Optimal plane change during constant altitude hypersonic flight

In a previous paper, we addressed the problem of choosing constant values of altitude, speed, and angle of attack such that the orbital plane change during hypersonic flight is maximized for a fixed amount of propellant consumption. In the present paper, the restrictions of constant speed and angle of attack are removed. Necessary conditions for solutions to the resulting optimal control problem are derived. Numerical solutions are obtained for several specific cases under the assumption that the constant altitude trajectory that maximizes the plane change is primarily a singular arc. 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 range over which the flight takes place increases. On the other hand, the optimum speed is nearly constant.