Basic_Helicopter_Aerodynamics_Second_Edi

Basic Helicopter Aerodynamics Second Edition An account of first principles in the fluid mechanics and flight dynamics of the single rotor helicopter J. Seddon PhD, DSc, CEng, CFF, FRAeS and Simon Newman MSc (Eng), PhD, CEng, MRAeS, FIMA, CMath

© 2002, estate of J. Seddon and Blackwell  Science Marston Book Services Ltd Blackwell Science Ltd PO Box 269 Editorial Offices: Abingdon Osney Mead, Oxford OX2 0EL Oxon OX14 4YN 25 John Street, London WC1N 2BS (Orders: Tel: 01235 465500 23 Ainslie Place, Edinburgh EH3 6AJ 350 Main Street, Malden Fax: 01235 465555) MA 02148 5018, USA Canada 54 University Street, Carlton Login Brothers Book Company 324 Saulteaux Crescent Victoria 3053, Australia Winnipeg, Manitoba R3J 3T2 10, rue Casimir Delavigne (Orders: Tel: 204 837-2987 Fax: 204 837-3116) 75006 Paris, France Australia Other Editorial Offices: Blackwell Science Pty Ltd 54 University Street Blackwell Wissenschafts-Verlag GmbH Carlton, Victoria 3053 Kurfürstendamm 57 (Orders: Tel: 03 9347 0300 10707 Berlin, Germany Fax: 03 9347 5001) Blackwell Science KK A catalogue record for this title MG Kodenmacho Building is available from the British Library 7–10 Kodenmacho Nihombashi Chuo-ku, Tokyo 104, Japan ISBN 0-632-05283-X Iowa State University Press Library of Congress Cataloging-in- A Blackwell Science Company Publication Data 2121 S. State Avenue Ames, Iowa 50014-8300, USA Seddon, J. Basic helicopter aerodynamics : an The right of the Author to be identified as the Author of this Work has been asserted account of first principles in the fluid in accordance with the Copyright, Designs mechanics and flight dynamics of the and Patents Act 1988. single rotor helicopter / J. Seddon and Simon Newman. All rights reserved. No part of this publication may be reproduced, p. cm. stored in a retrieval system, or Includes bibliographical references and transmitted, in any form or by any index. means, electronic, mechanical, ISBN 0-632-05283-X photocopying, recording or otherwise, 1. Helicopters – Aerodynamics. except as permitted by the UK I. Newman, Simon, 1947– II. Title. Copyright, Designs and Patents Act TL716 .S43 2001b 1988, without the prior permission 629.133¢352 – dc21 of the publisher. 2001043019 First edition published 1990 Second edition published 2002 For further information on Blackwell Science, visit our website: Set in Times New Roman www.blackwell-science.com by Best-set Typesetter Ltd, Hong Kong Printed and bound in Great Britain by MPG Books, Bodmin, Cornwall The Blackwell Science logo is a trade mark of Blackwell Science Ltd, registered at the United Kingdom Trade Marks Registry

Preface to First Edition During the past decade and a half, several noteworthy textbooks have been published in the previously neglected field of helicopter aerody- namics, spurred no doubt by a growing acceptance world-wide of the importance of the helicopter in modern society. One may cite in this context Bramwell’s Helicopter Dynamics (1976), Johnson’s Helicopter Theory (1980) and Rotary Wing Aerodynamics (1984) by Stepniewski and Keys. The appearance now of another book on the subject requires some explanation, therefore. I have three specific reasons for writing it. The first reason is one of brevity. Bramwell’s book runs to 400 pages, that of Stepniewski and Keys to 600 and Johnson’s extremely comprehensive treatment to over 1000. The users I have principally in mind are University or Polytechnic students taking a short course of lectures – say one year – in the subject, probably as an ‘optional’ or ‘elective’ in the final undergraduate or early post-graduate year. The object in that time is to provide them with a grounding while hope- fully stimulating an interest which may carry them further in the subject at a later data. The amount of teaching material required for this purpose is only a fraction of that contained in the standard text- books and a monograph of around 150 pages is more than sufficient to contain what is needed and hopefully may be produced at a price not beyond the individual student’s pocket. My second reason, which links with the first, concerns the type of approach. This book does not aim at a comprehensive treatment but neither is it content to consign problems to the digital computer at the earliest opportunity. In between lies an analytical route to solu- tions, taken far enough to produce results of usable accuracy for many practical purposes, while at the same time providing a physical under- standing of the phenomena involved, which rapid recourse to the ix

x Preface to First Edition computer often fails to do. It is this route that the book attempts to follow. The analytical approach is usually terminated when it is thought to have gone far enough to serve the stated purpose, the reader being left with a reference to one of the standard textbooks in case he should wish to pursue the topic further. The third reason is one of content. Despite the need for brevity, I have thought it worthwhile to include, in addition to treatments of the standard topics – momentum theory, blade element theory, basic performance, stability and control – a strong flavour of research and development activity (Chapter 6) and of forward-looking, if specula- tive, calculations (Chapter 7). It might be considered that these items are of such a transitory nature as not to be suitable for a textbook, but my criterion of stimulating the student’s interest is what has deter- mined their inclusion. Certainly they have proved to be interesting in classroom presentation and there seems no reason why that should not be so for the written word. In addition to meeting the needs of students, to whom it is pri- marily addressed, the book should have an appeal as background material to short courses held in or on behalf of industry: such courses are increasing in popularity. Companies and research estab- lishments may also find it useful for new entrants and for more estab- lished workers requiring a ‘refresher’ text. Reverting to the matter of brevity, the recent publication Helicopter Aerodynamics by Prouty is a most admirable short exposition, well worth studying as an adjunct to any other textbook: however it shuns the mathematics completely and therefore will not suffice alone for the present purposes. Saunders’ Dynamics of Helicopter Flight is not greatly beyond the target length but as the title implies it is concerned more with flight dynamics than with aerodynamics and is adapted more to the needs of pilots than to those of engineering students already equipped with a general aerodynamic background. I have taken it as a starting point that my readers have a knowledge of the aerodynamics of lifting wings as they exist in fixed-wing air- craft. A helicopter rotor blade performs the same function as a lifting wing but in a very different environment; and to note the similarities on the one hand and the distinctions on the other can be a consider- able fillip to the learner’s interest, one which I have tried to nurture by frequent references back to fixed-wing situations. This again is a somewhat non-standard approach. Substantial omissions from the book are not hard to find. A his- torical survey might have been included in Chapter 1 but was thought

Preface to First Edition xi not necessary despite its undoubted interest. To judge by the work effort it attracts, wake analysis (‘Vortex theory’) deserves a more extensive treatment than it gets (Chapters 2 and 5) but here it was necessary to refrain from opening a Pandora’s box of different approaches. Among topics which could have been included in Chapter 5 are autorotation in forward flight, pitch-flap coupling and blade flexibility but these were seen as marginally ‘second-line’ topics. The forward look in Chapter 6 might have contained a discussion of the potential of circulation control, the only system which is capable of attacking all the three non-uniformities of rotor blade flow, chord- wise, spanwise and azimuthal; but the subject is too big and too distinct from the main line of treatment. The reference to autostabilization in Chapter 8 is brief in the extreme but again the choice was between this and a much lengthier exposition in which aerodynamics would have been largely submerged beneath system mechanics and electronics. In compiling the book I have been greatly helped by discussions with Mr D.E.H. (‘Dave’) Balmford, Head of Advanced Engineering at Westland Helicopters, to whom my thanks are expressed. Other Westland staff members whose assistance I wish to acknowledge in specific contexts are Dr M.V. Lowson (now Professor of Aerospace Engineering at Bristol University) for Section 7.10, Mr F.J. Perry for Section 6.6, Mr R.V. Smith for Section 7.11 and Mr B. Pitkin for Chapter 8. Naturally the standard textbooks, particularly those men- tioned earlier, have been invaluable in places and I trust that this fact is duly recognized in the text and diagrams. Formal acknowledgement is made to Westland Helicopters for per- mission to reproduce the photographs at Figs 2.11, 4.10, 4.11, 7.6 and 7.7; to Edward Arnold, Publishers, for the use of Figs 2.10, 2.13, 5.1, 5.3, 6.3, 8.5 and 8.6 from A.R.S. Bramwell’s book Helicopter Dynam- ics (1976); to Mr P.G. Wilby of the Royal Aircraft Establishment for Figs 6.2 and 6.5, which are reproduced with the permission of the Controller of Her Majesty’s Stationery Office; and to Dr J.P. Jones for the use of Figs 2.12, 4.2 and 4.4. My thanks are due to Molly Gibbs of Bristol University who copy- typed the manuscript and to my grandson Daniel Cowley who drew the figures. J. Seddon

