de Oliveira, P. and de Freitas Pinto, R., "Flight Path Optimization for Competition Sailplanes through State Variables Parameterization," SAE Technical Paper 2004-01-3472, 2004, doi:10.4271/2004-01-3472.
This paper presents a numerical process for determination of optimal flight paths for competition soaring. The issue is reduction of flight time in order to soar towards an ascending thermal and climb, through thermal flying, to the initial altitude. The optimization procedure consists in the application of a Direct Method in order to obtain suboptimal solutions through parameterization of state variables, unlike a previous study by the same authors which was based on control parameterization. A mathematical programming procedure is used in order to determine the sub-optimal values for the parameterized state variables. The optimal control law, which is necessary for the generation of the sub-optimal state, is obtained through a step by step penalty technique. The obtained results demonstrate that the optimization of transitory phases is important for the minimization of total flight time.