A maximum principle application shows that a fuel-optimal aircraft trajectory which arrives at an assigned time is also a direct operating cost-optimal trajectory for certain time cost. The time cost is minimum for maximum endurance cruise. Only for minimum time cost can an optimal trajectory contain a hold or path stretching segment. These concepts are illustrated for three aircraft: the Boeing 737, 747, and 767. Complete optimal trajectories are shown for the 747. Cruise control implications are investigated using the 767 model. Finally, optimal descents are compared to Mach/CAS descents for the 737.
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James W. Burrows (1983) studied this question.
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