Optimum Rocket Trajectories

Abstract
Some general considerations regarding maximum range missile trajectories are presented. It is shown that under certain simplifying assumptions maximum range is achieved if the thrust attitude angle is held constant during the entire powered flight. This result is exact for a constant gravitational force field if aerodynamic forces and altitude dependence of rocket thrust are neglected. For motion in the earth's inverse square, central force field, constant thrust attitude is a good approximation to the optimum program, provided the distance covered during powered flight is small compared to the radius of the earth. Equations for the value of the optimum attitude angle are presented for both constant and Kepler force fields. The results provide a convenient means of estimating an upper limit for the range which could be achieved with a given missile.
Keywords