(A) Ventral view of a bat's left wing; 17 markers were painted on the bat, then tracked in numerous camera views. Markers used were: anterior and posterior sternum (a and b, respectively), shoulder (c), elbow (d), wrist (e), the metacarpophalangeal and interphalangeal joints and tips of digits III (f, g, h), IV (i, j, k), and V (l, m, n), the hip (o), knee (p) and foot (q). (B) Right lateral view of a bat in the body-centered coordinate system, with the left wing shown in grey. The path of the wrist (green dots) and wingtip (red dots) over a wingbeat cycle are shown. Stroke plane angle (β) was calculated as the angle between horizontal and the reduced major axis regression best fit line of the wingtip path in the x_b–z_b plane (blue dashed lines). By convention, β is expressed as a negative number (Norberg, 1990). (C) Right lateral view of the bat in the global coordinate system, with the paths of the wrist (green dots) and wingtip (red dots) over the wingbeat cycle shown. The position and posture of the left wing are shown at three time points in the wingbeat cycle.

Mid-downstroke wing camber and angle of attack were estimated as follows: (A) A parasagittal (x_g–z_g) cross section of the wing was taken at the y_g-value of the wrist at the time of maximum wingspan. Six triangular sections of the wing membrane crossed that plane and the intersections of triangle borders in the plane (red circles) were used as estimates of membrane position. (B) The actual curved shape of the membrane in the plane (solid black line) was estimated using the first term of a sine series fitted to those seven points. The maximum distance of the membrane line from the chord line (dashed grey line) was divided by the length of the chord line to give wing camber. (C) Angle of attack (α) was calculated as α₁ + α₂, where α₁ is the angle of the wing chord line above horizontal (blue dashed line), and α₂ is the angle between horizontal and the velocity vector of the wrist (red arrow) in the x_g–z_g plane.

Log–log phylogenetic GLS RMA regressions of wing shape parameters against body mass after phylogenetic correction. Circles represent medians for each species. Expected slopes under isometry are denoted by the grey dashed line. Where data approached or achieved statistically significant allometry, the best fit line is shown in black. (A) Maximum wingspan, (B) minimum wingspan, (C) wing chord, (D) maximum wing area, (E) wing loading, and (F) aspect ratio. Slope estimates are reported in Table 2.

Velocities and accelerations for the 135 wingbeat cycles in this study. The smallest bats (C. brachyotis; purple) were flown in a wind tunnel whereas other bats were flown in a flight corridor. (A) For corridor-flown bats, velocity increased with body mass as expected under isometry (V_horiz∝M_b^1/6; dashed grey line), but bats flown in the wind tunnel usually flew faster than would be predicted based upon extrapolation of that line to their range of masses. (B,C) The magnitudes of A_horiz (B) and A_vert (C) were centered close to zero, but no trial showed zero net acceleration.