Fixed-range optimal trajectories of supersonic aircraft by first-order expansions

Robert Windhorst, Mark Ardema, David Kinney

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


A near-optimal guidance law that generates minimum-fuel, minimum-time, or direct operating cost fixed-range trajectories for supersonic transport aircraft is developed. The approach uses singular perturbation techniques to timescale decouple the equations of motion into three sets of dynamics, two of which are studied here: weight/range and energy. The two-point boundary-value problems obtained by application of the maximum principle to the dynamic systems are solved using the method of matched asymptotic expansions. Both the weight/range and the energy dynamic solutions are carried out to first order. The two solutions are combined using the matching principle to form a uniformly valid approximation of the full fixed-range trajectory. Results show that the minimum-fuel trajectory has three segments: a minimum-fuel energy climb, a cruise climb, and a minimum-drag glide. The minimum-time trajectory also has three segments: a maximum dynamic pressure climb, a constant altitude cruise, and a maximum dynamic pressure descent. The minimum direct operating cost trajectory is an optimal combination of the preceding two trajectories. It is shown that for representative costs of fuel and flight time, the minimum direct operating cost trajectory is very similar to the minimum-fuel trajectory.

Original languageEnglish
Pages (from-to)700-709
Number of pages10
JournalJournal of Guidance, Control, and Dynamics
Issue number4
StatePublished - Jul 2001
Externally publishedYes


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