Preface to Second Edition The original Basic Helicopter Aerodynamics was conceived and written by Dr John Seddon. It found a respected place in the subject of rotary wing aircraft and has informed many. Sadly John Seddon has since passed away and I was very flattered to be asked to revise his manuscript for a second edition. This brought an immediate problem. Do I strip the work down to nuts and bolts or do I revise it as it stands but add my own contributions. Since the book is now under joint authorship, it would have been unfeeling to have pursued the former option since the original concept of John Seddon would have disappeared. For that reason I decided to pursue the latter option of revising the text and adding to it – particularly in the field of illustrations. The design, manufacture and operation of the helicopter rotor tend to be rather esoteric for the newcomer and long textual descriptions can be dry and not helpful. I have added, therefore, a substantial number of images to illustrate and clarify the discussions. The original diagrams were created by hand, which did not altogether succeed. Since that time, computer technology has improved greatly and the book’s graphics have been updated accordingly. The book’s size has increased to allow for the additions but I have been mindful of the need to retain the compactness of the original work. Helicopter rotor aerodynamics continues to be investigated. It is essential to introduce recent developments to the student and I intend to maintain this book in a form that will introduce the latest devel- opments. While an introductory text cannot hope to describe new techniques in detail it must be capable of establishing the correct thoughts in the reader’s mind, thus preparing them for more intensive study. xiii

xiv Preface to Second Edition The revisions have been aimed at illustrating, more fully, the various features of rotor aerodynamics and helicopter design. The helicopter is unique in its linking of the aerodynamic and mechanical features and a full appreciation of these air vehicles can only be achieved by understanding these interactions. Many of the extra figures illustrate the diversity in the design and operation of a helicopter and these dif- ferences are highlighted in the text. As with all things aeronautical, a team effort is always needed, and the assembly of this book is no exception. A picture says a thousand words so I have called upon the skills of many people to provide as many photographs as possible to amplify and, hopefully, clarify the explanations. While I have been able to supply a number of these pho- tographs personally, a considerable number have been kindly supplied and I would like to sincerely thank the following people for their gen- erosity. Denny Lombard of Lockheed Martin, Alan Vincent, Alan Brocklehurst and Alan Jeffrey of GKN Westland Helicopters, Harry Parkinson of Advanced Technologies Incorporated, Stewart Penney, Guy Gratton, David Long of Kaman and Steve Shrimpton. While I am quite pleased with my own photographic attempts, I am mindful that the pictures were taken on the ground, usually on a pleasant warm day with plenty of time to press the shutter release. In contrast, the above mentioned people have obtained better quality results while often hanging out of an aircraft in very difficult situa- tions. This marks the difference between the amateur and the true professional. I would also like to thank my colleagues and researchers who have provided much thought provoking discussion, which I hope, is reflected in the book. I am very grateful to David Balmford for his suggestions in correcting the text. I also would like to express my thanks to Ian Simons for his constant advice on all matters aeronau- tical. I offer many thanks to Julia Burden at Blackwell Science for her forbearance. The manuscript was late and she stuck with it, probably biting her lip but giving me valuable support. She offered me the task of revising the book and I hope she is not disappointed. Finally I would like to thank my wife, Stella, for putting up with my constant whizzing around putting the final touches to this work, snatching a cup of coffee as I speed by. Simon Newman Winchester January 2001

Notation List General a lift curve slope dCL/da a0 first term in Fourier expansion of b a1 coefficient of second term in Fourier expansion of b a2 coefficient of fourth term in Fourier expansion of b A area of rotor disc Ab total blade area (N blades) A1 coefficient of second term in Fourier expansion of q A2 coefficient of fourth term in Fourier expansion of q Ap projected frontal area of rotorhead (Chapter 6) As flow spoiling factor (Chapter 6) Az boundary layer shielding factor (Chapter 6) b1 coefficient of third term in Fourier expansion of b b2 coefficient of fifth term in Fourier expansion of b B tip loss factor in r = BR B1 coefficient of third term in Fourier expansion of q B2 coefficient of fifth term in Fourier expansion of q c blade chord CD drag coefficient CL lift coefficient CH H-force coefficient CP power coefficient CQ torque coefficient CT thrust coefficient d differential operator D aerodynamic drag e hinge offset ratio f equivalent flat-plate area H H-force xv

xvi Notation List I moment of inertia k empirical constant in expression for profile power K empirical constant in Glauert expression for induced velocity l moment arm of tail rotor thrust about main shaft L aerodynamic lift m blade mass per unit span M figure of merit M Mach number M moment (Figs, 8.4, 8.5) MT aerodynamic moment about flapping axis n inertia number (Chapter 8) N number of blades p static pressure P power q torque coefficient (Bramwell definition) q dynamic pressure, –21 rV2 Q torque r fraction of blade span from axis (= y/R) R blade radius S stiffness number tc thrust coefficient (Bramwell definition) T thrust u component velocity (non-dimensional, U/WR) U component velocity (dimensional) v induced velocity V stream velocity (flight speed) V¢ hypothetical velocity in Glauert formula for forward flight Vc climbing speed w disc loading, T/A W aircraft weight y distance along blade span from axis z height of rotor plane above ground Greek a incidence (angle of attack) of blade, positive nose-up a incidence of fuselage (Chapter 6), positive nose-up ar angle of attack of tip path plane to flight direction, positive nose-down b flapping angle (blade span to reference plane) b compressibility factor 1 - M 2 (Chapter 6) g Lock number d relative density of air, r/r0

Notation List xvii D prefix denoting increment, thus DP q blade pitch angle k empirical constant in expression for induced power l inflow factor (non-dimensional induced velocity) l blade natural flapping frequency (Chapter 8) m advance ratio, V/WR p pi r absolute density of air s blade solidity factor f angle of resultant velocity at blade to reference plane y angle of azimuth in blade rotation W blade rotational speed, radians per sec Suffixes av available b blade c suffix for thrust coefficient (Bramwell definition) C in climb D drag h hover value H H-force i induced L lift max maximum o basic or constant value p parasite P power Q torque req required t blade tip tw blade twist T thrust • conditions ‘at infinity’, i.e. where flow is undisturbed

Units The metric system is taken as fundamental, this being the educational basis in the UK. Imperial units are still used extensively, however, par- ticularly in the USA but also by industry and other organizations in the UK. For dimensional examples in the text and diagrams, there- fore, those units are used which it is felt have stood the test of time and may well continue to do so. Often units in both systems are quoted: in other cases reference may need to be made to the conver- sion tables set out below. In either system, units other than the basic one are sometimes used, depending on the context; this is particularly so for velocity, where for example aircraft flight speed is more conveniently expressed in kilometres/hour or in knots than in metres/second or in feet/second. The varieties used in the book are included in the table. xix

xx Units Quantity Metric unit and symbol Imperial equivalent Primary quantities kilogram (kg) 0.0685 slug Mass newton (N) 0.2248 pound (lb) Weight metre (m) 3.281 feet (ft) Length second (s) 1.0 second (sec) Time kelvin (K) Celsius (°C) Temperature Temp(K) = temp (°C) + 273.15 kilogram force Derived quantities 9.807 N (kG) 2.2046 lb Weight (force) kg/m3 0.00194 slug/ft3 N/m2 0.0209 lb/ft2 Density 0.1020 kG/m2 Pressure m/s 3.281 ft/sec 3.600 km/h 196.86 ft/min Velocity 1.941 knots m/s2 3.281 ft/sec2 Acceleration 9.807 m/s2 (g) 32.2 ft/sec2 Accel. of gravity watt, N m/s (W) 0.7376 ft.lb/sec Power 75 kG m/s (mhp) 0.9863 HP Metric horsepower 76.04 kG m/s 550 ft.lb/sec English horsepower

