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.     

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.     

A potential role for bat tail membranes in flight control

Wind tunnel tests conducted on a model based on the long-eared bat Plecotus auritus indicated that the positioning of the tail membrane (uropatagium) can significantly influence flight control. Adjusting tail position by increasing the angle of the legs ventrally relative to the body has a two-fold effect; increasing leg-induced wing camber (i.e., locally increased camber of the inner wing surface) and increasing the angle of attack of the tail membrane. We also used our model to examine the effects of flying with and without a tail membrane. For the bat model with a tail membrane increasing leg angle increased the lift, drag and pitching moment (nose-down) produced. However, removing the tail membrane significantly reduced the change in pitching moment with increasing leg angle, but it had no significant effect on the level of lift produced. The drag on the model also significantly increased with the removal of the tail membrane. The tail membrane, therefore, is potentially important for controlling the level of pitching moment produced by bats and an aid to flight control, specifically improving agility and manoeuvrability. Although the tail of bats is different from that of birds, in that it is only divided from the wings by the legs, it nonetheless, may, in addition to its prey capturing function, fulfil a similar role in aiding flight control.     

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.     

Kinematic compensation for wing loss in flying damselflies

Flying insects can tolerate substantial wing wear before their ability to fly is entirely compromised. In order to keep flying with damaged wings, the entire flight apparatus needs to adjust its action to compensate for the reduced aerodynamic force and to balance the asymmetries in area and shape of the damaged wings. While several studies have shown that damaged wings change their flapping kinematics in response to partial loss of wing area, it is unclear how, in insects with four separate wings, the remaining three wings compensate for the loss of a fourth wing. We used high-speed video of flying blue-tailed damselflies (Ischnura elegans) to identify the wingbeat kinematics of the two wing pairs and compared it to the flapping kinematics after one of the hindwings was artificially removed. The insects remained capable of flying and precise maneuvering using only three wings. To compensate for the reduction in lift, they increased flapping frequency by 18 ± 15.4% on average. To achieve steady straight flight, the remaining intact hindwing reduced its flapping amplitude while the forewings changed their stroke plane angle so that the forewing of the manipulated side flapped at a shallower stroke plane angle. In addition, the angular position of the stroke reversal points became asymmetrical. When the wingbeat amplitude and frequency of the three wings were used as input in a simple aerodynamic model, the estimation of total aerodynamic force was not significantly different (paired t-test, p = 0.73) from the force produced by the four wings during normal flight. Thus, the removal of one wing resulted in adjustments of the motions of the remaining three wings, exemplifying the precision and plasticity of coordination between the operational wings. Such coordination is vital for precise maneuvering during normal flight but it also provides the means to maintain flight when some of the wings are severely damaged.     

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     

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.     

Development of wing morphology in the Indian pygmy batPipistrellus mimus

The growth and development of the wing parameters of the Indian pygmy batPipistrellus mimus was studied under natural conditions. Newborn young were marked with nontoxic coloured paint and were later marked with split rings. The wingspan and wing area showed linear growth until the age of five weeks, after which the rate of growth decreased. The observations on flight showed that at the age of 19 days the young were able to flutter their wings, at the age of 22 days they flew for a short distance and at the age of 29 days they exhibited sustained flight. The development of wing loading and aspect ratio are also presented. The decrease in wing loading as the bat grows is discussed as an advantage to sustain flight. The aspect ratio showed a high degree of scatter at early stages of life which decreased at the later period of growth. In general the development of wing morphology ofP. mimus is similar to that of other vespertilionid bats.     

