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Principles of Helicopter Aerodynamics_图文

Principles of Helicopter Aerodynamics
University of Maryland


The Pitt Building, Trumpington Street, Cambridge, United Kingdom

The Edinburgh Building, Cambridge CB2 2RU, UK 40 West 20th Street, New York, NY 10011-4211, USA 10 Stamford Road, Oakleigh, Melbourne 3166, Australia Ruiz de Alarc? n 13, 28014 Madrid, Spain o

Cambridge University Press 2000

This book is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2000 Printed in the United States of America Typeface Times Roman 10/12 pt.
A System L TEX 2ε


A catalog record for this book is available from the British Library. Library of Congress Cataloging in Publication Data Leishman, J. Gordon. Principles of helicopter aerodynamics / J. Gordon Leishman. p. cm. Includes bibliographical references (p. ). ISBN 0-521-66060-2 (hardcover) 1. Helicopters – Aerodynamics. TL716.L43 2000 629.133 352 – dc21

99-38291 CIP

ISBN 0 521 66060 2 hardback


Preface Acknowledgments List of Main Symbols List of Figures List of Tables 1 Introduction: A History of Helicopter Flight 1.1 Introduction 1.2 Early Attempts at Vertical Flight 1.3 The Era of the Autogiro 1.4 The First Successes with Helicopters 1.5 Maturing Technology 1.6 Tilt-Wings and Tilt-Rotors 1.7 Chapter Review 1.8 Questions Bibliography 2 Fundamentals of Rotor Aerodynamics 2.1 Introduction 2.2 Momentum Theory 2.2.1 Flow near a Hovering Rotor 2.2.2 Conservation Laws of Fluid Mechanics 2.2.3 Application to a Hovering Rotor 2.2.4 Disk Loading and Power Loading 2.2.5 Induced In?ow Ratio 2.2.6 Thrust and Power Coef?cients 2.2.7 Nonideal Effects on Rotor Performance 2.2.8 Figure of Merit 2.2.9 Worked Example 2.2.10 Induced Tip Loss 2.2.11 Rotor Solidity and Blade Loading Coef?cient 2.2.12 Power Loading 2.3 Axial Climb and Descent 2.3.1 Axial Climb 2.3.2 Axial Descent 2.3.3 The Region ?2 ≤ Vc /vh ≤ 0 2.3.4 Power Required 2.3.5 Working States of the Rotor in Axial Flight 2.3.6 Autorotation

page xvii xxi xxiii xxxi xliii 1 1 2 12 14 22 27 28 29 30 33 33 36 37 38 39 42 43 43 44 46 47 48 50 52 53 53 55 57 59 60 60


x 2.4 Momentum Analysis in Forward Flight 2.4.1 Induced Velocity in Forward Flight 2.4.2 Special Case, α = 0 2.4.3 Numerical Solution to In?ow Equation 2.4.4 Validity of the In?ow Equation 2.4.5 Rotor Power in Forward Flight 2.4.6 Other Applications of the Momentum Theory 2.5 Chapter Review 2.6 Questions Bibliography 3 Blade Element Analysis 3.1 Introduction 3.2 Blade Element Analysis in Hover and Axial Flight 3.2.1 Integrated Rotor Thrust and Power 3.2.2 Thrust Approximations 3.2.3 Untwisted Blades, Uniform In?ow 3.2.4 Linearly Twisted Blades, Uniform In?ow 3.2.5 Torque/Power Approximations 3.2.6 Tip-Loss Factor 3.3 Blade Element Momentum Theory (BEMT) 3.3.1 Ideal Twist 3.3.2 BEMT – A Numerical Approach 3.3.3 Distributions of In?ow and Airloads 3.3.4 The Optimum Hovering Rotor 3.3.5 Circulation Theory of Lift 3.3.6 Power Estimates 3.3.7 Prandtl’s Tip-Loss Function 3.3.8 Figure of Merit 3.3.9 Further Comparisons of BEMT with Experiment 3.3.10 Compressibility Corrections 3.3.11 Equivalent Chords and Weighted Solidity 3.3.12 Mean Wing Chords 3.3.13 Thrust Weighted Solidity 3.3.14 Power/Torque Weighted Solidity 3.3.15 Weighted Solidity of the Optimum Rotor 3.3.16 Weighted Solidities of Tapered Blades 3.3.17 Mean Lift Coef?cient 3.4 Blade Element Analysis in Forward Flight 3.4.1 Blade Forces 3.4.2 Induced Velocity Field 3.5 Chapter Review 3.6 Questions Bibliography 4 Rotating Blade Motion 4.1 4.2 4.3 Introduction Types of Rotors Equilibrium about the Flapping Hinge

Contents 63 64 65 66 67 68 69 73 73 76 78 78 80 82 82 83 84 84 85 87 91 92 93 96 99 100 102 105 106 107 110 110 111 111 112 112 113 113 114 115 123 124 126 128 128 129 131