Basic Helicopter Aerodynamics Second Edition An account of first principles in the fluid mechanics and flight dynamics of the single rotor helicopter J. Seddon PhD, DSc, CEng, CFF, FRAeS and Simon Newman MSc (Eng), PhD, CEng, MRAeS, FIMA, CMath

© 2002, estate of J. Seddon and Blackwell  Science Marston Book Services Ltd Blackwell Science Ltd PO Box 269 Editorial Offices: Abingdon Osney Mead, Oxford OX2 0EL Oxon OX14 4YN 25 John Street, London WC1N 2BS (Orders: Tel: 01235 465500 23 Ainslie Place, Edinburgh EH3 6AJ 350 Main Street, Malden Fax: 01235 465555) MA 02148 5018, USA Canada 54 University Street, Carlton Login Brothers Book Company 324 Saulteaux Crescent Victoria 3053, Australia Winnipeg, Manitoba R3J 3T2 10, rue Casimir Delavigne (Orders: Tel: 204 837-2987 Fax: 204 837-3116) 75006 Paris, France Australia Other Editorial Offices: Blackwell Science Pty Ltd 54 University Street Blackwell Wissenschafts-Verlag GmbH Carlton, Victoria 3053 Kurfürstendamm 57 (Orders: Tel: 03 9347 0300 10707 Berlin, Germany Fax: 03 9347 5001) Blackwell Science KK A catalogue record for this title MG Kodenmacho Building is available from the British Library 7–10 Kodenmacho Nihombashi Chuo-ku, Tokyo 104, Japan ISBN 0-632-05283-X Iowa State University Press Library of Congress Cataloging-in- A Blackwell Science Company Publication Data 2121 S. State Avenue Ames, Iowa 50014-8300, USA Seddon, J. Basic helicopter aerodynamics : an The right of the Author to be identified as the Author of this Work has been asserted account of first principles in the fluid in accordance with the Copyright, Designs mechanics and flight dynamics of the and Patents Act 1988. single rotor helicopter / J. Seddon and Simon Newman. All rights reserved. No part of this publication may be reproduced, p. cm. stored in a retrieval system, or Includes bibliographical references and transmitted, in any form or by any index. means, electronic, mechanical, ISBN 0-632-05283-X photocopying, recording or otherwise, 1. Helicopters – Aerodynamics. except as permitted by the UK I. Newman, Simon, 1947– II. Title. Copyright, Designs and Patents Act TL716 .S43 2001b 1988, without the prior permission 629.133¢352 – dc21 of the publisher. 2001043019 First edition published 1990 Second edition published 2002 For further information on Blackwell Science, visit our website: Set in Times New Roman www.blackwell-science.com by Best-set Typesetter Ltd, Hong Kong Printed and bound in Great Britain by MPG Books, Bodmin, Cornwall The Blackwell Science logo is a trade mark of Blackwell Science Ltd, registered at the United Kingdom Trade Marks Registry

Preface to First Edition During the past decade and a half, several noteworthy textbooks have been published in the previously neglected field of helicopter aerody- namics, spurred no doubt by a growing acceptance world-wide of the importance of the helicopter in modern society. One may cite in this context Bramwell’s Helicopter Dynamics (1976), Johnson’s Helicopter Theory (1980) and Rotary Wing Aerodynamics (1984) by Stepniewski and Keys. The appearance now of another book on the subject requires some explanation, therefore. I have three specific reasons for writing it. The first reason is one of brevity. Bramwell’s book runs to 400 pages, that of Stepniewski and Keys to 600 and Johnson’s extremely comprehensive treatment to over 1000. The users I have principally in mind are University or Polytechnic students taking a short course of lectures – say one year – in the subject, probably as an ‘optional’ or ‘elective’ in the final undergraduate or early post-graduate year. The object in that time is to provide them with a grounding while hope- fully stimulating an interest which may carry them further in the subject at a later data. The amount of teaching material required for this purpose is only a fraction of that contained in the standard text- books and a monograph of around 150 pages is more than sufficient to contain what is needed and hopefully may be produced at a price not beyond the individual student’s pocket. My second reason, which links with the first, concerns the type of approach. This book does not aim at a comprehensive treatment but neither is it content to consign problems to the digital computer at the earliest opportunity. In between lies an analytical route to solu- tions, taken far enough to produce results of usable accuracy for many practical purposes, while at the same time providing a physical under- standing of the phenomena involved, which rapid recourse to the ix

x Preface to First Edition computer often fails to do. It is this route that the book attempts to follow. The analytical approach is usually terminated when it is thought to have gone far enough to serve the stated purpose, the reader being left with a reference to one of the standard textbooks in case he should wish to pursue the topic further. The third reason is one of content. Despite the need for brevity, I have thought it worthwhile to include, in addition to treatments of the standard topics – momentum theory, blade element theory, basic performance, stability and control – a strong flavour of research and development activity (Chapter 6) and of forward-looking, if specula- tive, calculations (Chapter 7). It might be considered that these items are of such a transitory nature as not to be suitable for a textbook, but my criterion of stimulating the student’s interest is what has deter- mined their inclusion. Certainly they have proved to be interesting in classroom presentation and there seems no reason why that should not be so for the written word. In addition to meeting the needs of students, to whom it is pri- marily addressed, the book should have an appeal as background material to short courses held in or on behalf of industry: such courses are increasing in popularity. Companies and research estab- lishments may also find it useful for new entrants and for more estab- lished workers requiring a ‘refresher’ text. Reverting to the matter of brevity, the recent publication Helicopter Aerodynamics by Prouty is a most admirable short exposition, well worth studying as an adjunct to any other textbook: however it shuns the mathematics completely and therefore will not suffice alone for the present purposes. Saunders’ Dynamics of Helicopter Flight is not greatly beyond the target length but as the title implies it is concerned more with flight dynamics than with aerodynamics and is adapted more to the needs of pilots than to those of engineering students already equipped with a general aerodynamic background. I have taken it as a starting point that my readers have a knowledge of the aerodynamics of lifting wings as they exist in fixed-wing air- craft. A helicopter rotor blade performs the same function as a lifting wing but in a very different environment; and to note the similarities on the one hand and the distinctions on the other can be a consider- able fillip to the learner’s interest, one which I have tried to nurture by frequent references back to fixed-wing situations. This again is a somewhat non-standard approach. Substantial omissions from the book are not hard to find. A his- torical survey might have been included in Chapter 1 but was thought

