Calif., Dec. 

1972. 

175. Yamakawa, G. M.; Buckanin, R. M.; Hagen, J. F.; and Burch, T. E.: Preliminary 

Airworthiness Evaluation OH-58C Helicopter USAAEFA Project No. 76-11-2, U.S. 

Army Aviation Engineering Flight Activity, Edwards Air Force Base, Calif., Mar. 

1978. 

176. Marshall, A. R. et al.: Airworthiness and Flight Characteristics Test of an OH-58C 

Configured to a Light Combat Helicopter (LCH). USAAEFA Project No. 81-07, U.S. 

Army Aviation Engineering Flight Activity, Edwards Air Force Base, Calif., 1981. 

177. Brown, J. D. et al.: Airworthiness and Flight Characteristics Evaluation of the OH58D Helicopter. USAAEFA Project No.83-27-1, U.S. Army Aviation Engineering 

Flight Activity, Edwards Air Force Base, Calif, 1990. 

178. Johns, S. L.; and Colvin, G. L.: YUH-1B Category II Performance Tests. AFFTC 

Report No. 62-21, Air Force Flight Test Center, Edwards Air Force Base, Calif., 1962. 

179. Porter, D. W.; and Flanigen, E. G.: Category II Performance Tests of the YUH-1D 

With a 48-Foot Rotor. AFFTC Report No. 64-27, Air Force Flight Test Center, 

Edwards Air Force Base, Calif., 1964. 

180. Smith, E. D.; and Flanigen, E. G.: UH-1F Category II Performance. AFFTC Report 

No. 65-05, Air Force Flight Test Center, Edwards Air Force Base, Calif., 1965. 

181. Shultz, A.: BHT Hover Performance Methodology. BHTI Report No. 212-099-052, 

Bell Helicopter Textron, Inc., Ft. Worth, Tex., 1970. 

182. Anon.: BHT Hover Performance Methodology for Model 214B. Report No. BHTI 

214-099-303 Rev. A, Bell Helicopter Textron, Inc., Ft. Worth, Tex., 1970. 

183. Anon.: BHT Hover Performance Methodology for Model 222. Report No. BHTI 222-

993-013, Bell Helicopter Textron, Inc., Ft. Worth, Tex., 1978. 

184. Kidwell, J. C.; and Foster, J. K.: Engineering Flight Evaluation of the Bell Model 209 

Armed Helicopter. USATECOM Project No. 4-6-0300-01, U.S. Army Test and 

Evaluation Command, Edwards Air Force Base, Calif., 1966. 

185. Finnestead, R. L. et al.: Engineering Flight Test, AH-1G Helicopter (Hueycobra) 

Phase D, Part 2—Peformance (also Phase B, Part 6). USAASTA Project No.66-06, 

U.S. Army Aviation Systems Test Activity, Edwards Air Force Base, Calif., 1970. 

186. Nagata, J. I. et al.: Attack Helicopter Evaluation Model 309 Kingcobra Helicopter. 

USAASTA Project No. 72-10, U.S. Army Aviation Systems Test Activity, Edwards 

Air Force Base, Calif., 1972. 
4. REFERENCES 

713 

187. Crawford, C. C.; and Hodgson, W. J.: YHC-1A Flight Evaluation. AFFTC TR-61-1, 

Air Force Flight Test Center, Edwards Air Force Base, Calif. See also NATC Project 

TED PTR AD 3097, Naval Air Test Center, Patuxent River, Md., 1961. 

188. Dallas, S.; Bumstead, R.; and Tuttle, D. T.: Performance Data and Substantiation 

Report for the CH-46E Helicopter. Boeing-Vertol Report No. D331-10042-1, Boeing 

Vertol Co., Philadelphia, Pa., Mar. 14, 1977. 

189. McHugh, F.: Letter to F. D. Harris, Aug. 6, 1982. 

190. Bender, G. L. et al.: Airworthiness and Flight Characteristics Test (A&FC) of the CH47D Helicopter. USAAEFA Project No. 82-07, U.S. Army Aviation Engineering 

Flight Activity, Edwards Air Force Base, Calif., 1984. 

191. Koelle, E. A.; and Hodgson, W. J.: YH-41 Performance Evaluation. AFFTC-TR-60-7 

Addendum I, Air Force Flight Test Center, Edwards Air Force Base, Calif., 1960. 

192. Kidwell, J. C. et al.: High Altitude Evaluation of the Hiller Model 1961 UH-12E. ATO 

TR-61-3, U.S. Army Aviation Test Office, Edwards Air Force Base, Calif., Mar. 1961. 

193. Ferrell, K. R.; and Honaker, J. S.: Category II Performance Tests of the H-43B. 

AFFTC Report No. 62-11, Air Force Flight Test Center, Edwards Air Force Base, 

Calif., 1963. 

194. Plaks, A.; and Collins, R. E.: Substantiating Data for the SH-2F, Standard Aircraft 

Characteristics Charts. Kaman Report No. P-65 (see also Nav Air System AIR530122), Aug. 1, 1973. 

195. Johnson, J. N. et al.: Attack Helicopter Evaluation AH-56A Cheyenne Compound 

Helicopter—Final Report. USAASTA Project No. 72-08, U.S. Army Aviation 

Systems Test Activity, Edwards Air Force Base, Calif., 1972. 

196. Sharon, G. A. et al.: Preliminary Airworthiness Evaluation of the MBB BK-117 

Helicopter (Germany/Japan). USAAEFA Project No. 84-22, U.S. Army Aviation 

Engineering Flight Activity, Edwards Air Force Base, Calif., 1985. 

197. Ferrell, K. R.; and Ferry, R. G.: YHO-2HU Air Force Flight Evaluation. AFFTC-TR60-2, Air Force Flight Test Center, Edwards Air Force Base, Calif., 1960. 

198. Nagata, J. I.; and Shapley, J. J.: Engineering Flight Test of the OH-6A Helicopter 

(Cayuse) Phase D—Final Report. USAASTA Project No. 65-37, U.S. Army Aviation 

Systems Test Activity, Edwards Air Force Base, Calif., 1969. 

199. Webe, J. L. et al.: Airworthiness and Flight Characteristics Test of the OH-6A 

Configured to a Light Combat Helicopter (JOH-6A LCH). USAAEFA Project No. 81-

04, U.S. Army Aviation Engineering Flight Activity, Edwards Air Force Base, Calif., 

1983. 

200. Webre, J. L. et al.: Airworthiness and Flight Characteristics Evaluation of the 

McDonnell Douglas Helicopter Corporation (MDHC) 530FF Helicopter, Final Report. 

USAAEFA Project No. 86-15, U.S. Army Aviation Engineering Flight Activity, 

Edwards Air Force Base, Calif., 1989. 

201. Steward, R. L. et al.: Development Test I, Advanced Attack Helicopter Competitive 

Evaluation, Hughes YAH-64 Helicopter. USAAEFA Project No. 74-07-2, U.S. Army 

Aviation Engineering Flight Activity, Edwards Air Force Base, Calif., 1977. 
4. REFERENCES 

714 

202. Picasso, B. D. et al.: Airworthiness and Flight Characteristics (A&FC) Test of YAH64 Advanced Attack Helicopter, Prototype Qualification Test—Government (PQT-G), 

Part 3, and Production Validation Test—Government (PVT-G) for Handbook 

Verification—Final Report. USAAEFA Project No. 80-17-3, U.S. Army Aviation 

Engineering Flight Activity, Edwards Air Force Base, Calif., 1982. 

203. Ferrell, K. R.; and Honaker, J. S.: H-37A Limited Stability and Control Evaluation. 

AFFTC-TR-60-15, Air Force Flight Test Center, Edwards Air Force Base, Calif., 

1960. 

204. Turk, R. N.; and Watts, J. C.: Final Report of Engineering Flight Test of the CH-37 B. 

USAATA Project No. 62-28, U.S. Army Aviation Systems Test Activity, Edwards Air 

Force Base, Calif., June 15, 1964. 

205. Anon.: Performance Flight Tests of the S-64F (CH-54B) Helicopter for FAA 

Certification. Sikorsky Aircraft Report No. SER-64511, Sikorsky Aircraft Corp., 

Stratford, Conn., 1970. 

206. Seto, E. I. et al.: Category II Performance Test on the CH-3C Helicopter. AFFTC 

Report No. 65-39, Air Force Flight Test Center, Edwards Air Force Base, Calif., 1966. 

207. Ritter, R. L. et al.: Limited High Altitude Performance Evaluation of the HH-53C 

Helicopter. AFFTC-TR-71-54, Air Force Flight Test Center, Edwards Air Force Base, 

Calif., 1971. 

208. Anon.: Substantiating Data Report for NATOPS Flight Manual Performance of the 

Production CH-53E. Sikorsky Aircraft Report No. SER-13441, Sikorsky Aircraft 

Corp., Stratford, Conn., 1987. 

209. Anon.: SA 341/01 Report of Analysis. Aerospatiale RD/DA/MM-H/EV No. 3226, 

Aerospatiale, Paris, France, 1970. 

210. Ruddell, A. J.: Advancing Blade Concept (ABC) Technology Demonstrator. 

AVRADCOM TR-81-D-5, Aviation Research and Development Command, Ft. Eustis, 

Va., Apr. 1981. 

211. Harris, F. D.: Rotary Wing Aerodynamics—Historical Perspective and Important 

Issues. Proc. National Specialists’ Mtg. on Aerodynamic and Aeroacoustics Sponsored 

by the American Helicopter Society Southwest Region, Arlington, Tex., 1987. 

212. McKee, J. W.; and Naeseth, R. L.: Experimental Investigation of the Drag of Flat 

Plates and Cylinders in the Slipstream of a Hovering Rotor. NACA TN 4239, 1958. 

213. Bousman, W.: Power Measurement Errors on a Utility Aircraft. Proc. American 

Helicopter Society Aerodynamics, Acoustics, and Test and Evaluation Technical 

Specialists’ Mtg., San Francisco, Calif., Jan. 23–25, 2002. 

214. Amer, K. B.; and Gessow, A.: Charts for Estimating Tail-Rotor Contribution to 

Helicopter Directional Stability and Control. NACA Report 1216, 1953. 

215. Lynn, R. R. et al.: Tail Rotor Design, Part I: Aerodynamics. J. American Helicopter 

Society, vol. 15, no. 4, 1969. 

216. Balke, R. W. et al.: Tail Rotor Design Part II: Structural Dynamics. J. American 

Helicopter Society, vol. 15, no. 4, 1970. 

217. Mouille, R.: The “Fenestron” Shrouded Tail Rotor of the SA-341 Gazelle. J. American 

Helicopter Society, vol. 15, no. 4, 1970. 
4. REFERENCES 

715 

218. Huston, R. J.; and Morris, C. E. K.: A Note on a Phenomenon Affecting Helicopter 

Directional Control in Rearward Flight. J. American Helicopter Society, vol. 15, no. 4, 

1970. 

219. Robinson, F.: Increasing Tail Rotor Thrust and Comments on Other Yaw Control 

Devices. J. American Helicopter Society, vol. 15, no. 4, 1970. 

220. Huston, R. J.; and Morris, C. E. K.: A Wind-Tunnel Investigation of Helicopter 

Directional Control in Rearward Flight in Ground Effect. NASA TN-D-6118, Mar. 

1971. 

221. Wiesner, W.; and Kohler, G.: Tail Rotor Design Guide. USAAMRDL TR 73-99, U.S. 

Army Air Mobility Research and Development Laboratories, Ft. Eustis, Va., 1974. 

222. Sheridan, P. F.: Interactional Aerodynamics of the Single Rotor Helicopter 

Configuration, Volume I—Final Report. USARTL-TR-78-23A, U.S. Army Research 

and Technical Laboratories, Ft. Eustis, Va., Sept. 1978. 

223. Cook, C. V.: A Review of Tail Rotor Design and Performance. International J. of 

Rotorcraft and Powered Lift Aircraft, vol. 2, no. 3/4, 1978. 

224. Yeager, W. T.; Young, W. H.; and Mantay, W. R.: A Wind Tunnel Investigation of 

Parameters Affecting Helicopter Directional Control at Low Speeds in Ground Effect. 

NASA TN-D-7694, Nov. 1974. 

225. Paul, W. F.; and Zincone, R.: Advanced Technology Applied to the UH-60A and S-76 

Helicopters. International J. of Rotorcraft and Powered Lift Aircraft, vol. 2, no. 3/4, 

1978. 

226. Signor, D. B., et al.: Performance and Loads Data from an Outdoor Hover Test of a 

Lynx Tail Rotor. NASA TM-101057, 1989. 

227. Vuillet, A.; and Morelli, F.: New Aerodynamic Design of the Fenestron for Improved 

Performance. AGARD CP-423, Rotorcraft Design for Operations Symposium, 

Amserdam, The Netherlands, Oct. 13–16, 1986. 

228. Lehman, A. F.: Model Studies of Helicopter Tail Rotor Flow Patterns In and Out of 

Ground Effect. USAAVLABS TR 71-12, U.S. Army Aviation Material Laboratories, 

Ft. Eustis, Va., 1971. 

229. Balch, D. T. et al.: Experimental Study of Main Rotor/Tail Rotor/Airframe 

Interactions in Hover. Volume 1: Text and Figures. NASA-CR-166485, June 1983. 

230. Menger, R. P. et al.: Effects of Aerodynamic Interaction Between Main and Tail 

Rotors on Helicopter Hover Performance and Noise. NASA CR-166477, Feb. 1983. 

231. Balch, D. T.; and Lombardi, J.: Experimental Study of Main Rotor Tip Geometry and 

Tail Rotor Interactions in Hover. Volume 1. Text and Figures. NASA CR-177336-

Vol-1, Feb. 1985. 

232. Balch, D. T.; and Lombardi, J.: Experimental Study of Main Rotor Tip Geometry and 

Tail Rotor Interactions in Hover. Volume 2. NASA CR-177336-Vol-2, 1985. 

233. Garry, R. M., Col.: French Helicopters. J. Helicopter Association of Great Britain, vol. 

3, no. 4, 1950. 

234. Gessow, A.; and Myers, G. C., Jr.: Aerodynamics of the Helicopter. New York, N.Y.: 

Frederick Ungar Publishing Co., 1967. 

235. Johnson, W.: Helicopter Theory. Princeton, N.J.: Princeton University Press, 1980. 
4. REFERENCES 

716 

236. Leishman, J. G.: Principles of Helicopter Aerodynamics. Cambridge, England: 

Cambridge University Press, 2000. 

237. Stepniewski, W. Z.: Introduction to Helicopter Aerodynamics. Morton, Pa.: Rotorcraft 

Publishing Committee, 1950. 

238. Stepniewski, W. Z.; and Keys, C. N.: Rotary-Wing Aerodynamics. Mineola, N.Y.: 

Dover Publications, 1984. 

239. Nikolsky, A. A.: Helicopter Analysis. New York, N.Y.: John Wiley & Sons, Inc., 

1951. 

240. McCormick, B. W.: Aerodynamics of V/STOL Flight. Orlando, Fla.: Academic Press, 

1967. 

241. Bramwell, A. R. S.: Helicopter Dynamics. New York, N.Y.: John Wiley & Sons, Inc., 

1976. 

242. Prouty, R.: Helicopter Performance, Stability, and Control. Boston, Mass.: PWS 

Engineering, 1986. 

243. Knight, M.; and Hefner, R. A.: Static Thrust Analysis of the Lifting Airscrew. NACA 

TN 626, Dec. 1937. 

244. Knight, M.; and Hefner, R. A.: Analysis of Ground Effect on the Lifting Airscrew. 

NACA TN 835, Dec. 1941. 

245. Bhagwat, M. J. et al.: Development and Application of a CFD-based Engineering 

Analysis of Hover Performance. Proc. American Helicopter Society 62nd Annual 

Forum, Phoenix, Ariz.. May 9–11, 2006. 

246. Landgrebe, A. J.: An Analytical and Experimental Investigation of Helicopter Rotor 

Hover Performance and Wake Geometry Characteristics. USAAMRDL TR-71-24, 

U.S. Army Air Mobility Research and Development Laboratories, Ft. Eustis, Va., 

1973. 

247. Stepniewski, W. Z. et al.: Experimental Investigation of PV-14 Overlap. Part II—

Thrust and Power. Piasecki Helicopter Corp. Report No. 14-A-03, 1948. 

248. Sweet, G. E.: Hovering Measurements for Twin-Rotor Configurations With and 

Without Overlap. NASA TN-D-534, Nov. 1960. 

249. Crawford, C. C.: Rotorcraft Analytical Improvement Needed to Reduce 

Developmental Risk—The 1989 Alexander A. Nickolsky Lecture. J. American 

Helicopter Society, vol. 35, no. 1, 1990. 

250. Arents, D. N.: An Assessment of the Hovering Performance of the XH-59A 

Advancing Blade Concept Demonstartion Helicopter. USAAMRDL-TN-25, U.S. 

Army Air Mobility Research and Development Laboratories, Ft. Eustis, Va., 1977. 

251. Mikheyev, S. V. et al.: Ka-50 Attack Helicopter Aerbatic Flight. Proc. 24th European 

Rotorcraft Forum, Marseilles, France, Sept. 15–17, 1998. 

252. Harrington, R. D.: Full-Scale-Tunnel Investigation of the Static-Thrust Performance of 

a Coaxial Helicopter Rotor. NACA TN 2318, 1951. 

253. Coleman, C. P.: A Survey of Theoretical and Experimental Coaxial Rotor 

Aerodynamic Research. NASA TP-3675, 1997. 

254. Stepniewski, W. Z.; and Sloan, L. H.: Experimental Investigation of PV-14 Overlap. 

Part I—Downwash Distribution. Piasecki Helicopter Corp. Report No. 14-A-03, 1948. 
4. REFERENCES 

717 

255. Harris, F. D.: Twin Rotor Hover Performance. J. American Helicopter Society, vol. 

44, no. 1, 1994. 

256. Dingeldein, R. C.: Wind-Tunnel Studies of the Performance of Multirotor 

Configurations. NACA TN 3236, Aug. 1954. 

257. Cheney, M. C.: The ABC Helicopter. Proc. AIAA/AHS VTOL Research, Design, and 

Operations Mtg., Georgia Institute of Technology, Atlanta, Ga., Feb. 17–19, 1969. 

258. Burgess, R. K.: The ABC Rotor—A Historical Perspective. Proc. American Helicopter 

Society 60th Annual Forum, Baltimore, Md., June 7–10, 2004. 

259. Phelps, A. E.; and Mineck, R. E.: Aerodynamic Characteristics of a Counter-Rotating, 

Coaxial, Hingeless Rotor Helicopter Model With Auxiliary Propulsion. NASA TM78705, May 1978. 

260. Felker, F. F., III: Performance and Loads Data from a Wind Tunnel Test of a FullScale, Coaxial, Hingeless Rotor Helicopter. NASA TM-81329, Oct. 1981. 

261. Stroub, R. H. et al.: An Investigation of a Full-Scale Advancing Blade Concept Rotor 

System at High Advance Ratio. NASA TM-X- 62081, Aug. 1971. 

262. McAlister, K. W. et al.: Experimental and Numerical Study of a Model Coaxial Rotor. 

Proc. American Helicopter Society 62nd Annual Forum, Phoenix, Ariz., May 9–11, 

2006. 

263. Leishman, J. G.; and Ananthan, S.: Aerodynamic Optimization of a Coaxial Proprotor. 

Proc. American Helicopter Society 62nd Annual Forum, Phoenix, Ariz., May 9–11, 

2006. 

264. Wachspress, D. A.; and Quackenbush, T. R.: Impact of Rotor Design on Coaxial 

Performance, Wake Geometry,SW and Noise. Proc. American Helicopter Society 

62nd Annual Forum, Phoenix, Ariz., May 9–11, 2006. 

265. Kussner, H. G.: Helicopter Problems. NACA TM 827, May 1937. 

266. Platt, H. H.: The Helicopter: Propulsion and Torque. J. Aeronautical Sciences, vol. 3, 

no. 11, Sept. 1936, pp. 398–405. 

267. Zbrozek, J.: Ground Effect on the Lifting Rotor. Aeronautical Research Council R&M 

No. 2347, July 1941. 

268. Hayden, J. S.: The Effect of the Ground on Helicopter Hovering Power Required. 

Proc. American Helicopter Society 32nd Annual Forum, Washington, D.C., May 10–

12, 1976. 

269. Tetervin, N.: Airfoil Section Data From Tests of 10 Practical-Construction Sections of 

Helicopter Rotor Blades Submitted by the Sikorsky Aircraft Div., United Aircraft 

Corp. NACA WR-L-643, Sept. 1944. 

270. Dingeldein, R. C.; and Schaefer, R. F.: Static Thrust Tests of Six Rotor-Blade Designs 

on a Helicopter in the Langley Full-Scale Tunnel. NACA ARR No. L5F25b, Sept. 

1945. 

271. Dingeldein, R. C.; and Schaefer, R. F.: Full-Scale Investigation of Aerodynamic 

Characteristics of a Typical Single-Rotor Helicopter in Forward Flight. NACA TR 

905, 1948. 

272. Gustafson, F. B.; and Gessow, A.: Analysis of Flight-Performance Measurements on a 

Twisted, Plywood-Covered Helicopter Rotor in Various Flight Conditions. NACA TN 

1595, June 1948. 
4. REFERENCES 

718 

273. Gessow, A.: Flight Evaluation of Effects of Rotor-Blade Twist on Helicopter 

Performance in the High-Speed and Vertical-Autorotative-Descent Conditions. Aug. 

1948. 

274. Ward, J. F.: Rotorcraft Research—A National Effort. J. American Helicopter Society, 

vol. 32, no. 2, 1986. 

275. Phillips, E. H.: Piper—A Legend Aloft. Eagan, Minn.: Flying Books International, 

1993. 

276. Kitchens, Dr. J. W.: Organic Army Aviation in World War II. Army Aviation Digest, 

May/June and June/July, 1992. 

277. Neel, S. H., Lt. Col.: Helicopter Evacuation in Korea. U.S.Armed Forces Medical 

Journal, vol. VI, no. 5, 1955. 

278. Anon.: Pilot’s Flight Operating Instructions for Army Models L-4A, L-4B, and L-4H 

Airplanes. Yorkshire, England: Air Publications and Forms Store. Sept. 5, 1943 

(revised Oct. 25, 1944). 

279. Anon.: Erection and Maintenance Instructions for Army Models L-4A, L-4B, L-4H, 

and L-4J Airplanes. Yorkshire, England: Air Publications and Forms Store. Aug. 25, 

1943 (revised Mar. 5, 1945). 

280. Anon.: Phase II Flight Test of the Cessna L-19A. WCTSE-WCT-2355, 1951. 

281. Kidwell, J. C.; and Clay, W.: Evaluation of L-19A Equipped with Continental O-470-

11C1 Fuel Injected Engine. ATO-TR-61-1, 1961. 

282. Davidson, J. D.; and Ferry, R. G.: TL-19D Phase IV Performance. AFFTC-TR-57-14, 

Air Force Flight Test Center, Edwards Air Force Base, Calif., 1957. 

283. Oswald, W. B.: General Formulas and Charts for the Calculation of Airplane 

Performance. NACA TR 408, 1932. 

284. Perkins, C. D.; and Hage, R. E.: Airplane Peformance, Stability and Control. New 

York, N.Y.: John Wiley & Sons, Inc., 1949. 

285. Diehl, W. S.: The Reduction of Observed Airplane Performance to Standard 

Conditions. NACA TR 297, 1928. 

286. Herrington, R. M. et al.: Flight Test Engineering Handbook. USAF-TR-6273, 1951. 

287. Miller, R.; and Sawers, D.: The Technical Development of Modern Aviation. New 

York, N.Y.: Praeger Publishers, 1970. 

288. Rosen, G.: Thrusting Forward: A History of the Propeller. Hartford, Conn.: Hamilton 

Standard, 1987. 

289. Green, W.; and Swanborough, G.: The Great Book of Fighters (an Illustrated 

Encyclopedia of Every Fighter Aircraft Built and Flown). Osceola, Wis.: MBI 

Publishing Co., 1994. 

290. Durand, W. F.; and Lesley, E. P.: Comparison of Tests on Air Propellers in Flight 

With Wind Tunnel Model Tests on Similar Forms. NACA TR 220, 1927. 

291. Crowley, J. W., Jr.; and Mixson, R. E.: Characteristics of Five Propellers in Flight. 

NACA TR 292, 1927. 

292. Weick, F. E.; and Wood, D. H.: The Twenty-Foot Propeller Research Tunnel of the 

National Advisory Committee for Aeronautics. NACA TR 300, 1928. 

293. Weick, F. E.: Full Scale Tests of Wood Propellers on a VE-7 Airplane in the Propeller 

Research Tunnel. NACA TR 301, 1928. 
4. REFERENCES 

719 

294. Weick, F. E.: Full-Scale Wind-Tunnel Tests of a Series of Metal Propellers on a VE-7 

Airplane. NACA TR 306, 1928. 

295. Harris, F. D.: Performance Analysis of Two Early NACA High-Speed Propellers With 

Application to Civil Tiltrotor Configurations. NASA CR-196702, Aug. 1996. 

296. Jackson, P. (Ed.): Jane’s All the Worlds Aircraft 2004–2005. Surrey, United 

Kingdom: Jane’s Information Group Ltd., 2005. 

297. Fradenburgh, E. A.: Aerodynamic Design of the Sikorsky S-76 Helicopter. Proc. 

American Helicopter Society 34th Annual National Forum, Washington, D.C., May 

15–17, 1978. 

298. Prouty, R.: A Second Approximation to the Induced Drag of a Rotor in Forward 

Flight. J. American Helicopter Society, vol. 21, no. 3, 1976. 

299. Seto, E. I.; and Hodgson, W. J.: Flight Evaluation of the H-21C, HU-1A, and H-34C 

Equipped with XM-153 Armament Kit. FTC-TDR-62-29, Air Force Flight Test 

Center, Edwards Air Force Base, Calif., 1962. 

300. Boyne, W. J.; and Lopez, D. S.: Vertical Flight—The Age of the Helicopter. 

Washington, D.C.: Smithsonian Institution Press, 1984. 

301. Coleman, R. P.; Feingold, A. M.; and Stempin, C. W.: Evaluation of the Induced 

Velocity Field of an Idealized Helicopter Rotor. NACA WR-L-126, June 1945. 

302. Castles, W., Jr.; and De Leeuw, J. H.: The Normal Component of the Induced Velocity 

in the Vicinity of a Lifting Rotor and Some Examples of Its Application. NACA TR 

1184, 1952. 

303. Heyson, H. H.: A Brief Survey of Rotary Wing Induced-Velocity Theory. NASA TM78741, June 1978. 

304. Glauert, H.: A General Theory of the Autogiro. Aeronautical Research Committee 

R&M No. 1111, Nov. 1926. 

305. Heyson, H. H.; and Katzoff, S.: Induced Velocities Near a Lifting Rotor With 

Nonuniform Disk Loading. NACA TR 1319, 1956. 

306. Piziali, R. A.; and Du Waldt, F. A.: A Method for Computing Rotary Wing Airload 

Distribution in Forward Flight. Cornell Aeronautical Laboratory Report BB-1495-S-1 

(see also TCREC TR 62-44), 1962. 

307. Crimi, P.: Prediction of Rotor Wake Flows. Proc. CAL/USAAVLABS Symposium, 

Vol. I, Propeller and Rotor Aerodynamics, Buffalo, N.Y., 1966. (Orignial work in 

CAL BB-1994-S, Sept. 1965.) 

308. McCroskey, W. J.: Vortex Wakes of Rotorcraft. AIAA Paper No. 95-0530, Proc. 

AIAA 33rd Aerospace Sciences Mtg. and Exhibit, Reno, Nev., Jan. 9–12, 1995. 

309. Huston, R. J.: A Study of the Interference Effects in a Tandem Rotor Helicopter. 

NASA TM-X-67027, June 1961. 

310. Jewel, J. J.; and Heyson, H. H.: Charts of the Induced Velocities Near a Lifting Rotor. 

NASA Memo 4-15-59L, May 1959. 

311. Huston, R. J.: Wind-Tunnel Measurements of Performance, Blade Motions, and Blade 

Air Loads for Tandem-Rotor Configurations With and Without Overlap. NASA TND-1971, Oct. 1963. 
4. REFERENCES 

720 

312. Pruyn, R. R.; and Alexander, W. T.: USAAVLABS Tandem Rotor Airloads 

Measurement Program. American Institute of Aeronautics and Astronautics (AIAA) J. 

Aircraft, vol. 4, no. 3, 1967. 

313. Pruyn, R. R., et al.: Inflight Measurement of Rotor Blade Airloads, Bending Moments 

and Motions, Together With Rotor Shaft Loads and Fuselage Vibration, on a Tandem 

Rotor Helicopter. USAVLABS TR 67-9, U.S. Army Aviation Material Laboratories, 

Ft. Eustis, Va. (see also Boeing Document D8-0382), 1967. 

314. Pearcy, A.: Douglas Propliners. Shrewsbury, England: Airlife Publishing, Ltd., 1995. 

315. Anon.: Project Hummingbird, Economic Report—The Helicopter and Other V/STOL 

Aircraft in Commercial Transport Service. Federal Aviation Agency, Economic 

Branch, Office of Plans (Call No. TL 718 1960 U), Nov. 1960. 

316. Davies, R. E. G.: Airlines of the United States Since 1914. Washington, D.C.: 

Smithsonian Institution Press, 1972. 

317. Anon.: A Technical Summary and Compilation of Characteristics and Specifications 

on Steep-Gradient Aircraft. Federal Aviation Agency, Aircraft Branch, Air Commerce 

Div., Office of Plans (Call No. TL 718 1960 U), 1961. 

318. Anon.: Civil Air Regulations, Part 7—Rotorcraft Airworthiness; Transport Categories. 

Civil Aeronautics Board, Washington, D.C., 1956. 

319. Anon.: Type Certificate Data Sheet No. H8SO (Model HH-52A, SH-62). Department 

of Transporation, Federal Aviation Administration, Washington, D.C., 2003. 

320. Anon.: Type Certificate Data Sheet No. 1H15 (Sikorsky S-61L). Department of 

Transporation, Federal Aviation Administration, Washington, D.C., 2003. 

321. Anon.: Type Certificate Data Sheet No. 1H16 (Boeing Model 107-II). Department of 

Transporation, Federal Aviation Administration, Washington, D.C., 2007. 

322. Gerber, P. J.; and Weiland, C.: Detailed Specification, Vertol 107-II-10 Airliner 

Helicopter (for New York Airways) Twin Turbine Engine, Tandem Rotor. Report No. 

107-X-13, Boeing Airplane Co., Vertol Div., Philadelphia, Pa., 1960. 

323. Anol, R. K.; McConkey, E. D.; Edwin, D.; and Hawley, R. J.: Helicopter Rejected 

Takeoff Airspace Requirements. DOT/FAA/RD-90/7, Systems Control Technology 

Inc., Arlington, Va., Aug. 1991. 

324. Cole, J. L. et al.: Development and Qualification of the S-76C+ Helicopter with 30-

Second/2-Minute OEI Power Ratings. J. American Helicopter Society, vol. 46, no. 2, 

2001. 

325. Hall, S. R.; Yang, K. Y.; and Hall, K. C.: Helicopter Rotor Lift Distribution for 

Minimum-Induced Power Loss. American Institute of Aeronautics and Astronautics 

(AIAA) J. Aircraft, vol. 31, no. 4, 1994. 

326. Wachspress, D. A.; Quackenbush, T. R.; and Solomon, C. L.: On Minimum Induced 

Power of the Helicopter Rotor. CDI Report No. 05-04, Continuum Dynamics, Inc., 

Ewing, N.J., 2005. 

327. Rand, O.; Khromov, V.; and Peyran, R. J.: Minimum-Induced Power Loss of a 

Helicopter Rotor via Circulation Optimization. American Institute of Aeronautics and 

Astronautics (AIAA) J. Aircraft, vol. 41, no. 1, 2004. 
4. REFERENCES 

721 

328. Hall, K. C.; and Hall, S. R.: A Variational Method for Computing the Optimal 

Aerodynamic Performance of Conventional and Compound Helicopters. J. American 

Helicopter Society, vol. 55, no. 4, 2010. 

329. Hunt, W. E.: Heelicopter. London, England: Airlife Publishing Ltd., 1998. 

330. Kowalonek, J. M.: Email to F. D. Harris; VS-300 World Endurance Record. 2007. 

331. Bréguet, L.: Aerodynamical Efficiency and the Reduction of Air Transport Costs. J. 

Royal Aeronautical Society, vol. 26, 1922. 

332. Cavcar, M.: Bréguet Range Equation? American Institute of Aeronautics and 

Astronautics (AIAA) J. Aircraft, vol. 43, no. 5, Sept–Oct. 2006. 

333. Von Parseval, A.: Lindbergh’s Flight. NACA TM 423, 1927. 

334. Hall, D. H.: Technical Preparation of the Airplane “Spirit of St. Louis.” NACA TN 

257, July 1927. 

335. Hufton, P. A.; Nutt, A. E. W.; and Bigg, F. J.: General Investigation Into the 

Characteristics of the C.30 Autogiro. Aeronautical Research Committee R&M No. 

1859, Mar. 1939. 

336. Fries, G.; and Wiesner, W.: A Summary of References, Methods and Procedures 

Useful in Estimating Parasite Drag. Kellett Aircraft Corp. Engineering Report 

1430.12, Feb. 1945. 

337. Hoerner, S. F.: Fluid-Dynamic Drag. Brick Town, N.J.: Author Published, 1965. 

338. Harrington, R. D.: Reduction of Helicopter Parasite Drag. NACA TN 3234, Aug. 

1954. 

339. G. E. Dausman: Private letter to J. Diamond; Helicopter Drag Data. July 25, 1960. 

340. Sweet, G. E.; and Jenkins, J. L., Jr.: Wind Tunnel Tests of Four Helicopter Fuselage 

Models and Various Appendages in the Langley 7- by 10-Foot Wind Tunnel. NASA 

Preliminary Data Report L-1470 (see also NASA TN-D-1363), 1960. 

341. Jenkins, J. L., Jr.; Sweet, G. E.; and Winston, M. M.: Full-Scale Wind Tunnel Tests of 

an Aerodynamically Clean Helicopter Fuselage and Appendages. NASA Preliminary 

Data Report L-1469 (see also NASA TN-D-1364), 1960. 

342. Moser, H., Lt.: Full-Scale Wind Tunnel Investigation of Helicopter Drag. J. American 

Helicopter Society, vol. 6, no. 1, 1961. 

343. Flood, R. L.; Rohtert, R. E.; and La Forge, S. V.: Aerodynamic Tests of an 

Operational OH-6A Helicopter in the Ames 40’ x 80’ Wind Tunnel. HTC-AD Report 

No. 369-A-8020, Hughes Tool Co., Aircraft Div., Culver City, Calif. (see also ASTIA 

AD 742891), May 1970. 

344. Squires, P. K.: Investigation of Correlation Between Full-Scale and Fifth-Scale Wind 

Tunnel Tests of a Bell Helicopter Textron Model 222. NASA CR-166362, June 1982. 

345. Williams, R. M., Chairman: Special Report by the Ad Hoc Committee on Rotorcraft 

Drag. Proc. American Helicopter Society 31st Annual National Forum, Washington, 

D.C., May 13–15, 1975. 

346. Venegoni, M.; Magni, E.; and Baldassarrini, R.: An Industrial Rational for the 

Aerodynamic Design of the Fuselage for a High Performance Light Helicopter. Paper 

No. 44, Proc. Third European Rotorcraft and Powered Lift Aircraft Forum, Aix-enProvence, France, Sept. 1977. 
4. REFERENCES 

722 

347. Perry, F. J.: Aerodynamics of the Helicopter World Speed Record. Proc. 43rd Annual 

National Forum of the American Helicopter Society, St. Louis, Mo., May 18–20, 

1987. 

348. Jones, J. P.: The Helicopter Rotor. J. Royal Aeronautical Society, vol. 74, no. 719, 

1970. 

349. Jones, J. R.; and Lund, P. D.: Full-Scale Investigation of Rotor Hub Fairing for a 

Sikorsky H-5 Rotor Hub. McCulloch Motors Corp. Report No. 55McC103R (ASTIA 

AD No. 93925), 1955. 

350. Harris, F. D.: An Overview of Autogyros and The McDonnell XV-1 Convertiplane. 

NASA/CR-2003-212799, Oct. 2003. 

351. Culver, I. H.: Designing the High-Speed Rigid Rotor Helicopter. J. Astronautics and 

Aerospace Engineering, June 1963. 

352. Heppe, R. R.: The Single-Rotor Helicopter With Rigidly-Mounted Blades. J. Royal 

Aeronautical Sciences, vol. 67, no. 634, 1963, pp. 651–663. 

353. Hibbard, H. L.; and Heppe, R. R.: Concept and Development of a Simple, Stable, and 

Economic VTOL Vehicle. IAS Paper No. 62-18, Proc. Institute of the Aerospace 

Sciences 30th Annual Mtg., New York, N.Y., Jan 22–24, 1962. 

354. Logan, A. H.; Prouty, R. W.; and Clark, D. R.: Wind Tunnel Tests of Large- and 

Small-Scale Rotor Hubs and Pylons. USAAVRADCOM TR 80-D-21, U.S. Army 

Aviation Research and Development Command, Ft. Eustis, Va., 1981. 

355. Sung, D. Y.; Lance, M. B.; Young, L. A.; and Stroub, R. H.: An Experimental 

Investigation of Helicopter Rotor Hub Fairing Drag Characteristics. NASA-TM102182, Sept. 1989. 

356. Gabriel, E.: Wind Tunnel Test and Analysis Report of Flow Visualization Test of a 

One-Third-Scale HC-1B Rotor Hub with Blade Shank Fairings. Report No. R-285, 

Boeing Airplane Co., Vertol Div., Philadelphia, Pa., 1962. 

357. Bousman, W. G.; Ormiston, R. A.; and Mirick, P. H.: Design Considerations for 

Bearingless Rotor Hubs. Paper No. A-83-39-62-1000, Proc. 39th Annual Forum of the 

American Helicopter Society, St. Louis, Mo., May 9–11, 1983. 

358. Alldridge, P. J.: High-Speed Rotor Performance Methodology—Investigation of the 

Aerodynamic Characteristics of the Integrated Technology Hub. BHT Engineering 

Interoffice Memo 81:PA/dd-1070, Bell Helicopter Textron, Inc., Ft. Worth, Tex, 1986. 

359. B. Ormiston: Letter to F. D. Harris; Rotor Hubs. June 30, 1993. 

360. Schindler, R.; and Pfisterer, E.: Impacts of Rotor Hub Design Criteria on the 

Operational Capabilities of Rotorcraft Systems. AGARD CP-423, Rotorcraft Design 

for Operations Symposium, Amsterdam, The Netherlands, Oct. 13–16, 1986. 

361. Hanson, T. F.: A Designer Friendly Handbook of Helicopter Rotor Hubs. Newhall, 

Calif.: Author Published, 2005. 

362. Mosinskis, V. S.; and Schneider, E.: Design and Development of an ElastomericBearing Rotor Hub. Proc. 24th Annual National Forum of the American Helicopter 

Society, Washington, D.C., 1968. 

363. Culver, I. H.; and Rhodes, J. E.: Structural Coupling in the Blades of Rotating Wing 

Aircraft. IAS Paper No. 62-33, Proc. 30th Annual Mtg. of the Institute of Aerospace 

Sciences, New York, N.Y., Jan. 22–24, 1962. 
4. REFERENCES 

723 

364. Cardinale, S.: Soft In-plane Matched-Stiffnes/Flexure-Root-Blade Rotor System 

Summary Report. USAAVLABS TR 68-72, U.S. Army Aviation Material 

Laboratories, Ft. Eustis, Va., 1969. 

365. Harris, F. D.; Cancro, P. A.; and Dixon, P. G. C.: The Bearingless Main Rotor. Proc. 

Third European Rotorcraft and Powered-Lift Aircraft Forum, Aix-en-Provence, 

France, Sept. 1977. 

366. Dixon, P. G. C.; and Bishop, H. E.: The Bearingless Main Rotor. J. American 

Helicopter Society, vol. 25, no. 3, 1980. 

367. Harris, F. D.; and Dixon, P. G. C.: Boeing BMR Preliminary Design—Volume C, 

Oral Briefing. Boeing Vertol Report D210-11120-1, Boeing Vertol Co., Philadelphia, 

Pa., 1976. 

368. Staley, J. A.; Gabel, R.; and MacDonald, H. I.: Full-Scale Ground and Air Resonance 

Testing of the Army-Boeing Vertol Bearingless Main Rotor. Preprint no. 79-23, Proc. 

35th Annual National Forum of the American Helicopter Society Washington, D.C., 

May 21–23, 1979. 

369. Dawson, S.: An Experimental Investigation of the Stability of a Bearingless Model 

Rotor in Hover. Proc. 38th Annual Forum of the American Helicopter Society, 

Anaheim, Calif., May 4–7, 1982. 

370. Huber, H.: “Will Rotor Hubs Lose Their Bearings?” A Survey of Bearingless Main 

Rotor Development. Paper No. 506, Proc. 18th European Rotorcraft Forum, Avignon, 

France, Sept. 15–18, 1992. 

371. Norman, T. R.; Cooper, C. R.; Fredrickson, C. A.; and Herter, J. R.: Full-Scale Wind 

Tunnel Evaluation of the Sikorsky Five-Bladed Bearingless Main Rotor. Proc. 49th 

Annual Forum of the American Helicopter Society, St. Louis, Mo., May 19–21, 1993. 

372. Johnson, W.: Recent Developments in the Dynamics of Advanced Rotor Systems. 

AGARD Lecture Series No. 139, Helicopter Aeromechanics (also see DTIC ADA155946), Apr. 1985. 

373. Harvey, K. W.: Aeroelastic Analysis of a Bearingless Rotor. Symposium on Rotor 

Technology sponsored by the Mideast Region of the American Helicopter Society, 

Arlington, Tex., Aug. 11–13, 1976. 

374. Nguyen, K.; McNulty, M.; Anand, V.; and Lauzon, D.: Aeroelastic Stability of the 

McDonnell Douglas Advanced Bearingless Rotor. Proc. 49th Annual Forum of the 

American Helicopter Society, St. Louis, Mo., May 19–21, 1993. 

375. Donham, R. E.; Cardinale, S. V.; and Sachs, I. B.: Ground and Air Resonance 

Characteristics of a Soft In-Plane Rigid-Rotor System. AIAA Paper No. 69-205, Proc. 

AIAA/AHS VTOL Research, Design, and Operations Mtg., Atlanta, Ga., 1969. 

376. Churchill, G. B.; and Harrington, R. D.: Parasite-Drag Measurements of Five 

Helicopter Rotor Hubs. NASA Memo 1-31-59L, Feb. 1959. 

377. Keys, C. N.; and Wiesner, R.: Guidelines for Reducing Helicopter Parasite Drag. J. 

American Helicopter Society, vol. 20, no. 1, 1975. 

378. Sheehy, T. W.: A General Review of Helicopter Rotor Hub Drag Data. J. American 

Helicopter Society, vol. 22, no. 2, 1977. 

379. Keys, C. N.; and Rosenstein, H. J.: Summary of Rotor Hub Drag Data. NASA CR152080, Mar. 1978. 
4. REFERENCES 

724 

380. Teleki, A.: High-Speed Flight Tests With the Bo. 105. The Aeronautical Journal, vol. 

79, no. 778, Oct. 1975, pp. 425–430. See also DGLR76-222, 9th Annual DGLR mtg., 

Munich, Germany, Sept. 1976. 

381. Martin, D. M.; Mort, R. W.; Young, L. A.; and Squires, P. K.: Experimental 

Investigation of Advanced Hub and Pylon Fairing Configurations to Reduce 

Helicopter Drag. NASA TM-4540, Sept. 1993. 

382. Fradenburgh, E. A.: The First 50 Years Were Fine....But What Should We Do for an 

Encore. J. American Helicopter Society, vol. 40, no. 1, 1995. 

383. Fradenburgh, E. A.: High-Performance Single Rotor Helicopter Study. U.S. Army 

Transportation Research Command Report No. TREC 61-44, 1961. 

384. Obukata, M.; and Nakadate, M.: Aerodynamic Design of Bearingless Rotor Hub. 

Paper 98 T1-2, Heli Japan 98, Gifu, Japan, Apr. 21–23, 1998. 

385. Lynn, R. R.: Fifty Years of Challenge. Royal Aeronautical Society, 37th Cierva 

Memorial Lecture, London, England, Oct. 1996. 

386. Prouty, R. W.; and Yackle, A. R.: The Lockheed AH-56 Cheyenne—Lessons Learned. 

AIAA Paper No. 92-4278, Proc. AIAA Aircraft Design Systems Mtg., Hilton Head, 

S.C., Aug. 24–26, 1992. 

387. Amer, K. B.; Prouty, R. W.; Korkosz, G.; and Fouse, D.: Lessons Learned During the 

Development of the AH-56A Apache Attack Helicopter. Proc. 48th Annual Forum of 

the American Helicopter Society, Washington, D.C., June 3–5, 1992. 

388. Yeo, H.; Bousman, W. G.; and Johnson, W.: Performance Analysis of a Utility 

Helicopter with Standard and Advanced Rotors. Proc. American Helicopter Society 

Aerodynamics, Acoustics, and Test and Evaluation Specialists’ Mtg., San Francisco, 

Calif., Jan. 23–25, 2002. 

389. Harris, F. D.; Kocurek, J. D.; McLarty, T. T.; and Trept, T. J.: Helicopter Performance 

Methodology at Bell Helicopter Textron. Preprint No. 79-2, Proc. 35th Annual 

National Forum of the American Helicopter Society, Washington, D.C., May 21–23, 

1979. 

390. Anderson, W. D.: REXOR Rotorcraft Simulation Model, Volume I—Engineering 

Documentation. USAAMRDL-TR-76-28A, U.S. Army Air Mobility Research and 

Development Laboratories, Ft. Eustis, Va., 1976. 

391. Potsdam, M. P.; Yeo, H.; and Johnson, W.: Rotor Airloads Prediction Using Loose 

Aerodynamic/Structural Coupling. Proc. American Helicopter Society 60th Annual 

Forum, Baltimore, Md., June 7–10, 2004. (Also see AIAA J. Aircraft, vol. 43, no. 3, 

May–June 2006.) 

392. Yeo, H.; and Johnson, W.: Prediction of Rotor Structural Loads with Comprehensive 

Analysis. J. American Helicopter Society, vol. 53, no. 2, 2008. 

393. Bhagwat, M. J.; and Ormiston, R. A.: Examination of Rotor Aerodynamics in Steady 

and Maneuvering Flight Using CFD and Conventional Methods. Proc. American 

Helicopter Society Specialists’ Conference on Aeromechanics, San Francisco, Calif., 

Jan 23–25, 2008. 

394. Berry, J. D.: Unsteady Velocity Measurements Taken Behind a Model Helicopter 

Rotor Hub in Forward Flight. NASA TM-4738, Mar. 1997. 
4. REFERENCES 

725 

395. Le Chuiton, F.; Kneisch, T.; Schneider, S.; and Kramer, P.: Industrial Validation of 

Numerical Aerodynamics About Rotor Heads: Towards a Design Optimisation at 

Eurocopter. Proc. 35th European Rotorcraft Forum, Hamburg, Germany, Sept. 22–25, 

2009. 

396. Vogel, F.; Brietsamter, C.; and Adams, N. A.: Aerodynamic Investigation on a 

Helicopter Main Rotor Hub. Proc. 66th Annual Forum of the American Helicopter 

Society, Phoenix, Ariz., May 11–13, 2010. 

397. Bridgeman, J. O.; and Lancaster, G. T.: Physics-Based Analysis Methodology for Hub 

Drag Prediction. Proc. 66th Annual Forum of the American Helicopter Society, 

Phoenix, Ariz., May 11–13, 2010. 

398. de la Cierva, J.: New Developments of the Autogyro. J. Royal Aeronautical Society, 

vol. 39, no. 8, Dec. 1935. 

399. Moore, H.: Twirlybirdings: Recollections From the Early Days of Helicopter Training. 

AHS Vertiflite, vol. 52, no. 3, 2006. 

400. Wagner, R. A.: Vibration Handbook for Helicopters. Prewitt Aircraft Co., 1954. 

401. Gerstenberger, W. et al.: The Rotary Round Table: How Can Helicopter Vibration Be 

Minimized? J. American Helicopter Society, vol. 2, no. 3, 1957. 

402. White, R. P.; and Yeates, J. E. (Eds.): Vol I—Propeller and Rotor Aerodynamics; Vol 

II—Propulsion and Interference; and Vol. III—Aerodynamic Research on Boundary 

Layers. CAL/USAAVLABS Symposium, Buffalo, N.Y., June 22–24, 1966. 

403. Carter, E.S., Jr.: Rotorcraft Dynamics. NASA SP-352, Feb. 1974. 

404. Gabel, R.: When Helicopter Smooth Surpasses Jet Smooth. Proc. American Helicopter 

Society Northeast Region National Specialists’ Mtg. on Helicopter Vibration, 

Hartford, Conn., Nov. 2–4, 1981. 

405. Loewy, R. G.: Helicopter Vibrations: A Technology Perspective. J. American 

Helicopter Society, vol. 29, no. 4, 1984. 

406. Hansford, R. E.; and Vorwald, J.: Dynamics Workshop on Rotor Vibratory Loads. 

Proc. 52nd Annual Forum of the American Helicopter Society, Washington, D.C., 

June 4–6, 1996. 

407. Griffen, M. J.: Handbook of Human Vibration. London, England: Elsevier Academic 

Press, 2004. 

408. Rosen, J.; and Arcan, M.: Modeling the Human Body/Seat System in a Vibration 

Environment. J. Biomechanical Engineering, vol. 125, 2003. 

409. Anon.: MIL-H-8501. Helicopter Flying and Ground Handling Qualities; General 

Requirements for. Department of Defense, Washington, D.C., Nov. 1952. 

410. Anon.: MIL-H-8501A. Helicopter Flying and Ground Handling Qualities: General 

Requirements for. Department of Defense, Washington, D.C., Sep. 1961 w/amend. 

Apr. 1962. 

411. Gabel, R.; Henderson, B. O.; and Reed, D. A.: Pilot and Passenger Vibration 

Environment Sensitvity. J. American Helicopter Society, vol. 16, no. 3, 1971. 

412. Schrage, D. P., Captain; and Peskar, R. E.: Helicopter Vibration Requirements. Proc. 

33rd Annual National Forum of the American Helicopter Society, Washington, D.C., 

May 9–11, 1977. 
4. REFERENCES 

726 

413. Prouty, R. W.: Vibration Criteria: Finding Discomfort Levels. Rotor & Wing 

International, Mar. 1992. 

414. Crews, S. T.; Lewis, W. D.; and Dulaney, K. E.: Requirements for Rotorcraft 

Vibration Specifications, Modeling and Testing. U.S. Army Aviation Engineering 

Directorate, ADS-27A-SP, 2006. 

415. Crews, S. T.: Army Helicopter Crew Seat Vibration—Past Performance, Future 

Requirements. Preprint No. 3, Proc. American Helicopter Society Northeast Region 

National Specialists’ Mtg. on Helicopter Vibration, Hartford, Conn., Nov. 2–4, 1981. 

416. Chen, Y.; Wickramasinghe, V.; and Zimick, D. G.: Investigation of Helicopter Seat 

Structural Dynamics for Aircrew Vibration Mitigation. J. American Helicopter 

Society, vol. 56, no. 1, 2011. 

417. Anon.: MIL-HDBK-5J. Metallic Materials and Elements for Aerospace Vehicle 

Structures. Department of Defense, Washington, D.C., 2003. 

418. Anon.: Composite Materials Handbook, Vol. 1. Polymer Matrix Composites 

Guidelines for Characterization of Structural Materials: U.S. Department of Defense, 

Washington, D.C., 2002. 

419. Anon.: Composite Materials Handbook, Vol. 2. Polymer Matrix Composites Materials 

Properties: U.S. Department of Defense, Washington, D.C., 2002. 

420. Anon.: Composite Materials Handbook, Vol. 3. Polymer Matrix Composites Materials 

Usage, Design, and Analysis: U.S. Department of Defense, Washington, D.C., 2002. 

421. Anon.: Composite Materials Handbook, Vol. 4. Metal Matrix Composites. U.S. 

Department of Defense, Washington, D.C., 2002. 

422. Anon.: Composite Materials Handbook, Vol. 5. Ceramic Matrix Composites. U.S. 

Department of Defense, Washington, D.C., 2002. 

423. Caldwell, F. W.: Conventional Propeller Calculations. SAE Paper No. 180041, 

Transactions of the Society of Automobile Engineers, vol. 1, no. 1, 1918. 

424. Nelson, J. H.: The Strength of One-Piece Solid, Build-Up and Laminated Wood 

Airplane Wing Beams. NACA Report No. 35, 1920. 