Contents 4.4 Equilibrium about the Lead/Lag Hinge 4.5 Equation of Motion for Flapping Blade 4.6 Physical Description of Blade Flapping 4.6.1 Coning Angle 4.6.2 Longitudinal Flapping 4.6.3 Lateral Flapping 4.7 Dynamics of Blade Flapping with a Hinge Offset 4.8 Blade Feathering and the Swashplate 4.9 Review of Rotor Reference Axes 4.10 Dynamics of a Lagging Blade with Hinge Offset 4.11 Coupled Flap–Lag Motion 4.12 Introduction to Rotor Trim 4.13 Chapter Review 4.14 Questions Bibliography 5 Basic Helicopter Performance 5.1 Introduction 5.2 Hovering and Axial Climb Performance 5.3 Forward Flight Performance 5.3.1 Induced Power 5.3.2 Blade Pro?le Power 5.3.3 Parasitic Power 5.3.4 Climb Power 5.3.5 Tail Rotor Power 5.3.6 Total Power 5.3.7 Effect of Gross Weight 5.3.8 Effect of Density Altitude 5.3.9 Lift-to-Drag Ratios 5.3.10 Climb Performance 5.3.11 Speed for Minimum Power 5.3.12 Speed for Maximum Range 5.3.13 Range–Payload and Endurance–Payload 5.3.14 Factors Affecting Maximum Attainable Forward Speed 5.3.15 Performance of Coaxials and Tandems 5.4 Autorotation Revisited 5.4.1 Autorotation in Forward Flight 5.4.2 Height–Velocity (HV) Curve 5.4.3 Autorotation Index 5.5 Ground Effect 5.6 Chapter Review 5.7 Questions Bibliography 6 Conceptual Design of Helicopters 6.1 6.2 6.3 Introduction Design Requirements Design of the Main Rotor

xi 133 134 139 139 139 140 141 142 144 147 149 150 155 156 157 159 159 159 163 164 164 166 166 166 167 168 169 169 170 171 173 174 174 176 178 180 182 184 185 189 190 191 193 193 193 194

xii 6.3.1 Rotor Diameter 6.3.2 Tip Speed 6.3.3 Rotor Solidity 6.3.4 Number of Blades 6.3.5 Blade Twist 6.3.6 Blade Planform and Tip Shape 6.3.7 Airfoil Sections 6.3.8 The BERP Rotor 6.4 Fuselage Design 6.4.1 Fuselage Drag 6.4.2 Vertical Drag or Download 6.4.3 Fuselage Side-Force 6.5 Empennage Design 6.5.1 Horizontal Stabilizer 6.5.2 Vertical Stabilizer 6.5.3 Modeling 6.6 Design of Tail Rotors 6.6.1 Physical Size 6.6.2 Thrust Requirements 6.6.3 Pushers Versus Tractors 6.6.4 Design Requirements 6.6.5 Aerodynamic Interactions 6.6.6 Typical Tail Rotor Designs 6.6.7 Other Antitorque Devices 6.7 High Speed Rotorcraft 6.7.1 Compound Helicopters 6.7.2 Tilt-Rotors 6.7.3 Other High Speed Rotorcraft 6.8 Chapter Review 6.9 Questions Bibliography 7 Rotor Airfoil Aerodynamics 7.1 7.2 7.3 7.3.1 7.3.2 7.3.3 7.4 7.5 7.5.1 7.5.2 7.5.3 7.6 7.6.1 7.6.2 7.6.3 7.7 Introduction Rotor Airfoil Requirements Reynolds Number and Mach Number Reynolds Number Concept of the Boundary Layer Mach Number Airfoil Shape De?nition Airfoil Pressure Distributions Pressure Coef?cient Synthesis of Chordwise Pressure Measurements of Chordwise Pressure Aerodynamics of a Typical Airfoil Section Integration of Distributed Forces Pressure Integration Typical Force and Moment Results Pitching Moment

Contents 195 197 199 201 203 204 208 209 212 213 218 219 219 220 222 222 222 223 224 225 226 226 227 239 232 232 233 234 235 236 237 243 243 244 245 246 247 251 253 256 256 257 258 260 260 262 264 264

Contents 7.7.1 Aerodynamic Center 7.7.2 Center of Pressure 7.7.3 Effect of Airfoil Shape on Moments 7.7.4 Use of Tabs 7.8 Maximum Lift and Stall Characteristics 7.8.1 Effects of Reynolds Number 7.8.2 Effects of Mach Number 7.9 Advanced Rotor Airfoil Design 7.10 Representing Static Airfoil Characteristics 7.10.1 Linear Aerodynamics 7.10.2 Nonlinear Aerodynamics 7.10.3 Table Look-Up 7.10.4 Direct Curve Fitting 7.10.5 Beddoes Method 7.10.6 High Angle of Attack Range 7.11 Chapter Review 7.12 Questions Bibliography 8 Unsteady Aerodynamics 8.1 Introduction 8.2 Sources of Unsteady Aerodynamic Loading 8.3 Blade Wake 8.4 Reduced Frequency and Reduced Time 8.5 Unsteady Attached Flow 8.6 Quasi-Steady Thin-Airfoil Theory 8.7 Theodorsen’s Theory 8.7.1 Pure Angle of Attack Oscillation 8.7.2 Pure Plunging Oscillation 8.7.3 Pitch Oscillations 8.8 The Returning Wake: Loewy’s Problem 8.9 The Sinusoidal Gust: Sears’s Problem 8.10 Indicial Response: Wagner’s Problem 8.11 The Sharp-Edged Gust: K¨ ssner’s Problem u 8.12 Traveling Sharp-Edged Gust: Miles’s Problem 8.13 Time-Varying Incident Velocity 8.14 Indicial Response Method 8.14.1 Recurrence Solution to the Duhamel Integral 8.14.2 State-Space Solution 8.15 Subsonic Compressible Flow 8.15.1 Approximations to the Indicial Response 8.15.2 Indicial Lift from Angle of Attack 8.15.3 Indicial Lift from Pitch Rate 8.15.4 Determination of Indicial Function Coef?cients 8.15.5 Indicial Pitching Moment from Angle of Attack 8.15.6 Indicial Pitching Moment from Pitch Rate 8.15.7 Unsteady Axial Force and Drag 8.15.8 State-Space Aerodynamic Model for Compressible Flow 8.16 Comparison with Experiment

