Kinematic plasticity during flight in fruit bats: individual variability in response to loading

All bats experience daily and seasonal fluctuation in body mass. An increase in mass requires changes in flight kinematics to produce the extra lift necessary to compensate for increased weight. How bats modify their kinematics to increase lift, however, is not well understood. In this study, we investigated the effect of a 20% increase in mass on flight kinematics for Cynopterus brachyotis, the lesser dog-faced fruit bat. We reconstructed the 3D wing kinematics and how they changed with the additional mass. Bats showed a marked change in wing kinematics in response to loading, but changes varied among individuals. Each bat adjusted a different combination of kinematic parameters to increase lift, indicating that aerodynamic force generation can be modulated in multiple ways. Two main kinematic strategies were distinguished: bats either changed the motion of the wings by primarily increasing wingbeat frequency, or changed the configuration of the wings by increasing wing area and camber. The complex, individual-dependent response to increased loading in our bats points to an underappreciated aspect of locomotor control, in which the inherent complexity of the biomechanical system allows for kinematic plasticity. The kinematic plasticity and functional redundancy observed in bat flight can have evolutionary consequences, such as an increase potential for morphological and kinematic diversification due to weakened locomotor trade-offs.     

Hindlimb Motion during Steady Flight of the Lesser Dog-Faced Fruit Bat,Cynopterus brachyotis

In bats, the wing membrane is anchored not only to the body and forelimb, but also to the hindlimb. This attachment configuration gives bats the potential to modulate wing shape by moving the hindlimb, such as by joint movement at the hip or knee. Such movements could modulate lift, drag, or the pitching moment. In this study we address: 1) how the ankle translates through space during the wingbeat cycle; 2) whether amplitude of ankle motion is dependent upon flight speed; 3) how tension in the wing membrane pulls the ankle; and 4) whether wing membrane tension is responsible for driving ankle motion. We flew five individuals of the lesser dog-faced fruit bat, Cynopterus brachyotis (Family: Pteropodidae), in a wind tunnel and documented kinematics of the forelimb, hip, ankle, and trailing edge of the wing membrane. Based on kinematic analysis of hindlimb and forelimb movements, we found that: 1) during downstroke, the ankle moved ventrally and during upstroke the ankle moved dorsally; 2) there was considerable variation in amplitude of ankle motion, but amplitude did not correlate significantly with flight speed; 3) during downstroke, tension generated by the wing membrane acted to pull the ankle dorsally, and during upstroke, the wing membrane pulled laterally when taut and dorsally when relatively slack; and 4) wing membrane tension generally opposed dorsoventral ankle motion. We conclude that during forward flight in C. brachyotis, wing membrane tension does not power hindlimb motion; instead, we propose that hindlimb movements arise from muscle activity and/or inertial effects.     

Falling with Style: Bats Perform Complex Aerial Rotations by Adjusting Wing Inertia

The remarkable maneuverability of flying animals results from precise movements of their highly specialized wings. Bats have evolved an impressive capacity to control their flight, in large part due to their ability to modulate wing shape, area, and angle of attack through many independently controlled joints. Bat wings, however, also contain many bones and relatively large muscles, and thus the ratio of bats’ wing mass to their body mass is larger than it is for all other extant flyers. Although the inertia in bat wings would typically be associated with decreased aerial maneuverability, we show that bat maneuvers challenge this notion. We use a model-based tracking algorithm to measure the wing and body kinematics of bats performing complex aerial rotations. Using a minimal model of a bat with only six degrees of kinematic freedom, we show that bats can perform body rolls by selectively retracting one wing during the flapping cycle. We also show that this maneuver does not rely on aerodynamic forces, and furthermore that a fruit fly, with nearly massless wings, would not exhibit this effect. Similar results are shown for a pitching maneuver. Finally, we combine high-resolution kinematics of wing and body movements during landing and falling maneuvers with a 52-degree-of-freedom dynamical model of a bat to show that modulation of wing inertia plays the dominant role in reorienting the bat during landing and falling maneuvers, with minimal contribution from aerodynamic forces. Bats can, therefore, use their wings as multifunctional organs, capable of sophisticated aerodynamic and inertial dynamics not previously observed in other flying animals. This may also have implications for the control of aerial robotic vehicles.     

