Abstract Range optimal trajectories for an aircraft flying in the vertical plane are obtained from Pontryagin's minimum principle. Control variables are the load factor, which appears nonlinearly in the equations of motion, and the throttle setting, which appears only linearly. Both controls are subject to fixed bounds. For fixed flight time, initial coordinates, and final coordinates of the trajectory, the effect of the load factor limit on the resulting optimal switching structure is studied.
All trajectories involve singular control along arcs with active dynamic pressure limit.
For large flight times the optimal switching structures have not yet been found.