Preyss/Willes' "corner-velocity" optimum and the Boyd/Christie "'corridor", both techniques for optimal airplane turns, need no longer be thought contradictory; both appear in a consistent way among the family generated by a reduced-order approximation scheme.
S~mmry--A brief review is given of some recent theoretical work on optimal atmospheric flight, comprising an extension of so-called "energy climbs" to three=dimensiooal flight and an analytical recasting in terms of singular perturbation theory.
A family of variable-altitude turns obtained by numerical integration in the reduced-order ("cocrgy") approximation is presented for a hypothetical supersonic aircraft, including the effects of constraints on altitude, dynamic pressure, Mach number, lift coefficknt, and normal load factor. An important part of the family consists of full-throttle turning maneuver; another part features throttle closed and speed brakes extended for various initial periods of flight along the "cornsx-velocity locus", the path in the Mac.h-altitude chart along which maximum rift coefficient and maximum normal load factor can he obtained simultaneously, followed by a period of full-throttle turning. The highest sustainable turning rate appears transonically at low altitude and such a steady turn is a member of the family. Extended=duration optimal turns tend to approach this equilibrium during central portions of their histories.