Design and analysis of optimal ascent trajectories for stratospheric airships

Abstract

Stratospheric airships are lighter-than-air vehicles that have the potential to provide a long-duration airborne presence at altitudes of 18-22 km. Designed to operate on solar power in the calm portion of the lower stratosphere and above all regulated air traffic and cloud cover, these vehicles represent an emerging platform that resides between conventional aircraft and satellites. A particular challenge for airship operation is the planning of ascent trajectories, as the slow moving vehicle must traverse the high wind region of the jet stream. Due to large changes in wind speed and direction across altitude and the susceptibility of airship motion to wind, the trajectory must be carefully planned, preferably optimized, in order to ensure that the desired station be reached within acceptable performance bounds of flight time and energy consumption. This thesis develops optimal ascent trajectories for stratospheric airships, examines the structure and sensitivity of these solutions, and presents a strategy for onboard guidance. Optimal ascent trajectories are developed that utilize wind energy to achieve minimum-time and minimum-energy flights. The airship is represented by a three-dimensional point mass model, and the equations of motion include aerodynamic lift and drag, vectored thrust, added mass effects, and accelerations due to mass flow rate, wind rates, and Earth rotation. A representative wind profile is developed based on historical meteorological data and measurements. Trajectory optimization is performed by first defining an optimal control problem with both terminal and path constraints, then using direct transcription to develop an approximate nonlinear parameter optimization problem of finite dimension. Optimal ascent trajectories are determined using SNOPT for a variety of upwind, downwind, and crosswind launch locations. Results of extensive optimization solutions illustrate definitive patterns in the ascent path for minimum time flights across varying launch locations, and show that significant energy savings can be realized with minimum-energy flights, compared to minimum-time time flights, given small increases in flight time. The performance of the optimal trajectories are then studied with respect to solar energy production during ascent, as well as sensitivity of the solutions to small changes in drag coefficient and wind model parameters. Results of solar power model simulations indicate that solar energy is sufficient to power ascent flights, but that significant energy loss can occur for certain types of trajectories. Sensitivity to the drag and wind model is approximated through numerical simulations, showing that optimal solutions change gradually with respect to changing wind and drag parameters and providing deeper insight into the characteristics of optimal airship flights. Finally, alternative methods are developed to generate near-optimal ascent trajectories in a manner suitable for onboard implementation. The structures and characteristics of previously developed minimum-time and minimum-energy ascent trajectories are used to construct simplified trajectory models, which are efficiently solved in a smaller numerical optimization problem. Comparison of these alternative solutions to the original SNOPT solutions show excellent agreement, suggesting the alternate formulations are an effective means to develop near-optimal solutions in an onboard setting.