Stability of steady flight

CHAPTER 9

The preceding chapters have provided the analytical and aerodynamic tools needed to analyze the dynamic behavior of flight vehicles. We now apply them to a consideration of the stability of small disturbances from steady flight. This is an extremely important property of aircraft—first, because steady flight conditions make up most of the flight time of airplanes, and second, because the disturbances in this condition must be small for a satisfactory vehicle. If they were not it would be unacceptable for either commercial or military use. The required dynamic behavior is ensured by design—by making the small-disturbance properties of concern (the natural modes, Fig. 3.6) such that either human or automatic control can keep the disturbances that ensue from atmospheric motion, movement of passengers, etc., to an acceptably small level. Finally, as pointed out in Sec. 5.10, the small-disturbance model is actually valid for disturbance magnitudes that seem quite violent to human occupants.

To study the stabihty of the linear/invariant systems that result from the small-disturbance approximation, we need only the eigenvalues of the system. If the real parts are negative, the system is stable. More complete information about the characteristic modes is usually wanted, however, and is supplied by the eigenvectors. The complete solution for arbitrary initial conditions in the autonomous case follows directly from the eigenvalues and eigen­vectors—it is given by any of (3.3,9), (3.3,13), or (3.3,49).

For the most part, the equations of motion are too complicated, even when linearized and simplified as far as is reasonable, to arrive at analytical results of general validity. Hence the technique we use is to demonstrate repre­sentative behavior by numerical examples. From these, certain useful analytical approximations can be inferred.