Modeling and simulation of aerospace vehicle dynamics

557 Pages·2000·6.72 MB·English

by  Peter H. Zipfel

Modeling and Simulation of
Aerospace Vehicle Dynamics
Peter H. Zipfel
University of Florida
Gainesville, Florida
AIAA
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.
1081 Alexander Bell Drive, Reston, AV 20191-4344
American Institute of Aeronautics and Astronautics, Inc., Reston, Virginia
2 3 4 5
Library of Congress Cataloging-in-Publication Data
Zipfel, Peter H.
Modeling and simulation of aerospace vehicle dynamics / Peter H. Zipfel.
p. cm.--(AIAA education series)
Includes bibliographical references and index.
.1 Aerodynamics-Mathematics. .2 Airplanes-Mathematical models.
.3 Space vehicles-Dynamics-Mathematical model. I. Title. II. Series.
TL573.Z64 2000 629.132'3'0151~1c21 00-046444
ISBN 1-56347-456-5 (alk. paper)
Copyright © 2000 by the American Institute of Aeronautics and Astronautics, Inc. All
rights reserved. Printed in the United States of America. 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 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.
"To Him who sits on the throne and to the Lamb
be praise and honor and glory and power,
for ever and ever!"
Revelation 5:13b (NIV)
AIAA Education Series
Editor-in-Chief
John S. Przemieniecki
Air Force Institute of ygolonhceT (retired)
Editorial Board
Earl H. Dowell Michael L. Smith
Duke University .S.U Air Force Academy
Eric J. Jumper Peter J. Turchi
University of Notre Dame Ohio State University
Robert G. Loewy David M. Van Wie
Georgia Institute of ygolonhceT Johns Hopkins University
Michael N. Mohaghegh Anthony J. Vizzini
The Boeing Company University of Maryland
Conrad E Newberry Jerry Wallick
Naval Postgraduate School Institute for Defense Analysis
Terrence A. Weisshaar
Purdue University
Foreword
Modeling and Simulation of Aerospace elciheV Dynamics by Peter H. Zipfel is an
excellent introduction to the important subject of computer modeling and simu-
lation of dynamics of aerospace vehicles that in recent years has evolved into a
major discipline. This new discipline is used not only in the design process but also
in the development and improvement of performance and operation of civil and
military aircraft and missiles. The text is divided into two parts: Part 1 Modeling
of Flight Dynamics and Part 2 Simulation of Aerospace Vehicles. Part 1 discusses
the theoretical concepts that provide mathematical foundation for the simulation
of aerospace systems. This includes frames of reference and coordinate systems,
kinematics of translation and rotation, translational and attitude dynamics, as well
as perturbation techniques used for modeling. In Part 2 the author describes in great
detail the various types of simulations for aerospace vehicles for three-, five-, and
six-degree-of-freedom systems, including real-time simulators.
Many of the AIAA Education Series texts include now either CDs or diskettes
for computer programs, problem exercises, and any additional information. This
author has introduced a novel approach of providing an Internet service for dis-
tributing such materials directly. This additional material for the present text can
be obtained from the CADAC Web site, which can be accessed through the AIAA
home page (www.aiaa.org) by selecting Market Pulse and then Web Links, where
CADAC is listed. The advantage of this approach is obvious: it proves to be an easy
avenue for disseminating any future new or updated materials (e.g., new classroom
problems for the basic text). In writing this text, the author drew on his many years
of experience as an educator at the University of Florida and as a research scientist
with the U.S. Army and Air Force. This experience allowed him to produce an out-
standing teaching text and a practical reference book on modeling and simulation
of aerospace vehicles.
The AIAA Education Series of textbooks and monographs, inaugurated in 1984,
embraces a broad spectrum of theory and application of different disciplines in
aeronautics and astronautics, including aerospace design practice. The series also
includes texts on defense science, engineering, and management. The books serve
both as teaching texts for students and reference materials for practicing engineers,
scientists, and managers. The complete list of textbooks published in the series
(over 60 titles) can be found on the end pages of this volume.
