Optimal plane change during constant altitude hypersonic flight

Abstract

In a previous paper, we addressed the problem of choosing constant values of altitude, speed, and angle of attack such that the plane change during hypersonic flight is maximized for a fixed amount of propellant consumption. In the present paper, the assumptions of constant speed and angle of attack are removed. Necessary conditions for solutions to the resulting optimal control problem are derived, and the general characteristics of the optimal controls are described using the domain of maneuverability. Numerical solutions are obtained for several specific cases. We find that, under the condition of constant altitude flight, it is not in general optimum to fly at constant angle of attack. The reduction in plane change capability resulting from a constant angle of attack program increases as the the range over which the flight takes place increases. On the other hand, the optimum speed is nearly constant.