425. Hartman, E. C.: Comparison of Weights of 17ST and Steel Tubular Structural 

Members Used in Aircraft Construction. NACA TN 378, May 1931. 

426. Schatzberg, E.: Wings of Wood, Wings of Metal. Princeton, N.J.: Princeton University 

Press, 1999. 

427. Miner, M. A.: Cumulative Damage in Fatigue. J. Applied Mechanics, vol. 12, no. 3, 

1945. 

428. Cooper, W. E.: Materials and the Fatigue Aspect. J. Helicopter Association of Great 

Britain, vol. 4, no. 3, 1950. 

429. Williams, J. K.: The Fatigue Problem With Emphasis on the Airworthiness Aspects. J. 

Helicopter Association of Great Britain, vol. 5, no. 1, 1951. 

430. Hirch, H.; and Kline, J.: An Experimental Investigation of the H-5 Variable Stiffness 

Blade Program. Part 3. Evaluation of Rotor Resonance Bending Effects. WADC Air 

Force TR 6329, Part 3. (See AD No. 8445 for Part 1, AD No. 8444 for Part 2, AD No. 

6265 for Part 3, AD No. 6161 for Part 4, AD No. 6794 for Part 5, and AD No. 8443 

for Part 6), 1952. 
4. REFERENCES 

727 

431. Yeates, J. E.; Brooks, G. W.; and Houbolt, J. C.: Flight and Analytical Methods for 

Determining the Coupled Vibration Response of Tandem Helicopters. NACA Report 

1326, 1957. 

432. Bender, G. L.; Yamakawa, G. M.; Herbst, M. K.; Sullivan, P. J.; Robbins, R. D.; and 

Williams, R. A.: Airworthiness and Flight Characteristics Test (A&FC) of the CH47D Helicopter. USAAEFA Project No. 82-07, U.S. Army Aviation Engineering 

Flight Activity, Edwards Air Force Base, Calif., 1984. 

433. Laing, E. J.: Army Helicopter Vibration Survey Methods and Results. J. American 

Helicopter Society, vol. 19, no. 3, 1974. 

434. Johnson, J. C.; and Priser, D. B.: Vibration Levels in Army Helicopters—

Measurement Recommendations and Data. USAARL Report No. 81-5, U.S. Army 

Aeromedical Research Laboratory, Biodynamics Research Div., Ft. Rucker, Ala., 

1981. 

435. Laing, E. J.: Vibration and Temperature Survey Production UH-1H Helicopter. 

USAASTA Project No. 70-15-2, U.S. Army Aviation Systems Test Activity, Edwards 

Air Force Base, Calif., 1973. 

436. Millott, T. A.; Wong, J. K.; Correia, J. R.; Goodman, R. K.; Welsh, W. A.; and Cassil, 

C. E.: Risk Reduction Flight Test of a Pre-Production Active Vibration Control 

System for the UH-60M. Proc. 59th Annual Forum of the American Helicopter 

Society, Phoenix, Ariz., May 6–8, 2003. 

437. Snyder, W. J.; Cross, J. L.; and Kufeld, R. M.: NASA/Army Rotor Systems Flight 

Research Leading to the UH-60 Airloads Program. Innovations in Rotorcraft Test 

Technology for the 1990s, Proc. AHS Specialists’ Mtg., Phoenix, Ariz., Oct. 8–12, 

1990. 

438. Watts, M. E.; and Cross, J. L.: The NASA Modern Technology Rotors Program. Paper 

No. AIAA-86-9788, Proc. AIAA/AHS/CASI/DGLR/ISA/ITEA/SETP/SFE 3rd Flight 

Testing Conference, Las Vegas, Nev., Apr. 2–4, 1986. 

439. Studebaker, K.: A Survey of Hub Vibration for the UH-60A Airloads Research 

Aircraft. Proc. American Helicopter Society Aeromechanics Specialists’ Conference, 

San Francisco, Calif., 1994. 

440. Silveira, M. A.; and Brooks, G. W.: Analytical and Experimental Determination of the 

Coupled Natural Frequencies and Mode Shapes of a Dynamic Model of a SingleRotor Helicopter. NASA Memo 11-5-58L, 1958. 

441. Ricks, R. G.: A Study of Tandem Helicopter Fuselage Vibration. ASD-TDR-62-284 

(AD 0290317), Air Force Systems Command, Aeronautical Systems Div., WrightPatterson Air Force Base, Ohio, Sept. 1962. 

442. Gabel, R.: AVID Program—Advanced Vibration Development. Boeing Vertol Report 

107M-D-09 (now 62-0177-f), Boeing Vertol Co., Philadelphia, Pa, 1965. 

443. Rutkowski, M. J.: The Vibration Charteristics of a Coupled Helicopter Rotor-Fuselage 

by a Finite Element Analysis. NASA TP-2118 (see also AVRADCOM TR 82-A-15), 

Jan. 1983. 

444. Anon.: Final Report for NASTRAN Project. NASA CR-112405, Mar. 1970. 
4. REFERENCES 

728 

445. Dinyovszky, P.; and Twomey, W. J.: Plan, Formulate, and Discuss a NASTRAN 

Finite Element Model of the UH-60A Helicopter Airframe. NASA CR-181975, Feb. 

1990. 

446. Howland, G. R.; Durno, J. A.; and Twomey, W. J.: Ground Shake Test of the UH-60A 

Helicopter Airframe and Comparison With NASTRAN Finite Element Model 

Predictions. NASA CR-181993, Mar. 1990. 

447. Idosor, F. R.; and Seible, F.: NASTRAN Modeling of Flight Test Components for the 

UH-60A Airloads Program Test Configuration. NASA CR-193614, Feb. 1993. 

448. Kvaternik, R. G.: The NASA/Industry Design Analysis Methods for Vibrations 

(DAMVIBS) Program—A Government Overview. NASA TM-107579, Apr. 1992. 

449. Kvaternik, R. G.: Langley Rotorcraft Structural Dynamics Program—Background, 

Status, Accomplishments, Plans. NASA TM-101618, June 1989. 

450. Domka, R. V.: Investigation of Difficult Component Effects on FEM Vibration 

Prediction for the AH-1G Helicopter. Proc. 44th Annual American Helicopter Society 

National Forum, Washington, D.C., June 16–18, 1988. 

451. Cronkhite, J. D.: A Government/Industry Summary of the Design Analysis Methods 

for Vibrations (DAMVIBS) Program, Kvaternik, R. G. (Ed.); also see The 

Nasa/Industry Design Analysis Methods for Vibration (DAMVIBS) Program—Bell 

Helicopter Textron Accomplishments. Apr. 13–15, 1992. 

452. Smith, F. C.; and Howard, D. M.: Calculation and Measurement of Normal Modes of 

Vibration of an Aluminum-Alloy Box Beam With and Without Large Discontinuities. 

NACA TN 2884, Jan. 1953. 

453. Cronkhite, J. D.; Dompka, R. V.; Rogers, J. P.; Corrigan, J. C.; Perry, K. S.; and 

Sadler, S. G.: Coupling Rotor/Fuselage Dynamic Analysis of the AH1G Helicopter 

and Correlation With Flight Vibrations Data. NASA CR-181723, Jan. 1989. 

454. DiTaranto, R. A.; and Sankewitsch, V.: Calculation of Flight Vibration Levels of the 

AH-1G Helicopter and Correlation With Existing Flight Vibration Measurements. 

NASA CR-181923, Nov. 1989. 

455. Sangha, K.; and Shamie, J.: Correlation of AH-1G Airframe Flight Vibration Data 

With a Coupled Rotor-Fuselage Analysis. NASA CR-181974, Aug. 1990. 

456. Sopher, R.; and Twomey, W. J.: Calculation of Flight Vibration Levels of the AH-1G 

Helicopter and Correlation with Existing Flight Vibration Measurements. NASA CR182031, Apr. 1990. 

457. Cronkhite, J. D.; Berry, V. L.; and Brunken, J. E.: A NASTRAN Vibration Model of 

the AH-1G Helicopter Airframe. U.S. Army Armament Command Report No. R-TR74-045 (Vol. I—ADA 009482, Vol. II—ADA 009483), 1974. 

458. Domka, R. V.; and Cronkhite, J. D.: Summary of AH-1G Flight Vibration Data for 

Validation of Coupled Rotor-Fuselage Analysis. NASA CR-178160, Nov. 1986. 

459. Shockey, G. A.; Williamson, J. W.; and Cox, C. R.: AH-1G Helicopter Aerodynamics 

and Structural Loads Survey. USAAMRDL TR-76-39, U.S. Army Air Mobility 

Research and Development Laboratories, Ft. Eustis, Va., 1976. 

460. Gessow, A.; and Crim, A. D.: A Method for Studying the Transient Blade-Flapping 

Behavior of Lifting Rotors at Extreme Operating Conditions. NACA TN 3366, Jan. 

1955. 
4. REFERENCES 

729 

461. Van Gaasbeek, J. R.: Validation of the Rotorcraft Flight Simulation Program (C81) 

Using Operational Loads Survey Flight Test Data. USAAVRADCOM TR-80-D-4, 

U.S. Army Aviation Research and Development Command, Ft. Eustis, Va., July 1980. 

462. Kvaternik, R. G.: A Government/Industry Summary of the Design Analysis Methods 

for Vibrations (DAMVIBS) Program. NASA CP-10114, Jan. 1993. 

463. Yeo, H.; and Chopra, I.: Coupled Rotor/Fuselage Vibration Analysis for Teetering 

Rotor and Test Data Comparison. American Institute of Aeronautics and Astronautics 

(AIAA) J. Aircraft, vol. 38, no. 1, Jan.–Feb. 2001. 

464. Bousman, W. G.: Rotorcraft Airloads Measurements—Extraordinary Costs, 

Extraordinary Benefits. Proc. 67th Annual Forum of the American Helicopter Society, 

Virginia Beach, Va., May 3–5, 2011. 

465. Romander, E.; Norman, T. R.; and Chang, I.: Correlating CFD Simulation With Wind 

Tunnel Test for the Full-Scale UH-60A Airloads Rotor. Proc. 67th Annual Forum of 

the American Helicopter Society, Virginia Beach, Va., May 3–5, 2011. 

466. Durno, J. A.; Howland, G. R.; and Twomey, W. J.: Comparison of Black Hawk Shake 

Test Results with NASTRAN Finite Element Analysis. Proc. 43rd Annual Forum of 

the American Helicopter Society, St. Louis, Mo., May 18–20, 1987. 

467. Idosor, F. R.; and Seible, F.: NASTRAN Modeling of Flight Test Components for 

UH-60A Airloads Program Test Configuration. NASA CR-193614, Feb. 1993. 

468. Goodman, R.: UH-60A NASA/AEFA Configuration Ground Vibration Test Results. 

SER-701619, Sikorsky Aircraft, Stratford, Conn., 1990. 

469. Johnson, W.: Milestones in Rotorcraft Aeromechanics. NASA/TP-2011-215971, May 

2011. 

470. Caradonna, F. X.; Tung, C.; and Desopper, A.: Finite Difference Modeling of Rotor 

Flows Including Wake Effects. J. American Helicopter Society, vol. 29, no. 2, 1984. 

471. Tung, C.; Caradonna, F. X.; and Johnson, W.: The Prediction of Transonic Flows on 

an Advancing Rotor. J. American Helicopter Society, vol. 31, no. 3, 1986. 

472. Datta, A.; Sitaraman, J.; Baeder, J. D.; and Chopra, I.: Prediction of UH-60 Main 

Rotor Structural Loads Using CFD/Comprehensive Analysis Coupling. Proc. 32nd 

European Rotorcraft Forum, Maastricht, The Netherlands, Sept. 12–14, 2006. 

473. Potsdam, M. P.; Yeo, H.; and Johnson, W.: Rotor Airloads Prediction Using Loose 

Aerodynamic/Structural Coupling. American Institute of Aeronautics and Astronautics 

(AIAA) J. Aircraft, vol. 43, no. 3, 2006. 

474. Datta, A.; Nixon, M.; and Chopra, I.: Review of Rotor Loads Prediction with the 

Emergence of Rotorcraft CFD. J. American Helicopter Society, vol. 52, no. 4, 2007. 

475. Lim, J. W.: Improved Performance Prediction for Bo-105 Model Rotor in Cruise 

Using Computational Fluid Dynamics. Proc. 37th European Rotorcraft Forum, Ticino 

Park, Italy, Sept. 13–15, 2011. 

476. Norman, T. R.; Shinoda, P. M.; Kitaplioglu, C.; Jacklin, S. A.; and Sheikman, A.: 

Low-Speed Wind Tunnel Investigation of a Full-Scale UH-60 Rotor System. Proc. 

58th Annual Forum of the American Helicopter Society, Montreal, Canada, June 11–

13, 2002. 
4. REFERENCES 

730 

477. van Aken, J. M.; Shinoda, P. M.; and Haddad, F.: Development of a Calibration Rig 

for a Large Multi-Component Rotor Balance. 46th International Instrumentation 

Symposium of the Instrument Society of America, Bellevue, Wash., Apr. 30–May 4, 

2000. 

478. Peterson, R. L.; and van Aken, J. M.: Dynamic Calibration of the NASA Ames Rotor 

Test Apparatus Steady/Dynamic Rotor Balance. NASA TM-110393, Apr. 1996. 

479. Bain, L. J.: Comparison of Theoretical and Experimental Model Blade Vibratory 

Shear Forces. AAVLABS TR66-77, U.S. Army Aviation Material Laboratories, Ft. 

Eustis, Va., 1967. 

480. Gabel, R.; Sheffler, M.; Tarzanin, F.; and Hodder, D.: Wind Tunnel Modeling of 

Rotor Vibratory Loads. J. American Helicopter Society, vol. 28, no. 2, 1983. 

481. Norman, T. R.; Shinoda, P.; Peterson, R. L.; and Datta, A.: Full-Scale Wind Tunnel 

Test of the UH-60A Airloads Rotor. Proc. 67th Annual Forum of the American 

Helicopter Society, Virginia Beach, Va., May 3–5, 2011. 

482. Bailey, F. J., Jr.; and Gustafson, F. B.: Observations in Flight of the Region of Stalled 

Flow over the Blades of an Autogiro Rotor. NACA TN 741, Dec. 1939. 

483. Gustafson, F. B.; and Myers, G. C., Jr.: Stalling of Helicopter Blades. NACA TN 

1083, June 1946. 

484. Gustafson, F. B.; and Gessow, A.: Effect of Blade Stalling on the Efficiency of a 

Helicopter Rotor as Measured in Flight. NACA TN 1250, Apr. 1947. 

485. Falabella, G.; and Meyer, J. R.: Determination of Inflow Distributions from 

Experimental Aerodynamic Loading and Blade-Motion Data on a Model Helicopter 

Rotor in Hovering and Forward Flight. NACA TN 3492, Nov. 1955. 

486. Tanner, W. H.; and Wohlfeld, R. M.: New Experimental Techniques in Rotorcraft 

Aerodynamics and Their Application. J. American Helicopter Society, vol. 15, no. 2, 

1970. 

487. Harris, F. D.: A Note about Self-Induced Velocity Generated by a Lifting-Line Wing 

or Rotor Blade. NASA/CR-2006-213478, Feb. 2006. 

488. Yen, J. G.; and Yuce, M.: Correlation of Pitch-Link Loads in Deep Stall on 

Bearingless Rotors. J. American Helicopter Society, vol. 37, no. 4, 1992. 

489. Kufeld, R.; and Loschke, P.: UH-60 Airloads Program: Status and Plans. Proc. AIAA 

Aircraft Design Systems and Operations Mtg., Baltimore, Md., Sept. 23–25, 1991. 

490. Veca, A. C.: Vibration Effects on Helicopter Reliability and Maintainability. 

USAAMRDL TR 73-11, U.S. Army Air Mobility Research and Development 

Laboratories, Ft. Eustis, Va., 1973. 

491. Richards, E. J.: Problems of Noise in Helicopter Design. J. Helicopter Association of 

Great Britain, vol. 9, no. 1, 1955. 

492. Stein, J. (Ed.): The Random House Dictionary of the English Language. New York, 

N.Y.: Random House, Inc., 1967. 

493. Fletcher, H.; and Munson, W. A.: Loudness, Its Definition, Measurement and 

Calculation. J. Acoustical Society of America, vol. 5, 1933, pp. 82–108. 

494. Anon.: ISO 226:2003. Acoustics—Normal Equal-Loudness-Level Contours. 

International Organization for Standardization, Geneva, Switzerland, 2003. 
4. REFERENCES 

731 

495. Robinson, D. W.; and Dadson, R. S.: A Re-determination of the Equal-Loudness 

Relations for Pure Tones. British J. Applied Physics, vol. 7, 1956. 

496. Kryter, K. D.: Scaling Human Reactions to the Sound from Aircraft. J. Acoustical 

Society of America, vol. 31, no. 11, 1959. 

497. Kryter, K. D.: The Meaning and Measurement of Perceived Noise Level. Noise 

Control Engineering Journal (NCEJ), Sept./Oct. 1960. 

498. van der Linden, F. R.: Airlines & Airmail—The Post Office and the Birth of the 

Commercial Aviation Industry. Lexington Ky.: The University Press of Kentucky, 

2002. 

499. Hammack, J. B.; Kurbjun, M. C.; and O’Bryan, T. C.: Flight Investigation of a 

Supersonic Propeller on a Propeller Research Vehicle at Mach Numbers to 1.01. 

NACA RM L57E20, July 10, 1957. 

500. Kurbjun, M. C.: Noise Survey of a 10-Foot Four-Blade Turbine-Driven Propeller 

Under Static Conditions. NACA TN 3422, July 1955. 

501. Kurbjun, M. C.: Noise Survey of a Full-Scale Supersonic Turbine-Driven Propeller 

Under Static Conditions. NACA TN 4059, July 1957. 

502. Kurbjun, M. C.: Noise Survey Under Static Conditions of a Turbine-Driven Full-Scale 

Modified Supersonic Propeller With an Advance Ratio of 3.2. NACA TN 4172, Jan. 

1958. 

503. Kurbjun, M. C.: Noise Survey Under Static Conditions of a Turbine-Driven Transonic 

Propeller With an Advance Ratio of 4.0. NASA Memorandum 4-18-59L, May 1959. 

504. O’Bryan, T. C.; and Hammack, J. B.: Flight Performance of a Transonic TurbineDriven Propeller Designed for Minimum Noise. NASA Memorandum 4-19-59L, May 

1959. 

505. Hammack, J. B.; and O’Bryan, T. C.: Effect of Advance Ratio on Flight Performance 

of a Modified Supersonic Propeller. NACA TN 4389, Sept. 1958. 

506. Hubbard, H. H.: Propeller-Noise Charts for Transport Airplanes. NACA TN 2968, 

June 1953. 

507. Gutin, L.: On the Sound Field of a Rotating Propeller. NACA TM 1195, Oct. 1948. 

508. Yudin, E. Y.: On the Vortex Sound from Rotating Rods. NACA TM 1136, Mar. 1947. 

509. Evans, A. J.; and Liner, G.: A Wind Tunnel Investigation of the Aerodynamic 

Characteristics of a Full-Scale Supersonic-Type Three-Bladed Propeller at Mach 

Numbers to 0.96. NACA Report 1375, 1958. 

510. Hager, R. D.; and Vrabel, D.: Advanced Turboprop Project. NASA SP-495, 1988. 

511. Vogeley, A. W.: Flight Mearsurements of Compressibility Effects on a Three-Bladed 

Thin Clark Y Propeller Operating at Constant Advanced-Diameter Ratio and Blade 

Angle. NACA WR L-505, 1945. 

512. Hansen, J. R.: Engineer In Charge—A History of the Langley Aeronautical 

Laboratory, 1917–1958: NASA SP-4305, 1987. 

513. Vogeley, A. W.: Sound-Level Measurements of a Light Airplane Modified to Reduce 

Noise Reaching the Ground. NACA TR 926, 1948. 

514. Henderson, H. R.; Pegg, R. J.; and Hilton, D. A.: Results of the Noise Measurment 

Program on a Standard and Modified OH-6A Helicopter. NASA TN D-7216, Sept. 

1973. 
4. REFERENCES 

732 

515. Ferrell, K. R.: Limited Stability and Control Evaluation of the S-62A Helicopter. 

AFFTC-TR-61-8, Air Force Flight Test Center, Edwards Air Force Base, Calif., Mar. 

1961. 

516. Pegg, R. J.; Henderson, H. R.; and Hilton, D. A.: Results of the Flight Noise 

Measurement Program Using a Standard and Modified SH-3A Helicopter. NASA TN 

D-7330, Dec. 1973. 

517. Hayden, J. S.; and Lake, W. R.: YH-32 Limited Performance and Stability. AFFTCTR-58-23, Air Force Flight Test Center, Edwards Air Force Base, Calif., 1958. 

518. Hayden, J. S.; and Lake, W. R.: Performance Evaluation of the Djinn Helicopter. 

AFFTC-TR-60-8, Air Force Flight Test Center, Edwards Air Force Base, Calif., 1960. 

519. Deming, A. F.: Propeller Rotation Noise Due to Torque and Thrust. NACA TN 747, 

Jan. 1940. 

520. Stowell, E. Z.; and Deming, A. F.: Vortex Noise From Rotating Cylindrical Rods. 

NACA TN 519, Feb. 1935. 

521. Williams. J. E. F; and Hawkings, D. L.: Sound Generation by Turbulance and Surfaces 

in Arbiturary Motion. Philosophical Transactions of the Royal Society of London, vol. 

264, no. 1151, May 1969. 

522. Brentner, K. S.; and Farassat, F.: Modeling Aerodynamically Generated Sound of 

Helicopter Rotors. Progress in Aerospace Sciences, vol. 39, 2003, pp. 83–120. 

523. Hennes, C. H.; Lopes, L.; Shirey, J.; and Erwin, J.: PSU-WOPWOP 3.3 User’s Guide. 

Pennsylvania State University, University Park, Pa., 2007. 

524. Gopalan, G.; and Schmitz, F. H.: Understanding Far Field Near-In-Plane High Speed 

Harmonic Helicopter Noise in Hover: Governing Parameters and Active Control 

Possibilities. Proc. American Helicopter Society Specialists’ Conference on 

Aeromechanics, San Francisco, Calif., Jan. 2008. 

525. Magliozzi, B.; Metzger, F. B.; Bausch, W.; and King, R. J.: A Comprehensive Review 

of Helicopter Noise Literature. FAA-RD-75-79, Systems Research and Development 

Service, Federal Aviation Administration, Washington, D.C., June 1975. 

526. Fryer, B. A.: Publications in Acoustics and Noise Control From the NASA Langley 

Research Center During 1940–1979. NASA TM-80211, Jan. 1980. 

527. Anon.: Helicopter Acoustics. NASA CP-2052-PT-1. Proc. International Specialists’ 

Symposium, NASA Langley Research Center, Hampton, Va., May 22–24, 1978. 

528. Anon.: NASA CP-2495, Vols. 1, 2, and 3. NASA/Army Rotorcraft Technology. Vol. 

1: Aerodynamics, and Dyamcs and Aeroelasticity; Vol. 2: Materials and Structures, 

Propulsion and Drive Systems, Flight Dynamics and Control, and Acoustics; and 

Vol. 3: Systems Integration, Research Aircraft, and Industry. NASA Ames Research 

Center, Moffett Field, Calif., 1988. 

529. George, A. R.; and Kim, Y. N.: Helicopter Noise: State-of-the-Art. American Institute 

of Aeronautics and Astronautics (AIAA) J. Aircraft, vol. 15, no. 11, Nov. 1978. 

530. Yamauchi, G. K.; and Young, L. A.: A Status of NASA Rotorcraft Research. 

NASA/TP-2009-215369, Sept. 2009. 

531. Deming, A. F.: Noise From Propellers With Symmetrical Sections at Zero Blade 

Angle, II. NACA TN 679, Dec. 1938. 
4. REFERENCES 

733 

532. Hicks, C. W.; and Hubbard, H. H.: Comparison of Sound Emission From Two-Blade, 

Four-Blade, and Seven-Bladed Propellers. NACA TN 1354, July 1947. 

533. Hubbard, H. Y. H.; and Lassiter, L. W.: Some Aspects of the Helicopter Noise 

Problem. NACA TN 3239, Aug. 1954. 

534. Hubbard, H. H.: Noise Characteristics of Helicopter Rotors at Tip Speeds up to 900 

Feet Per Second. J. Acoustical Society of America, vol. 32, no. 9, 1960. 

535. Cox, C.; and Lynn, R. R.: A Study of the Origin and Means of Reducing Helicopter 

Noise. TCREC TR-62-73, Bell Helicopter Textron Inc., Ft. Worth, Tex., Nov. 1962. 

536. Powell, A.: Theory of Vortex Sound. J. Acoustical Society of America, vol. 36, no. 1, 

1964. 

537. Schlegel, R.; King, R.; and Mull, H.: Helicopter Rotor Noise Generation and 

Propagation. USAAVALABS TR 66-4, U.S. Army Aviation Material Laboratories, 

Ft. Eustis, Va., Oct. 1966. 

538. Sternfeld, H., Jr.: Influence of the Tip Vortex on Helicopter Rotor Noise. AGARD 

CP-22, Gottingen, Germany, Sept. 1967. 

539. Leverton, J. W.: Helicopter Noise—Blade Slap. Part 1: Review and Theoretical Study. 

NASA CR-1221, Oct. 1968. 

540. Leverton, J. W.: Helicopter Noise—Blade Slap. Part 2: Experimental Results. NASA 

CR-1983, Mar. 1972. 

541. Robinson, F.: Component Noise Variables of a Light Observation Helicopter. NASA 

CR-114761, 1973. 

542. Hubbard, H. H.: Sound Measurements for Five Shrouded Propellers at Static 

Conditions. NACA TN 2024, Apr. 1950. 

543. Hubbard, H. H.; and Lassiter, L. W.: Oscilating Pressures Near a Static Pusher 

Propeller at Tip Mach Numbers Up to 1.2 With Special Reference to the Effects of the 

Presence of the Wing. NACA TN 3202, July 1954. 

544. Hubbard, H. H.: Aeroacoustics of Flight Vehicles: Theory and Practice. Vol. 1—Noise 

Sources, Vol. 2—Noise Control. NASA RP 1258, Aug. 1991. 

545. Hubbard, H. H.: Aeroacoustic of Flight Vehicles: Theory and Practice. Volume 1: 

Noise Sources. NASA RP 1258-Vol-1, Aug. 1991. 

546. Cox, C. R.; and Lynn, R. R.: A Study of the Orgin and Means of Reducing Helicopter 

Noise. U.S. Army Transportation Research Command TREC TR 62-73, 1962. 

547. Schmitz, F.: Gaurav Gopalan 1975–2011. AHS Vertiflite, vol. 57, no. 4, 2011. 

548. Barlow, W. H.; McCluskey, W. C.; and Ferris, H. W.: OH-6A Phase II Quiet 

Helicopter Program. USAMRDL TR 72-29, U.S. Army Air Mobility Research and 

Development Laboratories, Ft. Eustis, Va., Sept. 1972. 

549. Hilton, D. A.; Henderson, H. R.; and Pegg, R. J.: Ground Noise Measurements During 

Flyover, Hover, Landing, and Take-off Operations of a Standard and a Modified HH43B Helicopter. NASA TM X-2226, Feb. 1971. 

550. Chiles, J. R.: Air America’s Black Helicopter—The Secret Aircraft That Helped the 

CIA Tap Phones in North Vietnam. Air & Space, Mar. 2008. 

551. Anon.: Noise Standards for Helicopters in the Normal, Transport, and Restricted 

Categories. Code of Federal Regulations (CFR) Title 14: Aeronautics and Space; Parts 

21 and 36, 1979. 
4. REFERENCES 

734 

552. Anon.: Fly Neighborly Guide: Helicopter Association International, Alexandria, Va., 

2012. 

553. Cox, C. R.: Helicopter Noise Reduction and Its Effects on Operations. J. American 

Helicopter Society, vol. 15, no. 1, 1970. 

554. Halwes, D.: Flight Operations to Minimize Noise. AHS Vertiflite, vol. 17, no. 2, 1971. 

555. Cox, C. R.: How to Operate the Medium Helicopter More Quietly. U.S. Army 

Aviation Digest, vol. 19, no. 9, 1973. 

556. Anon.: Annex 16—Enviromental Protection, Volume I—Aircraft Noise. International 

Civil Aviation Organization (ICAO), Montreal, Canada. 2012. 

557. Anon.: Code of Federal Regulations (CFR) Title 14: Aeronautics and Space; Part 36—

Noise Standards: Aircraft Type and Airworthiness Certification, Appendices H and J, 

2012. 

558. Anon.: Code of Federal Regulations (CFR) Title 14: Aeronautics and Space; Part 36—

Noise Standards: Aircraft Type and Airworthiness Certification, Appendix A2, 

Section A36.4. 2012. 

559. Schmitz, F.; and Boxwell, D.: In-Flight Far-Field Measurement of Helicopter 

Impulsive Noise. J. American Helicopter Society, vol. 21, no. 4, 1976. 

560. Schmitz, F.; and Yu, Y. H.: Theoretical Modeling of High-Speed Helicopter Impulsive 

Noise. J. American Helicopter Society, vol. 24, no. 1, 1979. 

561. Brentner, K. S.; and Farassat, F.: Helicopter Noise Prediction: The Current Status and 

Future Direction. J. Sound and Vibration, vol. 170, no. 1, 1994, pp. 79–96. 

562. Boxwell, D. A.; Schmitz, F. H.; Splettstoesser, W. R.; and Schultz, K. J.: Model 

Helicopter Rotor High-Speed Impulsive Noise: Measured Acoustics and Blade 

Pressures. NASA TM-85850, Sept. 1983. 

563. Schmitz, F. H.; and Yu, Y. H.: Helicopter Impulsive Noise: Theoretical and 

Experimental Status. NASA TM-84390, Nov. 1983. 

564. Boxwell, D. A.; and Schmitz, F. H.: Full-Scale Measurements of Blade-Vortex 

Interaction Noise. Proc. 36th Annual Forum of the American Helicopter Society, 

Washington, D.C., May 13–14, 1980. 

565. Yamauchi, G. K.; Signor, D. B.; Watts, M. E.; Hernandez, F. J.; and LeMasurier, P.: 

Flight Measurements of Blade-Vortex Interaction Noise Including Comparisons With 

Full-Scale Wind Tunnel Data. J. American Helicopter Society, vol. 41, no. 4, 1996. 

566. Signor, D. B.; Watts, M. E.; Hernandez, F. J.; and Felker, F. F.: Blade-Vortex 

Interaction Noise: A Comparison of In-Flight, Full-Scale and Small-Scale 

Measurements. Proc. AHS Aeromechanics Specialists’ Conference, San Francisco, 

Calif., Jan 19–21, 1994. 

567. Splettstoesser, W. R.; Schultz, K. J.; Boxwell, D. A.; and Schmitz, F. H.: Helicopter 

Model Rotor-Blade Vortex Interaction Impulsive Noise: Scalability and Parametric 

Variations. NASA TM-86007, Dec. 1984. 

568. Zinner, R. A.; Boxwell, D. A.; and Spencer, R. H.: Review and Analysis of 

DNW/Model 360 Rotor Acoustic Data Base. NASA TM-102253, Nov. 1989. 

569. Dawson, S.; Jordan, D.; Smith, C.; Ekins, J.; Silverthorn, L.; and Tuttle, B.: HARP 

Model Rotor Test at DNW. Proc. 45th American Helicopter Society Annual Forum, 

Boston, Mass., May 22–24, 1989. 
4. REFERENCES 

735 

570. Liu, S. R.; and Marcolini, M. A.: The Acoustic Results of a United Technologies Scale 

Model Helicopter Rotor Tested at DNW. Proc. 46th Annual Forum and Technology 

Display of the American Helicopter Society, Washington, D.C., May 21–23, 1990. 

571. Yu, Y. H., et al.: The HART-II Test: Rotor Wakes and Aeroacoustics With HigherHarmonic Pitch Control (HHC) Inputs—The Joint German/French/Dutch/U.S. Project. 

Proc. American Helicopter Society 58th Annual Forum, Montreal, Canada, June 11–

13, 2002. 

572. Boxwell, D. A.; Yu, Y. H.; and Schmitz, F. H.: Hovering Impulsive Noise—Some 

Measured and Calculated Results. Vertica—The International Journal of Rotorcraft 

and Powered Lift Aircraft, vol. 3, no. 1, 1979. 

573. Baeder, J. D.: Euler Solution to Nonlinear Acoustics of Non-Lifting Hovering Rotor 

Blades. Proc. International Technical Specialists’ Mtg., Rotorcraft Acoustics and 

Rotor Fluid Dynamics, Philadelphia, Pa., Oct. 15–17, 1991. 

574. Brooks, T. F.; Boyd, D. D.; Burley, C. L.; and Jolly, J. R.: Aeroacoustic Codes for 

Rotor Harmonic and BVI Noise—CAMRAD.Mod 1/Hires. J. American Helicopter 

Society, vol. 45, no. 2, 2000. 

575. Brooks, T. F.; and Burley, C. L.: Blade Wake Interaction Noise for a Main Rotor. J. 

American Helicopter Society, vol. 49, no. 1, 2004. 

576. Burley, C. L.; and Brooks, T. F.: Rotor Broadband Noise Prediction With Comparison 

to Model Data. J. American Helicopter Society, vol. 49, no. 1, 2004. 

577. Howlett, J. T.; Clevenson, S. A.; Rupf, J. A.; and Snyder, W. J.: Interior Noise 

Reduction in a Large Civil Helicopter. NASA TN D-8477, July 1977. 

578. Cox, C. R.: Helicopter Noise Certification Experience and Compliance Cost 

Reductions. Proc. 19th European Rotorcraft Forum, Cernpbbio (Como), Italy Sept. 

14–16, 1993. 

579. Marze, H. J.: Helicopter External Noise: ICAO Standards and Operational 

Regulations. Proc. Eighth European Rototcraft and Powered Lift Aircraft Forum, Aixen-Provence, France, Aug. 31–Sept. 3, 1982. 

580. Conner, D. A.; Burley, C. L.; and Smith, C. D.: Flight Acoustic Testing and Data 

Acquistion for the Rotor Noise Model (RNM). Proc. 62nd American Helicopter 

Society Annual Forum, Phoenix, Ariz., May 9–11, 2006. 

581. Johnson, C. L.: Kelly—More Than My Share of It All: Smithsonian Books, 

Washington, D.C., 1985. 

582. Augustine, N. R.: Augustine’s Laws and Major System Development Programs: 

American Institute of Aeronautics and Astronautics, 1984. 

583. Anon.: The Official Helicopter Blue Book®, vols. XIV and later: HeliValue$, Inc., 

Wauconda, Ill., 2010. 

584. Harris, F. D.; and Scully, M. P.: Rotorcraft Cost Too Much. J. American Helicopter 

Society, vol. 43, no. 1, 1998. 

585. Lloyd’s Aviation Dept. (complier): Aircraft Types and Prices. London, England: 

Lloyd’s of London Press, 1974. 

586. Shute, N.: Stephen Morris. Heather Felicity Norway and Union Trustee Company of 

Australia, Ltd., 1961. 
4. REFERENCES 

736 

587. Harper, W.; and Richey, M.: Comanche RAH-66: Lessons Learned. U.S. Army 

Program Executive Office (PEO) Aviation, Ft. Rucker, Ala., 1995. 

588. Galindo, J. L.: A Case History of the United States Army RAH-66 Comanche 

Helicopter. Master’s Thesis, Naval Postgraduate School, Monterey, Calif., 2000. 

589. McNerney, W. J., President: The Boeing Company 2011 Annual Report. The Boeing 

Company, Chicago, Ill., 2012. 

590. Anon.: Helicopter Growth History Report. Forge Aerospace, Inc., Oct. 1978. 

591. Wright, T. P.: Factors Affecting the Cost of Airplanes. J. Aeronautical Sciences, vol. 

3, no. 4, 1936. 

592. Raborg, R. W.: Mechanics of the Learning Curve. Aero Digest, vol. 65, no. 5, 1952. 

593. Anon.: Source Book of World War II Basic Data: Airframe Industry, Vol. I—Direct 

Man-Hours – Progress Curves. Army Air Forces, Air Material Command (see also 

DTIC ADA 800199), 1946. 

594. Alchian, A.: Reliability of Progress Curves in Airframe Production. RM-260-1, The 

RAND Corp., Santa Monica, Calif., Feb. 1950. 

595. Joiner, W.: Private correspondance email to Frank Harris dated April 24, 2012. 

596. Arrow, K.: The Economic Implications of Learning by Doing. The Review of 

Economic Studies, vol. 29, 1962. 

597. Benkard, C. L.: Learning and Forgetting: The Dynamics of Aircraft Production. The 

American Economic Review, vol. 90, no. 4, 2000. 

598. Nichols, J. B.: Sources of Helicopter Development and Manufacturing Costs. IAS 

Report No. 59-11, Proc. IAS 27th Annual Mtg., New York, N.Y., Jan. 26–29, 1959. 

599. Anon.: Joint Design-to-Cost Guide, Life Cycle Cost as a Design Parameter. DTIC 

ADA048254, Departments of the U.S. Army, Navy, and Air Force, 1976. 

600. Anon.: MIL-STD-881C. Work Breakdown Structures (WBS) for Defense Material 

Items. Department of Defense, Washington, D.C., Oct. 2011. 

601. Heinemann, E. H.; and Rausa, R.: Ed Heinemann—Combat Aircraft Designer. 

Annapolis, Md.: Naval Institute Press, May 1980. 

602. Anderson, J. L.: Price Determination of General Aviation, Helicopter, and Transport 

Aircraft. SAWE Paper No. 1224. Proc. 37th Annual Conference of the Society of 

Allied Weight Engineers, Inc., Munich, W. Germany, May 8–10, 1978. 

603. Dubey, M.; and Yackle, A. R.: Establishing a Designer’s Cost Target. Preprint No. 

712, Proc. 29th AHS Annual National Forum, Washington, D.C., May 1973. 

604. Lew, J. N.: Planning a General-Aviation Product. J. Astronautics & Aeronautics, Jan. 

1977. 

605. Dix, D. M.: Projecting Cost-Performance Trade-Offs for Military Vehicles. J. 

Astronautics & Aeronautics, Sept. 1976. 

606. Bedard, P.: LHX in Trouble. Defense Week, vol. 7, no. 44, 1986. 

607. Anon.: DoD Acquisition—Case Study of the Army Light Helicopter Program. 

GAO/NSIAD-86-45S-1, U.S. General Accounting Office, 1986. 

608. Anon.: Defense Update—LH Team Scoring Analyzed. Rotor & Wing, June 1991, 

p. 10. 

609. Harvey, D. S.: First Team’s Perspective on the LH Competition. Rotor & Wing, June 

1991, pp. 70–71. 
4. REFERENCES 

737 

610. Anon.: 1300 Comanches Replace 3100 Old Warriors. Boeing Sikorsky Advertisement 

in Army Magazine, June 1992. 

611. Anon.: Defense Update—Boeing Sikorsky Reveals Design Change for Comanche 

Rotor. Rotor & Wing, Dec. 1991. 

612. Bond, D. F.: Army Boosts RAH-66 Weight by 6%, Plans Extra Equipment. Aviation 

Week & Space Technology, Jan. 13, 1992. 

613. Lytie, T.: Sikorsky’s Comanche Helicopter Imperiled. New Haven Register, New 

Haven, Conn., June 11, 1992. 

614. Bolkcom, C.: Army Aviation: The RAH-66 Comanche Helicopter Issue. CRS 

RS20522, Congressional Research Service, Library of Congress, Jan. 9, 2002. 

615. Morris, J.: Army Cancels RAH-66 Comanche Helicopter After 20 Years, $8 Billion. 

Aviation Week, Feb. 24, 2004. 

616. McDaniels, R.: An Assessment of Developmental Risk for the RAH-66 Comanche 

Helicopter Development. Personal communication to F. D. Harris, Sept. 1991. 

617. McDaniels, R.: The Case for Terminating the RAH-66 Comanche Helicopter 

Development. Personal communication to F. D. Harris, 1992. 

618. Tishchencho, M. N.; Nagaraj, V. T.; and Chopra, I.: Preliminary Design of Transport 

Helicopters. J. American Helicopter Society, vol. 48, no. 2, 2003. 

619. Jackson, P.; Peacock, L.; and Munson, K. (Eds.): Jane’s All The World’s Aircraft 

2011–2012. London, England: Jane’s Information Group, May 2011. 

620. Anon.: National Defense Budget Estimates for FY 2012 (also called the Green Book). 

Office of the Under Secretary of Defense (Comptroller), Mar. 2011. 

621. Anon.: Consumer Price Index (All Urban Consumers). U. S. Department of Labor, 

Bureau of Labor Statistics, Washington, D.C., 2012. 

622. Patnode, C. A., Jr.: The Decision to Develope the UTTAS—A Case Study. DTIC AD765 438, U.S. Army War College, Carlisle Barracks, Penn., Mar. 13, 1972. 

623. Patnode, C. A., Jr.: Letter to F. D. Harris; comments on UTTAS Program. May 10, 

2012. 

624. Lammering, T.; Franz, K.; Risse, K.; Hoernschemeyer, R.; and Stumf, E.: Aircraft 

Cost Model for Preliminary Design Systhesis. AIAA 2012-0686, Proc. 50th AIAA 

Aerospace Mtg., Nashville, Tenn., Jan. 9–12, 2012. 

625. Burns, J. W.: Aircraft Cost Estimating Methodolgy and Value of a Pound Derivation 

for Preliminary Design Development Applications. J. Society of Allied Weight 

Engineers, Fall 1994. 

626. Brooks, P. W.: The Modern Airliner: Its Origins and Development. London, England: 

Putnam & Co. Ltd., 1961. 

627. Brooks, P. W.: The World’s Airliners. London, England: Putnam & Co. Ltd., 1962. 

628. Miller, R. E.; and Sawers, D.: The Technical Development of Modern Aviation. New 

York, N.Y.: Praeger Publications, 1970. 

629. Loftin, L. K., Jr.: Quest for Performance—The Evolution of Modern Aircraft. NASA 

SP-468, 1985. 

630. Warner, E. P.: Technical Development and Its Effect on Air Transportation: A 

Lecture: Norwich University, Northfield, Vt., 1938. 
4. REFERENCES 

738 

631. Harris, F. D.: Some Aviation History. Seminar at NASA Ames Research Center, 

Moffett Field, Calif., July 23, 2008 (rev. July 29, 2009). 

632. Anderson, J. L.; and Andrastek, D. A.: Operating Cost Model for Local Service 

Airlines. SAWE Paper No. 1098, Index Category No. 29, Proc. Society of Allied 

Weight Engineers 35th Annual Conference, Philadelphia, Pa., 1976. 

633. Maddalon, D. V.: Estimating Airline Operating Costs. NASA TM-78694, 1978. 

634. Anon.: Standard Method of Estimating Comparative Direct Operating Costs of 

Turbine Powered Transport Airplanes. Air Transportation Association of America, 

Dec. 1967. 

635. Brennan, T. J.; and Finizie, L. T.: Gas Turbine Cost Estimating. Proc. AIAA/SAE 

12th Propulsion Conference, Palo Alto, Calif., July 26–29, 1976. 

636. Harris, F. D.: An Economic Model of U.S. Airline Operating Expenses. NASA/CR2005-213476, Dec. 2005. 

637. Anon.: Operations Manual for Form 41 (inc. CD). Data Base Products, Inc., Dallas, 

Tex., 1999. 

638. Davies, R. E. G.: Air Transport Directions in the 21st Century (The Lessons of 

History). Handbook of Airline Economics, Aviation Week, Div. of the McGraw-Hill 

Co., 2002. 

639. Stoessel, R. F.; and Gallagher, J. E.: A Standard Method for Estimating VTOL 

Operating Expense (a More Realistic Approach). AIAA Paper No. 67-828, Proc. 

AIAA 4th Annual Mtg. and Technical Display, Anaheim, Calif., Oct. 23–27, 1967. 

640. Conklin, A.; and de Decker, W.: Aircraft Cost Evaluator—Helicopters. Conklin & de 

Decker, Orleans, Mass., 2011. 

641. Anon.: Sikorsky Commercial Links. Sikorsky Aircraft Corp., July 2005. 

642. Anon.: When America Flies, It Works. Air Transport Assocation (ATA) 2010 

Economic Report, Washington, D.C., 2011. 

643. Anon.: Guide for the Presentation of Helicopter Operating Cost Estimates. Economics 

Committee, Helicopter Association International (HAI), Alexandria, Va., 2010. 

644. Anon.: OH-58D System Specification AV-SS-NTSH-B10000A (special FCA edition). 

Bell Helicopter Textron, Inc., Ft. Worth, Tex., May 4, 1984. 

645. Anon.: RotorBreeze Q1 issue, Bell Helicopter Textron Inc., Ft. Worth, Tex., 2012. 

646. Pociask, M. J. (Ed.): 2009 Helicopter Annual, 27th Edition. The Helicopter 

Association International (HAI), Alexandria, Va., Jan. 2009. 

647. Anon.: R22 Illustrated Parts Catalog: Robinson Helicopter Co. Inc., Torrance, Calif., 

2007. 

648. Anon.: Bell Model 206A/B/B3 Illustrated Parts Breakdown Manual: Bell Helicopter 

Textron, Inc., Ft. Worth, Tex., 2001. 

649. Anon.: The Official Helicopter Specification Book. HeliValue$, Inc., Wauconda, Ill., 

2004. 

650. Anon: Bell Model 206 Series Maintenance Manual. Bell Helicopter Textron, Inc., Ft. 

Worth, Tex., 1998. 

651. Anon.: R22 Beta II Estimated Operating Costs. Robinson Helicopter Co., Torrance, 

Calif., 2012. 
4. REFERENCES 

739 

652. Norling, A. H.: Outlook for Vertical-Lift Aircraft in Scheduled Commercial 

Transportation. United Research Inc., Cambridge, Mass., 1963. 

653. Kruesi, F. E.: Civil Tiltrotor Development Advisory Committee Report to Congress. 

Volume I: Final Report (see ADA306654). U.S. Department of Transportation, 

Washington, D.C., Dec. 1995. 

654. Kruesi, F. E.: Civil Tiltrotor Development Advisory Committee Report to Congress. 

Volume 2: Technical Supplement (see ADA306655). U.S. Department of 

Transportation, Washington, D.C., 1995. 

655. Anon.: Helicopters. Report No. 198, American Society of Planning Officials, Chicago, 

Ill., 1965. 

656. Anon.: The World’s Air Transportation Services. Data as to Passengers, Mail, and 

Goods Carried by American and European Transportation Services. NACA TM 108, 

June 1922. 

657. Tete, A.: Organization and Exploitation of Regular Aerial Transportation Lines. 

NACA TM 83, Apr. 1922. 

658. Mayo, R. H.: Aviation and Insurance. NACA TM 93, May 1922. 

659. Anon.: Aircraft Accidents—Method of Analysis. NACA TR 308, Aug. 1928. 

660. Anon.: Aircraft Accidents—Method of Analysis. NACA TR 357, Jan. 1930. 

661. Anon.: Aircraft Accidents—Method of Analysis. NACA TR 576, June 1936. 

662. Anon.: Statistical Handbook of Civil Aviation. U.S. Department of Commerce, Civil 

Aeronautics Administration, Washington, D.C., 1944. 

663. Anon.: Current Procedures for Collecting and Reporting U.S. General Aviation 

Accident and Activity Data. Safety Report NTSB/SR-05/02, PB205-917002 (Notation 

7573A), National Transportation Safety Board Safety Report, Washington, D.C., 

2005. 

664. Anon.: Re-Registration and Renewal of Aircraft Registration. Code of Federal 

Regulations (CFR) Title 14: Aeronautics and Space; Parts 13, 47, and 91. U.S. 

Department of Transportation, Federal Aviation Administration, Washington, D.C., 

2010. 

665. Anon.: Rotorcraft Activity Survey. Executive Resource Associates, Inc., Arlington, 

Va. (also available as ADA 236698), 1989. 

666. Harris, F. D.; Kasper, E. F.; and Iseler, L. E.: U.S. Civil Rotorcraft Accidents, 1963 

through 1997. NASA/TM-2000-209597, Dec. 2000. 

667. Persinos, J. F.: I Am Not A Compromising Woman. Rotor & Wing, Feb. 1999. 

668. Allard, S.: CHC Presentation. International Helicopter Safety Symposium (IHSS), 

Montreal, Canada, Sept. 2005. 

669. Downey, D. A.: The International Safety Team. Heliprops, vol. 20, no. 3, 2008. 

670. Lamon, W.: Safety Saves $$ as Well as Lives. Rotor, Spring 1991. 

671. Harris, F. D.: No Accidents—That’s the Objective. J. American Helicopter Society, 

vol. 52, no. 1, 2007. 

672. Wood, T.: High Energy Rotor System. Proc. American Helicopter Society 32nd 

Annual Forum, Washington, D.C., May 10–12, 1976. 

673. Price, H. L.: Safety in Numbers—An Inaugural Lecture, The University of Leeds. 

West Yorkshire, England: Leeds University Press, 1967. 
4. REFERENCES 

740 

674. Johnson, W.; Yamauchi, G. K.; and Watts, M. E.: NASA Heavy Lift Rotorcraft 

Systems Investigation. NASA/TP-2005-213467, Dec. 2005. 

675. Scott, M. W.: Aircraft Design Considerations to Meet One Engine Inoperative Safety 

Requirements. NASA CR-2012-216037, Aug. 2012. 

676. Wood, T.: One Engine Inoperative (OEI) and Autorotation for Heavy Lift Rotorcraft 

System. NASA CR-2012-216038, Aug. 2012. 

677. Karapetyan, G.: Mi-26 Autorotational Landings. Proc. American Helicopter Society 

48th Annual Forum, Washington, D.C., June 3–5, 1992. 

678. Anon.: Low Speed Flight Characteristics Which Can Result in Unanticipated Right 

Yaw. RotorBreeze, May/June 1991. 

679. Dugan, D. C.; and Delamer, K. J.: The Implications of Handling Qualities in Civil 

Helicopter Accidents Involving Hover and Low Speed Flight. NASA/TM-2005-

213473, Nov. 2005. 

680. Anon.: Type Certificate Data Sheet (TCDS) No. H10WE, Rev. I. Department of 

Transportation, Federal Aviation Administration, Washington, D.C., Mar. 16, 1979. 

681. Robertson, R.: Danger in the Sky. The Arizona Republic—Final Edition, Phoenix, 

Ariz., Nov. 15, 1992. 

682. Anon.: Special Investigation Report—Robinson Helicopter Company R22 Loss of 

Main Rotor Control Accidents. NTSB/SIR-96/03, National Transportation Safety 

Board, Washington, D.C., Apr. 1996. 

683. Anderson, S. B.: Historical Overview of Stall/Spin Charcteristics of General Aviation 

Aircraft. AIAA J. Aircraft, vol. 16, no. 7, 1979. 

684. Lebow, C.C. et al.: Safety in the Skies—Personnel and Parties in NTSB Aviation 

Accident Investigations. RAND Publishing, Santa Monica, Calif., Feb. 2008. 

685. Boivin, D. L., Lt. Col.; and Forbes, D. T., Jr.: OH-6A Mishap Experience Report 

USAAAVS, U.S. Army Agency for Aviation Safety, Ft. Rucker, Ala., Oct. 1973. 

686. Labun, L. C.: Rotorcraft Crash Mishap Analysis. Safe, Inc., Tempe, Ariz., 2009. 

687. Waters, K. T.: Research Requirements to Improve Safety of Civil Helicopters. NASA 

CR-145260, Nov. 1977. 

688. Fox, R. G.: Helicopter Accident Trends. Proc. AHS-FAA-HAI National Specialists’ 

Mtg. on Vertical Flight Training Needs and Solutions, Arlington, Tex., Sept. 17–18, 

1987. 

689. Fox, R. G.: Measuring Risk in Single- and Twin-Engine Helicopters. American 

Helicopter Society 2nd Asian Vertiflite Seminar, Singapore, Feb 24, 1992. 

690. Fox, R. G.: Measuring Safety Investment Effectiveness Relative to Risks. Proc. 

American Helicopter Society 54th Annual Forum, Washington, D.C., May 20–22, 

1998. 

691. Schwirzke, M. F. J.: Near Term Gains in Rotorcraft Safety—Strategies for Investment. 

Workshop sponsored by NASA Ames Research Center, Moffett Field, Calif., Feb. 

1999. 

692. Hart, S. G. (Ed.): Final Report of the Helicopter Accident Analysis Team. Flight 

Control and Cockpit Integration Branch, Army/NASA Rotorcraft Div., NASA Ames 

Research Center, Moffett Field, Calif. July 1998 (Limited Distribution). 

