Optimization of a Dual-Mixture-Ratio Hydrogen-Fuel Rocket

Abstract

The problem of optimizing rocket performance in the absence of gravitational and aerodynamic forces is analyzed by considering the possibility of varying the propellant mixture ratio. The rocket operation with a piecewise constant mixture ratio, that presents lower complexity in comparison to a continuously variable mixture ratio, is examined in this paper. The theory of optimal control is applied in order to minimize either the gross mass or the dry mass for the assigned pay load and velocity increment, when the tank mass is assumed to be proportional to the propellant volume. The approach is more flexible than the classical one (i.e., the ordinary differentiation of the function to be minimized), as it can easily be extended to cases where the performance index is not an explicit function of the parameters (for example, if gravitational and aerodynamic losses are taken into account). The results show that mixture-ratio control can significantly improve rocket performance and that most of the benefit is obtained simply by dividing the trajectory into two phases with different constant mixture ratios. single-stage-to-orbit (SSTO) vehicle feasible. The continuous control of the mixture ratio renders the engine design more complex, whereas comparable benefits can be obtained by means of a simpler control law, namely, the dual mixture-ratio operation, which is the main object of this analysis.