Minimum-Time Loop Maneuvers of Jet Aircraft

Abstract

Minimum-time loop maneuvers of jet aircraft are investigatedvby means of the calculus of variations. The optimal control (lift coefficient and thrust) is determined as a function of the state variables and Lagrange multipliers for an arbitrary maneuver in the vertical plane. Intermediate thrust arcs and intermediate lift arcs with minimum thrust are shown to be nonoptimal for the dynamic models considered. Rules are established for joining trajectory segments with different types of control behavior. Using these results, optimal loop trajectories are generated for a given set of initial conditions and a large number of values of maximum lift coefficient and maximum thrust. The control history and the maneuver time are found to be strongly affected by the latter two parameters. Two aerodynamic models are considered, one relatively simple and the other somewhat more complicated.