Nonoptimality of the steady-state cruise for aircraft

For a fairly general aircraft model and a large class of drag models, steady-state cruise for a long time span is nonoptimal with respect to fuel economy. This is proved by a second-order variational analysis, using a frequency-domain version of the classical Jacobi (conjugate point) optimality condition. The variational analysis suggests a sinusoidal perturbation away from steady-state cruise which improves fuel economy (as confirmed numerically), but is still not optimal. The form of the optimal trajectory for long duration cruise is unknown. However, two intuitive reasons for improved fuel economy using cycle cruise paths are given.