1 Effect of Aeropropulsive Interactions and Design Sensitivities on Optimal Hypersonic Ascent Trajectories

Hypersonic vehicles with single-stage-to-orbit (SSTO) capability present a major design challenge. Such vehicles reflect highly integrated airframe and propulsion systems and are also known to exhibit a large degree of interaction between the airframe and engine dynamics. Consequently, even simplified hypersonic models are characterized by tightly coupled nonlinear equations of motion. The vehicle's overall mission performance is a function of its subsystem efficiencies, including structural, aerodynamic, propulsive, and operational. Further, all subsystem efficiencies are interrelated (hence, independent optimization of the subsystems likely will not lead to the optimum design). A standard indicator of overall mission performance is the maximum payload that can be taken into orbit. Trajectory optimization is the basic tool used to determine the flight path that will yield maximum weight to orbit for a specified vehicle and mission. Using an existing generic hypersonic model, previous efforts on this topic include solving a minimumfuel trajectory for orbit injection; evaluating the performance loss due to heating constraints placed on the vehicle; and performing a trade analysis to determine the sensitivities between subsystem efficiencies and mission performance. The emphasis in this paper is to expand on the existing generic hypersonic model to include the significant aeropropulsive interactions characteristic of this class of vehicle. As will be seen, the propulsive characteristics of the model vary with angle of attack. After detailing each new aerodynamic and propulsive coupling term to be added to the model, a static fueloptimum climb analysis is then performed These results will serve to illustrate the effect of engine/airframe dynamic coupling--namely the angle of attackdependence--on mission performance. * Graduate Fellow. ** Prof. and Chairman, University of Maryland. Copyright © 1994 by David K. Schmidt. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission. Nomenclature a sonic velocity Ad engine diffuser area ratio Ae engine exit area An engine nozzle area ratio CD vehicle drag coefficient CDo profile drag coefficient CL vehicle lift coefficient D vehicle drag E vehicle energy height FAR vehicle fuel-to-air ratio Fturn force due to turning of flow at engine inlet Fplume force due to exhaust plume pressure distribution g gravitational constant h vehicle altitude above Earth's surface k ratio of specific heats L vehicle lift l1 vehicle forebody length l2 vehicle aftbody length l3 vehicle length (length of upper surface) mf vehicle fuel flow rate (by mass) M• freestream Mach No. M1 engine inlet Mach No. Me engine exit Mach No. p• freestream pressure p1 engine inlet pressure pe engine exit pressure pfb surface pressure on vehicle forebody pus pressure on upper surface of vehicle q• freestream dynamic pressure Q vehicle heat load R vehicle distance from Earth's center