Flight Dynamics

Flight Dynamics is focused on fixed-wing aircraft flight dynamics and is concerned with explaining how aircraft and other flying machines behave given their particular physical attributes. This subject is of importance to aerospace engineers, which is the reason that almost every university with an aerospace engineering department features specialized courses devoted to flight dynamics and control. Given the importance of the subject, several textbooks have been devoted to the subject over the years, for example [1]–[6]. Given the large number of existing books on this topic, why write a new book? After all, it appears as if the subject is mature, and several good textbooks already exist. One reason is that flight dynamics is a constantly evolving subject and has seen several important

1066-033X/06/$20.00©2006IEEE

new developments in both the understanding of flight dynamics itself and the methods used to control aircraft. As such, any book providing the aerospace community with an up-to-date account of the subject is a welcome addition to the literature.

The book fulfills this role by providing a modern presentation of flight dynamics. I say “modern” for the following reasons: 1) the mathematical tools are elegantly interlaced with the appropriate subject matter, 2) advances in computing power are acknowledged in the form of numerous references to computer-based engineering tools, 3) several control methods that were still considered experimental a few years ago are now standard, and 4) nonlinear behaviors that arise in flight dynamics are discussed in depth.

The text covers a wide range of topics. The introduction begins with a description of aircraft components and includes a representative taxonomy of modern aircraft. Far from offering a restricted list, the introduction takes us on a world tour across the entire spectrum of winged machines. A pleasant surprise is the use of paper airplanes

(p. 23). Easy to build and safe to test, the paper airplane provides an instant flight mechanics experimental testbed that is accessible to all readers. The author does an excellent job of describing the endless range of experiments that can be performed with paper airplanes. Coupled with the flight simulation code given at the end of the book, the reader is provided with a rudimentary, yet complete, suite of tools covering the entire range, from simulation to flight test, for performing aircraft design. Paper airplanes can take a variety of forms, and in my experience the pointed nose design is not the easiest to fly or to experiment with. My favorite paper airplane, which I learned how to make in elementary school, is described in [7] and shown in Figure 1(b). Although slightly more complex to build than the pointed-nose design, this airplane features improved flight qualities. For example, by positioning one or more paper clips at various locations, a host of experiments can be performed by varying the mass distribution.

The remainder of the book focuses on the description of flight mechanics itself, beginning with simple static behavior such as trimmed flight and then extending into dynamic analysis. The author successfully strikes a balance between discussing the properties of general dynamical systems and analyzing flight-specific behavior.

Chapter 2, “Exploring the Flight Envelope,” describes the environment surrounding the aircraft and all forces that affect its behavior, including thrust and aerodynamic forces. As a result, the title of this chapter is somewhat misleading since the discussion does not specifically focus on the flight envelope. This chapter also introduces the reference frames and coordinate systems used throughout the field of flight mechanics. While Chapter 2 discusses Euler angles, quaternions are introduced in a later chapter.

Chapter 3 logically progresses with a study of the dynamics of aircraft motion by deriving the basic translational and rotational equations of motion for a rigid aircraft. By the end of the chapter, the reader has been exposed to quite general equations of flight, including the effect of control mechanisms such as thrust and aerodynamic surfaces. The author spends significant effort showing how these complex equations of motion can be implemented on a computer for numerical simulation. This chapter also shows how dynamic characteristics of the aircraft, such as its stability derivatives, can be represented numerically. The emphasis that the author places on utilizing neural networks for identifying and representing aircraft dynamics may not appeal to all instructors. Later, the author relates the equations of motion to aircraft behavior such as angular rate-dependent effects. For example, a detailed analysis of adverse yaw motion created by roll-rate motion and yaw-rate-induced roll effects is provided. This chapter also rederives the rotational motion of the aircraft in terms of quaternions.

