Optimization of three-dimensional range and ascent trajectories of a two-stage hypersonic vehicle

The optimization of a three-dimensional range and ascent flight of a two-stage hypersonic flight system with air-breathing engines is considered. The combined orbital and carrier stages system performs a range flight until separation. Afterwards the carrier stage returns to the launch site, while the orbital stage ascends to its orbit. It is shown that the separation manoeuvre and the curve necessary for the carrier stage return are constituent parts of the overall range/ascent trajectory, thus yielding a distinctive three-dimensional trajectories combination. The range trajectory is rather unsteady, even for a flight distance of more than 6000 km. Particular emphasis is put on the realistic modelling of the vehicles, including control and state variable constraints. A particular topic of this article concerns the modelling of the thrust force direction. Three cases are considered: thrust force direction; (1) fixed on the vehicle, (2) parallel to the speed vector and (3) used as a control.