Flight Physics
E. Torenbeek H. Wittenberg Flight Physics Essentials of Aeronautical Disciplines and Technology, with Historical Notes
E. Torenbeek H. Wittenberg Delft University of Technology Delft, The Netherlands From the original Dutch Aëronautiek: Grondslagen en Techniek van het Vliegen, Delft University Press, 2002. Translated and re-edited by Simeon Calvert and Egbert Torenbeek. Every effort has been made to contact the copyright holders of the figures which have been reproduced from other sources. Anyone who has not been properly credited is requested to contact the publishers, so that due acknowledgement may be made in subsequent editions. ISBN 978-1-4020-8663-2 e-isbn 978-1-4020-8664-9 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2009931043 Springer Science+Business Media, B.V. 2009 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording orotherwise, withoutwritten permission from the Publisher, withthe exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Contents Preface... ix 1 History of Aviation... 1 1.1 Introduction...... 1 1.2 Early history and the invention of ballooning...... 3 1.3 The period between 1799 and 1870... 8 1.4 The decades between 1870 and 1890... 12 1.5 From 1890 until the Wright Flyer III... 15 1.6 European aviation between 1906 and 1918... 22 1.7 Aviationbetweentheworldwars... 29 1.8 Development after 1940.... 37 Bibliography... 45 2 Introduction to Atmospheric Flight... 47 2.1 Flying Howisthatpossible?... 47 2.2 Static and dynamic aviation....... 49 2.3 Forcesontheaeroplane... 55 2.4 Lift, drag and thrust... 58 2.5 Properties of air... 62 2.6 Theearth satmosphere... 67 2.7 Thestandardatmosphere... 69 2.8 Atmosphericflight... 78 Bibliography... 84 3 Low-Speed Aerodynamics... 87 3.1 Speed domains and compressibility... 88 3.2 Basicconcepts... 89 3.3 Equationsforsteadyflow... 93 3.4 Viscousflows...102 v
vi Contents 3.5 The boundary layer....105 3.6 Flowseparationanddrag...109 3.7 Shape and scale effects on drag....116 Bibliography...123 4 Lift and Drag at Low Speeds...125 4.1 Functionandshapeofaeroplanewings...125 4.2 Aerofoilsections...128 4.3 Circulation and lift...137 4.4 Aerofoil section properties.... 145 4.5 Winggeometry...153 4.6 High-aspectratiostraightwings...158 4.7 Low-aspectratiowings...169 4.8 Thewholeaircraft...172 Bibliography...178 5 Aircraft Engines and Propulsion...181 5.1 Historyofenginedevelopment...181 5.2 Fundamentals of reaction propulsion...196 5.3 Engineefficiencyandfuelconsumption...205 5.4 Pistonenginesinaviation...209 5.5 Gas turbine engine components.... 215 5.6 Non-reheatedturbojetandturbofanengines...221 5.7 Turboprop and turboshaft engines....227 5.8 Gasturbineengineoperation...231 5.9 Propellerperformance...236 Bibliography...251 6 Aeroplane Performance...253 6.1 Introduction......253 6.2 Airspeed and altitude...258 6.3 Equations of motion for symmetric flight....260 6.4 Steadystraightandlevelflight...265 6.5 Climb and descent....279 6.6 Glidingflight...288 6.7 Cruisingflight...292 6.8 Take-offandlanding...302 6.9 Horizontalsteadyturn...314 6.10Manoeuvreandgustloads...319 Bibliography...324
Flight Physics vii 7 Stability and Control...327 7.1 Flying qualities...328 7.2 Elementaryconceptsanddefinitions...333 7.3 Tail surfaces and flight control....342 7.4 Pitchingmomentofaerofoils...349 7.5 Static longitudinal stability...358 7.6 Dynamic longitudinal stability....368 7.7 Longitudinalcontrol...371 7.8 Static lateral stability...384 7.9 Dynamic lateral stability...388 7.10Lateralcontrol...391 7.11 Stalling and spinning...395 Bibliography...401 8 Helicopter Flight Mechanics...405 8.1 Helicoptergeneralarrangements...406 8.2 Hoveringflight...408 8.3 Therotorinlevelflight...413 8.4 Flightperformance...417 8.5 Stability and control...422 Bibliography...429 9 High-Speed Flight...431 9.1 Complications due to the compressibility of air....431 9.2 Compressible flow relationships...436 9.3 Speed of sound and Mach number...441 9.4 Flowinachannel...446 9.5 Shockwavesandexpansionflows...450 9.6 High-subsonicspeed...460 9.7 Transonicspeed...468 9.8 Supersonicspeed...476 9.9 Supersonic propulsion...488 9.10Performanceandoperation...496 Bibliography...509 A Units and Dimensions...511 B Principles of Aerostatics...517 Index...523
Preface Knowledge is not merely everything we have come to know, but also ideas we have pondered long enough to know in which way they are related, and how these ideas can be put to practical use. 1 Modern aviation has been made possible as a result of much scientific research. However, the very first useful results of this research became available a considerable length of time after the aviation pioneers had made their first flights. Apparently, researchers were not able to find an adequate explanation for the occurrence of lift until the beginning of the 21st century. Also, for the fundamentals of stability and control, there was no theory available that the pioneers could rely on. Only after the first motorized flights had been successfully made did researchers become more interested in the science of aviation, which from then on began to take shape. In modern day life, many millions of passengers are transported every year by air. People in the western societies take to the skies, on average, several times a year. Especially in areas surrounding busy airports, travel by plane has been on the rise since the end of the Second World War. Despite becoming familiar with the sight of a jumbo jet commencing its flight once or twice a day, many find it astonishing that such a colossus with a mass of several hundred thousands of kilograms can actually lift off from the ground. It will then climb to over 10 kilometres altitude within half an hour, maintain a cruising speed of about 900 km/h for several hours, and evidently it costs the crew little or no effort to keep this aerial giant under control. Obviously, it is impossible to unravel this mystery in just a few well-formulated sentences or mathematical expressions. 1 Free citation of the German philosopher Georg Christoph Lichtenberg (1742 1799). ix
