Improved Endurance of Optimal Periodic Flight

For a class of subsonic aircraft, endurance can be improved significantly by flying in a periodic path rather than in steady state. The optimal periodic endurance problem is formulated in which the performance criterion for endurance, fuel used over flight time, is minimized and the aircraft is constrained to fly in a periodic path. The optimal steady-state endurance problem is formulated in which the instantaneous fuel rate is minimized subject to the aircraft dynamics being in equilibrium. For both optimization problems, the aircraft is further constrained to fly on the surface of a vertical cylinder. In practice, this allows the aircraft to circle above a target on the ground. Because the missions that require maximal endurance often take place in a confined airspace (e.g., surveillance, reconnaissance, and loitering before strike), this assumption appears to be more appropriate than the usual assumption in which the aircraft is constrained in a vertical plane and. flies straight ahead. An example shows that for a subsonic aircraft with maximal lift-to-drag ratio of 17.4 and thrust-to-weight ratio of 0.5, the endurance of the optimal periodic flight is over three times the endurance of the optimal steady-state flight.