693. Shute, N.: Slide Rule. London, England: William Heinemann Ltd., 1954. 
741 

APPENDIX A 

ROTORCRAFT STABILITY AND CONTROL IN HOVER 

 For the early helicopters, this subject might be better titled Control and Instability. 

The quadrotor helicopter in and about hover was, however, very nearly stable in both 

longitudinal/ pitch and lateral/roll because of its widely displaced rotors. The tandem rotor 

helicopter is nearly inherently stable in longitudinal/pitch for the same reason. However the 

tandem rotor helicopter lacks comparable stability in its lateral/roll motion because both rotor 

hubs lie in the plane of symmetry. The most inherently unstable helicopter is the single-mainrotor plus anti-torque tail rotor helicopter. Despite this shortcoming, this latter configuration 

has gained the widest acceptance because of its relative mechanical simplicity. A simple 

introduction to coupled longitudinal/pitch stability and control for the single-main-rotor 

helicopter provides considerable insight into the general problem. It also affords a jumpingoff point for more advanced study. 

Longitudinal/Pitch Equations of Motion 

 The simplified force-and-moment diagram for a single-main-rotor helicopter in hover 

was shown in Fig. 1-5 on page 10 and is repeated here for convenience. 

θcg

Ts

w

Hs

θcg

Ts

w

Hs

The primary forces and moments involved in longitudinal helicopter stability and 

control in hover. 
APPENDIX A 

742 

 The equations for all six components of motion can be reduced, based on more 

advanced work, to (1) fore and aft or longitudinal motion at nearly constant height and (2) 

helicopter pitching motion. The two equations describing the motion of this rotorcraft’s center 

of gravity (cg) are 

(1) 

2

cg

x cg S 2

W x

F W H 0, and

g t

∂

=− ×θ − − =

∂ 

(2) 

2

cg M hH M I 0 cg S P cg 2

t

∂ θ

=× + − =

∂  . 

These two equations of motion assume that rotor thrust (Ts) is equal to helicopter weight (W) 

and that the body pitch angle (θcg) is a small angle. The rotor inplane force, called the rotor 

H-force (Hs), acts in the rotor plane perpendicular to the rotor shaft and is positive when 

directed aft. Thus, the H-force acts at the hub, which is a distance (h) above the center of 

gravity. The rotor blades can introduce a hub pitching moment (MP). 

 Small perturbations from a trim condition in both longitudinal displacement (xcg) and 

body pitch angle are usually assumed when solving these simplified equations of motion. 

Also, it is common to replace the longhand notations of 2 2

cg ∂ ∂ x t and 2 2cg ∂θ ∂ t with 

cg cg Δ Δθ x and   and then dropping the subscript, cg, to study the engineering problem in 

shorthand. Following this notation practice leads to rewriting Eqs. (1) and (2) as 

(3) S

W x H W 0 , and

g

×Δ + Δ + ×Δθ = 

(4) P S I MhH0 ×Δθ− Δ − ×Δ =  . 

The fact that the problem is one of small perturbations is highlighted by using the Greek letter 

delta (Δ), which also gets dropped later in the analysis as you might have guessed. 

 The perturbations in the rotor force and moments are created as 

(5) SS S

S hub hub cyclic

hub hub cyclic

HH H H V , and V∂∂ ∂ Δ = × Δ + × Δθ + × Δδ

∂ ∂θ ∂δ

 

(6) PP P

P hub hub cyclic

hub hub cyclic

MMM M V

V

∂∂∂ Δ = × Δ + × Δθ + × Δδ

∂ ∂θ ∂δ

  . 

These simplified equations for perturbations in rotor force and moments do not include the 

effect of body accelerations, which do exist but can be assumed to be of second-order in 

importance. On the other hand, a provision is made in Eqs. (5) and (6) for the pilot input or 

control through the longitudinal cyclic stick motion (Δδcyclic). 
APPENDIX A 

743 

 It is important to note that the velocities at the rotor hub are not necessarily the same 

as those seen by the rotorcraft center of gravity. While there can be very important structural 

deformations between these two points within the body, only the geometry of the problem is 

considered in this elementary analysis. The velocity relations between the center of gravity 

and the hub as shown in Fig. 1-5 are 

(7) Δθ = Δθ = θ hub cg , 

(8) Δθ = Δθ = θ hub cg

  , and 

(9) Δ = Δ − × Δθ = − θ V x h xh hub cg cg

    . 

 The several relationships defined by Eqs. (3) through (9) can now be combined to 

rewrite the equations of motion a third time. First Eqs. (8) and (9) are inserted in Eqs. (5) and 

(6). Then the expanded expressions for ΔHS and ΔMP are substituted into Eqs. (3) and (4). 

Finally, a collection of terms is made. The result of these few steps is 

(10) v v ( ) W x H x H hH W H 0

g

+ + − θ+ θ+ δ= θ

 δ    , and 

(11) I h M hH M hH M hH x M hH 0 ( ) v v ( ) θ θ ( )( ) δδ δδ θ+ + − + θ− + − + δ=          . 

 Simplifying this math problem is really quite easy if a less classical approach is taken. 

You need only differentiate the moment equation, Eq. (11), once with respect to time, which 

defines the longitudinal acceleration called for in Eq. (10). Then this result, along with the 

longitudinal velocity from Eq. (11), are substituted into the force equation, Eq. (10). This 

quickly gives a third-order, ordinary differential equation for the body pitch motion of 

(12) 

( ) () ( )

( ) ( )( )

v v v v v

v v v v

WI W h M hH M hH IH M H M H g g

W M hH M hH M H M H W

g

θ θ θ θ

δδ δ δ

  θ+ + − + + θ+ − θ        

+ + θ= + δ+ − δ

      



. 

You have no doubt noticed at this point that some more shorthand has been applied in 

reaching the preceding result. All the force-and-moment partial derivatives that were written 

in longhand in Eqs. (5) and (6) have been replaced with a subscript notation. For example, 

∂HS/∂ Vhub has been replaced with Hv, and so on. 

Solutions to the Equations of Motion 

 There are three solutions to Eq. (12) that are of considerable interest. The first solution 

sheds light on the motion immediately following a wind gust or a pilot's abrupt control input. 

The second solution investigates the “stick-fixed” inherent stability characteristics. The third 

solution is obtained when the equations of motion are installed in a flight simulator, and a 

“pilot is put into the loop.” This third solution is more applicable to advanced work and will 
APPENDIX A 

744 

not be discussed further here.1 Generally, however, all three solutions accept the same initial 

conditions: that at time equals zero, the initial pitch angle and initial pitch rate are both zero 

(i.e., at t = 0, Δθcg = θ = 0 and d θ/dt = 0). Consider the time history solution around t = 0 first. 

 The solution to Eq. (12) for the first several seconds of a time history (i.e., from t = 0 

to, say, t = 4 or 5 seconds) is obtained in a very straightforward manner by assuming a 

Maclaurin power series in time. That is, let 

(13) 

2 3

(t) (0) (0) (0) (0)

tt t (A 13) 1! 2! 3!

− θ =θ +θ × +θ × +θ × +    

 

.

 

 Now consider a common situation where the rotorcraft is hit by a gust of wind (Vgust) 

that upsets the vehicle trim. Assume that the gust remains constant over the initial 4- or 

5-second time frame of interest. Or perhaps the pilot puts in an initial displacement of 

longitudinal cyclic stick (δcyclic) and then holds the stick fixed over these few seconds. This 

latter case would be a step input that can simulate a gust in a controlled manner. These 

preceding statements define the initial conditions of the problem in the following way. 

For t = 0, 

(14) 

( )

( ) ( ) ( )

( ) ( )

( ) ( )

cyclic step gust

v

gust step

v v

gust step

v v

v

v v

step

x0 0 and / or x V 0

gH x V from Eq. 10 0 W

M hH M hH

V from Eq. 11 I I

h M hH M hH g H

I W

g MH MH from Eq.12 WI

δ δ

θ θ

δ δ

= θ= δ =δ = θ=

=− δ =

+ + θ= + δ

    + −+   θ=− + θ  

 

− + δ

 

 

 



 

With these initial conditions, the power series solution approach to finding the rotorcraft pitch 

response in the first few seconds of motion yields directly 

(15) 

( ) ( ) ( )

( ) ( ) ( ) ( )

2 3

v v v v

gust v

2 3 3 v v v v

step v step

M hH tt g h M hH M hH

V H

I 26 I W

M hH g M H M H tt g t h M hH M hH

H .

I 2 6 I W IW 6

θ θ

δδ θ θ δ δ

+       + −+

θ=+ − +    

     

+ −       + −+   +δ − + + δ     

       

 

 

 

1 A simple solution using a small personal computer plus a “joy stick” will immediately show how hard a 

helicopter can be to hover. It is also fun! 
APPENDIX A 

745 

The longitudinal velocity is defined from Eq. (10) in terms of the pitch angle (θ) and its two 

derivatives with respect to time as 

(16) ( ) v v ( )

vv vv

h M hH M hH I

x

M hH M hH

θ θ   + −+   = θ+ θ       + +  

     . 

The distance the rotorcraft travels from the spot over the ground where the disturbance 

occurred is the integral of the relative velocity with respect to time. This distance is simply 

(17) ( ) t

gust 0

x x V dt = −   . 

 Now consider the second solution for longitudinal and pitch motion when the control 

is fixed. This is a matter of solving Eq. (12) in its homogeneous form where the right-hand 

side is set to zero. Information about the dynamic motion such as damping or lack of damping 

and the associated frequency of any mode that oscillates is generally sought. The solution 

method is available in any number of mathematical textbooks so only the result is given here: 

(18) ( )

( )

v v ( ) t Rt Rt

gust 2 2

M hH R

V e e cos t e sin t

I R

+ −   λ λ

θ =   − ω + ω   λ− +ω   ω  

. 

Again, the longitudinal velocity is defined from Eq. (10) in terms of the pitch angle (θ) and its 

two derivatives with respect to time. The parameters of λ, R, and ω that complete the solution 

are found by finding the roots to the following cubic: 

(19) ( ) ( )

( )

3 2

vv v

v v

WI W X h M hH M hH IH X

g g

MH MH X W 0

θ θ

θ θ

 

+ + −+ +        

+ − +=

 

 

. 

Given that the basic motion is oscillatory, this cubic will have one real root, λ, and a pair of 

complex roots, R ± i ω. Solving this cubic is a minor matter in this day and age. The cubic 

roots from Eq. (19) are, of course, then substituted into Eq. (18), which completes the solution 

of the stick-fixed stability problem. 

Stability Derivative Approximations 

 Six rotor stability derivatives must be defined to make practical use of the general 

solutions given above. The first-order approximations for the rotor H-force and hub pitching 

moment (MP ) were introduced in Volume I as 

(20) C

P 1S

Frb

M a

2

β = × , and 

(21) 

2

S d0 t

S S 1S S hub S

t T

2a R bcRV C H Ta T

V C 4

  σ λ   ρ = × − × ×θ +    ×μ γ    

 . 
APPENDIX A 

746 

You will recall from Volume I that the nomenclature involved here is: 

d0

2

4

f

R 2 32

f C t 0

R 2 b

C 0 0 0

a 5.73 per radian, blade airfoil lift curve slope

C 0.01 blade airfoil drag coefficient

bcR R rotor solidity

acR I blade Lock number

I r dm 2F R 3V blade moment of inertia

L W F r dm blade

b

=

≈

σ= π

γ=ρ

= ≈

=Ω ≈ ≈

β β





( )

2 2

T S t

S T

S hub

S

t t

centrifigual force

C T R V rotor thrust coefficient

C 2 rotor inflow negative for flow down

V cos V rotor advance ratio

V V

= ρπ

λ =−

α

μ= ≈

With this nomenclature in mind, the rotor H-force can be put in the more practical form of 

(22) 

2

T t d0

S 1S hub S

0

2 W 2C bcRV C H Wa

3 4

ρ = × + ×θ + ×μ Ω β

 . 

The middle term in the H-force equation accounts for a somewhat reduced level in damping 

provided to the rotorcraft by this inplane force. This effect was brought to the industry’s 

attention nearly simultaneously in 1950 by Rene Miller2 and by Ken Amer3 of the N.A.C.A. 

Amer’s results included the influence of forward speed. Amer showed that a potentially 

serious roll instability could occur at high speed, even for the single rotor helicopters of that 

day. Flight test data confirmed the undesirable trait. 

 The final approximation to have in hand deals with the longitudinal flapping (a1S). A 

reasonably accurate approximation for operation in and about hover is 

(23) T

1S T S hub 1C

16C 16 a 2C B

a

    = + ×μ − ×θ −     σ Ωγ    

 . 

 The six rotor derivatives can be written down almost by inspection, simply by 

referring to Eqs. (20, 22, and 23) and following the chain rule. An example of the chain rule is 

P P 1S S

v

hub 1S S hub

M Ma M

Va V

∂ ∂∂∂μ = = ××

∂ ∂ ∂μ ∂ . 

 

2 Miller, R.: Helicopter Control and Stability in Hovering Flight. Journal of the Aeronautical Sciences, Aug. 

1948. 

3 Amer, K. B.: Theory of Helicopter Damping in Pitch and Roll and a Comparison with Flight Measurements. 

NACA TN 2136, 1950. 
APPENDIX A 

747 

Thus, the four stability derivatives are approximated to the first order as 

(24) 

( )

( )

( )

( )

2

T t d0

v T

t t

T

0

C T

v T

t

C

16C 1 1 bcRV C a H W 2C

a V 4V

16 32 W 2C

b HW

3

Frb 16C 1 c M 2C

2a V

Frb 16 dM .

2

θ

β

β

θ

    ρ =× + ×+ ×       σ  

  − =× +     γΩ Ωβ

 

=×+ ×     σ

  − = ×     γΩ





In a similar manner, the two control derivatives are approximated to the first order as 

(25) 

( ) ( )

( ) ( )

1C

C 1C

B a H W 1 , and

Frb B b M 1.

2

δ

β

δ

∂

= ×− ×

∂ δ

∂

= ×− ×

∂ δ

These four rotor stability and two control derivatives can be calculated with any number of 

successively higher order theories given today’s computer power. For example, Wayne 

Johnson provides state-of-the-art rotorcraft technology in a very comprehensive analysis 

called CAMRAD II. At the opposite end of the scale is the most rudimentary evaluation found 

here that accurately captures 90 percent of the fundamental physics in 10 percent of the time. 

 Two helpful points are illustrated by the rotor-force-and-moment derivatives tabulated 

by Eqs. (24) and (25). The first is that each derivative depends on rotorcraft weight (in this 

case, where TS = W). You can see this by noting that centrifugal force in the hub pitching 

moment per unit of longitudinal flapping can be replaced by W/bβ0. This substitution can be 

very helpful because a general rule of thumb is that (β0), the steady coning angle, is on the 

order of 0.1 radians. The hub pitching moment (MP) is then restated as 

(26) C

P 1S 1S

0

F r b Wr

M aa

2 2

β β = ×= ×

β . 

The second point is that a new rotorcraft parameter is introduced in Eq. (25). This parameter 

measures the connection between the pilot and the rotor blade. The connection between the 

longitudinal cyclic stick (δcyclic) and the longitudinal blade feathering angle (i.e., the 

longitudinal cyclic pitch angle, B1C) is defined by the control system. Common, everyday 

engineering practice expresses this key linkage ratio (∂B1C/∂δcyclic) in degrees of B1C per inch 

of δcyclic travel. The sign convention is that (1) nose-up blade feathering at the advancing blade 

azimuth of ψ = 90 degrees is created by –B1C, and (2) the pilot pulling aft on the stick is 
APPENDIX A 

748 

+ δcyclic travel.4 Typical ratios are on the order of plus 2 degrees of nose-up blade feathering at 

ψ = 90 degrees per inch of aft stick travel for rotor systems that have a flapping hinge offset 

(rβ). When rβ = 0, the linkage ratio is more like 3 degrees per inch. From the pilot’s point of 

view, he expects that 1 inch of aft stick will tilt the tip path plane 2 or 3 degrees aft. 

 Studying rotorcraft inherent stability and response in the first 4 to 5 seconds is much 

more interesting using real numbers from a represented single rotor helicopter. Bramwell5

suggests a configuration having the following physical properties: 

Example Helicopter 

Input Data

Calculated Data

W lbs slug ft g ft

I slug ft h feet r foot

R feet c foot b blades

V ft and rad

B inch rad inch

rad C and C

F lbs I slug ft

M

a

F r b Wr

cg

t

C

cyclic

T

T

C f

P

S

C

== =

= −= =

= ==

= =≈

≈− =−

== =

= = =−

= =

10 000 0 002378 32 174

25 000 7 1

25 1 4

685 0 075 4 3

2 0 03491

27 4 0 004564 0 08962

33 333 7 193 740

2 2

3 2

2

0

1

2

1

, , . / , . / sec

, ,,

, ,

/ sec . . deg

deg / . /

. / sec, . .

, , .,

ρ

β

∂

∂ δ

σ

γ

∂

∂

β

β β

Ω

β0

= − 66 667 , / ft lbs rad

Following Eqs. (24) and (25), the six rotor longitudinal derivatives are then calculated as 

v

v

Stability Derivatives

H 5.455 lbs per ft / sec

H 501.877 lbs per rad / sec

M 33.654 ft lbs per ft / sec

M 5412.198 ft lbs per rad / sec

Control Derivatives

H 349.066 lbs per inch

M 2327.106 ft lbs per inch

θ

θ

δ

δ

= +

= −

=+ −

= − −

= +

= + −





 

4 Refer to the discussion in Volume I, pages 76–77. 

5 Bramwell, A. R. S.: Bramwell’s Helicopter Dynamics. John Wiley & Sons, New York, N.Y., 1976. 
APPENDIX A 

749 

 It is more convenient to use these first-order stability and control derivatives in the 

groupings suggested by Eq. (12). This helps to see the key rotorcraft parameters. Therefore, 

calculate 

( ) ( )

v v

v v

v v

v v

M h H 71.841

M h H 8925.334

M H M H 12,633.372

h M h H M h H 9428.220

M h H 4770.567

M H M H 947.673

θ θ

θ θ

θ θ

δ δ

δ δ

+ =+

+ =−

− =+

+ − + =+

+ =+

− =+

 

 

 

Response in the First 4 to 5 Seconds

 The initial response to a wind gust was given in Eq. (15) as 

(27) ( ) ( ) ( ) 2 3

v v v v

gust v

M hH tt g h M hH M hH

V H

I 26 I W

θ θ +    + −+    θ=+ − +    

     

 

. 

Suppose the example single rotor helicopter is upset by a mild, 5-foot-per-second gust and 

that this gust remains constant for about 5 seconds. Then the initial response would be for the 

rotorcraft to pitch up. The pitch angle, numerically expressed in degrees, would be described 

as 

(28) ( )

( )

2 3

2 3

2

t t .8232 .3771 .0176 .4116 t .05415 t

2 6

.4116 t 1 .1316 t in degrees

  θ=+ − + =+ −    

=+ −

. 

The initial response to a gust is clearly a nose-up pitch motion. The motion increases as the 

square of time, which is a rather abrupt response. On the other hand, there is some pseudo 

damping in that the coefficient of t

 3 is negative. The pitch-up, therefore, reaches a maximum 

and then the helicopter begins to return to a level attitude. However, the motion is unstable 

and the next cycle becomes more extreme. 

Inherent Stability 

 The early helicopters were clearly unstable in and about hover. The example 

helicopter illustrates this point quite vividly. The exact solution to the two-degrees-offreedom flying qualities problem was given as 

(18) ( )

( )

v v ( ) t Rt Rt

gust 2 2

M hH R

V e e cos t e sin t

I R

+ −   λ λ

θ =   − ω + ω   λ− +ω   ω  
APPENDIX A 

750 

in which the parameters of λ, R, and ω for the example helicopter are determined from the 

roots of the cubic given by Eq. (19) as 

 λ=− =+ =+ 0.627154 R 0.116236 0.365939 ω . 

These numerical results give the pitching motion in response to the 5-foot-per-second gust, 

expressed in degrees, as 

(29) () ()

( )( )

0.627t 0.116t 0.116t

0.627t 0.116t

1.19911 e e cos 0.366 t 2.031e sin 0.366 t

1.2e 2sin 0.366 t cos 0.366 t e

− + +

− +

θ= − +    

≈+ −    

. 

 Fig. A-1 gives you an idea of just how unstable this example helicopter is in response 

to the gust. In about 10 seconds, the motion would be truly frightening to a first-time student. 

The helicopter would (1) be pitching down at a rate of 3 degrees per second, (2) be some 

75 feet from the original hovering spot, and (3) still be going backwards at about 15 feet per 

second. Of course the pilot, well before 10 seconds had passed, would have pushed the 

longitudinal cyclic stick forward as the nose came up. (The trick to flying such an unstable 

aircraft is to time the control input well in advance of the diverging behavior. Pilots seem, 

therefore, to be clairvoyant.) 

-20

-15

-10

-5

0

5

10

15

20

0 2 4 6 8 10 12 14 16 18 20

Aircraft 

Pitch 

Attitude 

(deg)

Nose Up

Time (sec)

Exact Response

Eq. (29)

Approximate 

Response

Eq. (28)

Fig. A-1. Helicopters are inherently unstable in hover. Example helicopter response to a 

5-ft/sec gust with controls fixed. 
APPENDIX A 

751 

 A feeling for the level of instability can be obtained without even graphing the actual 

motions by using the complex roots of the cubic equation. The positive value for R—the real 

part of the complex roots of the cubic, defined from R ± i ω—establishes the time it takes for 

the motion to double in amplitude. That is, 

(30) ln 2 0.693315 Time to double amplitude in seconds R R = = . 

For this example helicopter, the motion doubles in amplitude every 6 seconds, which is very 

quick when first learning to hover. The time to complete one cycle of the oscillation is found 

from the imaginary part of the complex roots, ω, quite simply as 

(31) 2 Time for one cycle Period in seconds π ≡ = ω . 

In this example, the time to complete one cycle, which is commonly referred to as the period, 

is about 17 seconds. This is also rather quick and does not allow one to really let go of the 

control stick. 

 The approximation to the exact solution given by Eq. (28) is also shown in Fig. A-1. 

The conclusion reached by both results is that helicopter hovering instability is caused by the 

rotor flapping—specifically, the flapping in response to the changes in speed. 

Pilot Control 

 Control of an unstable helicopter in hover is accomplished with well-timed, but small, 

stick movements. In fact, if the control could be applied at the instant a gust upset occurred, 

there would be no nose-up pitch motion of the helicopter. You can see this from Eq. (15) by 

setting θ = 0. The stick travel needed to cancel a wind gust would then be 

(32) ( )

( )

v v

step gust

M hH

V

M hH δ δ

+ δ ≈−

+ . 

For the example helicopter, this amounts to less than 0.1 inch of forward longitudinal cyclic 

stick to counteract a 5-foot-per-second gust hitting the helicopter head-on. Of course, the 

longer the pilot waits to make a control input, the larger the input must be. 

 The question of what control movements the pilot might make to at least give the 

helicopter neutral stability is rather easy to answer. The pilot is, of course, sensitive to 

accelerations, rates, and displacements in each of the six degrees of freedom. But suppose, as 

a minimum, the pilot’s senses are restricted to just pitch angle and pitch rate. Then the control 

input, δcyclic , would be reduced to 

(33) cyclic cyclic

cyclic cg cg

cg cg

θ θ

∂δ ∂δ δ = ×θ + ×θ =δ ×θ+δ ×θ

∂θ ∂θ     , 
APPENDIX A 

752 

and the derivative of stick motion with respect to time becomes 

(34) cyclic θ θ δ =δ ×θ+δ ×θ     . 

The basic stability and control differential equation (A-12) can now be rewritten to include 

the pilot input as 

(35) 

( ) ( ) ( )

( ) ( )( )

( )( )

v v v

v v v v

v v vv

WI

g

W h M hH M hH IH M hH W

g g

M H M H M hH M H M H W

g

W M hH M H M H 0

θθ θ δ δ

θ θ δ δθ δ δ θ

δ δθ

θ

    + + − + + θ− + δ θ            

  + − θ− + δ + − δ θ    

+ + θ− − δ θ=    

  

  



 

 

. 

To successfully stabilize the helicopter, the pilot must learn the two stick movement constants 

from Eqs. (33) and (34): 

cyclic

cg

cyclic

cg

inches of stick per pitch rate (rad / sec) and

inches of stick per pitch angle (rad) = .

θ

θ

∂δ = =δ

∂θ

∂δ = δ

∂θ

 

The pilot’s objective is, as a minimum, to correct the inherent stability equation, Eq. (18), so 

that the complex roots have R = 0. In this more controlled and desirable situation, he would 

feel the helicopter motion improved to 

(36) ( ) v v t

gust 2 2

M hH

V e cos t sin t

I

+   λ λ θ= − ω − ω  ω    λ +ω    

, 

which would be an initial transient motion in response to the gust, followed by a constant 

amplitude oscillation. 

 There is, in fact, a rather broad combination of and θ θ δ δ  that can satisfy this 

minimum requirement. With a little arithmetic, the combinations can be found explicitly by 

solving the characteristic cubic equation introduced by Eq. (19) with the restriction that 

R = 0. (A little shorthand is required because the cubic equation starts to become 

cumbersome). Suppose then that you redefine the cubic as 

(37) 3 2 X AX BX C 0 + + += , 

where the coefficients of A, B, and C are written in terms of the basic helicopter derivatives 

plus the pilot input terms. Thus, 
APPENDIX A 

753 

(38) 

( ) ( ) ( )

( ) ( ) ( )

( ) ( )

v v

v

v v v v

v v vv

h M hH M hH g M hH

A H

I WI

g MH MH M hH g M H M H B

WI I WI

M hH g M H M H C .

I WI

θ θ δ δ

θ

θ θ δ δ δ δ

θ θ

δ δ

θ

    + −+   + =+ + − δ          

    −  + −   

= +   −    δ −  δ

       

   + −

= +   −   δ

  

 



 



Note in the preceding definitions for A, B, and C that the basic helicopter stability terms have 

been grouped within the { } brackets while the pilot input is grouped within the [ ] brackets. 

 It is much easier now to continue the discussion by using some numbers. The example 

helicopter numerically gives the cubic coefficients as 

 

{ } [ ]

{ } [ ][ ]

{ } [ ]

A 0.394681 0.190823

B 0.001626 0.190823 0.000121962

C 0.092456 0.000121962 .

θ

θ θ

θ

= − ×δ

= − ×δ − ×δ

= − ×δ





Now solve the cubic defined by Eq. (37) with the restriction that R = 0. This is not as hard as 

it might seem because the cubic has the following roots 

 2 2 X 0X 0 −λ= +ω =

so that 

(39) 3 2 3 22 2 X AX BX C X X X 0 + + + = −λ +ω −λω = . 

This result shows that 

 2

2

A

B

C and most importantly A B C.

−λ =

+ω =

−λω = × =

The neutral stability criteria of R = 0 is reduced to the simple identity that A×B = C. But A, B, 

and C only depend on the pilot inputs given a basic helicopter configuration that sets the 

stability derivatives. Therefore, one equation in the two pilot-stick-movement constants of 

 and θ θ δ δ  is explicitly obtained. For the example helicopter, this straightforward algebra 

problem yields 

(40) () ()

( )

2

0.0918 0.000358 0.00002327

0.0752 0.0364

θ θ

θ

θ

− − δ+ δ

δ =

− δ

 



. 

Thus, the pilot who finds a practical combination of and θ θ δ δ  that satisfies Eq. (40) will 

bring the helicopter under control following an upset situation such as a gust of wind. 
APPENDIX A 

754 

 The boundary between stable and unstable control is shown in Fig. A-2. As the pilot 

becomes more proficient, he is able to smooth out the control inputs. This has the effect of 

increasing the period and reducing the gust response. In short, the ride goes from jerky to 

precision hovering as the pilot stabilizes the helicopter by flying more by pitch rate and less 

by pitch angle. By being more responsive to pitch rate, the pilot can achieve a very 

comfortable hover at a much reduced workload. As a final note, if no control input is made, 

the very unstable response shown in Fig. A-1 would be what this example helicopter has in 

store for the pilot. 

 The electronic world of autopilots descended on the industry when helicopters got 

“power steering.” The ability to tailor helicopter flying qualities to any criteria, military or 

civil, has now become the task. The search for the inherently stable helicopter has long since 

stopped being even a desirable goal. Now, the only practical limit to polishing a new 

helicopter’s flying qualities appears to be the number of lines of software code that must be 

absolutely proven accurate before the date of first flight. 

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

-16 -14 -12 -10 -8 -6 -4 -2 0

Control 

Derivative 

with 

Respect to

Aircraft

Pitch 

Angle

(in. per rad.)

Control Derivative with Respect to Aircraft Pitch Rate (in. per rad. per sec.)

High Pitch Rate 

Control Gives 36 

sec. Period

Low Pitch Rate 

Control Gives 18 

sec. Period

Unstable

Stable

Neutral Stability Boundary

Fig. A-2. The pilot learns to respond to aircraft pitch rate more than aircraft pitch 

attitude in stabilizing hover. 
755 

APPENDIX B 

SELF-INDUCED VELOCITY GENERATED BY A 

LIFTING LINE WING OR ROTOR BLADE 

 This appendix serves as an elementary introduction to the induced velocity created by 

a field of vortices that reside in the wake of a rotor blade. The approach is to build a bridge 

between familiar fixed-wing theory over to a rotor blade in forward flight. This bridge is built 

in four parts plus concluding remarks. 

 By way of background, rotorcraft technologists, after a nearly seven-decade effort, 

have finally begun to provide accurate computer-based predictions of the airloads and 

dynamic response of a helicopter rotor blade. The decades-long effort was capped during the 

last 4 years by tying airload prediction (with advanced computational fluid dynamics (CFD) 

methods) to completely coupled structural dynamic response (calculated with very advanced 

modal methods). Typical results1,2 confirm the progress of what this relatively small band of 

engineers have achieved after some 70 years of dedicated work. 

 In September 1969, I presented a paper at the V/STOL Technology and Planning 

Conference sponsored by the Air Force Flight Dynamics Laboratory.3 This paper included a 

figure showing the progress in removing assumptions from the original rotor performance 

theory developed by Juan de la Cierva in the late 1920s. The figure is reproduced here as 

Fig. B-1. You can see from the dashed line in Fig. B-1 that I was, in 1969, confident that by 

1975 we would be done. Of course, a revision to that 1969 view reflecting history is quite in 

order. So, the solid line in Fig. B-1 now shows the more accurate progress in hindsight. 

 One of the toughest assumptions to remove was that of uniform downwash. Professor 

Rene Miller of Massachusetts Institute of Technology (MIT) showed the way in 1962.4 Work 

that followed is discussed rather completely in Chapter 13 of Wayne Johnson’s Helicopter 

Theory. The interaction between the rotor blades that create the induced velocity field and the 

effect the induced velocity feeds back on each blade was a daunting complexity that needed a 

computer before even rudimentary solutions became tractable. 

 

1

 Potsdam, M.; Yeo, Hyeonsoo; and Johnson, Wayne: Rotor Airloads Prediction Using Loose Aerodynamic/ 

Structural Coupling. Presented at the American Helicopter Society 60th Annual Forum, Baltimore, MD, June 7–

10, 2004. 

2

 Datta, A.; Sitaraman, J.; Chopra, I.; and Baeder, J.: Analysis Refinements for Prediction of Rotor Vibratory 

Loads in High-Speed Forward Flight. Presented at the American Helicopter Society 60th Annual Forum, 

Baltimore, MD, June 7–10, 2004. 

3

 Harris, F. D.; Tarzanin, F. J.; and Fisher, R. K.: Rotor High-Speed Performance, Theory Versus Test. Presented 

at the Air Force Flight Dynamics Laboratory V/STOL Technology and Planning Conference, Sept. 1969 (also 

AHS Journal, vol. 15, no. 3, July 1970). This conference was held in Las Vegas, Nevada, a city—I was led to 

believe—that was the V/STOL technical capital of the world. 

4

 Miller, R. H.: Rotor Harmonic Air Loading. Institute of the Aerospace Sciences, IAS Paper no. 62-82, Jan. 

1962. 
APPENDIX B 

756 

 There is some interesting knowledge to be gained, however, from disconnecting the 

blade loading from the induced field. That is the purpose of this appendix: to calculate the 

induced velocity at a blade where the blade’s bound circulation is given in terms of radius and 

azimuth. Once specified, the blade’s bound circulation and lift distribution remain unchanged 

despite the resulting induced velocity field. This is, of course, a comparatively simple 

problem compared to the real problem. Furthermore, in this appendix only a one-bladed rotor 

is considered and, to make the problem even simpler, only a prescribed, rigid wake is 

considered. 

 An interesting advantage of these simplifications is that it is quite easy to construct a 

bridge from the fixed wing to the rotary wing. To make the bridge secure, I have tried to leave 

nothing to the imagination concerning the sign conventions, the mathematical notations, and 

the steps under discussion. 

0

5

10

15

20

25

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

Assumption 

Number

Original Theory

Reverse Flow

Quasi-Static Blade Stall

Digital Computer 

Introduced

Compressibility

Non-uniform Downwash

Unsteady, 3-D 

Aero

Blade 

element 

Fig. B-1 

.
APPENDIX B 

757 

Part I—Introduction to the Fixed Wing 

The Classical Fixed-Wing Problem 

 The classical fixed-wing induced velocity problem begins, as explained in most 

aerodynamic textbooks, by assuming a bound circulation that is elliptical. The wing is placed 

in straight and level flight. An array of horseshoe vortices is envisioned. The resulting 

induced velocity at the wing is found to be constant from the port wing tip to the starboard 

wing tip. In summary, 

(1) 

2

o

xw o xw

2xw if 1 then v

b 2b

  Γ Γ =Γ − =    

where Γo is the maximum circulation in square feet per second, b is the wingspan in feet, and 

xw is the span station (xw = –b/2 at the port wing tip and xw = +b/2 at the starboard wing tip). 

The induced velocity, vxw, is in feet per second and is constant from tip to tip. 

 Now think of the wing rotating, not flying straight. It is quite helpful to approach the 

fundamental geometry used in the classical derivation from a different point of view. Suppose 

a fixed wing is East of a pylon and flying North past the pylon. Ignore, for the moment, an 

anticipated 180-degree U-turn around the pylon.5 (The U-turn results will be discussed after 

reconstructing the classical problem.) The situation is illustrated with Fig. B-2. 

Fig. B-2

 

5

 Imagine a rotor blade at the traditional downwind, zero azimuth station, which will, after the U-turn, be at the 

180-degree upwind azimuth station. 
APPENDIX B 

758 

 In Fig. B-2, the right-hand axis system gives a positive Z-axis coming up out of the 

paper. The “pylon” is located at X = Y = Z = 0. The wing centerline is placed at a distance, D, 

from the pylon in the plus X direction. The wing coordinates are measured from the wing 

centerline. The station on the wing where induced velocity is sought is denoted by xw. A 

vortex trails downstream from the wing at wing station xv. A small element of the vortex, dS, 

is shown located at a distance L from wing station xw. The reference angle θ is used to locate 

the vortex element in relation to the wing. When θ is equal to minus π/2, the vortex element is 

at – ∞. When θ equals zero, the vortex element is located at the wing. The calculation of 

induced velocity by the Biot–Savart law, as derived from vector notation, is simply 

(2) ( ) v x i j ji w i j ji

xw 3 3

xw xv

L dS L dS 1 d L dS L dS

d dv d dxv d

4 L 4 dxw L =

γ   − −    Γ  = θ= − θ        π π        

. 

This fundamental equation is deceptively simple because to calculate the induced velocity, 

vxw, at any station along the wing, xw, only a double integral has to be performed. That is 

(3) 

b/2 0

xw i j ji

xw 3

/ 2 xw xv b/2

1 d L dS L dS

v dxv d

4 dxw L

+

−π = −

   Γ   −  =− θ      π      

     

. 

 

 The double integration required by Eq. (3) is hampered (to put it mildly) whenever 

xw d

dxw

Γ equals either plus or minus infinity. The double integration can be an even bigger 

problem whenever L = 0. If the double integration is performed numerically, situations where 

numbers approach plus or minus 1010 can become quite frustrating. Modern computers, using 

so called double precision and advanced numerical integration schemes, have helped to lower 

this frustration. But the fundamental basis of numerical integration is the Taylor series. The 

hope is that—without a breach in engineering accuracy—dθ and dxw can be replaced by Δθ

and Δxw when the integral operators are replaced by summation operators. There are, of 

course, a number of ingenious coordinate transformations that can completely remove an 

apparent integrating road block. 

 Here is an example of a coordinate transformation that helps lower frustrations with 

the fixed-wing problem. Consider the situation when a wing’s lifting line is loaded with an 

elliptical bound circulation defined as 

(4) 

2

xw o

2xw 1

b

  Γ =Γ −    , 

where xw = –b/2 at the port wing tip and xw = +b/2 at the starboard wing tip. The derivative 

that the Biot–Savart law requires is 
APPENDIX B 

759

(5) 

1

2 2

xw o

v o 2 xw xv

d 1 2xv 2xv 2 2 2xv dxw 1 2 dxv dxv

dxw 2 b b b b b 2xv 1

b

−

=

     

Γ Γ                  γ =− =− Γ − − =+                                         −        

where xv = –b/2 at the port wing tip and xv = +b/2 at the starboard wing tip. You can 

immediately see that the required derivative is plus infinity at the starboard wing tip and 

minus infinity at the port wing tip. Now look at what happens with the coordinate 

transformation of 

(6) b b xv cos and dxv sin d

2 2 = − β = β β

where β = 0 is the port wing tip and β = π is the starboard wing tip. Then the bound 

circulation becomes 

(7) 

2 2

2

o oo

2 b 1 cos 1 cos sin , b 2 β

   Γ =Γ − − β =Γ − β=Γ β      

and the required Biot–Savart derivative becomes 

(8) ( ) xw o

v o 2 xw xv

d 2 b dxv cos sin d cos d

dxw b 2 = 1 cos

Γ Γ       γ = − =   − β ββ   = −Γ β β       − β    

. 

Clearly, singularities caused by the derivative xw d

dxw

Γ at the wing tips have been removed. 

 The preceding coordinate transformation, when placed in the Biot–Savart law for this 

fixed-wing problem, gives 

(9) [ ]

0

i j ji

xw o 3

0 / 2

1 L dS L dS

v cos d d

4 L

π

−π

 −  = −Γ β β θ   π  

     

. 

 The next step is to construct the second portion of the integrand required by Eq. (3), 

which is 

i j ji

3

L dS L dS

d

L

 −  θ    

. 

The geometric dimensions, L, Li, Lj, dSi, and dSj are components of vectors. When looking at 

Fig. B-2, there is a choice of reference systems. Since this fixed wing is flying straight and 

level past the pylon, there is no advantage to including the distance, D, or using the reference 
APPENDIX B 

760 

angle, θ, in the wake geometry.6

 Therefore, continue using just the reference angle δ. That 

means 

i j ji i j ji

3 3

L dS L dS L dS L dS

d is replaced by d , L L

  − − θ δ    

and δ is positive counterclockwise. The vortex segment farthest downstream is located at 

δ = 0, and a vortex segment right at the wing is located by δ = +π/2. 

 Now, from Fig. B-2, the distance L is written as 

(10) 

i jk

3/2 3 2 32

L L L L (Xw Xv)i (Yw Yv)j (Zw Zv)k

with Xw xw Yw 0 Zw 0

xv xw Xv xv Yv Zv 0

tan

and L (Xw Xv) (Yw Yv) (Zw Zv) .

=++ = − + − + −

== =

− == = δ

= − +− +−    

Therefore, with the usual “substitute and simplify” phrase, 

(11) ( )

3/2 2

3

2

xv xw

L

sin

  − =  

  δ  

. 

In a similar manner, the vortex is describe by the vector 

(12) S S S S Xv i Yv j Zv k =++ = + + i jk ()()()

and, therefore, 

(13) ( )

i

i

j

j 2

k

k

S Xv dS d d 0

S Yv xv xw

dS d d

sin

S Zv dS d d 0

∂ ∂ = δ= δ= ∂δ ∂δ

∂ ∂ − = δ= δ=

∂δ ∂δ δ

∂ ∂ = δ= δ=

∂δ ∂δ

. 

Here the assumption about the trailed vortex geometry is that it extends straight aft of the 

wing without descending or climbing, remaining perpendicular to the wing lifting line. Again, 

by substitution and simplification, 

(14) i j ji

3

L dS L dS 1 d sin d

L xv xw

  − − δ= δ δ     − . 

 

6

 The next part of this note addresses the U-turning wing. That problem requires, of course, some reference 

system that includes D and uses the reference angle as θ. 
APPENDIX B 

761

 The double integral created by the Biot–Savart law now appears, after substituting 

Eq. (14) into Eq. (9), as 

(15) [ ]

/ 2

xw o

0 0

1 1

v cos d sin d

4 xv xw

π π

 −  = −Γ β β δ δ   π −  

      . 

A minor problem is immediately observed in Eq. (15). Formal integration really requires that 

xv and xw be related, in some fashion, to β and/or δ. This minor problem is overcome using 

Eq. (6) where b

xv cos

2 = − β rather than have the vortex wing station keyed by the angle β. 

Because the wing station is keyed to xv, you can make the substitution that b

xw cos

2

=− α . 

These substitutions result in 

(16) [ ]

/ 2

o

0 0

1 1 v cos d sin d

2b cos cos

π π

α

 −  = −Γ β β δ δ   π α− β  

      . 

A much, much bigger problem with Eq. (15) and Eq. (16) is that any integration, whether 

formal or numerical, must face the possibility that (xv – xw) might be zero. Looking at 

Eq. (16) more closely shows that real trouble will occur if β = α. 

 The integration of Eq. (16) with respect to wake age (i.e., with respect to δ) can be 

done, and the result can also be integrated with respect to β. That is, 

(17) o oo

0 0

cos cos vd d

2b cos cos 2b cos cos 2b

π π

α

Γ   β β Γ   Γ = β=− β=−   π α− β π β− α  

      . 

Note immediately that the preceding derivation gives a negative value for induced velocity 

created by a wing carrying positive lift! The reason for this outcome is the right-hand rule axis 

system of Fig. B-2 where the Z-axis is positive up. Therefore, the induced velocity is directed 

in the negative Z direction. Of course, reason prevails in all text books on the subject, so the 

negative induced velocity is simply called downwash, and the sign is changed to positive. 

This is equivalent to letting v o γ = +Γ cos dβ β. 

 Incidentally, Glauert proved the integration with respect to β equals π long ago. Also, 

Alan Pope, in appendix 3 of his book Basic Wing and Airfoil Theory, shows that 

(18) 

[ ] [ ]

o o

0 0

o o oo

0 0

cos cos v d 1 d

2b cos cos 2b cos cos

1 d cos d cos 0

2b 2b cos cos 2b 2b

π π

α

π π

Γ   β α Γ   = β= + β    π β− α π β− α   

Γ Γ   Γ Γ = β+ α β= π + α   π π β− α π π  

     

     

. 
APPENDIX B 

762 

 But now suppose numerical integration (rather than formal, closed form integration) of 

Eq. (16) is the solution approach. I took an approach with the MathSoft, Inc. product called 

MathCad Plus 6.0 that goes like this: 

( )

o

s

o m

n,m n

m s

n

m

89 n,m n 1,m

m

n 0

179

m m1

s

n 0

s s

2 b1

s 0,1......179

s 1/2

180

cos dvd d sin

2b cos cos

n 0,1........90 n 180

m 0,1......180 m 180

dvd d dvd d

dvd

180 2

dvd dvd

v

180 2

b

xw cos

2

+

=

+

=

Γ= =

=

π

α= +

Γ   β β δ =   δ π β− α  

π = δ =

π = β =

π βδ + βδ β =

π β+ β =

=− α





This numerical solution “programmed” in MathCad gave +0.9999746151 accuracy nearly 

within a blink of an eye, using a Dell Optiplex high-end computer bought in 2001. The 

answer from Eq. (17) is exactly unity (when you ignore the minus sign). As a reminder, the 

fixed wing represented by a lifting line and an elliptical bound circulation produces a lift 

calculated from 

(19) 

b/2 2 /2 2

o o /2

b/2

/2 2

o o oo /2

2xw b L V 1 dxw V 1 sin cos d

b 2

b b 4L V cos d V bV so .

2 2 2 4 b V

+

+π

−π

−

+π

−π

    =ρ Γ − =ρ Γ − θ θ θ        

  π π =ρ Γ θ θ=ρ Γ = ρ Γ Γ =     πρ





 



The wing incurs an induced drag to carry this lift that is 

(20) ( )

2

xw o 2

o o 2 2

v L Induced drag L bV V 4 2bV 8 2 V b

  π π   Γ = = ρ Γ = ρΓ =       ρ π . 

This drag can be used to calculate a horsepower required by multiplying both sides of the 

equation by velocity, V, and dividing by 550. Thus, 

(21) ( ) ( )

2 2

2

i 22 2

V L Vq L Induced Horsepower HP with q 2 V 550 2 V b 550 qb

    ≡ =   =   = ρ

  ρπ π  

. 
APPENDIX B 

763

 A numerical example calculated here will be a useful result to compare later to 

rotating wing calculations. Suppose both a wing and a rotor have an equal span, say, 44 feet. 

In rotor notation, the rotor radius is 22 feet. Assume, for example, that each lifting device 

carries a lift of 2,712 pounds, each is flying at sea level (ρ = 0.002378 slug/ft2

), and each is 

flying at V = 301.8 ft/sec or 178 knots. Then, using Eq. (21), the induced horsepower required 

by the wing is 6.13 horsepower. 

 Keep in mind that the elliptical bound circulation distribution used in the preceding 

discussion is the first term of the more general distribution used in fixed-wing analyses. 

Recall that the general distribution is seen in the form 

(22) n

1

2bV A sin n

∞

Γ =  β . 

Everything read in this appendix, including the rotor analyses, could be extended by this 

fixed-wing logic of Eq. (22). 

 And there you have the fixed wing flying North past the pylon located off its port 

wing tip. Now consider the situation after the fixed wing does a 180-degree U-turn. 

The Fixed Wing After Completing a 180-Degree U-turn 

 The next step in bridging the gap between a fixed wing and a rotary wing was actually 

taken by H. Glauert in 1923, although I doubt he had a bridge in mind when he published 

R&M 866. After all, in 1923 Juan de la Cierva’s earliest autogyro experiments were just 

coming to fruition in Spain, and a practical helicopter was still 15 years away. The title of 

Glauert’s 1923 report was Calculation of the Rotary Derivatives Due to Yawing for a 

Monoplane Wing. He was dealing with the wing rolling and yawing moments created by an 

induced velocity field that trailed the wing in one-half of a circle. The problem was, in fact, 

quite akin to a hovering one-bladed rotor where only a small part of the wake is taken into 

account. Glauert obtained a very simple closed-form solution by assuming that the wing made 

the U-turn with a large turning radius (D) relative to the wingspan (b) (i.e., D>>b). His quite 

useable engineering result for the induced velocity over the wingspan was (in the notations I 

am using in this appendix) 

(23) o

xw

1 xw v 1

2b 2 D

Γ   = +     . 

The purpose of this portion of the appendix is to explore this problem when the turning radius 

is considerably smaller than what Glauert assumed. The objective is to think of the “pylon” as 

a rotor hub and place the port wing tip a small distance from the hub, which gives the 

appearance of a “root cutout” in rotorcraft terminology. Glauert’s approach is presented first, 

and then a numerical integrating approach is shown. 
APPENDIX B 

764 

 The geometry of the problem is illustrated in Fig. B-3. In contrast to Fig. B-2, the 

wing has now advanced 180 degrees. Immediately note that the X-axis is positive to the left, 

but the Y-axis is left in its commonly found, ordinate position. By the right-hand rule then, the 

positive Z-axis now points down, which is into the paper. The wing is doing a U-turn of 

distance D, which is measured from the “pylon” to the wing mid-span point. The wing is 

represented by a lifting line vortex having an elliptical bound circulation, just as with the 

classical fixed-wing problem. The Biot–Savart law is again invoked so 

(24) ( ) v i j ji

xw 3

L dS L dS

d dv d

4 L

γ  −  = θ   π  

, 

and the dimensions are expressed as vectors. However, the basic vortex geometry has changed 

going from Fig. B-2 to Fig. B-3. Now 

(25) 

( ) ( )

i jk

3/2 3 2 32

L L L L (Xw Xv)i (Yw Yv)j (Zw Zv)k

where Xw D xw Yw 0 Zw 0

Xv D xv cos Yv D xv sin Zv 0

and L (Xw Xv) (Yw Yv) (Zw Zv) .

=++ = − + − + −

= + = =

= + θ =− + θ =

= − +− +−    

Fig. B-3 
APPENDIX B 

765

The reference angle, θ, is taken positive counterclockwise in Fig. B-3. In a similar manner, 

the vortex is describe by 

(26) S S S S Xv i Yv j Zv k, =++ = + + i jk ( )()()

but with changed vortex geometry reflecting the one-half circle wake, the vortex element 

geometry is 

(27) 

( ) ( )

( ) ( )

i

i

j

j

k

k

S Xv D xv cos

dS d d d D xv sin

S Yv D xv sin

dS d d d D xv cos

S Zv dS d d 0

∂ ∂ ∂+ θ = θ= θ= θ=− + θ

∂θ ∂θ ∂θ

∂ ∂ ∂− + θ     = θ= θ= θ=− + θ

∂θ ∂θ ∂θ

∂ ∂ = θ= θ=

∂θ ∂θ

. 

Here the assumption about the trailed vortex geometry is that it extends in a circular arc aft of 

the wing for 180 degrees without descending or climbing. Furthermore, any given vortex has 

constant circulation, γv, from when it leaves the wing all the way back to when the turn began 

(i.e., θ = 0 back to θ = – π). 

 The substitution of this U-turn geometry into the Biot–Savart law gives, with 

simplification 

(28) ( ) ( )( ) ( )

( ) ( ) ( )( )

2

v

xw 3/2 2 2

D xv D xw cos D xv

d dv d

4 D xv D xw 2 D xv D xw cos

 

γ  + + θ− +  = θ  

π   + ++ − + + θ     

. 

 The wake-age integral problem is immediately seen as requiring elliptical integrals—

even if the wing’s bound vortex circulation varies with wake age. For this example, assume, 

as Glauert did, that γv does not vary with θ. Now, at the risk of boring you, the transformation 

to complete elliptical integrals (i.e., E and K) begins by letting 

θ = π – 2φ and dθ = – 2 dφ. You also need to recall that 

( ) () 2 cos cos 2 cos 2 2sin 1. θ= π− φ = − φ = φ −

Then, a couple of substitutions and rearrangements immediately show that 

(29) 

( ) ( )( )

( )

( )( )

( )

v

xw 3/2 3/2 2 2

2

v

3/2 3/2 2 2

2 D xv 2D xw xv 1 d dv d

4 2D xw xv 1 k sin

4 D xv D xw sin d

4 2D xw xv 1 k sin

  γ + ++   =   φ − π + +     − φ    

  γ + +   φ − φ  

π + +     − φ    
APPENDIX B 

766 

where 

(30) ( )( )

( )

2

2

4 D xw D xv

k

2D xv xw

+ + = + + . 

 This substitution changes the wake-age integrating limits from θ = – π to θ = 0 over to 

φ = 0 to φ = +π/2. The two budding integrals can be found, for example, in the translated 

Russian handbook written by I. S. Gradshteyn and I. M. Ryzhik, and edited by Alan Jeffrey, 

titled Tables of Integrals, Series, and Products. Thus, 

(31) 

/ 2

3/2 2 2 2

0

/ 2 / 2 / 2

2 2

3/2 3/2 3/2 22 22 22

0 0 0

2 22

1 1 d E

1 k 1 k sin

sin 1 cos ddd

1 k sin 1 k sin 1 k sin

1 11 E KE

1k k k

π

π π π

φ =   − φ −  

φ φ φ = φ − φ    −φ −φ −φ   

  = −−   −  







        

where the complete elliptical integrals, E and K, are computed as 

(32) 

/ 2

/ 2 2 2

0 2 2

0

1 E 1 k sin d K d

1 k sin

π

π

= − φ φ = φ − φ





  , 

and their values depend on the modulus, k2

, which for this U-turning wing problem is given 

by Eq. (30). Note that when xv = xw, k2

 = 1.0, E = 1.0, and K = +∞. 

 In this way 

(33) ( )( ) ( )

( ) ( ) ( )( )

0

2

v

xw 3/2 2 2

D xv D xw cos D xv

dv d

4 D xv D xw 2 D xv D xw cos −π

 

γ   + + θ− +

= θ  

π     + ++ − + + θ    











is converted into 

(34) 

( )( )

( )

( )( )

( )

/ 2

v

xw 3/2 3/2 2 2

0

/ 2

2

v

3/2 3/2 2 2

0

2 D xv 2D xw xv 1 dv d

4 2D xw xv 1 k sin

4 D xv D xw sin d

4 2D xw xv 1 k sin

π

π

  γ + ++   =   φ − π + +     − φ    

  γ + +   φ − φ  

π + +     − φ    

















which, upon simplification, reduces to 
APPENDIX B 

767

(35) v

xw

E K dv

4 xv xw 2D xv xw

γ   = +   π − ++  . 

