Fixedrrange optimal trajectories of supersonic aircraft by first-order expansions

Robert Windhorst, Mark Ardema, Dave Kinney

Research output: Contribution to conferencePaperpeer-review

1 Scopus citations

Abstract

This paper develops a near-optimal guidance law that generates minimum fuel, time, or direct operating cost fixed-range trajectories for supersonic transport aircraft. The approach uses singular perturbation techniques to time-scale de-couple 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 realistic costs of fuel and flight time, the minimum direct operating cost trajectory is very similar to the minimum fuel trajectory.

Original languageEnglish
Pages690-703
Number of pages14
StatePublished - 1999
Externally publishedYes
EventGuidance, Navigation, and Control Conference and Exhibit, 1999 - Portland, United States
Duration: Aug 9 1999Aug 11 1999

Conference

ConferenceGuidance, Navigation, and Control Conference and Exhibit, 1999
Country/TerritoryUnited States
CityPortland
Period08/9/9908/11/99

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