A faster cruising speed increases drag and thereby the thrust (T) needed to fly, while the weight and lift (L) requirement remains constant. Birds can adjust their wingbeat in multiple ways to accommodate this change in aerodynamic force, but the relative costs of different strategies remain largely unknown. To evaluate the efficiency of several kinematic strategies, I used a robotic wing (Ajanic et al., 2023) and quantitative flow measurements. I found that, among the tested strategies, changing the mean wingbeat elevation provides the most efficient solution to changing T/L, offering insight into why birds tend to beat their wings with a greater ventral than dorsal excursion. I also found that although propulsive efficiency (ηp) may peak at a Strouhalnumber (St, measure of relative flapping speed) near 0.3, the overall efficiency of generating force decreases with St. This challenges the expectance of a specific optimal St for flapping flight and instead suggest the chosen St depends on T/L. This may explain the variation in preferred St among birds and why bats prefer flying at higher St than birds (Taylor et al., 2003) since their body shape imposes relatively higher thrust requirements (Muijres et al., 2012). In addition to explaining flapping strategies used by birds, my results suggest alternative, efficient, flapping motions for drones to explore aiming to extend their flight range.

The data was collected using stereo particle image velocimetry in a plane transverse to the free-stream flow of a wind tunnel, capturing the wake of a flapping bio-hybrid robotic wing. The images were processed using Davis 10.2.1 (Lavision).