Dynamics is concerned with the time history of the motion of physical systems. An aircraft is such a system, and its dynamic stability behavior can be predicted through mathematical analysis of the aircraft's equations of motion and verified through flight test. During this study of aircraft dynamics, the solutions to both first order and second order systems will be of interest, and several important descriptive parameters will be used to define the dynamic response of either a first or a second order system.
This chapter studies the algebra and calculus of vectors and matrices, as specifically applied to the USAF Test Pilot School curriculum. The course is a prerequisite for courses in Equations of Notion, Dynamics, Linear Control Systems, Flight Control Systems, and Inertial Navigation Systems. The course deals only with applied mathematics; therefore, the theoretical scope of the subject is limited.
The performance of an aircraft can adequately be described by assuming the aircraft is a point mass concentrated at the aircraft's center of gravity (cg). The flying qualities of an aircraft, on the other hand, cannot be described in such a simple manner. The flying qualities of an aircraft must, instead, be described analytically as motions of the aircraft's cg as well as motions of the airframe about the cg, both of which are caused by aerodynamic, thrust and other forces and moments. In addition, the aircraft must be considered a three dimensional body and not a point mass. The applied forces and moments on the aircraft and the resulting response of the aircraft are traditionally described by a set of equations known as the aircraft equations of motion. This chapter presents the form of the aircraft equations of motion used in the Flying Qualities phase of the USAF Test Pilot School curriculum.
Static stability is the reaction of a body to a disturbance from equilibrium. To determine the static stability of a body, the body must be initially disturbed from its equilibrium state. If, when disturbed from equilibrium, the initial tendency of the body is to return to its original equilibrium position, the body displays positive static stability or is stable. If the initial tendency of the body is to remain in the disturbed position, the body is said to be neutral stable. However, should the body, when disturbed, initially tend to continue to displace from equilibrium, the body has negative static stability or is unstable. Longitudinal static stability or gust stability of an aircraft is determined in a similar manner. If an aircraft in equilibrium is momentarily disturbed by a vertical gust, the resulting change in angle of attack causes changes in lift coefficients on the aircraft (velocity is constant for this time period). The changes in lift coefficients produce additional aerodynamic forces and moments in this disturbed position. If the aerodynamic forces and moments created tend to return the aircraft to its original undisturbed condition, the aircraft possesses positive static stability or is stable. Should the aircraft tend to remain in the disturbed position, it possesses neutral stability. If the forces and moments tend to cause the aircraft to diverge further from equilibrium, the aircraft possesses negative longitudinal static stability or is unstable.
Your study of flying qualities to date has been concerned with the stability of the airplane flying in equilibrium on symmetrical flight paths. More specifically, you have been concerned with the problem of providing control over the airplane's angle of attack and thereby its lift coefficient, and with ensuring static stability of this angle of attack. This course considers the characteristics of the airplane when its flight path no longer lies in the plane of symmetry. This means that the relative wind will make some angle to the aircraft centerline which we define as Beta. The motions which result from Beta being applied to the airplane are motion along the y-axis and motion about the x and z axes.
This chapter reviews the mathematical tools and techniques required to solve differential equations. Study of these operations is a prerequisite for courses in aircraft flying qualities and linear control systems taught at the USAF Test Pilot School. Only analysis and solution techniques which have direct application for work at the School will be covered.
The term 'dynamic parameter analysis' is used in this course to mean a discussion of (1) the general systems identification problem, (2) parameter estimation techniques, and (3) parameter analysis methods. Systems identification is the determination of the characteristics of a physical system from experimental test data. Parameter estimation techniques are methods used in systems identification problems, and parameter analysis is putting the results of these experiments to good use.
The second edition of Flight Stability and Automatic Control presents an organized introduction to the useful and relevant topics necessary for a flight stability and controls course. Not only is this text presented at the appropriate mathematical level, it also features standard terminology and nomenclature, along with expanded coverage of classical control theory, autopilot designs, and modern control theory. Through the use of extensive examples, problems, and historical notes, author Robert Nelson develops a concise and vital text for aircraft flight stability and control or flight dynamics courses.
The method used to analyze maneuvering flight will be to determine a stick-fixed maneuver point (Hm) and stick-free maneuver point (H'm). These are analogous to their counterparts in static stability, the stick-fixed and stick-free neutral points. The maneuver points will also be derived in terms of the neutral points, and their relationship to cg location will be shown.
Pilots might be inclined to associate the phrase control system with only aircraft flight control systems. Although the control system theory of this course has a large application to flight control sysems, this material applies to any process or system in which control is exercised over some output variable. Examples of these controlled variables are: the speed of an automotile, the temperature of a room, the attitude of a spacecraft, ad infinitum.
