The aerodynamic cost of flight in the short-tailed fruit bat (Carollia perspicillata): comparing theory with measurement.

Aerodynamic theory has long been used to predict the power required for animal flight, but widely used models contain many simplifications. It has been difficult to ascertain how closely biological reality matches model predictions, largely because of the technical challenges of accurately measuring the power expended when an animal flies. We designed a study to measure flight speed-dependent aerodynamic power directly from the kinetic energy contained in the wake of bats flying in a wind tunnel. We compared these measurements with two theoretical predictions that have been used for several decades in diverse fields of vertebrate biology and to metabolic measurements from a previous study using the same individuals. A high-accuracy displaced laser sheet stereo particle image velocimetry experimental design measured the wake velocities in the Trefftz plane behind four bats flying over a range of speeds (3-7 m s(-1)). We computed the aerodynamic power contained in the wake using a novel interpolation method and compared these results with the power predicted by Pennycuick's and Rayner's models. The measured aerodynamic power falls between the two theoretical predictions, demonstrating that the models effectively predict the appropriate range of flight power, but the models do not accurately predict minimum power or maximum range speeds. Mechanical efficiency--the ratio of aerodynamic power output to metabolic power input--varied from 5.9% to 9.8% for the same individuals, changing with flight speed.

Flight metabolism in relation to speed in Chiroptera: testing the U-shape paradigm in the short-tailed fruit bat Carollia perspicillata.

Aerodynamic theory predicts that flight for fixed-wing aircraft requires more energy at low and high speeds compared with intermediate speeds, and this theory has often been extended to predict speed-dependent metabolic rates and optimal flight speeds for flying animals. However, the theoretical U-shaped flight power curve has not been robustly tested for Chiroptera, the only mammals capable of flapping flight. We examined the metabolic rate of seven Seba's short-tailed fruit bats (Carollia perspicillata) during unrestrained flight in a wind tunnel at air speeds from 1 to 7 m s(-1). Following intra-peritoneal administration of (13)C-labeled Na-bicarbonate, we measured the enrichment in (13)C of exhaled breath before and after flight. We converted fractional turnover of (13)C into metabolic rate and power, based on the assumption that bats oxidized glycogen during short flights. Power requirements of flight varied with air speed in a U-shaped manner in five out of seven individuals, whereas energy turnover was not related to air speed in two individuals. Power requirements of flight were close to values predicted by Pennycuick's aerodynamic model for minimum power speed, but differed for maximum range speed. The results of our experiment support the theoretical expectation of a U-shaped power curve for flight metabolism in a bat.

Kinematics and wing shape across flight speed in the bat, Leptonycteris yerbabuenae.

The morphology and kinematics of a flying animal determines the resulting aerodynamic lift through the regulation of the speed of the air moving across the wing, the wing area and the lift coefficient. We studied the detailed three-dimensional wingbeat kinematics of the bat, Leptonycteris yerbabuenae, flying in a wind tunnel over a range of flight speeds (0-7 m/s), to determine how factors affecting the lift production vary across flight speed and within wingbeats. We found that the wing area, the angle of attack and the camber, which are determinants of the lift production, decreased with increasing speed. The camber is controlled by multiple mechanisms along the span, including the deflection of the leg relative to the body, the bending of the fifth digit, the deflection of the leading edge flap and the upward bending of the wing tip. All these measures vary throughout the wing beat suggesting active or aeroelastic control. The downstroke Strouhal number, St(d), is kept relatively constant, suggesting that favorable flow characteristics are maintained during the downstroke, across the range of speeds studied. The St(d) is kept constant through changes in the stroke plane, from a strongly inclined stroke plane at low speeds to a more vertical stroke plane at high speeds. The mean angular velocity of the wing correlates with the aerodynamic performance and shows a minimum at the speed of maximum lift to drag ratio, suggesting a simple way to determine the optimal speed from kinematics alone. Taken together our results show the high degree of adjustments that the bats employ to fine tune the aerodynamics of the wings and the correlation between kinematics and aerodynamic performance.

Kinematics of flight and the relationship to the vortex wake of a Pallas' long tongued bat (Glossophaga soricina).

To obtain a full understanding of the aerodynamics of animal flight, the movement of the wings, the kinematics, needs to be connected to the wake left behind the animal. Here the detailed 3D wingbeat kinematics of bats, Glossophaga soricina, flying in a wind tunnel over a range of flight speeds (1-7 m s(-1)) was determined from high-speed video. The results were compared with the wake geometry and quantitative wake measurements obtained simultaneously to the kinematics. The wingbeat kinematics varied gradually with flight speed and reflected the changes observed in the wake of the bats. In particular, several of the kinematic parameters reflected the differences in the function of the upstroke at low and high flight speeds. At lower flight speeds the bats use a pitch-up rotation to produce a backward flick which creates thrust and some weight support. At higher speeds this mechanism disappears and the upstroke generates weight support but no thrust. This is reflected by the changes in e.g. angle of attack, span ratio, camber and downstroke ratio. We also determined how different parameters vary throughout a wingbeat over the flight speeds studied. Both the camber and the angle of attack varied over the wingbeat differently at different speeds, suggesting active control of these parameters to adjust to the changing aerodynamic conditions. This study of the kinematics strongly indicates that the flight of bats is governed by an unsteady high-lift mechanism at low flight speeds and points to differences between birds and bats.

The near and far wake of Pallas' long tongued bat (Glossophaga soricina).

The wake structures of a bat in flight have a number of characteristics not associated with any of the bird species studied to this point. Unique features include discrete vortex rings generating negative lift at the end of the upstroke at medium and high speeds, each wing generating its own vortex loop, and a systematic variation in the circulation of the start and stop vortices along the wingspan, with increasing strength towards the wing tips. Here we analyse in further detail some previously published data from quantitative measurements of the wake behind a small bat species flying at speeds ranging from 1.5 to 7 m s(-1) in a wind tunnel. The data are extended to include both near- and far-wake measurements. The near-/far-wake comparisons show that although the measured peak vorticity of the start and stop vortices decreases with increasing downstream distance from the wing, the total circulation remains approximately constant. As the wake evolves, the diffuse stop vortex shed at the inner wing forms a more concentrated vortex in the far wake. Taken together, the results show that studying the far wake, which has been the standard procedure, nevertheless risks missing details of the wake. Although study of the far wake alone can lead to the misinterpretation of the wake topology, the net, overall circulation of the main wake vortices can be preserved so that approximate momentum balance calculations are not unreasonable within the inevitably large experimental uncertainties.