Trajectory Design of a Rocket-Scramjet-Rocket Multistage Launch System

The integration of a reusable scramjet vehicle as the second stage of a multistage space launch system has the potential to reduce the cost of small-payload orbital launches. This paper determines the maximum payload to orbit trajectory of a multistage rocket-scramjet-rocket system. This trajectory is calculated by formulating the problem as an optimal control problem, and then solving it using the pseudospectral method. Using this method, it is determined that the optimal trajectory for the scramjet stage involves an initial decrease in dynamic pressure, followed by constant-dynamic-pressure flight, and finally a pullup maneuver. This optimal trajectory results in an 8.35% improvement in payload mass to orbit when compared to a constant-dynamic-pressure trajectory with minimum pullup. Furthermore, the optimal pullup maneuver decreases the maximum dynamic pressure experienced by the final rocket stage by 20.3%. The sensitivity of the trajectory is tested by varying the maximum allowable dynamic pressure and the drag produced by the vehicle. A maximum dynamic pressure variation of +/- 5 kPa is shown to produce only +3.8% and -3.5% variations in the payload mass. A drag increase of 10% is shown to produce a similar optimal trajectory shape, indicating robustness with variation of the vehicle aerodynamics.