Extended Tsiolkovskii Equation and Its Application to Launch Vehicles

Abstract

To estimate mass transported to an orbit by the rockets with better accuracy and to compare transport ability of a two-stage-to-orbit aerospace plane with that of conventional rockets, the Tsiolkovskii equation of the mass ratio is modified and extended by use of the fundamental equations of motion of a vehicle. The calculated mass ratios with the modified equations show reasonable agreement with the ratios of the actual flights of H-IIA and H-IIB rockets. From the modification of the equation, the extended effective specific impulse is derived. The impulse incorporates the effects of angle of attack, flight-path angle, lift, drag, and specific impulse and can evaluate vehicle transportation ability. Transport capability of a two-stage-to-orbit aerospace plane with rocket-based combined-cycle engine is examined with the impulse and the modified equations. When the plane flies with the ramjet mode in a small change of the flight-path angle and flies with the scramjet mode in a large change of the angle, the mass to an orbit becomes larger. A two-stage-to-orbit aerospace plane will transport a larger amount of mass to an orbit than conventional rockets.