Introduction to Aircraft Flight Dynamics

410 Pages·1998·14.59 MB·English

by  Louis V. Schmidt

Introduction to
Aircraft Flight Dynamics
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Introduction to
Aircraft Flight Dynamics
Louis V. Schmidt
Naval Postgraduate School
Monterey, California
4A1AA
EDUCATION SERIES
J. S. Przemieniecki
Series Editor-in-Chief
Air Force Institute of Technology
Wright-Patterson Air Force Base, Ohio
Published by
American Institute of Aeronautics and Astronautics, Inc.
1801 Alexander Bell Drive, Reston, VA 20191
American Institute of Aeronautics and Astronautics, Inc., Reston, Virginia
Library of Congress Cataloging-in-Publication Data
Schmidt, Louis V.
Introduction to Aircraft Flight Dynamics / Louis V. Schmidt
p. cm.—(AIAA education series)
Includes bibliographical references and index.
ISBN 1-56347-226-0 (alk. paper)
1. Aerodynamics. 2. Stability of airplanes. I. Title. II. Series.
TL570.S33 1998
629.132'3—DC21 97-20180
CIP
Copyright © 1998 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
Printed in the United States. No part of this publication may be reproduced, distributed, or transmitted,
in any form or by any means, or stored in a database or retrieval system, without the prior written
permission of the publisher.
Data and information appearing in this book are for informational purposes only. AIAA is not re-
sponsible for any injury or damage resulting from use or reliance, nor does AIAA warrant that use or
reliance will be free from privately owned rights.
MATLAB™ is a registered trademark of The Math Works, Inc.
Foreword
Introduction to Aircraft Flight Dynamics by Louis V. Schmidt is a comprehensive
textbook that incorporates the latest theories and concepts used in the analysis
and design of modern aircraft. The text evolved over a number of years, and it
reflects the author's extensive knowledge of the subject and his practical experience
initially as an engineer with the U.S. Navy and then as a professor while teaching
the subject matter at the Naval Postgraduate School, Monterey, California.
The first four chapters provide an introduction to the basic definitions, stability
derivatives, and static stability and control, followed by the formulation of the
equations of motion for the airframe as a dynamic system (Chapters 1 through 4).
Chapter 5 discusses the mathematical principles used to analyze the dynamics of
the whole system, including its stability. Chapters 6 and 7 deal with the longitudinal
and lateral-directional dynamics, while Chapter 8 deals with the nonlinear dynam-
ics involved in inertial cross coupling, wing rock, and stall dynamics. Chapter 9
provides an introduction to atmospheric turbulence and to aircraft response due
to random gusts. Several appendices provide useful supplementary information
on atmospheric properties, aircraft stability derivatives, span load program, linear
algebra principles, and the usage of MATLAB™ programs. A very useful feature
of this text is the extensive use of MATLAB software in conjunction with personal
desktop computers.
The Education Series of textbooks and monographs published by the American
Institute of Aeronautics and Astronautics embraces a broad spectrum of theory
and application of different disciplines in aeronautics and astronautics, includ-
ing aerospace design practice. The series also includes texts on defense science,
engineering, and management. The complete list of textbooks published in the
series (more than 50 titles) can be found after the Index. The series serves as
teaching texts as well as reference materials for practicing engineers, scientists,
and managers.
J. S. Przemieniecki
Editor-in-Chief
AIAA Education Series
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Table of
Contents
Preface ................................................xi
Chapter 1. Introduction ................................... 1
1.1 Background ....................................... 1
1.2 Definitions ........................................ 1
1.3 Coordinate Transformations............................. 7
1.4 Wing Properties ..................................... 8
1.5 Dimensions and Units ................................ 11
References ....................................... 12
Problems ........................................ 12
Chapter 2. Aerodynamic Principles ......................... 15
2.1 Background ...................................... 15
2.2 Longitudinal Stability Derivatives ........................ 17
2.3 Lateral-Directional Stability Derivatives ................... 29
2.4 Wing Theory ...................................... 46
2.5 Stability Derivatives Using Wing Theory ................... 56
References ....................................... 62
Problems ........................................ 63
Chapter 3. Static Stability and Control ....................... 67
3.1 Background ...................................... 67
3.2 Longitudinal Stability and Control ....................... 67
3.3 Lateral-Directional Stability and Control ................... 83
References ....................................... 90
Problems ........................................ 90
Chapter 4. Airframe Equations of Motion ..................... 93
