Analytic performance considerations for lifting ascent trajectories of winged launch vehicles

The so-called rocket equation, which was first derived by Konstantin Tsiolkovsky, allows to determine the velocity increase of a rocket-propelled vehicle as a function of propellant consumption and the effective velocity of the exhaust gases. It is, however, strictly valid only for a constant effective exhaust velocity and in the absence of external forces, such as atmospheric drag or gravity. Empirical corrections and analytic approximations have been developed to account for deviations from these conditions for ballistic launch vehicles. The rocket equation is, however, inadequate for performance calculations of winged launch vehicles with aerodynamic ascent and especially air breathing propulsion, which may experience significant aerodynamic forces and large variations in the effective exhaust velocity. In order to enable fast, yet accurate performance assessments for such vehicles, a class of analytic solutions for the equation of motion along the trajectory of launch vehicles with lifting ascent has been derived.