Introduction to Aircraft Flight Mechanics

Introduction to Aircraft Flight MechanicsPerformance, Static Stability, Dynamic Stability, and Classical Feedback Control
This page intentionally left blank
Introduction to Aircraft Flight Mechanics:
Performance, Static Stability, Dynamic Stability, and Classical Feedback Control
Thomas R. Yechout
Blacksburg, Virginia
Published by
American Institute of Aeronautics and Astronautics, Inc., Reston, Virginia
1 2 3 4 5
Library of Congress Cataloging-in-Publication Data
[CIP Data to come]
Copyright # 2003 by the American Institute of Aeronautics and Astronautics, Inc. This work was created in the performance of a Cooperative Research and Development Agreement with the Department of the Air Force. The Government of the United States has certain rights to use this work.
Data and information appearing in this book are for informational purposes only. AIAA is not responsible 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.
AIAA Education Series
Editorial Board
Foreword
Introduction to Aircraft Flight Mechanics: Performance, Static Stability, Dynamic Stability, and Classical Feedback Control by Thomas R. Yechout with Steven L. Morris, David E. Bossert, and Wayne F. Hallgren as contribu- tors, all from the Department of Aeronautics of the U.S. Air Force Academy, is an outstanding textbook for use in undergraduate aeronautical engineering curricula. The text evolved from lecture notes at the Academy and it incorpo- rates many suggestions literally from hundreds of cadets to improve its peda- gogical value. The text reflects a wealth of experience by the authors. It covers all the essential topics needed to teach performance, static and dynamic stability, and classical feedback control of the aircraft at the introductory level.
The ten chapters of this text cover the following topics: (1) Review of Basic Aerodynamics, (2) Review of Basic Propulsion, (3) Aircraft Performance, (4) Aircraft Equations of Motion, (5) Aircraft Static Stability, (6) Linearizing Equations of Motion, (7) Aircraft Dynamic Stability, (8) Classical Feedback Control, (9) Aircraft Stability and Control Augmentation, and (10) Special Topics (mainly additional analysis techniques for feedback control and the various types of aircraft flight control systems). This text should contribute greatly to the learning of the fundamental principles of flight mechanics that is the crucial requirement in any aeronautical engineering curricula.
The AIAA Education Series of textbooks and monographs, inaugurated in 1984, embraces a broad spectrum of theory and application of different disci- plines in aeronautics and astronautics, including aerospace design practice. The series also includes texts on defense science, engineering, and management. These texts serve as teaching tools as well as reference materials for practicing engineers, scientists, and managers. The complete list of textbooks published in the series can be found on the end pages of this volume.
J. S. PRZEMIENIECKI Editor-in-Chief (Retired) AIAA Education Series
vii
Table of Contents
1.1 Fundamental Concepts and Relationships . . . . . . . . . . . . . . . . 1
1.2 The Standard Atmosphere . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.3 Airfoil Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.4 Finite Wings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
1.5 Aircraft Aerodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Effort . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
2.1 Types of Propulsion Systems . . . . . . . . . . . . . . . . . . . . . . . . 59
2.2 Propulsion System Characteristics . . . . . . . . . . . . . . . . . . . . . 64
2.3 Historical Snapshot—Aircraft Performance Modeling and
the Learjet Model 35 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.1 Airspeed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Flight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.5 Gliding Fight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
3.10 Historical Snapshot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
4.1 Aircraft Axis Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
4.2 Coordinate Transformations . . . . . . . . . . . . . . . . . . . . . . . . . 147
4.4 Moment Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
4.6 Kinematic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
5.1 Static Stability Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
5.2 Stability, Control Power, and Cross-Control Derivatives,
and Control Deflection Sign Convention . . . . . . . . . . . . . . . . . 174
5.3 Longitudinal Applied Forces and Moments . . . . . . . . . . . . . . . 177
5.4 Longitudinal Static Stability . . . . . . . . . . . . . . . . . . . . . . . . . 191
5.5 Lateral-Directional Applied Forces and Moments . . . . . . . . . . . 202
5.6 Lateral-Directional Static Stability . . . . . . . . . . . . . . . . . . . . . 215
5.7 Summary of Steady-State Force and Moment Derivatives . . . . . 229
5.8 Historical Snapshot—The X-38 Mid-Rudder Investigation . . . . . 230
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
