Trajectory Optimization and Analytic Solutions for High-Speed Dynamic Soaring

Dynamic soaring is a non-powered flight mode that enables extremely high speeds by extracting energy from thin shear wind layers. Trajectory optimization is applied to construct solutions of the maximum speed achievable with dynamic soaring and to determine characteristic properties of that flight mode, using appropriate models of the vehicle dynamics and the shear wind layer. Furthermore, an energy-based flight mechanics model of high-speed dynamic soaring is developed, with reference made to trajectory optimization. With this model, analytic solutions for high-speed dynamic soaring are derived. The key factors for the maximum speed performance are identified and their effects are determined. Furthermore, analytic solutions for other, non-performance quantities of significance for high-speed dynamic soaring are derived. The analytic solutions virtually agree with the results achieved with the trajectory optimization using the vehicle dynamics model. This is considered a validation of the energy-based model yielding analytic solutions. The analytical solutions are also valid for the high subsonic Mach number region involving significant compressibility effects. This is of importance for future developments in high-speed dynamic soaring, as modern gliders are now capable of reaching that Mach number region.