Numerical solution of a simultaneous staging and trajectory optimization problem of a hypersonic space vehicle

In the development phase of multi-stage space vehicles one usually solves a large number of trajectory optimization problems for different mass designs. If certain functional relationships between the mass of important components are available it is desirable to include into the optimization process of the flight path a variation of the mass design. As an example of this approach we present a simultaneous stage separation and trajectory optimization to a realistic model of a hypersonic two-stage space vehicle system. We consider equality constraints which define a functional relationship between the used structure and fuel mass. Therefore reductions of the necessary fuel mass achieved by optimizing the flight path are used immediatly to reduce the previously asigned fuel tank volume. Generalized and more detailed mass models can be handled by the described method, too. The numerical solutions are computed by an indirect method. Due to the simultaneous occurrence of piecewise defined model functions and several state and control constraints the necessary conditions of optimal control theory had to be extended.