A Unified Optimal Control Approach for Maximum Endurance and Maximum Range

This paper proposes a unified optimal control framework that can be used to formulate and solve aircraft performance problems, such as maximum endurance and maximum range, for both propeller-driven airplanes and jet-propelled aircraft. It is proved in this paper that such problems have a common mathematical formulation and, under strict convexity assumptions, they have a unique feedback solution for the speed as a function of weight. The feedback solution yields an analytic expression for the optimal speed. For maximum endurance, the solution corresponds to the minimization of the rate of fuel consumption per unit time. For maximum range, the rate of fuel consumption per unit distance is minimized. Moreover, the optimal solution for maximum range will be interpreted geometrically using the concept of convex conjugate function and Legendre transformation. Although the optimal control framework is illustrated for maximum range and maximum endurance, it is a general approach that can be used for other aircraft performance problems.