P1: JSN/FIO P2: JSN/UKS QC: JSN/UKS T1: JSN CB329-FM CB329/Katz October 3, 2000 15:18 Char Count= 0 Low-Speed Aerodynamics, Second Edition Low-speed aerodynamics is important in the design and operation of aircraft fly- ing at low Mach number and of ground and marine vehicles. This book offers a modern treatment of the subject, both the theory of inviscid, incompressible, and irrotational aerodynamics and the computational techniques now available to solve complex problems. A unique feature of the text is that the computational approach (from a single vortex element to a three-dimensional panel formulation) is interwoven throughout. Thus, the reader can learn about classical methods of the past, while also learning how to use numerical methods to solve real-world aerodynamic problems. This second edition, updates the first edition with a new chapter on the laminar boundary layer, the latest versions of computational techniques, and additional coverage of interaction problems. It includes a systematic treatment of two-dimensional panel methods and a detailed presentation of computational techniques for three- dimensional and unsteady flows. With extensive illustrations and examples, this book will be useful for senior and beginning graduate-level courses, as well as a helpful reference tool for practicing engineers. Joseph Katz is Professor of Aerospace Engineering and Engineering Mechanics at San Diego State University. Allen Plotkin is Professor of Aerospace Engineering and Engineering Mechanics at San Diego State University. i P1: JSN/FIO P2: JSN/UKS QC: JSN/UKS T1: JSN CB329-FM CB329/Katz October 3, 2000 15:18 Char Count= 0 ii P1: JSN/FIO P2: JSN/UKS QC: JSN/UKS T1: JSN CB329-FM CB329/Katz October 3, 2000 15:18 Char Count= 0 Cambridge Aerospace Series Editors: MICHAEL J. RYCROFT AND WEI SHYY 1. J. M. Rolfe and K. J. Staples (eds.): Flight Simulation 2. P. Berlin: The Geostationary Applications Satellite 3. M. J. T. Smith: Aircraft Noise 4. N. X. Vinh: Flight Mechanics of High-Performance Aircraft 5. W. A. Mair and D. L. Birdsall: Aircraft Performance 6. M. J. Abzug and E. E. Larrabee: Airplane Stability and Control 7. M. J. Sidi: Spacecraft Dynamics and Control 8. J. D. Anderson: A History of Aerodynamics 9. A. M. Cruise, J. A. Bowles, C. V.Goodall, and T. J. Patrick: Principles of Space Instrument Design 10. G. A. Khoury and J. D. Gillett (eds.): Airship Technology 11. J. Fielding: Introduction to Aircraft Design 12. J. G. Leishman: Principles of Helicopter Aerodynamics 13. J. Katz and A. Plotkin: Low Speed Aerodynamics, Second Edition iii P1: JSN/FIO P2: JSN/UKS QC: JSN/UKS T1: JSN CB329-FM CB329/Katz October 3, 2000 15:18 Char Count= 0 iv P1: JSN/FIO P2: JSN/UKS QC: JSN/UKS T1: JSN CB329-FM CB329/Katz October 3, 2000 15:18 Char Count= 0 Low-Speed Aerodynamics Second Edition JOSEPH KATZ San Diego State University ALLEN PLOTKIN San Diego State University v CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo, Delhi, Dubai, Tokyo, Mexico City Cambridge University Press 32 Avenue of the Americas, New York, NY 10013-2473, USA www.cambridge.org Information on this title: www.cambridge.org/9780521665520 © Cambridge University Press 2001 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2001 10th printing 2010 A catalog record for this publication is available from the British Library. Library of Congress Cataloging in Publication Data Katz, Joseph, 1947– Low-speed aerodynamics / Joseph Katz, Allen Plotkin. – 2nd ed. p. cm. – (Cambridge aerospace series : 13) ISBN 0-521-66219-2 1. Aerodynamics. I. Plotkin, Allen. II. Title. III. Series. TL570 .K34 2000 629.132'3 – dc21 00-031270 ISBN 978-0-521-66219-2 Hardback ISBN 978-0-521-66552-0 Paperback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party Internet Web sites referred to in this publication and does not guarantee that any content on such Web sites is, or will remain, accurate or appropriate. P1: JSN/FIO P2: JSN/UKS QC: JSN/UKS T1: JSN CB329-FM CB329/Katz October 3, 2000 15:18 Char Count= 0 Contents Preface page xiii Preface to the First Edition xv 1 Introduction and Background 1 1.1 Description of Fluid Motion 1 1.2 Choice of Coordinate System 2 1.3 Pathlines, Streak Lines, and Streamlines 3 1.4 Forces in a Fluid 4 1.5 Integral Form of the Fluid Dynamic Equations 6 1.6 Differential Form of the Fluid Dynamic Equations 8 1.7 Dimensional Analysis of the Fluid Dynamic Equations 14 1.8 Flow with High Reynolds Number 17 1.9 Similarity of Flows 19 2 Fundamentals of Inviscid, Incompressible Flow 21 2.1 Angular Velocity, Vorticity, and Circulation 21 2.2 Rate of Change of Vorticity 24 2.3 Rate of Change of Circulation: