Rho-Isp Revisited and Basic Stage Mass Estimating for Launch Vehicle Conceptual Sizing Studies

The ideal rocket equation is manipulated to demonstrate the essential link between propellant density and specific impulse as the two primary stage performance drivers for a launch vehicle. This is illustrated by examining volume-limited stages such as first stages and boosters. This proves to be a good approximation for first-order or Phase A vehicle design studies for solid rocket motors and for liquid stages, except when comparing to hydrogen-fueled stages. A next-order mass model is developed that is able to model the mass differences between hydrogen-fueled and other stages. Propellants considered range in density from liquid methane to inhibited red fuming nitric acid. Calculated comparisons are shown for solid rocket boosters, liquid first stages, liquid upper stages, and a balloon-deployed single-stage-to-orbit concept. The derived relationships are ripe for inclusion in a multi-stage design space exploration and optimization algorithm, as well as for single-parameter comparisons such as those shown herein.