Analysis of optimal aircraft cruise with fixed arrival time including wind effects

Minimum-fuel cruise at constant altitude with the constraint of a fixed arrival time is analyzed, including the effects of average horizontal winds. The analysis is made using the theory of singular optimal control. The optimal control is of the bang-singular-bang type, and the optimal trajectories are formed by a singular arc and two minimum/maximum-thrust arcs joining the singular arc with the given initial and final points. The effects of average horizontal winds on the optimal results are analyzed, both qualitatively and quantitatively. The influence of the initial aircraft weight and the given cruise altitude is analyzed as well. Two applications are studied: first, the cost of meeting the given arrival time under mismodeled winds, and, second, the cost of flight delays imposed on a nominal optimal path. The optimal results are used to assess the optimality of cruising at constant speed; the results show that the standard constant-Mach cruise is very close to optimal. Results are presented for a model of a Boeing 767-300ER.