Constant thrust programming for a multistage rocket flown in vacuum with a given initial/final thrust-to-weight ratio in an arbitrary stage

The multistage performance of a rocket in a vacuum is considered. Analytical solutions are obtained for the burn time and velocity of the rocket assuming constant thrust throughout the burn phase and a prescribed initial/final thrust-to-weight ratio in the rth stage. Comparison of the analytical solutions with the results of Miele's (1962) calculations showed agreement with respect to the distribution of payload ratios, structural factors, and equivalent exhaust velocities in the different stages. The analytical solutions for the overall burn period were greater than those of Miele's analysis. An analysis was performed in order to determine the burn time and burnout velocity of a multistage rocket flown vertically in a vacuum with constant thrust tangential to the flight path, and a prescribed initial/final thrust-to-weight ratio, in an arbitrary stage.