The wake integration being complete, the problem is reduced to the spanwise collection of all 

vortices trailed from the wing. 

 The insightful step Glauert took next was to make use of the approximations for E and 

K, when k2

 was closer to 1.0 than to 0, rather than calculate them using Eq. (32). These 

approximations are 

(36) 

( )

( )

2

2

2

2 2

1 16 1 E 1 ln 1 k

4 1k 2

1 16 1 16 K ln ln 1 1 k

2 1k 8 1k

    ≈ +   − −       −

   

≈ + −−       − −  

. 

The fact that the approximation for E begins with one (1) is enormously important, as shown 

when these approximations are substituted into Eq. (35). Of course, a lengthy integration 

problem results, which is 

(37) 

( )

b/2

v

xw

b/2

b/2

v 2

2

b/2

b/2

v

2

b/2

b/2

v

2

b/2

1

v

4 xv xw

1 1 16 1 ln 1 k

4 xv xw 4 1 k 2

1 1 16 ln

4 2D xv xw 2 1 k

1 1 16 ln 1

4 2D xv xw 8 1 k

+

−

+

−

+

−

+

−

γ   =   π −  

γ       

+ −      −   π− −       

γ     

+      π ++ −     

γ     

+ −     π ++ −    























 ( ) 2 1 k     −    

. 

But now look very closely at the first integral obtained in Eq. (37). Recognize that 

b/2

v

xw

b/2

1

v

4 xv xw

+

−

γ   =   π −  







is nothing more than the classical fixed-wing problem presented in Part I of this appendix. 

 This is a key result that Glauert provided in his 1923 report because it says that the 

so-called “near wake” of a U-turning fixed wing (i.e., think of a rotor blade’s near wake) is a 

no tougher problem than the straight-flying wing with the added influence of a curved “far 

wake.” For the elliptical bound circulation used as the example in this appendix, the spanwise 

integration becomes 
APPENDIX B 

768 

(38) 

( )

( )

o

x

b/2

v 2

2

b/2

b/2

v

2

b/2

b/2

v 2

2

b/2

v

2b

1 1 16 1 ln 1 k

4 xv xw 4 1 k 2

1 1 16 ln

4 2D xv xw 2 1 k

1 1 16 ln 1 1 k

4 2D xv xw 8 1 k

+

−

+

−

+

−

Γ =

γ       

+ −      −   π− −       

γ     

+      π ++ −     

γ       

+ −−        π ++ −       



















. 

 The additional three integrals can be grouped into one integral. But first, the vortex 

circulation strength, assuming an elliptical bound circulation for the wing lifting line, Eq. (8), 

is substituted into Eq. (38). Next the elliptic integral modulus, k2

, from Eq. (30), is substituted 

into Eq. (38).7

 Then a selection of wingspan stations, xw, is made (say 50) and, in short order, 

MathCad calculated the induced velocity distributions at any turning distance, D. 

 Despite the appearance of possible singularities in Eq. (38), MathCad actually 

experienced no numerical integration problems. I did not let MathCad try to simplify the 

integrand. The temptation is to fiddle with 1-k2

, which MathCad or I fouled up. It was a very 

unproductive effort given MathCad’s speed on my Dell computer. 

 Glauert, in R&M 866, assumed that the turning radius was considerably greater than 

the wingspan, which allowed simple integration of Eq. (38), the result being Eq. (23). But 

consider the results as the wing makes tighter and tighter U-turns. A nondimensional measure 

of the semicircle tightness is wingspan (b) divided by the distance from the “pylon” (D). The 

tightest turn would be when the port wing tip is touching the “pylon,” in which case D = b/2 

or b/D = 2.0. This corresponds to a rotor blade with zero root cutout. A turning ratio of 

b/D = 1 corresponds to a 0.33 root cutout. The extreme in the other direction would be, of 

course, not turning at all, and so D = ∞ and b/D = 0. 

 For simple illustration purposes, let the wingspan be unity (i.e., b = 1.0 foot) and let 

the maximum elliptical bound circulation, which occurs at the wing mid-span, be two (i.e., 

Γo = 2.0 square feet per second). Thus, for the following examination, Γo /2b = 1.0 foot per 

second. Two results shown in Table B-1 are immediately known from the preceding 

discussion. 

Table B-1 

Turn Parameter, b/D Spanwise Induced Velocity, vx Source 

Not Turning vx = Γo /2b = 1.0 Eq. (1) 

Wide Turn vx = (1+xw)/2D Eq. (23) 

 

7

 I would have included the results of these substitutions, but the resulting expression is way too long. 
APPENDIX B 

769

 The results for several tighter and tighter turns are shown in Figs. B-4 through 

B-7. For a turn distance, D, that is 10 times the wingspan, Glauert’s approximation is very 

useful as Fig. B-4 shows. When the turn distance is equal to the wingspan (equivalent to a 

rotor blade root cutout of 1/3), the distortion in induced velocity across the wingspan is 

significant as shown in Fig. B-5. This distortion grows more pronounced as the turn distance 

shrinks, which is illustrated in Figs. B-6 and B-7. These two figures correspond to a rotor 

blade root cutout of 0.1667 and 0.0476, respectively. 

 Now consider the numerical double integration involved in this U-turning wing 

problem. Fig. B-6 offers a virtually exact example to which numerical integration can be 

compared. The integration problem at hand is 

(39) ( )( ) ( )

( ) ( ) ( )( )

b/2 0

2

v

xw 3/2 2 2

b/2

D xv D xw cos D xv

v d dxv

4 D xv D xw 2 D xv D xw cos

+

− −π

 

γ   + + θ− +

= θ  

π     + ++ − + + θ    

         

. 

0.97

0.98

0.99

1

1.01

1.02

1.03

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

Not Turning

Glauert Approximation

b/D = 1/10 from MathCad

Induced 

Velocity

Wing Span Station, x/(b/2) 

Fig. B-4 
APPENDIX B 

770 

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

Not Turning

Glauert Approximation

b/D = 1/1 from MathCad

Induced 

Velocity

Wing Span Station, x/(b/2) 

Fig. B-5 

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

Not Turning

Glauert Approximation

b/D = 1/0.7 = 1.43 from MathCad

Induced 

Velocity

Wing Span Station, x/(b/2) 

Fig. B-6 
APPENDIX B 

771

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

Not Turning

Glauert Approximation

b/D = 1/0.55 = 1.82 from MathCad

Induced 

Velocity

Wing Span Station, x/(b/2) 

Fig. B-7 

 Philosophically, Glauert found the fixed-wing induced velocity equation is buried 

obscurely within the U-turning wing problem posed by Eq. (39). Therefore, the MathCadprovided integration scheme encounters all of the fixed-wing problems at the wing tips. 

(MathCad returns the notice “will not converge,” which makes for frustration.) A second 

thing you know is that the denominator of the integrand can get very, very small, or even be 

zero when θ = 0. Both of these probable problems suggest using the fixed-wing coordinate 

transformations, which to repeat, are 

(40) bb b xv cos dxv sin xw cos

22 2 = − β = β =− α

and assume an elliptical bound circulation along the wing’s lifting line so that 

(41) v o γ = −Γ cos dβ β . 

 With the preceding thoughts in mind, a “brute force” numerical integration scheme 

goes like this: 
APPENDIX B 

772 

o 2 b 1 D 0.7

Dimension integration.

Number of radial stations at which vortices leave wing, M 90 

Number of azimuthal stations between 0 and 180 degrees, N 18,000

Range of radial stations where induced v

Γ= = =

=

=

s

n

m

m sn

o

n,m m

elocity is calculated, s 0,1.......M 1

Then proceed with these calculations

1

= s

M 2

n 0,1........N n N

m 0,1......M m M

bb b D cos D cos cos D c

22 2 dvd d cos

4

= −

π   α +    

  π = θ =   −

 

  π = β =    

     − β − α θ− −   Γ    βθ = β

π

2

m

3/2 2 2

m s m sn

N 1 n,m n 1,m

m

n 0

M 1

m m1

s

m 0

s s

os

b b bb D cos D cos 2 D cos D cos cos

2 2 22

dvd d dvd d

dvd

N 2

dvd dvd

v

M 2

b

xw cos

2

− +

=

−

+

=

 

      β    

                    − β +− α− − β − α θ           

π βθ + βθ β =

π β+ β =

=− α





 The brute force aspects of the above scheme are obvious. The wake age from 

θ = 0 to 180 degrees is divided into 18,000 segments, or 0.01 of a degree. The spanwise 

segmentation is a little more rational. Ninety vortices are trailed, and induced velocity at the 

wing is calculated in between each pair of trailed vortices. This density is far from practical 

for the real problems rotorcraft engineers are solving everyday with computers. Calculating 

area as the sum of rectangular slivers is hardly advanced. Despite the obvious improvements 

that might be made, the scheme works. 

 The first numerical integration result, compared to the virtually exact solution 

obtained by following Glauert, is shown in Fig. B-8. The agreement over 99.9 percent of the 

wingspan is more than acceptable for engineering purposes. The only problem that occurred 

was calculation of induced velocity at the most outboard span station (i.e., s + 1/2 = 89.5 or 

xw = 0.4999238476). This span station is halfway between the vortex trailed from the tip 

(i.e., m = 90) and the next vortex inboard at m = 89. The numerical solution gave v = 19.65 

feet/second versus the virtually exact 1.206 feet/second. In contrast, the port wing tip 

encountered no such problems. Other than this one ridiculous answer at the starboard wing tip 

(plus being rather slow), the numerical integration scheme functioned in a satisfactory 

manner. 
APPENDIX B 

773

-1

-0.5

0

0.5

1

1.5

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

b/D = 1/0.7 = 1.43, following Glauert

Numerical Solution With Full Wake, 0 to 180

deg.

Solution With Wake From 15 to 180 deg.

Induced 

Velocity

ft/sec

Wing Span Station, x/(b/2) 

Fig. B-8 

 There are several interesting features to this U-turning wing problem. For example, the 

numerical integration proceeded from port to starboard wing tip with the numerous trailed 

vortices in between. Fig. B-9 illustrates what the induced velocity wake-age summation 

appears like for the calculation point next to the wing mid-span. The span station of interest is 

s + 1⁄2 (αs = 90.5 degrees, xw = 0.0087). Fig. B-9 shows that dv/dβ sees the impending 

discontinuity at the span station point, but the summation averages the calculation to the left 

of the point with the calculation to the right of the point. Therefore, the induced velocity is the 

integral found from 

dv induced velocity, v area under versus d = β β

and is obtained with quite reasonable results. 

 Another interesting behavior of this U-turning wing problem is shown in Fig. B-10. 

This figure looks at the wake-age integration involved with 

dv d d

dv d d area under versus θ

d d

  β     β β = β θ . 

The summation is illustrated at the two vortex trailed wing stations of β = 160 and 

β = 162 degrees (i.e., m = 80 and m = 81). The station at which induced velocity is sought is 

αs = 161 degrees. The fascinating point made here is that the two vortices appear to make 

enormous contributions to induced velocity within the first 2 degrees of wake age. This 
APPENDIX B 

774 

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 20 40 60 80 100 120 140 160 180

Wing Span Station, β, deg.

dv

dβ

Wing Span Point 

at which induced 

velocity is sought

Fig. B-9 

-25,000

-20,000

-15,000

-10,000

-5,000

0

5,000

10,000

15,000

20,000

25,000

30,000

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

d dv d ( )

d

β

θ

Wake Age, -θ, deg.

Vortex starboard of span point 

where induced velocity is sought

Vortex starboard of span point 

where induced velocity is sought

Fig. B-10 
APPENDIX B 

775

-60

-40

-20

0

20

40

60

80

120 130 140 150 160 170 180

dv

dβ

Wing Span Station, β, deg.

Fig. B-11 

is one of the reasons such small increments in wake age (i.e., 180 degrees of wake divided 

into 18,000 segments) are required for the rudimentary rectangular area summation scheme. 

The spanwise distribution of dv/dβ, provided with Fig. B-11, shows just how large the 

numbers are that, when summed, however, come out v = 1.1968318858. 

 The situation near the port wing tip, which is closest to the pylon, is quite similar to 

that near the starboard wing tip. The conclusion is that the first 15 degrees of wake age must 

be very densely populated with points if a rudimentary numerical integration is used. 

Fortunately, advanced methods currently used in the rotorcraft industry accomplish the 

numerical integration much more efficiently. 

 Rotorcraft engineers have improved their nonuniform induced velocity calculating 

methods by dividing the wake into a near wake and a far wake. Thus, Fig. B-8 shows that the 

near wake (i.e., θ = 0 to –15 degrees in this case) is the most troublesome for numerical 

integration, particularly at the wing tips. The far wake (i.e., θ from –15 to θ = –180 degrees in 

this case) responds to numerical integration with virtually no problems. In fact, the wake age 

can be divided into 1-degree segments versus 0.01-degree segments, and virtually the same 

contribution of the far wake to the induced velocity at the wing will be obtained. 

 The U-turning wing problem can be divided into a near wake and a far wake with 

relative ease. The induced velocity at the wing due to 180 degrees of circular arc wake in 

elliptic integral form is 
APPENDIX B 

776 

(42) 

b/2 / 2

/ 2 2 2

2 2

0 0

xw

b/2

1 d 1 k sin d 1 k sin xv v dxv

4 xv xw 2D xv xw

+ π

π

−

  ∂Γ   φ − − φφ − φ ∂ = +

π − ++

 

     









 . 

Keep in mind that φ = π/2 is closest to the wing. Conversely, φ = 0 corresponds to the end of 

the wake, or where the wing was before it started the U-turn. Therefore, the wake integration 

amounts to integrating from zero up to the start of the near wake, say φNW, and then adding 

the near-wake contribution, which extends from φ = φNW to φ = π/2. It is, however, much 

more direct in this case to subtract the wake behind the near wake (i.e., NW

0 f ( )d φ

φ φ  ) from the 

total wake (i.e., 

/ 2

0 f ( )d π

φ φ  ). Thus, the two elliptic integrals are rearranged as follow: 

(43) 

NW

NW

/ 2 22 22 22 2

NM 00 0

/ 2

22 22 22

00 0

Near wake 1 k sin d 1 k sin d 1 k sin d k sin sin

1 11 Near wake d d d

1 k sin 1 k sin 1 k sin

πφ χ

πφ χ

= − φ φ − − φ φ = − φ φ − φ χ

= φ − φ = φ

−φ −φ −φ

 

   

 

where the angle, χ, a new upper limit of integration, is given as 

(44) 

2 2 2

NW NW

NW

1 k sin sin 1 k

2arctan

cos

  − φ−φ − χ =  

φ  

. 

Then, in elliptic integral shorthand, the near-wake contribution to induced velocity at the wing 

is simply 

(45) ( )

b/2

2

NM

Near xw Wake

b/2

xv E( ,k) k sin sin F( ,k) v dxv

4 xv xw 2D xv xw

+

−

∂Γ −

∂   χ− φ χ χ = +   π − ++  









where 

(46) 

2 2

0

2 2

0

E( ,k) 1 k sin d

1 F( , k) d v

1 k sin

χ

χ

χ = − φ φ

χ = φ

− φ







 . 

In like manner, the induced velocity at the wing due to the far wake becomes 
APPENDIX B 

777

(47) ( )

NW

NW

b/2

2 2

2 2

0 0

Far xw Wake

b/2

1 d 1 k sin d 1 k sin xv v dxv

4 xv xw 2D xv xw

+ φ

φ

−

  ∂Γ   φ − − φφ − φ ∂ = +

π − ++

 

     











where, to repeat, ( )( )

( )

2

2

4 D xw D xv

k

2D xv xw

+ + = + + . 

 This completes the discussion of the U-turning wing problem. Two points have been 

made: 

(1) A virtually exact calculation of induced velocity without numerical integration 

questions has been provided. Figure B-6 gives an example to which any numerical 

integration result may be compared. 

(2) The so-called near wake is built upon the fundamental integral solved by the 

fixed-wing community, which is 

(48) ( )

b/2

xw

b/2

xv 1 Fixed Wing v dxv 4 xv xw

+

−

∂Γ −

∂   =   π −  









. 
APPENDIX B 

778 

Part II—The Rotating Wing Done With Rotor Notation 

 The next step along the bridge from the fixed-wing world to the rotary wing world is 

rotor blade geometry and notations. This geometry is provided in Fig. B-12. The intent here is 

to think of a one-bladed rotor in hovering flight. (The case of forward flight is addressed in 

Part III of this appendix.) The rotating wing is again represented as a lifting line having an 

elliptical bound circulation. The trailing vortex wake structure resembles a lock washer or, 

perhaps more descriptively, a “slinky” spring-like toy. That is, each vortex has a circular path 

just like the U-turning wing problem. The addition is that each trailing vortex spirals 

downward at a constant rate, and the wake age can extend back to the beginning of time. In 

short, the wake of this rotating wing or, better yet, a one-bladed hovering rotor, need not stop 

at minus 180 degrees as was the case with the U-turning wing. 

 Now study the geometry of Fig. B-12 quite closely. The rotor blade is shown rotating 

around the Z-axis, which is positive down. The blade rotates in the X–Y plane where X is 

taken positive “forward,” although what forward means in this case of no forward speed is not 

really meaningful. The Y-axis is normal to the X–Z plane. This X-, Y-, Z-axis system does 

not rotate with the blade, nor does it move with time. 

Fig. B-12 
APPENDIX B 

779

 The blade itself has a radius, R, measured from the Z-axis. The blade is shown in 

Fig. B-12 with a root cutout, rc. Thus, the blade’s span (thinking in terms of a wing) is simply 

R – rc. Any radial station measured positive outward from the Z-axis and along the lifting line 

is denoted by (r). 

 The rotation angle of the blade is measured by the azimuth angle (ψ), which, for 

convenience, equals zero when the blade lies along the negative X-axis. The azimuth angle 

increases with time, simply as the rotational speed (Ω) in radians per second times time in 

seconds. Obviously, Fig. B-12 is a snapshot at any given time you care to start the watch. The 

blade is simply going round and round, and the trailed vortex structure is left in space to 

descend at a prescribed rate (dZ/dt) in feet per second. Fig. B-12 is drawn to imply that the 

blade has been rotating for the time it takes to complete about two revolutions. However, the 

arrowhead shown at the end of the one trailed vortex implies that time has been going on 

forever and, with a longer piece of paper, the spiral would extend down and around the Z-axis 

to infinity. 

 As with the preceding fixed-wing examples, the Biot–Savart law requires a very 

careful mathematical definition for the blade and vortex wake dimensions. This is especially 

true when tackling the rotor blade problem. Using Fig. B-12 as the geometric model of a 

single bladed rotor, the radius station (r) at which the induced velocity is sought is set relative 

to the X – Y – Z axis by 

(49) Xr r cos Yr r sin Zr 0 = − ψ = + ψ = . 

A vortex trails aft from the blade from radius station rv. Any segment of this long, spiraling 

vortex is therefore deposited at a point behind the blade and below the X–Y plane. This vortex 

segment, dS, is located at the coordinates 

(50) dZv Xv rv cos Yv rvsin Zv t

dt

=− θ =+ θ =+ Δ . 

Eq. (50) introduces the possibility that the wake trailing behind the rotor blade does not stay 

in the X–Y plane in which the rotor blade turns. This is quite different from classical fixedwing wake geometry assumptions. The rotor blade wake descends with some velocity 

(dZv/dt), and this velocity need not be constant. In fact, in the more complete analyses 

of rotor systems, freedom is given for any given vortex segment to wander throughout the 

X – Y – Z axis system. For elementary discussion purposes, just assume a constant diameter 

spiral (i.e., neither rv nor dZv/dt are influenced by time). Furthermore, it is not necessary at 

this point in the discussion to be more specific about the descent velocity of the vortex 

segment. 

 Now consider the matter of time introduced by Eq. (50). For the rotor blade, the time 

increment (Δt) represents the time (t) it takes to travel back from the blade, which is at the 

snapshot azimuth angle (ψ) (at time, to) to the vortex segment, dS, which is located at θ (at 

time, t). That is, 

(51) o Δ= − ttt . 

Because the blade’s angular rotation speed is Ω, it follows that 
APPENDIX B 

780 

(52) o t tt

θ −ψ Δ= − =

Ω , 

which immediately says that 

(53) dzv dzv dzv dzv Zv t

dt dt dt d

  θ−ψ =+ Δ = = θ= θ     ΩΩ θ . 

In many propeller studies, dZv/dθ is a measure of helix angle or sometimes propeller pitch. 

 Now, quite methodically, begin with the Biot–Savart law as previous stated: 

(54) ( ) v i j ji

x 3

L dS L dS

d dv / dxv d

4 L

γ   − = θ   π  

where the dimensions are expressed as vectors. The distance (L) between the vortex segment 

and the radius station (r) at which the induced velocity is sought, is determined by 

(55) 

i jk

3/2 3 2 32

L L L L (Xr Xv)i (Yr Yv)j (Zr Zv)k

where Xr r cos Yr r sin Zr 0

dzv Xv rvcos Yv rvsin Zv

d

and L (Xr Xv) (Yr Yv) (Zr Zv) .

=++ = − + − + −

=− ψ =+ ψ =

=− θ =+ θ =+ θ

θ

= − +− +−    

In a similar manner, the vortex is describe by 

(56) S S S S Xv i Yv j Zv k =++ = + + i jk ()()()

but with rotor blade vortex geometry, 

(57) 

( )

( )

i

i

j

j

k

k

S Xv dS d d rvsin d

S Yv dS d d rv cos d

S zv dS d .

∂ ∂ = θ= θ= θ θ

∂θ ∂θ

∂ ∂ = θ= θ= θ θ

∂θ ∂θ

∂ ∂ = θ= θ

∂θ ∂θ

The substitution of this rotor blade geometry into the Biot–Savart law gives, with 

simplification 

(58) ( ) () ( )

() ( )

2

v

r 3/2 2

22 2

rv r rv cos

d dv / drv d

4 dzv rv r 2r rv cos

d

 

 

γ − ψ−θ = θ  

π         + − ψ−θ + θ     θ    

. 
APPENDIX B 

781

 Because this is a single bladed rotor in hover, there is an opportunity to chose the 

blade azimuth position at any value that is convenient. This is because the hover problem is 

completely symmetrical around the Z-axis and “forward” has no meaning. (This is not 

possible in the forward flight case as you will see in Part III of this appendix.) Given this 

latitude, choose ψ = 0. This reduces Eq. (58) to 

(59) ( ) ( )

( )

2

v

r 3/2 2

22 2

rv r rv cos

d dv / drv d

4 dzv rv r 2r rv cos

d

 

 

γ − θ

= θ  

π         + − θ+ θ     θ    

, 

which is a variation on Eq. (28) arrived at for the fixed wing after a U-turn. The variation is, 

of course, the addition of the term 

2

dzv 2

d

  θ     θ . 

 Now let me address the wake-age parameter (θ). The vortex wake leaves the blade 

lifting line referenced to ψ = 0. Therefore, the smallest that θ can be is θ = ψ = 0. The vortex 

spirals backwards (round and round and down) to θ = – ∞. While it is not practical to go all 

the way back to θ = – ∞, the intent is to go as far back as possible to avoid missing any 

influence of what many refer to as the far wake. Nevertheless, the integration over the wake 

age becomes 

(60) ( )

( )

0

2

v

r 3/2 2

22 2

rv r rv cos

dv / drv d

4 dzv rv r 2r rv cos

d −∞

 

 

γ − θ

= θ  

π         + − θ+ θ     θ    















. 

 The immediate objective is to perform the integration required by Eq. (60). Suppose 

the vortex circulation, γv, does not vary with wake age, and suppose the vortex descent 

measure, dzv/dθ, is constant. The only immediate numerical problem that is apparent in 

Eq. (60) is when the integrand’s denominator is identically zero, or so close to zero that 

numerical integration built into MathCad flounders. This situation will only occur when θ is 

actually zero and when r = rv. 

 To illustrate the results of integrating Eq. (60) over the wake age using MathCad’s 

built-in scheme, choose some rational values for a single bladed rotor (Table B-2). For this 

example, MathCad was quite happy to whip out the answer so long as the input was chosen 
APPENDIX B 

782 

Table B-2 

Parameter Value 

Rotor radius, R, feet 30.0 

Root cutout, rc, feet 3.0 

Trail vortex from radius, rv, feet 27.0 

Calculate induced velocity at radius, r, feet 16.5 

Trailed vortex strength, γv, ft2 per second 1,265.0 

Vortex descent measure, dzv/dθ, feet per radian 2.0 

Wake age, θend, radians –157.0 

Number of 360 degree spirals 25 

Distance from rotor down to last spiral, zv, feet 314 

that avoids r = rv by a considerable margin. (Just imagine the wake-age integral in summation 

form with wake-age segments of 0.01 degrees! It would take forever.) In the blink of an eye 

MathCad produced Fig. B-13. Fig. B-13 shows that induced velocity accumulates very 

quickly with the increasing number of spirals included in the integration. Closer inspection of 

Fig. B-14, an enlargement of Fig. B-13, shows that the vortex segments included in the firsthalf spiral contribute in a rather linear fashion to the induced velocity at blade radius station, 

r. But as the spiral continues around, it comes back underneath the blade (see 

Fig. B-12), and the close proximity allows the vortex to become very influential. In short, the 

denominator in Eq. (60) with θ around –360 degrees is very influenced by the vortex descent 

measure, dzv/dθ. 

 In advanced, modern numerical integration of the real rotor system problem, 

wandering vortices do come close and, indeed, even intersect the lifting line or lifting surface 

of the blade that trailed the vortices. This is to say that the denominator of Eq. (60) finds some 

way to go to zero in the real problem. Furthermore, when there are more blades to consider, 

the ensuing possibilities of this denominator going to zero have been a major source of 

frustration in achieving accurate solutions for the rotor hovering and forward-flight problems. 

The current crutch most widely used has been to add what is called a vortex core to the 

denominator of Eq. (60) so zero can never occur. The fact that a vortex does have a real 

physical core of measurable diameter makes the core’s inclusion in Eq. (60) reasonable. This 

concept of a vortex core diameter (VCD) means that Eq. (60) can be written as 

(61) ( )

( )

0

2

v

r 3/2 2

22 2 2

rv r rv cos

dv / drv d

4 dzv rv r 2r rv cos VCD

d −∞

 

 

γ − θ

= θ  

π         + − θ+ θ +     θ    















. 

To make progress over recent years, technologists have achieved considerable numerical 

stability even when tackling the hardest problems using this concept of a vortex core. For this 

part of the appendix, let me completely dismiss the whole VCD issue. 
APPENDIX B 

783

0

5

10

15

20

25

30

35

40

45

50

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28

Number of 360 degree Spirals

Induced 

velocity 

(fps)

Parameter Value 

Rotor radius, R, feet 30.0 

Root cut out, rc, feet 3.0 

Trail vortex from radius, rv, feet 27.0 

Calculate induced velocity at radius, r, feet 16.5 

Trailed vortex strength, γv, ft2

 per second 1,265.0 

Vortex descent measure, dzv/dθ, feet per 

radian 

2.0 

Wake age, θend, radians –157.0 

Number of 360 degree spirals 25 

Distance from rotor down to last spiral, zv, 

feet 

314 

Fig. B-13 

0

5

10

15

20

25

30

35

40

0 0.5 1 1.5 2 2.5

Induced 

velocity 

(fps)

Number of 360 degree Spirals

Fig. B-14 
APPENDIX B 

784 

 Proceeding then, consider the collection of all the trailed vortices by performing the 

radial integration over the blade span from the root cutout (rc) to the blade tip, r = R. This step 

begins by assuming a bound circulation distribution carried on the lifting line. Assume the 

bound circulation has an elliptical distribution8

 described by 

(62) ( )

( )

2

c

r o 2

c

2r r R

1

R r

− − Γ =Γ − − , 

which gives the circulation strength of a vortex trailing from radius station, rv, as 

(63) 

( )

( )

( )

o c

v 2 2

c c

2

c

2R 2rv r R 1 drv

2rv r R R r

1

R r

 

 

− Γ −−  

γ =−    

  − −   −   − −  

. 

The induced velocity along the blade’s radius collecting all vortices is then 

(64) 

( )

( )

( )

( )

( )

R 0

2

o c

r 2 3/2 2 2

c c 22 2

2

c rc

1 2 2rv r R rv r rv cos

v d drv

4 2rv r R R r dzv 1 rv r 2r rv cos

R r d −∞

 

 

Γ −−   − θ =     θ

π − −   −         −     + − θ+ θ   −     θ    

             

.

 Now, let me illustrate a completely numerical solution for this double integral. From 

Parts I and II of this appendix, the numerical integration of Eq. (64) does not converge to a 

solution because of any number of singular points. MathCad’s built-in integration scheme 

flounders even if a close proximity situation occurs. You also know that the induced 

velocity—given an elliptical bound circulation along the lifting line—must contain the 

solution for a fixed wing. That is, at the very least 

( ) o

r

c

v

2R r

Γ = − . 

The approach, therefore, is to first borrow the fixed-wing solution technique of letting 

(65) 

c c

c c

c

Rr Rr

r cos a bcos

2 2

Rr Rr

rv cos a bcos

2 2

R r drv sin d bsin d

2

   + −

= − α= − α      

   + − = − β = − β      

  − = β β= β β    

 

8

 Keep in mind that the more general distribution used by fixed-wing engineers, Eq. (22), could be used to 

extend the results beyond an elliptical distribution. 
APPENDIX B 

785

where β goes from 0 to π. This coordinate system change at least transforms the vortex 

circulation strength, γv, of Eq. (63) to the much simpler 

(66) v o γ = −Γ cos dβ β . 

The completed substitution of Eqs. (65) and (66) into Eq. (64) restates the induced velocity 

double integral problem as 

(67)

( )( ) ( )

( ) ( ) ( )( )

0

2

o

r 3/2 2

2 2 2

0

cos a bcos a bcos cos a bcos

v dd.

4 dzv a bcos a bcos 2 a bcos a bcos cos

d

π

−∞

 

 

−Γ β − α − β θ− − β =   θ β

π         − β + − α − − α − β θ+ θ     θ    

             

 

 So now, let me numerically integrate Eq. (67). The scheme allows MathCad to 

perform the wake-age integral, but the spanwise integration is performed with a summation. 

This takes advantage of MathCad’s very, very fast integration over wake age. Thus, a useable 

numerical integration scheme reads like this: 

o c

INPUT

dzv 2 R 1.2 r 0.2 0

d

Dimension integration.

Extent of wake age, WA

Number of radial stations at which vortices leave rotor blade, M 90 

Range of radial stations where induced velocity is calcul

Γ= = = = θ

= −π

=

( )( ) ( )

( ) ( ) ( )( )

c c

s

m

2

o

m

2 2

ated, s 0,1.......M 1

Then proceed with these calculations

Rr Rr a b

2 2

1

= s

M 2

m 0,1......M m M

cos a bcos a bcos cos a bcos

dvd

4 dzv a bcos a bcos 2 a bcos a bcos cos

d

= −

− + = =

π   α +    

  π = β=    

−Γ β − α − β θ− − β β =

π   − β + − α − − α − β θ+ 

  θ

0

3/2 2

2

WA

M 1

m m1

s

m 0

s s

d

dvd dvd

v

M 2

r a bcos

−

+

=

 

 

  θ

   

   θ

   

π β+ β =

=− α
















APPENDIX B 

786 

 Notice that this sample input corresponds to the U-turning wing problem of D = 0.7, 

b = 1, Γo = 2, which gives the induced velocity distribution shown in Fig. B-8. This check 

case did check. MathCad was faster and more accurate with the wake-age integral broken into 

several ranges. The following seemed best 

() () ( ) () () 00 5 3

180

WA 5 3 WA

180

f ,d f ,d f ,d f ,d f ,d

π − −π − π

π − −π − π α β θ= α β θ+ α β θ+ α β θ+ α β θ    . 

 Now consider a practical case of a four-bladed, 44-foot-diameter rotor lifting about 

10,800 pounds while operating at a tip speed of Vt = ΩR = 600 ft/sec. The preceding input 

requires an estimate for maximum bound circulation, Γo, and the vortex segment descent rate, 

dzv/dθ. Rational estimates for both parameters can be obtained. To begin with, assume each 

blade has a root cutout of rc = R/6, and each blade has an elliptical bound circulation over its 

span. The maximum of the bound circulation is Γo = 225 ft2

/sec, which is calculated from 

(68) 

( )

2

to o 2

t

rc 8L Lift per blade RV 1 so 8 R RV 1 rc R

π     =ρ Γ −     Γ =   πρ −        

. 

Next, assume a vortex segment, dS, is carried downward with the downwash velocity. From 

simple momentum theory, this downwash or induced velocity is 19.3 feet/second when 

calculated with 

(69) i 2

L Momentum induced velocity v 2 R ≡ = ρπ . 

Then, in one second, a segment descends 19.3 feet. But in one second, the rotor blade moves 

through a wake age angle of θ = Ω times one second. Therefore, the vortex segment descent 

rate is simply 

(70) i i i

t t

dzv v times 1 second v v R

d times 1 second V R V = == θ Ω , 

which is roughly 0.7 feet per radian for this representative example. This means that in one 

complete spiral revolution, the vertical distance will be 0.7(2π) feet, or roughly 4.4 feet for 

every revolution. This is a measure of the spiral spacing or pitch of Fig. B-12. 

 To summarize this typical operating situation of a one-bladed rotor, the representative 

calculations that follow were based on 

2

o c

INPUT

dzv 225ft / sec R 22ft r R / 6 0.7 ft / rad

d

Dimension integration.

Extent of wake age, WA variable for this example

Number of radial stations at which vortices leave rotor blade, M 90 

Range of radial 

Γ = = = = θ

=

=

stations where induced velocity is calculated, s 0,1.......M 1 = −
APPENDIX B 

787

 An immediate question is, “How many spirals does it take to accurately approximate 

an infinite wake?” As seen from Fig. B-15, perhaps about 100 360-degree spirals capture the 

problem in a promising way. This amounts to 440 feet of wake or about 10 rotor diameters. 

 A more quantitative measure of a practical engineering solution is induced 

horsepower, HPi. This major contributor to total power is calculated as 

(71) ( ) R R

i r r r rr rc rc

1 1 HP v dL v V dr

550 550 = = ρΓ   . 

The calculation was made using the summation of 90 rectangular slivers. The results, 

tabulated in Table B-3, indicate that even 20 spirals will neglect about 2 to 3 horsepower, 

which is on the order of 2 to 3 percent missing horsepower because the wake age was not 

extended to infinity. The ratio of calculated induced horsepower to ideal momentum 

horsepower (i.e., Lvi/550 = 95.524 horsepower) is the fourth column in Table B-3. The 

reciprocal of this ratio, known as Figure of Merit, is provided by the sixth column. A Figure 

of Merit above 1.0 is not possible, and thus at least 10.5 spirals are required before a rational 

answer starts to become apparent. Clearly, an elliptical bound circulation, which is ideal for a 

fixed wing (i.e., the equivalent of FM = 1 for a rotating wing), is far from ideal for a rotating 

wing. 

-5

0

5

10

15

20

25

30

0 2 4 6 8 10 12 14 16 18 20 22

1/2 spiral

1+1/2 spirals

2+1/2 spirals

3+1/2 spirals

5+1/2 spirals

10+1/2 spirals

20+1/2 spirals

100+1/2 spirals

Induced 

Velocity 

ft/sec

Rotor Span Station, r, feet

Fig. B-15 
APPENDIX B 

788 

Table B-3 

Number of 

Spirals Blade Lift 

Calculated 

Induced HP 

Ideal Induced 

HP 

Calculated 

HP/HPideal

Figure of 

Merit 

0.5 2712.52 29.57 95.52 0.31 3.23 

1.5 55.31 0.58 1.73 

2.5 70.41 0.74 1.36 

3.5 80.32 0.8408 1.189 

5.5 92.33 0.9666 1.0346 

10.5 104.44 1.0934 0.9146 

20.5 110.25 1.1541 0.8665 

100.5 112.79 1.1808 0.8469 

200.5 112.84 1.1813 0.8465 

Do not assume that this example provides anything more than a crude estimate for the actual 

performance of a single bladed rotor. The prescribed wake geometry used is very, very far 

from the wake visually observed in any number of experiments. The example would surely 

come out differently—and more accurately compared to experiment—if (or when) this sample 

problem is calculated with advanced methods in use today. For the sake of completeness, 

Fig. B-16 gives the running lift (ΔLr) and running horsepower (ΔHPi) versus radius station. 

This data is for 100.5 spirals. 

 This concludes Part I and Part II of this appendix. The next step is to apply this 

background to the single bladed rotor in forward flight. 

0

1

2

3

4

5

6

7

0 2 4 6 8 10 12 14 16 18 20 22

Rotor Span Station, r, feet

( ) r

r

dL 0.1

dr

dHP

dr

0.1*Running Lift, 

lbs/ft

Running 

Horsepower, 

hp/ft

Fig. B-16 
APPENDIX B 

789

Part III—A Rotating Blade in Forward Flight 

 The next step in the bridge between a fixed and rotating wing is examined in this 

portion of the appendix. The rotating wing in forward flight deposits a rather complicated 

vortex wake in space as it flies away. A hint of the wake’s complexity is shown below in 

Fig. B-17. 

X Direction 

of Flight

Y

ψ

Trailing

 Vortex

Rotating

Blade

Planform View

Z axis positive

into the paper

Vortex goes to 

infinity

 

X Direction 

of Flight

Z

Side View

Y axis positive

into the paper

Trailing

 Vortex

Fig. B-17
APPENDIX B 

790 

 In the preceding sketch, the rotating wing, the single bladed rotor, is rotating about the 

Z-axis in the X–Y plane at angular velocity (Ω) in radians per second. The blade is attached to 

a hub. The hub is located at X = Y = Z = 0. The X – Y – Z axis system moves through space 

straight along the plus X direction with forward velocity (V) in feet per second. The axis 

system neither pitches nor rolls, and it does not climb or descend. The rotor blade has a radius 

(R) in feet and a root cutout (rc) in feet. The tip speed of the rotor is Vt = ΩR in feet per 

second. The one vortex shown illustrates the drifting, down spiraling path typical of all 

vortices. 

 A more complete picture of the wake complexity is provided with Figs. B-18 through 

B-21. These figures have been drawn for an advance ratio, μ = V/Vt = 0.5, and show the 

planform view. Start with Fig. B-18 where the blade is at the azimuth angle (ψ) of 90 degrees. 

This azimuth is generally referred to as the advancing side of the rotor disc. In the fixed-wing 

problem, all vortices trail straight back, parallel to the X-axis. Obviously, this is not true for a 

rotor blade. The tip vortex traces out a prolate cycloid, while the root cutout vortex follows a 

curtate cycloid. 

Y

X

B

l

a

d

e

Hub

Tip Vortex

75% Radius

Root Cutout

50% Radius

Fig. B-18 
APPENDIX B 

791

Y

X

Blade Hub

75% Radius

Root Cutout

Tip Vortex

50% Radius

Fig. B-19 

Y

X

B

l

a

d

e

Hub

75% Radius

50% Radius

Root Cutout

Tip Vortex

Fig. B-20 
APPENDIX B 

792 

Y

X

Blade

Hub

75% Radius

50% Radius

Tip Vortex

Root Cutout

Fig. B-21 

Fig. B-19 shows the planform view with the blade at the 180-degree azimuth position. 

Fig. B-20 places the blade at ψ = 270 degrees, which is the retreating side of the rotor disc. 

Notice with the blade at ψ = 270 degrees that the two outboard vortices trailed from the blade 

sharply turn nearly back on the blade itself. Finally, Fig. B-21 shows the blade at its most 

downwind position of ψ = 360, or zero degrees. Here the trailed vortices really attack the 

blade. The possibilities of any given vortex directly intersecting the generating lifting line are 

quite real in the practical problem. 

 Before bringing the Biot–Savart law to bear on this problem, there are a few aspects of 

the notations to observe. To begin with, rather than deal with the geometry dimensionally, use 

the conventional rotor nondimensional notations of 
APPENDIX B 

793

(72) 

v

tpp

tpp

t

i

r x radius station where induced velocity is sought R

r xv radius station where vortex is trailed

R

angle of attack of the tip path plane, positive nose up

V cos advance ratio

V

v induced velocity

=

=

α ≡

μ= α

≡

tpp i

tpp

t

 calculated by momentum theory

Vsin v

 inflow ratio. 

V

α − λ =

 Now, using Fig. B-22 as the reference, methodically begin with the Biot–Savart law as 

previous stated: 

(73) ( ) v i j ji

x 3

L dS L dS

d dv / dxv d

4 L

γ   − = θ   π  

where the dimensions are expressed as vectors as displayed in Fig. B-22. For the distance (L) 

between the vortex segment (dS) to the radius station (x) at which the induced velocity is 

sought, you have 

(74) [ ] [ ]

( ) [ ] ( )

i jk

tpp

3/2 3 2 32

L L L L (Xr Xv)i (Yr Yv)j (Zr Zv)k

where Xr R x cos Yr R x sin Zr 0

Xv R xvcos Yv R xvsin Zv R

and L (Xr Xv) (Yr Yv) (Zr Zv) .

=++ = − + − + −

=− ψ =+ ψ =

=− θ+μ ψ−θ =+ θ =− λ ψ−θ    

= − +− +−    

In a similar manner, the vortex is describe by 

(75) S S S S Xv i Yv j Zv k =++ = + + i jk ()()()

but with rotor blade vortex geometry, you have 

(76) 

( )

( )

i

i

j

j

k

k tpp

S Xv dS d d R xvsin d

S Yv dS d d R xv cos d

S dS d R .

∂ ∂ = θ= θ=+ θ+ μθ θ

∂θ ∂θ

∂ ∂ = θ= θ=+ θ θ

∂θ ∂θ

∂ = θ=+ λ θ

∂θ

The substitution of this rotor blade and wake geometry into the Biot–Savart law gives, with 

simplification 
APPENDIX B 

794 

Fig. B-22 

(77) 

() ( ) ( )

{ ( ) ( ) ( )( ) ( ) ( )}

2

i j ji

3 3

2 2 2 2 2 2

tpp

L dS L dS xv x xv cos xvsin xsin xv cos

L

R xv x 2x xv cos 2 xvcos x cos

  − − ψ−θ +μ θ− ψ+ ψ−θ θ     =       + − ψ−θ + μ θ− ψ ψ−θ + ψ−θ μ +λ  

 As an intermediate step, I integrated the Biot–Savart law with respect to wake age 

assuming the vortex circulation is simply a constant. That is, I tackled 

(78) ( ) v i j ji

x 3

L dS L dS

dv / dxv d

4 L

ψ

ψ

−∞

γ   − = θ   π  







. 

The purpose of this step was to test MathCad’s built-in integrator and be sure it did not 

flounder at any azimuth (ψ) or radius station (x) with the provision that x ≠ xv. To perform 

this test, I set γv = 4π and R = 1. I found that the near wake needed integration in several parts 

and finally selected integration as follows: 
APPENDIX B 

795

(79) 

12515 i j ji 180 180 180 180

3 1 25 15 90 180 180 180 180 180

90 5

180

180 5 20

180

L dS L dS

d

L

.

ψ ππ π π ψ ψ− ψ− ψ− ψ−

π ππ π π ψ− ψ− ψ− ψ− ψ− −∞

π ψ− ψ−π − π

π ψ− −π − π

  − θ= + + + + +    

+ +





   

 

MathCad’s built-in integrator struggled with the calculation at and near the blade’s root end 

(i.e., around the root cutout region) in the azimuth region from ψ = 330 to 360 degrees. The 

reason for this struggle is, of course, the near-zero value of the distance (L) as Fig. B-21 

clearly shows. Adding a vortex core diameter would obviate the problem in regions where the 

vortices are so closely packed. 

 The next step requires picking a bound circulation for the blade lifting line. Suppose 

the elliptical distribution is chosen and this distribution does not vary with azimuth. This 

means there will only be trailed vortices and no shed vortices to add to the problem for this 

example. (The case of a shed wake will be addressed shortly.) Thus, 

(80) ( )

( )

2

c

x, o 2

c

2x x 1

1 does not vary with azimuth, 

1 x ψ

− − Γ =Γ − ψ − . 

Then, borrowing from the fixed-wing solution technique, let 

(81) 

c c

vc c

c

r 1x 1x x cos a bcos

R2 2

r 1x 1x xv cos a bcos

R2 2

1 x dxv sin d bsin d

2

   + −

= = − α= − α      

   + − == − β = − β      

  − = β β= β β    

where β goes from 0 to π. This coordinate system change at least transforms the trailed vortex 

circulation strength, γv, to the very much simpler 

(82) v o γ = −Γ cos dβ β , 

and thus the induced velocity double integral problem for an elliptical bound circulation that 

does not vary with azimuth is restated as 

(83)

() ( ) ( )

{ ( ) ( ) ( )( ) ( ) ( )}

2

o

r 3

2 2 2 2 2 2

tpp

0

cos xv x xv cos xvsin x sin xv cos

v d d.

4 R

xv x 2x xv cos 2 xv cos x cos

π ψ

−∞

 

−Γ β  − ψ−θ +μ θ− ψ+ ψ−θ θ        =   θ β

π     + − ψ−θ + μ θ− ψ ψ−θ + ψ−θ μ +λ    

        

 
APPENDIX B 

796 

 The question now arises as to what value of the maximum bound circulation (Γo) is 

representative for this example. The calculation of the average or steady lift of this single 

bladed rotor follows as: 

(84) 

( )

( ) ( )

( )

( ) ( )

( )

( )( )

c

c

r, r, r,

2

c

x, x, x, t o 2

c

1

2

1 c

x, t o 2 x

c x

to c c

steady

dL V dr both V and are vectors

2x x 1

dL V Rdx V x sin 1 Rdx

1 x

2x x 1

L dL V x sin 1 Rdx

1 x

L RV 1 x 1 2 sin x

8

1 L L

2

ψ ψψ

ψ ψψ

ψ ψ

ψ

=ρ ×Γ Γ

  − − =ρ Γ =ρ +μ ψ Γ −      −  

  − − = = ρ +μ ψ Γ −      −  

π = ρ Γ − + μ ψ+

= π











 

( )( )

2 2

to c c 0 0

2 Steady

to c o 2

t c

1 d RV 1 x 1 2 sin x d

2 8

8L

Steady lift per blade RV 1 x so . 8 RV 1 x

π π

ψ

π ψ= ρ Γ − + μ ψ+ ψ

π

π = ρ Γ − Γ=     πρ −    





 

On this basis, chose the blade geometry from Part II 

 R = 22 feet 

 xc = 1/6 nondimensional 

and the forward flight conditions for this Part III problem are: 

 ρ = 0.002378 slugs per cubic feet 

 Vt = 603.605 feet per second 

 μ = 0.5 nondimensional 

 λtpp = –0.03 nondimensional 

 Γo = 225 square feet per second 

in which case the steady lift per blade is 2,712 pounds at 178 knots. 

 With this information as input, MathCad and its built-in integrator is used to calculate 

Eq. (83) as follows: 
APPENDIX B 

797

o c tpp

INPUT

0.5 225 R 22 x 1/ 6 0.03

Dimension integration.

Select azimuth station, = variable for this problem

Extent of wake age, WA 20

Number of radial stations at which vortices leave rotor blade,

μ= Γ = = = λ =−

ψ

=− π

c c

s

c c

s ss

 M = 90 

Range of radial stations where induced velocity is calculated, s 0,1.......M 1

Then proceed with these calculations

1x 1x a b

2 2

1

= s

M 2

r 1x 1x x cos a b cos

R2 2

m 0,1

= −

− + = =

π   α +    

   + −

= = − α= − α      

=

() ( ) ( )

{ ( ) ( ) ( )( ) ( ) ( )}

m

vc c

m mm

2

o

s,m 3

2 2 2 2 2 2

tpp WA

......M m

M

r 1x 1x

xv cos a b cos

R2 2

cos xv x xv cos xvsin x sin xv cos

dvd d

4 R

xv x 2x xv cos 2 xv cos x cos

ψ

  π β =    

   + − = = − β=− β      

 

−Γ β  − ψ−θ +μ θ− ψ+ ψ−θ θ        β =   θ

π     + − ψ−θ + μ θ− ψ ψ−θ + ψ−θ μ +λ    









M 1 s,m s,m 1

s,

m 0

s s

dvd dvd

v

M 2

x a b cos

− +

ψ

=

π β+ β =

=− α





 The calculation of induced velocity at the lifting line—as created by the trailed 

vortices from the lifting line—now follows from the above scheme. Additionally, lift and 

horsepower distributions are calculated from 

(85) 

( ) ( )

( )

2

s c

s, t s o s 2

c

M 1

s,

s 0

s, s, s,

M 1

s,

s 0

2x x 1

L V x sin R 1 Running lift

1 x

L L Single blade lift at input azimuth

1 HP v L Running horsepower 550

HP HP Single blade horsepower at inp

ψ

−

ψ ψ

=

ψ ψψ

−

ψ ψ

=

    − − Δ = ρ +μ ψ Γ − Δ       

  −  

= Δ 

Δ= Δ 

= Δ 





( ) c

s

ut azimuth

1 x where cos s cos s 1

2MM

  +     π π  Δ =    − +         
APPENDIX B 

798 

 A representative illustration of azimuth-varying induced velocity at several radial 

stations is shown in Figs. B-23 and B-24. Remember that this result is for a single-bladed 

rotor lifting 2,712 pounds at 0.5 advance ratio (i.e., V = 178 knots at Vt = 603.6 fps). Even 

more interesting is the azimuthal variation of the blade’s total lift and induced horsepower 

shown in Fig. B-25. The average or steady induced horsepower is obtained by 

(86) 

2

i 0

1 Steady Induced Horsepower HP HP 2

π

≡ = ψ π  . 

The result is HPi = 50.1 hp. This induced horsepower, calculated with the prescribed wake, 

compares to the ideal induced horsepower calculated in Part I as 

(87) i ( ) 2

1 Lift Ideal Induced Horsepower Ideal HP Lift for 0.2, 550 2 R V

 

≡ ≈ μ>     ρπ 

which yields ideal HPi = 6.13 hp. This means that the elliptically loaded, single-bladed rotor 

requires about eight times the power calculated by simple momentum theory! 

 An additional point made by Fig. B-25 is that the highest lift is carried primarily on 

the advancing side of the rotor disc. As such, the rotor is out of trim because of the rolling 

moment inferred by Fig. B-25. 

 This leads to the question, “If the rotor has an elliptical bound circulation that varies 

with azimuth so that the rolling moment is zero, what is the induced power?” And this leads 

to the fourth and final part of this appendix. 

-150

-100

-50

0

50

100

150

200

0 30 60 90 120 150 180 210 240 270 300 330 360

x = r/R = 0.25

Induced 

Velocity

ft/sec

Blade Azimuth, ψ , deg

Fig. B-23 
APPENDIX B 

799

-10

0

10

20

30

40

50

0 30 60 90 120 150 180 210 240 270 300 330 360

x = r/R = 0.50

x = 0.75

Induced 

Velocity

ft/sec

Blade Azimuth, ψ , deg

Fig. B-24 

0

20

40

60

80

100

120

0 30 60 90 120 150 180 210 240 270 300 330 360

Blade Total

Lift (lbs)

&

Induced 

Horsepower

Blade Azimuth, ψ , deg

HPi

Lift/100

Fig. B-25 
APPENDIX B 

800 

Part IV—A Rotating Blade in Forward Flight With Zero Rolling Moment 

 The last step in the bridge between a fixed and rotating wing is addressed in this 

portion of the appendix. A fixed wing generally flies with zero rolling moment, RM. This 

same criterion can be applied to a rotating wing. (I refer to a rotating wing with 

RM = 0 as a “balanced” rotor.) Suppose the bound circulation of the single-bladed rotor is 

describe by 

(88) ( ) ( )

( )

2

c

x, o 1 2

c

2x x 1

sin 1

1 x ψ

− − Γ = Γ +Γ ψ − − . 

In this case, the lift and rolling moment are found as 

(89) 

( )

( ) ( )

Steady t o c c o 1

2 2

Steady t o c c o c c 1

L RV 1 x 1 x

8

RM R V 1 x 8 1 x 5 6x 5x

128

π = ρ Γ − + Γ + μΓ      

π = − ρ Γ −   μ + Γ+ + + Γ    

, 

and if the rolling moment is set to zero 

(90) 

( )

( )

( )

c o

1 2

c c

2

2

Steady t o c 2 o

c c

8 1x

5 6x 5x

8 L RV 1 x 1

8 5 6x 5x

μ+ Γ Γ =−

+ +

  π μ = ρ Γ− −   Γ    + +  

. 

