Abstract
The long-range aircraft cruise problem is very important for airlines which desire to minimize fuel consumption. Many papers have been appeared including the case which the criteria involve cruising time. Most of them, however, solve the problems under condition of a steady-state flight. In other word, they optimize the constrained problem. In the present operation, the altitude and velocity are chosen the optimal ones that are derived from the solution of a minimum fuel problem for a steady-state level flight. This solution satisfies the neccessary conditions of optimality. However, it is shown that the steady cruise is non-convex. The non optimality of a steady cruise is also reported, and the optimal solutions are solved using a periodic control that repeats the same sequence of unsteady controls and trajectories.
In this paper, the long range minimum fuel problem is solved numerically under the assumption that the optimal thrust control becomes a bang-bang type. The aircraft weight change during one period is ignored. Under the boundary condition that the initial states are the same as the terminal ones, the optimal problem is solved. The equations of motion for an aircraft is the point-mass model, the atomospheric density is a funcion of the altitude.
It is shown that the optimal arc consists of two quasi-steady subarcs. It is also shown that the same subarcs are derived by using a reduced order model. The optimal controls for this model become the chattering type. The control and state variables of this solution are characteristic of the unsteady optimal cruise.
