Oscillatory cruise — A perspective

The problem of minimum fuel/km is examined using various simplifications, introduced in the last three decades, leading to order reduction. In particular, the second variation about steady cruise, ignoring only the slow change in total weight, reveals two separate physical reasons for the possible advantage of oscillatory cruise. A linear analysis with quadratic payoff (the second variation) and with bounds on thrust variation yields quite good agreement with an exact solution, published recently, for the optimal periodic cruise of a particular airplane. Finally, an explanation is given for the much more substantial percentage saving obtainable by oscillatory maneuvers in the “endurance” problem: minimum fuel/hour.