Comparing aerodynamic efficiency in birds and bats suggests better flight performance in birds

Flight is one of the energetically most costly activities in the animal kingdom, suggesting that natural selection should work to optimize flight performance. The similar size and flight speed of birds and bats may therefore suggest convergent aerodynamic performance; alternatively, flight performance could be restricted by phylogenetic constraints. We test which of these scenarios fit to two measures of aerodynamic flight efficiency in two passerine bird species and two New World leaf-nosed bat species. Using time-resolved particle image velocimetry measurements of the wake of the animals flying in a wind tunnel, we derived the span efficiency, a metric for the efficiency of generating lift, and the lift-to-drag ratio, a metric for mechanical energetic flight efficiency. We show that the birds significantly outperform the bats in both metrics, which we ascribe to variation in aerodynamic function of body and wing upstroke: Bird bodies generated relatively more lift than bat bodies, resulting in a more uniform spanwise lift distribution and higher span efficiency. A likely explanation would be that the bat ears and nose leaf, associated with echolocation, disturb the flow over the body. During the upstroke, the birds retract their wings to make them aerodynamically inactive, while the membranous bat wings generate thrust and negative lift. Despite the differences in performance, the wake morphology of both birds and bats resemble the optimal wake for their respective lift-to-drag ratio regimes. This suggests that evolution has optimized performance relative to the respective conditions of birds and bats, but that maximum performance is possibly limited by phylogenetic constraints. Although ecological differences between birds and bats are subjected to many conspiring variables, the different aerodynamic flight efficiency for the bird and bat species studied here may help explain why birds typically fly faster, migrate more frequently and migrate longer distances than bats.     

Mechancial properties of bat wing membrane skin

The skin of the bat wing in functionally unique among mammals: it serves as a major locomotor organ in addition to its protective and regulatory functions. We used tensile testing to investigate the mechanical capabilities of wing membrane skin, and compared stiffness, strength, load at failure, and energy absorption among specific wing regions and among a variety of bat taxa. We related these characteristics to the highly architectural fibrous supporting network of the wing membrane. We found that all material properties showed a strong anisotropy. In particular, wing membrane skin shows maximum stiffness and stregth parallel to the wing skeleton, and greatest extensibility parallel to the wing's trailing edge. We also found significant variation among wing regions. The uropatagium (tail membrane) supported the greatest load at failure, and the plagiopatagium (proximal wing membrane between laterl body wall and hand skeleton) is the weakest and most extensible part of the wing. We believe that the increased load bearing ability of the uropatagium relats to its key role in capture of insect prey, and that the great extensibility of the plagiopatagium promotes development of camber near the wing's centre of lift. In interspecific comparisons, energy absorpion and load to failure were greatest in Artibeus jamaicensis , the largest bat in our sample and the species with the highest wing loading, suggesting that wing loading may play a role in dictating the fuctional design of wing membranes.     

Two-and Three-Dimensional Simulations of Beetle Hind Wing Flapping during Free Forward Flight

Aerodynamic characteristic of the beetle, Trypoxylus dichotomus, which has a pair of elytra (forewings) and hind wings, is numerically investigated. Based on the experimental results of wing kinematics, two-dimensional (2D) and three-dimensional (3D) computational fluid dynamic simulations were carried out to reveal aerodynamic performance of the hind wing. The roles of the spiral Leading Edge Vortex (LEV) and the spanwise flow were clarified by comparing 2D and 3D simulations. Mainly due to pitching down of chord line during downstroke in highly inclined stroke plane, relatively high averaged thrust was produced in the free forward flight of the beetle. The effects of the local corrugation and the camber variation were also investigated for the beetle's hind wings. Our results show that the camber variation plays a significant role in improving both lift and thrust in the flapping. On the other hand, the local corrugation pattern has no significant effect on the aerodynamic force due to large angle of attack during flapping.     