 The Biot–Savart law of Eq. (83) now must include the trailed vortex circulation, γv, 

which is azimuth varying according to Eq. (88). Therefore, for this Part IV 

(91) 

( ) () ( ) ( )

{ ( ) ( ) ( )( ) ( ) ( )}

2

o 1

x, 3

2 2 2 2 2 2

tpp

0

sin cos xv x xv cos xvsin xsin xv cos v dd.

4 R

xv x 2x xv cos 2 xvcos xcos

π ψ

ψ

−∞

 

− Γ +Γ ψ β  − ψ−θ +μ θ− ψ+ ψ−θ θ     =   θ β

π     + − ψ−θ + μ θ− ψ ψ−θ + ψ−θ μ +λ    

        

 

The numerical integration of this slightly different equation (i.e., with azimuth-varying 

circulation) follows exactly that given in Part III of this appendix. 

 The contribution of trailed vorticity to induced velocity at the lifting line of this 

“balanced” rotor is show in Figs. B-26 and B-27. The total blade lift and induced power is 

given in Fig. B-28. These results are for the balanced rotor producing 2,712 pounds of lift at 

178 knots and can be compared to Fig. B-25, which is for the “unbalanced” rotor. Only trailed 

vortices are contributing to the induced power at this point. The additional induced velocity 

and horsepower due to the shed wake still need to be included. 
APPENDIX B 

801

-300

-200

-100

0

100

200

300

0 30 60 90 120 150 180 210 240 270 300 330 360

x = r/R = 0.25

Induced 

Velocity

ft/sec

Blade Azimuth, ψ , deg

Fig. B-26 

-20

-10

0

10

20

30

40

50

60

70

80

0 30 60 90 120 150 180 210 240 270 300 330 360

x = r/R = 0.50

x = 0.75

Induced 

Velocity

ft/sec

Blade Azimuth, ψ , deg

Fig. B-27 
APPENDIX B 

802 

0

50

100

150

200

250

300

0 30 60 90 120 150 180 210 240 270 300 330 360

Blade Total

Lift (lbs)

&

Induced 

Horsepower

Blade Azimuth, ψ , deg

HPi

Lift/100

Fig. B-28 

 A numerical solution scheme for the shed wake is relatively simple compared to the 

trailed wake. In the shed wake problem, the vortex left behind the blade has a radial geometry 

and circulation just like the blade’s when the blade was at that azimuth, however, the vortex 

circulation is the negative of the blade’s bound circulation at azimuth. The geometry of this 

shed wake problem is shown in Fig. B-29. Again, the conventional rotor nondimensional 

notations are: 

(92) 

v

tpp

tpp

t

i

r x radius station where induced velocity is sought R

r xv radius station where vortex is trailed

R

angle of attack of the tip path plane, positive nose up

V cos advance ratio

V

v induced velocity

=

=

α ≡

μ= α

≡

tpp i

tpp

t

 calculated by momentum theory

Vsin v

 inflow ratio. 

V

α − λ =
APPENDIX B 

803

Fig. B-29 

 

 Now, using Fig. B-29 as the reference, begin with the Biot–Savart law 

(93) ( ) v i j ji

x 3

L dS L dS

d dv / dxv d

4 L

γ   − = θ   π  

, 

where the dimensions are expressed as vectors. The distance, L, between the shed vortex 

segment, dS, to the radius station, x, at which the induced velocity is sought, is 

(94) 

[ ] [ ]

( ) [ ] ( )

( ) ( ) ( )( ) ( )

i jk

tpp

3/2 3 2 32

2 3 22 2

L L L L (Xr Xv)i (Yr Yv)j (Zr Zv)k

where Xr R x cos Yr R x sin Zr 0

Xv R xv cos Yv R xvsin Zv R

and L (Xr Xv) (Yr Yv) (Zr Zv)

so L R xv x 2x xv cos 2 xv cos x cos

=++ = − + − + −

=− ψ =+ ψ =

=− θ+μ ψ−θ =+ θ =− λ ψ−θ    

= − +− +−    

= + − ψ−θ + μ θ− ψ ψ−θ + ψ−θ μ     { ( )}

3

2 2

tpp + λ .
APPENDIX B 

804 

Notice that the length (L) is the same for the shed wake as for the trailed wake. To continue 

then, the vortex element is describe by 

(95) S S S S Xv i Yv j Zv k =++ = + + i jk ()()() , 

but with rotor blade shed vortex geometry, the vortex extends radially so the partial 

derivatives of S are with respect to xv. Thus 

(96) 

i

i

j

j

k

k

S Xv dS dxv dxv R cos dxv

xv xv

S Yv dS dxv dxv R sin dxv

xv xv

S Zv dS dxv dxv 0.

xv xv

∂ ∂ = = =− θ

∂ ∂

∂ ∂ = = =+ θ

∂ ∂

∂ ∂ === ∂ ∂

 With this information, the geometric part of the Biot–Savart law becomes 

(97) i j ji ( )( )

3 3

L dS L dS x sin sin

dxv

L L

  −   ψ−θ +μ ψ−θ θ   = −     

. 

The Biot–Savart also needs the shed vortex circulation as it varies with wake age. Thus, 

(98) ( ) ( )

( )

2

x, c

v 1 2 at

and c x xv

d 2xv x 1

Shed d cos 1 d

d 1 x

ψ

ψ=θ

=

  Γ − − γ = −  θ=− Γ θ − θ

  ψ − , 

and the double integral giving induced velocity at any radius station, x, and azimuth, ψ, using 

Eqs. (97) and (98) is 

(99) ( ) ( )

( )

( )( )

c

1

2

c

x, 1 2 3

c x

2xv x 1 x sin sin

v cos 1 d dxv

1 x L

ψ

ψ

−∞

  − − ψ−θ +μ ψ−θ θ   = Γ θ−    θ −    

       

. 

 It is particularly important to study the integration with respect to wake age, θ, before 

discussing a complete integration of Eq. (99). The reason is that this portion of the integration 

has a definite possibility of “blowing up.” Therefore, reverse the integration order of Eq. (99) 

to read as 

(100)

( ) ( )

( )

( )( )

c

1

2

c

x, 1 2 3

c x

2xv x 1 x sin sin

v cos 1 dxv d .

1 x L

ψ

ψ

−∞

      − − ψ−θ +μ ψ−θ θ   = Γ θ−      θ

  −      

       
APPENDIX B 

805

In the first place, the integration is not a problem when θ = ψ because the numerator of the 

integrand is zero (i.e., ψ – θ = 0). Furthermore, from Eq. (94), the distance, L, between the 

vortex segment and the point on the blade where induced velocity is sought, reduces to 

{ } ( ) () { } ( )

3 3

2 3 22 2 2 L R xv x 2x xv cos 0 R xv x = +− = −     , 

which is only zero when x = xv. The physical meaning of this situation when θ = ψ is that the 

only vortex that exists is the blade’s bound circulation, and this straight line vortex cannot 

induce a velocity on itself. 

 Now look at the solution when a shed vortex is in the region ψ = – θ to 0 or, if you 

prefer, in the near wake. Suppose, for example, that the blade is at the 135-degree azimuth 

and θ is in the range 135 degrees backwards to 132 degrees in 1/30-of-a-degree increments. 

This represents 3 degrees of near wake. Assume the induced velocity is sought at the blade 

station, x = 0.5, and place the blade at azimuth ψ = 135 degrees. The accumulation of the shed 

wake influence is 

x, dv

area under versus

d

ψ θ

θ . 

The curve of x, dv d ψ θ versus wake age is illustrated in Fig. B-30. This figure suggests an 

impending singularity as computations are made very close to the blade’s lifting line. In fact, 

the velocity induced at the blade station, x = 0.5, of the lifting line becomes so large that a 

semi-log scale for the ordinate in Fig. B-30 is helpful in capturing how rapidly the shed 

wake’s influence drops off as the blade moves away from the deposited shed wake. 

 An empirical solution to the situation illustrated by Fig. B-30 is to add a vortex core 

diameter (VCD) nondimensionalized by rotor radius (R) to the L dimension of the shed wake 

problem [refer back to the discussion surrounding Eq. (61)].9

 This solution is effective as 

Fig. B-31 shows. Of course, it is the integrated value 

135

180 x,

x 0.5

132

180

dv

v d

d

π ψ=

ψ

= π

= θ

θ







that is more important, and this integrated result is shown versus VCD ratioed to radius in 

Fig. B-32 for x = 0.5 and ψ = 135 degrees. And even more important is the integrated value of 

induced velocity considering the wake extending all the way back to, say, θ = –20π. The 

induced velocity at x = 0.5 (and with ψ = 135 degrees) including this far wake is also shown 

in Fig. B-32. 

 

9

 The correct approach is to changed from a lifting line to a lifting surface representation of the rotor blade. 
APPENDIX B 

806 

1

10

100

1000

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3

x, dv

d

ψ

θ

Wake Age deg.

Fig. B-30 

0.1

1

10

100

1000

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3

Vortex Core Diameter 

Ratioed to Rotor 

Radius

VCD/R

 0

0.005

0.010

0.020

0.030

x, dv

d

ψ

θ

Wake Age deg.

Fig. 31 
APPENDIX B 

807

0

0.3

0.6

0.9

1.2

1.5

1.8

2.1

2.4

2.7

3

3.3

3.6

3.9

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Induced 

velocity

fps

Vortex Core Diameter, VCD/R

First 3 degrees

 of wake age

Wake age of

θ = 0 to -20π

Fig. B-32 

 To examine the influence of the shed wake further, select, somewhat arbitrarily, the 

ratio of VCD to rotor radius equal to 0.015. Now the distance, L, between the vortex segment 

and rotor blade station where induced velocity is sought, x, is rewritten as 

(101) 

() ( )

( )( )

( ) ( )

3

2

2 2

3

2

2 2 2

tpp

xv x 2x xv cos

L R 2 xv cos x cos

VCD

R

 

    + − ψ−θ  

= + μ θ− ψ ψ−θ  

    + ψ−θ μ +λ +      

. 

MathCad’s built-in numerical integrator had absolutely no problem calculating the induced 

velocity at all radius stations and any azimuth: 

(102) ( ) ( )

( )

( )( )

c

1

2

c

x, 1 2 3

c x

2xv x 1 x sin sin

v cos 1 d dxv

1 x L

ψ

ψ

−∞

  − − ψ−θ +μ ψ−θ θ   = Γ θ− θ    −    

       

. 

The calculation could be performed even at x = xv because the distance, L, can never be 

smaller than VCD/R. Furthermore, because the shed wake’s circulation goes smoothly to zero 

at both the blade root and tip, there is no need to perform a fixed-wing coordinate 

transformation, as was helpful for the trailed wake integration of both fixed and rotary wings. 
APPENDIX B 

808 

 The next objective is to calculate the induced velocity for the geometry and operating 

condition of the sample problem. To begin the numerical integration, however, additional 

input is required. The additional input that satisfies rotor lift = 2,712 pounds at an advance 

ratio of 0.5 is that Γo = 334 and Γ1 = – 253.9. For convenience, the complete input for the 

shed wake numerical integration is: 

 R = 22 feet 

 xc = 1/6 nondimensional 

 ρ = 0.002378 slugs per cubic feet 

 VCD/R = 0.015 nondimensional 

 Vt = 603.605 feet per second 

 μ = 0.5 nondimensional 

 λtpp = – 0.03 nondimensional 

 Γo = 334 square feet per second 

 Γ1 = – 253.9 square feet per second. 

 With this information as input, put MathCad and it’s built-in integrator to work 

calculating Eq. (102) as follows: 

o 1 c tpp

INPUT

0.5 334 253.9 R 22 x 1/ 6 0.03 VCD / R 0.015

Dimension integration.

Select azimuth station, = variable for this problem

Extent of wake age, WA 20

Maximum number of radial stations, M = 90

R

μ= Γ = Γ =− = = λ =− =

ψ

=− π

c c

s

ange of radial stations where induced velocity is calculated, s = 0,1.......M 1

Then proceed with these calculations

1 x 1 x a b

2 2

1 = s To correspond to radius stations used in trailed wake p M 2

−

− + = =

π   α +     

( ) ( )

( )

( )( )

() ( )

( )( )

( ) ( )

c c

s ss

2

c

s, 1 2 3

c 2

2 2

2

2 2 2

tpp

roblem

r 1x 1x x cos a b cos

R2 2

2xv x 1 x sin sin

v cos 1

1 x

xv x 2x xv cos

R 2 xv cos x cos

VCD

R

ψ

   + −

= = − α= − α      













    − − ψ−θ +μ ψ−θ θ = Γ θ−   

−            + − ψ−θ   

   + μ θ− ψ ψ−θ

    + ψ−θ μ +λ +        c

1

x

s s

d dxv

x a b cos

ψ

−∞

















 θ 







  



=− α

                                 
APPENDIX B 

809

 The calculation of induced velocity at the lifting line—as created by the shed vortices 

from the lifting line—follows from the preceding scheme. Additionally, lift and horsepower 

distributions are calculated from 

(103) 

( )( ) ( )

( )

2

s c

s, t s o 1 s 2

c

M 1

s,

s 0

s, s, s,

M 1

s,

s 0

2x x 1

L V x sin R sin 1 Running Lift

1 x

L L Single-blade lift at input azimuth

1 HP v L Running horsepower 550

HP HP Single-blade horsepower

ψ

−

ψ ψ

=

ψ ψψ

−

ψ ψ

=

    − − Δ = ρ +μ ψ Γ +Γ ψ − Δ       

  −  

= Δ 

Δ= Δ 

= Δ 





( ) c

s

 at input azimuth

1 x where cos s cos s 1 .

2MM

  +     π π  Δ= − +            

 The shed wake significantly contributes to the total induced velocity that the rotor 

blade sees, primarily over the mid-span portion of the blade. For example, the azimuthal 

variation in induced velocity at the three radius stations under examination (i.e., x = 0.25, 

0.50, and 0.75) is provided by Figs. B-33, B-34, and B-35, respectively. It is at the mid-span 

that the shed wake’s additional induced velocity is the greatest. 

 The blade’s azimuthally varying lift for the balanced rotor is illustrated in 

Fig. B-36. Note, in contrast to the unbalanced rotor shown in Fig. B-25, the balanced rotor 

carries lift in the fore and aft quadrants of the revolution. This gives, in effect, a short 

wingspan or low aspect ratio characteristic to the balanced rotor. As Fig. B-37 shows, this 

concentration of balanced rotor lift in the fore and aft direction is accompanied by excessive 

induced horsepower when compared to the unbalanced rotor in Fig. B-25. The average or 

steady induced horsepower for the balanced rotor is HPi = 76.4 hp versus 50.1 hp for the 

unbalance rotor and versus 6.13 hp for the ideal fixed wing. 

 The requirement for a rotor to have zero rolling moment is clearly adverse to the 

induced power required to produce lift. The ratio of balanced rotor-induced horsepower to 

ideal fixed-wing-induced horsepower is 76.4/6.13 = 12.4. But, keep in mind that while an 

elliptical bound circulation is ideal for a fixed wing, it is not obviously true for a rotary wing. 
APPENDIX B 

810 

-300

-200

-100

0

100

200

300

0 30 60 90 120 150 180 210 240 270 300 330 360

Trailed

Shed

Trailed + Shed

x = r/R = 0.25

Induced 

Velocity

ft/sec

Blade Azimuth, ψ , deg

Fig. B-33 

-30

-20

-10

0

10

20

30

40

50

60

70

80

0 30 60 90 120 150 180 210 240 270 300 330 360

Trailed

Shed

Trailed + Shed

x = r/R = 0.50

Induced 

Velocity

ft/sec

Blade Azimuth, ψ , deg

Fig. B-34 
APPENDIX B 

811

-20

-10

0

10

20

30

40

50

0 30 60 90 120 150 180 210 240 270 300 330 360

Trailed

Shed

Trailed + Shed

x = r/R = 0.75

Induced 

Velocity

ft/sec

Blade Azimuth, ψ , deg

Fig. B-35 

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 30 60 90 120 150 180 210 240 270 300 330 360

Rotor

Blade

Lift

pound

Blade Azimuth, ψ , deg

Fig. B-36 
APPENDIX B 

812 

-100

-50

0

50

100

150

200

250

300

0 30 60 90 120 150 180 210 240 270 300 330 360

Trailed

Shed

Trailed + Shed Induced 

Horsepower

HPi

Blade Azimuth, ψ , deg

Fig. B-37 
APPENDIX B 

813

Part V—Closing Remarks 

 This elementary introduction to induced velocity has been presented assuming an 

elliptical bound circulation distributed along a lifting line to represent both the wing and the 

rotor. The assumption has been that 

n

1

A sin n

∞

Γ ∝  β , 

and that A1 = 1 while A2 through A∞ = 0. An extension of the fundamental equations provided 

by this appendix could easily be made using a full set of the Fourier series. This extension, if 

made, would completely generalize the lift distribution for the rotor just as in the case of 

fixed-wing theory. 

 The spiraling vortex wake structure of the lifting rotor leads to very high induced 

power when compared to the ideal wing. For an advance ratio of 0.50, interference created by 

the spiraling rotor wake leads—just for a single blade—to induced power on the order of 10 

times that of the wing when the comparison is made at wingspan equals rotor diameter and 

equal lift. While an elliptical bound circulation is known to be ideal for the fixed wing, it is 

not ideal for the rotary wing in high-speed forward flight. 

 A single-bladed rotor and prescribed wake geometry have been selected for this rotary 

wing introduction. This has been useful for an elementary discussion. However, the practical 

problem includes any number of blades, and a vortex wake structure that is free to deform 

based on fundamental principles. Furthermore, representing the rotor blade by a lifting line is 

quite unsatisfactory when the rotor lift distribution varies with time. Fortunately, advanced 

analyses, coupled with powerful digital computers, give today’s rotorcraft engineers insight 

and practical answers to the effect of a rotor system’s wake on the lifting surfaces that created 

the wake. 
814 
815 

APPENDIX C 
APPENDIX C 

816 
APPENDIX C 

817 
APPENDIX C 

818 
APPENDIX C 

819 
APPENDIX C 

820 
APPENDIX C 

821 
APPENDIX C 

822 
APPENDIX C 

823 
APPENDIX C 

824 
APPENDIX C 

825 
APPENDIX C 

826 
APPENDIX C 

827 
APPENDIX C 

828 
APPENDIX C 

829 
APPENDIX C 

830 
APPENDIX C 

831 
832 
833 

APPENDIX D 

ROTOR HUBS 

The following drawings of hubs came from four sources, namely 

a. Bill Bousman’s collection.1

 Bill collected photos of many hubs from several 

manufacturers. Then he had the NASA Ames Research Center graphic arts 

department create line drawings on vellum. He had the drawings framed. They 

were mounted on the second floor wall in Building 215 at Ames Research Center. 

b. Schindler’s and Pfisterer’s AGARD paper,2 which I consider an exceptionally 

thorough piece of work. 

c. Tom Hanson’s small book titled A Designers Friendly Handbook of Helicopter 

Rotor Hubs, which he publishes himself and is extremely valuable.3

d. A few out of my own files. 

The aircraft and/or hubs shown are: 

1. Eurocopter AS-365, AS-360, SA-342, SA-330, AS-332, Triflex 

2. Agusta/Westland EH-101 

3. Bell Model 47, Model 206, Model 222, Model 412, Model 407/OH-58D, Model 

680 

4. Boeing Vertol BMR, CH-46, CH-47 

5. Doman LZ-5 

6. Cessna CH-1 

7. Hiller Model 360/UH-12 

8. Hughes AH-64, OH-6, HARP 

9. Lockheed AH-56, CL-475, XH-51 

10. Messerschmitt-Bölkow-Blohm (MBB), BMR, BO-105, PAH-2 

11. McDonnell XV-1 

12. Mil Mi-26 

13. Robinson R-22 

14. Sikorsky H-34, S-61, S-76, UH-60 

15. Westland Lynx 

 Lastly, you will find Ray Prouty’s article in the January 1983 issue of Rotor & Wing 

International magazine (pages 26–28) very, very helpful. His article is at the end of this 

appendix.

 

1

 Bousman, W. G.; Ormiston, R. A; and Mirick, P. H.: Design Considerations for Bearingless Rotor Hubs. Paper 

No. A-83-39-62-1000, Proc. 39th Annual Forum of the American Helicopter Society, St. Louis, Mo., May 9–11, 

1983. 

2 Schindler, R. and Pfisterer, E.: Impacts of Rotor Hub Design Criteria on the Operational Capabilities of 

Rotorcraft Systems. AGARD CP-423, Rotorcraft Design for Operations Symposium, Amsterdam, The 

Netherlands, Oct. 13–16, 1986. 

3

 Hanson, T. F.: A Designer Friendly Handbook of Helicopter Rotor Hubs. Newhall, Calif.: Author Published, 

2005. 
APPENDIX D 

834 

Fig. D-1. Eurocopter AS-365 (author’s collection). 
APPENDIX D 

835 

Fig. D-2. Eurocopter AS-365 (courtesy of Tom Hanson). 

Fig. D-3. Eurocopter AS-360 (Schindler/Pfisterer AGARD paper). 
APPENDIX D 

836 

Fig. D-4. Aerospatiale SA 342 (courtesy of Bill Bousman). 

Fig. D-5. Aerospatiale SA 330 (courtesy of Bill Bousman). 
APPENDIX D 

837 

Fig. D-6. Eurocopter AS-332 (Schindler/Pfisterer AGARD paper). 

Fig. D-7. Aerospatiale Triflex (Schindler/Pfisterer AGARD paper).
APPENDIX D 

838 

Fig. D-8. Agusta/Westland EH-101 (Schindler/Pfisterer AGARD paper).

Fig. D-9. Bell Model 47 (courtesy of Tom Hanson). 
APPENDIX D 

839 

Fig. D-10. Bell Model 206 (Schindler/Pfisterer AGARD paper).

Fig. D-11. Bell Model 222 (courtesy of Tom Hanson). 
APPENDIX D 

840 

Fig. D-12. Bell Model 412 (courtesy of Bill Bousman). 

Fig. D-13. Bell Model 407/OH-58D (courtesy of Tom Hanson). 
APPENDIX D 

841 

Fig. D-14. Bell OH-58D (courtesy of Bill Bousman). 
APPENDIX D 

842 

Fig. D-15. Bell Model 680 (courtesy of Bill Bousman). 

Fig. D-16. Boeing Vertol BMR (courtesy of Bill Bousman). 
APPENDIX D 

843 

Fig. D-17. Boeing Vertol BMR (author’s collection). 

Fig. D-18. Boeing Vertol BMR (author’s collection). 
APPENDIX D 

844 

Fig. D-19. Boeing Vertol CH-46. Hinge sequence flap-lag-pitch 

(courtesy of Bill Bousman). 

Fig. D-20. Boeing Vertol CH-47. Hinge sequence flap-pitch-lag (author’s collection). 
APPENDIX D 

845 

Fig. D-21. Boeing Vertol CH-47 (courtesy of Tom Hanson). 

Fig. D-22. Doman LZ-5 (courtesy of Tom Hanson). 
APPENDIX D 

846 

Fig. D-23. Cessna CH-1 (author’s collection).
APPENDIX D 

847 

Fig. D-24. Hiller Model 360 (courtesy of Tom Hanson). 

Fig. D-25. Hiller Model 360 (author’s collection). 
APPENDIX D 

848 

Fig. D-26. Hughes AH-64 (courtesy of Bill Bousman).

Fig. D-27. Hughes AH-64 (courtesy of Bill Bousman). 
APPENDIX D 

849 

Fig. D-28. Hughes AH-64 (Schindler/Pfisterer AGARD paper). 
APPENDIX D 

850 

Fig. D-29. Hughes OH-6 (courtesy of Tom Hanson). 

Fig. D-30. Hughes HARP (Schindler/Pfisterer AGARD paper). 
APPENDIX D 

851 

Fig. D-31. Lockheed AH-56 (courtesy of Bill Bousman).

Fig. D-32. Lockheed AH-56 (courtesy of Tom Hanson). 
APPENDIX D 

852 

Fig. D-33. Lockheed AH-56 (author’s collection). 
APPENDIX D 

853 

Fig. D-34. Lockheed CL-475 (author’s collection). 
APPENDIX D 

854 

Fig. D-35. Lockheed XH-51 (courtesy of Tom Hanson).

Fig. D-36. MBB Bearingless Main Rotor (Schindler/Pfisterer AGARD paper).
APPENDIX D 

855 

Fig. D-37. MBB BO-105 (courtesy of Bill Bousman).

Fig. D-38. MBB BO-105 (courtesy of Tom Hanson). 
APPENDIX D 

856 

Fig. D-39. MBB BO-105 (author’s collection). 
APPENDIX D 

857 

Fig. D-40. MBB BO-105 (author’s collection). 
APPENDIX D 

858 

Fig. D-41. MBB PAH-2 (Schindler/Pfisterer AGARD paper).

Fig. D-42. McDonnell XV-1 (author’s collection). 
APPENDIX D 

859 

Fig. D-43. McDonnell XV-1 (author’s collection). 

Fig. D-44. McDonnell XV-1 (author’s collection). 

Open C 

Section 
APPENDIX D 

860 

Fig. D-45. Mil Mi-26 (author’s collection). 

Fig. D-46. Robinson R-22 (courtesy of Tom Hanson).
APPENDIX D 

861 

Fig. D-47. Sikorsky H-34 (courtesy of Bill Bousman).

Fig. D-48. Sikorsky S-61 (courtesy of Tom Hanson). 
APPENDIX D 

862 

Fig. D-49. Sikorsky S-76 (courtesy of Tom Hanson).

Fig. D-50. Sikorsky UH-60 (courtesy of Bill Bousman). 
APPENDIX D 

863 

Fig. D-51. Sikorsky UH-60 (Schindler/Pfisterer AGARD paper).

Fig. D-52. Westland Lynx (Schindler/Pfisterer AGARD paper). 
APPENDIX D 

864 

Fig. D-53. Westland Lynx (courtesy of Tom Hanson).

Fig. D-54. Westland W.G.-13 (courtesy of Bill Bousman). 
APPENDIX D 

865 
APPENDIX D 

866 
APPENDIX D 

867 
868 
869 

APPENDIX E 
APPENDIX E 

870 
APPENDIX E 

871 
APPENDIX E 

872 
APPENDIX E 

873 
874 
875 

APPENDIX F 

DYNAMICS OF A FREE–FREE UNIFORM BEAM 

 When a helicopter airframe is subjected to hub forces and moments, there can be 

serious airframe responses that impact all components and occupants of the aircraft. This 

appendix illustrates the dynamics of the situation with the simplest example I could think of—

a beam shaken in the middle of its span by either a vertical force or a moment. To create this 

example, I imagined an empty Sikorsky UH-60, Fig. F-1, with the main- and tail-rotor blades 

removed. Then I melted it down and made a 50-foot-long rod out of the materials, which are 

mostly aluminum and steel. This rod, Fig. F-2, is a 50-foot-long, solid aluminum rod, 14.25 

inches in diameter. This amounts to a volume of 95,690 cubic inches. Given that aluminum 

weighs about 0.1 pounds per cubic inch, this beam weights slightly more than 9,569 pounds. 

Thus, the mass per unit length (m) is 9,569/32.174/50, which gives m = 5.948 slugs per foot. 

The moment of inertia (I) of the beam’s cross-section1 is πR4/4 or 2,024 inches cubed. 

Because the modulus of elasticity (E) of aluminum is 10×106 pounds per square inch, the 

beam’s stiffness is EI = 20,240×106

 pounds-inch squared or 140.6×106 pounds-feet squared. 

Therefore, the beam parameter of EI/mL4 equals 3.766 per second squared. 

Fig. F-1. The general arrangement of the Sikorsky UH-60. 

Fig. F-2. Elementary beam model.

 

1

 Roark, R. J. and Young, W. C.: Roark’s Formulas for Stress and Strain, 5th Edition, McGraw-Hill Book Co., 

New York, N.Y., 1965. 

Fx

–L/2 +L/2 l

h 

 Fz
APPENDIX F 

876 

 My elementary beam has a constant stiffness (EI) in pounds-feet squared and a mass 

per unit length (m) in slugs per foot from one end to the other. Admittedly, this is a poor 

assumption about a helicopter airframe that has many portions filled with engines, fuel, gear 

boxes, shafts, electronic boxes, cargo, and humans. This makes the assumption that the mass 

per foot is constant over the whole beam length hardly reasonable. Certainly the assumption 

that the beam has constant stiffness is unreasonable because a fuselage has “holes” such as 

doors, windows, and joints. Still, this example introduces you to the mathematics of the basic 

helicopter dynamics problem. 

 Now let me first calculate this elementary beam’s response to a hub vertical vibratory 

force (Fz), and second, calculate the response to a horizontal vibratory force (Fx), which 

acts at a height (h) above the beam’s center of gravity (c.g.) and, therefore, really creates 

a moment. Thirdly, I want to covey the possible responses when the two forces act 

simultaneously. 

Beam Response to a Vertical Vibratory Force 

 The elementary beam I have assumed is shaken in the middle as Fig. F-2 shows. No 

forces or moments are applied at the ends of the beam, which is what free-free means. 

Because I have placed the shaking force dead center in the middle of the beam, the 

mathematics can be developed using just one-half of the beam. That is, whatever shape the 

right-hand side takes, the left-hand side is the mirror image. Notice that I have denoted any 

station from the beam’s center along the beam to the right by the script letter (  ) measured in 

feet. Vertical deflection of the beam is denoted by (z), which is also in feet. The right-hand 

end of the beam is reached when  = L/2, where L is the total length of the beam in feet. 

This type of vibration problem is studied in several textbooks, but my favorite reference has 

always been Timoshenko’s third edition.2

 The vibrating beam problem is approached by equating the moments at some station 

( )  . That is, a moment at ( )  is created by each beam element inertia force (ma) times its 

distance to the station of interest ( )   − . This moment due to inertia is resisted by the beam’s 

structural moment, which leads to the equation 

(1) ( )

2 2 L 2

,t ,t

2 2 ,t

z z

EI M m d

t

∂ ∂ = =− − ∂ ∂







 







 . 

The integral form of the beam equation is put in the fourth-order partial differential equation 

classical form by taking the second derivative of Eq. (1) with respect to beam length, which 

leads to 

(2) 

4 2

,t ,t

4 2

z z

EI m

t

∂ ∂ = − ∂ ∂

 

 .

 

2

 Timoshenko, S. and Young, D. H.: Vibration Problems in Engineering, D. Van Nostrand Company, Inc., 

Princeton, New Jersey, Jan. 1955. 
APPENDIX F 

877 

The solution process is to assume an analytical equation that satisfies Eq. (2). Based on some 

experience, I chose 

(3) ,t () () () () z z A cosh k Bsinh k Ccos k Dsin k F = + ++       

where the vertical vibratory force (Fz) in pounds is defined as 

(4) () () 2 2 zcos

z zsin h zcos h zsin zcos h

zsin

F F F sin t F cos t F F sin t arc tan

F

  

= ω + ω = + ω+      

. 

Note that this forcing equation contains both a sine and a cosine component, and that the 

shaking frequency (ωh) is in radians per second. 

 Now the first step towards a solution of this partial differential equation problem is to 

establish the value of the constant (k) required by Eq. (3). First, you take the fourth derivative 

of deflection with respect to the beam station (l), which, it turns out, is simply 

(5) 

4

,t 4

4 ,t

z

k z

∂ = ∂



  , 

and then you take the second derivative of deflection with respect to time (t), which also turns 

out to be simply 

(6) 

2

,t 2

2 H ,t

z

z

t

∂

= −ω ∂



 . 

Inserting these two derivatives into Eq. (2) gives 

(7) () ( ) 4 2 EI k z m z   ,t H ,t = − −ω , 

and this leads to the constant (k) being defined as 

(8) 

1/4 2 m H k

EI

  ω =    

. 

 The question now becomes one of finding out what A, B, C, and D equal. These 

constants are found from the boundary conditions, which are values associated with the center 

of the beam and the free end of the beam. At the free end of the beam, where  = L/2, no 

forces or moments are applied. Therefore, the moment (i.e., the second derivative of Eq. 3) 

and the shear (i.e., the third derivative Eq. 3) must be zero. At the center of the beam ( )  = 0

where the vibratory force is applied, the beam shear must equal one-half of the applied 

vibratory force (i.e., Fz/2). Lastly, because the left-hand side of the beam must mirror the 

right-hand side, the beam slope (i.e., the first derivative) must be zero. These boundary 

conditions lead to four equations in the four unknowns (A, B, C, and D) and appear 

mathematically as 
APPENDIX F 

878 

(9) 

() () () () ()

() () () () ()

() () () () ()

2

L 2,t 2

2 z

3

L 2,t 3

3 z

3

0,t 3

3 z z

0,t

z

EI EI k A cosh k Bsinh k Ccos k Dsin k F 0 moment

z

EI EI k Asinh k Bcosh k Csin k Dcos k F 0 shear

z

EI EI k Asinh k Bcosh k Csin k Dcos k F F 2 shear

z

k Asin

=

=

=

=

∂

= + −− =     ∂

∂

= + +− =     ∂

∂

= + +− =     ∂

∂ = ∂









 



  



  



 () () () () z   h k Bcosh k Csin k Dcos k F 0 + −+ = slope.     

When these four equations are evaluated at the correct boundary condition stations, things 

simplify to 

(10) 

( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) ( )

( ) [ ]

[ ]

2

z

3

z

3

z z

z

EI k A cosh k L 2 Bsinh k L 2 C cos k L 2 Dsin k L 2 F 0 moment

EI k A sinh k L 2 Bcosh k L 2 Csin k L 2 D cos k L 2 F 0 shear

EI k B D F F 2 shear

k B D F 0 slope.

  + −− =  

  + +− =  

− =

+ =

From these four equations, it is immediately clear that D = – B and that ( ) 3

1 B

4k EI = . 

 With values for B and D, you have reduced the problem to two equations in two 

unknowns (A and C). Admittedly, the expressions for A and C are a little messy, but 

nevertheless 

(11) 

( )

( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

( )

( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

3

3

1 cosh k L 2 cos k L 2 sinh k L 2 sin k L 2 1

A

4k EI sinh k L 2 cos k L 2 cosh k L 2 sin k L 2

1 1 cosh k L 2 cos k L 2 sinh k L 2 sin k L 2

C

4k EI sinh k L 2 cos k L 2 cosh k L 2 sin k L 2

−   + + =   +  

−   + − =   +  

. 

Remember that k was obtained at Eq. (8), which is, to repeat, 

1/4 2 m H k

EI

  ω =    

. 

 The equations for A and C both contain a denominator that has the potential to go to 

zero given certain values of the product of k and L/2. The denominator goes to zero at several 

values of (kL/2). To see this, consider the following equation: 

sinh k L 2 cos k L 2 cosh k L 2 sin k L 2 0 ( ) ( ) + = ( ) ( ) . 

In mathematics, this equation is called a transcendental equation because the values of (kL/2) 

that make the equation zero must be found numerically. One simple way to attack this 

problem is to reform the equation by dividing through by cosh(kL/2), and then by cos(kL/2), 

to obtain 
APPENDIX F 

879 

(12) tanh k L 2 tan k L 2 0 ( ) + = ( ) , 

and then graph this sum versus ( )1/4 2 4

H kL m L EI = ω . I have done this as you can see in 

Fig. F-3. The roots of Eq. (12) are shown in Table F-1. 

Because the hyperbolic tangent of large numbers becomes virtually 1.0, the roots at 4 and 

beyond are found with adequate engineering precision from 

(13) ( ) ( ) 1/4 2 4

H kL m L EI 4 Root No. 1

2

π

=ω = −    . 

 The importance of Eq. (13) cannot be overstated because it defines the frequency (ωH) 

in radians per second at which response (say deflections or accelerations) of this uniform 

beam will be extreme. Of course, this does not happen in practice because there is always 

some structural damping, which I have not considered in this example. 

 With the preceding background, consider a shake test of a uniform beam. The beam is 

hanging from a rigid ceiling by the softest of springs so that the beam response is not 

influenced by the support system. In the middle of the beam is a weightless shaker that can 

apply a vibratory force in pounds of 

(14) F 100sin t z h = ω( ). 

 The shaker is turned on and the frequency (ωH) is increased from zero while you are 

watching the beam’s response. You know in advance that certain frequencies must be avoided 

because the beam will go into resonance. These critical frequencies—converted to cycles per 

second or hertz (Hz)—are calculated using (kL) from Table F-1 and Eq. (13) as 

(14) ( )4

4

1 EI f kL in cycles / sec or Hz 2 mL = π

and this means to take care as the frequency approaches 6.91 Hz, and then again as the 

frequency approaches 37.3 Hz, the first two resonance frequencies of the beam when shaken 

with a vertical force. 

Table F-1. kL Values to Be Avoided 

Root Number Value of kL 

1 4.7300407449 

2 10.9956078380 

3 17.2787596574 

4 23.5619449023 
APPENDIX F 

880 

-4

-3

-2

-1

0

1

2

3

4

0 2 4 6 8 10 12 14 16 18 20 22 24

( )

( )

tanh k L 2

+ tan k L 2

1/4 2 4 m LH

EI

  ω    

Fig. F-3. Roots of Eq. (12) found graphically. 

 Now think about the recording equipment you would use for this relatively simple test. 

A high-speed motion picture camera would be nice so the deflected shape of the beam could 

be seen and deflection measured, and an array of accelerometers attached to the beam all 

along its length would give you a measurement of beam vertical accelerations from beam 

nose (+L/2) to tail (–L/2). 

 First, imagine what you could learn from just one frame recorded by the high-speed 

camera at shaker frequencies of 6 and 36 cycles per second. You could, for example, select a 

frame from each input frequency and compare theory to test. Based on what you have learned 

above, the theory would be computed as 

(15) ,t () () () () ( ) z H z A cosh k Bsinh k Ccos k Dsin k F sin t = + ++ ω        . 

Notice that the maximum deflection occurs when sin (ωHt) equals ±1.0, so pick those frames 

where the deflection is maximum. What you would see is shown in Figs. F-4 and F-5. In each 

figure the solid lines goes with sin (ωHt) = +1.0 and the dash lines go with sin (ωHt) = –1.0. 

The applied force is 100 pounds in both cases. Keep in mind that the deflection is directly 

proportional to the applied force, so the shapes shown in Figs. F-4 and F-5 can be scaled to 

any other applied force. 

 Fig. F-5 makes an important point. If a six-bladed rotor were applying the vibratory 

force and its once-per-revolution frequency was 6 Hz, then its next higher frequency input 

would be at six per revolution, which is 36 Hz. It would be nice if the pilot’s and copilot’s 

seats were near the nose and specifically at beam station +20 feet. That station is a beam node 

as Fig. F-5 shows. At the node there is no deflection. Furthermore, a few passengers could be 

located near beam station +7 feet to enjoy a better ride. 
APPENDIX F 

881 

-0.002

-0.0015

-0.001

-0.0005

0

0.0005

0.001

0.0015

0.002

-25 -20 -15 -10 -5 0 5 10 15 20 25

Deflection 

(ft)

Beam 

Station

Tail Nose

Beam 

Node

Beam 

Node

Fig. F-4. Beam vibratory maximum deflection extremes. Forcing frequency of 6 Hz, 

force of Fz = 100 sin (ωHt). 

-0.0002

-0.00015

-0.0001

-0.00005

0

0.00005

0.0001

0.00015

0.0002

0.00025

-25 -20 -15 -10 -5 0 5 10 15 20 25

Deflection 

(ft)

Beam 

Station

Beam 

Nodes

Tail Nose

Fig. F-5. Beam vibratory maximum deflection extremes. Forcing frequency of 36 Hz, 

force of Fz = 100 sin (ωHt).

 

 
APPENDIX F 

882 

 The important factor for the human occupants and the aircraft structure is the beam’s 

acceleration from nose to tail. This acceleration is, from Eq. (6), 

(16) () () () ()

2

,t 2 2

2 H ,t H z

z

z A cosh k Bsinh k Ccos k Dsin k F

t

∂

= −ω = −ω + + +     ∂



  

where, to repeat, the vertical vibratory force (Fz) is defined as 

(4) () () 2 2 zcos

z zsin h zcos h zsin zcos h

zsin

F F F sin t F cos t F F sin t arc tan

F

  

= ω + ω = + ω+      

. 

 

 The accelerometers installed along the beam mentioned earlier are the most important 

sensors. Suppose an oscillograph or digital recording of the accelerometer placed at the 

beam’s nose is chosen as the key sensor to watch during a sweep of vibratory frequency from 

3 to 45 hertz. This sensor would be at beam station  = L/2. An accelerometer at this nose 

location simplifies the calculation of Eq. (16) to 

(17) ( ) ( )

( ) ( ) ( ) ( )

2 1 1

L 2,t 2 2 2 2 z

2 H ,t H 1 1 11 3

2 2 22

z cosh kL cos kL F

z

t sinh kL cos kL cosh kL sin kL 2k EI

= ∂   +   = −ω = ω    ∂ +    

 . 

Notice again that the acceleration is proportional to the vertical vibratory force so the 

acceleration can be scaled on the basis of a pound of Fz. Expressing the acceleration in units 

of gravity is also quite common. Following this practice yields 

(18) ( ) ( )

( ) ( ) ( ) ( )

2 2 1 1 L 2,t H 2 2 cos

2 3 h 2 2 1 1 11

2 2 22 sin sin cos

1 z cosh kL cos kL F sin t arc tan

F F t 2gk EI sinh kL cos kL cosh kL sin kL F

=   ∂   ω   +       = ω+          + ∂ +            . 

Now, by picking time (t) where the sine term in Eq. (18) is ±1.0, the maximum acceleration 

will be immediately clear, because 

(19) ( ) ( )

( ) ( ) ( ) ( )

2 2 1 1 L 2,t H 2 2

2 2 2 3 1 1 11

2 2 22 sin cos MAX

1 z cosh kL cos kL

F F t 2gk EI sinh kL cos kL cosh kL sin kL

=     ∂   ω  +      = ±         + ∂ +      . 

Throughout the preceding discussion you must keep in mind that the denominator in 

Eqs. (17), (18), and (19) can go to zero. That situation means the beam will be in resonance, 

and the acceleration in g’s and a per-pound basis can get very large. 

 Now let me do a frequency sweep from 3 to 45 Hz with the example beam. Figure F-6 

shows the maximum vibratory acceleration in g’s per pound of 2 2 F F sin cos + versus frequency 

in cycles per second (i.e., hertz). Because I have not included structural damping in the 

discussion, you can see that the maximum acceleration can be extremely large around 

frequencies of 7 and 37 Hz. In fact, this simple mathematical analysis gives an infinite 

acceleration, but I limited my choice of frequencies to graph in order to emphasize the danger 

of resonance. At a vibratory frequency of 6 Hz (recall Fig. F-4), a resultant force (i.e., 

2 2 F F zsin zcos + ) of 1,000 pounds will produce ± 0.8632 g acceleration at the beam’s nose. 
APPENDIX F 

883 

 Because I used this elementary beam as a model for the full-scale Sikorsky UH-60, it 

is worth a moment to calculate the response for the UH-60’s four-bladed rotor. This rotor’s 

normal speed is 258 rpm, which is 4.3 Hz. At that speed, the rotor might create vertical 

vibration at once per revolution (i.e., 4.3 Hz), four per rev (17.2 Hz), and probably eight per 

rev (34.4 Hz). Figure F-6 notes these frequencies with large, solid black symbols. Now let me 

guess that the vertical vibratory forces at each of these frequencies is ±100 pounds, ±1,000 

pounds, and ±500 pounds, respectively. Then, the acceleration at the nose would be as shown 

in Table F-2. 

 Of course, the example beam can be vibrated by forces other than vertical. Now 

consider a horizontal force acting above the beam’s center of gravity (c.g.), which is at the 

half span of the beam. 

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0 5 10 15 20 25 30 35 40 45

Shaker Frequency (f in Hz)

2 2

z sin z cos Max

Acceleration

F F

g per pound

      +  

±

UH-60 at 

Normal 258 

RPM (1/rev)

UH-60 

8/rev

UH-60 

4/rev

Fig. F-6. Nose maximum acceleration response to vertical vibratory response of the 

example beam. 

Table F-2. Vertical Force Response 

UH-60 Rotor 

Vertical Force (lbs) 

and Frequency (Hz) 

Nose Acceleration 

Per Fig. F-6 

Nose 

Acceleration (g) 

1/rev 100 at 4.3 0.000229 0.023 

4/rev 1,000 at 17.2 0.000270 0.270 

8/rev 500 at 34.4 0.001746 0.873 
APPENDIX F 

884 

Beam Response to a Horizontal Vibratory Force Acting Above the Beam’s c.g. 

 When a horizontal force (Fx) is applied at some distance (h) above the example beam’s 

c.g., say at a height of 5 feet, the beam has a vibratory moment acting on it. Figure F-2 

illustrates the geometry. The mathematics of this example parallels the preceding discussion. 

In fact, the starting point (the beam equation) is Eq. (2), which is repeated here for 

convenience 

(2) 

4 2

,t ,t

4 2

z z

EI m

t

∂ ∂ = − ∂ ∂

 

 . 

The same assumed solution works again, but with the horizontal force being applied at a 

distance (h) so 

(20) ,t ( ) ( ) ( ) ( )( ) x z A cosh k Bsinh k Ccos k Dsin k hF = + ++        , 

and the horizontal vibratory force (Fx) in pounds is defined as 

(21) () () 2 2 x cos

x x sin h x cos h xsin x cos h

xsin

F F F sin t F cos t F F sin t arc tan

F

  

= ω + ω = + ω+      

. 

Furthermore, the beam constant (k) that was obtained with Eq. (8) is valid, so keep in mind 

that 

1/4 2 m H k

EI

  ω =    

, and remember that the shaking frequency (ωh) is in radians per second. 

 The question again becomes one of finding out what A, B, C, and D equal. These 

constants are found from the boundary conditions, which are values associated with the center 

of the beam and the free end of the beam. At the free end of the beam where  = L/2, no 

forces or moments are applied. These are the same conditions applied with the vertical force 

vibration studied above. At the center of the beam ( )  = 0 , the boundary conditions are 

different because a moment equal to hFx/2 is applied. In this moment case, the loading is zero 

at the beam center, which means the deflection is also zero. Therefore, you have four 

equations in the four unknowns ( ) A, B, C, and D appearing as 

(22) 

( ) ( ) ( ) ( ) ( )( )

( ) ( ) ( ) ( ) ( )( )

( ) ( )

( )

2

x

3

x

2

x x

x

EI k A cosh k L 2 Bsinh k L 2 Ccos k L 2 Dsin k L 2 hF 0 moment

EI k A sinh k L 2 Bcosh k L 2 Csin k L 2 D cos k L 2 hF 0 shear

EI k A C hF hF 2 moment

A C hF 0 deflection

  + −− =  

  + +− =  

  − =  

  + =  

. 

From these four equations, it is immediately clear that C A = − and that ( ) 2

1 A

4k EI = . 
APPENDIX F 

885 

 With values for A and C, you have reduced the problem to two equations in two 

unknowns ( ) B and D , and these constants are found as 

(23) 

( )

( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

( )

( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

2

2

1 cosh k L 2 cos k L 2 sinh k L 2 sin k L 2 1

B

4k EI cosh k L 2 sin k L 2 sinh k L 2 cos k L 2

1 1 cosh k L 2 cos k L 2 sinh k L 2 sin k L 2

D

4k EI cosh k L 2 sin k L 2 sinh k L 2 cos k L 2

  − + =   −  

−   + + =   −  

. 

The equations for ( ) B and D both contain a denominator that has the potential to go to zero 

given certain values of the product of k and L/2. However the transcendental equation from 

which the critical roots are found in the applied vibratory moment case is noticeably 

different— it is the difference between the hyperbolic tangent and the tangent. That is, 

(24) tanh k L 2 tan k L 2 0 ( ) − = ( ) . 

A graph of this difference versus ( )1/4 2 4

H kL m L EI = ω is shown in Fig. F-7. The roots of 

Eq. (24) are shown in Table F-3. 

-4

-3

-2

-1

0

1

2

3

4

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28

1/4 2 4 m LH

EI

  ω    

( )

( )

tanh k L 2

− tan k L 2

Fig. F-7. Roots of Eq. (24) found graphically.

Table F-3. kL Values to Be Avoided 

Root Number Value of kL 

1 7.853204624096 

2 14.13716549125 

3 20.42035224561 

4 26.70353755551 
APPENDIX F 

886 

Because the hyperbolic tangent of large numbers becomes virtually 1.0, the roots at 4 and 

beyond are found, with adequate engineering precision, from 

(25) ( ) ( ) 1/4 2 4

H kL m L EI 4 Root No. 1

2

π

=ω = +     . 

 The importance of Eq. (24) cannot be overstated because it defines the frequency (ωH) 

at which response (say deflections or accelerations) of this uniform beam will be extreme. Of 

course, this does not happen in practice because there is always some structural damping, 

which I have not considered in this example. 

 Now let me shake this example beam with an applied moment (hFx) of 500 footpounds. I will select a shaker frequency of 18 cycles per second because this value is close to 

resonance for the example beam. The beam’s response is calculated as 

(26) ,t ( ) ( ) ( ) ( )( ) ( ) x H z A cosh k Bsinh k Ccos k Dsin k hF sin t = + ++ ω        , 

and the maximum deflection will occur when sin (ωHt) equals ±1.0. The beam’s response for 

this shaker frequency is shown in Fig. F-8. In this figure, the solid lines goes with sin (ωHt) = 

+1.0 and the dash lines go with sin (ωHt) = –1.0. The applied moment is 500 pounds. Keep in 

mind that the deflection is directly proportional to the applied moment, so the shape shown in 

Fig. F-8 can be scaled to any other applied moment. 

 Now let me again perform a frequency sweep from 3 to 45 Hz with the example beam. 

For the sake of contrast, I will add the maximum acceleration due to a vibratory horizontal 

force (really a moment caused by this force acting above the beam’s c.g.) calculated by 

Eq. (28) to Fig. F-6, which showed the maximum vibratory acceleration in g’s per pound 

of vertical force versus frequency in cycles per second. The composite result is shown in 

Fig. F-9. 

-0.0006

-0.0004

-0.0002

0

0.0002

0.0004

0.0006

-25 -20 -15 -10 -5 0 5 10 15 20 25

Deflection 

(ft)

Beam 

Station

Tail Nose

Beam 

Node

Beam 

Node

Fig. F-8. Beam vibratory maximum deflection extremes. Forcing frequency of 18 Hz, 

moment of hFx = 500 sin (ωHt). 
APPENDIX F 

887 

(27) ( ) ( )

( ) ( ) ( ) ( )

2 2 1 1 L 2,t H 2 2

2 2 2 3 1 1 11

2 2 22 xsin x cos MAX

1 z sinh kL sin kL

h

F F t 2gk EI sinh kL cos kL cosh kL sin kL

=     ∂   ω  +      = ±          + ∂ −      . 

Suppose the horizontal force is created by the Sikorsky UH-60, four-blade rotor system. And 

suppose the horizontal forces at once per revolution (i.e., 4.3 Hz), four per rev (17.2 Hz), and 

eight per rev (34.4 Hz) are ±100 pounds, ±1,000 pounds, and ±500 pounds, respectively. 

Then, the acceleration at the nose would be as shown in Table F-4. This result may be directly 

compared to the response to the same vertical vibratory forces given in Table F-2. 

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0 5 10 15 20 25 30 35 40 45

Shaker Frequency (f in Hz)

2 2

xsin xcos Max

Acceleration

F F

g per pound

      +  

±

UH-60 at 

Normal 258 

RPM (1/rev)

UH-60 

4/rev UH-60 

8/rev

Fig. F-9. Nose maximum acceleration responses of the example beam to vertical 

vibratory force (solid line) and horizontal vibratory force (dashed line), which 

creates a vibratory moment. Horizontal force acts 5 feet above the beam’s c.g.

Table F-4. Response to Horizontal Force Acting 5 Feet Above the Beam’s c.g. 

UH-60 Rotor 

Horizontal Force (lbs) 

and Frequency (Hz) 

Nose Acceleration 

Per Fig. F-6 

Nose 

Acceleration (g) 

1/rev 100 at 4.3 0.000073213 0.007 

4/rev 1,000 at 17.2 0.001011340 1.011 

8/rev 500 at 34.4 0.000417755 0.209 
APPENDIX F 

888 

Simultaneous Application of Rotor Hub Forces and Moments 

 It should now become clearer that a rotor shaking an airframe has more than a few 

factors influencing just what the structural and human response might be. To help in this 

understanding, recognize that the rotor hub can shake with three forces (vertical, horizontal, 

and lateral) and the corresponding three moments. This makes a total of six loads to consider. 

But then each load can have, at a minimum, sine and cosine components. For a four-bladed 

rotor such as the Sikorsky UH-60, this means sine and cosine values at 1 per rev, 4 per rev, 

and probably 8 per rev. The amount of required numbers is growing rapidly before an 

accurate calculation of even my simple beam’s response can be obtained. 