xiii 267 268 269 272 274 276 279 285 288 288 289 289 290 291 293 295 296 298 302 302 303 303 306 307 308 309 313 315 315 318 322 323 326 328 333 336 337 340 342 345 346 348 349 351 351 353 355 357

xiv 8.17 Nonuniform Vertical Velocity Field 8.17.1 Exact Subsonic Linear Theory 8.17.2 Approximations to the Sharp-Edged Gust Functions 8.17.3 Response to an Arbitrary Vertical Gust 8.17.4 Blade Vortex Interaction (BVI) Problem 8.17.5 Convecting Vertical Gusts in Subsonic Flow 8.18 Dynamic In?ow 8.19 Chapter Review 8.20 Questions Bibliography 9 Dynamic Stall 9.1 Introduction 9.2 Flow Topology of Dynamic Stall 9.3 Dynamic Stall in the Rotor Environment 9.4 Effects of Forcing Conditions on Dynamic Stall 9.5 Modeling of Dynamic Stall 9.5.1 Engineering Models of Dynamic Stall 9.5.2 Capabilities of 2-D Dynamic Stall Modeling 9.6 Torsional Damping 9.7 Effects of Sweep Angle on Dynamic Stall 9.8 Effect of Airfoil Shape on Dynamic Stall 9.9 Three-Dimensional Effects on Dynamic Stall 9.10 Time-Varying Velocity Effects 9.11 Prediction of In-Flight Airloads 9.12 Chapter Review 9.13 Questions Bibliography 10 Rotor Wakes and Tip Vortices 10.1 Introduction 10.2 Flow Visualization Techniques 10.2.1 Smoke Flow Visualization 10.2.2 Density Gradient Methods 10.2.3 Natural Condensation Effects 10.3 Characteristics of the Rotor Wake in Hover 10.4 Characteristics of the Rotor Wake in Forward Flight 10.4.1 Wake Boundaries 10.4.2 Blade–Vortex Interactions (BVIs) 10.5 Other Characteristics of Rotor Wakes 10.5.1 Periodicity 10.5.2 Vortex Perturbations and Instabilities 10.6 Detailed Structure of the Tip Vortices 10.6.1 Velocity Field 10.6.2 Models of the Vortex 10.6.3 Vorticity Diffusion Effects and Vortex Core Growth 10.6.4 Correlation of Rotor Tip Vortex Data 10.7 Vortex Models of the Rotor Wake 10.7.1 Biot–Savart Law

Contents 358 359 361 363 365 367 369 371 372 374 378 378 379 382 383 389 390 393 397 399 403 405 410 410 412 413 414 418 418 418 419 419 421 421 425 426 427 431 431 431 432 434 435 440 442 443 425

Contents 10.7.2 Blade Model 10.7.3 Governing Equations for the Vortex Wake 10.7.4 Prescribed Wake Models for Hovering Flight 10.7.5 Prescribed Vortex Wake Models for Forward Flight 10.7.6 Free-Vortex Wake Analyses 10.8 Effects of Maneuvers 10.9 Advanced Computational Models 10.10 Interactions between the Rotor and the Airframe 10.11 Chapter Review 10.12 Questions Bibliography Appendix Index

xv 446 448 450 453 458 470 476 477 479 479 481 487 489


Introduction: A History of Helicopter Flight

The idea of a vehicle that could lift itself vertically from the ground and hover motionless in the air was probably born at the same time that man ?rst dreamed of ?ying. Igor Sikorsky (1938)



