Optimal three-dimensional reentry trajectories subject to deceleration and heating constraints

The lateral maneuver of a lifting reentry vehicle, exemplified by the Shuttle entry, is severely restricted by deceleration and heating constraints. This paper investigates the decrease in the lateral reachable domain when different constraints are imposed on the optimal trajectories. A characteristic of hypersonic reentry trajectories is that the deceleration and heating rate pass through several maxima. The first peak is always higher than the following maxima so that it suffices to control the first maximum to the required level. Thermal constraint is encountered at higher altitude so that, in general, thermal control usually limits the deceleration to acceptable level. Using the equilibrium glide assumption, the optimal lift and bank control to maximize the lateral range is obtained in explicit form. Numerical results have been obtained for a typical value of maximum lift-to-drag ratio, and for several values of deceleration and thermal constraints imposed on the entry trajectories. It is found that the peak deceleration and the peak heating rate can be lowered significantly with only a slight penalty on the reachable domain.