Models for the Optimization of Air Refueling Missions

This research follows A. Yamani's work on the problem of minimizing total fuel costs for airlift missions that require in-flight refueling. Yamani's major assumptions were removed and the resulting enhanced formulation was applied the the original problem and the related problem of maximizing allowable cabin load. This optimization is accomplished selecting the rendezvous point and initial fuel for each aircraft. The formulation considers a C-141B airlifter refueled once by a KC-135E tanker. Flight is assumed to be at constant altitude and follow great-circle routes. The fuel costs of climb and cruise flight are modeled as functions of gross weight, while fuel costs associated with the air refueling maneuver, descent, landing, and required reserve are modeled as constant numbers. An air refueling track is represented along with the effects of a constant wind. The necessity of a refueling alternate is also included. The method of Sequential Quadratic Programming was used to obtain numerical results. Comparison of model results with a computer-generated flight plan shows that substantial fuel savings and a large increase of allowable cabin load are possible through the selection of an optimal rendezvous point and initial fuel combination. However, minimization of the mission fuel cost is only appropriate in situations where the cargo weight is a fixed quantity less than the maximum capacity of the aircraft. Otherwise, the cargo load should be maximized as this reduces the total number of missions required, and thus provides the greatest savings.