 Perhaps Table F-5 puts the problem in the proper perspective. There are 36 values to 

be accurately obtained. If you consider that there are no perfectly matched blade sets, then the 

Sikorsky UH-60 would need contributions to hub forces and moments from each blade 

individually, which becomes a daunting task—to put it mildly. 

 Of course, having the hub loads is only half the battle. How a complicated beam such 

as a real helicopter is going to respond—even to perfectly calculated hub loads—is pure 

conjecture. As I write this during April 2012, neither half of the problem has been solved by 

any member of the rotorcraft community. There is, however, no doubt in my mind that it will 

be done. 

Table F-5. A Bare Minimum of 36 Hub Force and Moment Components Must Be 

Accurately Obtained Before a Prediction of Helicopter Vibration Is Possible 

Parameter 

Vertical 

Force 

Horizontal 

Force 

Lateral 

Force 

Yawing 

Moment 

Rolling 

Moment 

Pitching 

Moment 

1/rev Sin 

1/rev Cos 

4/rev Sin 

4/rev Cos 

8/rev Sin 

8/rev Cos 
889 

APPENDIX G 

 This appendix contains my conversion of the original report from double-row spacing 

to single-row spacing to reduce the page count in Volume II. I have a PDF of the original or 

you may be able to find it on the internet. 
APPENDIX G 

890 

FEDERAL AVIATION AGENCY 

THE HELICOPTER AND OTHER V/STOL AIRCRAFT 

IN COMMERCIAL TRANSPORT SERVICE 

Growth to Date 

And Forecasted Growth 

to 1965 and 1970 

Prepared by 

Economics Branch Office of Plans 

November 1960 
APPENDIX G 

891 

FOREWORD 

 Taking note of an advancing technology resulting in large part from research and 

development sponsored by the military services, and noting also the continuing active interest 

by the aviation community as a whole in steep-gradient aircraft, the Federal Aviation Agency 

has established a program bearing the name “Project Hummingbird” to investigate this field. 

The purpose of this effort is to provide FAA and the aviation community with planning 

guidance regarding the future role and utilization of steep-gradient aircraft in civil aviation. 

 The focus of this report, which is the first to be published under “Project 

Hummingbird,” is on the uses of the helicopter and other vertical take-off and landing aircraft 

in short-haul commercial air transportation during the next ten years. Its basic objective is to 

develop forecasts both of the number of these aircraft which will be in airline service in 1965 

and 1970 in the United States and of the number of passengers they will carry. The impending 

conversion of the helicopter airlines to multi-engine turbine powered equipment make a 

comprehensive evaluation of the role that steep-gradient aircraft will play in commercial air 

transportation during the next decade particularly timely. While small size helicopters have 

achieved a considerable use in patrol and survey work, aerial application and in business 

flying, such activity is more appropriately considered in the context of the overall general 

aviation uses of aircraft in business and industry. 

 The preparation of this report was materially aided by many individuals in industry 

and government. Members of the staffs of aircraft manufacturers, certificated airlines, the 

Civil Aeronautics Board, the Port of New York Authority, the National Aeronautics and 

Space Administration, and a number of experts privately employed contributed special 

background information and statistics for use herein. Industry replies to an FAA questionnaire 

also provided new information on V/STOL aircraft development and markets. Chicago 

Helicopter Airways, New York Airways and Los Angeles Airways each provided members of 

the FAA staff with an opportunity to observe scheduled helicopter operations at first hand. 

For this assistance and cooperation the FAA staff expresses its appreciation. It should be 

stated, however, that the responsibility for the forecasts and opinions presented herein, and for 

the particular analytical use made of the information which was made available by industry 

and Government sources, belongs solely with the FAA staff. 
APPENDIX G 

892 

TABLE OF CONTENTS 

I. SUMMARY AND CONCLUSIONS 893 

II. POTENTIAL SHORT-HAUL MARKETS FOR THE HELICOPTER AND 

 V/STOL TRANSPORT AIRCRAFT 

 Background 895 

 Nature of V/STOL Transport Aircraft 895 

 Extent of Federal Government Regulation 897 

 Identity of Types of Markets 897 

 General Aviation Uses 898 

III. THE GROWTH OF COMMERCIAL TRANSPORT OPERATIONS TO 1960 

 The Beginnings of Certificated Helicopter Services 899 

 Passenger Traffic Trends 900 

 Mail and Cargo 901 

 Passenger Traffic Pattern 902 

 Helicopter Passenger Trip Length 903 

 Passenger Load Factors 903 

 Operational Trends 904 

 Performance Factors 905 

 The Helicopter Fleet 906 

 Economic Trends 907 

 Unit Costs 907 

 Helicopter Direct Operating Costs 908 

 Summary of Record to Data 909 

IV. THE METROPOLITAN MARKET, 1965–1970 

 New Transport Aircraft 912 

 Unit Costs and Fares 914 

 Attitude of the Civil Aeronautics Board 915 

 Other Growth Factors 917 

 1965–1970 Passenger Traffic and Aircraft Fleet Forecasts 918 

 Air Taxi Operations 919 

 New Metropolitan Area Services 920 

V. THE INTERCITY AND COMMUTER MARKETS, 1965–1970 

 Short-Haul Intercity Travel 925 

 The Problem of Speed 927 

 The Cost Problem 929 

 The Commuter Market 931 
APPENDIX G 

893 

I. SUMMARY AND CONCLUSIONS 

1. The unique characteristic possessed by the helicopter and V/STOL aircraft which 

distinguishes them from conventional aircraft and makes them ideally suited technically 

for the short-haul passenger markets is their ability to operate from small landing areas 

with steep approach and departure paths. Three types of short-haul passenger markets 

have generally been regarded as susceptible to development by the helicopter and 

V/STOL transport aircraft. They are: (1) the airport-metropolitan area market; (2) the 

short-haul intercity market. and (3) the commuter or intra-city market. 

2. The transport helicopter is presently being used for scheduled, certificated airline service 

in the metropolitan areas of New York, Chicago and Los Angeles. Passenger traffic 

carried by the three helicopter airlines has grown rapidly, amounting to 366,000 

passengers in calendar year 1959. However, operations are considered experimental as yet 

and all three helicopter airlines are dependent for their continued existence on Federal 

Government subsidy which provided 63 percent of total revenues in 1959. 

3. The transport helicopter has achieved its greatest success in airline service as a special 

purpose vehicle transferring fixed-wing air passengers between airports in the Chicago 

and New York areas. There has been limited development of helicopter traffic between 

the airports and the downtown city centers and between the airports end suburban points 

in these two areas. In the Los Angeles area where there is only one major airline airport, 

helicopter traffic flow is between the airport and suburban communities but this market 

has grown at a slower rate than the airport shuttle services provided in New York and 

Chicago. 

4. The high operating costs of the relatively small, single-engine, piston-powered helicopters 

currently in use have been the major problem confronting the helicopter airlines. The 

lowest direct operating cost achieved so far has been approximately 20 cents per available 

seat mile. 

5. The impending re-equipment of the helicopter airlines with turbine-powered helicopters is 

expected to provide new impetus to traffic growth. There are now 21 multi-engine, 

turbine-powered helicopters on order or on option by the three operators with deliveries 

scheduled to begin in 1961. 

6. Equipment purchase plans of the three helicopter airlines beyond 1964–1965 are not 

known at this time, but appear to depend on traffic growth and the availability of 

improved versions of the multi-engine, turbine-powered types of helicopters. Some 

interest has been reported in the compounded helicopter which may become available by 

1965, but this aircraft still has cost and serious noise problems to overcome. 

7. Direct operating costs of the new turbine-powered helicopters are estimated at 10 to 16 

cents per available seat mile. However, even with these projected lower unit costs the 

helicopter airlines will be unable to achieve a self-sufficient operation. A continuing 
APPENDIX G 

894 

requirement for Federal subsidy appears in prospect at least until more economic 

helicopter types are forthcoming. 

8. In addition to the stimulus provided by new equipment, passenger traffic of the helicopter 

airlines is expected to grow rapidly during the 1960–1970 period as a result of increasing 

fixed-wing traffic, greater penetration of the available market, and improved dependability 

of service. Airport shuttle service is expected to remain the mainstay of operations. It 

appears unlikely that helicopter fares will be reduced. 

9. Traffic of the three helicopter airlines is forecast to increase from 366,000 passengers in 

1959 to an estimated 1.2 million passengers by 1965 and to 2.0 million passengers by 

1970. The number of helicopters in service with these airlines is forecast to increase from 

24 at the close of 1959 to 30–32 by 1965, and to 40–45 by 1970. 

10. Washington, D.C. and San Francisco/Oakland are the most likely metropolitan areas for 

new scheduled helicopter services. Other metropolitan areas which appear to have a 

potential requirement for scheduled helicopter services are Miami, Dallas/Fort Worth, 

Boston, Detroit, Atlanta, Cleveland, Pittsburgh, Philadelphia and St. Louis. However, the 

Civil Aeronautics Board, noting the increasing subsidy requirements of the presently 

certificated helicopter airline, is on record that it has no current intention to certificate 

additional helicopter airlines. 

11. Penetration of the short-haul intercity passenger market by V/STOL aircraft operating 

between city centers depends on the availability of suitable aircraft and the necessary 

ground facilities. Such aircraft are still in a very early stage of development but might be 

available toward the close of the forecast period. While V/STOL city center operations 

can provide impressive time savings for many travelers, costs now projected for these 

aircraft appear to preclude fares which would be reasonably competitive with other means 

of transport. 

12. Commuter travel by helicopter between suburban points and city centers seems likely to 

develop only to a very limited extent for the foreseeable future and then merely as an 

extension of service by existing metropolitan area helicopter operators. 
APPENDIX G 

895 

II. POTENTIAL SHORT-HAUL MARKETS FOR THE HELICOPTER 

AND V/STOL TRANSPORT AIRCRAFT 

Background 

 The continued domination of the short-haul passenger markets in the United States by 

surface means of transport is regarded by many as commercial aviation’s greatest challenge. 

Although these markets have never been surveyed in their entirety, sample data have shown 

that the traffic carried by the airlines remains insignificant in comparison to the sum of the 

traffic carried by the railroads, bus lines and the private automobile. The efforts of the airlines 

since the end of World War II to penetrate these markets have not been without success, it 

should be noted. But the fact that the overwhelming majority of short-haul passengers today 

still travel by surface means of transport establishes the air traffic growth which has occurred 

to date as one of the few disappointments in the record of commercial aviation in the United 

States. 

 It has long been recognized that the key to successful entry into any of the short-haul 

passenger markets is a suitable transport vehicle. The challenge of the short-haul passenger 

markets is, therefore, a challenge primarily to the aircraft manufacturing industry. The 

potential for spectacular air traffic growth which exists in these markets has not been 

overlooked by the aircraft manufacturers. From their market and engineering research and 

from their experience in producing a variety of both military and civil short-range aircraft 

since the end of World War II, and particularly since the end of the Korean hostilities, there 

has evolved a conviction that the greatest promise of success in capturing significant shares of 

the short-haul passenger markets for air transportation lies in the development of helicopters 

and other V/STOL aircraft. 

 During the past two years market and engineering research directed. towards the 

design and production of economically competitive types of these newer aircraft has become 

both more intense and more widespread within the aircraft manufacturing industry, The great 

spur to this increased activity has been the likelihood of large amounts of unused plant 

capacity and productive capability in the industry in the 1960’s as requirements diminish for 

manned aircraft by the military services and for jet transports by the larger airlines of the 

world. Additionally, this activity has been spurred by a new promise of success—the 

availability of turbine-powered engine designs which are largely the outgrowth of military 

development and production. 

Nature of V/STOL Transport Aircraft 

 It is, of course, the flight characteristics of transport aircraft which determine the kind 

of markets in which they can operate. The unique characteristics possessed by the helicopter 

and other V/STOL aircraft which distinguish them from conventional aircraft and make than 

ideally suited technically for the short-haul passenger markets are their vertical or near 

vertical lift capability. and the attendant slow flight maneuver-ability and hovering ability. 

Because of these attributes helicopters and other V/STOL aircraft need no long runways to 
APPENDIX G 

896 

take off and land and can be operated from relatively small areas. These areas obviously can 

be located with far greater freedom than the large airports required by conventional aircraft—

in city centers, for example, or at other locations close to the true origin and destination of 

travelers. V/STOL aircraft are singularly capable, therefore, in theory at least, of freeing air 

travel from one of its most serious handicaps—the requirement it places on the traveler to 

make time consuming trips to and from an airport. This requirement is most onerous to the 

travelers making short trips. 

 In actual commercial transportation, it should be noted, the vertical lift capability of 

helicopters is not used to ascend to and descend from cruising altitudes. Although the 

helicopter is capable with limitations of vertical ascent to, and descent from, any desired 

height, and can hover in a stationary position before commencing horizontal motion, the 

factors of safety, load capacity and economy of operation dictate an angular ascent and 

descent. Thus, in takeoffs, for example, a vertical rise of only three to ten feet is generally 

made, after which horizontal acceleration is begun. The forward speed then provides 

additional lift. Multi-engine helicopters, however, will have the safe capability to increase the 

vertical portion of their takeoff and landing and this ability may be utilized in clearing 

obstacles and in making landings and takeoffs under zero-zero visibility conditions. 

 It may be assumed that other V/STOL aircraft, when operational in commercial 

transport service, will also ascend and descend angularly. But it is in no way required that the 

angle be comparable to that required for conventional aircraft. The result is that the area 

required for takeoff and landing for steep-gradient aircraft will always be small compared to 

the area required for takeoff and landing of conventional aircraft. 

 It is the hope of the aviation industry that the new turbine-powered engines now 

becoming available will enable helicopters and other V/STOL aircraft to compete 

economically in the short-haul passenger markets to support the technical advantage provided 

by their vertical lift capability. However, a difficult problem in achieving profitable 

commercial operations exists for these aircraft because of the price paid for this lift capability. 

At their present stage of development helicopters are small, slow, and complex. But more 

importantly, they are expensive to purchase and to operate. It may be expected that the 

handicap of complexity will always exist for the helicopter, and for the newer V/STOL 

aircraft, but that this will not be a crippling handicap. It may also be expected that engineering 

developments will overcome the problems of small size and slowness. The degree of success 

helicopters and other V/STOL aircraft achieve in commercial transport will depend, therefore, 

largely on the extent to which advances in engine design eliminate the handicaps of high 

initial and high operating costs. The requirement is not necessarily that these costs be reduced 

to a level below that of competing vehicles, but rather to a level which will enable them to 

compete on the basis of service. 
APPENDIX G 

897 

Extent of Federal Government Regulation 

 A factor important to the commercial transport use, of helicopters and other V/STOL 

aircraft is that of Federal Government regulation. The method of this regulation is the same as 

that which applies to fixed-wing aircraft. In order to offer scheduled V/STOL air transport 

service in interstate commerce,1

 the applicant operator must obtain from the Civil Aeronautics 

Board a certificate of public convenience and necessity. The authority to grant such 

certificates is given the Board under Section 401 of the Federal Aviation Act of 1958. The 

aircraft operator, or the airline, which receives a certificate of public convenience and 

necessity is then subject to the Board’s authority over almost all phases of its operation— 

routes served, schedules operated, fares charged, agreements entered into, etc. It is required to 

submit traffic and financial reports periodically. The certificate which is granted by the Board 

specifically authorizes the carriage of passengers or cargo or United States mail, or some 

combination of the three, and may or may not provide for eligibility to receive Federal 

Government subsidy upon establishment of need under honest, efficient and economical 

airline management. At the present time only three airlines have been awarded certificates 

providing subsidy eligibility for scheduled helicopter passenger, mail and cargo operations in 

the United States. Approximately 75 additional applications for certificates are on file with 

the Civil Aeronautics Board. 

 Any operator or airline proposing to provide scheduled or charter transport service 

solely with aircraft having a certificated take-off weight of 12,500 pounds or less is not 

required to obtain a certificate of public convenience and necessity from the Civil Aeronautics 

Board. Part 298 of the Board’s economic regulations exempts the operators of these aircraft in 

commercial transport service from the requirements of Section 401 of the Federal Aviation 

Act of 1958. The Board does not require any traffic or financial reports of these operators, and 

allows them to operate generally without restrictions except for routes. They are not 

authorized to carry United States mail and are not eligible for Federal Government subsidy. 

However, such operators must obtain an air taxi. operating certificate from the Federal 

Aviation Agency. This certificate is granted only after FAA inspects the operator’s aircraft 

and facilities and determines that they meet the safety requirements of the Civil Air 

Regulations. At the end of 1959 there were in the United States about 2,300 air taxi operators, 

of which 71 were utilizing helicopters. 

Identity of Types of Markets 

 It is the consensus of opinion in the aviation industry that three types of short-haul 

passenger markets are susceptible to development by steep-gradient aircraft because of their 

ability to operate from small areas. These markets are: 

1. The aerobus market; sometimes referred to as the aerocab or aerolimousine market; 

it consists of travel between a Community airport and its business or commercial 

 

1

 It should be noted that the service may physically be intrastate but if it links interstate commerce, it is legally 

defined as interstate commerce. 
APPENDIX G 

898 

centers, and of travel between airports of those larger communities having more 

than one air commerce airport. 

2. The intercity market; it consists of travel of less than 250 miles between city 

centers, and of feeder travel into and out of large community airports. 

3. The commuter market; sometimes referred to as the suburban market; it consists of 

travel of some 15 to 50 miles between the downtown areas of a community and its 

surrounding or adjacent suburbs. 

 It is apparent that in terms of distances these markets overlap. But their classification 

is based on the function of the travel rather than the travel distance. The distances are not 

regarded as rigidly defined. For example, the intercity market is sometimes defined to include 

travel of less than 200 miles to fit an aircraft type under consideration, and sometimes, for 

other aircraft types being considered, to include travel of 300 to 400 miles. The commuter 

market, too, is sometimes defined to include travel of not only from 15 to 50 miles but also 

from 5 to 75 miles. 

General Aviation Uses 

 Although the focus of this report is on the usage of helicopters and V/STOL aircraft in 

commercial transport service, it should be noted that the helicopter has played a modest but 

increasing role in general aviation in the last several year. As of January 1, 1960, there were 

525 active helicopters in a total general aviation fleet of 68,727 aircraft. This number 

compares with 237 helicopters four years earlier. 

 The more important general aviation uses of the helicopter include patrol and survey 

work, petroleum and mineral prospecting, detailed mapping in rugged terrain, police traffic 

control and search and rescue. A number of helicopters are also being used by corporations 

for the movement of personnel between offices and plants in congested metropolitan areas 

and by petroleum companies for transportation to off-shore drilling stations as well as for 

other corporate purposes. Other uses include the aerial treatment of crops and land and 

passenger and cargo transportation for hire in many varied activities. Use of the helicopter in 

air taxi services is discussed in greater detail in a later section of the report. 

 It is generally anticipated that because of its unique operating characteristics and its 

ability to do special tasks which cannot be performed by conventional aircraft, usage of the 

helicopter in general aviation will expand significantly. Despite this growth their wide 

geographic dispersion and the nature of their use, much of which is in thinly populated areas, 

would appear to limit their potential impact on the air traffic control and navigation system 

except insofar as air taxi operations and corporate usage in metropolitan areas increase. 

However, the certification of engines and airframes and the development of appropriate 

operational rules and regulations will represent a sizeable workload. 
APPENDIX G 

899 

III. THE GROWTH OF COMMERCIAL TRANSPORT OPERATIONS TO 1960 

The Beginnings of Certificated Helicopter Services 

 Only the helicopter has operated as a V/STOL aircraft in commercial transport service 

in the United States to date. Other transport V/STOL aircraft—the compounded helicopter 

and the convertiplane, for example, have at present advanced no farther than the prototype 

stage. 

 All transport helicopters now in commercial use are an outgrowth of military 

development and production. The first practical helicopter, as it is known today, was flown 

experimentally in the United States by its designer, Igor Sikorsky, in 1939—21 years ago. It 

won the immediate interest of the United States Army and, in the form of subsequent models, 

was used to a minor extent during World War II. The first transport helicopter was flown in 

1945 but it was not until the Korean War that the helicopter won widespread notice as an 

important transport vehicle. Its success on missions of supply, reconnaissance and mercy over 

difficult terrain spurred its development and established the Army as the largest single 

purchaser of helicopters, a position it holds to this day. 

 Commercial transport use of the helicopter followed on the heels of military use. The 

Civil Aeronautics Board scheduled its first prehearing conference on a helicopter application 

for a certificate of convenience and necessity to operate scheduled service as long ago as 

1944. The hearing was postponed because the war was still in progress and no helicopters for 

civilian use were available. But the applicant in that case, Los Angeles Airways, was awarded 

a certificate by the Board in 1947 to operate scheduled helicopter mail and property service. 

Since that first award the Board has granted certificates to Chicago Helicopter Airways and to 

New York Airways to conduct scheduled helicopter service for passengers as well as for 

property and mail, and has amended the certificate of Los Angeles Airways to allow the 

carriage of passengers. 

TABLE 1. 

DATES OF CERTIFICATION AND INAUGURATION OF SERVICE, 

CERTIFICATED HELICOPTER AIRLINES 

Item 

Los Angeles 

Airways 

Chicago Helicopter 

Airways 

New York 

Airways 

Effective Date of 

Certificate for:

 Mail and property 

 Passengers 

 Oct. 1947 

 Oct. 1951 

 July 1949 

 August 1956 

 March 1952 

 March 1952 

Date Scheduled Service 

Began for:

 Mail and property 

 Passengers 

 Oct. 1947 

 Nov. 1954 

 Sept. 1949 

 Nov. 1956 

 Oct. 1952 

 July 1953 

 
APPENDIX G 

900 

 Each of the certificates awarded these three airlines provided for subsidy payments. In 

1947 the Board also certificated the Yellow Cab Company of Cleveland, Ohio to carry 

passengers and property, but not mail, between the city airport and its downtown area. No 

operations were ever conducted, however, apparently because the non-mail certificate meant 

no subsidy, and the certificate expired. Only two airlines in the United States have offered 

scheduled passenger service in helicopters without specific subsidy support from the Civil 

Aeronautics Board. National Airlines, a trunk airline, operated an experimental helicopter 

service in Florida in 1954 as an adjunct to its regular scheduled passenger operations. In the 

same year Mohawk Airlines, a local service airline, operated a scheduled passenger helicopter 

service over one of its routes originating at Newark Airport. Both these airlines abandoned 

their helicopter operations. 

 Because Federal Government regulation requires periodic and detailed traffic and 

financial reporting from the certificated airlines, a substantial body of data on commercial 

helicopter operations is available for the three helicopter airlines now offering scheduled 

transport service in the metropolitan areas of Los Angeles, Chicago and New York. The 

experience accumulated by these airlines since 1947 provides a valuable insight into the 

future of the commercial transport helicopter and to a lesser extent other V/STOL aircraft; 

accordingly a comprehensive examination of this record follows. 

Passenger Traffic Trends 

 In general, the three certificated helicopter airlines have been authorized to provide 

service within a 50 to 60 mile radius of the metropolitan areas in which they operate. Within 

these areas they offer service from airport to airport and between airports and business 

centers. In addition, service is provided to suburban communities which fall within their 

authorized area of operations. In total the three airlines provided service to about 60 locations 

in 1959. 

 Although scheduled helicopter service was initially established for the purpose of 

carrying mail and property, the carriage of passengers, subsequently authorized, quickly 

became the most important form of traffic. Since its beginning, passenger traffic has shown a 

sharply rising growth trend; in calendar year 1959 366,000 passengers were flown 7.5 million 

passenger miles. This volume is small compared to the domestic trunk line volume (44.5 

million passengers) and to the local service volume (5.2 million passengers), but for the three 

helicopter airlines it represented an increase of 60 percent over the number of passengers 

carried in calendar year 1958. 

 Measured by passenger traffic, Chicago Helicopter Airways is by far the largest of the 

three helicopter airlines, with New York Airways the next largest and Los Angeles Airways 

the smallest. CHA’s passenger traffic between Midway and O’Hare airports boomed with the 

inauguration of jet flights at O’Hare, and total passenger traffic in 1959 was nearly four times 

the 1957 level. During the same period helicopter passenger traffic increased 76 percent in 

New York and 40 percent in Los Angeles. Passengers now account for 84 percent of the total 

revenue ton miles flown by the throe helicopter airlines. Table 3 shows the passengers carried 

by each of the airlines during the past three years. 
APPENDIX G 

901 

TABLE 2. 

DOMESTIC SCHEDULED AIRLINE PASSENGER TRAFFIC, 1959 

Airline 

Group 

Revenue 

Passengers 

(Originations) (000) 

Revenue 

Passenger Miles 

(000,000) 

Trunk 44,489 28,127.2 

Local Service 5,213 1,023.5 

Helicopter 366 7.5 

TOTAL 50,068 29,158.2 

TABLE 3. 

REVENUE PASSENGERS CARRIED BY CERTIFICATED 

HELICOPTER AIRLINES, 1957–1959 

(000 omitted) 

Year Total Chicago Los Angeles New York 

1957 153 55 30 68 

1958 229 108 31 90 

1959 366 204 42 120 

Mail and Cargo 

 While the passenger traffic has been rising, the volume of U. S. mail has been 

declining fairly steadily. In 1959 some 87,000 ton miles of mail were flown or 30 percent less 

than in 1953. The decrease appears partly due to the greater concentration of the carriers on 

their growing passenger traffic and the fact that they are scheduling their operations more to 

meet the needs of the passengers than the mail service. During periods of peak mail loads, the 

helicopter carriers have been unable to handle all of the traffic offered and the Post Office has 

been forced to divert mail traffic to trucks. Additionally, the helicopter carriers have cut back 

mail routes. Chicago Airways discontinued service between the airport and the downtown 

Chicago Post Office while New York Airways is no longer providing service to a 

considerable number of outlying communities it formerly served. 

 Freight and express are a relatively minor part of the helicopter airline traffic, 

constituting less than 7 percent of total revenue ton miles flown. In 1959 traffic totaled 48,000 

ton miles, an increase of one-third since 1955. Chicago Airways does not carry either freight 

or express and Los Angeles does not handle freight. 

 Table 4 shows traffic trends of the three certificated helicopter air carriers since 1953. 
APPENDIX G 

902 

TABLE 4. 

TOTAL TRAFFIC CARRIED BY CERTIFICATED HELICOPTER AIRLINES, 

1953–1959 

Year 

Revenue 

Passengers 

(000) 

Revenue 

Passenger 

Miles 

(000) 

Mail 

Ton Miles 

(000) 

Freight and Express 

Ton Miles 

(000) 

Total Revenue 

Ton Miles 

(000) 

1953 1 26 123 1 

1954 8 183 115 16 150 

1955 28 628 97 36 194 

1956 63 1,585 90 42 282 

1957 153 3,275 92 40 449 

1958 229 4,885 83 38 594 

1959 366 7,477 87 48 857 

Passenger Traffic Pattern 

 Although origin and destination data on helicopter passenger traffic are not available, 

an analysis of passenger originations provides a reasonably good indication of the passenger 

traffic pattern of the three helicopter airlines. Approximately 85 percent of the passengers 

carried in 1959 originated at major scheduled airline airports. Only 6.5 percent of the 

passengers carried originated in the downtown city centers, and the remaining 8.2 percent 

originated at other points within the metropolitan areas served. 

 The distributions of passenger traffic by origin points indicate that in Chicago and 

New York most of the helicopter passenger traffic is between terminal airports—between 

Midway and O’Hare airports in Chicago and between Idlewild, LaGuardia and Newark 

airports in New York. A relatively small portion of the traffic moves between the city centers 

(West 30th Street in New York and Meigs Field in the Chicago Loop) and the major airports, 

and between other locations in the New York and Chicago metropolitan areas and the airports 

or downtown. 

 The traffic pattern in Los Angeles is somewhat different because of the widely 

dispersed business and residential areas and the fact that the metropolitan area has only one 

major airline airport. There the traffic is between Los Angeles International Airport and 

approximately 15 communities in the metropolitan area, the largest of which in terms of 

originated passengers is Anaheim. No passenger service between the airport and downtown 

Los Angeles is provided by Los Angeles Airways. 

 Table 5 shows the concentration of helicopter passenger originations at the major 

terminal airports, and the limited development of traffic at the downtown city centers and at 

other communities in the metropolitan areas served. 
APPENDIX G 

903 

TABLE 5. 

HELICOPTER PASSENGER ORIGINATIONS IN 1959, 

CERTIFICATED HELICOPTER AIRLINES 

Originating 

Point 

Total Los Angeles Chicago New York 

Number Percent Number Percent Number Percent Number Percent

Terminal 

 Airport 312,640 85.3 20,252 48.5 177,449 86.8 114,939 95.6 

Downtown 

 City Center(1) 23,750 6.5 – – 20,903 10.2 2,847 2.4 

Other Area 

Communities 29,925 8.2 21,484 51.5 6,037 3.0 2,404 2.0 

Total 366,315 100.0 41,736 100.0 204,389 100.0 120,190 100.0 

 1. Includes Meigs Field, Chicago. 

Helicopter Passenger Trip Length 

 As is to be expected, distances traveled by passengers over helicopter routes are 

extremely short. The average helicopter passenger trip in 1959 was 20.4 miles. As is shown in 

the table below, however, Los Angeles Airways with an average passenger trip length of 35.4 

miles was significantly higher than the average. Available information reveals that there has 

been little change in recent years in the length of the average passenger trip of each of the 

helicopter carriers. 

TABLE 6. 

AVERAGE LENGTH OF HELICOPTER PASSENGER TRIP (MILES) 

1958–1959 

Airline 1959 1958 

Chicago 17.9 18.4 

Los Angeles 35.4 37.7 

New York 19.4 19.2 

3-Airline Average 20.4 21.3 

Passenger Load Factors 

 The increase in passenger traffic has been accompanied by a steady improvement in 

the revenue passenger load factor. Load factors for the three operators averaged 51.5 percent 

in 1959 compared with 40.3 percent in 1957 and 25.6 percent in 1954. Los Angeles Airways 

which had a 56.4 percent load factor in 1959 has consistently recorded the highest load factor 

of the three carriers largely because of the limited capacity it has offered and the small size 

helicopters it has been operating. 

 The 1959 load factors of the helicopter operators were substantially higher than the 

44.3 percent average of the local service airlines but were still well below the trunk line 

average of 61.4 percent. As traffic and the capacity of equipment utilized increased, the 

average passenger load per aircraft also rose. 
APPENDIX G 

904 

TABLE 7. 

REVENUE PASSENGER LOAD FACTOR LOAD AND PASSENGER 

LOAD PER AIRCRAFT, CERTIFICATED HELICOPTER AIRLINES 

1953-1959 

Year 

Revenue Passenger 

Load Factor 

Passenger Load Per 

Aircraft 

1953 13.67% 0.38 

1954 25.6 1.03 

1955 36.8 1.44 

1956 44.5 2.26 

1957 40.3 3.05 

1958 42.8 3.93 

1959 51.5 5.00 

Operational Trends 

 Both the aircraft miles flown and the number of aircraft departures made by the 

helicopter carriers have registered substantial increases since 1953. However, their rate of 

growth has been appreciably less than that of traffic carried because of steady increases in the 

size of helicopter utilized and in the passenger load factor. In 1959 a total of 1,899,000 

revenue aircraft miles were flown, up 89 percent from 1953, while aircraft departures totaled 

138,000 or 53 percent more than in 1953. Comparatively, revenue ton miles flown rose by 

564 percent during the same period. 

 Because of the nature of the route patterns being operated, the average flight stage of 

the helicopter operators is very short. In 1959 the average hop was 13.7 miles with Los 

Angeles Airways’ average flight somewhat longer than either New York’s or Chicago’s. The 

short stages being flown, of course, contribute significantly to the high cost of current 

helicopter operations. 

 Although aircraft operations by the helicopter operators represent only a minute 

fraction of the total aircraft operations handled by FAA airport traffic control towers, they 

represent a fairly sizeable proportion of the landings and take-offs at the major airports in 

New York, Chicago and Los Angeles. At these high density airline terminals helicopter 

aircraft operations constitute 5 to 13 percent of the total aircraft operations. At Meigs Field, 

which is a leading helicopter traffic point but is not served by any domestic trunk or local 

service airline, helicopter aircraft operations account for 18 percent of all operations handled. 
APPENDIX G 

905 

TABLE 8. 

REVENUE AIRCRAFT MILES FLOWN, AIRCRAFT DEPARTURES, AND 

AVERAGE FLIGHT STAGE, CERTIFICATED HELICOPTER AIRLINES 

1953-1959 

Year 

Revenue Aircraft 

Miles Flown 

(000) 

Aircraft 

Departures 

(000) 

Average Flight 

Stage 

(miles) 

1953 1,006 90 11.2 

1954 1,071 90 12.0 

1955 1,152 94 12.3 

1956 1,317 104 12.7 

1957 1,603 126 12.7 

1958 1,675 127 13.3 

1959 1,899 138 13.7 

TABLE 9. 

SCHEDULED AIRLINE HELICOPTER AIRCRAFT OPERATIONS AS A PERCENT 

OF TOTAL AIRCRAFT OPERATIONS AT MAJOR AIRPORTS IN 1959 

Airport 

Total Aircraft 

Operations 

Helicopter Aircraft 

Operations(1)

Percent Scheduled 

Helicopter 

La Guardia 274,732 .27,610 10.0 

Newark 187,099 13,938 7.4 

New York International 239,836 13,132 5.5 

Meigs 106,791 19,384 18.2 

Midway 431,600 34,788 8.1 

O’Hare 234,983 30,164- 12.8 

Los Angeles International 316,068 22,708 7.2 

 1. Estimated by multiplying departures by two. 

Performance Factors 

 The growth of helicopter traffic appears to have been adversely affected by the 

relatively poor schedule reliability maintained. The best available measure of dependability of 

operations is the performance factor which is the ratio of scheduled aircraft miles completed 

to aircraft miles scheduled. During the past three years the performance factor of the 

helicopter operators averaged 88 percent. Comparatively the domestic trunk lines and local 

service carriers averaged over 97 percent during the same period. 
APPENDIX G 

906 

TABLE 10. 

COMPARISON OF PERFORMANCE FACTORS, CERTIFICATE HELICOPTER, 

TRUNK AND LOCAL SERVICE AIRLINES 

1955-1959 

Year Helicopter 

Airlines 

Trunk 

Airlines 

Local Service 

Airlines 

1955 85.9% 97.8% 97.5% 

1956 85.9 96.4 96.7 

1957 88.0 97.5 96.7 

1958 88.5 96.6 97.5 

1959 88.0 97.4 97.2 

 The performance factors of the three helicopter carriers has varied widely. Chicago 

has consistently had the highest percentage of completions with 96.4 percent in 1958 and 93.6 

percent in 1959, thus comparing favorably with the fixed-wing operators. Los Angeles 

completed 89.7 percent of its scheduled mileage in 1959. New York has regularly made the 

poorest showing in this area with a performance factor of only 76.5 percent in 1959. The 

primary cause of this relatively unfavorable record appears to have been the inability to fly 

during bad weather conditions. Maintenance problems appear to have been a contributing 

although less significant factor. 

TABLE 11. 

PERFORMANCE FACTORS, CERTIFICATED HELICOPTER AIRLINES 

1955–1959 

Year Chicago Los Angeles New York 

1955 97.1% 89.4% 82.1% 

1956 94.2 89.0 77.2 

1957 92.9 90:9 79.8 

1958 96.4 87.2 78.6 

1959 93.6 89.7 76.4 

The Helicopter Fleet 

 At the end of 1959 the fleet of the three helicopter airlines consisted of 24 pistonpowered helicopters, an increase of five aircraft since 1955. The period was marked by the 

introduction into service of the 12 passenger S-58 in 1956 and by the 15 passenger Vertol 

44-B in 1958. The smaller Bell 47’s continued in operation. Although both Chicago and New 

York Airways made changes in the composition of their fleets during the period, Los Angeles 

Airways made no change either in the number or type of helicopters operated (2 S-51’s and 5 

S-55’s). The tabulation shows trends in the structure of the helicopter airline fleet since 1955. 
APPENDIX G 

907 

TABLE 12. 

AIRCRAFT FLEET OF THE CERTIFICATED HELICOPTER AIRLINES 

1955–1959 

As of Dec. 31 Total B-47 S-58 S-55 S-51 V-44B 

1955 19 7 – 10 2 – 

1956 20 7 3 8 2 – 

1957 26 6 6 12 2 – 

1958 22 4 5 6 2 5 

1959 24 6 6 5 2 5 

Economic Trends 

 Financially the helicopter airlines have made steady progress. Commercial revenues 

have increased sharply with the growth of traffic and net income has improved steadily. 

Despite these gains subsidy requirements have continued to rise although at a considerably 

lesser rate than commercial revenues. Each of the three airlines is still dependent on Federal 

subsidy for its continued existence. 

 Table 13 shows trends since 1955 in revenues and subsidy. In 1959 Federal subsidy 

represented over 63 percent of total operating revenue with subsidy needs amounting to $4.9 

million compared to total passenger revenues of $2.3 million. This has meant that while the 

average passenger fare was $6.31, the average subsidy per passenger was $13.43. 

TABLE 13. 

REVENUES AND FEDERAL SUBSIDY, CERTIFICATED HELICOPTER AIRLINES 

1955–1959 

Year 

Passenger 

Revenues 

(000) 

Federal 

Subsidy 

(000) 

Total Operating 

Revenues 

(000) 

Percent, Subsidy 

of Total Operating 

Revenues 

1955 $208 $2,710 $3,355 80.87 

1956 438 2,834 3,711 76.4 

195 968 4,173 5,032 82.9 

1958 1,459 4,616 6,289 73.4 

1959 2,309 4,914 7,760 63.3 

Unit Costs 

 High operating costs have been the major economic problem encountered by the 

helicopter operators. In 1959 it cost these carriers an average of $4.05 per available ton mile 

and $8.29 to carry one ton mile of revenue pay load. 

 To provide some perspective on these costs it is of interest to compare them with the 

unit costs experienced by the domestic trunk line and the local service air carriers. 
APPENDIX G 

908 

TABLE 14. 

COMPARISON OF TOTAL OPERATING COSTS IN 1959 

Airline Group Per Available Ton Mile Per Revenue Ton Mile 

Helicopter $4.05 $8.29 

Domestic Trunk 0.28 0.53 

Local Service 0.51 1.12 

 While helicopter unit operating costs are thus still extremely high, it is encouraging to 

note that they have shown a marked improvement; in 1959 they averaged approximately 40 

percent below the level of 1955. This decline appears largely due to the increasing efficiency 

of the newer helicopters which have been put into service and the expansion in volume of 

traffic. However, it should be noted that the cost problem of the helicopter carriers is not 

merely one of high direct operating costs. Indirect costs are also extremely high as is indicated 

in the following table. Moreover, there are wide differences in indirect unit costs among the 

three carriers with Chicago averaging $0.95, Los Angeles $1.61 and New York $2.30 per 

available ton mile. 

TABLE 15. 

DIRECT AND INDIRECT OPERATING COSTS, CERTIFICATED 

HELICOPTER AIRLINES, 1955–1959 

Dollars Per Available Ton Mile Dollars Per Revenue Ton Mile 

Year Total Direct Indirect Total Direct Indirect 

1955 $6.75 $3.62 $3.13 $15.22 $8.16 $7.06 

1956 6.37 3.22 3.15 12.96 6.55 6.41 

1957 4.82 2.93 1.89 11.50 6.99 4.51 

1958 3.98 2.47 1.51 10.04 6.22 3.82 

1959 4.05 2.54 1.51 8.29 5.20 3.09 

Helicopter Direct Operating Costs 

 To focus more closely on the problem of helicopter costs, an analysis has been made 

of the direct operating costs of the various helicopter types now being flown by the 

certificated helicopter airlines. The results of this analysis are almost startling to those who 

have been accustomed to think in terms of fixed-wing aircraft costs. In its most efficient 

usage, the S-58, the most economical helicopter now in service, has a direct operating cost of 

approximately 20 cents per available seat mile. Comparatively, fixed-wing aircraft have direct 

operating costs of about two to three cents per available seat mile. 

 The table which follows compares the direct costs of the various helicopters now in 

service. The table shows a range for each type because of the wide differences in costs among 

the three operators. Additionally, a direct comparison between the S-58 and V-44B is difficult 

since these two aircraft are not now being flown by any one operator. However, New York 

Airways has flown both types, and its experience appears to indicate that while direct costs 

per hour are relatively comparable, ton mile and seat mile costs on the S-58 are slightly lower 

than on the V-44B. 
APPENDIX G 

909 

TABLE 16. 

DIRECT OPERATING COSTS OF HELICOPTERS IN CERTIFICATED AIRLINE 

SERVICE 1958-1959(1) 

Helicopter Type Year Entered 

Service Per Hour Flown Per Available Ton Mile 

Per Available 

Seat Mile 

Sikorsky S-51(2) 1947 – – – 

Bell B-47 1949 $54.37–54.75 $4.95–5.33 – 

Sikorsky S-55 1952 77.97–142.10 2.38–7.35 $0.28–0.35 

Sikorsky S-58 1956 208.05–260.92 1.67–3.02 0.20–0.33 

Vertol V-44B 1958 256.28–260.35 3.35–3.47 0.36–0.40 

1. For years ended June 30, 1958 and September 30, 1959. Cost experience is shown only where there was 

substantial utilization of the particular helicopter type. 

2. The S-51 was flown too few hours for any meaningful cost experience. 

Summary of Record to Date 

 The foregoing data on the record to date of the three certificated helicopter airlines 

reveal two significant developments: 

1. The helicopter has achieved its greatest success in commercial transport services as 

a special purpose vehicle transferring fixed-wing air passengers between airports in 

the Chicago and New York metropolitan areas; and 

2. despite the achievement of a sizeable growth in passenger traffic and improved 

operating efficiency, the three helicopter airlines have been unable to reduce their 

aggregate subsidy requirements with the single-engine, piston-powered helicopters 

which have been available for purchase. 

 The inability of the helicopter airlines to achieve any significant progress toward 

economic self-sufficiency utilizing their relatively small, high unit cost helicopters has not 

been entirely unexpected. The Civil Aeronautics Board has indicated several times in 

certificate renewal and mail rate decisions that no final judgment of the helicopter experiment 

would be made until larger aircraft had become available and had been placed in service. For 

example, in the Los Angeles Airways Renewal Case (Docket No. 8178) decided July 28, 1958 

the Board stated: 

“Until a larger commercial helicopter is in operation and has been shown to be economically 

feasible, operations by rotary wing carriers must still be considered as developmental in 

nature and as requiring a further period of experimentation.” 

This statement was repeated in the New York Renewal Case (Docket No. 8569) decided 

March 17, 1960. 

 
APPENDIX G 

910 

 The emergence of inter-airport transfers as the mainstay of helicopter traffic has 

undoubtedly been the outstanding market development in helicopter airline operations to date. 

To a considerable extent it may be noted this has been an unexpected turn of events. Although 

there was early recognition of airport shuttle service as an important helicopter market, 

proponents of the helicopter generally have emphasized its potential use in city center 

operations and the community service that such operations would provide. However, as the 

record shows there has been only limited development of the airport-city center and suburban 

markets so far. 

 The use of the helicopter as an airport shuttle vehicle has developed most notably in 

the Chicago metropolitan area. Although Chicago Helicopter Airways was the last of the three 

helicopter airlines to offer scheduled passenger service, it has by far the largest passenger 

traffic volume. This achievement appears due almost entirely to the heavy air passenger 

movement between O’Hare International Airport, which handles all jet aircraft flights to and 

from Chicago, and Midway Airport, which has more passenger traffic than any other airport 

in the world. Chicago’s Department of Aviation has estimated that perhaps 60 percent or more 

of Chicago’s air passengers make transfers from one plane to another. 

 On the other hand, Los Angeles Airways which operates in an area with only one large 

air commerce airport is the smallest of the three helicopter airlines. Although New York 

Airways operates in an area with three large airports and has been providing passenger service 

three years longer than Chicago, its traffic is now less than half that of Chicago. This appears 

due to the lesser requirement for plane transfers generated in New York. According to a Port 

of New York Authority survey, about one-fifth of New York’s outbound domestic passengers 

transfer from one airport to another. This proportion, however, has probably increased 

somewhat with the concentration of jet service at New York International Airport. 

 The fact that helicopter traffic so far is confined largely to airport shuttle service (and 

the steady increase in aggregate subsidy requirements) point up the developmental nature of 

current commercial helicopter operations. In attempting to forecast the 1965 and 1970 

passenger traffic and aircraft fleet size of the three certificated helicopter airlines therefore, 

the two traditional methods of projection (trend analysis and correlation analysis) are of little 

value. Both methods appear unsuitable because the scheduled arrival early in 1961 of turbinepowered helicopters will bring down the curtain on the piston-engine era. The data applicable 

to that era will manifestly be inadequate, when used solely mathematically, to describe the 

new era. What remains then, is the method of subjective evaluation of the factors which have 

had an impact on traffic in the past and of the new factors which will have an impact on traffic 

in the future. 

 Before listing these factors and then proceeding to the forecast data, two pertinent 

assumptions should be noted. The first is in regard to the duration of the operating authority of 

the three currently certificated helicopter airlines. All three airlines have only temporary 

certificates; the Civil Aeronautics Board has refused in the renewal applications of each 

airline to grant permanent certificates. The Board stated its position in this regard as recently 

as March 1960 in the New York Airways Renewal Case (Docket No. 8569): 
APPENDIX G 

911 

 “We agree ... that continuation of New York Airways’ operating authority is required by the 

public convenience and necessity. But we do not find that renewal of the carrier’s certificate 

on a permanent basis is warranted at this time in view of the substantial Government support 

that is still required. We recognize that the inter-airport shuttle service and the suburban 

airport - feeder service offered by New York Airways in the New York metropolitan area 

provides substantial public benefits and that probable improvement in the carriers’ total 

subsidy position may occur if the large capacity direct lift equipment presently in the 

developmental stage proves feasible in commercial use. Yet we cannot overlook the high 

price the Government is presently paying for the amount of benefits being provided and the 

probability that the carrier will continue to need substantial amounts of subsidy for some time 

to come ... The Board recently denied permanent certification to Los Angeles Airways even 

though that carrier has been a certificated carrier longer than New York Airways and also 

provides a unique and valuable service in the sprawling and densely populated Los Angeles 

area. We find the factors which led the Board to deny permanent certification to Los Angeles 

Airways are equally applicable to New York Airways’ request for a certificate of unlimited 

duration in this proceeding.” 

 New York Airways’ operating authority now extends through March 16, 1967; that of 

Los Angeles through December 31, 1964; and that of Chicago Helicopter Airways through 

April 6, 1963. Whether or not the Board will grant permanent certificates upon expiration of 

the current certificates, or whether the Board will or will not renew the present certificates for 

even a temporary period, are not properly subjects for forecasting. An assumption has been 

made here, therefore, that the three currently certificated helicopter airlines will retain at least 

temporary certificates, authorizing service over the routes now being served, through 1970. 

(The question of whether additional carriers will be certificated for helicopter operations in 

cities other than New York, Chicago and Los Angeles is discussed in a subsequent part of this 

report.) 

 The second assumption made for purposes of this report is that passenger traffic, 

rather than freight, express or mail traffic will determine the size of the helicopter operations 

and the helicopter aircraft fleet during the next ten years in New York, Chicago and Los 

Angeles. As noted in the previous section, cargo ton miles were only six percent of the three 

airlines’ total revenue ton miles in 1959. Mail traffic was a somewhat more important source 

of traffic (about ten percent of the total revenue ton miles in 1959) but in absolute volume it 

has declined almost steadily since 1953. Passenger traffic is the most important part of the 

operations of the helicopter airlines and it appears certain to remain so during the forecast 

period. 
APPENDIX G 

912 

IV. THE METROPOLITAN AREA MARKET, 1965–1970 

 The prospects for further development and growth of helicopter and V/STOL airline 

operations can be analyzed most meaningfully in terms of the different markets in which these 

aircraft may be utilized. In this section the outlook during the next decade for the metropolitan 

area operators in New York, Chicago and Los Angeles will be examined. In the following 

sections, the V/STOL potential in other segments of the short-haul travel market will be 

analyzed. 

New Transport Aircraft 

 Undoubtedly the most important single operational factor affecting the future growth 

of scheduled helicopter service in the three metropolitan areas of New York, Los Angeles and 

Chicago is the one of new turbine-powered transport aircraft. The helicopter industry may be 

said to have entered the turbine-powered era in September 1960, with the delivery to Los 

Angeles Airways of a Sikorsky S-62—a single turbine-engine helicopter with a capacity for 

nine to twelve passengers and a cruising speed of about 100 mph. However, this one new 

helicopter is being leased by Los Angeles Airways only as an interim aircraft to gain turbine 

experience pending delivery of the five larger turbine-powered helicopters it has on order. 

 Early in 1961, a long-awaited, large-scale fleet modernization program will get under 

way with the introduction into service by the helicopter airlines of the first twin-turbine 

transport helicopters. These new aircraft will have appreciably greater capacities and cruising 

speeds than the piston-powered helicopters now in operation. The airlines are hopeful that the 

improved performance, greater comfort and all-weather capability of these aircraft will 

provide the basis for substantial traffic growth. 

 As of September 1960, the three airlines had 21 twin-turbine helicopters on order and 

on option. Both Los Angeles Airways and Chicago Helicopter Airways have ordered S-61’s, a 

25-28 passenger turbine transport with a cruising speed of 140 mph. Los Angeles Airways has 

ordered five S-61’s for delivery beginning in April 1961, and Chicago Helicopter Airways has 

ordered six S-61’s for delivery beginning in June 1961. It is expected that when the S-61’s are 

received, the piston-engine helicopters now being used will gradually be phased out of 

service. Whether Los Angeles Airways will retain or return to Sikorsky, after delivery of its 

S-61’s, the one S-62-it leased in September 1960, is not known at present; a decision will 

apparently await actual delivery of the S-61’s. 

 New York Airways has contracted to purchase five Vertol 107’s, a 25-passenger, 

158 mph twin-turbine engine helicopter for 1961 delivery and has an option on five more, 

with delivery dates to be determined by traffic requirements. It has been reported that the New 

York Airways purchase contract provides for trading in the five Vertol 44B’s they are now 

operating. 

 
APPENDIX G 

913 

 Because of their larger capacities and higher cruising speeds, the annual productivity 

of the new helicopters will be appreciably greater than that of the smaller piston-engine 

helicopters currently in service. Thus, the new helicopters are expected to be of particular 

value to the airlines during peak travel times. Both Chicago Helicopter Airways and New 

York Airways, for example, have reported losing passengers in their airport-to-airport shuttle 

service because of a lack of available seats during their busiest hours of the day. 

 The turbine-powered helicopters are also expected to attract new passengers because 

of their greater appeal in terms of size, speed and comfort. The aircraft will look more 

substantial, and more like the larger fixed-wing aircraft to which the air traveler is 

accustomed. The twin-turbine engines will provide a smoother ride than do the single piston 

engines on present helicopters. And although the greater speed of the new aircraft will not 

bring about large aggregate time savings to air travelers because of the shortness of helicopter 

trips, the flying public is expected to be increasingly receptive to any possible time savings 

because of the impact of jet airlines in reducing flight times on intercity routes. The air 

traveler who saves travel time by flying a jet airliner will not wish to lose that time getting to, 

from or between airports. 

 The newer helicopters are also expected to aid traffic growth by providing all-weather 

capability and improving schedule reliability significantly. Lack of instrument flying has 

adversely affected helicopter traffic growth at each of the three metropolitan areas that now 

have scheduled helicopter service. New York Airways has estimated, for example, that bad 

weather forced cancellation of approximately 20 percent of its scheduled flights. 

 Equipment purchase plans of the three metropolitan area operators beyond 1964–1965 

are unknown at this time and appear to depend both on the rate at which traffic grows in the 

next three to four years, and on the availability of more efficient helicopters. Past experience 

indicates that there will be a continuing improvement in the state of the art, which should 

result in more comfortable, more efficient helicopters, with seating capacities fitted to specific 

market requirements. Improved versions of the S-61 and V-107 types of helicopters may 

therefore reasonably be expected to be available to the helicopter airlines in the 1965–1970 

period. 

 Additionally, there is the possibility that compounded helicopters may became 

available in the 1965–1970 time period for use in metropolitan area service or short-haul 

intercity service. The British manufactured Rotodyne is most often reported in this respect. 

New York Airways has expressed its interest in acquiring five Rotodynes in 1964 or 

thereafter. However, a number of problems are attached to this aircraft. One is noise, which at 

present appears to be unacceptably high for close-in operations. Another is high unit costs for 

very short haul, i.e., 10 to 50 miles, stage lengths. The Rotodyne is a 55-64 passenger aircraft 

which appears designed for the 150–250 mile intercity passenger markets rather than for the 

airport-metropolitan area markets now served by New York Airways and the other two 

helicopter airlines. Efficient utilization of this aircraft would probably be limited, therefore, to 

a few longer route segments, such as La Guardia Airport–New Haven unless the Civil 

Aeronautics Board extended the airline’s present route authorization. However, the Board is 
APPENDIX G 

914 

on record as opposing extensions of service into areas already served by fixed-wing airlines. 

