Optimal air-breathing launch vehicle design

A generalized two-point boundary problem methodology, similar to techniques used in deterministic optimal control studies, is applied to the design and flight analysis of a two-stage air-breathing launch vehicle. Simultaneous consideration is given to configuration and trajectory by treating geometry, dynamic discontinuities, and time-dependent flight variables all as controls to be optimized with respect to a single mathematical performance measure. While minimizing fuel consumption, inequality constraints are applied to dynamic pressure and specific force. The optimal system fuel consumption and staging Mach number are found to vary little with changes in the inequality constraints due to substantial geometry and trajectory adjustments. Staging, from an air-breathing first stage to a rocket-powered second stage, consistently occurs near Mach 3.5. The dynamic pressure bound has its most pronounced effects on vehicle geometry, particularly the air-breathing propulsion inlet area, and on the first-stage altitude profile. The specific force has its greatest influence on the second-stage thrust history.