Maximum Endurance of a Turboprop in Cruise with Head and Tail-Wind

This paper proposes an optimal control approach to formulate and solve the maximum endurance problem for turboprop aircraft in steady cruise. Furthermore, the problem formulation also considers the effect of head and tail-winds on total endurance time. An analytical state-feedback solution is provided for the maximum endurance airspeed of a turboprop, as well as an analytical expression for the maximum endurance time. The sensitivity of the total endurance time with respect to air density is also provided to illustrate the strong effect cruising altitude has on total endurance time. Finally, an example using the Beechcraft King Air turboprop aircraft is provided to validate the results.