Singular Arc Time-Optimal Climb Trajectory of Aircraft in a Two-Dimensional Wind Field

Abstract

This paper presents a study of a minimum time-to-climb trajectory analysis for aircraft flying in a twodimensional altitude dependent wind field. The time optimal control problem possesses a singular control structure when the lift coefficient is taken as a control vari able. A singular arc analysis is performed to obtain an optimal control solution on the singular arc. Using a time-scale separation with the flight path angle treated as a fast state, the dimensionality of the optimal control solution is reduced by eliminating the lift coefficient control. A further singular arc analysis is used to decompose the original optimal control solution into the flight path angle solution and a trajectory solution as a function of the airspeed and altitude. The optimal control solutions for the initial and final climb segments are comput ed using a shooting method with known starting values on the singular arc. The numerical results of the shooting method show that the optimal flight path angle on the initial and final climb segments are constant. Th e analytical approach provides a rapid means for analyzing a time optimal trajectory for aircraft performance.