Preface to First Edition xi not necessary despite its undoubted interest. To judge by the work effort it attracts, wake analysis (‘Vortex theory’) deserves a more extensive treatment than it gets (Chapters 2 and 5) but here it was necessary to refrain from opening a Pandora’s box of different approaches. Among topics which could have been included in Chapter 5 are autorotation in forward flight, pitch-flap coupling and blade flexibility but these were seen as marginally ‘second-line’ topics. The forward look in Chapter 6 might have contained a discussion of the potential of circulation control, the only system which is capable of attacking all the three non-uniformities of rotor blade flow, chord- wise, spanwise and azimuthal; but the subject is too big and too distinct from the main line of treatment. The reference to autostabilization in Chapter 8 is brief in the extreme but again the choice was between this and a much lengthier exposition in which aerodynamics would have been largely submerged beneath system mechanics and electronics. In compiling the book I have been greatly helped by discussions with Mr D.E.H. (‘Dave’) Balmford, Head of Advanced Engineering at Westland Helicopters, to whom my thanks are expressed. Other Westland staff members whose assistance I wish to acknowledge in specific contexts are Dr M.V. Lowson (now Professor of Aerospace Engineering at Bristol University) for Section 7.10, Mr F.J. Perry for Section 6.6, Mr R.V. Smith for Section 7.11 and Mr B. Pitkin for Chapter 8. Naturally the standard textbooks, particularly those men- tioned earlier, have been invaluable in places and I trust that this fact is duly recognized in the text and diagrams. Formal acknowledgement is made to Westland Helicopters for per- mission to reproduce the photographs at Figs 2.11, 4.10, 4.11, 7.6 and 7.7; to Edward Arnold, Publishers, for the use of Figs 2.10, 2.13, 5.1, 5.3, 6.3, 8.5 and 8.6 from A.R.S. Bramwell’s book Helicopter Dynam- ics (1976); to Mr P.G. Wilby of the Royal Aircraft Establishment for Figs 6.2 and 6.5, which are reproduced with the permission of the Controller of Her Majesty’s Stationery Office; and to Dr J.P. Jones for the use of Figs 2.12, 4.2 and 4.4. My thanks are due to Molly Gibbs of Bristol University who copy- typed the manuscript and to my grandson Daniel Cowley who drew the figures. J. Seddon

Preface to Second Edition The original Basic Helicopter Aerodynamics was conceived and written by Dr John Seddon. It found a respected place in the subject of rotary wing aircraft and has informed many. Sadly John Seddon has since passed away and I was very flattered to be asked to revise his manuscript for a second edition. This brought an immediate problem. Do I strip the work down to nuts and bolts or do I revise it as it stands but add my own contributions. Since the book is now under joint authorship, it would have been unfeeling to have pursued the former option since the original concept of John Seddon would have disappeared. For that reason I decided to pursue the latter option of revising the text and adding to it – particularly in the field of illustrations. The design, manufacture and operation of the helicopter rotor tend to be rather esoteric for the newcomer and long textual descriptions can be dry and not helpful. I have added, therefore, a substantial number of images to illustrate and clarify the discussions. The original diagrams were created by hand, which did not altogether succeed. Since that time, computer technology has improved greatly and the book’s graphics have been updated accordingly. The book’s size has increased to allow for the additions but I have been mindful of the need to retain the compactness of the original work. Helicopter rotor aerodynamics continues to be investigated. It is essential to introduce recent developments to the student and I intend to maintain this book in a form that will introduce the latest devel- opments. While an introductory text cannot hope to describe new techniques in detail it must be capable of establishing the correct thoughts in the reader’s mind, thus preparing them for more intensive study. xiii

xiv Preface to Second Edition The revisions have been aimed at illustrating, more fully, the various features of rotor aerodynamics and helicopter design. The helicopter is unique in its linking of the aerodynamic and mechanical features and a full appreciation of these air vehicles can only be achieved by understanding these interactions. Many of the extra figures illustrate the diversity in the design and operation of a helicopter and these dif- ferences are highlighted in the text. As with all things aeronautical, a team effort is always needed, and the assembly of this book is no exception. A picture says a thousand words so I have called upon the skills of many people to provide as many photographs as possible to amplify and, hopefully, clarify the explanations. While I have been able to supply a number of these pho- tographs personally, a considerable number have been kindly supplied and I would like to sincerely thank the following people for their gen- erosity. Denny Lombard of Lockheed Martin, Alan Vincent, Alan Brocklehurst and Alan Jeffrey of GKN Westland Helicopters, Harry Parkinson of Advanced Technologies Incorporated, Stewart Penney, Guy Gratton, David Long of Kaman and Steve Shrimpton. While I am quite pleased with my own photographic attempts, I am mindful that the pictures were taken on the ground, usually on a pleasant warm day with plenty of time to press the shutter release. In contrast, the above mentioned people have obtained better quality results while often hanging out of an aircraft in very difficult situa- tions. This marks the difference between the amateur and the true professional. I would also like to thank my colleagues and researchers who have provided much thought provoking discussion, which I hope, is reflected in the book. I am very grateful to David Balmford for his suggestions in correcting the text. I also would like to express my thanks to Ian Simons for his constant advice on all matters aeronau- tical. I offer many thanks to Julia Burden at Blackwell Science for her forbearance. The manuscript was late and she stuck with it, probably biting her lip but giving me valuable support. She offered me the task of revising the book and I hope she is not disappointed. Finally I would like to thank my wife, Stella, for putting up with my constant whizzing around putting the final touches to this work, snatching a cup of coffee as I speed by. Simon Newman Winchester January 2001

Notation List General a lift curve slope dCL/da a0 first term in Fourier expansion of b a1 coefficient of second term in Fourier expansion of b a2 coefficient of fourth term in Fourier expansion of b A area of rotor disc Ab total blade area (N blades) A1 coefficient of second term in Fourier expansion of q A2 coefficient of fourth term in Fourier expansion of q Ap projected frontal area of rotorhead (Chapter 6) As flow spoiling factor (Chapter 6) Az boundary layer shielding factor (Chapter 6) b1 coefficient of third term in Fourier expansion of b b2 coefficient of fifth term in Fourier expansion of b B tip loss factor in r = BR B1 coefficient of third term in Fourier expansion of q B2 coefficient of fifth term in Fourier expansion of q c blade chord CD drag coefficient CL lift coefficient CH H-force coefficient CP power coefficient CQ torque coefficient CT thrust coefficient d differential operator D aerodynamic drag e hinge offset ratio f equivalent flat-plate area H H-force xv

xvi Notation List I moment of inertia k empirical constant in expression for profile power K empirical constant in Glauert expression for induced velocity l moment arm of tail rotor thrust about main shaft L aerodynamic lift m blade mass per unit span M figure of merit M Mach number M moment (Figs, 8.4, 8.5) MT aerodynamic moment about flapping axis n inertia number (Chapter 8) N number of blades p static pressure P power q torque coefficient (Bramwell definition) q dynamic pressure, –21 rV2 Q torque r fraction of blade span from axis (= y/R) R blade radius S stiffness number tc thrust coefficient (Bramwell definition) T thrust u component velocity (non-dimensional, U/WR) U component velocity (dimensional) v induced velocity V stream velocity (flight speed) V¢ hypothetical velocity in Glauert formula for forward flight Vc climbing speed w disc loading, T/A W aircraft weight y distance along blade span from axis z height of rotor plane above ground Greek a incidence (angle of attack) of blade, positive nose-up a incidence of fuselage (Chapter 6), positive nose-up ar angle of attack of tip path plane to flight direction, positive nose-down b flapping angle (blade span to reference plane) b compressibility factor 1 - M 2 (Chapter 6) g Lock number d relative density of air, r/r0

Notation List xvii D prefix denoting increment, thus DP q blade pitch angle k empirical constant in expression for induced power l inflow factor (non-dimensional induced velocity) l blade natural flapping frequency (Chapter 8) m advance ratio, V/WR p pi r absolute density of air s blade solidity factor f angle of resultant velocity at blade to reference plane y angle of azimuth in blade rotation W blade rotational speed, radians per sec Suffixes av available b blade c suffix for thrust coefficient (Bramwell definition) C in climb D drag h hover value H H-force i induced L lift max maximum o basic or constant value p parasite P power Q torque req required t blade tip tw blade twist T thrust • conditions ‘at infinity’, i.e. where flow is undisturbed

