Altitude Transitions in Energy Climbs

Abstract

The aircraft energy-climb trajectory for configurations with a sharp transonic drag rise is well known to possess two branches in the altitude/Mach-number plane. Transition in altitude between the two branches occurs instantaneously, a “corner” in the minimum-time solution obtained with the energy-state model. If the initial and final values of altitude do not lie on the energy-climb trajectory, then additional jumps (crude approximations to dives and zooms) are required at the initial and terminal points. With a singular-perturbation approach, a “boundary-layer” - correction is obtained for each altitude jump, the transonic jump being a so-called “internal” boundary layer, different in character from the initial and terminal layers. The determination of this internal boundary layer is examined and some computational results for an example presented.