Figure 1.
Orchestrating a tail-membrane flap.
A) 1–2. Fringed myotis (Myotis thysanodes) illustrating adduction of its rear limbs to collapse the tail-membrane during the upstroke. 3–4. Abduction of the hind-limbs at the top of the upstroke occurs in preparation for the tail-membrane downstroke, thereby maximizing surface area and air displacement leading to rearward thrust. 5. Collapsing of the tail-membrane at the bottom of the downstroke in preparation for the next upstroke. B) Sequence drawings illustrating motion and timing between wings and tail-membrane motions during initial phase of a platform takeoff by Townsend's big-eared bat (Corynorhinus townsendii).
Figure 2.
Stroke offsets between the left wing and tail-membrane are illustrated by plotting the digitized motions of the left wrist (blue line) and tip of the tail (red line) for the little brown myotis (Myotis lucifugus) through three wingbeat cycles. In this example, the individual used intitiation offsets of the upstroke and downstroke timings in order to produce asynchronous flapping between the wings and the tail-membrane. Black lines indicate degree of divergence in timing of downstroke motions (oscillation offsets).
Figure 3.
Stroke tempo offsets between left wing and tail-membrane as illustrated by plots of the digitized motions of the wrist (blue line) and tail tip (red line) for the fringed myotis (Myotis thysanodes) across wingbeat cycles one through five. In this example, the individual showed little to no stroke intiation offsets, but instead used differential flap rates between the wings and tail-membrane to afford asynchrony of motion. The angles of the red and the blue arrows indicate oscillation offsets via stroke tempo.
Figure 4.
Takeoff trajectory and wing versus tail-membrane motions.
Digitized tracings of left wing tip (blue) and tail tip (red) for three takeoff trajectories observed in little brown myotis (Myotis lucifugus). Angle of flight trajectories are represented by tilt of each cylinder. Data are provided below each cylinder indicating least degree of left wing stroke angle to body plane (β) and maximal tail-membrane stroke angles above the body plane (θ = +angle) and below the body plane (θ′ = −angle) for each individual adjusted to the horizontal for comparison. Hinge indicates a pivot-point presumably at the sacral/caudal vertebral joint. Body plane is indicated by the dotted arrow and U = velocity.
Figure 5.
Tail-membrane extension relative to body mass.
Model two regression analysis showed a significantly positive relationship between (LogN) dorsal extension of the tail-membrane above the body plane and (LogN) mass (g) of individual little brown myotis (M. lucifugus), indicating that degree of dorsal extension of the tail-membrane is mechanically adjusted relative to mass to be lifted.
Figure 6.
Change in oscillation offsets relative to body mass A.
Histogram showing extent of oscillation offsets between the left wing and tail tip during the upstroke (blue bars) and downstroke (red bars) for the little brown myotis (M. lucifugus), plotted against individuals that varied in body mass. B. Regression plot of the offset data shows the switch-over point of regression lines where downstroke offsets (red line) become more pronounced than upstroke offsets (blue line) in relation to body mass. Although neither regression line is statistically significant due to high variation in the sample, the consistent trend towards greater offsets occuring during downstrokes as body mass increases suggests meaningful shifting of kinematics with mass.
Figure 7.
Use of the tail-membrane across species.
Integration of ecomorphology with use of the tail-membrane showed significant differences among species (P = 0.01) most broadly separated ecomorpholgically. Mean tail-stroke values (degrees of arc across the body-axis) were highest for the little brown myotis (MYLU) that has the highest wing loading and a preference for open-aerial flight as compared to the other three species. The ground foraging pallid bat (Antrozous pallidus, ANPA) has the lowest wing loading of the group and had the shortest tail sweep on average. Post-hoc pair-wise comparisons showed that MYLU was signficantly different from the long-eared myotis (M. evotis, MYEV) and ANPA, whereas the fringed myotis (M. thysanodes, MYTH) was not significantly different from any other species . ** = significant difference at the P = 0.01. Connecting lines show which groups were signficant different. See Table 1 for details.
Table 1.
Post hoc Tukey-Kramer Multiple-Comparison Test showed significant differences (DF = 35, Critical Value = 3.814, Alpha = 0.05) among vespertilionid species in degree of tail-membrane sweep during takeoff from a horizontal platform.
Figure 8.
Using comparable still images between species (upper, long-eared myotis, Myotis evotis; lower, short-tailed fruit bat, Carollia perspicillata) we show how the long-eared myotis used extensive dorsal extension of tail-membrane to initiate rearward thrust production, whereas the short-tailed fruit bat did not.
Figure 9.
Angle of attack of the tail-membrane during fanning motion.
Graphic illustrating how the tail-membrane produces foreward thrust during a platform takeoff. The tip of the tail moves along a sinusoidal path through each stroke cycle represented by the curved black-line. Blue lines indicate the position of the tail-membrane relative to the sinusoidal path. The upstroke of the folded tail-membrane would likely be aerodynamically passive, whereas the downstroke provides a thrust force realtive to pitch angle and angle of attack. Numbers indicate tail-membrane position from top to bottom for a single downstroke. T = Thrust, L = Lift, D = Drag. Inset diagram illustrates how angle of attack and pitch angle were calculated for each tail-membrane position during the downstroke. A path tangent was drawn for each point position of the tail tip. α is the angle of attack of the tail-membrane relative to path (here illustrated for position 4 of the downstroke).
Figure 10.
Illustration of hypothetical model of how thrust and lift may be generated.
Using the tail-membrane fanning motions (black arrow indicates direction of travel) of a long-eared myotis (Myotis evotis), we illustrate a hypothetical duel-use of the tail-wing wherein dorsal extension and downstoke above the body plane delivers thrust, whereas ventral flexion generates thrust and also lift when held in a curved position below the body axis. This positioning would be analogous to an airplane extending its flaps to increase air-speed above a flight surface.