In Chapter 4, the author simplifies the equations of motion by linearization. After discussing the numerous simplifications in the motion equations that occur when the aircraft is symmetric, this chapter begins a generic discussion of the theory of linear systems. In particular, state-space models and the associated notions of controllability and observability are introduced. Using the state-space description, more complex dynamic effects arising in flight mechanics, such as fuel slosh and aeroelastic effects, are considered. Aeroelastic effects, which result from the interaction of aircraft flexibility with aerodynamics, have always been critical in flight mechanics. In fact, aeroelastic effects are becoming even more important because modern aircraft, such as the A340-600, are becoming increasingly flexible to reduce mass and direct operating costs. The next part of the chapter, devoted to uncertainty modeling and robustness analysis, falls somewhat short of the mark. Although this chapter contains a discussion of topics with definite engineering value such as the stochastic root-locus, it lacks in other respects. Specifically, I believe that modern robust system analysis methods [8]–[10] are now sufficiently mature to be mentioned, at least in passing, in a comprehensive book such as this. Finally, this chapter concludes with a discussion of pertinent control design methods, with a strong focus on the linear quadratic regulator. Although these methods are well-known, they are not readily accessible to the average undergraduate student. It would have been nice to see a discussion of some elementary control methods presented first, such as proportional-integral compensation.

Chapters 5 and 6 cover the essentials of flight mechanics, exploiting the decoupling that usually arises between longitudinal motions and lateral-directional motions. These chapters also cover control mechanisms for these modes of flight. Here the development makes systematic use of state-space and frequency-domain system design and analysis methods. As a result, the reader must have had previous exposure to these areas or have carefully studied Chapter 4 in its entirety.

Chapter 7, “Coupled Longitudinal and Lateral-Directional Motions,” covers many more topics than its title indicates, since it also provides the reader with an in-depth study of flight dynamics in fully nonlinear regimes such as poststall flight. Two sections discuss gyroscopic coupling mechanisms due to rotating machinery, yawing moments due to the different efficiency of upward and downward propeller blades, and asymmetric flight and coupling control surfaces, followed by a discussion on coupling due to inertial aircraft properties. While most aircraft are symmetric enough to warrant inertial decoupling, modern designs are likely to break that mold and convince the public, airlines, and the federal government that asymmetric designs have many desirable qualities. This trend is illustrated by designs from scaled composites as well as projects such as the oblique-wing aircraft concept, promoted by the late R.T. Jones, which offers the potential for flight at higher subsonic speeds without developing the shocks typically found in conventionally shaped aircraft. The author does not miss this important point, and his book correctly reminds the reader of the vitality of this field.

What makes Chapter 7 especially unique is its thorough treatment of nonlinear aircraft behavior at high angle of attack. In a long section, the author discusses the behavior of nonlinear systems with multiple equilibria, as well as catastrophe theory and how it applies to flight mechanics. These concepts are used to explain how aircraft can enter into very nonlinear and often dangerous flight conditions, including deep stall, spin, and others. Although the treatment is mathematically thorough, little connection is made with recommended practices for pilots when an aircraft enters unusual flight conditions. These include, for example, a comprehensive description of the central role of rudder action to control aircraft attitude during deep stall and to recover from spin conditions in conventionally shaped aircraft. Far from distracting the readers from the mathematical concepts presented in this section, such analogies can help practicing pilots better relate these mathematical developments to their own flight experience. As an educator specializing in control systems, I realize that the mathematics of poststall flight may appear somewhat advanced for undergraduate students. However, as a private pilot, I expect any engineer who develops new aircraft to be at least aware of such degraded flight conditions.

Who is the target audience of this text? Indisputably, this book is a detailed reference source that the engineer and the flight mechanics instructor can refer back to throughout their professional careers. The book is not only thorough but also contains numerous references. The author should be commended for the comprehensiveness of the bibliography. I believe the text could be placed next to [11], because the two books complement each other very well. However, [11] arguably gives a more in-depth presentation of basic control design methods for aircraft than the current book. As a reference book, this text could also be placed next to [12]. Finally, since this text does not focus on helicopter dynamics, it could be placed next to [13].