Biomechanics and physiology of gait selection in flying birds

Two wing-beat gaits, distinguished by the presence or absence of lift production during the upstroke, are currently used to describe avian flight. Vortex-visualization studies indicate that lift is produced only during the downstroke in the vortex-ring gait and that lift is produced continuously in the continuous-vortex gait. Tip-reversal and feathered upstrokes represent different forms of vortex-ring gait distinguished by wing kinematics. Useful aerodynamic forces may be produced during tip-reversal upstroke in slow flight and during a feathered upstroke in fast flight, but it is probable that downstroke forces are much greater in magnitude. Uncertainty about the function of these types of upstroke may be resolved when more data are available on wake structure in different flight speeds and modes. Inferring from wing kinematics and available data on wake structure, birds with long wings or wings of high aspect ratio use a vortex-ring gait with tip-reversal upstroke at slow speeds, a vortex-ring gait with a feathered upstroke at intermediate speeds, and a continuous-vortex gait at fast speeds. Birds with short wings or wings of low aspect ratio use a vortex-ring gait with a feathered upstroke at all speeds. Regardless of wing shape, species tend to use a vortex-ring gait for acceleration and a continuous-vortex gait for deceleration. Some correlations may exist between gait selection and the function of the muscular and respiratory system. However, overall variation in wing kinematics, muscle activity, and respiratory activity is continuous rather than categorical. To further our understanding of gait selection in flying birds, it is important to test whether upstroke function varies in a similar manner. Transitions between lifting and nonlifting upstrokes may be more subtle and gradual than implied by a binomial scheme of classification.     

Flight style in bats as predicted from wing morphometry: the effects of specimen preservation

An as yet unconsidered potential error in studies that predict flight style from morphological measurements of bats is the effect of the specimen type employed. On the basis of the finding that morphological measurements taken from fluid-preserved bat specimens may not yield values equivalent to those taken from the live animal, we compared the values of several variables (lifting surface area, wingspan, mass, aspect ratio, wing loading and minimum power speed) for live and fluid-preserved little brown bats ( Myotis lucifugus ) with the accepted standards for this species given by Norberg & Rayner (1987). Significant differences were detected for lifting surface area, wingspan, mass, aspect ratio and wing loading values taken from live bats and their respective values reported by Norberg & Rayner. Differences between preserved bats and Norberg & Rayner's numbers were limited to lifting surface area and wingspan (extended wing positions only), aspect ratio (all wing positions), and mass (both 70% ethanol- and 45% isopropyl alcohol-preserved specimens). Thus, Norberg & Rayner's values correspond most closely to values obtained from preserved museum specimens, a fact reflecting the source of their data in this instance. This and other limitations involved in attempting to predict the flight style of bats from a few morphological characters are discussed.     

A wing-assisted running robot and implications for avian flight evolution

DASH+Wings is a small hexapedal winged robot that uses flapping wings to increase its locomotion capabilities. To examine the effects of flapping wings, multiple experimental controls for the same locomotor platform are provided by wing removal, by the use of inertially similar lateral spars, and by passive rather than actively flapping wings. We used accelerometers and high-speed cameras to measure the performance of this hybrid robot in both horizontal running and while ascending inclines. To examine consequences of wing flapping for aerial performance, we measured lift and drag forces on the robot at constant airspeeds and body orientations in a wind tunnel; we also determined equilibrium glide performance in free flight. The addition of flapping wings increased the maximum horizontal running speed from 0.68 to 1.29 m s?1, and also increased the maximum incline angle of ascent from 5.6° to 16.9°. Free flight measurements show a decrease of 10.3° in equilibrium glide slope between the flapping and gliding robot. In air, flapping improved the mean lift:drag ratio of the robot compared to gliding at all measured body orientations and airspeeds. Low-amplitude wing flapping thus provides advantages in both cursorial and aerial locomotion. We note that current support for the diverse theories of avian flight origins derive from limited fossil evidence, the adult behavior of extant flying birds, and developmental stages of already volant taxa. By contrast, addition of wings to a cursorial robot allows direct evaluation of the consequences of wing flapping for locomotor performance in both running and flying.     

