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FIFI'H EDITION L E. LoH oughton PW Carpenter Aerodynamics for Engineering Students Frontispiece (see overleaf) Aircraft wake (photo courtesy of Cessna Aircraft Company). This photograph first appeared in the Gallery of Fluid Motion, Physics of Fluids (published by the American Institute of Physics), Vol. 5, No. 9, Sept. 1993, p. S5, and was submitted by Professor Hiroshi Higuchi (Syracuse University). It shows the wake created by a Cessna Citation VI flown immediately above the fog bank over Lake Tahoe at approximately 313 km/h. Aircraft altitude was about 122 m above the lake, and its mass was approximately 8400 kg. The downwash caused the trailing vortices to descend over the fog layer and disturb it to make the flow field in the wake visible. The photograph was taken by P. Bowen for the Cessna Aircraft Company from the tail gunner’s position in a B-25 flying slightly above and ahead of the Cessna. Aerodynamics for Engineering Students Fifth Edition E.L. Houghton and P.W. Carpenter Professor of Mechanical Engineering, The University of Warwick ! E I N E M A N N OXFORD AMSTERDAM BOSTON LONDON NEW YORK PARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO Butterworth-Heinemann An imprint of Elsevier Science Linacre House, Jordan Hill, Oxford OX2 8DP 200 Wheeler Rd, Burlington MA 01803 First published in Great Britain 1960 Fourth edition published in 1993 by Edward Arnold Fifth edition published by Butterworth-Heinemann 2003 Copyright 0 2003, E.L. Houghton and P.W. Carpenter. All rights reserved The right of E.L. Houghton and P.W. Carpenter to be identified as the authors of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988 No part of this publication may be reproduced in any material form (including photocopying or storing in any medium by electronic means and whether or not transiently or incidentally to some other use of this publication) without the written permission of the copyright holder except in accordance with the provisions of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London, England W1T 4LP. Applications for the copyright holder’s written permission to reproduce any part of this publication should be addressed to the publisher British Library Cataloguing in Publication Data Houghton, E.L. (Edward Lewis) Aerodynamics for engineering students. - 5th ed. 1 Aerodynamics I Title I1 Carpenter, P.W. 629.1’323 Library of Congress Cataloguing in Publication Data Houghton, E.L. (Edward Lewis) Aerodynamics for engineering students / E.L. Houghton and P.W. Carpenter. - 5th ed. p. cm. Includes index. ISBN 0 7506 51 11 3 1 Aerodynamics 2 Airplanes-Design and construction I Carpenter, P.W. (Peter William), 1942- I1 Title. TL570 .H587 2002 629.132’3-dc21 2002029945 ISBN 0 7506 5111 3 - For information on all Butterworth-Heinemann publications visit our website at www.bh.com Contents ... Preface xlll 1 Basic concepts and defdtions 1 Preamble 1 1.1 Units and dimensions 1 1.1.1 Fundamental dimensions and units 2 1.1.2 Fractions and multiples 2 1.1.3 Units of other physical quantities 3 1.1.4 Imperial units 4 1.2 Relevant properties 4 1.2.1 Forms of matter 4 1.2.2 Fluids 5 1.2.3 Pressure 5 1.2.4 Temperature 8 1.2.5 Density 8 1.2.6 Viscosity 8 1.2.7 Speed of sound and bulk elasticity 10 1.2.8 Thermodynamic properties 11 1.3 Aeronautical definitions 15 1.3.1 Wing geometry 15 1.3.2 Aerofoil geometry 17 1.4 Dimensional analysis 19 1.4.1 Fundamental principles 19 1.4.2 Dimensional analysis applied to aerodynamic force 22 1.5 Basic aerodynamics 26 1.5.1 Aerodynamic force and moment 26 1.5.2 Force and moment coefficients 28 1.5.3 Pressure distribution on an aerofoil 29 1S .4 Pitching moment 30 1.5.5 Types of drag 35 1.5.6 Estimation of the coefficients of lift, drag and pitching moment from the pressure distribution 38 1.5.7 Induced drag 41 1.5.8 Lift-dependent drag 44 1S .9 Aerofoil characteristics 44 