In the New York Airways Renewal Case, referred to earlier, the Board stated: 

 “In renewing New York Airways’ authority without the customary rotary-wing limitations, it 

should be emphasized, however, that in doing so we have no intention of permitting the 

carrier to duplicate the short-haul services now being provided by the local service carriers. 

We fully expect that New York Airways will continue to provide service complementary to 

and not competitive with fixed-wing operators.” 

Unit Costs and Fares 

 In addition to greatly improved performance characteristics, the new twin-turbine 

helicopters ordered by the three certificated operators are also expected to provide important 

reductions in unit costs. Actual operating experience with the new turbocopters is lacking, of 

course, but available estimates show a range of about 10 cents to 16 cents for direct operating 

costs per available seat mile. Comparatively, direct operating costs of the piston-powered 

S-58 are 20 cents per seat mile. 

 If these unit coat estimates are realized, they will therefore represent a substantial 

improvement over current levels which suggest the possibility of lower fares as a factor which 

will promote traffic growth. The fact is, however, that the passenger fares currently charged 

by the helicopter airlines are largely unrelated to costs. In 1959 the total direct, indirect and 

capital costs of providing helicopter service to the average passenger was $19.74. The fare 

charged the average passenger was only $6.31, however—the difference being made up by 

subsidy payments. As a practical matter, the fares charged by the helicopter airlines appear to 

be set at levels which in the judgment of airline management produce the maximum gross 

revenues while meeting requirements to be competitive with limousine and cab fares and to 

contribute to traffic development. Because current helicopter fares are developmental, it 

appears unlikely, therefore, that they will be lowered upon the showing of an improvement in 

direct operating costs. 

 There is the question, too, whether any small or nominal reduction in fares, based on 

an improvement in direct operating costs, would bring about an increase in passenger traffic. 

No analytical data on the elasticity of demand for helicopter travel are available, but the 

airlines have made surveys which indicate that business, expense-account travelers account 

for most of the passenger traffic. A six-week survey in 1957 conducted by the Port of New 

York Authority in collaboration with New York Airways reported, for example: 

 “The business traveler accounts for three-fourths of all helicopter passengers, and two-thirds 

of the people connecting planes. Of those linking air and ground transportation, four-fifths are 

on business trips. The proportion of helicopter passengers on business trips is considerably 

higher than that of airplane passengers.” 

 This composition of helicopter passenger traffic may be attributable in part to the 

relatively high level of helicopter fares. They range from 15 to 20 cents per passenger mile on 

airport-suburban routes to 50 to 60 cents on inter-airport, high density routes and average 

about 30 cents per passenger mile on all routes. On the other hand, air travel by fixed-wing 

aircraft costs, in most instances, between five and eight cents per passenger mile. Although by 
APPENDIX G 

915 

no means conclusive, the evidence is that the demand for helicopter travel is relatively 

inelastic. In these circumstances the possibility cannot be ignored that helicopter fares might 

well be increased in order to lessen subsidy requirements. 

 One promotional factor in the matter of helicopter fares has been the development of 

joint fare agreements with connecting fixed-wing airlines which provide for much of the costs 

of the helicopter fare to be included in the regular fixed-wing fare. Such agreements have 

meant in Los Angeles, for example, that fixed-wing air travelers destined for eastern points 

can fly from any local heliport to Los Angeles International Airport via Los Angeles Airways 

for just two dollars more than the regular air fare from the airport. 

Attitude of the Civil Aeronautics Board 

 Because of the dependence of certificated helicopter operations on Federal subsidy 

and the probability of a continuing subsidy requirement until more economical helicopters 

become available, the attitude of the Civil Aeronautics Board will be a decisive factor in 

determining the future scope of airline helicopter operations. The Board occupies this position 

of control by virtue of its statutory authority to grant or withhold certificates of public 

convenience and necessity and subsidy eligibility, and to determine the duration and amount 

of subsidy which will be paid to eligible airlines. 

 Current CAB policy is to maintain the certificated helicopter experiment in 

approximately its present framework until such time as a more economical helicopter type can 

be produced. On the question of subsidy, the Board has taken the position that there is a limit 

to the subsidy support it can reasonably provide for the helicopter experiment. Statements 

from Board decisions involving the helicopter airlines and quoted in part in prior sections of 

this report indicate the Board’s intention to try to hold subsidy costs to the Government at 

approximately their current level. In furtherance of this Objective, the Board has consistently 

refused to award unlimited or permanent certificates to the helicopter airlines so that it might 

maintain control over the duration of subsidy payments. In the Los Angeles Airways Renewal 

Case (Docket No. 8178) decided July 28, 1958, the Board stated, for example: 

“The Examiner concluded that, in view of the sizeable amount of subsidy LAA is presently 

receiving and the fact that the Government’s obligation to support helicopter operations with 

substantial sums of subsidy mail pay will continue for some time to come, renewing LAA’s 

certificate on a permanent basis, as requested by the applicant, is not warranted at this time. 

We concur with his finding in this regard. We find that LAA’s certificate should be renewed 

for a temporary period of approximately seven years, or until December 31, 1964, as 

recommended by the Examiner. In that way, the Board will have an opportunity to review the 

results of the carrier’s operations for a reasonable period after the introduction of the S-61’s 

and will be in a better position to evaluate the benefits of the service in relation to the cost to 

the Government.” 

The Board has also limited the amount of routes to be served by helicopter in order to hold 

down subsidy payments. In the Chicago Area Service Case (Docket No. 6600 et al.) decided 

June 7, 1956, the Board stated: 
APPENDIX G 

916 

“....None of the foregoing arguments have convinced us that we should expand the certificate 

authority of CHA beyond that recommended by the Examiner. In view of the experimental 

nature of the proposed passenger operations, the fluid character of the service to be rendered, 

the prospective cost to the Government, and the need of the carrier for maximum operational 

flexibility, we believe it is necessary to limit CHA’s certificated operations to the inner 

triangle route. Although the record contains no reliable estimate of the total cost of 

establishing and maintaining a combined passenger and mail service to the outlying cities, we 

are convinced that the annual cost to the Government in the form of subsidy pay would be 

substantial.” 

Thus the Board has moved cautiously in granting certificate authority to serve additional 

points requested by the helicopter airlines and has limited their operations to metropolitan 

area service. 

 In view of the Board’s position, the basic question to be answered is whether during 

the next ten years scheduled helicopter service will become profitable to the extent that 

Government subsidy would not be required. If subsidy is not required, then obviously the 

Civil Aeronautics Board would not be bound in its certificate award and renewal decisions by 

concern of costs to the Government, and the restraining influence of subsidy requirements 

would not exist to limit helicopter operations. 

 An evaluation of available data, particularly that presented by the helicopter airlines to 

the Board in recent certificate renewal and mail pay cases, indicates no likelihood of 

helicopter subsidy requirements being eliminated during the next five years. In fact, the Board 

anticipates that the subsidy needs of the three operators may increase initially when the new 

turbine-powered helicopters are placed in service. The picture beyond 1965 is much less clear 

in this regard, but the magnitude of the subsidy requirements forecast by the helicopter 

airlines and the Board’s staff for initial turbine powered operations, together with evidence 

that periods of three to five years are needed to develop and place into service newer and 

more economical aircraft, point to the continuance of subsidy requirements in the 1965–1970 

period also. 

 As noted previously, the direct operating costs per available seat mile for the new 

helicopters which the three helicopter airlines will put into service in 1961 are estimated at 10 

to 16 cents—about 20 to 50 percent lower than the seat mile costs for the piston-engined S-58 

helicopter. However, it appears unlikely that even with these projected cost reductions, the 

helicopter airlines will be able to achieve a self-sufficient operation by 1965. Assuming that 

direct costs would actually average about 12 to 13 cents per seat mile for the new helicopters 

and that indirect costs would average about 10 to 14 cents per seat mile, total costs would be 

approximately 22 to 27 cents per seat mile. With an average passenger load factor of 50 to 55 

percent those seat mile costs become 40 to 54 cents per passenger mile. The current average 

yield of the helicopter operators is about 30 cents per passenger mile. Thus, if current fare 

levels are maintained, about 10 to 24 cents of the total direct and indirect cost, or 25 to 40 

percent would have to be made up by subsidy payments. 

 
APPENDIX G 

917 

 Under such circumstances it appears unlikely. that any significant changes in the scope 

of the present helicopter experiment can be expected for the next five years at least and 

possibly for the next ten years. Obviously however, in view of the evolving helicopter 

technology, no final judgment on this point can be made at this stage, particularly for the 

latter part of the 1960s. 

Other Growth Factors 

 New York, Los Angeles, and Chicago are the largest and most congested metropolitan 

areas in the United States. As such they provide the most promising markets for utilization of 

the unique capabilities of the helicopter. The size and population concentrations of these 

communities have created serious surface transport problems. Distances between airports, and 

between airports, city centers and other important commercial or residential areas are 

generally long, and surface travel is inconvenient and time consuming. These three 

communities, more than any others, therefore, present the helicopter airlines with a great 

potential for traffic growth. 

 These three communities are also the busiest fixed-wing air traffic hubs in the United 

States. Together they account for approximately 27 percent of the total national air passenger 

market. Surveys taken by the three helicopter airlines show that almost all of their passengers 

are fixed-wing aircraft passengers who use the helicopter to transfer from one airport to 

another in a metropolitan area, or to begin or end an intercity air journey. In 1959, more than 

33 million passengers arrived at or departed from these three metropolitan areas. The 366,000 

helicopter passengers in 1959 represent only slightly more than one percent of this total. 

 The continuing growth in total fixed-wing air passenger traffic provides an additional 

potential for helicopter service. The Los Angeles Airport Commission estimates that 

passengers at Los Angeles International Airport will total 9 million by 1965 and 13 million by 

1970, increases of 53 and 120 percent respectively over the 1959 total. The Port of New York 

Authority expects New York’s air passengers to grow to 24.7 million by 1965 and to 45 

million by 1975—increases of 58 and 189 percent over the 1959 total. As air traffic grows it 

is likely that the helicopter operators will establish additional gate positions at the major 

airports in New York, Chicago and Los Angeles, thereby improving the convenience and 

accessibility of their services, which in turn should lead to greater penetration of the available 

market. 

 No major changes in the traffic flow pattern of the helicopter airlines appear likely 

during the next ten years. Thus, in the New York and Chicago areas the major portion of the 

passenger traffic is expected to consist, as it does now, of travel between terminal airports. 

The possible construction of another major airport in both New York and Los Angeles during 

the latter part of the 1960’s would substantially expand the available market. The Los Angeles 

helicopter operation in particular should grow with the opening of an additional large air 

commerce airport and the establishment of an airport shuttle route which now does not exist. 
APPENDIX G 

918 

 Growth in city center airport traffic which now constitutes a relatively small 

proportion of total helicopter traffic appears to depend largely on the availability of additional 

and more conveniently located heliports. The FAA National Airport Plan contains 

recommendations for a sizable program of heliport development. It appears likely that this 

program will move forward as air traffic grows. In New York the planned opening late in 

1960 of another heliport in Manhattan in an area close to the financial district should develop 

more downtown traffic. It should be recognized, however, that while the helicopter can 

provide time savings over surface transport between many downtown areas and the airports, 

this is dependent on the nearness of the heliport to the traveler; there will also be many air 

passengers who will begin or end their trips at downtown or near downtown points from 

which time savings by helicopter to and from the airports will be marginal or nonexistent. 

 Traffic between suburban points and the airports may also be expected to increase 

with more frequent flights and with the inauguration of service at additional heliports. 

However, so far there is no evidence of any real development of traffic between the city 

centers and suburban points. Thus the suburban routes appear likely to remain the weakest 

part of the New York and Chicago helicopter operations. Only in the faster growing, more 

widely dispersed Los Angeles area does it appear that the suburban routes will account for a 

significant share of the total helicopter passenger traffic. 

 While past growth trends cannot be used mathematically for forecasting purposes, as 

previously noted, the growth the three helicopter airlines have achieved since their beginnings 

has meaning which cannot be ignored. Passenger traffic has maintained a consistent and sharp 

upward trend. Passengers carried in 1959 were almost six times the number carried in 1956. 

Data for the first six months of 1960 reveal a further marked advance with traffic up 

63 percent over the corresponding months of 1959. Such a remarkable rate of growth 

indicates a growing acceptance and popularity of helicopter service which augurs well for the 

three helicopter airlines. 

1965–1970 Passenger Traffic and Aircraft Fleet Forecasts 

 An evaluation of the factors discussed in the proceeding sections indicates the three 

helicopter airlines in New York, Chicago and Los Angeles will carry approximately 1.2 

million passengers in 1965 and 2.0-million passengers in 1970. This traffic will require a fleet 

of 30 to 32 helicopters in 1965 and of 40 to 45 helicopters in 1970. It will generate an 

estimated 210,000 aircraft departures in 1965 and 290,000 aircraft departures in 1970. 

 These forecasts are limited to the operations at the three metropolitan areas now 

served by the helicopter airlines, it should be noted, and must be regarded as subject to a 

sizeable margin of error due to the developmental mature of helicopter operations to date, and 

to the circumstance of the major change in the type of flight equipment scheduled for the near 

future. The 1.2 million passengers forecasted for 1965 is presented, therefore, as the midpoint 

in a forecast ranging from a low of 1.0 million passengers to a high of 1.4 million passengers. 

Similarly, the 1970 forecasts of 2.0 million passengers is presented as the midpoint of a 

forecast ranging from a low of 1.7 million passengers to a high of 2.3 million passengers. 
APPENDIX G 

919 

 The low estimates of 1.0 million for 1965 and 1.7 million for 1970 will allow for 

growth in passenger traffic at approximately the same aggregate annual increments as was 

experienced by the three helicopter airlines in the three year 1958-1960 period. The high 

estimates at 1.4 million for 1965 and 2.3 million for 1970 call for a more rapid traffic build-up 

and larger aggregate annual traffic increments, with a substantial traffic bulge following the 

introduction of the new turbine-powered helicopters. 

 In Table 17 forecasts of passenger-miles and aircraft operations are also presented. 

The passenger-mile forecasts provide for approximately the same growth rate as the passenger 

forecasts, and assume no significant change in the average passenger trip during the next ten 

years. 

TABLE 17. 

SCHEDULED HELICOPTER OPERATIONS IN THE METROPOLITA AREAS OF NEW YORK, 

CHICAGO AND LOS ANGELES: REPORTED FOR 1959 AND FORECASTED FOR 

1965 AND 1970 

Calendar Year 

Item 1959 1965 1970 

Revenue Passengers (000) 366 – – 

Low – 1,000 1,700 

Intermediate – 1,200 2,000 

High – 1,400 2,300 

Revenue Passenger Miles (000) 7,477 – – 

Low – 23,000 41,000 

Intermediate – 25,000 44,000 

High – 27,000 47,000 

Aircraft Departures 138,374 – – 

Low – 190,000 260,000 

Intermediate – 210,000 290,000 

High(1) – 230,000 320,000 

Aircraft Operations 276,748 – – 

Low – 380,000 520,000 

Intermediate – 420,000 580,000 

High – 460,000 640,000 

Number of Helicopters in Service 24 30–32 40–45 

1. Aircraft operations have been estimated by multiplying departures forecast totals by two. 

Air Taxi Operations 

 In addition to the certificated helicopter airlines, there are a number of air taxi 

operators who use helicopters for the commercial transportation of passengers and cargo. In 

general, these air taxi operators are authorized by the Civil Aeronautics Board to engage in air 

transportation utilizing aircraft up to 12,500 pounds maximum certificated take-off weight, 

without restrictions as to frequency or regularity of service. However, they are expressly 

prohibited from offering any service by helicopter, or regular service by fixed-wing aircraft, 
APPENDIX G 

920 

between any two points which already have scheduled helicopter service provided by the 

holder of a certificate of public convenience and necessity issued by the Board. The air taxi 

operators have been denied permission by the Board to compete directly with the certificated 

helicopter airlines because of the likelihood that competition would bring about increased 

subsidy requirements for the certificated helicopter airlines. 

 Because the air taxi operators are not required to report traffic and financial data to the 

Civil Aeronautics Board, data on the extent and size of their operations are sketchy. However, 

registration and maintenance records on file with FAA reveal that at the end of 1959, there 

were approximately 2,300 air taxi operators, of which 71, or about 3 percent, were using 

helicopters. These 71 operators were estimated to be flying about 90 to 100 helicopters, of 

which over 90 percent were small Bell 47’s. Additionally, of course, many of these 71 

operators use small fixed-wing aircraft. 

 FAA records show further that in 1959 these air taxi helicopters flew about 36,000 

hours compared to about 26,000 hours in 1957, an increase of about 5,000 hours annually. 

Services provided by helicopters used by the air taxi operators are by no means limited to 

metropolitan area services, it should be noted. Such services include not only the movement 

of executives between airports, plants and offices in metropolitan areas, but also movements 

of a more specialized nature, such as the carriage of workers to and from off-shore oil drilling 

platforms, and the provision of ambulance service for such platforms. 

 Continued but unspectacular growth appears in prospect for this category of helicopter 

flying. It appears likely that it will remain a relatively small part of the total air taxi industry; 

that is, subordinate in volume to fixed-wing aircraft flying, because charges are necessarily 

high—averaging $1.00 to $1.25 per mile or about $85 per hour on the Bell 47’s. Such charges 

tend to limit the use of the air taxi helicopters to busy executives, and to special temporary 

tasks and odd jobs that cannot be more easily performed by small fixed-wing aircraft. 

 However, in some metropolitan areas, fairly sizeable air taxi helicopter operations may 

develop. Two new scheduled services have recently been reported – one in St. Louis with 40 

flights daily and another in Atlanta with 30 flights daily. Both of these air taxi operators are 

flying Bell 47’s on airport-downtown routes. Pilgrim Helicopter Services of Washington, 

D.C., an air taxi operator, has announced that it will inaugurate turbine-powered helicopter 

service between downtown Washington and Baltimore’s Friendship Airport before the end of 

1960, using a 10-passenger Sikorsky S-62. When Dulles International Airport opens in the 

Washington, D. C. metropolitan area in 1961, there undoubtedly will be a requirement, in the 

absence of operations by a certificated, subsidized helicopter airline, for air taxi service 

between the new and the old airports. 

New Metropolitan Area Services 

 Assuming advances in helicopter technology with concomitant improvements in the 

economics of helicopter operations, the next important development in the commercial use of 

transport helicopters beyond the extension of air taxi service would appear to be inauguration 
APPENDIX G 

921 

of scheduled helicopter services by newly certificated airlines in additional metropolitan 

areas. Such services would logically be essentially similar to those now available in the New 

York, Chicago and Los Angeles metropolitan areas. 

 It is readily apparent, however, that such advances in technology and improvements in 

the economics of operations will not occur suddenly in the next two or three years. At the 

present time, there are about 75 applications on file with the Civil Aeronautics Board for 

proposed helicopter services in various locations throughout the United States. To date no 

action has been taken with respect to these applications. In view of the continuing large 

subsidy requirements of the three presently certificated helicopter airlines, it appears unlikely 

that new certificated operations carrying subsidy eligibility will be authorized by the Board 

within the next five years unless the applicants can show a pressing public need for the 

proposed services. However, should model improvements and hoped for advances in the state 

of the art improve the helicopter operators’ prospects for self-sufficiency, the 1965-1970 

period could see the inauguration of a number of additional metropolitan area helicopter 

services. 

 There are a number of objective criteria which provide an indication of the specific 

metropolitan areas which are likely to have a requirement for scheduled helicopter services of 

the type now provided in New York, Chicago and Los Angeles. 

1. The current helicopter experiment has revealed that the principal public need to be 

served is the movement of fixed-wing air passengers in the metropolitan area 

either (a) from airport to airport or, (b) between the airports and other points in the 

metropolitan area. Thus a basic guide to the potential for an airport type helicopter 

operation is the number of fixed-wing air passengers arriving in or departing from 

a community. 

2. Since the busiest helicopter routes by far are those between airports in a given 

metropolitan area, the number of major air commerce airports in a community 

provides another important yardstick for measuring the need for helicopter 

services. Helicopter traffic volume on these routes can be expected to be closely 

related to the distance between the airports and the time that can be saved by air 

over ground travel. The number of passengers transferring between airports also 

would provide a good measure of the total inter-airport markets. However, such 

data are not available for study. 

3. The population and area of a community provide a broad indication of the public 

need for helicopter services. As population density and the size of the metropolitan 

area increases, ground travel times between the city centers and the airport and 

between other points and the airport become even greater. In all but a few of the 

larger cities, air commerce airports are located relatively far from the city centers. 

The newer airports are generally located the farthest out. 

 Table 18 shows the 20 metropolitan areas which, on the basis of these criteria, can be 

considered the leading candidates for scheduled airport type helicopter services.
APPENDIX G 

922

TABLE 18. 

SELECTED DATA INDICATING POTENTIAL FOR CERTIFICATED HELICOPTER SERVICES IN MAJOR METROPOLITAN AREAS 

(In Rank Order of Airline Passengers Generated in 1959) 

Metropolitan Area

Fixed-Wing 

Air Passengers 

Enplaned 

1959

Population 

1960 (1)

Number of

Major Air 

Commerce 

Airports

Land Area 

(Sq. Miles)

Distance of

Airports From 

City Center 

(Miles)

Ground Travel

Time, Airports 

to City Center 

(Minutes)

Number of

Airports

Planned for 

1970 Time 

Period

New York 6,553,616 10, 604, 300 3 3,939 8; 12; 15 30–60 4

Chicago 4,573,770 6,172,127 2 3,617 10; 23 40–65 2

Los Angeles 2,797,189 6,683,563 1 4,853 14 60 3

Washington, D. C, 2,230,866 1,968,562 1 1,488 4; 24 15–50 2

San Francisco/Oakland 1,936,400 2,721,045 1 3,314 9; 16 25–60 2

Miami 1,889,785 917,851 1 2,054 7 15–30 2

Dallas/Fort Worth 1,378,500 1,642,057 2 1,770 7 25–30 2

Boston 1,366,667 2,566,872 1 770 3 20–30 1

Detroit 1,294,694 3,744,544 2 1,965 17; 30 25–60 2

Atlanta 1,082,048 1,014,349 1 1,287 9 15 1

Cleveland 1,000,344 1,780,263 1 688 14 35 1

Pittsburgh 978,286 2,395,249 1 3,053 16 25 1

Philadelphia 901,451 4,289,194 1 3,550 6 15–25 1

St. Louis 874,989 2,040,188 1 2,520 15 35–50 1

Denver 789,319 923,161 1 2,918 7 15 1

Seattle 786,652 1,096,778 1 2,134 12 30–50 2

Minneapolis–St. Paul 762,448 1,477,080 1 1,721 9 25–30 1

Kansas City 699,146 1,027,562 1 1,643 2 5 (2) 2

New Orleans 665,617 860,205 1 1,118 13 40 1

Houston 637,806 1,234,868 1 1,730 10 20–30 2

1. Source: Bureau of the Census preliminary reports, PC(P2)’s, 1960 Census of Population. 

2. Mid-continent airport is in the planning stage and will be 16 miles from city center; ground travel time is unknown. 

922

APPENDIX G
APPENDIX G 

923 

The communities are listed in rank order of the number of airline passengers enplaned. 

(Enplaned passengers have been used in the absence of data covering both arrivals and 

departures. It is reasonable to assume, however, that in most cases deplaned passengers will 

approximately equal enplaned passengers.) The New York, Chicago and Los Angeles 

metropolitan areas are included in the table for comparative purposes. 

 Washington, D. C. and San Francisco/Oakland show up as the most promising 

metropolitan areas for new scheduled helicopter services on the basis of the criteria shown. 

Traffic development at the new Dulles International Airport which is being constructed at a 

relatively remote location at the outer edge of the metropolitan area should provide the basis 

for a strong triangular route system between Dulles, Washington National Airport and 

downtown Washington. The inclusion of Baltimore Friendship Airport in this route system 

would also be a distinct possibility. In the San Francisco Bay Area, growth in passenger 

traffic between the two international airports plus the long ground travel times between the 

airports and the outer counties of Marin, Sonoma and Contra Costa are indicative of a sizeable 

potential market for helicopter operations. The metropolitan area of San Francisco has shown 

a high degree of interest in obtaining scheduled helicopter service as evidenced by the work of 

the San Francisco Bay Area Council. 

 Whether certificated helicopter services will actually be inaugurated in Washington 

and San Francisco cannot now be foretold. It is significant, however, that the CAB has 

received eight applications for service in San Francisco and seven proposals for service in 

Washington, a larger number than for any other cities in the country. Moreover, the 

Washington metropolitan area already has a small charter helicopter operation and one is 

expected to begin soon in the San Francisco metropolitan area. The ability of these operators 

to develop their markets should help pave the way for larger scheduled operations at a later 

data. 

 Other metropolitan areas which appear to have a public need for helicopter services 

include Miami, Dallas/Fort Worth, Boston, Detroit, Atlanta, Cleveland, Pittsburgh, 

Philadelphia and St. Louis. Applications proposing scheduled helicopter services in all of 

these communities are on file with the Civil Aeronautics Board. However, it will be noted 

from the table that as one moves down this list of communities, the potential market declines 

very rapidly. Pittsburgh, Philadelphia and St. Louis, for example, generate only about onethird of the fixed-wing air traffic of Los Angeles, which now has the smallest scheduled 

helicopter operation. Only three of these cities will have more than one major air commerce 

airport in the next ten years with a resulting need for inter-airport shuttle service. Moreover, 

with the exception of Detroit and St. Louis, the airports in these communities are considerably 

closer to the city centers in terms of ground travel time than in the largest metropolitan areas. 

 It would appear likely, therefore, that if certificated helicopter services were 

inaugurated in any of this group of cities, it would be on a considerably smaller scale than in 

New York, Chicago or Los Angeles. Initially operations would probably require no more than 

three to five helicopters. In this connection, the findings of a recent report titled, “Helicopter 

Service Requirements of Pennsylvania,” prepared for the Pennsylvania Aeronautics 
APPENDIX G 

924 

Commission in 1957, are pertinent. The report found “a limited need” for scheduled 

helicopter service “on a modest scale” in Philadelphia and Pittsburgh. Recognizing that 

subsidy would be required, it recommended an operation utilizing three passenger helicopters 

over a minimum route pattern in each community, linking the downtown area and the airport, 

with two or three spurs to outlying points. 
APPENDIX G 

925 

V. THE INTERCITY AND COMMUTER MARKETS, 1965–1970 

 The utilization of the helicopter in airport shuttle service within metropolitan areas and 

in air taxi service is regarded by steep-gradient aircraft enthusiasts as prologue. The greatest 

success of the transport helicopter and of the more sophisticated transport V/STOL aircraft 

now being designed and developed lies ahead, these advocates believe. They see two vast 

markets awaiting these transports – the short-haul intercity and the commuter travel markets. 

 There can be little doubt that if helicopters and V/STOL aircraft are to realize their full 

potentiality as important means of passenger transport, rather than as special purpose and oddjob vehicles, they will have to succeed in either or both of these two markets. It is the 

consensus of expert opinion that if success is achieved it will be in the intercity short-haul 

travel market first and later, perhaps, in the commuter travel market. 

Short-Haul Intercity Travel 

 To date air transportation has played a very limited role with fixed-wing aircraft in the 

short haul intercity travel Market. The market is dominated by the private automobile, but 

substantial volumes of passenger traffic are also carried by the railroads and motor buses. No 

recent data on the total size of this market are available, but an analysis of the common carrier 

data indicates the great majority of the 301.2 million passengers moving by rail and bus in 

1959 travelled less than 250 miles. The average passenger journey by rail was about 125 

miles and by bus about 80 miles. Comparatively, the average air passenger trip in 1959 in the 

United States was in excess of 500 miles, and only one-fourth of the total air passengers 

travelled less than 250 miles. 

TABLE 19. 

DISTRIBUTION OF DOMESTIC COMMON CARRIER INTERCITY PASSENGERS 

(Total Revenue Passengers in Thousands) 

Calendar Air Rail(1) Bus(2) Percent Air of Total 

1950 17,345 209,094 322,802 3.2 

1954 32,343 189,580 241,612 7.0 

1956 41,738 181,460 208,047 9.7 

1958 48,128 140,147 173,720 13.3 

1959 54,768 130,905 170,305 15.4 

1. For Class I Mine-Haul Railways; includes parlor and sleeping car traffic, but excludes commutation traffic. 

2. For Class I Motor Carriers; the relatively small amount of passengers carried by Class II and III Motor 

Carriers is not available. Excludes local, suburban and charter service. 

Source: Interstate Commerce Commission for rail and bus statistics; FAA Statistical Handbook of Aviation for 

Air Statistics. 

 
APPENDIX G 

926 

 The inability of air transport to capture a major share of the short-haul intercity travel 

market appears largely due to two factors: (1) the failure of fixed-wing airport-to-airport 

transport to provide appreciable overall time savings over surface transport on short distances; 

and (2) the substantially lower costs of travel by private automobile, rail coach and motor bus 

for short distance travel. Helicopters and V/STOL aircraft, with their ability to operate 

directly from city center to city center, provide the means for greatly reduced air travel time 

on short intercity routes. However, whether these aircraft in the foreseeable future can 

overcome the economic problem which has plagued the helicopter to date, and provide shorthaul transportation at reasonably competitive rates appears doubtful at this time. 

 While the pure helicopter appears to be the logical vehicle for the metropolitan area 

and commuter markets, the compounded helicopter or V/STOL aircraft is generally 

considered as more appropriate for the intercity market for distances up to about 250–400 

miles. No such vehicle is currently available. However, a compounded helicopter such as the 

Rotodyne in which New York Airways has expressed an interest may be commercially 

available by about 1965. 

 In the United States, considerable design work is being conducted with tilt-wing, tiltrotor, tilt-engine types of steep-gradient aircraft for the military services. Recently the 

Department of Defense established a joint tri-service program directed toward developing a 

prototype of an operational V/STOL transport aircraft for operational suitability testing. In 

announcing the program, the Department stated that while the technical feasibility of various 

approaches to V/STOL aircraft have been thoroughly explored, operational problems 

associated with these aircraft remain highly speculative. It went on to say that these 

operational questions must be answered before the military services can make realistic plans 

and prepare detailed requirements for advance types of V/STOL aircraft. 

 Studies of the National Aeronautics and Space Administration indicate that a tilt-wing, 

turbo-prop V/STOL transport of 40,000 to 80,000 pounds gross weight shows more ultimate 

promise for use as a short-haul transport aircraft than the compounded helicopter. However, 

such an aircraft is some three to four years behind the compounded helicopter in the 

development cycle because of the lack of flight research. NASA estimates that the V/STOL 

transport would not be available for military or commercial service before the 1970–1975 

time period. 

 In addition to uncertainties surrounding the actual availability of V/STOL transport 

aircraft for commercial airline use during the next ten years, there are a number of operational 

and economic factors which must be considered in evaluating their potential commercial 

acceptance and utilization. The most significant of these factors appear to be: (l) the actual 

speed differential between V/STOL transports and fixed-wing aircraft; and (2) their economic 

feasibility and ability to operate at rates which are reasonably competitive with fixed-wing 

aircraft and with surface means of transport. In the discussion which follows, a city-center-tocity-center type of operation is assumed in order to take full advantage of the inherent 

capabilities of the V/STOL vehicle. Such usage is, of course, dependent on the availability of 

close-in conveniently located heliports of a size suitable for high density intercity operations. 
APPENDIX G 

927 

However, it may be that initially V/STOL techniques may be utilized in an airport-to-airport 

type of operation. This more evolutionary course of development is considered a possibility 

by NASA because of the capability of V/STOL aircraft of using airspace and landing facilities 

unused by conventional airplanes in terminal areas, thereby permitting a reduction in flight 

delays. 

The Problem of Speed 

 Past studies of the potential traffic available for V/STOL aircraft generally agree that 

such aircraft would probably be most suitable for high density intercity routes for distances up 

to about 250 miles. Examples of such routes might include Boston–New York; Philadelphia–

New York and Washington–New York. It also has been thought that V/STOL aircraft would 

generally be suitable for local service airline routes. 

 The basic advantage cited for the V/STOL airliner is that it can operate from citycenter-to-city-center, rather than from airport-to-airport, with resultant savings in total journey 

time. A typical example might be the Boston-New York route, with an airport-to-airport 

distance of 185 miles. On this route total travel time via a 200 mile per hour V/STOL airliner 

would be approximately one hour less from city-center-to-city-center than fixed-wing flight 

time plus ground travel time to and from the airports. 

 Such examples of possible time savings are, of course, impressive, and indicate that 

V/STOL flight would provide important travel benefits to those travelers whose ultimate point 

of origin or destination is in the city center and is within walking distance or reasonably close 

to the heliport from which the V/STOL airliner operates. Available statistics show that the 

city centers are the most important points of origin or destination of an airline trip. A 

conveniently located city center heliport would thus give the V/STOL aircraft access to a 

major segment of the potential short-haul intercity travel market. 

 Nevertheless, it must be recognized that for many travelers time savings by V/STOL 

aircraft will be marginal. Because of the size of the central business districts of major 

metropolitan areas, it is likely that there will be many points at which passengers will start, or 

end, their journeys that will be nearly as close or closer to the airport as to the heliport. 

Moreover, the city centers are by no means the only points between which air travelers move. 

They originate and terminate their journeys in all parts of the metropolitan area and in many 

cases have no need or desire to go to the city center. In this connection the conclusions of a 

recent study of the points of origin and destination of airline passengers in and around a 

community are enlightening: 

“Trips of people traveling for such personal reasons as family visits, recreation, sightseeing, 

etc., most probably originate at their home which may be located anywhere within the 

community. Only a small number will be living in or close to the central business district or 

have a desire to pass through there on the way to the airport. At the destination city the 

personal travelers may go to a home in any part of the community, or to a nearby recreation 

area, and only in some cases to a hotel in the central business district. 
APPENDIX G 

928 

Business travelers at the origin city may proceed to the airport either directly from their home 

or else from their office, which may be in the central business district or otherwise, with a 

steady suburbanization of industry, somewhere else in the community. At the destination city 

they will go to a place of business either in the central business district or perhaps in a 

decentralized location. Upon return to their city of origin they may go to their office, but 

frequently such return will be after business hours and they will proceed directly home.”2

 The following table provides a distribution of the originating points of the journeys of 

airline passengers in a number of metropolitan areas. The usefulness of the data as an 

indicator of potential for V/STOL operation is limited, however, by the fact that the 

percentages shown for the city centers include all origins in the central county of the 

metropolitan areas. 

TABLE 20. 

ORIGINS OF ENPLANING PASSENGERS AT REPRESENTATIVE AIRPORTS2

Airport of Departure Passenger Origins 

City Center (County) Other Points 

New York–International 47% 53% 

New York–LaGuardia 53 47 

New York–Newark 38 62 

San Francisco International 56 44 

Minneapolis/St Paul–Wold–Chamberlain 46 54 

Cleveland–Hopkins 39 61 

 City center to city center V/STOL operations also would present some problems to 

local service airlines from the operational point of view. According to reports filed with the 

Civil Aeronautics Board, 45 percent of the passengers carried by the local service airlines are 

connecting passengers who continue their journeys on major air carriers. This is in accord 

with the concepts under which these airlines were originally established. The proportion 

varies by airline but represents a substantial proportion of the total traffic for each. 

Connecting passengers obviously would not want to go to the city center on at least one end 

of their local service flight. 

 

2 Source: V. J. Roggeveen and L. V. Hammell, Journal of the Air Transport Div., Proceedings of the American 

Society of Civil Engineers, July 1959, p. 41. 
APPENDIX G 

929 

TABLE 21. 

LOCAL SERVICE AIR CARRIERS—LOCAL AND CONNECTING PASSENGERS CARRIED 

(September 17–30, 1958) 

 Number of Passengers Percent of Passengers 

Carrier Total (One Carrier) Connecting Connecting 

Allegheny 19,598 11,990 7,608 38.8 % 

Bonanza 6,209 3,846 2,363 59.2 

Central 5,749 2,344 3,405 59.2 

Frontier 8,130 5,152 2,978 36.6 

Lake Central 7,309 3,964 3,345 34.8 

Mohawk 18,604 14,149 4,455 –23.9 

North Central 30,400 11,543 18,857 62.0 

Ozark 17,453 8,156 9,297 53.3 

Pacific 12,957 9,319 3,638 28.1 

Piedmont 16,719 8,253 8,466 50.6 

Southern 8,220 3,477 4,743 57.7 

Trans-Texas 8,561 4,429 4,132 48.2 

West Coast 9,107 6,661 2,446 26.9 

TOTAL 169,016 93,283 75,733 44.8 

Source: Civil Aeronautics Board; “Competition Among Domestic Air Carriers,” September 17–30, 1958. 

The Cost Problem 

 The major problem to be overcome by the V/STOL aircraft is that of high operating 

costs. If there is to be commercial acceptance and utilization, the V/STOL airliner must be 

able to operate at rates which are reasonably competitive with those of other means of 

transport. In the following discussion a range of V/STOL fares that might be considered 

competitive under varying assumptions in regard to the market are shown, using the 185-mile 

Boston-New York market as a specific example. Passenger fares of fixed-wing air travel, 

which is currently the fastest means of transport between Boston and New York, have been 

used as the basis for comparison. The first class fare for this trip (excluding Federal excise 

tax) is $15.00. Ground transportation between the city centers and the airports is $2.50. 

1. The first class fixed-wing air fare is 8.1 cents per mile. V/STOL aircraft would 

probably have to meet this fare level to attract those travelers for whom a V/STOL 

flight would provide no time savings over a fixed-wing flight. In this segment of 

the market would be those passengers whose journey origins and destinations are 

as close to the airports as they are to the city center heliport from which the 

V/STOL airliner presumably would be operating. 

 To break even at a 8.1 cents per mile fare would require V/STOL airliner direct 

operating costs of 2.4 cents per seat mile at a 60 percent load factor and with 100 

percent indirect cost. 
APPENDIX G 

930 

2. For those travelers whose journey origins and destinations are from city center to 

city center a competitive V/STOL airliner passenger fare would be of the order of 

$17.50 (the cost of fixed-wing transportation plus ground transport between city 

center and airport) or approximately 9.5 cents per passenger mile in those cases 

where the traveler places no additional value on the time saved by V/STOL flight, 

or where—because of the location of the journey origin and destination in the city 

center—the V/STOL flight provides little or no time savings over fixed-wing 

journey time. 

 To break even at a 9.5 cent per mile fare would require V/STOL direct operating 

costs of about 2.9 cents per seat mile at a 60 percent factor and with 100 percent 

indirect costs. 

3. If it is assumed that a passenger values his time at $5 per hour and that a 200 mile 

per hour V/STOL airliner would provide time savings of approximately one hour 

over fixed-wing travel on a city-center-to-city center journey, a competitive 

V/STOL fare might be on the order of $22.50 for this segment of the market or 

about 12.2 cents per passenger mile. 

 A break-even V/STOL operation would then require direct operating costs of 3.7 

cents per seat mile at a 60 percent load factor and with 100 percent indirect costs. 

4. The preceding discussion applies only to first class air travel. The coach fare 

between Boston–New York is $13.10 or 7.1 cents per passenger mile from airportto-airport and 8.4 cents from city-center-to-city-center. To be attractive to this 

segment of the air travel market, a breakeven V/STOL operation would require 

direct operating costs ranging from about 2.1 cents to 3.3 cents per seat mile under 

the same assumptions as were used above. 

 Insofar as can be determined at this time, no V/STOL aircraft which would be 

designed for speeds under approximately 300 knots appears capable of operating within the 

range of fares and seat mile costs shown above. Information on costs are very speculative at 

this stage. United States manufacturers place the prospective direct costs of V/STOL aircraft 

types in the neighborhood of 6 cents per seat mile. Available cost estimates on the 

compounded helicopter fall at approximately the same level, varying from over 4 cents to 

about 7 cents per se mile. In contrast the Fairchild F-27 had direct operating costs in local 

service airline operations in 1959 of 2.9 cents per seat mile. 

 The prospects that V/STOL aircraft will be able to support fares which would be 

attractive to travelers moving by surface carriers appear even more remote. Passenger fares by 

surface carriers are lower than first class air fares on a city-center-to-city-center basis, with 

the great majority of the short haul common carrier traffic moving by rail coach and motor 

bus at fares of about three to five cents per passenger mile. Although clearly a V/STOL 

operation from city center to city center could provide these travelers with substantial time 
APPENDIX G 

931 

savings, attainable costs with projected V/STOL aircraft appear for the foreseeable future to 

preclude passenger fares which would be attractive to any but a minute fraction of this travel 

market. 

The Commuter Market 

 There has been no more exciting use suggested for the helicopter than that of an air 

bus in the daily commuter market. This intra-city market is potentially even greater in terms 

of the number of people transported than the short-haul intercity market. In 1959, for 

example, more than seven billion passengers were carried by intra-city buses, trolleys, and 

electric railways of one kind or another. Not all these passengers are commuters, of course, 

but on the other hand this total does not include the many millions of automobile riders who 

are commuters. 

 Like the airport metropolitan area and short-haul intercity passenger market, the 

suburban commuter market is not rigidly defined. It is generally considered to include that 

travel to and from work by residents of a metropolitan area which involves getting into the 

city center in the morning and back to the suburbs in the evening. Because metropolitan areas 

vary in size in the United States the travel distances in this market may range from some 15 to 

50 miles. In many respects a helicopter commuter operation might be considered a natural 

extension of metropolitan area helicopter services as they are presently known. And at its 

outer boundaries the commuter service would to a limited extent overlap the very short-haul 

portion of the intercity market discussed in the previous section. 

 It is not great size alone that characterizes the suburban commuter market and attracts 

the helicopter enthusiasts. This is the travel market most sorely troubled by the inadequacies 

and complexities of surface transportation – the market in which millions of daily commuters 

could be helped if some way were found to rescue them from the acute traffic congestion, and 

all its attendant inconveniences, which plague our larger metropolitan areas during the 

morning and evening “rush hours.” 

 Enthusiasm for the helicopter as the ultimate solution to the metropolitan area mass 

transportation problem probably was highest during the period immediately after the Korean 

War had ended. The new aircraft, it was predicted by some market analysts, would 

revolutionize intra-city mass transportation within 15 years. However, developments since 

then have convinced most observers that this time table was unduly optimistic and that the 

helicopter will not play a significant role in this short-haul market for the foreseeable future. 

For the most part, the helicopter is no longer looked upon as the vehicle for low cost mass 

transportation commuting service; it is seen, rather, as a medium for premium rate service 

designed to meet special needs of the community. 

 
APPENDIX G 

932 

 The reasons for assigning the helicopter this less ambitious role in the commuter 

market are to be found in the speed and operating costs of the aircraft. In general it seems 

clear that air commuting would provide time savings on suburban routes in major 

metropolitan areas such as New York, Chicago and Los Angeles. Estimates made for the New 

York area show, for example, that if non-stop helicopter service were provided, travel time 

between typical outlying suburban points and Manhattan would be reduced from 50–75 

percent over rail time. However, as the distance between stops is reduced so as to permit a 

more widespread penetration of the market, this speed advantage diminishes. Thus, with an 

average flight stage of 5 miles, a helicopter with a cruising speed of about 150 miles per hour 

would have a block speed of about 65 miles per hour. 

 The bigger problem for the helicopter is one of costs and fares, however. Rail 

commuter fares are relatively low, averaging 2.57 cents per passenger mile for a total cost of 

51 cents for the average 20 mile trip. In contrast, helicopter fares on suburban-airport routes 

average about 15–20 cents per passenger mile and at this level require heavy subsidy support; 

a break-even operation with the new turbine-powered helicopters, as shown previously, would 

probably require fares of about 40–54 cents per passenger mile. Such fare levels would 

obviously not be feasible for the average commuter who would have to pay them from his 

own funds rather than charging them off as a business expense. Only the business traveler 

would be willing to pay these premium fares if the service were available. 

 In this connection it is of interest to note that the subsidy supported 15–20 cent per 

passenger mile fare level on helicopter suburban-airport routes has generated relatively little 

traffic in New York and Chicago despite the time saving provided by these flights for trunk 

line connections. In 1959 Gary and Winnetka, the two suburban points served by Chicago 

Helicopter Airways, provided only 3.4 passengers per flight while New York suburban points 

provided only 1.2 passengers per flight. And in the sprawling Los Angeles area, suburban 

points have provided an average of less than one passenger per flight. 

 Commuter air travel can also be expected to face a number of additional problems. 

Commuter travel is inherently highly directional and peaked. There is a heavy flow in the 

morning for about two hours into the city. In the late afternoon the reverse is true. Relatively 

little traffic moves during midday or in the evening. This situation has plagued the commuter 

railroads and would, of course, have an adverse impact on helicopter utilization and load 

factors, with a resultant effect on unit costs. While there has been some speculation that the 

flying crane might, because of its versatility, solve some of these problems, no information is 

available which would indicate that the crane would be economically feasible in such service. 

 Because of these problems it seems likely that commuter travel by air will develop 

only to a very limited extent during the next ten years and then merely as an extension of 

existing metropolitan area helicopter services at premium rates. It is only beyond 1970 that 

more widespread use of the helicopter and possibly the V/STOL transport in the commuter 

market may appear. Any numerical forecast of traffic to be carried, however, is obviously 

premature. 
933 

AIRPLANES, ENGINES, AND HELICOPTERS 

AIRPLANES 

Aeronca L-16, 208 

Boeing Clipper, 121 

Boeing Model 40, 586, 587, 588 

Boeing Model 247, 214, 251, 292, 587, 588, 669 

Boeing 307, 586 

Boeing B-29, 559, 560 

Boeing 737, 687 

Boeing 707, 555, 561, 562, 590 

Boeing 777, 687 

Cessna L-19, 208, 209, 237, 238 

Cessna TL-19D, 213, 214, 226, 227, 228, 229, 238 

Chance Vought VE-7, 214, 216, 217, 218 

Douglas DC-1, 214, 251, 261, 292 

Douglas DC-3, 251, 263, 350, 447, 548, 550, 553, 579, 

581, 582, 584, 585, 586, 587, 588, 590, 596, 601, 

661, 669, 687 

Douglas DC-3A, 584, 585, 588, 592, 593 

Ford Tri-Motor, 251, 550, 579, 580, 582, 584, 585, 586, 

587, 588, 590, 592, 593, 601, 668 

Grumman OV-1C, 519, 521 

Lockheed C-130, 356, 357, 568 

Lockheed Electra, 548 

Lockheed YO-3, 516, 526 

McDonnell XF-88B, 447 

Piper L-4, 96, 207, 208 

Spirit of St. Louis, 273, 275 

Stinson L-5, 207, 208, 455, 508 

Wright Flyer, 548 

ENGINES 

Allison 250-C18, 632 

Allison 250-C18B, 86 

Allison 250-C30, 631 

Allison 250-C40, 631 

Allison T-63, 77, 82, 287, 504 

Allison, 77, 78, 81, 82, 86, 100, 102, 275, 287, 446, 457, 

504, 506, 541, 569, 631, 632 

Boeing 505, 75, 238 

Continental R-975-34, 182 

Continental, A65-8 

Continental, O-470-11-C1 

Continental, R-975-34 

General Electric CT7, 632 

General Electric T-64-GE-416, 252 

General Electric YT-700-GE-700, 78, 79 

Hirth 2703, 84 

Light Helicopter Turbine Engine Co. LHTEC T-800, 81, 

82 

Lycoming, YT-53-L-1, 76 

Lycoming, LTS 101, 151, 152, 630, 631 

Lycoming, O-360-A1D, 84 

Lycoming, O-360-C2B, 62, 271 

Lycoming, O-360-J2A, 638 

Lycoming, T-53, 77, 81, 238, 240 

Lycoming, VO-435, 83, 100 

Pratt & Whitney, 251, 579, 584, 593, 612, 632 

Rolls Royce RR300, 632, 633 

Rotax 503, 84 

RTM 322-01/8, 252 

Turbomecca ARRIEL 1C1, 152 

Wright J-5-C, 275 

Wright R-1820, 60, 82, 240 

HELICOPTERS 

American Sportscopter Ultrasport 254, 84 

Armed Attack Helicopter (AAH), 138, 141, 142, 143, 

144, 145, 200, 202, 328, 576 

Augusta-Westland AW 139, 636 

Augusta-Westland EH 101, 214, 217, 236, 252, 292, 294, 

295, 377, 401, 405, 636, 640, 648, 686 

Bell 206B III, 541 

Bell 206B, 540, 541, 544, 587, 637, 646, 652 

Bell 206B-II, 540 

Bell AH-1G, 354, 372, 373, 377, 378, 379, 380, 383, 385 

Bell AH-1S, 524, 525, 526 

Bell AH-1Z, 304 

Bell AHIP/OH-58D, 96, 97, 99, 100, 104, 105, 128, 208, 

552, 566, 571, 573, 574, 575, 576, 577, 624, 625, 630 

Bell H-13, 96, 208, 209, 230, 231, 233, 235, 236, 237, 

238, 284, 343 

Bell H-13H, 209, 210, 211, 230, 232, 235, 252, 344 

Bell Huey, 76, 78, 88, 89, 124, 291, 310, 350, 354, 356, 

553, 555, 561, 563, 567, 568 

Bell Model 206, 77, 205, 541, 544, 693 

Bell Model 206B, 78, 86, 540, 542, 543, 544, 637, 646 

Bell Model 212, 636 

Bell Model 214ST, 205 

Bell Model 222, 149, 151, 152, 290, 291, 308, 630, 631, 

634 

Bell Model 30, 33, 34, 50 

Bell Model 412, 295, 296, 309, 329, 646 

Bell Model 430, 304, 307, 308, 631 

Bell Model 47, 9, 14, 15, 33, 50, 231, 343, 597, 659, 669, 

693 

Bell Model 680, 304, 308 

Bell OH-13, 284 

Bell OH-4A, 77, 78, 96 

Bell OH-58A, 78, 96, 354, 540, 541 

Bell OH-58C, 96, 97, 99, 100, 541 

Bell UH-1A, 89, 470 

Bell UH-1D, 89, 562 

Bell UH-1Y, 304 

Bell XH-40, 76, 88, 89, 285, 350, 351, 352, 353, 354, 555 

Bell YAH-1G, 555 

Bell YAH-63, 78, 79, 200
AIRPLANES, ENGINES, AND HELICOPTERS 

934 

Bell YUH-1D, 89, 457, 460, 461, 462, 484, 488, 489, 555 

Boeing (HLH) YCH-62A, 90 

Boeing CH-146, 329 

Boeing CH-46, 179, 185, 250, 255, 265 

Boeing CH-47, 91, 179, 185, 247, 250, 297, 298, 300, 

571 

Boeing CH-47C, 354 

Boeing CH-47D, 91, 349, 371 

Boeing Model 107, 179, 236, 255, 256, 257, 258, 259, 

261, 263, 265, 333, 368, 503, 526, 591, 596, 600, 

602, 611, 614 

Boeing Model 234 LR, 259 

Boeing Model 360, 18, 50, 343, 669 

Boeing YUH-61A, 78, 79, 125, 143, 144, 200, 356, 357 

Boeing/Vertol HC-1B, 297 

Boeing/Vertol Model 107-II, 256, 258, 265 

Boeing/Vertol Model 44, 60, 597 

Boeing/Vertol YHC-1B, 91 

Bréguet G-11E, 120 

Bréguet Type 314, 120, 121 

Eurocopter AS 355F, 259 

Eurocopter EC 225, 636 

Eurocopter/Aerospatiale Alouette II, 75, 465 

Eurocopter/Aerospatiale AS 332, 496, 562, 636, 673 

Eurocopter/Aerospatiale AS 332C, 259 

Eurocopter/Aerospatiale SA 365 N-1 Dauphin 2, 146, 

151 

Flettner FL 265, 3 

Flettner Fl-265, 281 

Focke Achgelis Fa 223, 2, 141 

Focke Achgelis Fa-284, 91 

Focke F. 61, 2, 8, 40, 43, 91, 94, 108, 141, 270 

Hiller FH-1100, 77, 86 

Hiller H-23, 96, 208, 209, 284, 343 

Hiller OH-23, 284 

Hiller OH-5A, 77, 96 

Hiller UH-12, 18, 343, 669, 670, 693 

Hiller UH-12E, 210 

Hiller UH-4, 17 

Hiller XH-32, 456 

Hiller YH-32, 484 

Hughes Model 269, 344, 345 

Hughes Model 269A, 62, 83 

Hughes 500P (The Quiet One), 499, 501-504,547, 508, 

550, 551, 552, 533, 554, 558, 592 

Hughes OH-6A, 77, 78, 96, 97, 99, 100, 102, 289, 354, 

456, 457, 459, 484, 488, 489, 498, 499, 500, 501, 

502, 503, 504, 505, 506, 507, 508, 509 

Hughes T-55 Osage, 344, 345, 346, 347 

Hughes YHO-2HU, 62, 271, 344, 345, 457, 458, 475, 

476, 477, 478, 479, 480, 483, 490, 491 

Hughes YOH-6A, 102, 274, 275, 276 

Kaman H-43, 75, 178, 179, 180, 191, 192, 196, 238, 239, 

241 

Kaman HH-43B, 498 

Kaman K-125, 50 

Kamov Ka-22, 90 

Kellett XR-8, 280, 281, 282 

Kellett XR-10, 280 

Light Helicopter Experimental (LHX), 469, 552, 566, 

567, 569, 571, 572, 575, 701 

Light Observation Helicopter (LOH), 48, 77, 284, 285, 

286, 287, 288, 289, 502, 503, 540, 541, 632 

Lockheed AH-56, 311, 312, 313, 571, 701 

Lockheed CL-475, 296, 297, 302 

Lockheed XH-51, 292, 293, 297, 302 

MBB BO-105, 50, 259, 302, 305, 306, 528, 529, 534 

McDonnell Douglas MD Explorer, 147 

McDonnell XV-1, 296, 302, 304, 465 

McDonnell Douglas/Hughes 500 D, 503, 553 

McDonnell Douglas/Hughes 500E, 304 

McDonnell Douglas/Hughes Model 500, 77, 86, 503 

McDonnell Douglas/Hughes YAH-64, 78, 79, 200 

Mil Mi-6, 90 

Mil Mi-10, 90 

Mil Mi-12, 90 

Mil Mi-26, 90, 688, 701 

NH Industries NH 90, 292 

Nord 1700, 146 

Nord NC-2001, 120 

Piasecki XHJP-1, 20, 180, 182, 185 

Piasecki/Vertol H-21, 60, 178, 179, 180, 238, 239, 241, 

246, 247, 248, 249, 250, 251, 252, 253, 285, 305, 

347, 348 

Piasecki/Vertol H-21B, 239, 240, 241, 247, 249, 250, 

252, 255, 347, 348, 368 

Piasecki/Vertol H-25, 178, 179 

Piasecki/Vertol HUP, 20, 178, 179, 180, 182, 183, 185, 

239, 349, 363, 365 

Piasecki/Vertol HUP-1, 20 

Platt-LePage XR-1, 43, 94 

Robinson R22 Beta II, 638, 639, 642, 658, 659 

Robinson R22, 637, 646, 694 

Robinson R-22, 83, 84, 540, 587 

Robinson R-44, 83, 540 

Robinson R-66, 504, 540, 632, 633, 659 

Schweizer/Hughes Model 300, 344, 345 

Sikorsky Advancing Blade Concept (ABC) XH-59A, 

180, 195, 196, 197 

Sikorsky CH-3, 255 

Sikorsky CH-37, 252 

Sikorsky CH-3C, 257, 261 

Sikorsky CH-53, 91, 252 

Sikorsky CH-53E, 91 

Sikorsky CH-54, 252 

Sikorsky H-19, 14, 20, 60, 285 

Sikorsky H-34, 60, 238, 239, 241, 249, 251, 252, 253, 

285, 348, 366 

Sikorsky H-37, 285, 418 

Sikorsky HSS-2, 255 

Sikorsky R‐4, 1, 2, 3, 43, 96, 101, 108, 315, 343, 559, 

669, 670 

Sikorsky R-4B, 97, 99, 100, 252, 285 

Sikorsky R‐5, 3, 96, 180, 343, 559, 669 

Sikorsky R‐6, 3, 96, 97, 99, 100, 101, 102, 343, 559, 

560, 669, 670 

Sikorsky S-51, 96, 180, 296, 341, 343, 550, 597, 600, 

602, 603, 669, 670 

Sikorsky S-55, 60, 239, 597, 600, 602, 604, 605, 606, 

607, 608, 610, 611, 612, 614, 615, 670 

Sikorsky S-56, 252
AIRPLANES, ENGINES, AND HELICOPTERS 

935 

Sikorsky S-58, 60, 238, 239, 366, 597, 600, 601, 670 

Sikorsky S-61, 255, 256, 257, 259, 261, 262, 263, 307, 

309, 600, 601, 602, 603, 606, 607, 608, 610, 611, 

612, 614, 615, 616, 617, 618, 621, 622, 623, 635 

Sikorsky S-61N, 596, 608, 616 

Sikorsky S-62, 256, 257, 596 

Sikorsky S-62A, 457, 463, 464, 484, 489 

Sikorsky S-64, 252 

Sikorsky S-67, 307, 309 

Sikorsky S-70, 329 

Sikorsky S-76, 231, 232, 291, 292, 293, 302, 526, 527, 

529, 548, 633, 646, 701 

Sikorsky S-76D, 634 

Sikorsky S-92, 292, 294, 360, 570, 571, 628, 636 

Sikorsky SH-3A, 457, 459, 465, 485, 486, 487, 489, 498 

Sikorsky UH-60, 124, 125, 126, 130, 202, 291, 306, 328, 

329, 332, 360, 361, 369, 373, 402, 403, 405, 406, 

417, 418, 489, 490, 491, 492, 493, 494, 495, 496, 

497, 553, 571, 573 

Sikorsky UH-60A, 124, 125, 126, 127, 128, 130, 131, 

132, 133, 134, 135, 136, 205, 247, 277, 278, 279, 

356, 357, 358, 359, 360, 361, 369, 370, 371, 373, 

374, 375, 376, 385, 386, 387, 388, 389, 390, 391, 

392, 393, 394, 396, 397, 400, 401, 405, 408, 410, 

415, 418, 42 

Sikorsky UH-60M, 360 

Sikorsky VS 300, 3 

Sikorsky VS-300A, 44 

Sikorsky XR‐4, 3, 14, 23, 24, 25, 27, 28, 29, 30, 32, 35, 

40, 42, 44, 46, 94, 95, 101, 102 

Sikorsky YR-4, 23 

Sikorsky YR-4B, 46, 47, 95, 202, 203, 204, 205, 280, 

281, 282 

Sikorsky YUH-60A, 78, 79, 80, 124, 125, 126, 127, 130, 

131, 132, 133, 134, 135, 138, 143, 144, 199, 200, 

201, 357 

Sikorsky/Boeing RAH-66, 81, 105, 304, 552, 567, 568, 

569, 571, 572, 575 

Sud Quest S.O. 1221 (Djinn), 457, 466, 484 

Utility Tactical Transport Aircraft System (UTTAS), 

138, 141, 142, 143, 144, 145, 200, 202, 328, 357, 576 

Vertol/Boeing YHC-1A, 255, 257, 261, 265 
936 
937 

INDIVIDUALS 

These men and women, with their thoughts, words, and deeds, helped crystallize my 

views about helicopters. 

