Optimization and Implementation of Periodic Cruise for a Hypersonic Vehicle

The optimal cruise trajectory for a detail designed hypersonic waverider vehicle is determined. Two possible local extrema are found representing the steady state and periodic cruise trajectories. The optimal steady state cruise is determined by minimizing the instantaneous fuel rate per distance subject to the dynamics being in equilibrium. The approximately optimal periodic cruise is determined by minimizing the fuel used over an optimal range period subject to a periodicity condition on the initial and terminal values of the altitude, velocity, and ∞ight path angle, assuming that the vehicle weight is given and held flxed over the range period. It is shown that if a door is placed over the inlet during the power-ofi phase increasing the drag by 50%, but increasing the lift by 35%, the periodic ∞ight over the cruise region is 13.27% better than ∞ying in steady state. Results for mechanizing the periodic ∞ight by a linear guidance rule allow the constant vehicle weight assumption to be removed, but retain the periodic cruise performance.