6.1 Small Perturbation Approach . . . . . . . . . . . . . . . . . . . . . . . . 239
6.2 Developing the Linearized Aircraft Equations of Motion . . . . . . 241
6.3 First-Order Approximation of Applied Aero Forces and
Moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
Moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
Investigation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
7.1 Mass-Spring-Damper System and Classical Solutions of
Ordinary Differential Equations . . . . . . . . . . . . . . . . . . . . . . . 303
Domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321
7.6 Experimental Determination of Second-Order Parameters . . . . . 372
7.7 Historical Snapshot—The A-10A Prototype Flight
Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380
8.1 Open-Loop Systems, Transfer Functions, and Block Diagrams . . 389
8.2 Closed-Loop Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392
8.4 Closed-Loop Transfer Functions . . . . . . . . . . . . . . . . . . . . . . 399
8.5 Time Response Characteristics . . . . . . . . . . . . . . . . . . . . . . . 403
8.6 Root Locus Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405
8.7 Historical Snapshot—The C-1 Autopilot . . . . . . . . . . . . . . . . . 427
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428
9.1 Inner-Loop Stability and Control . . . . . . . . . . . . . . . . . . . . . . 433
9.2 Outer-Loop Autopilot=Navigation Control . . . . . . . . . . . . . . . . 444
9.3 Compensation Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451
9.4 Combined Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457
Multimode Flight Control System Program . . . . . . . . . . . . . . . 463
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469
10.1 System Type and Steady-State Error . . . . . . . . . . . . . . . . . . . 473
10.2 Frequency Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492
10.3 Digital Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544
10.5 Reversible and Irreversible Flight Control Systems . . . . . . . . . 551
10.6 Spins. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 567
Appendix C Airfoil Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 577
Appendix D T-38 Performance Data . . . . . . . . . . . . . . . . . . . . . . 589
TABLE OF CONTENTS xi
Appendix G Development of Longitudinal and Lateral-Directional
Transfer Functions . . . . . . . . . . . . . . . . . . . . . . . . . 609
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 625
Preface
This textbook was created as a resource for teaching aircraft performance, static stability, dynamic stability, and classical feedback control as part of an undergraduate aeronautical engineering curriculum. Chapters 1 through 5 are intended for a one-semester course in performance and static stability, while Chapters 6 through 9 are intended for a sequential one-semester course in dynamic stability and feedback control. The text is intended to provide an understandable first exposure to these topics as well as a logical progression of subject matter. These courses are normally taken during the junior year follow- ing a fundamental course in aeronautics. This text in draft form was used as the course text for the first two courses in aircraft flight mechanics at the U.S. Air Force Academy during a four-year period preceding publication. The experience and student feedback obtained was used to improve and expand the text. The text was also used at the Air Force Academy for an undergraduate aeronautical engineering elective course in aircraft feedback control systems, normally taken after completion of the aircraft dynamic stability and feedback control course. Chapters 6 through 9 were covered at a fairly rapid pace and Chapter 10 provided new material and additional depth. This text may also serve as a reference for the practicing engineer.
Thomas R. Yechout January 2003
xiii
Acknowledgments
Many individuals contributed to the development of this textbook. First, I would like to thank Col. Michael L. Smith and Col. D. Neal Barlow, the past and present heads of the Department of Aeronautics at the U. S. Air Force Academy, for their encouragement and support throughout the five years required to bring this effort from concept to reality. Special thanks are due to Lt. Col. (Ret.) Steven L. Morris for his contributions to Chapters 2 and 4 and for his many years of contributing to the development of flight mechanics courses at the Air Force Academy. Thanks also to Col. (Ret.) Wayne F. Hallg- ren for his contributions to Chapters 1 and 3 and to Lt. Col. David E. Bossert for his contributions to Chapter 10. Excellent contributions and review were provided by Bill Blake and Dave Leggett of the Air Force Research Labora- tory, Flight Vehicles Directorate, Dr. Jeff Ashworth of Embry Riddle Aeronau- tical University, Dr. Dennis Bernstein of the University of Michigan, and Meredith Cawley of the AIAA staff. Thanks are also due to Lt. Col. Dave Bossert, Lt. Col. Steve Pluntze, Col. (Ret.) Gene Rose, Capt. Alex Sansone, Lt. Col. Scott Wells, and Dr. Tom Cunningham, all of the Air Force Academy Department of Aeronautics, for the time devoted to providing detailed…