Exercises 50 vi Contents 2 Governing equations of fluid mechanics 52 Preamble 52 2.1 Introduction 52 2.1.1 Air flow 53 2.1.2 A comparison of steady and unsteady flow 54 2.2 One-dimensional flow: the basic equations 56 2.2.1 One-dimensional flow: the basic equations of conservation 56 2.2.2 Comments on the momentum and energy equations 62 2.3 The measurement of air speed 62 2.3.1 The Pit&-static tube 62 2.3.2 The pressure coefficient 64 2.3.3 The air-speed indicator: indicated and equivalent air speeds 64 2.3.4 The incompressibility assumption 66 2.4 Two-dimensional flow 68 2.4.1 Component velocities 68 2.4.2 The equation of continuity or conservation of mass 71 2.4.3 The equation of continuity in polar coordinates 72 2.5 The stream function and streamline 73 2.5.1 The stream function 11, 73 2.5.2 The streamline 75 2.5.3 Velocity components in terms of 11, 76 2.6 The momentum equation 78 2.6.1 The Euler equations 83 2.7 Rates of strain, rotational flow and vorticity 83 2.7.1 Distortion of fluid element in flow field 83 2.7.2 Rate of shear strain 84 2.7.3 Rate of direct strain 85 2.1.4 Vorticity 86 2.7.5 Vorticity in polar coordinates 86 2.7.6 Rotational and irrotational flow 87 2.7.7 Circulation 87 2.8 The Navier-Stokes equations 89 2.8.1 Relationship between rates of strain and viscous stresses 89 2.8.2 The derivation of the Navier-Stokes equations 91 2.9 Properties of the Navier-Stokes equations 91 2.10 Exact solutions of the Navier-Stokes equations 95 2.10.1 Couette flow - simple shear flow 95 2.10.2 Plane Poiseuille flow - pressure-driven channel flow 96 2.10.3 Hiemenz flow - two-dimensional stagnation-point flow 97 Exercises 101 3 Potentialflow 104 Preamble 104 3.1 Introduction 104 3.1.1 The velocity potential 105 3.1.2 The equipotential 106 3.1.3 Velocity components in terms of q5 107 3.2 Laplace’s equation 109 3.3 Standard flows in terms of 11, and q5 110 3.3.1 Two-dimensional flow from a source (or towards a sink) 110 3.3.2 Line (point) vortex 112 Conbnts vii 3.3.3 Uniform flow 114 3.3.4 Solid boundaries and image systems 118 3.3.5 A source in a uniform horizontal stream 119 3.3.6 Source-sink pair 122 3.3.7 A source set upstream of an equal sink in a uniform stream 125 3.3.8 Doublet 126 3.3.9 Flow around a circular cylinder given by a doublet in a uniform horizontal flow 129 3.3.10 A spinning cylinder in a uniform flow 133 3.3.1 1 Bernoulli’s equation for rotational flow 136 3.4 Axisymmetric flows (inviscid and incompressible flows) 137 3.4.1 Cylindrical coordinate system 137 3.4.2 Spherical coordinates 138 3.4.3 Axisymmetric flow from a point source (or towards a point sink) 139 3.4.4 Point source and sink in a uniform axisymmetric flow 140 3.4.5 The point doublet and the potential flow around a sphere 142 3.4.6 Flow around slender bodies 144 3.5 Computational (panel) methods 147 A computational routine in FORTRAN 77 152 Exercises 155 4 Two-dimensional wing theory 159 Preamble 159 4.1 Introduction 159 4.1.1 The Kutta condition 160 4.1.2 Circulation and vorticity 162 4.1.3 Circulation and lift (Kutta-Zhukovsky theorem) 167 4.2 The development of aerofoil theory 169 4.3 The general thin aerofoil theory 171 4.4 The solution of the general equation 176 4.4.1 The thin symmetrical flat plate aerofoil 177 4.4.2 The general thin aerofoil section 178 4.5 The flapped aerofoil 1a 2 4.5.1 The hinge moment coefficient I a4 4.6 The jet flap 185 4.7 The normal force and pitching moment derivatives due to pitching 186 4.7.1 (Zq)(Mqw) ing contributions 186 4.8 Particular camber lines 190 4.8.1 Cubic camber lines 190 4.8.2 The NACA four-digit wing sections 193 4.9 Thickness problem for thin-aerofoil theory 196 4.9.1 The thickness problem for thin aerofoils 197 4.10 Computational (panel) methods for two-dimensional lifting flows 200 Exercises 207 5 Finite wing theory 210 Preamble 210 5.1 The vortex system 211 5.1.1 The starting vortex 211 5.1.2 The trailing vortex system 212