A minimum-time, thermal-to-thermal sailplane trajectory optimization problem is formulated as a nonlinear optimal control problem. Numerical solutions are obtained using a gradient projection algorithm which incorporates conjugate directions of search. Further insight into the nature of the solutions and the computational process is obtained through dn analysis of the linearized sailplane dynamics and the necessary conditions for optimality. Numerical results are presented for two sailplane types and various values of thermal strength and distance between thermals. An additional problem is formulated and solved for the case of bounded control rate.