The science of aerodynamics is the fundament of all ?ight. It is the role of aerodynamics in the engineering analysis and design of rotating-wing vertical lift aircraft that is the subject of this book. Igor Sikorsky’s vision of a rotating-wing aircraft that could safely hover and perform other desirable ?ight maneuvers under full control of the pilot was only to be achieved some thirty years after ?xed-wing aircraft (airplanes) were ?ying successfully. This rotating-wing aircraft we know today as the helicopter. Although the helicopter is considered by some to be a basic and somewhat cumbersome looking aircraft, the modern helicopter is indeed a machine of considerable engineering sophistication and re?nement and plays a unique role in modern aviation provided by no other aircraft. In the introduction to this book, the technical evolution of the helicopter is traced from a cumbersome, vibrating contraption that could barely lift its own weight into a modern and ef?cient aircraft that has become an indispensable part of modern life. Compared to ?xedwing ?ight, the development of which can be clearly traced to Lilienthal, Langley, and the ?rst fully controlled ?ight of a piloted powered aircraft by the Wright Brothers in 1903, the origins of successful helicopter ?ight are less clear. Nonetheless, there are many parallels in the development of the helicopter when compared to ?xed-wing aircraft. However, the longer and perhaps more tumultuous gestation period of the helicopter is directly attributable to the greater depth of scienti?c and aeronautical knowledge that was required before all the various technical problems could be understood and overcome. Besides the need to understand the basic aerodynamics of vertical ?ight and improve upon the aerodynamic ef?ciency of the helicopter, other technical barriers included the need to develop suitable high power-to-weight engines and high-strength, low-weight materials for the rotor blades, hub, fuselage, and transmission. A helicopter can be de?ned as any ?ying machine using rotating wings (i.e., rotors) to provide lift, propulsion, and control forces that enable the aircraft to hover relative to the ground without forward ?ight speed to generate these forces. The thrust on the rotor(s) is generated by the aerodynamic lift forces created on the spinning blades. To turn the rotor, power from an engine must be transmitted to the rotor shaft. It is the relatively low amount of power required to lift the machine compared to other vertical take off and landing (VTOL) aircraft that makes the helicopter unique. Ef?cient hovering ?ight with low power requirements comes about by accelerating a large mass of air at a relatively low velocity; hence we have the large diameter rotors that are one obvious characteristic of helicopters. In addition, the helicopter must be able to ?y forward, climb, cruise at speed, and then descend and come back into a hover for landing. This demanding ?ight capability comes at a price, including mechanical and aerodynamic complexity and higher power requirements 1


1 / Introduction: A History of Helicopter Flight

than for a ?xed-wing aircraft of the same gross weight. All of these factors in?uence the design, acquisition, and operational costs of the helicopter. Besides generating all of the vertical lift, the rotor is also the primary source of control and propulsion for the helicopter, whereas these functions are separated on a ?xed-wing aircraft. For forward ?ight, the rotor disk plane must be tilted so that the rotor thrust vector is inclined forward to provide a propulsive component to overcome rotor and airframe drag. The orientation of the rotor disk to the ?ow also provides the forces and moments to control the attitude and position of the aircraft. The pilot controls the magnitude and direction of the rotor thrust vector by changing the blade pitch angles (using collective and cyclic pitch inputs), which changes the blade lift and the distribution of thrust over the rotor disk. By incorporating articulation into the rotor design through the use of mechanical ?apping and lead/lag hinges that are situated near the root of each blade, the rotor disk can be tilted in any direction in response to these blade pitch inputs. As the helicopter begins to move into forward ?ight, the blades on the side of the rotor disk that advance into the relative wind will experience a higher dynamic pressure and lift than the blades on the retreating side of the disk, and so asymmetric aerodynamic forces and moments will be produced on the rotor. Articulation helps allow the blades to naturally ?ap and lag so as to help balance out these asymmetric aerodynamic effects. However, the mechanical complexity of the rotor hub required to allow for articulation and pitch control leads to high design and maintenance costs. With the inherently asymmetric ?ow environment and the ?apping and pitching blades, the aerodynamics of the rotor become relatively complicated and lead to unsteady forces. These forces are transmitted from the rotor to the airframe and can be a source of vibrations, resulting in not only crew and passenger discomfort, but also considerably reduced airframe component lives and higher maintenance costs. However, with a thorough knowledge of the aerodynamics and careful design, all these adverse factors can be minimized or overcome to produce a highly reliable and versatile aircraft. 1.2 Early Attempts at Vertical Flight

There are many authoritative sources that record the development of helicopters and other rotating-wing aircraft such as autogiros. These include Gregory (1944), Lambermont (1958), Gablehouse (1967), Gunston (1983), Apostolo (1984), Boulet (1984), Lopez & Boyne (1984), Taylor (1984), Everett-Heath (1986), Fay (1987) and Spenser (1999), amongst others. Boulet (1984) takes a unique approach in that he gives a ?rst-hand account of the early helicopter developments through interviews with the pioneers, constructors, and pilots of the machines. A remarkably detailed history of early helicopter developments is given by Liberatore (1950, 1988, 1998). For original publications documenting early technical developments of the autogiro and helicopter, see Warner (1920), von K? rm? n (1921), a a Balaban (1923), Moreno-Caracciolo (1923), Klemin (1925), Wimperis (1926), and Seiferth (1927). As described by Liberatore (1998), the early work on the development of the helicopter can be placed into two distinct categories: inventive and scienti?c. The former is one where intuition is used in lieu of formal technical training, whereas the latter is one where a trained, systematic approach is used. Prior to the nineteenth century there were few scienti?c investigations of ?ight or the science of aerodynamics. The inherent mechanical and aerodynamic complexities in building a practical helicopter that had adequate power and control, and did not vibrate itself to pieces, resisted many ambitious efforts. The history of ?ight documents literally hundreds of failed helicopter projects, which, at most, made

