Optimal trajectories for hypersonic launch vehicles

In this paper, we derive a near-optimal guidance law for the ascent trajectory from earth surface to earth orbit of a hypersonic, dual-mode propulsion, lifting vehicle. Of interest are both the optical flight path and the optimal operation of the propulsion system. The guidance law is developed from the energy-state approximation of the equations of motion. Because liquid hydrogen fueled hypersonic aircraft are volume sensitive, as well as weight sensitive, the cost functional is a weighted sum of fuel mass and volume; the weighting factor is chosen to minimize gross take-off weight for a given payload mass and volume in orbit.