Upstroke wing flexion and the inertial cost of bat flight

Flying vertebrates change the shapes of their wings during the upstroke, thereby decreasing wing surface area and bringing the wings closer to the body than during downstroke. These, and other wing deformations, might reduce the inertial cost of the upstroke compared with what it would be if the wings remained fully extended. However, wing deformations themselves entail energetic costs that could exceed any inertial energy savings. Using a model that incorporates detailed three-dimensional wing kinematics, we estimated the inertial cost of flapping flight for six bat species spanning a 40-fold range of body masses. We estimate that folding and unfolding comprises roughly 44 per cent of the inertial cost, but that the total inertial cost is only approximately 65 per cent of what it would be if the wing remained extended and rigid throughout the wingbeat cycle. Folding and unfolding occurred mostly during the upstroke; hence, our model suggests inertial cost of the upstroke is not less than that of downstroke. The cost of accelerating the metacarpals and phalanges accounted for around 44 per cent of inertial costs, although those elements constitute only 12 per cent of wing weight. This highlights the energetic benefit afforded to bats by the decreased mineralization of the distal wing bones.     

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.     

Non-Jumping Take off Performance in Beetle Flight （Rhinoceros Beetle Trypoxylus dichotomus）

In recent decades, the take-off mechanisms of flying animals have received much attention in insect flight initiation. Most of previous works have focused on the jumping mechanism, which is the most common take-off mechanism found in flying animals. Here, we presented that the rhinoceros beetle, Trypoxylus dichotomus, takes offwithout jumping. In this study, we used 3-Dimensional （3D） high-speed video techniques to quantitatively analyze the wings and body kinematics during the initiation periods of flight. The details of the flapping angle, angle of attack of the wings and the roll, pitch and yaw angles of the body were investigated to understand the mechanism of take-off in T. dichotomus. The beetle took off gradually with a small velocity and small acceleration. The body kinematic analyses showed that the beetle exhibited stable take-off. To generate high lift force, the beetle modulated its hind wing to control the angle of attack; the angle of attack was large during the upstroke and small during the downstroke. The legs of beetle did not contract and strongly release like other insects. The hind wing could be con- sidered as a main source of lift for heavy beetle.     

Normalized lift: an energy interpretation of the lift coefficient simplifies comparisons of the lifting ability of rotating and flapping surfaces

For a century, researchers have used the standard lift coefficient C(L) to evaluate the lift, L, generated by fixed wings over an area S against dynamic pressure, ?ρv(2), where v is the effective velocity of the wing. Because the lift coefficient was developed initially for fixed wings in steady flow, its application to other lifting systems requires either simplifying assumptions or complex adjustments as is the case for flapping wings and rotating cylinders.This paper interprets the standard lift coefficient of a fixed wing slightly differently, as the work exerted by the wing on the surrounding flow field (L/ρ·S), compared against the total kinetic energy required for generating said lift, ?v(2). This reinterpreted coefficient, the normalized lift, is derived from the work-energy theorem and compares the lifting capabilities of dissimilar lift systems on a similar energy footing. The normalized lift is the same as the standard lift coefficient for fixed wings, but differs for wings with more complex motions; it also accounts for such complex motions explicitly and without complex modifications or adjustments. We compare the normalized lift with the previously-reported values of lift coefficient for a rotating cylinder in Magnus effect, a bat during hovering and forward flight, and a hovering dipteran.The maximum standard lift coefficient for a fixed wing without flaps in steady flow is around 1.5, yet for a rotating cylinder it may exceed 9.0, a value that implies that a rotating cylinder generates nearly 6 times the maximum lift of a wing. The maximum normalized lift for a rotating cylinder is 1.5. We suggest that the normalized lift can be used to evaluate propellers, rotors, flapping wings of animals and micro air vehicles, and underwater thrust-generating fins in the same way the lift coefficient is currently used to evaluate fixed wings.     

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.     

