Table Of ContentIntroduction to Aircraft Flight Mechanics:
Performance, 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
with
Steven L. Morris
David E. Bossert
Wayne F. Hallgren
EDUCATION SERIES
Joseph A. Schetz
Series Editor-in-Chief
Virginia Polytechnic Institute and State University
Blacksburg, Virginia
Published by
American Institute of Aeronautics and Astronautics, Inc.
1801 Alexander Bell Drive, Reston, VA 20191-4344
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
Editor-in-Chief
Joseph A. Schetz
Virginia Polytechnic Institute and State University
Editorial Board
Daniel J. Biezad
California Polytechnic State
University
Aaron R. Byerley
U.S. Air Force Academy
Kajal K. Gupta
NASA Dryden Flight Research
Center
John K. Harvey
Imperial College
David K. Holger
Iowa State University
Rakesk K. Kapania
Virginia Polytechnic Institute and
State University
Brian Landrum
University of Alabama,
Huntsville
Robert G. Loewy
Georgia Institute of Technology
Michael Mohaghegh
The Boeing Company
Dora Musielak
Northrop Grumman Corporation
Conrad F. Newberry
Naval Postgraduate School
David K. Schmidt
University of Colorado,
Colorado Springs
Peter Turchi
Los Alamos National Laboratory
David M. Van Wie
Johns Hopkins University
This page intentionally left blank
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
This page intentionally left blank
Table of
Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xiii
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xv
Chapter 1
A Review of Basic Aerodynamics . . . . . . . . . . . . . . . . .
1
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
1.6
Historical Snapshot—The AC-130H Drag Reduction
Effort . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
55
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
56
Chapter 2
A Review of Basic Propulsion . . . . . . . . . . . . . . . . . . .
59
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
Chapter 3
Aircraft Performance . . . . . . . . . . . . . . . . . . . . . . . . .
81
3.1
Airspeed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
81
3.2
Equations of Motion for Straight, Level, and Unaccelerated
Flight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
85
3.3
Thrust and Power Curves . . . . . . . . . . . . . . . . . . . . . . . . . .
87
3.4
Takeoff and Landing Performance . . . . . . . . . . . . . . . . . . . .
91
3.5
Gliding Fight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
102
3.6
Climbs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
108
3.7
Endurance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
110
3.8
Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
116
3.9
Turn Performance and V-n Diagrams. . . . . . . . . . . . . . . . . . .
127
3.10
Historical Snapshot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
135
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
140
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
140
ix
Chapter 4
Aircraft Equations of Motion . . . . . . . . . . . . . . . . . . .
145
4.1
Aircraft Axis Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
145
4.2
Coordinate Transformations . . . . . . . . . . . . . . . . . . . . . . . . .
147
4.3
Aircraft Force Equations . . . . . . . . . . . . . . . . . . . . . . . . . . .
153
4.4
Moment Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
155
4.5
Longitudinal and Lateral-Directional Equations of Motion . . . . .
164
4.6
Kinematic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
164
4.7
Historical Snapshot—Genesis 2000 Flight Simulator. . . . . . . . .
169
Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
170
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
170
Chapter 5
Aircraft Static Stability . . . . . . . . . . . . . . . . . . . . . . . .
173
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
Chapter 6
Linearizing the Equations of Motion . . . . . . . . . . . . . .
239
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
6.4
First-Order Approximation of Perturbed Thrust Forces and
Moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
279
6.5
Recasting the Equations of Motion in Acceleration
Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
285
6.6
Historical Snapshot—The X-38 Parafoil Cavity
Investigation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
291
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
296
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
296
Chapter 7
Aircraft Dynamic Stability . . . . . . . . . . . . . . . . . . . . .
303
7.1
Mass-Spring-Damper System and Classical Solutions of
Ordinary Differential Equations. . . . . . . . . . . . . . . . . . . . . . .
303
7.2
Root Representation Using the Complex Plane . . . . . . . . . . . .
316
7.3
Transforming the Linearized EOM to the Laplace
Domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
321
x
TABLE OF CONTENTS
7.4
Dyanmic Stability Guidelines . . . . . . . . . . . . . . . . . . . . . . . .
356
7.5
Cooper–Harper Ratings . . . . . . . . . . . . . . . . . . . . . . . . . . . .
371
7.6
Experimental Determination of Second-Order Parameters . . . . .
372
7.7
Historical Snapshot—The A-10A Prototype Flight
Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
377
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
380
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
380
Chapter 8
Classical Feedback Control . . . . . . . . . . . . . . . . . . . . .
389
8.1
Open-Loop Systems, Transfer Functions, and Block Diagrams . .
389
8.2
Closed-Loop Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
392
8.3
Closed-Loop Analysis of a Second-Order System. . . . . . . . . . .
394
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
Chapter 9
Aircraft Stability and Control Augmentation. . . . . . . . .
433
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
9.5
Historical Snapshot—The A-7D DIGITAC Digital
Multimode Flight Control System Program . . . . . . . . . . . . . . .
463
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
469
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
469
Chapter 10
Special Topics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
473
10.1
System Type and Steady-State Error. . . . . . . . . . . . . . . . . . .
473
10.2
Frequency Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
492
10.3
Digital Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
544
10.4
Advanced Control Algorithms . . . . . . . . . . . . . . . . . . . . . . .
549
10.5
Reversible and Irreversible Flight Control Systems . . . . . . . . .
551
10.6
Spins. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
554
10.7
Historical Snapshot—The F-16 Fly-by-Wire System . . . . . . . .
558
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
567
Appendix A
Conversions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
571
Appendix B
Properties of the U.S. Standard Atmosphere. . . . . . . .
573
Appendix C
Airfoil Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
577
Appendix D
T-38 Performance Data . . . . . . . . . . . . . . . . . . . . . .
589
TABLE OF CONTENTS
xi
Appendix E
Selected Laplace Transforms. . . . . . . . . . . . . . . . . . .
603
Appendix F
Cramer’s Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
605
Appendix G
Development of Longitudinal and Lateral-Directional
Transfer Functions . . . . . . . . . . . . . . . . . . . . . . . . .
609
Appendix H
Stability Characteristics of Selected Aircraft . . . . . . .
613
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
623
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
625
Series listing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
631
xii
TABLE OF CONTENTS
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
This page intentionally left blank
