Maximum Endurance of a Turbofan in Cruise with Head or Tail-Wind

Maximizing the endurance of an aircraft is a problem with several applications. This paper proposes an optimal control framework to solve the maximum endurance problem of a turbofan in cruise, and takes into account the presence of head or tail-winds. Since the optimal solution of this problem involves finding the root of a quintic polynomial, an approximate state-feedback analytical solution is proposed using the first iteration of Newton's method. This is the main contribution of the paper. Upper error bounds are also derived for the proposed algorithm in order to validate its accuracy. Simulation results are shown and compared with the maximum endurance performance mode of a Boeing 737 FMS. The simulation results show that the proposed speed is closer to the optimal solution than the speed of a commercial FMS.

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