x Preface This book focuses on readers with a deeper interest in aerospace technology, who specifically seek insight into the movement of an aircraft through the atmosphere. The book is an expansion of lecture material for freshmen studying Aerospace Engineering at the Technical University of Delft in the Netherlands, who have been taught by both authors in the period 1970 to 2000. The subjects selected are appropriate to an introductory course for those participating in higher education in aerospace technology, also giving the lecturer the means of compiling an examination. The material selected is considered essential for students with the ambition to be active in aircraft design and development. The book can also serve as an orientation for those who are still considering studying aerospace engineering. The level of abstraction is appropriate to an introductory course in bachelor s as well as master s studies, the contents being in tune with the knowledge and ability of high-school graduates. Moreover, this book addresses those in some specific employment in the aviation world and who would like to orientate themselves in subjects not necessarily belonging to their area of expertise. The authors also hope to spark the interest of readers not necessarily involved with aviation professionally, but who seek to enrich their knowledge on the fascinating subject of flight physics. After all, aviation is a very rewarding field of study that is still in full development, captivating many people. For the title of this book, the terminology Flight Physics has been chosen. These words best indicate the primary disciplines and technology concerned with aeronautics, that is, applications to aircraft flight of aerodynamics, propulsion, performance, stability and control. The term flight mechanics is used for the combination of aircraft performance, stability and control. The essential elements of aeronautics will be discussed in later chapters. These will be preceded by a bird s eye view of the historical development of aviation and various basic aspects of flight physics, including properties of the atmosphere which have a great influence on the airflow around a moving aircraft and on its propulsion. This book is a translation into English of a book originally written in the Dutch language. Some attention is, therefore, paid to remarkable contributions to aeronautical research and development in the Netherlands that is not found in international textbooks and considered to be of general interest. The order in which the chapters in this book are set out is based on the practical side of the topic being considered of greater interest for a first introduction
Flight Physics xi than the theoretical side. The authors have tried to limit the depth of the material as far as possible without falling into the trap of oversimplification. Formulas and their derivation are explained without presenting unnecessary information, aiming for a broad insight into the physics of flight. To keep the teaching material sufficiently elementary, the first chapters concentrate on flight at (relatively) low airspeed, at which the compressibility of air does not have significant influence on aerodynamic characteristics. This is mostly the case with propeller aircraft and helicopters, but also jet-propelled aircraft have to operate satisfactorily in this airspeed regime. However, because most jet aircraft can reach higher speeds some can even exceed the velocity of sound the last chapter has been dedicated to complications that can be expected in high-speed flight. The flight dynamics treated pertains to aeroplanes that is, fixed-wing aircraft with the exception of a chapter dedicated to helicopter flight mechanics. Advancements in flight physics often take place at a high level of abstraction in particular aerodynamics is known as a difficult scientific discipline. Moreover, the different disciplines are highly interrelated, and many topics appear in several chapters. In the interest of good legibility, derivations and the results thereof presented in earlier or subsequent chapters are not always referred to again. In coping with this, the reader will find some assistance in an extensive index of essential terminology typeset in italics. As a stimulus for further reading, there is a fairly comprehensive bibliography at the end of each chapter referring to (mainly) recently issued books. General books dealing with aeronautics and aircraft design are listed at the end of the second chapter, references to aerodynamics are spread over the third, fourth and ninth chapter. Subjects discussed in this book are often indirectly related to several other disciplines of aeronautics. Specifically, these entail the study of aircraft structures and materials, manufacture and production engineering, instruments and avionics, control systems engineering, aircraft operation, and aircraft conceptual design. For many of these specializations, knowledge of the presented material will be useful, and sometimes even indispensable. For example, it is impossible to compute the loads acting on a wing structure under design without any knowledge of aerodynamics. The interdisciplinary character of aeronautical technology is certainly a complication in digesting the presented material, but hopefully many readers will experience this as an interesting challenge. The authors of the original book in Dutch have tried for many years to give their students a clear insight in the most essential aspects of flight physics and aircraft design. It is regrettable that the second author did not live to enjoy the
xii Preface completion of this translation. He was a man with extensive knowledge about and deep insight into flight physics. The present author is greatly indebted to him for his teaching of the principles that have made aviation possible, and that have come into full fruition during the second half of the 20th century. It is hoped that the reader of this book will be able to contribute to this endeavor in the 21st century. Delft, December 2008 E. Torenbeek