Units The metric system is taken as fundamental, this being the educational basis in the UK. Imperial units are still used extensively, however, par- ticularly in the USA but also by industry and other organizations in the UK. For dimensional examples in the text and diagrams, there- fore, those units are used which it is felt have stood the test of time and may well continue to do so. Often units in both systems are quoted: in other cases reference may need to be made to the conver- sion tables set out below. In either system, units other than the basic one are sometimes used, depending on the context; this is particularly so for velocity, where for example aircraft flight speed is more conveniently expressed in kilometres/hour or in knots than in metres/second or in feet/second. The varieties used in the book are included in the table. xix

xx Units Quantity Metric unit and symbol Imperial equivalent Primary quantities kilogram (kg) 0.0685 slug Mass newton (N) 0.2248 pound (lb) Weight metre (m) 3.281 feet (ft) Length second (s) 1.0 second (sec) Time kelvin (K) Celsius (°C) Temperature Temp(K) = temp (°C) + 273.15 kilogram force Derived quantities 9.807 N (kG) 2.2046 lb Weight (force) kg/m3 0.00194 slug/ft3 N/m2 0.0209 lb/ft2 Density 0.1020 kG/m2 Pressure m/s 3.281 ft/sec 3.600 km/h 196.86 ft/min Velocity 1.941 knots m/s2 3.281 ft/sec2 Acceleration 9.807 m/s2 (g) 32.2 ft/sec2 Accel. of gravity watt, N m/s (W) 0.7376 ft.lb/sec Power 75 kG m/s (mhp) 0.9863 HP Metric horsepower 76.04 kG m/s 550 ft.lb/sec English horsepower

Basic Helicopter Aerodynamics Second Edition An account of first principles in the fluid mechanics and flight dynamics of the single rotor helicopter J. Seddon PhD, DSc, CEng, CFF, FRAeS and Simon Newman MSc (Eng), PhD, CEng, MRAeS, FIMA, CMath

© 2002, estate of J. Seddon and Blackwell  Science Marston Book Services Ltd Blackwell Science Ltd PO Box 269 Editorial Offices: Abingdon Osney Mead, Oxford OX2 0EL Oxon OX14 4YN 25 John Street, London WC1N 2BS (Orders: Tel: 01235 465500 23 Ainslie Place, Edinburgh EH3 6AJ 350 Main Street, Malden Fax: 01235 465555) MA 02148 5018, USA Canada 54 University Street, Carlton Login Brothers Book Company 324 Saulteaux Crescent Victoria 3053, Australia Winnipeg, Manitoba R3J 3T2 10, rue Casimir Delavigne (Orders: Tel: 204 837-2987 Fax: 204 837-3116) 75006 Paris, France Australia Other Editorial Offices: Blackwell Science Pty Ltd 54 University Street Blackwell Wissenschafts-Verlag GmbH Carlton, Victoria 3053 Kurfürstendamm 57 (Orders: Tel: 03 9347 0300 10707 Berlin, Germany Fax: 03 9347 5001) Blackwell Science KK A catalogue record for this title MG Kodenmacho Building is available from the British Library 7–10 Kodenmacho Nihombashi Chuo-ku, Tokyo 104, Japan ISBN 0-632-05283-X Iowa State University Press Library of Congress Cataloging-in- A Blackwell Science Company Publication Data 2121 S. State Avenue Ames, Iowa 50014-8300, USA Seddon, J. Basic helicopter aerodynamics : an The right of the Author to be identified as the Author of this Work has been asserted account of first principles in the fluid in accordance with the Copyright, Designs mechanics and flight dynamics of the and Patents Act 1988. single rotor helicopter / J. Seddon and Simon Newman. All rights reserved. No part of this publication may be reproduced, p. cm. stored in a retrieval system, or Includes bibliographical references and transmitted, in any form or by any index. means, electronic, mechanical, ISBN 0-632-05283-X photocopying, recording or otherwise, 1. Helicopters – Aerodynamics. except as permitted by the UK I. Newman, Simon, 1947– II. Title. Copyright, Designs and Patents Act TL716 .S43 2001b 1988, without the prior permission 629.133¢352 – dc21 of the publisher. 2001043019 First edition published 1990 Second edition published 2002 For further information on Blackwell Science, visit our website: Set in Times New Roman www.blackwell-science.com by Best-set Typesetter Ltd, Hong Kong Printed and bound in Great Britain by MPG Books, Bodmin, Cornwall The Blackwell Science logo is a trade mark of Blackwell Science Ltd, registered at the United Kingdom Trade Marks Registry

Preface to First Edition During the past decade and a half, several noteworthy textbooks have been published in the previously neglected field of helicopter aerody- namics, spurred no doubt by a growing acceptance world-wide of the importance of the helicopter in modern society. One may cite in this context Bramwell’s Helicopter Dynamics (1976), Johnson’s Helicopter Theory (1980) and Rotary Wing Aerodynamics (1984) by Stepniewski and Keys. The appearance now of another book on the subject requires some explanation, therefore. I have three specific reasons for writing it. The first reason is one of brevity. Bramwell’s book runs to 400 pages, that of Stepniewski and Keys to 600 and Johnson’s extremely comprehensive treatment to over 1000. The users I have principally in mind are University or Polytechnic students taking a short course of lectures – say one year – in the subject, probably as an ‘optional’ or ‘elective’ in the final undergraduate or early post-graduate year. The object in that time is to provide them with a grounding while hope- fully stimulating an interest which may carry them further in the subject at a later data. The amount of teaching material required for this purpose is only a fraction of that contained in the standard text- books and a monograph of around 150 pages is more than sufficient to contain what is needed and hopefully may be produced at a price not beyond the individual student’s pocket. My second reason, which links with the first, concerns the type of approach. This book does not aim at a comprehensive treatment but neither is it content to consign problems to the digital computer at the earliest opportunity. In between lies an analytical route to solu- tions, taken far enough to produce results of usable accuracy for many practical purposes, while at the same time providing a physical under- standing of the phenomena involved, which rapid recourse to the ix

x Preface to First Edition computer often fails to do. It is this route that the book attempts to follow. The analytical approach is usually terminated when it is thought to have gone far enough to serve the stated purpose, the reader being left with a reference to one of the standard textbooks in case he should wish to pursue the topic further. The third reason is one of content. Despite the need for brevity, I have thought it worthwhile to include, in addition to treatments of the standard topics – momentum theory, blade element theory, basic performance, stability and control – a strong flavour of research and development activity (Chapter 6) and of forward-looking, if specula- tive, calculations (Chapter 7). It might be considered that these items are of such a transitory nature as not to be suitable for a textbook, but my criterion of stimulating the student’s interest is what has deter- mined their inclusion. Certainly they have proved to be interesting in classroom presentation and there seems no reason why that should not be so for the written word. In addition to meeting the needs of students, to whom it is pri- marily addressed, the book should have an appeal as background material to short courses held in or on behalf of industry: such courses are increasing in popularity. Companies and research estab- lishments may also find it useful for new entrants and for more estab- lished workers requiring a ‘refresher’ text. Reverting to the matter of brevity, the recent publication Helicopter Aerodynamics by Prouty is a most admirable short exposition, well worth studying as an adjunct to any other textbook: however it shuns the mathematics completely and therefore will not suffice alone for the present purposes. Saunders’ Dynamics of Helicopter Flight is not greatly beyond the target length but as the title implies it is concerned more with flight dynamics than with aerodynamics and is adapted more to the needs of pilots than to those of engineering students already equipped with a general aerodynamic background. I have taken it as a starting point that my readers have a knowledge of the aerodynamics of lifting wings as they exist in fixed-wing air- craft. A helicopter rotor blade performs the same function as a lifting wing but in a very different environment; and to note the similarities on the one hand and the distinctions on the other can be a consider- able fillip to the learner’s interest, one which I have tried to nurture by frequent references back to fixed-wing situations. This again is a somewhat non-standard approach. Substantial omissions from the book are not hard to find. A his- torical survey might have been included in Chapter 1 but was thought

