On the Calculation of Optimum Mass Distribution of a Multi-Stage Rocket Vehicle

Abstract

The effect of gravity on the optimum distribution of total required mass among the various stages of a multiple stage rocket arranged series has been considered by making the payload ratio minimum so as to obtain a specified mission velocity at the end of powered flight. The special case when the physical parameters for all the step rockets are each equal, has been discussed in detail. It has also been shown that if the mission requirement is to achieve a given all burnt height, then even at the expense of more total initial mass no more total a given all burnt velocity. Finally it is proved that in order to achieve a given all burnt velocity by arranging the stages in parallel results in an increase in the total initial mass compared to the case when they are arranged in series and the magnitude of this increase depends upon the number of stages.