A Hind-Wing in Bats Figure 8. Comparative takeoff dynamics. 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. doi:10.1371/journal.pone.0032074.g008 produced by a dolphin’s or manatee’s tail during slow-speed swimming or even a simple hand-fan when waved for cooling. We calculated both angle of attack (a = angle of tail-membrane axis relative to sinusoidal path) and pitch angle (a9 = angle between tail-membrane axis and translational movement of the animal) through one cycle. Attack angles by position were as follows: 0 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. a is the angle of attack of the tail-membrane relative to path (here illustrated for position 4 of the downstroke). doi:10.1371/journal.pone.0032074.g009 (top): 171u, 1: 146u, 2: 126u, 3: 105u, 4: 98u, 5: 94u, 6 (bottom): 90u. Pitch angles by position were as follows: 0: 73u, 1: 60u, 2: 90u, 3: 106u, 4: 119u, 5: 119u, 6: 128u. Greatest thrust production from fanning would hypothetically be produced when the tail- membrane is moved through position 1–4 as pitch angle passes through 90u with an angle of attack of 126u. Unlike the wings, the tail-membrane would predictably perform fanning uniformly along its span, thereby generating much greater propulsive force than lift [17]. Curiously, relative to maximal total degrees of tail-membrane sweep, M. lucifugus (134.9u of arc) used about a 40% greater tail- sweep than observed in female bottle-nosed dolphins (54u of arc) [21,22,23,24]. Of course, because of the largely different densities of water versus air, the efficiency of these motions will vary greatly between these two groups. Use of the tail by birds during takeoff flight Use of the tail during flight by birds is also understudied. However, during takeoff in pigeons (Columba livia), the majority of tail muscles underwent ‘conspicuous changes in the timing of activity,’ whereas the wing muscles retained the same pattern (mono- or biphasic) of activity in all flight modes (takeoff, slow level flapping flight, and landing) [26]. These data point to a decoupling of neuromuscular control patterns between the wings and tail flight surfaces. Although the tail did not undergo dramatic oscillations during any modes of flight in pigeons, the associated muscles showed changes in activity timing and intensity not exhibited in the standardized temporal activation of the forewing musculature [26]. Pigeons used the tail to minimize drag in order to help themselves accelerate during takeoff in which the tail stroke plane was tilted steeply downward supporting the authors hypothesis that this position would push air rearward to help accelerate the bird forward. The tail stroke plane in pigeons was tilted upward during landing implying that an upward-tilted stroke plane pushes more air forward to slow the bird down [27]. Consequently the tail in birds appears to have a stabilizing role and the use of the caudal musculature during takeoff appears to be used in fixing tail positions that reduced drag [27], as opposed to PLoS ONE | www.plosone.org 8 February 2012 | Volume 7 | Issue 2 | e32074