Mathematical Modeling for Optimization of Competition Sailplane Flight: a Preliminary Approach

In this work, sailplane symmetrical motion equations including pitch motion controlled by elevator angle are presented. The following effects are especially taken into consideration: i) tail damping due to pitch motion; ii) air density variation according to altitude; iii) presence of vertical and horizontal atmospheric air motions, and iv) non-linearity of CL ′ a curve near stall angle. The mathematical modeling includes the construction of an objective function for competition flight optimization. Making use of the concept of state variables, the minimum time trajectory problem is formulated as an optimal control problem with state constraints. Using simplified control laws and a mathematical programming algorithm, suboptimal trajectories are obtained for the sailplane PIK-20B.