Principles of Helicopter Aerodynamics
J.GORDON LEISHMAN
University of Maryland
PUBLISHED BY THE PRESS SYNDICATE OF THE UNIVERSITY OF CAMBRIDGE The Pitt Building,Trumpington Street,Cambridge,United Kingdom
CAMBRIDGE UNIVERSITY PRESS
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C Cambridge University Press2000
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 published2000
Printed in the United States of America
Typeface Times Roman10/12pt.System L A T E X2ε[TB]
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.
<
Includes bibliographical references(p.).
ISBN0-521-66060-2(hardcover)
1.Helicopters–Aerodynamics.
TL716.L432000
629.133 352–dc2199-38291
CIP
ISBN0521660602hardback
Contents
Preface page xvii Acknowledgments xxi List of Main Symbols xxiii List of Figures xxxi List of Tables xliii 1Introduction:A History of Helicopter Flight1
1.1Introduction1
1.2Early Attempts at Vertical Flight2
1.3The Era of the Autogiro12
1.4The First Successes with Helicopters14
1.5Maturing Technology22
1.6Tilt-Wings and Tilt-Rotors27
1.7Chapter Review28
1.8Questions29
Bibliography30 2Fundamentals of Rotor Aerodynamics33
2.1Introduction33
2.2Momentum Theory36
2.2.1Flow near a Hovering Rotor37
2.2.2Conservation Laws of Fluid Mechanics38
2.2.3Application to a Hovering Rotor39
2.2.4Disk Loading and Power Loading42
2.2.5Induced Inflow Ratio43
2.2.6Thrust and Power Coefficients43
2.2.7Nonideal Effects on Rotor Performance44
2.2.8Figure of Merit46
2.2.9Worked Example47
2.2.10Induced Tip Loss48
2.2.11Rotor Solidity and Blade Loading Coefficient50
2.2.12Power Loading52
2.3Axial Climb and Descent53
2.3.1Axial Climb53
2.3.2Axial Descent55
2.3.3The Region−2≤V c/v h≤057
2.3.4Power Required59
2.3.5Working States of the Rotor in Axial Flight60
2.3.6Autorotation60
ix
x Contents
2.4Momentum Analysis in Forward Flight63
2.4.1Induced Velocity in Forward Flight64
2.4.2Special Case,α=065
2.4.3Numerical Solution to Inflow Equation66
2.4.4Validity of the Inflow Equation67
2.4.5Rotor Power in Forward Flight68
2.4.6Other Applications of the Momentum Theory69
2.5Chapter Review73
2.6Questions73
Bibliography76 3Blade Element Analysis78
3.1Introduction78
3.2Blade Element Analysis in Hover and Axial Flight80
3.2.1Integrated Rotor Thrust and Power82
3.2.2Thrust Approximations82
3.2.3Untwisted Blades,Uniform Inflow83
3.2.4Linearly Twisted Blades,Uniform Inflow84
3.2.5Torque/Power Approximations84
3.2.6Tip-Loss Factor85
3.3Blade Element Momentum Theory(BEMT)87
3.3.1Ideal Twist91
3.3.2BEMT–A Numerical Approach92
3.3.3Distributions of Inflow and Airloads93
3.3.4The Optimum Hovering Rotor96
3.3.5Circulation Theory of Lift99
3.3.6Power Estimates100
3.3.7Prandtl’s Tip-Loss Function102
3.3.8Figure of Merit105
3.3.9Further Comparisons of BEMT with Experiment106
3.3.10Compressibility Corrections107
3.3.11Equivalent Chords and Weighted Solidity110
3.3.12Mean Wing Chords110
3.3.13Thrust Weighted Solidity111
3.3.14Power/Torque Weighted Solidity111
3.3.15Weighted Solidity of the Optimum Rotor112
3.3.16Weighted Solidities of Tapered Blades112
3.3.17Mean Lift Coefficient113
3.4Blade Element Analysis in Forward Flight113
3.4.1Blade Forces114
3.4.2Induced Velocity Field115
3.5Chapter Review123
3.6Questions124
Bibliography126 4Rotating Blade Motion128
4.1Introduction128
4.2Types of Rotors129
4.3Equilibrium about the Flapping Hinge131
Contents xi
4.4Equilibrium about the Lead/Lag Hinge133
4.5Equation of Motion for Flapping Blade134
4.6Physical Description of Blade Flapping139
4.6.1Coning Angle139
4.6.2Longitudinal Flapping139
4.6.3Lateral Flapping140
4.7Dynamics of Blade Flapping with a Hinge Offset141
4.8Blade Feathering and the Swashplate142
4.9Review of Rotor Reference Axes144
4.10Dynamics of a Lagging Blade with Hinge Offset147
4.11Coupled Flap–Lag Motion149
4.12Introduction to Rotor Trim150
4.13Chapter Review155
4.14Questions156
Bibliography157 5Basic Helicopter Performance159
5.1Introduction159
5.2Hovering and Axial Climb Performance159
5.3Forward Flight Performance163
5.3.1Induced Power164
5.3.2Blade Profile Power164
5.3.3Parasitic Power166
5.3.4Climb Power166
5.3.5Tail Rotor Power166
5.3.6Total Power167
solidity5.3.7Effect of Gross Weight168
5.3.8Effect of Density Altitude169
5.3.9Lift-to-Drag Ratios169
5.3.10Climb Performance170
5.3.11Speed for Minimum Power171
5.3.12Speed for Maximum Range173
5.3.13Range–Payload and Endurance–Payload174
5.3.14Factors Affecting Maximum Attainable Forward Speed174
5.3.15Performance of Coaxials and Tandems176
5.4Autorotation Revisited178
5.4.1Autorotation in Forward Flight180
5.4.2Height–Velocity(HV)Curve182
5.4.3Autorotation Index184
5.5Ground Effect185
5.6Chapter Review189
5.7Questions190
Bibliography191 6Conceptual Design of Helicopters193
6.1Introduction193
6.2Design Requirements193
6.3Design of the Main Rotor194

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