The Aerodynamic Cost of Head Morphology in Bats: Maybe Not as Bad as It Seems

At first sight, echolocating bats face a difficult trade-off. As flying animals, they would benefit from a streamlined geometric shape to reduce aerodynamic drag and increase flight efficiency. However, as echolocating animals, their pinnae generate the acoustic cues necessary for navigation and foraging. Moreover, species emitting sound through their nostrils often feature elaborate noseleaves that help in focussing the emitted echolocation pulses. Both pinnae and noseleaves reduce the streamlined character of a bat’s morphology. It is generally assumed that by compromising the streamlined charactered of the geometry, the head morphology generates substantial drag, thereby reducing flight efficiency. In contrast, it has also been suggested that the pinnae of bats generate lift forces counteracting the detrimental effect of the increased drag. However, very little data exist on the aerodynamic properties of bat pinnae and noseleaves. In this work, the aerodynamic forces generated by the heads of seven species of bats, including noseleaved bats, are measured by testing detailed 3D models in a wind tunnel. Models of Myotis daubentonii, Macrophyllum macrophyllum, Micronycteris microtis, Eptesicus fuscus, Rhinolophus formosae, Rhinolophus rouxi and Phyllostomus discolor are tested. The results confirm that non-streamlined facial morphologies yield considerable drag forces but also generate substantial lift. The net effect is a slight increase in the lift-to-drag ratio. Therefore, there is no evidence of high aerodynamic costs associated with the morphology of bat heads.     

Pitching Moment Generation in an Insect-Mimicking Flapping-Wing System

Unlike birds, insects lack control surfaces at the tail and hence most insects modify their wing kinematics to produce control forces or moments while flapping their wings. Change of the flapping angle range is one of the ways to modify wing kinematics, resulting in relocation of the mean Aerodynamic force Center （mean AC） and finally creating control moments. In an attempt to mimic this feature, we developed a flapping-wing system that generates a desired pitching moment during flap- ping-wing motion. The system comprises a flapping mechanism that creates a large and symmetric flapping motion in a pair of wings, a flapping angle change mechanism that modifies the flapping angle range, artificial wings, and a power source. From the measured wing kinematics, we have found that the flapping-wing system can properly modify the flapping angle ranges. The measured pitching moments show that the flapping-wing system generates a pitching moment in a desired direction by shifting the flapping angle range. We also demonstrated that the system can in practice change the longitudinal attitude by generating a nonzero pitching moment.     

Absorption of visible spectrum radiation by the wing membranes of living pteropodid bats

The wing membranes of bats present a large surface area upon which radiation might be taken up, increasing heat load to the animals. This, combined with the high amount of heat produced during flight, has been advanced as one hypothesis explaining the fact that bats are almost exclusively nocturnal. The proportion of short-wave (visible) radiation absorbed by bat wing membrane has previously been measured at between 0.7 and 0.92. These measurements were made on pieces of membrane taken from the wings of dead, mainly insectivorous bats from temperate regions. Here we examined the amount of light transmitted through and reflected off the wing membranes of four species of live pteropodid bats. There were significant differences in wing reflection between species. At 0.68, the average proportion of light absorbed into the wing membranes was lower than previously reported. This might be because we worked with live animals or because ours were tropical bats which are routinely exposed to tropical sun when roosting. Variation in wing tension strongly affected light absorption. It was predicted that the relaxed state of wing membrane through part of the wing beat cycle would increase the absorption of light into the wings of day-flying bats. The proportion of light absorbed into wings was shown to be an important factor in the heat balance of hypothetical bats flying during the day. Our results raise the predicted temperature at which bats flying during the day might experience hyperthermia by approximately 2 °C and suggest that variation in albedo of wings between species may make some species more susceptible to overheating than others. Accepted: 6 December 1998     

Aerodynamic Characteristics of a Feathered Dinosaur Measured Using Physical Models. Effects of Form on Static Stability and Control Effectiveness