1.2 Early Attempts at Vertical Flight


only brief uncontrolled hops into the air. Some designs provided a contribution to new knowledge that ultimately led to the successful development of the modern helicopter. Yet, it was not until the more scienti?c contributions of engineers such as Juan de la Cierva, Heinrich Focke, Raoul Hafner, Igor Sikorsky, Arthur Young, and others did the design of a truly safe and practical helicopter become a reality. Six fundamental technical problems can be identi?ed that limited early experiments with helicopters. These problems are expounded by Sikorsky (1938, and various editions) in his autobiography. In summary, these problems were: 1. Understanding the aerodynamics of vertical ?ight. The theoretical power required to produce a ?xed amount of lift was an unknown quantity to the earliest experimenters, who were guided more by intuition than by science.1 2. The lack of a suitable engine. This was a problem that was not to be overcome until the beginning of the twentieth century, through the development of internal combustion engines. 3. Keeping structural weight and engine weight down so the machine could lift a pilot and a payload. Early power plants were made of cast iron and were heavy.2 4. Counteracting rotor torque reaction. A tail rotor was not used on most early designs; these machines were either coaxial or laterally side-by-side rotor con?gurations. Yet, building and controlling two rotors was even more dif?cult than for one rotor. 5. Providing stability and properly controlling the machine, including a means of defeating the unequal lift produced on the advancing and retreating blades in forward ?ight. These were problems that were only to be fully overcome with the use of blade articulation, ideas that were pioneered by Cierva, Breguet, and others, and with the development of blade cyclic pitch control. 6. Conquering the problem of vibrations. This was a source of many mechanical failures of the rotor and airframe, because of an insuf?cient understanding of the dynamic and aerodynamic behavior of rotating wings. The relatively high weight of the structure, engine, and transmission was mainly responsible for the painfully slow development of the helicopter until about 1920. However, by then gasoline powered piston engines with higher power-to-weight ratios were more widely available, and the antitorque and control problems of achieving successful vertical ?ight were at the forefront. This resulted in the development of a vast number of prototype helicopters. Many of the early designs were built in Great Britain, France, Germany, Italy, and the United States, who led the ?eld in several technical areas. However, with all the various incremental improvements that had been made to the basic helicopter concept during the pre–World War II years, it was not until the late inter war period that signi?cant technical advances were made and more practical helicopter designs began to appear. The most important advances of all were in engine technology, both piston and gas turbines, the latter of which revolutionized both ?xed-wing and rotating-wing ?ight. A time-line documenting the evolution of rotating-wing aircraft through 1950 is shown in Fig. 1.1. The ideas of vertical ?ight can be traced back to early Chinese tops, a toy ?rst used about 400 BC. Everett-Heath (1986) and Liberatore (1998) give a detailed history of such devices. The earliest versions of the Chinese top consisted of feathers at the end of
1 2

The ?rst signi?cant application of aerodynamic theory to helicopter rotors came about in the early 1920s. Aluminum was not available commercially until about 1890 and was inordinately expensive. It was not used in aeronautical applications until about 1915.

Toys Birth of scientific principles First ideas of man-carrying vertical flight First flying small-scale models

1 / Introduction: A History of Helicopter Flight
400 BC 200BC 1400
Da Vinci (1483)

Chinese tops


1700 1800 1900 1910
First attempts at man-carrying machines Successful autogiros First hops and semi-controlled flight

Lomonosov (1754) Paucton (1768) Cayley (1843) Phillips (1842)

Launoy & Bienvenu (1784) Cayley (1792)

d’Amecourt (1863) Edison (1880) Denny (1907) Berliner (1909)

Invention of internal combustion engine

Breguet-Richet (1907-08) Cornu (1907) Sikorsky (1910) Yur’ev (1912)

Ellehammer (1914) Berliner (1919-25)

Oemichen (1920-24) Excel (1920-30) de Bothezat (1922) Cierva’s first Autogiro (1923) Pescara (1924) von Baumhauer (1924-30) Brennan (1925) Cierva C-8 autogiro (1928) Florine (1929-30)

First significant successes - fully controlled flight

Curtiss-Bleecker (1930) d’Ascanio (1930) Pitcairn PCA-2 autogiro (1930) TsAGI 1-EA/5-EA (1931-34) Cierva C-19 autogiro (1934) Hafner AR III autogiro (1935)

Breguet-Dorand (1935) Focke-Achgelis Fa-61 (1937) Weir W-5 (1938) Sikorsky VS-300 (1939) Kellett KD-1 autogiro (1939)

Maturing technology


Flettner FL-282 (1940) Sikorsky R-4 (1942) Piasecki PV-2 (1943) Bell 47 (1945) Piasecki XHRP-1 (1946) Westland S-51 (1946) Kaman K-125 (1947) Bristol 171 (1947) Hiller 360 (1948)

Bell 30 (1943) Hiller XH-44 (1943) Sikorsky R-5 (1943-46) Piasecki HUP-1 (1948) Kaman K-190 (1949) Sikorsky S-55 (1949) Sud-Aviation SE3120 (1949) Mi-1 (1949)

Development of gas-turbine engines First production machines


Figure 1.1 Time-line showing development of helicopters and autogiros prior to 1950.

a stick, which was rapidly spun between the hands to generate lift and then released into ?ight. More than 2,000 years later in 1784, Launoy & Bienvenu used a coaxial version of the Chinese top in a model consisting of a counterrotating set of turkey feathers, powered by a string wound around its shaft and tensioned by a crossbow. It is also recorded that Mikhail Lomonosov of Russia had developed, as early as 1754, a small coaxial rotor modeled after the Chinese top but powered by a wound-up spring device. In 1786, the French mathematician