4.1 Background ...................................... 93
4.2 Euler Angle Transformations ........................... 93
4.3 Rotation of a Rigid Body............................. 100
4.4 Airframe Equations of Motion ......................... 107
4.5 Linearized Equations of Motion ........................ 107
4.6 Matrix Formulation of the Equations of Motion ............. 110
References ...................................... 118
Problems ....................................... 118
Chapter 5. Dynamic System Principles ...................... 119
5.1 Background ..................................... 119
5.2 Laplace Transforms ................................ 119
5.3 First-Order Linear System ............................ 128
VIII
5.4 Second-Order Linear System .......................... 132
5.5 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 142
5.6 State-Space Fundamentals ............................ 144
5.7 Stability in the Sense of Lyapunov ...................... 157
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 161
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 161
Chapter 6. Longitudinal Dynamics . . . . . . . . . . . . . . . . . . . . . . . .. 165
6.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 165
6.2 Aircraft Longitudinal Dynamics ........................ 166
6.3 Modal Approximations .............................. 177
6.4 Control Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 186
6.5 Maneuvering Flight ................................ 198
References ...................................... 204
Problems ....................................... 204
Chapter 7. Lateral-Directional Dynamics .................... 207
7.1 Background ..................................... 207
7.2 Pure Rolling Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 208
7.3 Lateral-Directional Dynamics ......................... 214
7.4 Control Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 223
7.5 Design Guidelines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 236
7.6 Yaw Damper for Stability Augmentation .................. 237
7.7 Controllability and Pole Placement ...................... 248
References ...................................... 254
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 254
Chapter 8. Nonlinear Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . .. 257
8.1 Background ..................................... 257
8.2 Inertia! Cross Coupling .............................. 258
8.3 Wing Rock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 265
8.4 Stall Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 275
References ...................................... 287
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 288
Chapter 9. Atmospheric Turbulence ........................ 291
9.1 Background ..................................... 291
9.2 Discrete Gust Response Solutions ....................... 293
9.3 Random Processes ................................. 302
9.4 Random Gust Response ............................. 313
9.5 Lyapunov Equation Usage for Gust Responses .............. 319
References ...................................... 329
Problems ....................................... 329
Appendix A: Atmospheric Table ............................ 331
Appendix B: Aircraft Stability Derivatives ..................... 333
B.I U.S. Navy A-4D Attack Aircraft. ....................... 334
B.2 U.S. Navy A-7A Attack Aircraft. ....................... 336
B.3 U.S. Air Force F-4C Fighter Aircraft..................... 339
B.4 McDonnell-Douglas DC-8 Jet Transport .................. 341
B.5 Convair CV-880M Jet Transport........................ 345
B.6 Lockheed Jetstar Utility Jet Transport .................... 349
B.7 North American Navion General Aviation Aircraft ........... 352
References ...................................... 354
Appendix C: Span Load Program . . . . . . . . . . . . . . . . . . . . . . . . . .. 355
C.I Aerodynamic Influence Coefficients ..................... 355
C.2 Program Listing ................................... 358
Appendix D: Linear Algebra Principles ....................... 367
D.I Linear Algebra Usage ............................... 367
D.2 Linear Algebra and Vector Concepts . . . . . . . . . . . . . . . . . . . .. 369
D.3 Eigenvalue Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 373
D.4 Orthogonality Principles ............................. 376
D.5 Diagonalization of a Square Matrix ...................... 377
D.6 Eigenvalue Problem for a Symmetric Matrix ............... 379
D.7 Eigenvalue Problem for an Unsymmetric Matrix ............. 379
D.8 Cayley-Hamilton Theorem ........................... 381
D.9 Linear Independence and Rank ........................ 383
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 384
Appendix E: Usage of MATLAB Programs . . . . . . . . . . . . . . . . . . .. 385
E.I Introductory Remarks ............................... 385
E.2 Elementary Use of MATLAB . . . . . . . . . . . . . . . . . . . . . . . . .. 385
E.3 Use of MATLAB Function Files ........................ 389
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 394
Index ............................................... 395