Energy methods for hypersonic trajectory optimization

A family of near-optimal guidance laws for the ascent and descent trajectories between earth surface and earth orbit of fully reusable single-stage-to-orbit launch vehicles is derived. Of interest are both the optimal operation of the propulsion system and the optimal flight path. The method is based on selecting propulsion system modes and flight-path parameters that maximize a certain performance function. This function is derived from consideration of the energy-state model of the aircraft equations of motion. For ascent trajectories of vehicles employing hydrogen fuel, because the density of liquid hydrogen is relatively low, the sensitivity to perturbations in volume needs to be taken into consideration as well as weight sensitivity. The cost functional is then a weighted sum of fuel mass and volume; the weighting factor is chosen to minimize vehicle empty weight for a given payload mass and volume in orbit. Both airbreathing/rocket and all rocket propulsion systems are considered. For airbreathing/rocket vehicles, the optimal propulsion switching Mach numbers are determined and the use of liquid oxygen augmentation is investigated. For the vehicles with all rocket power, the desirability of tripropellant systems is investigated. In addition, time and heat load is minimized as well. For descent trajectories, the trade-off between minimizing heat load into the vehicle and maximizing cross range distance is investigated, as well as minimum time and minimum temperature paths. The results show that the optimization methodology can be used to derive a wide variety of near-optimal launch vehicle trajectories.