1.2 Early Attempts at Vertical Flight


A. J. P. Paucton published a paper entitled “Th? orie de la vis D’Archim` des,” where he e e proposed a human-carrying ?ying machine, with one rotor to provide lift and another for propulsion. Amongst his many intricate drawings, Leonardo da Vinci shows what is a basic humancarrying helicopterlike machine, an obvious elaboration of an Archimedes water-screw. His sketch of the “aerial-screw” device, which is shown in Fig. 1.2, is dated to 1483 but was ?rst published nearly three centuries later. The device comprises a helical surface that da Vinci describes should be “rotated with speed that said screw bores through the air and climbs high.” He realized that the density of air is much less than that of water, and so da Vinci describes how the device needed to be relatively large to accomplish this feat (the number “8” in his writing to the left of the sketch indicates that the size of the rotor is 8 braccia or arm lengths). He also describes in some detail how the machine should be built using wood, wire, and linen cloth. Although da Vinci worked on various concepts of

Figure 1.2 Leonardo da Vinci’s aerial screw machine, dated to 1483. Original drawing is MS 2173 of Manuscript (codex) B, folio 83 verso, in the collection of the Biblioth` que e L’Institut de France (Paris).


1 / Introduction: A History of Helicopter Flight

engines, turbines, and gears, he did not unite the ideas of his aerial-screw machine to an engine nor did he appreciate the problems of torque reaction. See Hart (1961) or Giacomelli (1930) for further details of da Vinci’s aeronautical work. Sir George Cayley is famous for his work on the basic principles of ?ight, which dates from the 1790s – see Pritchard (1961). By the end of the eighteenth century, Cayley had constructed several successful vertical-?ight models based on Chinese tops driven by wound-up clock springs. He designed and constructed a whirling-arm device in 1804, which was probably one of the ?rst scienti?c attempts to study the aerodynamic forces produced by lifting wings. Cayley (1809–10) published a three-part paper that was to lay down the foundations of aerodynamics – see Anderson (1997). In a later paper, published in 1843, Cayley gives details of a vertical ?ight aircraft design that he called an “Aerial Carriage,” which had two pairs of lateral side-by-side rotors. Also, in the 1840s, another Englishman, Horatio Phillips, constructed a steam-driven vertical ?ight machine, where steam generated by a miniature boiler was ejected out of the blade tips. Although impractical, Phillips’s machine was signi?cant in that it marked the ?rst time that a model helicopter had ?own under the power of an engine rather than stored energy devices such as wound-up springs. In the early 1860s, Ponton d’Am? court of France ?ew a number of small helicopter e models. He called his machines h? licopt` res, which is a word derived from the Greek e e adjective elikoeioas, meaning spiral or winding, and the noun pteron, meaning feather or wing – see Wolf (1974) and Liberatore (1998). In 1863, d’Am? court built a steam propelled e model helicopter, but it could not generate enough lift to ?y. However, the novelist Jules Verne was still impressed with d’Am? court’s attempts, and in 1886 he wrote “The Clipper e of the Clouds” where the hero cruised around the skies in a giant helicopterlike machine that was lifted by thirty-seven small coaxial rotors and pulled through the air by two propellers. Other notable vertical ?ight models that were constructed at about this time include the coaxial design of Bright in 1861 and the twin-rotor steam-driven model of Dieuaide in 1877. Wilhelm von Achenbach of Germany built a single rotor model in 1874, and he was probably the ?rst to use the idea of a tail rotor to counteract the torque reaction from the main rotor. Later, Achenbach conducted experiments with propellers, the results of which were published by NACA – see Achenbach (1923). About 1869 a Russian helicopter concept was developed by Lodygin, using a rotor for lift and a propeller for propulsion and control. Around 1878, Enrico Forlanini of Italy also built a ?ying steam-driven helicopter model. This model had dual counterrotating rotors, but like many other model helicopters of the time, it had no means of control. In the 1880s, Thomas Alva Edison experimented with small helicopter models in the United States. He tested several rotor con?gurations driven by a guncotton engine, which was an early form of internal combustion engine. Later, Edison used an electric motor for power, and he was one of the ?rst to realize from his experiments the need for a large diameter rotor with low solidity to give good hovering ef?ciency [Liberatore (1998)]. Unlike other experimenters of the time, Edison’s more scienti?c approach to the problem proved that both high aerodynamic ef?ciency of the rotor and high power from an engine were required if successful vertical ?ight was to be achieved. In 1910, Edison patented a rather cumbersome looking full-scale helicopter concept with boxkite-like blades, but there is no record that it was ever constructed. In 1907, about four years after the Wright brothers’ ?rst successful powered ?ights in ?xed-wing airplanes at Kitty Hawk in the United States, Paul Cornu of France constructed a vertical ?ight machine that carried a human off the ground for the ?rst time. Boulet (1984) gives a good account of the work. The airframe was very simple, with a rotor at each end

1.2 Early Attempts at Vertical Flight


Figure 1.3 The Cornu helicopter, circa 1907. (Courtesy NASM, Smithsonian Institution, SI Neg. No. 74-8533.)