Preface to First Edition xi not necessary despite its undoubted interest. To judge by the work effort it attracts, wake analysis (‘Vortex theory’) deserves a more extensive treatment than it gets (Chapters 2 and 5) but here it was necessary to refrain from opening a Pandora’s box of different approaches. Among topics which could have been included in Chapter 5 are autorotation in forward flight, pitch-flap coupling and blade flexibility but these were seen as marginally ‘second-line’ topics. The forward look in Chapter 6 might have contained a discussion of the potential of circulation control, the only system which is capable of attacking all the three non-uniformities of rotor blade flow, chord- wise, spanwise and azimuthal; but the subject is too big and too distinct from the main line of treatment. The reference to autostabilization in Chapter 8 is brief in the extreme but again the choice was between this and a much lengthier exposition in which aerodynamics would have been largely submerged beneath system mechanics and electronics. In compiling the book I have been greatly helped by discussions with Mr D.E.H. (‘Dave’) Balmford, Head of Advanced Engineering at Westland Helicopters, to whom my thanks are expressed. Other Westland staff members whose assistance I wish to acknowledge in specific contexts are Dr M.V. Lowson (now Professor of Aerospace Engineering at Bristol University) for Section 7.10, Mr F.J. Perry for Section 6.6, Mr R.V. Smith for Section 7.11 and Mr B. Pitkin for Chapter 8. Naturally the standard textbooks, particularly those men- tioned earlier, have been invaluable in places and I trust that this fact is duly recognized in the text and diagrams. Formal acknowledgement is made to Westland Helicopters for per- mission to reproduce the photographs at Figs 2.11, 4.10, 4.11, 7.6 and 7.7; to Edward Arnold, Publishers, for the use of Figs 2.10, 2.13, 5.1, 5.3, 6.3, 8.5 and 8.6 from A.R.S. Bramwell’s book Helicopter Dynam- ics (1976); to Mr P.G. Wilby of the Royal Aircraft Establishment for Figs 6.2 and 6.5, which are reproduced with the permission of the Controller of Her Majesty’s Stationery Office; and to Dr J.P. Jones for the use of Figs 2.12, 4.2 and 4.4. My thanks are due to Molly Gibbs of Bristol University who copy- typed the manuscript and to my grandson Daniel Cowley who drew the figures. J. Seddon

Preface to Second Edition The original Basic Helicopter Aerodynamics was conceived and written by Dr John Seddon. It found a respected place in the subject of rotary wing aircraft and has informed many. Sadly John Seddon has since passed away and I was very flattered to be asked to revise his manuscript for a second edition. This brought an immediate problem. Do I strip the work down to nuts and bolts or do I revise it as it stands but add my own contributions. Since the book is now under joint authorship, it would have been unfeeling to have pursued the former option since the original concept of John Seddon would have disappeared. For that reason I decided to pursue the latter option of revising the text and adding to it – particularly in the field of illustrations. The design, manufacture and operation of the helicopter rotor tend to be rather esoteric for the newcomer and long textual descriptions can be dry and not helpful. I have added, therefore, a substantial number of images to illustrate and clarify the discussions. The original diagrams were created by hand, which did not altogether succeed. Since that time, computer technology has improved greatly and the book’s graphics have been updated accordingly. The book’s size has increased to allow for the additions but I have been mindful of the need to retain the compactness of the original work. Helicopter rotor aerodynamics continues to be investigated. It is essential to introduce recent developments to the student and I intend to maintain this book in a form that will introduce the latest devel- opments. While an introductory text cannot hope to describe new techniques in detail it must be capable of establishing the correct thoughts in the reader’s mind, thus preparing them for more intensive study. xiii

xiv Preface to Second Edition The revisions have been aimed at illustrating, more fully, the various features of rotor aerodynamics and helicopter design. The helicopter is unique in its linking of the aerodynamic and mechanical features and a full appreciation of these air vehicles can only be achieved by understanding these interactions. Many of the extra figures illustrate the diversity in the design and operation of a helicopter and these dif- ferences are highlighted in the text. As with all things aeronautical, a team effort is always needed, and the assembly of this book is no exception. A picture says a thousand words so I have called upon the skills of many people to provide as many photographs as possible to amplify and, hopefully, clarify the explanations. While I have been able to supply a number of these pho- tographs personally, a considerable number have been kindly supplied and I would like to sincerely thank the following people for their gen- erosity. Denny Lombard of Lockheed Martin, Alan Vincent, Alan Brocklehurst and Alan Jeffrey of GKN Westland Helicopters, Harry Parkinson of Advanced Technologies Incorporated, Stewart Penney, Guy Gratton, David Long of Kaman and Steve Shrimpton. While I am quite pleased with my own photographic attempts, I am mindful that the pictures were taken on the ground, usually on a pleasant warm day with plenty of time to press the shutter release. In contrast, the above mentioned people have obtained better quality results while often hanging out of an aircraft in very difficult situa- tions. This marks the difference between the amateur and the true professional. I would also like to thank my colleagues and researchers who have provided much thought provoking discussion, which I hope, is reflected in the book. I am very grateful to David Balmford for his suggestions in correcting the text. I also would like to express my thanks to Ian Simons for his constant advice on all matters aeronau- tical. I offer many thanks to Julia Burden at Blackwell Science for her forbearance. The manuscript was late and she stuck with it, probably biting her lip but giving me valuable support. She offered me the task of revising the book and I hope she is not disappointed. Finally I would like to thank my wife, Stella, for putting up with my constant whizzing around putting the final touches to this work, snatching a cup of coffee as I speed by. Simon Newman Winchester January 2001

Notation List General a lift curve slope dCL/da a0 first term in Fourier expansion of b a1 coefficient of second term in Fourier expansion of b a2 coefficient of fourth term in Fourier expansion of b A area of rotor disc Ab total blade area (N blades) A1 coefficient of second term in Fourier expansion of q A2 coefficient of fourth term in Fourier expansion of q Ap projected frontal area of rotorhead (Chapter 6) As flow spoiling factor (Chapter 6) Az boundary layer shielding factor (Chapter 6) b1 coefficient of third term in Fourier expansion of b b2 coefficient of fifth term in Fourier expansion of b B tip loss factor in r = BR B1 coefficient of third term in Fourier expansion of q B2 coefficient of fifth term in Fourier expansion of q c blade chord CD drag coefficient CL lift coefficient CH H-force coefficient CP power coefficient CQ torque coefficient CT thrust coefficient d differential operator D aerodynamic drag e hinge offset ratio f equivalent flat-plate area H H-force xv

xvi Notation List I moment of inertia k empirical constant in expression for profile power K empirical constant in Glauert expression for induced velocity l moment arm of tail rotor thrust about main shaft L aerodynamic lift m blade mass per unit span M figure of merit M Mach number M moment (Figs, 8.4, 8.5) MT aerodynamic moment about flapping axis n inertia number (Chapter 8) N number of blades p static pressure P power q torque coefficient (Bramwell definition) q dynamic pressure, –21 rV2 Q torque r fraction of blade span from axis (= y/R) R blade radius S stiffness number tc thrust coefficient (Bramwell definition) T thrust u component velocity (non-dimensional, U/WR) U component velocity (dimensional) v induced velocity V stream velocity (flight speed) V¢ hypothetical velocity in Glauert formula for forward flight Vc climbing speed w disc loading, T/A W aircraft weight y distance along blade span from axis z height of rotor plane above ground Greek a incidence (angle of attack) of blade, positive nose-up a incidence of fuselage (Chapter 6), positive nose-up ar angle of attack of tip path plane to flight direction, positive nose-down b flapping angle (blade span to reference plane) b compressibility factor 1 - M 2 (Chapter 6) g Lock number d relative density of air, r/r0

