a book by Robert F. Stengel

First Edition, Princeton University Press, 2004

Flight Dynamics takes a new approach to the science and mathematics of aircraft flight, unifying principles of aeronautics with contemporary systems analysis. It is a text and reference book for upper-level undergraduates and first-year graduate students as well as practicing engineers. While the book presents traditional material that is critical to understanding aircraft motions, it does so in the context of modern computational tools and multivariable methods. Particular attention is given to models and techniques that are appropriate for analysis, simulation, evaluation of flying qualities, and control system design. Bridges to classical analysis and results are established, and new territory is explored. The book is intended for readers with a broad background and interest in engineering and science. It begins with basic principles of trigonometry, calculus, linear algebra, and dynamics, and it continues with advanced topics, algorithms, and applications.

Dynamic analysis has changed dramatically during recent decades, with the introduction of powerful personal computers and scientific programming languages. Analysis programs have become so pervasive that it can be assumed that all students and practicing engineers working on aircraft flight dynamics have access to them. Therefore, this book presents the principles, derivations, and equations of flight dynamics with frequent reference to computed examples, and it includes MATLAB code for six-degree-of-freedom simulation and linear system analysis.

By using common notation and not assuming a strong background in aeronautics, Flight Dynamics is accessible to a wide variety of readers. Introductions to aerodynamics, propulsion, structures, and the atmospheric and gravitational environment precede the development of the aircraft's dynamic equations. Systeme International (SI) units are used for the majority of the text. These units take better advantage of decimal arithmetic than U.S. Customary Units, the majority of world industry and academe uses them, and virtually all high school and college students learn physics, chemistry, and mathematics with SI units.

Flight Dynamics is organized in seven chapters and an epilogue.

Flight Dynamics is accompanied by a nonlinear, six-degree-of-freedom simulation model for a generic business jet aircraft that is available online. The model is used for most examples, beginning with Chapter 2. The inertial and aerodynamic properties of the model are representative of business jets from subsonic to high-transonic airspeed and for angles of attack up to 90 deg. Together with the MATLAB nonlinear simulation program FLIGHT.m, the model is used to demonstrate motions across the spectrum of flight, including effects of compressibility, stalling, spinning, and control nonlinearity (e.g., limit cycles and chaotic motion). FLIGHT.m can generate linear, time-invariant (LTI) dynamic models at arbitrary flight conditions.

The LTI models can be subjected to various linear analyses in the MATLAB program SURVEY.m, including model order reduction through truncation or residualization, transient response, equilibrium response, controllability and observability, Bode, Nyquist, and Nichols plots, and root locus analysis. Longitudinal and lateral-directional motions can be analyzed separately or under fully coupled flight conditions. The FLIGHT.m and SURVEY.m programs are heavily commented, and they serve a tutorial role on their own.

Second Edition, Princeton University Press, to be published in Fall 2022

The first edition's chapter structure is retained. More examples and illustrations are included, and supporting material is arranged in text boxes. There is additional information on conventional and electric propulsion. While the emphasis is on fixed-wing flight within the atmosphere, an example of flight into space and reentry into the atmosphere is given. Example aircraft described in Chapter 1 are updated. Rotational transformations are presented in a more classical framework. The discussion of piloting actions and flying qualities criteria is integrated within a new section. Appendix E, which formerly was a bibliography of NASA reports, now presents exercises for each section of the book.

A new chapter on flight control design gives comprehensive coverage to techniques that apply for a wide range of linear and nonlinear dynamic models with analog or digital systems and cannot be found elsewhere.

Flight Dynamics provides links to online resources for nonlinear, six-degree-of-freedom analysis, generation of stability and control derivatives, and analysis of systems. The MATLAB programs FLIGHT.m and SURVEY.m have been extensively redesigned to become more user-friendly. SURVEY.m now includes software for design of linear-quadratic-Gaussian (LQG) controllers for state, output, model-following, integral, and filter compensation.

In addition to the business jet mathematical model used throughout the book, a model for an advanced jet trainer is included. Future additions include models for a narrow-body jet transport with conventional and electric propulsion, a supersonic transport, and a hypersonic cruiser. These new models are formulated with the program, ModelBuild.m, which uses the methods described in Chapters 4 and 5 of Flight Dynamics to formulate 6DOF descriptions of dynamics.