(Fig. 1.3). Power was supplied to the rotors by a gasoline motor and belt transmission. Each rotor had two blades, and the rotors rotated in opposite directions to cancel torque reaction. A primitive means of control was achieved by placing small wings in the slipstream below the rotor. The machine was reported to have made several tethered ?ights of a few seconds at low altitude. Also in France, the Breguet brothers had begun to conduct helicopter experiments about 1907. Their complicated quadrotor “Gyroplane” carried a pilot off the ground, albeit brie?y, but like the Cornu machine it was underpowered, and it lacked stability and a proper means of control. In the early 1900s, Igor Sikorsky and Boris Yur’ev independently began to design and build vertical-lift machines in Czarist Russia. By 1909, Sikorsky had built a nonpiloted coaxial prototype. This machine did not ?y because of vibration problems and the lack of a powerful enough engine. Sikorsky (1938) stated that he had to await “better engines, lighter materials, and experienced mechanics.” His ?rst design was unable to lift its own weight, and the second, even with a more powerful engine, only made short (nonpiloted) hops. Sikorsky abandoned the helicopter idea and devoted his skills to ?xed-wing (conventional airplane) designs at which he was very successful. Although he never gave up his vision of the helicopter, it was not until the 1930s after he had emigrated to the United States that he pursued his ideas again. Good accounts of the life and work of Igor Sikorsky are documented by Bartlett (1947), Delear (1969), Sikorsky (1964, 1971), Sikorsky & Andrews (1984), Finne (1987), and Cochrane et al. (1989). Unbeknown to Sikorsky, Boris Yur’ev had also tried to build a helicopter in Russia around 1912, but with a single rotor and tail rotor con?guration. Like Sikorsky’s machine, the aircraft lacked a powerful enough engine. Besides being one of the ?rst to use a tail rotor design, Yur’ev was one of the ?rst to propose the concept of cyclic pitch for rotor control. (Another early design was patented by Gaetano Crocco of Italy in 1906). Good accounts of Yur’ev’s machine are given by Gablehouse (1967) and Liberatore (1998). There is also evidence of the construction of a primitive coaxial helicopter by Professor Zhukovskii (Joukowski) and his students at Moscow University in 1910 – see Gablehouse (1967). Joukowski is well known for his theoretical contributions to aerodynamics, and he published several papers on the subject of rotating wings and helicopters; see also Margoulis (1922) and Tokaty (1971).


1 / Introduction: A History of Helicopter Flight

Figure 1.4 Danish aviation pioneer Jens Ellehammer ?ew a coaxial rotor helicopter design in 1914.

About 1914, the Danish aviation pioneer Jens Ellehammer designed a coaxial rotor helicopter. Boulet (1984) gives a good description of the machine, which is shown in Fig. 1.4. The rotor blades themselves were very short; six of these were attached to each of two large circular aluminum rings. The lower disk was covered with fabric and was intended to serve as a parachute in the event the rotors failed. A cyclic pitch mechanism was used to provide control, this being another one of many early applications of the concept. The pilot was supported in a seat that could be moved forward and sideways below the rotor, allowing for additional kinesthetic control. The aircraft made many short hops into the air but never made a properly controlled free ?ight. An Austrian, Stephan Petroczy, with the assistance of the well-known aerodynamicist Theodore von K? rm? n, built and ?ew a coaxial rotor helicopter during 1917–1920. Intera a esting design features of this machine included a pilot/observer position above the rotors, in?ated bags for landing gear, and a quick-opening parachute. While the machine never really ?ew freely, it accomplished numerous limited tethered vertical ?ights. The work is summarized in a report by von K? rm? n (1921) and published by the NACA. It is signifa a icant that von K? rm? n also gives results of laboratory tests on the “rotors,” which were a a really oversize propellers. With the work of William F. Durand [see Warner (1920) and the analysis by Munk (1923)] these were some of the ?rst attempts to scienti?cally study rotor performance and the power required for vertical ?ight. In the United States, Emile and Henry Berliner (a father and son) were interested in vertical ?ight aircraft. As early as 1909, they had designed and built a helicopter based on pioneering forward ?ight experiments with a wheeled test rig. In 1918 the Berliners patented a single-rotor helicopter design, but there is no record that this machine was built. Instead, by about 1919, Henry Berliner had built a counterrotating coaxial rotor machine, which made brief uncontrolled hops into the air. By the early 1920s at the College

1.2 Early Attempts at Vertical Flight


Figure 1.5 This Berliner helicopter with side-by-side rotors made short ?ights at College Park airport in Maryland in 1922. (Courtesy of College Park Airport Museum.)

Park airport, the Berliners were ?ying an aircraft with side-by-side rotors (Fig. 1.5). The rotors were oversized wooden propellers, but with special airfoil pro?les and twist distributions. Differential longitudinal tilt of the rotor shafts provided yaw control. On later variants, lateral control was aided by cascades of wings located in the slipstream of the rotors. All variants used a conventional elevator and rudder assembly at the tail, also with a small vertically thrusting auxiliary rotor on the rear of the fuselage. The Berliner’s early ?ights with the coaxial rotor and side-by-side rotor machines are credited as some of the ?rst rudimentary piloted helicopter developments in the United States. However, because true vertical ?ight capability with these machines was limited, the Berliners abandoned the pure helicopter in favor of a hybrid machine they called a “helicoplane.” This still used the rotors for vertical lift but incorporated a set of triplane wings and a larger oversized rudder. The Berliner’s ?nal hybrid machine of 1924 was a biplane wing con?guration with side-by-side rotors. See also Berliner (1908, 1915). In Britain during the 1920s, Louis Brennan worked on a helicopter concept with an unusually large single two-bladed rotor. Fay (1987) gives a good account of Brennan’s work. Brennan, who was an inventor of some notoriety, had a different approach to solving the problem of torque reaction by powering the rotor with propellers mounted on the blades (Fig. 1.6). Control was achieved by the use of “ailerons” inboard of the propellers. In 1922, the machine lifted off inside a balloon shed. Further brief low altitude ?ights outdoors were undertaken through 1925, but the machine crashed, and further work stopped because of increasing interest in the autogiro (see Section 1.3). During the early 1920s, Raul Pescara, an Argentinian living and working in Spain and France, was building and attempting to ?y a coaxial helicopter with biplane-type rotors (Fig. 1.7). As described by Boulet (1984), each rotor had a remarkable ?ve sets of biplane blades that were mounted rigidly to the rotor shaft. Pescara’s work focused on the need


1 / Introduction: A History of Helicopter Flight

Figure 1.6 The Brennan helicopter suspended in the balloon shed at RAE Farnborough, circa 1922.

