Optimum Staging with Varying Thrust Attitude Angle

Optimum staging programme for step rockets of arbitrary number of stages having different specific impulses and mass fractions with stages is derived, the optimization criterion being minimum take-off weight for a desired burntout velocity at an assigned altitude. Variation of thrust attitude angle from stage to stage and effects of gravity factor are taken into account. Analysis is performed for a degenerate problem obtained by relaxing the altitude constraint and it has been shown that problems of Weisbord, Subotowicz, Hall & Zambelli and Malina & Summerfield are the particular cases of the degenerate problem.