We report the effects of posture and morphology on the static aerodynamic stability and control effectiveness of physical models based on the feathered dinosaur, Microraptor gui, from the Cretaceous of China. Postures had similar lift and drag coefficients and were broadly similar when simplified metrics of gliding were considered, but they exhibited different stability characteristics depending on the position of the legs and the presence of feathers on the legs and the tail. Both stability and the function of appendages in generating maneuvering forces and torques changed as the glide angle or angle of attack were changed. These are significant because they represent an aerial environment that may have shifted during the evolution of directed aerial descent and other aerial behaviors. Certain movements were particularly effective (symmetric movements of the wings and tail in pitch, asymmetric wing movements, some tail movements). Other appendages altered their function from creating yaws at high angle of attack to rolls at low angle of attack, or reversed their function entirely. While M. gui lived after Archaeopteryx and likely represents a side experiment with feathered morphology, the general patterns of stability and control effectiveness suggested from the manipulations of forelimb, hindlimb and tail morphology here may help understand the evolution of flight control aerodynamics in vertebrates. Though these results rest on a single specimen, as further fossils with different morphologies are tested, the findings here could be applied in a phylogenetic context to reveal biomechanical constraints on extinct flyers arising from the need to maneuver.     

Flapping tail membrane in bats produces potentially important thrust during horizontal takeoffs and very slow flight

Historically, studies concerning bat flight have focused primarily on the wings. By analyzing high-speed video taken on 48 individuals of five species of vespertilionid bats, we show that the capacity to flap the tail-membrane (uropatagium) in order to generate thrust and lift during takeoffs and minimal-speed flight (<1 m ^s−1) was largely underestimated. Indeed, bats flapped the tail-membrane by extensive dorso-ventral fanning motions covering as much as 135 degrees of arc consistent with thrust generation by air displacement. The degree of dorsal extension of the tail-membrane, and thus the potential amount of thrust generated during platform launches, was significantly correlated with body mass (P = 0.02). Adduction of the hind limbs during upstrokes collapsed the tail-membrane thereby reducing its surface area and minimizing negative lift forces. Abduction of the hind limbs during the downstroke fully expanded the tail-membrane as it was swept ventrally. The flapping kinematics of the tail-membrane is thus consistent with expectations for an airfoil. Timing offsets between the wings and tail-membrane during downstrokes was as much as 50%, suggesting that the tail-membrane was providing thrust and perhaps lift when the wings were retracting through the upstoke phase of the wing-beat cycle. The extent to which the tail-membrane was used during takeoffs differed significantly among four vespertilionid species (P = 0.01) and aligned with predictions derived from bat ecomorphology. The extensive fanning motion of the tail membrane by vespertilionid bats has not been reported for other flying vertebrates.     

Rain increases the energy cost of bat flight

Similar to insects, birds and pterosaurs, bats have evolved powered flight. But in contrast to other flying taxa, only bats are furry. Here, we asked whether flight is impaired when bat pelage and wing membranes get wet. We studied the metabolism of short flights in Carollia sowelli, a bat that is exposed to heavy and frequent rainfall in neotropical rainforests. We expected bats to encounter higher thermoregulatory costs, or to suffer from lowered aerodynamic properties when pelage and wing membranes catch moisture. Therefore, we predicted that wet bats face higher flight costs than dry ones. We quantified the flight metabolism in three treatments: dry bats, wet bats and no rain, wet bats and rain. Dry bats showed metabolic rates predicted by allometry. However, flight metabolism increased twofold when bats were wet, or when they were additionally exposed to rain. We conclude that bats may not avoid rain only because of sensory constraints imposed by raindrops on echolocation, but also because of energetic constraints.     

Wing design and scaling of flying fish with regard to flight performance

Fin and body dimensions of six genera of flying fish (Exocoetidae) were examined to study variation in morphological parameters in relation to aerodynamics performance. The fins are modified as wings for gliding flight. Fin area and fin span increase with increasing body mass, whereas the percentage of wing area contributed by the pectoral fins and the percentage of the caudal fin area contributed by the hypocaudal lobe remain constant. The aerodynamic design of flying fish approximates the monoplane-biplane classification proposed by Breder (1930). Scaling relationships for wing loading and aspect ratio indicate that wing morphology in the Exocoetidae is more similar to birds and bats than to other gliders. The flight performance of flying fish is a high-speed glide with a relatively flat trajectory. The wing, as indicated by the aspect ratio, is designed for high lift with low drag characteristics.     