Kelvin’s Theorem 25 2.4 Irrotational Flow and the Velocity Potential 26 2.5 Boundary and Infinity Conditions 27 2.6 Bernoulli’s Equation for the Pressure 28 2.7 Simply and Multiply Connected Regions 29 2.8 Uniqueness of the Solution 30 2.9 Vortex Quantities 32 2.10 Two-Dimensional Vortex 34 2.11 The Biot–Savart Law 36 2.12 The Velocity Induced by a Straight Vortex Segment 38 2.13 The Stream Function 41 3 General Solution of the Incompressible, Potential Flow Equations 44 3.1 Statement of the Potential Flow Problem 44 3.2 The General Solution, Based on Green’s Identity 44 3.3 Summary: Methodology of Solution 48 3.4 Basic Solution: Point Source 49 3.5 Basic Solution: Point Doublet 51 3.6 Basic Solution: Polynomials 54 3.7 Two-Dimensional Version of the Basic Solutions 56 3.8 Basic Solution: Vortex 58 3.9 Principle of Superposition 60 vii P1: JSN/FIO P2: JSN/UKS QC: JSN/UKS T1: JSN CB329-FM CB329/Katz October 3, 2000 15:18 Char Count= 0 viii Contents 3.10 Superposition of Sources and Free Stream: Rankine’s Oval 60 3.11 Superposition of Doublet and Free Stream: Flow around a Cylinder 62 3.12 Superposition of a Three-Dimensional Doublet and Free Stream: Flow around a Sphere 67 3.13 Some Remarks about the Flow over the Cylinder and the Sphere 69 3.14 Surface Distribution of the Basic Solutions 70 4 Small-Disturbance Flow over Three-Dimensional Wings: Formulation of the Problem 75 4.1 Definition of the Problem 75 4.2 The Boundary Condition on the Wing 76 4.3 Separation of the Thickness and the Lifting Problems 78 4.4 Symmetric Wing with Nonzero Thickness at Zero Angle of Attack 79 4.5 Zero-Thickness Cambered Wing at Angle of Attack–Lifting Surfaces 82 4.6 The Aerodynamic Loads 85 4.7 The Vortex Wake 88 4.8 Linearized Theory of Small-Disturbance Compressible Flow 90 5 Small-Disturbance Flow over Two-Dimensional Airfoils 94 5.1 Symmetric Airfoil with Nonzero Thickness at Zero Angle of Attack 94 5.2 Zero-Thickness Airfoil at Angle of Attack 100 5.3 Classical Solution of the Lifting Problem 104 5.4 Aerodynamic Forces and Moments on a Thin Airfoil 106 5.5 The Lumped-Vortex Element 114 5.6 Summary and Conclusions from Thin Airfoil Theory 120 6 Exact Solutions with Complex Variables 122 6.1 Summary of Complex Variable Theory 122 6.2 The Complex Potential 125 6.3 Simple Examples 126 6.3.1 Uniform Stream and Singular Solutions 126 6.3.2 Flow in a Corner 127 6.4 Blasius Formula, Kutta–Joukowski Theorem 128 6.5 Conformal Mapping and the Joukowski Transformation 128 6.5.1 Flat Plate Airfoil 130 6.5.2 Leading-Edge Suction 131 6.5.3 Flow Normal to a Flat Plate 133 6.5.4 Circular Arc Airfoil 134 6.5.5 Symmetric Joukowski Airfoil 135 6.6 Airfoil with Finite Trailing-Edge Angle 137 6.7 Summary of Pressure Distributions for Exact Airfoil Solutions 138 6.8 Method of Images 141 6.9 Generalized Kutta–Joukowski Theorem 146 7 Perturbation Methods 151 7.1 Thin-Airfoil Problem 151 7.2 Second-Order Solution 154 7.3 Leading-Edge Solution 157 P1: JSN/FIO P2: JSN/UKS QC: JSN/UKS T1: JSN CB329-FM CB329/Katz October 3, 2000 15:18 Char Count= 0 Contents ix 7.4 Matched Asymptotic Expansions 160 7.5 Thin Airfoil between Wind Tunnel Walls 163 8 Three-Dimensional Small-Disturbance Solutions 167 8.1 Finite Wing: The Lifting Line Model 167 8.1.1 Definition of the Problem 167 8.1.2 The Lifting-Line Model 168 8.1.3 The Aerodynamic Loads 172 8.1.4 The Elliptic Lift Distribution 173 8.1.5 General Spanwise Circulation Distribution 178 8.1.6 Twisted Elliptic Wing 181 8.1.7 Conclusions from Lifting-Line Theory 183 8.2 Slender Wing Theory 184 8.2.1 Definition of the Problem 184 8.2.2 Solution of the Flow over Slender Pointed Wings 186 8.2.3 The Method of R. T. Jones 192 8.2.4 Conclusions from Slender Wing Theory 194 8.3 Slender Body Theory 195 8.3.1 Axisymmetric Longitudinal Flow Past a Slender Body of Revolution 196 8.3.2 Transverse Flow Past a Slender Body of Revolution 198 8.3.3 Pressure and Force Information 199 8.3.4 Conclusions from Slender Body Theory 201 8.4 Far Field Calculation of Induced Drag 201 9 Numerical (Panel) Methods 206 9.1 Basic Formulation 206 9.2 The Boundary Conditions 207 9.3 Physical Considerations 209 9.4 Reduction of the Problem to a Set of Linear Algebraic Equations 213 9.5 Aerodynamic Loads 216 9.6 Preliminary Considerations, Prior to Establishing Numerical Solutions 217 9.7 Steps toward Constructing a Numerical Solution 220 9.8 Example: Solution of Thin Airfoil with the Lumped-Vortex Element 222 9.9 Accounting for Effects of Compressibility and Viscosity 226 10 Singularity Elements and Influence Coefficients 230 10.1 Two-Dimensional Point Singularity Elements 230 10.1.1 Two-Dimensional