Bramwell’s Helicopter Dynamics

1 Bramwell s Helicopter DynamicsBramwell sHelicopter DynamicsSecond editionA. R. S. BramwellGeorge DoneDavid BalmfordOxford Auckland Boston Johannesburg Melbourne New DelhiButterworth-HeinemannLinacre House, Jordan Hill, Oxford OX2 8DP225 Wildwood Avenue, Woburn, MA 01801-2041A division of Reed Educational and Professional Publishing Ltd A member of the Reed Elsevier plc groupFirst published by Edward Arnold (Publishers) Ltd 1976 Second edition published by Butterworth-Heinemann 2001 A. R. S. Bramwell, George Done and David Balmford 2001 All rights reserved. No part of this publication may be reproduced inany material form (including photocopying or storing in any medium byelectronic means and whether or not transiently or incidentally to someother use of this publication) without the written permission of thecopyright holder except in accordance with the provisions of the Copyright,Designs and Patents Act 1988 or under the terms of a licence issued by theCopyright Licensing Agency Ltd, 90 Tottenham Court Road, London,England W1P OLP.

2 Applications for the copyright holder s writtenpermission to reproduce any part of this publication should beaddressed to the publishersBritish Library Cataloguing in Publication DataBramwell, s Helicopter Dynamics . 2nd Helicopters AerodynamicsI TitleII Done, GeorgeIII Balmford, DavidIV 33352 Library of Congress Cataloguing in Publication DataBramwell, s Helicopter Dynamics / Bramwell, George Done,David Balmford. 2nd ed. of: Helicopter Dynamics . c1976 Includes indexISBN 0 7506 5075 31 Helicopter Dynamics2 Helicopters AerodynamicsI Done, George TaylorSuttonII Balmford, DavidIII Bramwell, Helicopter dynamicsIV 352--dc2100-049381 ISBN 0 7506 5075 3 Typeset at Replika Press Pvt Ltd, 100% EOU, Delhi 110 040, IndiaPrinted and bound in Great Britain by Bath Press, to the second editionviiPreface to the first editionixAcknowledgementsxiNotationxiii1 .

3 Basic mechanics of rotor systems and Helicopter flight12. Rotor aerodynamics in axial flight333. Rotor aerodynamics and Dynamics in forward flight774. Trim and performance in axial and forward flight1155. Flight Dynamics and control1376. Rotor aerodynamics in forward flight1967. Structural Dynamics of elastic blades2388. Rotor induced vibration2909. Aeroelastic and aeromechanical behaviour319 Appendices360 Index371 Preface to the second editionAt the time of publication of the first edition of the book in 1976, Bramwell sHelicopter Dynamics was a unique addition to the fundamental knowledge of dynamicsof rotorcraft due to its coverage in a single volume of subjects ranging fromaerodynamics, through flight Dynamics to vibrational Dynamics and aeroelasticity.

4 Itproved to be popular, and the first edition sold out relatively quickly. Unfortunately,before the book could be revised with a view to producing a second edition, Bram (ashe was known to his friends and colleagues) succumbed to a short illness and well as leaving a sudden space in the Helicopter world, his death left the publisherswith their desire for further editions unfulfilled. Following an approach from thepublishers, the present authors agreed, with considerable trepidation, to undertakethe task of producing a second , being asked was an honour, particularly so for one of us (GD), since wehad been colleagues together at City University for a short period of two , although it may be one thing to produce a book from one s own lecturenotes and published papers, it is entirely a different proposition to do the same whenthe original material is not your own, as we were to discover.