Time-Varying Wing-Twist Improves Aerodynamic Efficiency of Forward Flight in Butterflies

Insect wings can undergo significant chordwise (camber) as well as spanwise (twist) deformation during flapping flight but the effect of these deformations is not well understood. The shape and size of butterfly wings leads to particularly large wing deformations, making them an ideal test case for investigation of these effects. Here we use computational models derived from experiments on free-flying butterflies to understand the effect of time-varying twist and camber on the aerodynamic performance of these insects. High-speed videogrammetry is used to capture the wing kinematics, including deformation, of a Painted Lady butterfly (Vanessa cardui) in untethered, forward flight. These experimental results are then analyzed computationally using a high-fidelity, three-dimensional, unsteady Navier-Stokes flow solver. For comparison to this case, a set of non-deforming, flat-plate wing (FPW) models of wing motion are synthesized and subjected to the same analysis along with a wing model that matches the time-varying wing-twist observed for the butterfly, but has no deformation in camber. The simulations show that the observed butterfly wing (OBW) outperforms all the flat-plate wings in terms of usable force production as well as the ratio of lift to power by at least 29% and 46%, respectively. This increase in efficiency of lift production is at least three-fold greater than reported for other insects. Interestingly, we also find that the twist-only-wing (TOW) model recovers much of the performance of the OBW, demonstrating that wing-twist, and not camber is key to forward flight in these insects. The implications of this on the design of flapping wing micro-aerial vehicles are discussed.     

Animal flight dynamics I. Stability in gliding flight

Stability is as essential to flying as lift itself, but previous discussions of how flying animals maintain stability have been limited in both number and scope. By developing the pitching moment equations for gliding animals and by discussing potential sources of roll and yaw stability, we consider the various sources of static stability used by gliding animals. We find that gliding animals differ markedly from aircraft in how they maintain stability. In particular, the pendulum stability provided when the centre of gravity lies below the wings is a much more important source of stability in flying animals than in most conventional aircraft. Drag-based stability also appears to be important for many gliding animals, whereas in aircraft, drag is usually kept to a minimum. One unexpected consequence of these differences is that the golden measure of static pitching stability in aircraft--the static margin--can only strictly be applied to flying animals if the equilibrium angle of attack is specified. We also derive several rules of thumb by which stable fliers can be identified. Stable fliers are expected to exhibit one or more of the following features: (1) Wings that are swept forward in slow flight. (2) Wings that are twisted down at the tips when swept back (wash-out) and twisted up at the tips when swept forwards (wash-in). (3) Additional lifting surfaces (canard, hindwings or a tail) inclined nose-up to the main wing if they lie forward of it, and nose-down if they lie behind it (longitudinal dihedral). Each of these predictions is directional--the opposite is expected to apply in unstable animals. In addition, animals with reduced stability are expected to display direct flight patterns in turbulent conditions, in contrast to the erratic flight patterns predicted for stable animals, in which large restoring forces are generated. Using these predictions, we find that flying animals possess a far higher degree of inherent stability than has generally been recognized. This conclusion is reinforced by measurements of the relative positions of the centres of gravity and lift in birds, which suggest that the wings alone may be sufficient to provide longitudinal static stability. Birds may therefore resemble tailless aircraft more closely than conventional aircraft with a tailplane.     

Comparison of Aerodynamic Forces and Moments Calculated by Three-dimensional Unsteady Blade Element Theory and Computational Fluid Dynamics

In previous work,we modified blade element theory by implementing three-dimensional wing kinematics and modeled the unsteady aerodynamic effects by adding the added mass and rotational forces.This method is referred to as Unsteady Blade Element Theory (UBET).A comparison between UBET and Computational Fluid Dynamics (CFD) for flapping wings with high flapping frequencies (＞30 Hz) could not be found in literature survey.In this paper,UBET that considers the movement of pressure center in pitching-moment estimation was validated using the CFD method.We investigated three three-dimensional (3D) wing kinematics that produce negative,zero,and positive aerodynamic pitching moments.For all cases,the instantaneous aerodynamic forces and pitching moments estimated via UBET and CFD showed similar trends.The differences in average vertical forces and pitching moments about the center of gravity were about 10％ and 12％,respectively.Therefore,UBET is proven to reasonably estimate the aerodynamic forces and pitching moment for flight dynamic study of FW-MAV.However,the differences in average wing drags and pitching moments about the feather axis were more than 20％.Since study of aerodynamic power requires reasonable estimation of wing drag and pitching moment about the feather axis,UBET needs further improvement for higher accuracy.     