Notation List xvii D prefix denoting increment, thus DP q blade pitch angle k empirical constant in expression for induced power l inflow factor (non-dimensional induced velocity) l blade natural flapping frequency (Chapter 8) m advance ratio, V/WR p pi r absolute density of air s blade solidity factor f angle of resultant velocity at blade to reference plane y angle of azimuth in blade rotation W blade rotational speed, radians per sec Suffixes av available b blade c suffix for thrust coefficient (Bramwell definition) C in climb D drag h hover value H H-force i induced L lift max maximum o basic or constant value p parasite P power Q torque req required t blade tip tw blade twist T thrust • conditions ‘at infinity’, i.e. where flow is undisturbed

Units The metric system is taken as fundamental, this being the educational basis in the UK. Imperial units are still used extensively, however, par- ticularly in the USA but also by industry and other organizations in the UK. For dimensional examples in the text and diagrams, there- fore, those units are used which it is felt have stood the test of time and may well continue to do so. Often units in both systems are quoted: in other cases reference may need to be made to the conver- sion tables set out below. In either system, units other than the basic one are sometimes used, depending on the context; this is particularly so for velocity, where for example aircraft flight speed is more conveniently expressed in kilometres/hour or in knots than in metres/second or in feet/second. The varieties used in the book are included in the table. xix

xx Units Quantity Metric unit and symbol Imperial equivalent Primary quantities kilogram (kg) 0.0685 slug Mass newton (N) 0.2248 pound (lb) Weight metre (m) 3.281 feet (ft) Length second (s) 1.0 second (sec) Time kelvin (K) Celsius (°C) Temperature Temp(K) = temp (°C) + 273.15 kilogram force Derived quantities 9.807 N (kG) 2.2046 lb Weight (force) kg/m3 0.00194 slug/ft3 N/m2 0.0209 lb/ft2 Density 0.1020 kG/m2 Pressure m/s 3.281 ft/sec 3.600 km/h 196.86 ft/min Velocity 1.941 knots m/s2 3.281 ft/sec2 Acceleration 9.807 m/s2 (g) 32.2 ft/sec2 Accel. of gravity watt, N m/s (W) 0.7376 ft.lb/sec Power 75 kG m/s (mhp) 0.9863 HP Metric horsepower 76.04 kG m/s 550 ft.lb/sec English horsepower

Contents Preface to First Edition ix Preface to Second Edition xiii Notation List xv Units xix List of Abbreviations xxi Chapter 1: Introduction 1 Chapter 2: Rotor in Vertical Flight: Momentum Theory and Wake 13 Analysis 13 2.1 Momentum theory for hover 17 2.2 Figure of merit 18 2.3 Momentum theory for vertical climb 20 2.4 Vertical descent 24 2.5 Complete induced-velocity curve 25 2.6 Autorotation 26 2.7 Summary remarks on momentum theory 26 2.8 Complexity of real wake 30 2.9 Wake analysis methods 31 2.10 Ground effect 35 35 Chapter 3: Rotor in Vertical Flight: Blade Element Theory 40 3.1 Basic method 3.2 Thrust approximations v

vi Contents 41 42 3.3 Non-uniform inflow 45 3.4 Ideal twist 46 3.5 Blade mean lift coefficient 48 3.6 Power approximations 50 3.7 Tip loss 3.8 Example of hover characteristics 51 Chapter 4: Rotor Mechanisms for Forward Flight 51 58 4.1 The edgewise rotor 60 4.2 Flapping motion 69 4.3 Rotor control 4.4 Equivalence of flapping and feathering 73 Chapter 5: Rotor Aerodynamics in Forward Flight 73 76 5.1 Momentum theory 77 5.2 Wake analysis 77 5.3 Blade element theory 80 82 Factors involved 84 Thrust 86 In-plane H force 89 Torque and power Flapping coefficients 93 Typical numerical values 93 Chapter 6: Aerodynamic Design 94 99 6.1 Introductory 102 6.2 Blade section design 107 6.3 Blade tip shapes 111 6.4 Parasite drag 112 6.5 Rear fuselage upsweep 6.6 Higher harmonic control 119 6.7 Aerodynamic design process 119 Chapter 7: Performance 121 7.1 Introductory 7.2 Hover and vertical flight

7.3 Forward level flight Contents vii 7.4 Climb in forward flight 7.5 Optimum speeds 123 7.6 Maximum level speed 126 7.7 Rotor limits envelope 127 7.8 Accurate performance prediction 128 7.9 A world speed record 128 7.10 Speculation on the really-low-drag helicopter 130 7.11 An exercise in high-altitude operation 131 132 Chapter 8: Trim, Stability and Control 136 8.1 Trim 141 8.2 Treatment of stability and control 8.3 Static stability 141 145 Incidence disturbance 146 Forward speed disturbance 146 Angular velocity (pitch or roll rate) disturbance 147 Sideslip disturbance 148 Yawing disturbance 148 General conclusion 149 8.4 Dynamic stability 149 Analytical process 149 Special case of hover 149 8.5 Hingeless rotor 150 8.6 Control 151 8.7 Autostabilization 152 155 Index 157

Chapter 1 Introduction ‘It is easy to invent a flying machine; more difficult to build one; to make it fly is everything’ Otto Lilienthal, 1848–1896 One may doubt whether Lilienthal, the pioneer par excellence of gliding flight, had the helicopter in mind when he wrote the above but his words could not have been more appropriate to our subject. To take the quotation line by line, the concept of a lifting rotor constitutes the essential invention. Making it large is simply taking advantage of Newton’s Second and Third Laws, which guarantee that blowing a large quantity of air at low speed is an efficient way of producing a thrust. When it comes to building a machine, the problems of directing it around the sky have to be thought out and translated into hardware: ultimately, however, the solutions for the helicopter are both straight- forward and impressive. Upward lift is obtained with the rotor shaft essentially vertical; forward (or backward or sideways) propulsion is achieved by tilting the shaft in the desired direction; and moments for manoeuvring are produced by tilting the rotor plane relative to the shaft. Here is a system more elegant in principle than that of a fixed- wing aircraft, where such integration of functions is not possible. And to pursue its virtues one stage further, when the direction of airflow through the rotor becomes reversed in descent, blade lift can be produced without power (‘autorotation’), allowing a controlled landing in the event of engine failure. These points were made by J.P. Jones in the 1972 Cierva Memorial Lecture1 to the Royal Aeronautical Society. To quote him at this juncture: 1

2 Basic Helicopter Aerodynamics Figure 1.1 Wing tip vortices generated by a McDonnell Douglas F4 Phantom. ‘Can we wonder that the conventional rotor has been a success? At this stage one might think the real question is why the fixed-wing air- craft has not died out’ But back to Lilienthal and there’s the rub. Making the helicopter fly has involved wrestling with a long catalogue of problems, of which some have been solved and others continue to be lived with. Thus it was necessary to invent the use of a tail rotor to stop the helicopter spinning round on the main rotor axis. It took the genius of Juan de la Cierva to devise a system of articulated blades to prevent the air- craft rolling over continuously. The helicopter can never fly fast judged by fixed-wing aircraft standards, the restriction, surprisingly enough, being one of blade stalling. Climbing is straightforward aerodynamically but descending involves a deliberate venture into an aerodynamicist’s nightmare of vortices, turbulence and separated flow. The behaviour of vortices left by an aerodynamic device is crucial to its performance and the locations of these vortices are critical. Figure 1.1 shows a typical wake from a fixed-wing aircraft (McDonnell Douglas F4 Phantom) where the wing tip vortices stream behind the aircraft. Figure 1.2 shows vortices being left by the pro- peller blade tips of a Lockheed C130 Hercules aircraft. Figure 1.3 shows the vortex wake off a helicopter rotor (AH56A Lockheed Cheyenne). Close examination of the wake structure shows interac- tion with the tail rotor and the rear fuselage. In addition to influencing any lifting surfaces, vortices interact with each other. Figure 1.4 shows the wake off a BAe Systems Hawk 200 aircraft after a tight pull up manoeuvre. The two tip vortices have closed together and on bursting (an unstable breakdown of the initial

Figure 1.2 Propeller tip vortices generated by a Lockheed C130 Hercules. Figure 1.3 Blade tip vortices generated by a Lockheed Cheyenne operating from Mammoth Lake Airport during high altitude testing in 1972. (Reproduced courtesy of Lock- heed Martin.) Figure 1.4 Tip vortex breakdown for a BAe Hawk 200.

