Optimal Minimum-Fuel Trajectories of Supersonic Passenger Aircraft

Abstract

Using the classical method of dynamic programming, the trajectories of the motion of a supersonic passenger aircraft, which are optimal in terms of fuel consumption, are constructed. The mathematical model of the aircraft, which maximally takes into account the usual restrictions imposed on the allowable maneuvers of the aircraft by its design features, is used. Optimal solutions are found without prior division of the flight into separate sections. Despite the fact that the calculations disregard the limitations imposed by the current flight rules for civil aircraft, it turns out that the optimal trajectories are quite convenient for use within these limitations. It is clarified that the sections of motion with a speed exceeding the speed of sound are at high altitude. It avoids an additional acoustic impact on people living near airports and, at the same time, reduces the fuel consumption. The sections of optimal trajectories corresponding to cruise flight are located at high altitudes and, therefore, the interference with the motion of conventional aircraft can be practically reduced to zero. The initial and final parts of the trajectory located in areas close to airports with high traffic density differ only slightly for various required flight durations and, therefore, require no great accuracy in practical implementation.