Optimized Solutions for Kistler K-1 Branching Trajectories Using Multidisciplinary Design Optimization Techniques

Fully reusable two-stage-to-orbit launch vehicle designs that incorporate branching trajectories during their ascent are of current interest in the advanced launch vehicle design community. Unlike expendable vehicle designs, the booster of a two-stage reusable system must fly to a designated landing site after staging. Because of a mutual dependence on the staging conditions, both the booster flyback branch and the orbital branch of the ascent trajectory must be simultaneously optimized to achieve an overall system objective. The optimum solution is often a compromise between the local objectives of the two branches. Current and notable designs in this class include the U.S. Air Force Space Operations Vehicle designs, the Kelly Astroliner, the Kistler K-1, and NASA's proposed liquid flyback booster designs (space shuttle booster replacement). Solution techniques are introduced that are well suited to solving this class of problem with existing single-segment trajectory optimization codes. In particular, these methods originate from the field of multidisciplinary design optimization and include optimization-based decomposition and collaborative optimization. The results of applying these techniques to the branching trajectory optimization problem for the Kistler K-1 launch vehicle are given and conclusions are drawn with respect to computational efficiency and quality of the results. In general, partial optimization-based decomposition was preferred due to its superior robustness, ease of setup, fast execution time, and optimality of the results.