Simultaneous optimization of staging and trajectory of launch vehicles using two different approaches

In this paper, two different approaches are proposed for simultaneous optimization of staging and trajectory of multistage launch vehicles. In the first approach, the problems of staging optimization and trajectory optimization are solved separately. These problems are linked together by an overhead problem to find the overall optimal solution. In the second approach, the optimal staging and trajectory are achieved during trajectory optimization in an integrated problem. In the first approach, staging is optimized based on ideal velocity and classic formulation of staging, and in the second approach, staging is optimized based on actual velocity and details of trajectory optimization problem. In both approaches, direct collocation method and nonlinear programming techniques are used for solving optimization problems. A numerical example is presented and solved to demonstrate and compare the capabilities of proposed approaches. Both approaches can lead to very similar solutions in spite of their differences in staging formulation. Integrated approach can lead to better results because of simultaneous consideration of objective functions and effective constraints of two optimization problems of staging and trajectory.