As a textbook, Flight Dynamics is suitable for a course devoted to the subject. However, the paucity of problem sets, as well as the tight weaving of mathematical concepts with the topics to which they apply, might make it challenging to use. On the other hand, students would end up owning a book that will continue to be useful as they develop throughout their professional careers.

Curricula that introduce state-space methods at an early stage could utilize this book at the undergraduate level. This is the case for Georgia Tech. Material to cover during a one-semester course would include Chapters 1– 6. Material taken out of Chapter 3 should focus on simulation at the expense of data representations using neural networks. The contents of Chapter 4 would have to be extensively scaled down and limited to the derivation of the linearized equations of motion for a rigid aircraft. A brief reminder of the relationship between state-space models and frequency-domain models would also have to be included. Chapters 5 and 6 could then be covered without much difficulty. Chapter 7 can be useful for making students aware of nonlinear flight regimes with at least an intuitive understanding.

At the graduate level, I believe this book would be an endless source of interesting lectures. Specifically, I highly recommend that Chapter 7, especially its coverage of nonstandard flight regimes, be included.

Overall, I believe this book provides a significant addition to the existing literature on flight mechanics. It deserves to be part of the library of scholars and practicing flight mechanics engineers alike. The use of this text in an undergraduate course would require skilled care but would provide a valuable resource to its owner well past graduation.

Eric Feron (eric.feron@aerospace.gatech.edu) has been on the faculty of the School of Aerospace Engineering at the Georgia Institute of Technology since 2005, where he is Dutton/Ducoffe Professor of Aerospace Software Engineering. From 1993–2005, he was with the Department of Aeronautics and Astronautics at the Massachusetts Institute of Technology. His work concentrates on control systems and optimization with application to aircraft dynamics, unmanned aerial vehicles and their certification, and transportation systems.

[1] D.T. McRuer, Aircraft Dynamics and Control. Princeton, NJ: Princeton Univ. Press, 1973.

[2] R.C. Nelson, Flight Stability and Automatic Control, 2nd ed. New York: McGraw Hill, 1998.

[3] J. Roskam, “Airplane flight dynamics and automatic flight control,” DARcorporation, Lawrence, KA, 2001.

[4] B. Etkin, Dynamics of Atmospheric Flight. New York: Wiley, 1971.

[5] B. Etkin and L.D. Reid, Dynamics of Flight: Stability and Control, 3rd ed. New York: Wiley, 1996.

[6] B.L. Stevens and F.L. Lewis, Aircraft Control and Simulation, 2nd ed. New York: Wiley, 2004.

[7] Paper Airplanes [Online]. Available: http://www.paperairplanes. co.uk/nickplan.html

[8] J. Doyle, “Analysis of feedback systems with structured uncertainties.” Proc. IEE, vol. 129-D, no. 6, pp. 242–250, Nov. 1982.

[9] M. Safonov, “Stability margins of diagonally perturbed multivariable feedback systems.” Proc. IEE, vol. 129-D, no. 6, pp. 242–250, Nov. 1982.

[10] D.S. Bernstein and W. Haddad, “Robust stability and performance analysis for linear dynamic systems.” IEEE Trans. Automat. Contr., vol. 34, no. 7, pp. 751–758, July 1989.

[11] A.E. Bryson, Jr., Control of Spacecraft and Aircraft. Princeton, NJ: Princeton Univ. Press, 1994.

[12] R.H. Cannon, Jr., Dynamics of Physical Systems. New York: McGraw Hill, 1967.

[13] G.D. Padfield, Helicopter Flight Dynamics: The Theory and Application of Flying Qualities and Simulation Modeling, AIAA Education Series, 1995.

JUNE 2006 « IEEE CONTROL SYSTEMS MAGAZINE 119