ON THE RECONSTRUCTION OF PTEROSAURS AND THEIR MANNER OF FLIGHT, WITH NOTES ON VORTEX WAKES

Classical pterosaur reconstructions are variants on a ‘bat-analogy’, whereby the wing is conceived as a simple membrane with no inherent bending strength, stretched between the arm and leg skeletons. The legs are considered to be splayed out to the sides, as in bats, so that the animal would have to adopt a quadrupedal stance on the ground, supported on its feet and the metacarpo-phalangeal joints. In recent years an alternative ‘bird-analogy’ has come to be generally accepted. This hypothesis, most elements of which are due to Padian (1983 a, b) calls for the animal to stand upright on its legs like a bird. The wings are independent of the legs, as in birds, are stiffened by skeletal fibres in the membrane, and have a very narrow, sharply pointed shape. There are difficulties in reconciling the bird-analogy with the evidence. The long-tailed rhamphorhynchs might conceivably have balanced their weight about their hip joints but this would not have been possible for the short-tailed pterodactyls. The bird pelvis shows modifications which permit bipedal standing in spite of the reduction of the tail, but no equivalent adaptations are seen in pterodactyls. Besides, all known pterosaur pelvises, except that of the giant pterodactyl Pteranodon were open ventrally, which would have precluded the legs from being brought to a parasagittal position, as required for bipedal walking. The notion that the wing was not attached to the legs is based on negative evidence, in that no clear impressions of the inner end of the wing membrane are preserved in the fossils. However one pterodactyl fossil shows a membrane edge approaching the ankle joint. In fossils that are preserved with the wings forward, the legs have been pulled forwards by the ankles. A tendon connecting the ankle to the wing tip is consistent with the evidence. The ‘fibres’ in the wing membranes are actually impressions of surface ridges, with no internal structure, and are better interpreted as surface wrinkles in the skin, caused by contraction of elastic fibres within the membrane. The bird analogy also results in a very unsatisfactory wing from an aerodynamic point of view. The structure of an animal wing is best understood in terms of the type of vortex wake it is adapted to generate. Hummingbirds, and insects capable of economical hovering, have wings that can be inverted on the upstroke, and when hovering, generate a wake consisting of two vortex rings per wingbeat cycle. The span of such wings is fixed, which implies that they create a ‘ladder wake’ in cruising flight, consisting of a pair of undulating wing-tip vortices, joined by a transverse vortex at each transition from downstroke to upstroke and back. Normal birds cannot invert their wings, and so are less efficient in hovering, but they can shorten the wing during the upstroke in cruising flight. This creates a ‘concertina wake’, with no transverse vortices. Hummingbirds show very limited migration performance, compared with normal birds, with the implication that a wing capable of creating a concertina wake is more economical in cruising flight than one creating a ladder wake, and is an essential adaptation for long-distance migration. A revised reconstruction of the pterosaur wing starts from the observations that, contrary to the currently popular bird-analogy, pterosaurs were not bipedal, their wings did not contain stiffening fibres but did contain elastic fibres, and the trailing edge of the membrane was supported by a tendon joining the tip of the wing finger to the ankle. A hypothetical arrangement of elastic fibres, that accounts well for the observed pattern of wrinkles in contracted wings, also allows the planform shape of the wing to be adjusted in much the same way as seen in birds, although using a completely different mechanism. It opens the possibility that pterosaurs could fly with a concertina wake, and thus could have been long-distance migrators like modern birds. Although this hypothetical wing is mechanically somewhat bat-like, it is not a return to the classical bat-analogy. It would not have the high degree of control over profile shape, which gives bats their outstanding manoeuvrability. On the other hand bats do not have the degree of control over their wingspan that is suggested here for pterosaurs, and consequently are not notable for migration performance.     