5 It was necessary to tryto understand why Bram s book was so popular with the Helicopter fraternity, inorder that any revisions should not destroy any of the vital qualities in this of the characteristics that we felt endeared the book to its followers was the wayexplanations of what are complicated phenomena were established from fundamentallaws and simple assumptions. Theoretical expressions were developed from the basicmathematics in a straightforward and measured style that was particular to Bram sway of thinking and writing. We positively wished and endeavoured to retain hisinimitable qualities and sections of the book are analytical, starting from fundamental principles, anddo not change significantly in the course of time; however, we have tried to eradicateerrors, printer s and otherwise, and improve explanations where considered are also many sections that are largely descriptive, and, over the space of 25years since the first edition, these had tended to become out of date, both in terms ofthe state-of-the-art and supporting references.

6 Thus, these have been , too, have been taken to expand the treatment of, and to include additionalinformation in, the vibrational Dynamics area, with both the additional and updatedcontent introduced, hopefully, in such a way as to be compatible with Bram s change which has taken place in the past quarter century is the nowgreater familiarity of the users of books such as this one with matrices and , Chapter 1 of the first edition, which was aimed at introducing and explainingthe necessary associated matrix and vector operations, has disappeared from thesecond edition. Also, some rather fundamental fluid Dynamics that also appeared inthis chapter was considered unnecessary in view of the material being readily availablein undergraduate textbooks.

7 What remained from the original Chapter 1 that wasthought still necessary now appears in the Appendix. Readers familiar with the firstedition will notice the inclusion of a notation list in the present edition. This becamean essential item in re-editing the book , because there were many instances in thefirst edition of repeated symbols for different parameters, and different symbols forthe same parameters, due to the fact that the much of the material in the original bookwas based on various technical papers published at different times. As far as has beenpossible, the notation has now been made consistent throughout all chapters; this hasresulted in some of the least used symbols being from the removal of the elementary material in the original Chapter 1, theoverall structure of the book has not changed to any great degree.

8 The order of thechapters is as before, although there has been some re-titling and compression of twochapters into one. Some of the sections in the last three chapters have been re-arranged to provide a more natural publication of the first edition, there have appeared in the market-placeseveral excellent scientific textbooks on rotorcraft which cover some of the contentof Bram s book to a far greater depth and degree of specialisation, and also othertexts which are aimed at a broad coverage but at a lower academic level. However,the comprehensive nature of the subject matter dealt with in this volume shouldcontinue to appeal to those Helicopter engineers who require a reasonably in-depthand authoritative text covering a wide range of BalmfordKewGeorge Done2001viiiPreface to the second editionPreface to the first editionIn spite of the large numbers of helicopters now flying, and the fact that helicoptersform an important part of the air strength of the world s armed services, the study ofhelicopter Dynamics and aerodynamics has always occupied a lowly place in aeronauticalinstruction.

9 In fact, it is probably true to say that in most aeronautical universities inGreat Britain and the United States the Helicopter is almost, if not entirely, absentfrom the curriculum. This neglect is also seen in the dearth of textbooks on thesubject; it is fifteen years since the last textbook in English was published, and overtwenty years have passed since the first appearance of Gessow and Myer s excellentintroductory text Aerodynamics of the Helicopter , which has not so far been object of the present volume is to give an up-to-date account of the moreimportant branches of the Dynamics and aerodynamics of the Helicopter . It is hopedthat it will be useful to both undergraduate and postgraduate students of aeronauticsand also to workers in industry and the research establishments.

10 In these days of fastcomputers it is a temptation to consign a problem to arithmetical computer calculationstraightaway. While this is unavoidable in many complicated problems, such as thecalculation of induced velocity, the important physical understanding is thereby oftenlost. Fortunately, most problems of the Helicopter can be discussed adequately withoutbecoming too involved mathematically, and it is usually possible to arrive at relativelysimple formulae which are not only useful in preliminary design but which alsoenable a physical interpretation of the dynamic and aerodynamic phenomena to beobtained. The intention throughout this book , therefore, has been to try to arrive atuseful mathematical results and working formulae and at the same time to emphasizethe physical understanding of the first chapter summarizes some essential mechanics, mathematics, andaerodynamics which find application in later parts of the book .