J. S. Przemieniecki
Editor-in-Chief
AIAA Education Series
Preface
The time has come to give an account of modeling and simulation to aerospace
students and professionals. What has languished in notebooks, papers, and re-
ports should be made available to a wider audience. With modeling and sim-
ulation (M&S) penetrating technical disciplines at every level, engineers must
understand its role and be able to exploit its strength. If you aspire to acquire a
working knowledge of modeling and simulation of aerospace vehicle dynamics,
this book is for you. It approaches modeling of flight dynamics in a novel way,
covers many types of aerospace vehicles, and gives you hands-on experience with
simulations.
The genesis of this text goes back to the years when the term M&S was still
unknown. The challenges then were as great as today. Every new generation of com-
puters was pressed into service as soon as it came on line. With analog computers,
we could solve linear differential equations. Later, digital computers empowered
us to master also nonlinear differential equations. Concurrently, flight dynam-
ics evolved from Etkin's linearized equations to today's dominance of nonlinear
equations of motion.
As computers became more powerful, the tasks grew more complex. The fidelity
of models increased, the number of vehicles multiplied, and coordinate systems
abounded. In the late 1960s, as I worked on my dissertation, it became clear
that these complex models called for compact computer coding. Matrices are the
conduit, and tensors are the theoretical underpinning. Thus evolved the invariant
modeling of flight dynamics, my contribution to M&S.
In the late 1970s, I began to teach this approach at the University of Florida.
What was first called "Advanced Flight Mechanics I and Ir' became in the 1990s
"Modeling and Simulation of Aerospace Vehicles" In the meantime, as I worked
for the U.S. Army and Air Force, I had the opportunity to apply these techniques
to rockets, missiles, aircraft, and spacecraft.
Thus matured the two tracks of this book: invariant modeling of flight dynamics
and computer simulations of aerospace vehicles theory and praxis. The first part
lays out the mathematical foundation of modeling with Cartesian tensors, matrices,
and coordinate systems. Replacing the ordinary time derivative with the rotational
time derivative and using the Euler transformation of frames enables the formu-
lation of the equations of motions in tensor form, invariant under time-dependent
coordinate transformations. Newton's law yields the translational equations, and
Euler's law produces the attitude equations. Perturbation equations and aerody-
namic derivatives complete the modeling of flight dynamics.
The second part applies these concepts to aerospace vehicles. Simple three
degree-of-freedom (three-DoF) trajectory simulations are built for hypersonic air-
craft, rockets, and single-stage-to-orbit vehicles. Adding two attitude degrees of
freedom forms the five-degree-of-freedom (five-DoF) simulations. Cruise missiles,
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xiv
air intercept missiles, and aircraft simulations are introduced with flight controllers
and guidance and navigation systems, culminating with six-degree-of-freedom
(six-DoF) simulations of hypersonic aircraft, and missiles. Their components are
modeled in greater detail. Aerodynamics, autopilots, actuators, inertial navigation
systems, and seekers are matched with the full translational and attitude equations
of motion. Real-time flight simulators and a glimpse at wargames round out the
second part.
The aerospace vehicles discussed in this book find their actualization in the
computer code stored on the CADAC Web site, which can be accessed through
the AIAA home page (www.aiaa.org). Under the category Market Pulse, select
Web Links to find CADAC among a list of Aerospace-related links. There you can
locate eight complete simulations and four data sets for your own projects. The
download is free of charge. I chose the Internet over the CD-ROM media because
software is ever changing. A CD-ROM is stale and would be outdated at the time
of publication, whereas the Web site is being updated periodically.
You can use the book in a formal class environment, or, with proper motivation,
for self-study; some of you experts may just keep it as a reference manual. The
following table gives suggestions for a one- or two-semester course. Chapters 2-7
can serve as a comprehensive study of flight dynamics with the complete nonlinear
and linearized equations of motion. It could be followed by a second semester of
immersion into flight vehicle simulations, using Chapters 8-11. If the students
already have a solid foundation in flight dynamics, one semester could be devoted
to just flight simulations, preceded by some familiarization with the notation.
Frequently, I use a third option. During a three-credit-hour course, I cover the
essentials of modeling, Chapters 2-6, and introduce the students to simple simula-
tions in a two-hour lab that meets every other week. The CADAC Primer, Appendix
B, jumpstarts the computer orientation. Once Newton's law has been discussed,
the students are prepared to work one of the projects of Chapters 8 or 9. For those
who want to pursue six-DoF simulations in independent study, I assign Chapter
10 and one of its projects. A similar path can be chosen for self-study.
