Wingbeat Frequency and the Body Drag Anomaly: Wind-Tunnel Observations on a Thrush Nightingale (Luscinia Luscinia) And a Teal (Anas Crecca)

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Abstract
A teal (Anas crecca) and a thrush nightingale (Luscinia luscinia) were trained to fly in the Lund wind tunnel for periods of up to 3 and 16 h respectively. Both birds flew in steady flapping flight, with such regularity that their wingbeat frequencies could be determined by viewing them through a shutter stroboscope. When flying at a constant air speed, the teal’s wingbeat frequency varied with the 0.364 power of the body mass and the thrush nightingale’s varied with the 0.430 power. Both exponents differed from zero, but neither differed from the predicted value (0.5) at the 1 % level of significance. The teal continued to flap steadily as the tunnel tilt angle was varied from —1 ° (climb) to +6 ° (descent), while the wingbeat frequency declined progressively by about 11 %. In both birds, the plot of wingbeat frequency against air speed in level flight was U-shaped, with small but statistically significant curvature. We identified the minima of these curves with the minimum power speed (Vmp) and found that the values predicted for Vmp, using previously published default values for the required variables, were only about two-thirds of the observed minimum-frequency speeds. The discrepancy could be resolved if the body drag coefficients (CDb) of both birds were near 0.08, rather than near 0.40 as previously assumed. The previously published high values for body drag coefficients were derived from wind-tunnel measurements on frozen bird bodies, from which the wings had been removed, and had long been regarded as anomalous, as values below 0.01 are given in the engineering literature for streamlined bodies. We suggest that birds of any size that have well-streamlined bodies can achieve minimum body drag coefficients of around 0.05 if the feet can be fully retracted under the flank feathers. In such birds, field observations of flight speeds may need to be reinterpreted in the light of higher estimates of Vmp. Estimates of the effective lift:drag ratio and range can also be revised upwards. Birds that have large feet or trailing legs may have higher body drag coefficients. The original estimates of around CDb=0.4 could be correct for species, such as pelicans and large herons, that also have prominent heads. We see no evidence for any progressive reduction of body drag coefficient in the Reynolds number range covered by our experiments, that is 21 600–215 000 on the basis of body cross-sectional diameter.