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 ΔV. 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.