Direct measurements of the kinematics and dynamics of bat flight

Experimental measurements and analysis of the flight of bats are presented, including kinematic analysis of high-speed stereo videography of straight and turning flight, and measurements of the wake velocity field behind the bat. The kinematic data reveal that, at relatively slow flight speeds, wing motion is quite complex, including a sharp retraction of the wing during the upstroke and a broad sweep of the partially extended wing during the downstroke. The data also indicate that the flight speed and elevation are not constant, but oscillate in synchrony with both the horizontal and vertical movements of the wing. PIV measurements in the transverse (Trefftz) plane of the wake indicate a complex 'wake vortex' structure dominated by a strong wing tip vortex shed from the wing tip during the downstroke and either the wing tip or a more proximal joint during the upstroke. Data synthesis of several discrete realizations suggests a 'cartoon' of the wake structure during the entire wing beat cycle. Considerable work remains to be done to confirm and amplify these results.     

Albedo and transmittance of short-wave radiation for bat wings

1. 1.|Independent of their diverse feeding habits almost all bats are nocturnal. One hypothesis for chiropteran nocturnality is that bats flying in the day experience fatal hyperthermia because their wings take up significant amounts of short-wave radiation which they are unable to dissipate convectively. Factors that will critically affect a bat's susceptibility to overheating are the albedo and transmittance of wing membranes to short-wave radiation.

2. 2.|Albedo of taut segments of bat wings from four species of insectivorous bats and one Pteropid varied between 0.026 (for Rhinolophus hipposideros) and 0.069 (Plecotus auritus).

3. 3.|Transmittance exceeded albedo in all species studied and varied from 0.077 (Pipistrellus pipistrellus) to 0.194 (P. auritus). In this small sample there was no relationship between albedo and transmittance.

4. 4.|Total absorbed short-wave radiation amounted to between 70 and 92% of the incident radiation, and averaged 81.9% (SE = 2.4%, n = 9). Given a clear sky short-wave flux density of about 971 W · m⁻² a typical small insectivorous bat (5g, wing AREA = 0.013 m², ABSORPTIVITY = 81.9%) with fully outstretched wings and the sun directly overhead would absorb about 10.65 W, compared with the maximum endogenous heat production from flight of 0.83 W.

5. 5.|Predicted maximum exogenous heat load relative to maximum endogenous heat load declined as a function of body mass, however, even in the largest known bats (1.4 kg) the exogenous burden exceeded by a factor of 3 the endogenous heat load.

Quantifying the complexity of bat wing kinematics

Body motions (kinematics) of animals can be dimensionally complex, especially when flexible parts of the body interact with a surrounding fluid. In these systems, tracking motion completely can be difficult, and result in a large number of correlated measurements, with unclear contributions of each parameter to performance. Workers typically get around this by deciding a priori which variables are important (wing camber, stroke amplitude, etc.), and focusing only on those variables, but this constrains the ability of a study to uncover variables of influence. Here, we describe an application of proper orthogonal decomposition (POD) for assigning importances to kinematic variables, using dimensional complexity as a metric. We apply this method to bat flight kinematics, addressing three questions: (1) Does dimensional complexity of motion change with speed? (2) What body markers are optimal for capturing dimensional complexity? (3) What variables should a simplified reconstruction of bat flight include in order to maximally reconstruct actual dimensional complexity? We measured the motions of 17 kinematic markers (20 joint angles) on a bat (Cynopterus brachyotis) flying in a wind tunnel at nine speeds. Dimensional complexity did not change with flight speed, despite changes in the kinematics themselves, suggesting that the relative efficacy of a given number of dimensions for reconstructing kinematics is conserved across speeds. By looking at subsets of the full 17-marker set, we found that using more markers improved resolution of kinematic dimensional complexity, but that the benefit of adding markers diminished as the total number of markers increased. Dimensional complexity was highest when the hindlimb and several points along digits III and IV were tracked. Also, we uncovered three groups of joints that move together during flight by using POD to quantify correlations of motion. These groups describe 14/20 joint angles, and provide a framework for models of bat flight for experimental and modeling purposes.