Stratospheric airships are lighter-than-air vehicles that have the potential to provide an extremely-long-duration airborne presence at altitudes of 18-22 km. In this paper, we examine optimal ascent trajectories that use 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 collocation 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 with minimum-time flights, given small increases in flight time. In addition, the effects of time-varying mass and Earth rotation are found to be comparable with the effects of wind rate, and they are used in the optimal solutions.
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This work was supported in part by a research grant from the National Science Foundation, award no. CCF—0515009, and by a NASA cooperative agreement, NNG05GG39H.
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