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Scaling bat wingbeat frequency and amplitude

R. D. Bullen^1,* and N. L. McKenzie²

¹ 43 Murray Drive, Hillarys, Western Australia, Australia 6025
² Department of Conservation and Land Management, PO Box 51, Wanneroo, Western Australia, Australia, 6065

View larger version (24K): [in a new window]   Fig. 1. Examples of wingbeat test point time histories. (A) A comparison of three recording formats at different frame rates recorded at the same time. The DigiBeta at 48 frames s-1 (diamonds) and VHS at 24 frames s-1 (triangles) sequences are offset from the cine recording at 200 frames s-1 (squares) for clarity. (B,C) Typical time histories of a large microbat (B) and a megabat (C) at low frame rates. The solid line in each case is a typical spline fit applied to the data. The broken lines in B are the author's interpolation. In B, Y and N denote the peaks used and not used, respectively, in the average amplitude range assessment. V, flight speed; fw, wingbeat frequency; w, wingbeat amplitude.

View larger version (14K): [in a new window]   Fig. 2. Example of (A) wingbeat frequency (fw) and (B) amplitude (w) data for one of the species included in the study, Chalinolobus gouldii (mass 0.0134 kg). Note this figure includes high-amplitude data (boxed points in B) taken from test points during accelerating flight at low-flight speed, because we have included them in the derivation of the maximum amplitude results in Table 5. They are not included in the derivation of the general amplitude versus flight speed (V) relationship of Equation 4. In A, + symbols are fw data from the observation chamber; X symbols, free flight fw data; crossed X symbols, hand-release test points. In B, squares are data from the observation chamber and diamonds are daylight hand-release data.

View larger version (14K): [in a new window]   Fig. 6. Wingbeat frequency (fw) data for Mormopterus planiceps. Equation 3 describing the general relationship between fw, mass (m) and flight speed (V) is superimposed over the data, showing the accurate prediction of the higher frequency range used by the bat. For this species, a lower fw range, approximately 3 Hz below the Equation 3 estimate, is also used by the bat. This is the only species observed to use two different frequency ranges.

View larger version (22K): [in a new window]   Fig. 3. Summary of wingbeat frequency (fw) data. (A) Low-speed data. For each species, the mean values ± S.D. of the data at maximum range velocity (Vmr) are presented. The linear regression curve may be used to estimate fw at Vmr for all species. (B) High-speed data. For each species, the mean value ± S.D. of the data (V>6 ms-1) are presented. The linear regression curve may be used to estimate fw for all species flying at high speeds. Mp, Mormopterus planiceps, Nts/w, the southwestern population of Nyctophilus timoriensis and Nl, Noctilio leporinus.

View larger version (28K): [in a new window]   Fig. 4. (A) Plot of the three-dimensional surface represented by the frequency (fw, solid line) versus log10m (in kg) versus log10V (in ms-1) model given by Equation 3. (B) Surface edge looking in the direction of decreasing flight speed. (C) Surface edge looking in the direction of increasing mass.

View larger version (12K): [in a new window]   Fig. 5. Proposed model for wingbeat frequency (fw, solid line) and amplitude (w, broken line) variation with mass and flight speed (V). For clarity and for direct comparison with the data in Fig. 2, the model for Chalinolobus gouldii of mass (m) 0.0134 kg is presented. SREF is wing area in m2.

View larger version (37K): [in a new window]   Fig. 7. (A) Plot of the three-dimensional surface represented by the wingbeat amplitude (w) versus flight speed (V) versus log10SREF (in m2) model given by Equation 4. (B) Surface edge looking in the direction of decreasing area. (C) Surface edge looking in the direction of decreasing flight speed.

View larger version (16K): [in a new window]   Fig. 8. Comparison of bat wingbeat frequency (fw) data with bird kinematics. For each bat species included in this study, the observed high-speed fw is plotted against a fw value calculated using the model applicable to birds from Pennycuick (1996). The values of the bat's mass, span and wing area from Table 1 are used for the calculated frequency. The upper bold line represents a regression showing that bat fw is 50 % higher than bird fw of similar morphological values. The lower thin line gives a hypothetical line of equivalence.