Optimization of Hybrid Upper-Stage Motor with Coupled Evolutionary/Indirect Procedure

Upper-stage motors used in small launchers constitute an application where hybrid rocket motors may be competitive. A coupled optimization of motor design and trajectory is needed for such an application due to mission characteristics and motor features. The present article presents a cooperative evolutionary method nested with an indirect approach to perform the coupled optimization of hybrid rocket motor and trajectory for an upper stage. The evolutionary method optimizes the parameters that affect the motor design (e.g., grain geometry) and feed system, whereas the indirect method optimizes the trajectory (i.e., thrust direction and motor switching times) for a given motor and mission. A mission profile based on the Vega launcher is considered and the performance index is the payload inserted into the final orbit. The hybrid rocket motor powers the third and last stage and has a pressurizing feed system that is partially regulated. The characteristics of the first and second solid rocket motor stages are assigned and kept constant, but the whole trajectory is optimized from liftoff to orbit. Different propellant combinations are considered and effects of throat erosion are discussed. Results show that the liquid oxygen/wax propellant combination has the best performance. This combination can be used with a single-port grain and presents a potential gain of about 350 kg with respect to other propellant combinations. Multiport grains must be adopted when more classical fuels are considered, to have acceptable values of the length-to-diameter ratio.