4 Basic Helicopter Aerodynamics vortex structure) are beginning to form the characteristic loops asso- ciated with parallel pairs of vortices. Figures 1.5(a) to 1.5(e) show a sequence of images of a small helicopter with a tip-driven rotor. The tip jet exhausts show the wake structures in several different flight regimes. Figure 1.5(a) illustrates a hovering condition close to the ground surface. The wake can be seen to contract immediately below the rotor but then expand as the downflow from the rotor is interrupted by the ground forcing it to spill outwards. This phenomenon is called ‘ground effect’ and is a very important feature of helicopter perfor- mance. The wake structure shows not only the ‘tube’ of vorticity, but also the individual blade tip vortices. Figure 1.5(b) shows the rotor at low forward speed. Ground effect is still present but the wake is now dispersed rearwards. As the forward speed increases, Fig. 1.5(c), the vortex ‘tube’ adopts a sheared profile for a short distance before mutual interaction between the vortices begins to distort the wake. The sheared vortex tube concept is a useful modelling technique, but, with vortex interactions, as shown in Fig. 1.5(c), needs care in appli- cation. As forward speed increases further, the individual wake vor- tices show a cycloidal shape (in plan) and a roll up character at the lateral rotor disc edges, not unlike a fixed wing. These characteristics are well shown in Figs 1.5(d) and 1.5(e). Blade articulation leads to sluggish control, which can be improved by going to the more modern system of a hingeless rotor, but only at the expense of worsening the aircraft stability. With any practical combination of stability and control characteristics the helicopter remains a difficult and taxing aircraft to fly and generally requires autostabilization to restrict the pilot workload to a safe and comfortable level. It would seem that we have on our hands a veritable box of tricks. What is certain, however, is that the modern world cannot do without it. The helicopter has become an invaluable asset in many fields of human activity and the variety of its uses continues to increase. Moreover, to come close to the purpose of this book, the problems that have been solved, or if only partly solved, at least understood, make good science, high in interest value. This the book purports to show. The period since World War II has seen a proliferation of different types of rotary-wing aircraft. The single-rotor helicopter (with tail rotor) was established firmly by Sikorsky during the war years and a typical example of a Sikorsky S61N is shown in Fig. 1.6. While this configuration is the most common, it has been joined over the years by several other rotor arrangements. They are the tandem rotor layout

Introduction 5 a b c Figure 1.5 Rotor wake. (Reproduced courtesy of Advanced Technologies Incorporated.) a. In hover (in ground effect) b. Moderate forward speed flight (in ground effect) c. Low forward speed flight d. High forward speed flight e. High forward speed flight

6 Basic Helicopter Aerodynamics d e Figure 1.5 Continued Figure 1.6 Coastguard Search & Rescue Sikorsky S61N. (Steve Shrimpton.)

Introduction 7 Figure 1.7 Boeing Vertol Chinook tandem helicopter in turning flight. Figure 1.8 Mil 12 side by side helicopter. (GKN Westland Helicopters.) (Boeing Vertol Chinook) shown in Fig. 1.7, the side by side rotor (Mil 12) shown in Fig. 1.8, the coaxial rotor (Kamov Helix) in Fig. 1.9 and the synchropter (Kaman K-Max) in Fig. 1.10. All of these helicopter configurations use the rotors to produce the lift and propulsive forces. They also power the rotors through a transmission system, which requires the provision of torque control in yaw. This is provided by a tail rotor or by the two main rotors rotating in oppo- site directions. When an external force, such as reaction from a tip jet drives the rotor, the torque reaction problem is not present. Yaw control is, of course, necessary, but there is not now a requirement to counteract the torque produced by an internally driven main rotor. The Fairey Rotodyne in Fig. 1.11 shows such an example. This par-

8 Basic Helicopter Aerodynamics Figure 1.9 Kamov Helix coaxial helicopter. (Guy Gratton) Figure 1.10 Kaman K-Max synchropter. (Kaman) ticular aircraft also introduces the concept of compounding where lift and/or propulsion is supplemented by extra devices. Such aircraft are designated lift compounded (lift alone), thrust compounded (propul- sion alone) or fully compounded (both lift and propulsion). For the Rotodyne, in forward flight, wings aid the rotor lift and airscrews provide the propulsion. It is therefore a fully compounded helicopter. The Lockheed Cheyenne, shown in Fig. 1.12, is also fully com-

Introduction 9 Figure 1.11 Fairey Rotodyne compound helicopter. (GKN Westland Helicopters.) Figure 1.12 Lockheed Cheyenne compound helicopter. (Lockheed Martin.) pounded. It has wings for lift and a pusher propeller at the rear of the tail boom. It possesses a standard tail rotor, which is synchronized with the propeller. The compound helicopter forms part of a second group of rotor- craft configurations, which were designed to increase the forward speed of the conventional helicopter. As will be seen in later discus- sions, the conventional helicopter main rotor is forced to operate in an essentially edgewise sense which produces aerodynamic limitations

10 Basic Helicopter Aerodynamics Figure 1.13 Bell Boeing V22 tilt rotor configuration in hover. (Corel.) Figure 1.14 Boeing V76 tilt wing research rotorcraft. (Corel.) on rotor thrust. This provides a limit to forward speed. As an example, the World Speed Record Lynx achieved approximately 250 mph in 1986. A fixed-wing aircraft, (Curtiss R4) exceeded that speed in 1923, fully 65 years ahead. The other rotorcraft variants within this second group are the tilt rotor and tilt wing layouts. The tilt rotor, in which, as the name implies, has rotors, which face upwards for vertical take- off and hover and rotate forwards for horizontal flight. It offers con- siderable potential to enable the vertical take-off and landing of a helicopter but also being able to bypass the forward speed limitation. An example is the Bell V22 shown in Fig. 1.13. The tilt wing layout is very similar except that the rotors are rigidly fixed to the wings and the entire wing unit rotates upward for vertical flight but forwards for horizontal flight. An example is the Boeing V76 research aircraft shown in Fig. 1.14. Up to the present, however, the single-rotor heli-

Introduction 11 Figure 1.15 The single main-rotor helicopter in essence. copter remains by far the most numerous worldwide and in this book we concentrate exclusively on that type. Its familiar profile, sketched in Fig. 1.15, is the result of practical considerations not readily varied. The engines and gearbox require to be grouped tightly around the rotor shaft and close below the rotor. Below them the payload com- partment is centrally placed fore and aft to minimize centre of gravity movements away from the shaft line. In front of the payload com- partment is the flight cabin. The transmission line from gearbox to tail rotor needs to be as straight and uninterrupted as possible. Put a fairing around these units so defined and the characteristic profile emerges. It will be helpful to explain certain logistics of the presentation. Symbols are defined when first introduced but for ease of reference are also collected in a table at the start of the book. As concerns units, where there is complete freedom of choice the metric system is pre- ferred: since, however, much use continues to be made of imperial units, particularly in the USA, I have also employed these units freely in numerical examples, sometimes giving both. Again there are tables at the start defining primary and derived units and listing the con- version factors. Lastly, on the question of references, these are num- bered in each chapter and listed at the end of the chapter in the usual way. Exception is made, however, in the case of three standard textbooks, which are referred to repeatedly, usually for further