Trapped in the darkness of the night: thermal and energetic constraints of daylight flight in bats

Bats are one of the most successful mammalian groups, even though their foraging activities are restricted to the hours of twilight and night-time. Some studies suggested that bats became nocturnal because of overheating when flying in daylight. This is because--in contrast to feathered wings of birds--dark and naked wing membranes of bats efficiently absorb short-wave solar radiation. We hypothesized that bats face elevated flight costs during daylight flights, since we expected them to alter wing-beat kinematics to reduce heat load by solar radiation. To test this assumption, we measured metabolic rate and body temperature during short flights in the tropical short-tailed fruit bat Carollia perspicillata at night and during the day. Core body temperature of flying bats differed by no more than 2°C between night and daytime flights, whereas mass-specific CO(2) production rates were higher by 15 per cent during daytime. We conclude that increased flight costs only render diurnal bat flights profitable when the relative energy gain during daytime is high and risk of predation is low. Ancestral bats possibly have evolved dark-skinned wing membranes to reduce nocturnal predation, but a low degree of reflectance of wing membranes made them also prone to overheating and elevated energy costs during daylight flights. In consequence, bats may have become trapped in the darkness of the night once dark-skinned wing membranes had evolved.     

Optimal discus trajectories

A general 3-D dynamic model for men's and women's discus flight is presented including precession of spin angular momentum induced by aerodynamic pitching moment. Dependence of pitching moment coefficient on angle of attack is estimated from experiment. Numerical integration of 11 equations of motion for nominal release speed v₀=25 m/s and axial spin p₀=42 rad/s also requires 3 other release conditions; initial discus flight path angle β₀, pitch attitude θ₀, and roll angle φ₀. Optimal values for these release conditions are calculated iteratively to maximize range and are similar for both men and women. The optimal men's trajectory and range R=69.39 m is produced by the strategy β₀=38.4°, θ₀=30.7°, and φ₀=54.4°. Initial angular velocities except spin are chosen to minimize wobble but an optimal initial spin rate p₀=25.2 rad/s exists that also maximizes range. Optimal 3-D range exceeds that predicted by 2-D models because, although angle of attack and lift are negative initially, 3-D motion allows advantageous orientation of lift later in flight, with tilt of the axis of symmetry from vertical becoming much smaller at landing. Optimal strategies are discontinuous with wind speed, resulting in slicing and kiting strategies in large head and tail winds, respectively. Sensitivity of optimal range is largest to initial β₀ and least to φ₀. Present calculations do not account for dependence of initial release angle or spin on release velocity or among other release conditions.     

Drivers affecting habitat use in Afrotropical hipposiderid and pteropodid bats

Assessing how bats respond to habitat attributes requires an integrative approach to reliably predict direct community-level effects. We focused on hipposiderid and pteropodid bats because of their diverse resource use patterns, body size ranges, and dispersal abilities. We combined an array of bat species-level characteristics with key forest stand characteristics that may covary with habitat use. Twelve stations were sampled in the Lomami and Yangambi landscapes, Democratic Republic of the Congo. We investigated whether species-level flight ability of bats and forest stand characteristics can affect bat commuting flights and community-level estimates of both species detection and habitat occupancy. We captured bats for 108 trap-nights. Three sampling events (early evening, middle of the night, and early morning) were replicated for each survey night. Hipposiderids showed an early evening flight peak, while flight activity of pteropodids was constant throughout the night, but increased around the middle of the night. Species capture probability decreased with higher wing loading in hipposiderids and was negatively correlated with higher wing aspect ratio in pteropodids. Forest occupancy of hipposiderids increased along the gradient towards waterways, while pteropodid occurrence was not directly linked to measured forest stand variables. This suggests a consequence of habitat patterns at larger spatial scales, which would need clarifying through additional data collection. We discuss these findings in terms of resource-use strategies of clutter-tolerant and clutter-intolerant species. We argue that the occurrence of specific bat species and their habitat use patterns can serve as surrogate measures of ecosystem health.