A Generalized Staging Optimization Program For Space Launch Vehicles

This paper addresses the staging optimization problem for multistage rockets which carry payloads from the Earth's surface into the Earth orbits. In the early design phases, requirements are not so strict, there are many unknowns and problem arises as to what is the optimum staging to achieve the given mission. Therefore, designers need simplified tools providing a quick insight on the vehicle performance with minimum basic vehicle data. For this purpose, a Matlab (R) based computer program has been written to determine staging parameters (number of stages, mass distribution between stages, and the propellant and structural masses for each individual stage) which minimize the gross lift-off mass of the launch vehicle for a specific mission. In this study, staging optimization problem has been formulated based on Delta-V equations and solved by method of Lagrange Multipliers. The problem has been stated in a general form to handle launch vehicles having arbitrary number of stages and with various configurations involving serial, parallel and clustered stages; and with different structural ratios and propellant exhaust velocities in each stage. Staging optimization program developed in this study has been verified for different missions using available data of existing launch vehicles. Thus, a quick and effective tool to find optimal vehicle configurations in the conceptual design phase of a generic multistage launch vehicle has been achieved.