Minimum-fuel turning climbout and descent guidance of transport jets

Abstract

The complete flightpath optimization problem for minimum fuel consumption from takeoff to landing including the initial and final turns from and to the runway heading is solved. However, only the initial and final segments which contain the turns are treated, since the straight-line climbout, cruise, and descent problems have already been solved. The paths are derived by generating fields of extremals, using the necessary conditions of optimal control together with singular arcs and state constraints. Results show that the speed profiles for straight flight and turning flight are essentially identical except for the final horizontal accelerating or decelerating turns. The optimal turns require no abrupt maneuvers, and an approximation of the optimal turns could be easily integrated with present straight-line climb-cruise-descent fuel-optimization algorithms. Climbout at the optimal IAS rather than the 250-knot terminal-area speed limit would save 36 lb of fuel for the 727-100 aircraft