Scaling bat wingbeat frequency and amplitude.

Wingbeat frequency (f(w)) and amplitude (theta;(w)) were measured for 23 species of Australian bat, representing two sub-orders and six families. Maximum values were between 4 and 13 Hz for f(w), and between 90 and 150 degrees for theta;(w), depending on the species. Wingbeat frequency for each species was found to vary only slightly with flight speed over the lower half of the speed range. At high speeds, frequency is almost independent of velocity. Wingbeat frequency (Hz) depends on bat mass (m, kg) and flight speed (V, ms(-1)) according to the equation: f(w)=5.54-3.068log10m-2.857log10V. This simple relationship applies to both sub-orders and to all six families of bats studied. For 21 of the 23 species, the empirical values were within 1 Hz of the model values. One species, a small molossid, also had a second mode of flight in which f(w) was up to 3 Hz lower for all flight speeds. The following relationship predicts wingbeat amplitude to within +/-15 degrees from flight speed and wing area (S(REF), m(2)) at all flight speeds: theta;(w)=56.92+5.18V+16.06log10S(REF). This equation is based on data up to and including speeds that require maximum wingbeat amplitude to be sustained. For most species, the maximum wingbeat amplitude was 140 degrees.