In 1951, Tsien and Evans successfully solved the problem of finding the optimum flight path for a vertically ascending sounding rocket (Ref. 1). Hibbs, in 1952, solved the problem of finding the optimum burning program for horizontal flight of a winged, rocket-propelled vehicle (Ref. 2). Since then work on optimal flight paths within the atmosphere has stagnated, most work being done for constant thrust, programmed in angle, in vacuo.

The present work extends Tsien and Evans', and Hibbs' work, to flight paths off the vertical. Although the simpler paths produced analytical solutions in the time domain, the present solution is not analytic and is carried out numerically using distance or path length as the independent variable.