Effects of Sidewinds on Optimal Flight Speed of Birds

The relationship between flight power and airspeed of birds, as derived from flight mechanical theory, can be used to predict the maximum range speed Vmr which is the optimal speed for minimizing the cost of transport. This speed is not constant but depends on the winds. Earlier predictions about the optimal adjustment of flight speed by birds in relation to winds are only valid in due head- and tailwind situations. We derive Vmr for birds flying along a constant track direction with an arbitrary wind. It emerges that the effect of sidewinds on Vmr depends on the marginal rate of return in groundspeed with an increasing airspeed. This marginal rate increases with the angle between the bird's track and heading direction. Hence, Vmr not only depends on the effect of wind on the bird's actual groundspeed but also on the bird's angle of compensation for the sidewinds. As a result, optimal flight speeds are faster in sidewinds than in tail- or headwinds with a corresponding speed increment caused by wind. The adjustments of optimal airspeed in relation to sidewinds will be analogous also for other characteristic flight speeds besides Vmr, such as the optimal flight speed associated with time-saving rather than energy-saving migration, and with food searching, flight between foraging patches and food delivery flights. We also discuss requirements for empirical tests of the predictions proposed in this paper.