Figure 1.7 Pescara’s helicopter hovering in a hanger about 1923. (Courtesy NASM Smithsonian Institution, SI Neg. No. 83-16343.)

1.2 Early Attempts at Vertical Flight


Figure 1.8 Between 1924 and 1930, A. G. von Baumhauer made attempts to ?y a single main rotor helicopter with a separately powered tail rotor. (Courtesy of NASM, Smithsonian Institution, Neg. No. 77-721.)

for complete control of the machine, which was achieved through cyclic-pitch changes that could be obtained by warping the blades periodically as they rotated. This was one of the ?rst successful applications of cyclic pitch. Yaw was controlled by differential collective pitch between the two rotors. Early versions of his machine were underpowered, which may not be surprising considering the high drag of the bracing wires of his rotor, and the aircraft did not ?y. With a later version of his helicopter using a more powerful engine, some successful ?ights were accomplished, albeit under limited control. However, most ?ights resulted in damage or serious crashes followed by long periods of rebuilding. By 1925, Pescara had abandoned his helicopter projects. Between 1924 and 1930, a Dutchman named A. G. von Baumhauer designed and built one of the ?rst single-rotor helicopters with a tail rotor to counteract torque reaction. Boulet (1984) gives a good description of the machine. Figure 1.8 shows that the fuselage consisted essentially of a tubular truss, with an engine mounted on one end. The other end carried a smaller engine mounted at right angles to the main rotor, which turned a conventional propeller to counter the main rotor torque reaction. The main rotor had two blades, which were restrained by cables so that the blades ?apped about a hinge like a seesaw or teeter board. Control was achieved by a swashplate and cyclic-pitch mechanism, which was another very early application of this mechanism. Unfortunately, the main and tail rotors were in no way connected, and this caused considerable dif?culties in achieving proper control. Nevertheless, the machine was reported to have made numerous short, semicontrolled ?ights. In the late 1920s, the Austrian engineer Raoul Hafner designed and built a single-seat helicopter called the R-2 Revoplane – see Everett-Heath (1986) and Fey (1987). The ?ights were mostly unsuccessful despite some brief tethered ?ights of up to a minute. His early machines used a single-rotor con?guration with a pair of ?xed wings located in the rotor


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参考资料: 1 王适存:《直升机空气动力学》 2 J.Gordon Leishman:《Principles of Helicopter Aerodynamics》 旋翼动力学国防科技重点实验室 直升机空气动力学 --...


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[2] Sun M. A study of helicopter rotor aerodynamics in ground effect[D]. Princeton: Princeton Univ, 1983. (4) 论文集,会议录 著录格式:[序号] 主要...


[2] Sun M. A study of helicopter rotor aerodynamics in ground effect[D]. Princeton: Princeton Univ, 1983. 4) 论文集,会议录 著录格式:[序号] 主要...


[2] Sun M. A study of helicopter rotor aerodynamics in ground effect[D]. Princeton: Princeton Univ, 1983. (4) 论文集,会议录 著录格式:[序号] 主要...


[2] Sun M. A study of helicopter rotor aerodynamics in ground effect[D]. Princeton: Princeton Univ, 1983. (4) 论文集,会议录 著录格式:[序号] 主要...


[2] Sun M. A study of helicopter rotor aerodynamics in ground effect[D]. Princeton: Princeton Univ, 1983. (4)论文集,会议录 著录格式:[序号] 主要...


(06) 2.LEISHMAN J G Principles of Helicopter Aerodynamics 2000 3.MCKERROW P Modelling the Draganflyer Four-Rotor Helicopter 2004 4.王琮泽 AVR ATmega...


[6]?Sun?M.A?study?of?helicopter?rotor?aerodynamics?in?ground?effect[D].Princeton:品册,1983.? [7]? 辛希孟.? 信息技术与信息服务国际研讨会论文集: A...


? J. Seddon, Basic Helicopter Aerodynamics, 2nd Edition, AIAA, Washington, DC, 2001. ? Leishman, J. G., Principles of Helicopter Aerodynamics, 2nd ...

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[2] Sun M. A study of helicopter rotor aerodynamics in ground effect[D]. Princeton: Princeton Univ, 1983. (4) 论文集,会议录 著录格式:[序号] 主要...


[2] Sun M. A study of helicopter rotor aerodynamics in ground effect[D]. Princeton: Princeton Univ, 1983. (4) 论文集,会议录 著录格式:[序号] 主要...

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Wings and Tilt-Rotors References Text on all pages ? J. G. Leishman 2000, with extracts from the author's book "Principles of Helicopter Aerodynamics"...

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