## Maximum-range trajectories for an unpowered reusable launch vehicle

##### Abstract

A software package has been developed that numerically maximizes the range of an unpowered reusable launch vehicle (RLV) during the Terminal Area Energy Management (TAEM) phase of reentry into Earth's atmosphere by adjusting the angle-of-attack control profile at preselected energy heights along its trajectory. The software computes the optimal trajectory in terms of angle-of-attack deviations from a maximum lift-to-drag trajectory, which is the traditional trajectory used to maximize range of an unpowered aerial vehicle. In order to test the optimization software, an aerodynamic model of the X-34 launch vehicle was developed to calculate lift and drag coefficients for a given angle of attack and Mach number. Consideration of different numbers of control nodes is made, primarily with gradient-based optimization, though particle-swarm optimization is briefly tested. The merits of alternative control laws, such as constant-velocity or constant-dynamic-pressure quasi-equilibrium glide (QEG) algorithms, have also been investigated in an attempt to find a control law that does not require the inherent computational costs associated with numerical optimization. A two-point boundary-value problem is set up using optimal control theory to describe the optimization problem with simplified aerodynamic and atmospheric models.

##### Degree

M.S.