Periodic optimal hypersonic scramjet cruise

Optimal periodic cruise paths are determined numerically for a hypersonic vehicle with a more realistic aerodynamic and scramjet engine model than used in previous work. A modification of the shooting method is used to increase the region of convergence to the solution of the two-point boundary-value problem related to the first-order necessary conditions. The resulting extremal trajectories are shown to be locally minimizing by a second-order sufficiency condition. Little fuel improvement is obtained over the steady-state cruise if the model with an engine-off-drag penalty is used. However, altitude changes of over 25% from its lowest value on the periodic path are obtained. If the model with no engine-off-drag penalty is used, the fuel improvement for the optimal periodic cruise is 5% over the steady-state cruise model.