Optimal Trajectory Study of a Small Size Waverider and ‎Wing-Body Reentry Vehicle at Suborbital Entry Speed of ‎Approximately 4 km/s with Dynamic Pressure and Heat ‎Rate Constraint

A numerical trajectory optimization study of two types of lifting-entry reentry vehicle has been ‎presented at low suborbital speed of 4.113 km/s and -15 degree entry angle. These orbital speeds are typical ‎of medium range ballistic missile with ballistic range of approximately 2000 km at optimum burnout angle ‎of approximately 41 degree for maximum ballistic range. A lifting reentry greatly enhances the reentry ‎range which leads to a higher overall range of approximately 3000 km for the same ?V. The optimum ‎reentry angle of lifting reentry vehicle for medium range missiles under constrained g-load lies between -‎‎15 to -20 degree for limited g-load trajectories. These entry angles result in high decent rates and the ‎vehicle quickly approaches the heat rate boundary. The heat rate problem is more severe for small size ‎vehicle because of small nose-radius. Limiting the heat rate restricts the trajectory and lowers the ‎downrange/cross-range performance of the reentry vehicle. A wing-body reentry vehicle has a larger nose ‎radius as compared to a waverider which results in comparatively low heat rates during flight. This type of ‎a vehicle has lower lift-to-drag ratio and therefore lesser range in comparison to a waverider type design. ‎The performance of the two vehicle types is studied at various heat rate limits with the objective to ‎calculate the optimum control deflections that would maximize the cross range. The results provide ‎performance of the two designs vis-à-vis maximum heat rate constraint at the stagnation point along with ‎the required control history. General pseudo-spectral optimal control software, GPOPS has been used for ‎the optimal trajectory studies. ‎