Suggestions for a one-/two-semester course
One semester
Chapter 1st semester 2nd semester with lab
)1 Overview Introductory reading
Part 1
2) Mathematical concepts
)3 Coordinate systems
Course in flight
4) Kinematics Lecture
dynamics
5) Translational equations
)6 Attitude equations
)7 Perturbation equations Optional study
Part 2
)8 Three DoF simulations Training in Lab
9) Five DoF simulations
flight-vehicle
)01 Six DoF simulations simulations Independent study
11) Real-time simulations Optional reading
XV
The problems at the end of each chapter are more than just exercises. Most of
them relate to applications found in aerospace simulations. Within each chapter
they increase in difficulty while also keeping pace with the development of the
material. Some of them, labeled "Projects," are quite time consuming. Particularly
the problems of Chapters 8-10 are better suited as semester projects. They chal-
lenge you to work with actual computer code and explore new designs. I trust the
troika of instructional text, realistic problems, and prototype simulations delivers
to you a complete learning environment.
I teach the course to aerospace (AE), operations research (OR), and electrical
engineering (EE) students at the graduate level. Once in a while even a physicist
may attend. The AE students come prepared with the prerequisite of a stability and
control course, and the EE students, majoring in control systems, succeed also if
they are willing to study the plant-to-be-controlled through some additional read-
ing. Even physicists manage to make honorable grades. Part 1 can also be taught
at the advanced undergraduate level, after the students have had an introductory
course in dynamics. Part 2 requires some specialized knowledge in subsystem tech-
nologies. Particularly, Chapter 10 assumes familiarity with aerodynamics, classical
and modem control, and stochastic effects. If you are a practicing engineer in the
aerospace industry, you should be able to master the book even without a tutor.
I am indebted to my teachers Hermann Stuemke and Bertrand Fang who stirred
in me the enthusiasm for flight mechanics and modeling techniques with tensors
and matrices. My students are always an inspiration to me with their probing
questions. Hopefully, they will find all the answers here. I must name four of
them for their diligent review of the manuscript: Becky Hundley, Phil Webb, Chris
Dennison, and Vy Nguyen. They rose to the challenge to spill red ink over the
professor's work for the promise of better grades. Pat Sforza, my director, at the
Research Center, was always ready with encouragement and useful suggestions. I
thank him and 1A Baker, my faithful colleague over two decades, for their cover-
to-cover review of the manuscript. I extend also my thanks to Lynn Deibler, who
reviewed the sections on radars and electro-optical sensors and made sure that I
would not mistreat the radar range equation.
The members of my family were my cheerleaders. My daughter Heidi baked
a bountiful supply of German Lebkuchen as "brain food" and my daughter Erika
provided the champagne for our celebrations. Giving his dad some sorely needed
advice, Jacob refereed the usage of the English language so that it would not come
across like a German translation. Above all, my wife Barbara sustained me with
her humor, despite my neglecting our nightly chess game.
Peter H. Zipfel
August 2000
List of Acronyms
AGL advanced guidance law
AMRAAM advanced medium range air-to-air missile
ARDC Air Research and Development Command
ASRAAM advanced short-range air-to-air missile
BOGAG bunch of guys and gals
BVR beyond visual range
c.g. center of gravity
center of mass
c.m.
CAD computer aided design
CADAC Computer Aided Design of Aerospace Concepts
CEO chief executive officer
CEP circular error probable
CIC close-in combat
CRT cathode ray tube
DEP deflection error probable
DIS distributed interactive simulation
DoF degrees of freedom
EO electro-optical
GPS global positioning system
HIL hardware-in-the-loop
HLA high level architecture
IMU inertial measuring unit
INS inertial navigation system
IP initial point
IR infrared
ISO International Standards Organization
LAR launch acceptable region
LOA line-of-attack
LOS line-of-sight
M&S modeling and simulation
MC Monte Carlo
MOI moment of inertia
MRAAM medium range air-to-air missile
MRE mean error probable
NASP National Aerospace Plane
NOAA National Oceanographic and Atmospheric Agency
PN proportional navigation
RCS reaction control system
RF radio frequency
S/N signal to noise ratio
xix
XX
SRAAM short-range air-to-air missile
SSTO single stage to orbit
TF/OA terrain following/obstacle avoidance
TM transformation matrix
TVC thrust vector control
wrt with respect to
WVR within visual range