While covering all the material in the book typically would require a two-semester course, a one-term undergraduate course can be based upon portions of the book, leaving the more advanced topics for independent reading. Flight Dynamics is written with a physics-based evolution of topics; a more flexible organization of material may be preferred for lectures and assignments. With this in mind, guidelines for first and second courses on flight dynamics and control are given. Lecture slides, assignments, and internet links for a third/fourth-year undergraduate course can be found online below and at Flight Dynamics, Second Edition.

A First Course in Aircraft Flight Dynamics

Aircraft Flight Dynamics introduces students to the performance, stability, and control of aircraft ranging from micro-uninhabited air vehicles through general aviation, jet transport, and fighter aircraft to Mars planes and re-entry vehicles. Particular attention is given to mathematical models and techniques for analysis, simulation, and evaluation of flying qualities, with brief discussion of guidance, navigation, and control. Topics include equations of motion, configuration aerodynamics, analysis of linear systems, and longitudinal/lateral/directional motions.

While the course focuses on the Science and Mathematics of flight dynamics, historical antecedents are presented as Case Studies in aircraft performance, stability, and control. The science and mathematics component is based on Flight Dynamics, Second Edition. The case studies were initially motivated by Airplane Stability and Control: A History of the Technologies that Made Aviation Possible (2005), M. J. Abzug and E. E. Larrabee, and they are enhanced by reference to current web-based content.

Syllabus and Assignments

Lecture Slides

Introduction to Aircraft Flight Dynamics: A Virtual Reference Book

Endorsements, Reviews, and Errata for First Edition

"A monumental piece of work. Its comprehensive treatment of flight dynamics makes it the broadest in its class and constitutes a major contribution to the aerospace community. Destined for students' shelves as well as mine, it will also be valuable as the methodological companion to the aircraft designer, flight test engineer, and pilot."-- Eric Feron, Massachusetts Institute of Technology (currently, Georgia Institute of Technology)
"This book is definitely a significant contribution to the field. It is more comprehensive than any other work on flight dynamics I have seen; it includes newer concepts, such as neural nets and wind shear effects, some of these reflecting the author's own research; and it gives a very broad view of flight dynamics. Not only is it a fine textbook on flight dynamics, but it is so thorough and so well written that it will undoubtedly catch the attention of practicing engineers and airplane enthusiasts."-- Haim Baruh, Rutgers University


Review by Michael Cook, Cranfield University, for The Aeronautical Journal

Review by John Hodgkinson, AeroArts LLC, for the AIAA Journal

Review by Eric Feron, Georgia Institute of Technology, for the IEEE Control Systems Magazine

Review by John Valasek, Texas A&M University, for the Journal of Guidance, Control, and Dynamics

Online comments:

"Originally bought this book for a Flight Dynamics course in college, but these days I'm working in the aerospace industry and it has proven an invaluable reference again and again. Superb development and explanation of a fundamental aircraft dynamics model, followed by in-depth analysis of the revealed modes of motion; this book is a tremendous resource for anyone interested or involved with aircraft." -- Anon., Amazon

"This is an excellent book that any flight controls or aviation engineer will find more than just useful. It provides a pretty complete treatment of the state variable approach and should serve as an excellent starting point for those wanting to design actual controllers for aircraft." -- Anon., Amazon

"This is an excellent book, I remembered it from university days and recently re-purchased it for work (flight simulator engineer). It covers almost every aspect of fixed wing aircraft dynamics you might want, and of course a fair amount reads across to rotary wing vehicles. The appendices summarising the Matlab models provided and relevant NASA papers are useful. The book language and notation doesn't assume too much prior specific aeronautics experience so it can be shared with colleagues from a different background." -- Anon, Amazon

MATLAB Code for Analysis and Simulation

Nonlinear Six-Degree-of-Freedom Aircraft Simulation [FLIGHT.m]

Linear System Survey [SURVEY.m]

Paper Airplane Simulation [PaperPlane.m]

Errata, 1st Edition

Course Summary and Lecture Slides


Robert F. Stengel is Professor Emeritus and former Associate Dean of Engineering and Applied Science at Princeton University. He is the author of Optimal Control and Estimation (Dover, 1994). He was principal designer of the Apollo Lunar Module manual attitude control logic.

key words: aircraft flight dynamics, flight mechanics, stability and control, short period, phugoid, Dutch roll, roll, spiral, aeronautical case histories, aircraft performance, longitudinal dynamics, lateral-directional dynamics, coupled motions, inertial coupling, high angle of attack, aeroelasticity, nonlinear equations of motion, flight simulation, flight vehicles, earth's atmosphere.
Last updated on March 21, 2022. Copyright 2022 by Robert F. Stengel. All rights reserved.