Alex, Ralph, 23, 44, 49, 50, 101, 102 

Allard, Sylvain, 673 

Alldridge, Phil, 300 

Allen, William, 566 

Ambrose, James, 566, 567 

Amer, Ken, 145, 311 

Anderson, Seth, 696, 703, 733, 734, 737 

Atkins, Jim, 561, 630 

Augustine, Norm, 539, 540, 550, 551, 565, 568, 574 

Baeder, Jim, 533 

Balzar, Stephen, 55 

Barlow, William, 498, 499, 502, 503, 506, 508 

Bell, Alexander Graham, 438 

Bell, Lawrence, 14, 33, 35, 50, 553 

Betz, Albert, 5, 7 

Bousman, Bill, 205, 247, 300, 313, 386, 397 

Boxwell, Don, 516, 517, 522, 528 

Bréguet, Louis, 2, 4, 51, 119, 120, 121, 122, 271, 273, 

274 

Brentner, Ken, 469, 497, 516, 533 

Brooks, George, 362, 365, 366, 367, 368, 369 

Brooks, Peter, 1, 8, 579 

Brooks, Thomas, 534 

Bruel, Andre, 146 

Burkam, John, 20, 21 

Burley, Casey, 537 

Caradonna, Frank, 400 

Carlson, Dick, 84, 687 

Carlson, Floyd, 33, 34, 35, 84, 687 

Carter, Ted, 316 

Cayley, George, 4 

Chanute, 663 

Chopra, Inder, 385, 570 

Churchhill, Gary, 305 

Cierva, Juan de la, 1, 8, 35, 36, 38, 40, 50, 114, 121, 211, 

278, 280, 310, 315, 336, 337, 339, 371, 379, 434, 

595, 637, 642, 648, 697, 702 

Claisse, Maurice, 119, 120, 121 

Cline, John, 371 

Cole, Jeffrey, 265 

Conner, David, 537 

Cox, Charlie, 470 

Craddock, Perry, 208 

Crawford, Charlie, 125, 202 

Crews, Sam, 328, 329, 354 

Crim, Al, 379 

Crimi, Peter, 244, 245 

Cronkhite, Jim, 371, 372, 378 

Culver, Irv, 102, 274, 296, 302 

Daimler, Gottlieb, 54 

Davies, R.E.G., 579, 595, 596, 665 

De Bothezat, George, 4, 94 

de Decker, Bill, 616, 650 

de Rochas, Beau, 53 

Delamer, Kevin, 693 

Deming, Arthur, 468 

Desfor, Sharon, 606 

Desopper, Andre, 400 

Diamond, Jack, 285, 286 

Dingeldein, Dick, 192, 204, 281, 283 

Doblhoff, Fred, 50, 302 

Domka, Bob, 372, 373 

Dorand, Rene, 4, 51, 119, 120, 121, 122 

Douglas, Donald, 251, 566, 596 

Drees, Jan, 7, 310 

Drzewiecki, M. Stefan, 7 

Dugan, Dan, 693, 736 

Durno, Jason, 373, 375, 390 

DuWaldt, Frank, 243, 244 

Ellis, Chuck, 356 

Farassat, Feri, 469, 516, 533 

Ferry, Bob, 102, 274, 276, 350, 351, 353 

Flax, Al, 84 

Fletcher, Harvey, 438, 440, 441 

Flettner, Anton, 1, 3, 5, 36, 43, 50, 108, 120, 141, 179, 

281 

Florine, Nicolas, 4 

Floyd, Jack, 574 

Focke, Henrich, 1, 2, 19, 23, 36, 40, 43, 50, 91, 94, 108, 

120, 141, 178, 179, 270, 697, 702 

Forster, William (Bud), 576, 577 

Fradenburgh, Evan, 231, 302, 307, 548 

Frederich, Lucretia, 594 

Fries, Gordon, 280, 283 

Froude, William, 5 

Gabel, Dick, 316, 317, 328, 329, 360, 368, 371, 418, 435 

Gabriel, Ed, 297 

Gallagher Jr., Jack, 602 

Gallagher, John (Jack), 602, 605, 606, 607, 608, 609, 

610, 611, 612, 614, 615, 616 

Gessow, Al, 45, 145, 155, 166, 202, 204, 205, 219, 379, 

473, 570 

Gibbs-Smith, Charles, 1, 537 

Glauert, Hermann, 7, 37, 38, 114, 115, 121, 237, 242, 

243, 265, 277 

Gopalan, Gaurav, 469, 471, 472, 473, 474, 475, 480, 481, 

483, 489, 493, 494, 495 

Gray, Harry, 435 

Gregory, Frank, 9, 10, 11, 12, 13, 14, 24, 25, 27, 28, 45, 

94, 101, 102 

Grina, Ken, 356 

Gustafson, Fred, 202, 204, 205, 281, 283 

Gutin, L. Ya, 448, 468 

Hall, Kenneth, 265
INDIVIDUALS 

938 

Hall, Steven, 265 

Hansford, Bob, 318 

Hanson, Tom, 300, 302, 313, 455 

Harper, Bill, 552, 571 

Harrington, Robert, 283, 284, 305, 306 

Hawkings, D. L., 469, 471, 516, 533 

Hayden, Jim, 198, 199, 201, 348 

Hayson, Harry, 246, 247, 248 

Hefner, Ralph, 153-168, 170, 174, 175, 176, 187, 192, 

193 

Heinemann, Ed, 566 

Heyson, Harry, 32, 242, 243, 244, 245, 246, 247, 248 

Hiller, Stanley, 17, 18, 19, 20, 36, 50, 693, 702 

Hoerner, Jack, 561 

Hoffman, Teddy, 128, 576 

Hohenemser, Kurt, 9, 19, 302, 304 

Houbolt, John, 362, 365, 366, 368 

Howland, Guy, 373, 375, 390 

Hubbard, Harvey, 469, 470, 485, 488, 516, 528 

Huber, Helmut, 304 

Huesca, Dan, 650 

Hunt, Bill, 269 

Huston, Bob, 246, 247, 371 

Iseler, Laura, 680 

Jellinek, Emil, 54 

Jellinek, Mercedes, 54 

Johnson, Kelly, 566, 702 

Johnson, Wayne, 186, 244, 368, 398, 399, 400, 430, 495, 

536, 537, 566, 571, 578 

Joiner, Webb, 561 

Kasper, Gene, 680, 684, 736 

Kawa, Mike, 574 

Kelley, Bart, 6, 15, 33, 50 

Keys, Chuck, 185, 305 

Kidd, Dave, 328 

Klemin, Alexander, 14, 18, 45, 49, 118, 216 

Knight, Montgomery, 153-168, 170, 174, 175, 176, 187, 

192, 193 

Kocurek, Dave, 172, 205 

Kryter, Karl, 444 

Kufeld, Bob, 386 

Kurbjun, Max, 447, 448, 450, 452 

Kvaternik, Ray, 371, 376, 384 

Laing, Emmett, 354, 356 

Lakinsmith, Barry, 312 

Landgrebe, Jack, 156, 168 

Launoy, Claude Jean Veau de and Bienvenue, Francois, 2 

Leoni, Ray, 124, 356, 357, 360, 553 

LePage, Laurence, 43, 44 

Leverton, John, 470 

Lewis, Dick, 136, 214, 455, 516 

Liberatore, Gene, 1, 315 

Lilienthal, Otto, 663 

Lindbergh, Charles, 251, 273, 663 

Lindenbaum, Bernie, 94 

Loewy, Bob, 316, 368 

Lynn, Bob, 310 

Mallen, Joe, 238 

Manly, Charles, 55 

Mashman, Joe, 33, 34, 35, 36 

McClarren, Ralph, 45 

McCroskey, Jim, 244 

McGuire, Frank, 51 

Metzger, Bob, 310, 311 

Mil, Mikhail, 570 

Miller, Rene, 19 

Miller, Ronald, 589 

Miner, Milton, 338, 339 

Morris, Charles, 14, 23, 24, 25, 27, 28, 29, 30, 32, 33, 35, 

101, 550, 567 

Morse, Andy, 530 

Moser, Herb, 286, 287, 288 

Munson, Wilden, 438, 440, 441 

Myers, Garry, 204 

Naumann, Gene, 371 

Nichols, Erickson, 45, 66, 564 

Nichols, John, 66 

Nikolsky, Alexander, 706 

Norman, Tom, 393, 401, 420, 423 

O'Bryan, Tom, 454 

Oehmichen, Etienne, 2, 4 

Ormiston, Bob, 300, 316, 368, 397, 404, 405 

Oswald, W. Bailey (Ozzy), 212, 213, 230, 233, 265 

Otto, Nikolaus, 53 

Parker, Don, 577 

Parkinson, Harry, 84 

Patnode, Clarence (Bud), 576 

Penaud, Alphonse, 4 

Pescara, Raul Pateras, 4 

Peterson, Randy, 423 

Piasecki, Frank, 19, 36, 50, 178, 180, 182, 239, 347, 349, 

702 

Pitcairn, Harold, 8, 36, 38, 43, 94, 211, 697, 702 

Piziali, Ray, 243, 244 

Platt, Haviland, 43, 44, 94, 95, 120 

Prandtl, Ludwig, 5, 8, 155, 166, 265 

Prouty, Ray, 233, 311, 328 

Pruyn, Dick, 247 

Putnam, Keith, 213, 350, 351, 353 

Raborg, William, 559, 564 

Rankine, William John Macquom, 5, 64, 168 

Reed, Albert, 336 

Reichert, Gunter, 50, 302, 304 

Richey, Mike, 552, 571 

Robinson, Frank, 83, 503, 504, 508, 632, 633, 659, 693 

Rohlfs, Ewald, 23, 40 

Romander, Ethan, 386, 393, 396, 400, 406, 424, 432 

Rosenstein, Hal, 305 

Russell, Carl, 533 

Rutkowski, Mike, 369 

Sawers, David, 589 

Schlegel, Ron, 470 

Schmitz, Fred, 469, 470, 471, 516, 517, 520, 522, 524, 

530 

Schrage, Dan, 328 

Scott, Mark, 687, 688 

Scully, Mike, 71, 368, 539, 545, 546, 548, 570 

Selfridge, Thomas, 663 

Sheehy, Tom, 306 

Shinoda, Rick, 401 

Shute, Nevil, 550, 567, 698 
INDIVIDUALS 

939 

Sikorsky, Igor, 1, 2, 3, 9, 13, 14, 19, 20, 23, 30, 36, 44, 

53, 108, 120, 239, 269, 270, 271, 343, 702 

Sissingh, Gerhard, 19, 20, 155 

Smith, Chuck, 537 

Spencer, Bob, 528 

Statler, Irv, 516, 530 

Stepniewski, Wieslaw (Steppy), 156, 182, 183, 184, 185, 

187, 188, 189, 192, 197, 241, 245, 246 

Sternfeld, Harry, 470 

Stoessel, Bob, 602, 605, 606, 607, 608, 609, 610, 611, 

612, 614, 615, 616 

Stroub, Bob, 307 

Stuart, Joe, 17, 18 

Studebaker (Fletcher), Karen, 361, 386, 387, 394 

Suggs, Mrs. Carroll, 673 

Sweet, George, 168, 192, 193, 194 

Tishchenko, Marat, 570 

Toossi, Mostafa, 371 

Tung, Chee, 400 

Turner, Leo, 576, 577 

Twomey, Bill, 371, 373, 375, 390 

Ulisnik, Harold, 12, 13, 108 

Wagner, Bob, 315, 470, 577 

Walton, Bill, 371 

Ward, John, 204, 371 

Warmbrodt, Bill, 289, 290, 386, 423, 500, 501, 591 

Warner, Edward, 582, 585, 586, 587, 588, 589, 592, 593, 

594 

Watt, Mike, 516, 536 

Weichsel, Hans, 341 

Weick, Fred, 216, 218, 219, 221, 222, 225, 226, 227 

Wheatley, John, 37, 38 

Whittle, Frank, 63 

Williams, Bob, 291 

Williams, J. E. Ffowcs, 469, 471, 516, 533, 576 

Wood, Edgar, 46 

Wood, Tom, 46, 260, 687, 688, 697 

Wright, Theodore (T. P.), 556, 557, 558, 559, 560, 561, 

564, 565 

Yamauchi, Gloria, 516, 536 

Yeates, John, 362, 365, 366, 368 

Yeo, Hyeonsoo, 385 

Young, Art, 14, 15, 16, 17, 19, 20, 33, 34, 36, 50 

Young, Larry, 307, 308, 516, 536, 693, 702 

Yu, Yung, 516, 524, 529, 530 

Yudin, E. Ya, 468 

Zinner, Russ, 528
940 
941 

INDEX 

accident 

accident bubble, 676 

accident rate, 663, 665, 673, 674, 675, 696 

accidents per 100,000 flight hours, 673 

by amateurs, 669, 681, 684, 691, 697 

classification, 666, 668, 679, 680 

crop dusting, 689 

crosswinds, 692, 693 

dead man’s curve, 697 

directional control, 13, 136, 141, 145, 691, 699 

engine structural failure, 685, 697 

failure or malfunction of the airframe, 681, 683, 694, 

695 

fatigue, 576, 646, 689, 695 

fuel exhaustion, 685 

fuel/air mixture, 685, 687, 697 

in-flight collision with objects, 681, 684, 689 

loss of control, 683, 684, 691, 693 

loss of engine power, 684, 685, 687, 688, 690,691, 

694 

loss of tail rotor effectiveness, 693 

main-rotor strikes, 689, 690 

multi-engine helicopter safety, 687 

power-off landing proficiency, 685 

situational awareness of objects, 690 

tail-rotor strikes, 689, 690 

wires, wires/poles, and trees, 689 

Advanced Technology Demonstrator Engine, 81 

Advanced Vibration Development (AVID), 368, 386 

Aeronautical Design Standard, ADS-27A-SP, 329 

aeroscout, 99, 102, 103, 104, 105, 106, 107, 109 

Aerospatiale, 51, 146, 149, 151, 259, 636 

airspeed, 212 

indicated (IAS), 212 

true (TAS), 212 

Air Transport Association (ATA), 602, 609, 610, 616, 

623 

Air Transport Association’s Specification 100, 609 

air transportability, 356, 357, 568 

Aircraft Cost Evaluator (ACE), 616, 617, 619, 620, 621, 

622, 623, 624, 625, 626, 627, 630, 631, 632, 634, 

635, 650, 657, 658, 659 

airfoil, 7 

drag coefficient, 183, 184, 214, 217, 227, 233, 234, 

235, 236, 260, 264, 300, 463 

drag, 7, 8, 137, 138, 161, 162, 164, 184, 217, 220, 

222, 230, 259, 299 

lift coefficient, 138, 157, 210, 311, 312, 326, 463 

lift, 184, 230, 259, 312 

lift-to-drag ratio, 183, 227 

pitching moment, 172, 399, 420, 424, 425, 426, 427, 

428, 429 

thickness, 490, 518, 540 

airlines, 49, 

helicopter, 251, 254, 255, 256, 258, 264, 265, 579, 

595, 596, 597, 598, 599, 600, 601, 602, 606, 607, 

609, 611, 612, 615, 635, 660, 661, 687 

airplane, 444, 455, 550, 579, 582, 586, 589, 590, 591, 

594, 595, 601, 602, 616, 623, 629, 660, 663, 664, 

673, 675, 687, 700 

short-haul, 597, 600, 608, 613, 660, 700 

trunk-line, 597 

Airworthiness Limitations, 646, 648 

airworthiness, 339, 340, 357, 359, 362, 509, 576, 646, 

647, 670 

American Helicopter Society (AHS), 19, 45, 46, 49, 94, 

118, 202, 204, 233, 238, 265, 286, 288, 291, 305, 

315, 338, 354, 386, 399, 534, 537, 675 

Army Aerodynamic and Acoustic Testing of Model 

Rotors (AATMR), 528, 529 

Army Helicopter Improvement Program (AHIP), 104, 

552 

Augusta Helicopter Company, 50, 252, 636 

autogyros, 8, 

Cierva C.30, 1, 278, 280, 337, 379 

Cierva C-30 parts count, 637 

Kellett XR-2/XR-3, 94 

Kellett YG-1B, 94, 97, 99, 100, 280, 282 

Kellett YO-60, 46, 47, 94, 97, 99, 100 

Pitcairn PCA-2, 33, 38 

Umbaugh Model 18-A, 84 

Groen Hawk, 84 

transition to helicopters, 43, 44, 45, 94, 95, 280, 281, 

339, 343, 434, 699 

versus airplane, 45, 207, 211 

versus helicopter, 23, 29, 31, 46, 47, 48, 619, 642, 

686, 697 

automatic flight control system, 20 

Avgas, 607 

Bell Aircraft Corporation, 14, 50, 670 

Bell Helicopter Company, 76, 77, 78, 553, 669 

Bell Helicopter Textron, 16, 35, 81, 149, 152, 176, 205, 

290, 291, 300, 307, 310, 328, 332, 343, 377, 434, 

498, 510, 540, 541, 542, 544, 552, 555, 561, 563, 

567, 568, 602, 627, 628, 631, 658, 693, 699 

blade element airloads, 398, 400 

blade element drag, 495, 496, 497 

blade element thrust, 154, 496 

blade elemental thrust integral, 422 

Boeing Bearingless Main Rotor (BMR), 302, 304 

Boeing Company, 552, 566 

Boeing Helicopters, 56, 75, 90, 125, 146, 179, 241, 377, 

528 

Boeing Vertol, 241, 285, 297, 300, 302, 304, 305, 328, 

348, 356, 368, 418, 470, 660 

Boeing Vertol V/STOL Wind Tunnel, 56 

C-60, 378, 380 

C-81, 369, 378, 434 

CAMRAD II + Overflow 2, 400, 420, 422, 424, 425, 

426, 430, 432, 435 

CHC Helicopters, Inc., 673 

Chicago Helicopter Airways, 254, 596, 615
INDEX 

942 

computational fluid dynamics (CFD), 172, 237, 244, 314, 

316, 318, 386, 393, 396, 399, 400, 401, 406, 410, 

415, 420, 424, 426, 430, 431, 435, 530, 533, 534 

computational structural dynamics (CSD), 393, 396, 399, 

400, 401, 406, 415, 424, 426, 431, 435 

Conklin & de Decker, 578, 616, 617, 618, 621, 623, 624, 

626, 627, 628, 631, 632, 634, 635, 650, 651, 652, 

657, 659 

cost, 19 

accounting, 97, 186, 193, 307, 471, 575, 582, 585, 

586, 594, 602, 619, 623, 624, 646, 653, 654 

Aircraft Cost Evaluator (ACE), xiv, 616, 617, 619, 

620, 621, 622, 623, 624, 625, 626, 627, 630, 631, 

632, 634, 635, 650, 657, 658, 659 

airframe maintenance costs, 609 

cost categories, 585 

cost-plus-fee contract, 552 

crew cost, 585 

depreciation cost, 587 

depreciation of flight equipment, 614 

Design to Unit Production Cost (DTUPC), 577 

Direct Operating Cost (DOC), viii, 582, 588, 589, 

590, 592, 593, 600, 602, 605, 606, 611, 612, 615, 

616, 617, 618, 619, 620, 622, 623, 624, 626, 630, 

631, 632, 633, 634, 635, 636, 657 (definition) 

dollars per available seat-mile, 620 

dollars per flight hour, 620, 623, 635 

economic operating cost model, 594 

engine maintenance costs, 611 

engine overhaul costs per flight hour, 632 

fatigue life-limited parts, 646 

fixed cost, 653,658 

flight crew cost, 606 

flight hours flown per year, 657 

flight profile, 511, 512, 605, 606, 607, 610, 615, 619 

flying operations, 592, 616, 617 

fuel and oil costs, 584, 607, 620 

ground-air-ground cycle, 336 

HAI Guide for the Presentation of Helicopter 

Operating Cost Estimates, 623, 624, 654, 655, 

657 

Indirect Operating Costs, 592, 601, 657 (definition) 

inflation, 543, 544, 545, 546, 563, 567, 570, 571, 589, 

590, 616, 636, 643, 646, 679 

insurance and reserve cost, 588, 608, 661, 665 

insurance, 585, 587, 593, 602, 606, 608, 661, 665 

labor rates, 610, 626 

Maintenance DOC Near-Term Goal, 635 

maintenance man-hours per flight hour (MMH/FH), 

610, 614, 624, 627, 636, 637, 650, 651, 652, 653, 

659 

major design-to-cost factors, 567 

man-hours, 559, 560, 574, 608, 610, 612, 613, 614, 

623, 628, 634, 635, 637, 649 

operating cost, 579, 582, 592, 653, 654 

overhaul, 101, 102, 132, 302, 586, 623, 631, 632, 

649, 650, 653, 659, 700 

price of fuel, 617 

refurbishing, 634, 635 

Robinson R22 Factory Overhaul, 646 

scheduled maintenance, 339, 498, 551, 552, 565, 574, 

577, 602, 606, 648, 649 

spare, 122, 636, 638, 639, 641, 642, 671 

time between overhaul (TBO), 102, 113, 541, 631, 

632, 636, 700 

TOC per flight hour, 657, 658 

total aircraft operating expenses, 594 

total of direct maintenance costs, 612 

total operating costs, 579, 592, 594, 599, 600, 616, 

653, 657, 658, 659, 660, 664 

unscheduled maintenance, 593, 606, 650, 651, 652 

variable costs, 579, 623, 653, 655, 657 

cyclic, 9, 10, 11, 12, 13, 14, 18, 19, 25, 33, 250, 262, 263, 

315, 380, 381, 382, 609 

cyclic control angles, 380 

Daimler, 54 

Design Analysis Methods for Vibrations (DAMVIBS), 

368, 371, 372, 373, 374, 376, 377, 378, 379, 382, 

383, 384, 385, 386, 390, 391, 392 

Data Base Products, 594 

Deutsch–Niederländischer Windkanal (DNW), 524, 528, 

529 

Douglas Aircraft Company, 338, 589, 593 

endurance limit, 333, 334, 338, 339, 340 

engine failure, 259, 262 

Eurocopter, 51, 146, 304, 636 

Fast Fourier Transform, 389 

fatigue, 231, 331, 332, 333, 334, 336, 338, 339, 340, 342, 

426, 576, 646, 689, 695 

Fenestron, 146, 147, 148, 149, 150, 151, 152 

Figure of Merit, 137, 180, 181, 182, 267, 271, 701 

fixed turbine, 63 

flapping, 10, 11, 13, 19, 34, 35, 89, 121, 364, 380, 382, 

392, 396 

free turbine, 63 

gas turbine engine, 48, 53, 59, 60, 63, 64, 66, 67, 70, 71, 

72, 74, 75, 77, 79, 81, 82, 83, 84, 86, 94, 100, 107, 

112, 114, 119, 121, 541, 546, 550, 566, 577, 618, 

632, 686 

General Aviation, 623, 672, 673, 679, 699 

General Electric, 78, 80, 82, 125, 130, 252, 265, 632, 660 

ground resonance, 8, 17, 19, 362 

Helicopter Association of Great Britain, 338 

Helicopter Association International, 509, 510, 512, 514, 

515, 623, 624, 629, 630, 653, 654, 675, 678 

Helicopter Association International Fly Neighborly 

Guide, 509, 510, 512, 513, 514, 515 

Helicopter Association International Helicopter Annual, 

629 

Helicopter Association International Safety Committee, 

678 

HeliValue$, 84, 539, 543, 608, 646, 653 

high-speed rail, 595 

Hiller Aircraft Corporation, 18, 20, 77, 210, 285, 315, 

457, 540, 564, 670 

Hiller Servo Paddle, 18, 20 

Hindenburg, 663 
INDEX 

943 

hub, xi, 

drag, 231, 292, 295, 296, 302, 304, 305, 306, 307, 

308, 310, 314 

fairing, 297, 307, 308, 309 

plane, 7, 35, 198, 237 

pitching moment, 10, 11 

teetering angle, 379, 380, 382 

types, (see Appendix D) 

vibratory loads, 318, 329, 343, 349, 351, 362, 364, 

368, 369, 373, 375, 376, 377, 385, 386, 390, 393-

397, 400, 403, 410, 418 

Hughes Tool Company, 62, 78, 102, 138, 285, 289, 302, 

304, 328, 344, 500, 501, 503, 504, 508, 509, 533, 

540, 700 

human, 318-331, 336, 354, 437, 438, 439, 441, 443, 470, 

504, 566, 590, 663, 675, 680, 698 

Integrated Product Teams (IPT), 572, 575 

International Civil Aviation Organization (ICAO), 509, 

510, 528 

International Helicopter Safety Team (IHST), 675, 698 

International Organization for Standardization (ISO), 71, 

326, 331, 329, 343, 344, 346, 375, 439, 441, 442, 

509, 510, 528 

ISO 2631 Guide for the Evaluation of Human Exposure 

to Whole-Body Vibration, 326, 331 

Jet A, 72, 607, 617, 618, 619, 621 

Kamov Design Bureau, 51, 90, 178, 179, 180, 195 

Kaman Aircraft, 36, 50, 75, 178, 179, 191, 196, 238, 239, 

240, 498, 504, 702 

Kellett Autogiro Corporation, 8, 36, 43, 46, 47, 94, 280, 

281, 282, 285, 697, 702 

LHX/RAH-66 program, 552, 571 

life, 332 

blade, 643, 646, 653 

cycle, 547, 551, 565, 566, 578 

drive train, 694 

engine, 584, 587, 593 

equipment, 587, 642, 654 

fatigue, 332, 334, 336, 339, 342, 426, 646 

limited, 637, 642 

on condition, 631, 632, 646, 700 

production, 541, 543, 544 

service, 336, 337, 339 

Lockheed Aircraft Company, 292, 293, 296, 297, 302, 

304, 310, 311, 313, 447, 539, 548, 586, 587 

Lockheed stiff inplane, hingeless rotor, 313 

Lord Manufacturing Company, 300 

Los Angeles Airways, 254, 256, 595, 596, 615 

materials 

aluminum, 54, 336, 337, 338 

duralumin, 336 

MIL-HDBK-5J, 333, 334, 339 

steel, 56, 332, 333, 334, 336, 337, 338, 339, 356, 392 

titanium, 340 

wood, 208, 336, 338, 341, 349, 369 

McDonnell Douglas Helicopter, 81, 146, 302, 371, 377, 

378, 384, 447, 529 

Messerschmitt-Bölkow-Blohm (MBB), 50, 146, 259, 

304, 305, 528 

Mil Moscow Helicopter Plant, 51, 90, 252, 570, 688 

Milestone Done-Done (MD2

) method, 573, 574, 575 

MIL-H-8501A, 328, 329, 345, 356, 368 

MIL-HDBK-5J, 333, 334, 339 

MIL-STD-1374A, 93 

MIL-STD-811C, 566 

MIL-W-25140, 93 

N number, 671 

NASA In-Flight Rotor Acoustic Program, 526 

Nash–Kelvinator, 560 

NASA Structural Analysis (NASTRAN), 369, 370, 371, 

372, 373, 376, 377, 384, 385, 386, 393, 701 

New York Airways, 254, 256, 595, 596, 602, 606, 609, 

611, 612, 615, 617, 635 

New York Yankee baseball team, 669 

Nikolsky Lecture, 202, 204, 307, 316, 386, 399, 548, 681 

noise, 437 (definition) 

A-, B-, and C-weightings, 443 

abatement, 510 

add thickness, thrust, and torque sound pressures, 478 

addition of pressures, 474 

aircraft noise standards, 510 

Anechoic Hover Chamber, 530, 531 

Army Aerodynamic and Acoustic Testing of Model 

Rotors (AATMR), 528, 529 

aural detection distance, 508 

blade vortex interaction (BVI), 512, 513, 514, 528, 

529, 530, 533 

Blade-Vortex Impulsive, 510 

broadband, 516, 529, 533 

decibel, 441, 450, 516, 525 

Doppler effect, 474, 475, 495 

drive train, 506 

ear, 309, 437, 438, 467 

Effective Perceived Noise (EPN), 536 

engine-alone, 506 

far field, 471 

HART II, 529, 534 

Helicopter Association International Fly Neighborly 

Guide, 509, 510, 512, 513, 514, 515 

high-speed impulsive, 510 

impulsive noise, 510, 512, 513, 516, 519, 524, 525, 

526, 529, 530, 532, 533, 534 

International Civil Aviation Organization (ICAO), 

509, 510, 528 

loudness curves, 441, 442, 443, 444 

loudness scale, 441 

Mach number, 444, 447, 448, 449, 450, 451, 455, 

472, 474, 475, 476, 483, 484, 489, 490, 492, 493, 

497, 510, 520, 524, 526, 530, 532, 533, 534 

main-rotor-alone, 507 

mosquito, 439 

NASA In-Flight Rotor Acoustic Program, 526 

Noise Sensitivity Trade Study, 489 

observer distance, 491 

observer distance to radius ratio (S/R), 484, 485, 490, 

491, 521 

observer time, 474, 475 

observer, 96, 207, 208, 471, 472, 474, 475, 476, 477, 

479, 480, 481, 483, 484, 490, 491, 495, 497, 510, 

522 
INDEX 

944 

overall sound pressure level (OSPL), 468, 469, 470, 

471, 478, 479, 480, 484, 488, 489, 491, 492, 496, 

497, 500, 502, 504, 505, 506, 507, 520, 521, 522 

pascals, 438, 441, 470, 472, 476, 480, 495, 516, 520, 

521, 534 

phon, 440, 443 

PSU-WOPWOP, 469 

Quiet Helicopter Program, 484, 485, 488, 498, 499, 

502, 508, 509 

reduction, 490, 493, 497, 498, 508 

reference hearing level, 441 

reflection, 485, 488 

root mean square, 438, 441 

rotational noise, 469, 488, 490, 493 

sound pressure level (SPL), 440, 441, 443, 453, 468, 

470, 471, 475, 476, 477, 478, 479, 480, 482, 483, 

484, 485, 488, 491, 492, 497, 498, 504, 507, 520, 

521, 522, 524, 526 

sound pressure time history, 470 

sound pressure waveforms, 475, 477, 518, 519, 520, 

521 

sound source, 467, 474 

tail-rotor-alone noise, 507 

The Quiet One, 499, 501, 502, 503, 504, 508, 533 

thickness sound pressure, 476, 497 

three weighting curves, 442, 444 

threshold, 438, 441 

tone, 438, 440, 441, 443, 444, 470, 474, 524 

WOPWOP, 469, 533, 534 

Outlook for Vertical-Lift Aircraft in Scheduled 

Commercial Transportation, 660 

part, 332(definition) 

parts count, 300, 301, 302, 309, 637, 638, 642 

performance, 119 

Army hover design requirement, 122 

autorotation, 24, 25, 28, 33, 34, 120, 679, 686, 687 

autorotational, 103, 686, 688, 697 

blade shank fairing, 298 

blade stall, 156, 157, 345, 350, 351, 352, 353, 424, 

426, 429, 491 

brake horsepower, 55, 56, 204, 213, 227, 228, 230, 

232, 235, 275 

flat plate, 213, 232, 233, 235, 278 

fuel efficiency, 267, 271, 619, 620 

fuel flow, 60, 62, 67, 69, 70, 71, 72, 76, 77, 79, 80, 

82, 83, 84, 251, 271, 273, 274, 618, 619, 620 

ground effect, 6, 7, 32, 112, 120, 124, 128, 142, 144, 

175, 176, 189, 198, 201, 202, 253, 270, 271, 456, 

467, 485, 489, 490 

height-velocity, 28, 32, 33, 37, 697, 699 

hover ceiling, 124, 130, 134, 200 

hover in ground effect (HIGE), 124, 144, 198, 199, 

200, 201 

hover out of ground effect (HOGE), 5, 6, 7, 39, 120, 

121, 122, 124, 126, 127, 130, 141, 142, 144, 145, 

198, 199, 200, 201, 202 

hover power required, 5, 8, 126, 128, 130, 134, 139, 

160, 172, 197, 251, 267 

hovering performance, 119, 124, 125, 126, 133, 134, 

178, 188, 192, 195, 204, 280, 283, 701 

hub drag, 305, 306, 314 

ideal horsepower required, 5, 120, 147 

induced drag, 233, 237, 238, 265 

induced power, 128, 162, 165, 168, 169, 170, 171, 

173, 174, 177, 182, 185, 188, 190, 219, 224, 227, 

228, 232, 233, 234, 235, 237, 238, 244, 249, 265, 

266, 314 

installed horsepower, 6, 114, 130, 252, 584 

intermediate rated power, 130, 200 

lift-to-drag ratio (L/D), 33, 115, 116, 137, 138, 170, 

171, 230, 272, 274, 275, 276, 277, 278, 279, 314 

Mach number, 168, 226, 227 

nautical mile per pound, 621 

NOTAR, 146, 147, 148, 151 

one-engine-inoperative (OEI), 252, 253, 254, 257, 

261, 262, 263, 265 

overlap correction factor, 185 

parasite drag, 227, 233, 235, 237, 245, 277, 278, 280, 

281, 283, 284, 285, 286, 287, 288, 289, 291, 292, 

293, 295, 296, 297, 300, 304, 306, 309, 314, 619, 

701 

power coefficient, 8, 142, 143, 149, 164, 188, 193, 

198, 225, 252, 253 

power margin, 119, 120, 122, 130, 182, 200, 231 

power-off landing, 23 

profile power, 8, 160, 162, 164, 165, 166, 168, 169, 

170, 171, 185, 188, 190, 219, 223, 227, 232, 233, 

234, 235, 238, 246, 314 

propeller Activity Factor, 218, 219, 222, 226 

propeller, 7, 46, 211-234, 238, 272, 275, 278, 312, 

444- 456, 470, 472, 491, 516, 523, 553 

propeller history, 336, 337 

propulsive efficiency, 455 

referred power, 69, 215 

rotor thrust, 5, 10, 29, 30, 88, 134, 138, 141, 142, 

143, 144, 168, 169, 173, 174, 187, 191, 196, 222, 

226, 234, 235, 237, 403, 405, 410, 415, 472, 489, 

491, 492, 493, 496, 503, 504, 526, 533 

shank drag, 300 

solidity, 8 

specific fuel consumption (SFC), 60, 62, 70, 71, 72, 

79, 80, 84, 111, 112, 267, 268, 269, 271, 272, 

275, 276SFC, , 112, 267, 268, 269, 271, 272, 273, 

274, 275, 276, 277, 584 

specific range, 275, 276, 617, 620, 621 

tail rotor, 14, 17, 140-151, 172-178, 204, 205, 234, 

235, 302, 329, 444, 465, 466, 487, 494, 489, 498, 

500, 501, 503, 504, 507, 541, 640, 646, 648, 690, 

693 

takeoff gross weight, 84, 88, 90, 91, 92, 93, 94, 

105, 113, 124, 252, 256, 269, 272, 275, 503, 548, 

701 

tandem-rotor induced velocity interference, 247 

thrust coefficient, 8, 143, 149, 155, 158, 164, 166, 

222, 226, 228, 455 

variable-pitch propeller, 214, 218 

wake skew angle, 242, 243, 247, 248 

Petroleum Helicopters, Inc., 673 

Piasecki Helicopter Corporation, 19, 60, 179, 180, 182, 

239, 241, 285 

piston engine, 53 
INDEX 

945 

Premier Congrés International de la Navigation Aérienne, 

663 

price 

average unit cost, 554, 555, 566 

Avgas, 607 

avionics, 546 

Bell Model 206, 

Consumer Price Index, 563, 571 

cost plus fixed fee contract, 552 

Douglas DC-3, 582, 584 

engine, 86 

Ford Tri-motor, 585, 584 

fixed price contract, 552, 576 

Joint Design-to-Cost Guide, Life Cycle Cost as a 

Design Parameter, 565 

Huey, 567, 568 

LHX/RAH-66, 567, 568 

list price, 539, 540, 542, 545, 546, 547, 548, 578, 

611, 617, 642, 657 

Learning Curve Factor, 557, 558, 560, 563, 567 

learning curve, 542, 555, 556, 557, 559, 560, 563, 

564, 565 

military, 546, 551, 578 

price of fuel, 617, 618 

price-estimating relationship, 546 

program, 569 

purchase price, 114, 116, 539, 542, 545, 546, 570, 

578, 630, 700 

Robinson R22, 638 

selling price, 87, 492, 503, 533, 539, 540, 542, 545, 

565, 636 

Sikorsky S-61, 617 

Sikorsky S-92, 570 

spares, 122, 636, 638, 639, 641, 642, 671 

Tishchenko view, 570 

The Official Helicopter Blue Book®, 539, 542, 543, 

544, 630, 646, 653 

productivity, 87, 115, 116, 118, 170, 547, 548, 549, 550 

Project Hummingbird, 254, 596, 599, 600, 601, 615, 660 

PSU-WOPWOP, 469 

Quiet Helicopter Program, 484, 485, 488, 498, 499, 502, 

508, 509 

rotor types (see Appendix D) 

bearingless rotor, 145, 297, 302, 304, 306, 307, 308, 

309, 529 

doorhinge rotor, 309, 310, 311, 314, 701 

hingeless rotor, 50, 302, 305, 306, 309, 311, 313, 634 

Rotor Airframe Comprehensive Aeroelastic Program 

(RACAP), 378 

Rotorcraft Dynamics Analysis (RDYNE), 378 

referred power, 69, 215 

Robinson Helicopter Company, 504, 540, 632, 637, 642, 

646, 649, 650, 658, 659, 694 

Rolls Royce, 252, 541, 631, 632, 633 

Rotor Breeze, 627 

rotorcraft 

inactive rotorcraft, 66 (FAA definition), 392, 670, 

671 

active rotorcraft, 66 (FAA definition), 128, 331, 360, 

564, 670, 671, 672, 673 

rotor inertia, 29, 33, 34, 35, 36, 37, 103, 686, 687, 697, 

699 

Bell RotorBreeze, 627, 628, 693 

San Francisco and Oakland Helicopter Airlines, 256, 595 

stability augmentation system (SAS), 699 

Hiller servo paddle control system, 17 

Sikorsky Aircraft, 34, 43, 46, 50, 96, 101, 108, 125, 130, 

141, 176, 182, 231, 238, 252, 256, 291, 296, 305, 

328, 341, 356, 357, 360, 370, 377, 559, 570, 571, 

628, 670, 687, 

Sikorsky Commercial Links, 628 

single turbine-powered helicopters, 676, 677, 684, 689, 

691, 695 

sound, 437 (definition) 

Spirit of St. Louis, 273, 275 

stabilizer bar, 14, 15, 19 

stress, 331, 332, 333, 334, 338, 339, 340, 701 

subsidy, 120, 254, 255, 265, 595, 596, 598, 600, 615, 

660, 661 

Sud-Aviation Company, 75 

supercharged engine, 57, 58 

synchropter, 3, 5, 75, 108, 111, 120, 141, 178, 179, 180, 

191, 195, 238, 268, 280, 281 

system engineering, 572, 573, 575, 638 

time between overhaul (TBO), 102, 113, 541, 631, 632, 

636, 700 

The Official Helicopter Blue Book®, 539, 542, 543, 544, 

630, 646, 653 

thermodynamic energy equation, 64 

tiltrotor, 214, 455, 544, 575, 661 

turbine inlet temperature (TIT), 70, 71, 72, 73, 74, 113, 

131 

transmission, 5 

belt drive, 5 

efficiency, 138, 142, 175, 176, 190, 192, 196, 197, 

204, 235, 236, 247, 249, 278 

limits, 122, 127, 131, 132, 133, 240, 257, 262 

Augusta/Westland EH 101, 252 

Bell H-13, 231 

Bell AH-1G, 385 

Boeing Model 107-II, 265 

cost to maintain, 609 

main rotor, 99 

oil temperature, 101 

overheating, 101, 102 

overhaul, 636 

gear reduction, 119 

Sikorsky YR-4B, 204 

Sikorsky YUH-60A, 132 

torque limits, 133 

Vertol YHC-1A, 257 

trim, 144, 212, 234, 245, 250, 378, 379, 380, 382, 385, 

415, 424, 528, 534 

turboshaft engine, 63, 70, 72, 75, 81, 82, 83, 84, 86, 252, 

287, 289, 602, 612, 615 

United States, 9 

Air Force Flight Test Center at Edwards Air Force 

Base Edwards, 60, 76, 77, 78, 124, 136, 213, 239, 

285, 343, 350, 354, 516, 524, 595 

Army Aviation Systems Test Activity, 77, 136, 216 

Civil Aeronautics Act of 1938, 696 
INDEX 

946 

Census of U.S. Civil Aircraft, 672 

Civil Aeronautics Administration (CAA), 9, 14, 231, 

343, 666, 668, 669, 670, 672 

Civil Aeronautics Board (CAB), 256, 259, 261, 582, 

589, 594, 595, 598, 600, 601, 668 

Defense Advanced Research Projects Agency 

(DARPA), 498 

Department of Defense (DoD), 71, 311, 332, 539, 

550, 552, 555, 565, 566, 572, 577, 578, 699 

Department of Transportation (DOT), 661, 696, 735 

U. S. Federal Aviation Administration (FAA), 9, 77, 

84, 102, 231, 254, 255, 259, 260, 261, 262, 263, 

265, 503, 504, 509, 510, 511, 512, 514, 515, 536, 

537, 541, 566, 594, 596, 597, 598, 601, 619, 623, 

646, 647, 648, 666, 671, 672, 673, 674, 675, 676, 

679, 680, 685, 687, 688, 696, 697, 699 

FAA Category A, 231, 256, 257 

FAA Master List, 671 

FAA Mike Monroney Aeronautical Center, 671 

FAA Notice of Proposed Rulemaking, 509 

FAA Registry, 671, 675, 676, 699 

FAA Statistics and Forecast Branch, 672 

National Transportation Safety Board (NTSB), 663, 

666, 668, 671, 672, 673, 674, 675, 679, 680, 681, 

684, 685, 687, 689, 690, 694, 695, 696, 697, 698 

National Transportation Safety Board (NTSB), 

Report CHI82DA034, 685 

National Transportation Safety Board (NTSB), 

Report ERA11CA166, 680 

Statistical Handbook of Civil Aviation, 666 

UH-1 Program, 553 

UH-60A Airloads Program, 361, 373, 386, 390, 391, 392, 

393, 394, 396, 400, 435 

United Research Inc., 660 

USAAMRDL, 498 

Vertol Aircraft Corporation, 241, 255, 597,600 

vibration, 40, 315 

1/rev, 329, 330, 331, 337, 343, 344, 345, 348, 393, 

394, 415 

acceleration, 320, 321, 322, 323, 325, 326, 354, 356, 

359, 365, 375, 376 

Advanced Vibration Development (AVID) Program, 

368, 386 

Aeronautical Design Standard, ADS-27A-SP, 329 

amplification factor, 323 

blade elastic twisting, 399, 422 

coupled rotor-fuselage, 126, 245, 349, 362, 364, 365, 

366, 367, 369, 396, 399, 434 

damping, 13, 304, 322, 323, 384, 408 

frequencies, 320, 325, 328, 330, 331, 340, 342, 356, 

360, 362, 366, 367, 369, 372, 373, 376, 384, 390, 

392, 440, 470, 500 

fuselage pitch attitude, 380 

fuselage-rotor coupled, 375 

hertz, 320, 331, 438, 439, 440, 441, 442, 443, 506 

inertia integral, 423 

inertia term, 410, 422, 423 

inplane bending, 399 

inplane shear loads, 397 

lateral vibration, 346 

mean stress, 333, 334 

natural frequency, 304, 320, 322, 323, 324, 362, 365, 

373 

out-of-plane bending, 398 

pitch link load, 396, 397, 398, 399, 410, 416, 423, 

424, 425, 426 

rotating blade root shears, 397 

shake tests, 343, 362, 363, 364, 370, 371 

steady loads, 410 

time history, 40, 323, 469, 470, 516, 520, 524 

trim, 144, 212, 234, 245, 250, 378, 379, 380, 382, 

385, 415, 424, 528, 534 

UH-60A Airloads Program, 361, 373, 386, 390, 391, 

392, 393, 394, 396, 400, 435 

vertical shear load, 397 

vertical vibration, 326, 345, 348, 350, 351, 359, 361, 

386 

vibrating beam, 340, 343 

vibration limits, 326 

Vibration Rating Scale (VRS), 349, 359 

vibration rating scale, 349 

vibratory loads, 318, 343, 368, 369, 373, 377, 379, 

385, 386, 393, 396, 418, 701 

vibratory pressure, 438, 441 

vibratory response, 319, 360 

whole body response, 320, 331 

VTOL, 94, 254, 328, 596, 602, 608, 609, 610, 611, 613, 

614, 660, 661, 687, 688, 700, 701 

Work Breakdown Structure (WBS), 565, 566, 573, 574, 

575 

weight, 5, 10, 26, 27, 28, 30, 31, 43, 51, 56, 72, 75, 77, 

81, 82, 84, 87 

GW-c.g. envelope, 348 

All Other Groups, 99, 103, 104, 105, 106, 108, 109, 

111, 112, 118 

design loads, 87, 88, 89, 90 

design weight, 87, 88, 89, 90 

empty weight, 87, 92 

load factors, 87, 88, 89, 90, 92, 660 

MIL-STD-1374A, 93 

MIL-STD-811C, 566

MIL-W-25140, 93 

mission equipment package (MEP), 96, 207, 568, 575 

primary mission, 92, 94, 102, 103, 126, 128, 130, 

200, 359, 503 

Propulsion Group, 97, 99, 100, 102, 107, 108, 111, 

112, 114, 118 

Structural Groups, 97, 99, 102, 103, 107, 108, 111, 

112, 113, 114, 118 

takeoff gross weight, 84, 88, 90, 91, 92, 93, 94, 105, 

113, 124, 252, 256, 269, 272, 275, 503, 548, 701 

useful load, 49, 87, 88, 91, 92, 93, 94, 96, 97, 98, 105, 

109, 114, 115, 117, 118, 122, 130, 134, 136, 200, 

252, 253, 503, 533, 548, 550, 699, 700, 701 

weight empty, 87, 88, 92, 94, 97, 102, 103, 105, 112, 

114, 503, 545, 547, 610, 613, 626 

Westland Helicopter, 50, 149, 150, 179, 252, 292, 294, 

318, 636 

WOPWOP, 469, 533, 534 

Young Stabilizer Bar, 15, 16, 20