Improved analytical methods for assessment of hypersonic drag-modulation trajectory control
Putnam, Zachary Reed
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During planetary entry, a vehicle uses drag generated from flight through the planetary atmosphere to decelerate from hyperbolic or orbital velocity. To date, all guided entry systems have utilized lift-modulation trajectory control. Deployable aerodynamic devices enable drag-modulation trajectory control, where a vehicle controls its energy and range during entry by varying drag area. Implementation of conventional lift-modulation systems is challenging for deployable systems. In contrast, drag-modulation trajectory control may be simpler and lower-cost than current state-of-the-art lift-modulation systems. In this investigation, a survey of analytical methods for computing planetary entry trajectories is presented and the approximate analytical solution to the entry equations of motion originally developed by Allen and Eggers is extended to enable flight performance evaluation of drag-modulation trajectory control systems. Results indicate that significant range control authority is available for vehicles with modestly sized decelerators. The extended Allen-Eggers solution is closed-form and enables rapid evaluation of nonlifting entry trajectories. The solution is utilized to develop analytical relationships for discrete-event drag-modulation systems. These relationships have direct application to onboard guidance and targeting systems. Numerical techniques were used to evaluate drag-modulation trajectory control for precision landing and planetary aerocapture missions, including development of prototype real-time guidance and targeting algorithms. Results show that simple, discrete-event drag-modulation trajectory control systems can provide landed accuracies competitive with the current state of the art and a more benign aerothermal environment during entry for robotic-scale exploration missions. For aerocapture, drag-modulation trajectory control is shown to be feasible for missions to Mars and Titan and the required delta-V for periapsis raise is insensitive to the particular method of drag modulation. Overall, results indicate that drag-modulation trajectory control is feasible for a subset of planetary entry and aerocapture missions. To facilitate intelligent system selection, a method is proposed for comparing lift and drag-modulation trajectory control schemes. This method applies nonlinear variational techniques to closed-form analytical solutions of the equations of motion, generating closed-form expressions for variations of arbitrary order. This comparative method is quantitative, performance-based, addresses robustness, and applicable early in the design process. This method is applied to steep planetary entry trajectories and shows that, in general, lift and drag-modulation systems exhibit similar responses to perturbations in environmental and initial state perturbations. However, significant differences are present for aerodynamic perturbations and results demonstrate that drag systems may be more robust to uncertainty in aerodynamic parameters. Finally, the results of these contributions are combined to build a set of guidelines for selecting lift or drag-modulation for a Mars Science Laboratory-class planetary entry mission.