Optimal trajectories for the short-distance foraging flights of swans

Optimal flight theory relates body measurements (wing span, body cross-section, body mass) and aerodynamic variables (air density, drag, profile and induced power ratios) to the most energy-efficient velocity for long distance migration. For short-range (2-10 km) foraging flights the theory is expanded to include non-negligible costs for take-off and energy savings/losses for climbing to altitude (drag decreases with air density and therefore with altitude). The theory predicts clear differences between Tundra and Trumpeter swans. Generally speaking, for flights between 2 and 10 km Trumpeter swans can be expected to fly approximately 5-10 m lower in altitude and 1-2 ms(-1)more slowly than Tundra swans. Moreover, the total energy required for these foraging flights is approximately 150% larger for a Trumpeter than a Tundra swan (80 vs. 120 kJ of direct mechanical energy for a 5 km flight), suggesting that Trumpeter swans may be less inclined to take-off than Tundra swans. These factors indicate that even Trumpeters native to the area (as opposed to recently translocated) would be more vulnerable to hunting than native Tundra swans. The expanded theory is compared to observations made in Utah's Bear River Migratory Bird Refuge.