The three-dimensional leading-edge vortex of a 'hovering' model hawkmoth

Recent flow visualisation experiments with the hawkmoth, Manduca sexta, revealed small but clear leading-edge vortex and a pronounced three-dimensional flow. Details of this flow pattern were studied with a scaled-up, robotic insect (''the flapper'') that accurately mimicked the wing movements of a hovering hawkmoth. Smoke released from the leading edge of the flapper wing confirmed the existence of a small, strong and stable leading-edge vortex, increasing in size from wingbase to wingtip. Between 25 and 75 per cent of the wing length, its diameter increased approximately from 10 to 50 per cent of the wing chord. The leading-edge vortex had a strong axial flow veolocity, which stabilized it and reduced its diamater. The vortex separated from the wing at approximately 75 per cent of the wing length and thus fed vorticity into a large, tangled tip vortex. If the circulation of the leading-edge vortex were fully used for lift generation, it could support up to two-thirds of the hawkmoth''s weight during the downstroke. The growth of this circulation with time and spanwise position clearly identify dynamic stall as the unsteady aerodynamic mechanism responsible for high lift production by hovering hawkmoths and possibly also by many other insect species.     

Structure of the vortex wake in hovering Anna's hummingbirds (Calypte anna)

Hummingbirds are specialized hoverers for which the vortex wake has been described as a series of single vortex rings shed primarily during the downstroke. Recent findings in bats and birds, as well as in a recent study on Anna''s hummingbirds, suggest that each wing may shed a discrete vortex ring, yielding a bilaterally paired wake. Here, we describe the presence of two discrete rings in the wake of hovering Anna''s hummingbirds, and also infer force production through a wingbeat with contributions to weight support. Using flow visualization, we found separate vortices at the tip and root of each wing, with 15% stronger circulation at the wingtip than at the root during the downstroke. The upstroke wake is more complex, with near-continuous shedding of vorticity, and circulation of approximately equal magnitude at tip and root. Force estimates suggest that the downstroke contributes 66% of required weight support, whereas the upstroke generates 35%. We also identified a secondary vortex structure yielding 8–26% of weight support. Lift production in Anna''s hummingbirds is more evenly distributed between the stroke phases than previously estimated for Rufous hummingbirds, in accordance with the generally symmetric down- and upstrokes that characterize hovering in these birds.     

The vortex wake of a 'hovering' model hawkmoth

Visualization experiments with Manduca sexta have revealed the presence of a leading-edge vortex and a highly three-dimensional flow pattern. To further investigate this important discovery, a scaled-up robotic insect was built (the ''flapper'') which could mimic the complex movements of the wings of a hovering hawkmoth. Smoke released from the leading edge of the flapper wing revealed a small but strong leading-edge vortex on the downstroke. This vortex had a high axial flow velocity and was stable, separating from the wing at approximately 75 per cent of the wing length. It connected to a large, tangled tip vortex, extending back to a combining stopping and starting vortex from pronation. At the end of the downstroke, the wake could be approximated as one vortex ring per wing. Based on the size and velocity of the vortex rings, the mean lift force during the downstroke was estimated to be about 1.5 times the body weight of a hawkmoth, confirming that the downstroke is the main provider of lift force.     

Hovering and intermittent flight in birds

Two styles of bird locomotion, hovering and intermittent flight, have great potential to inform future development of autonomous flying vehicles. Hummingbirds are the smallest flying vertebrates, and they are the only birds that can sustain hovering. Their ability to hover is due to their small size, high wingbeat frequency, relatively large margin of mass-specific power available for flight and a suite of anatomical features that include proportionally massive major flight muscles (pectoralis and supracoracoideus) and wing anatomy that enables them to leave their wings extended yet turned over (supinated) during upstroke so that they can generate lift to support their weight. Hummingbirds generate three times more lift during downstroke compared with upstroke, with the disparity due to wing twist during upstroke. Much like insects, hummingbirds exploit unsteady mechanisms during hovering including delayed stall during wing translation that is manifest as a leading-edge vortex (LEV) on the wing and rotational circulation at the end of each half stroke. Intermittent flight is common in small- and medium-sized birds and consists of pauses during which the wings are flexed (bound) or extended (glide). Flap-bounding appears to be an energy-saving style when flying relatively fast, with the production of lift by the body and tail critical to this saving. Flap-gliding is thought to be less costly than continuous flapping during flight at most speeds. Some species are known to shift from flap-gliding at slow speeds to flap-bounding at fast speeds, but there is an upper size limit for the ability to bound (~0.3 kg) and small birds with rounded wings do not use intermittent glides.     

Centripetal Acceleration Reaction: An Effective and Robust Mechanism for Flapping Flight in Insects

Despite intense study by physicists and biologists, we do not fully understand the unsteady aerodynamics that relate insect wing morphology and kinematics to lift generation. Here, we formulate a force partitioning method (FPM) and implement it within a computational fluid dynamic model to provide an unambiguous and physically insightful division of aerodynamic force into components associated with wing kinematics, vorticity, and viscosity. Application of the FPM to hawkmoth and fruit fly flight shows that the leading-edge vortex is the dominant mechanism for lift generation for both these insects and contributes between 72–85% of the net lift. However, there is another, previously unidentified mechanism, the centripetal acceleration reaction, which generates up to 17% of the net lift. The centripetal acceleration reaction is similar to the classical inviscid added-mass in that it depends only on the kinematics (i.e. accelerations) of the body, but is different in that it requires the satisfaction of the no-slip condition, and a combination of tangential motion and rotation of the wing surface. Furthermore, the classical added-mass force is identically zero for cyclic motion but this is not true of the centripetal acceleration reaction. Furthermore, unlike the lift due to vorticity, centripetal acceleration reaction lift is insensitive to Reynolds number and to environmental flow perturbations, making it an important contributor to insect flight stability and miniaturization. This force mechanism also has broad implications for flow-induced deformation and vibration, underwater locomotion and flows involving bubbles and droplets.     

Flow Visualization of Rhinoceros Beetle (Trypoxylus dichotomus) in Free Flight

Aerodynamic characteristics of the beetle,Trypoxylus dichotomus,which has a pair of elytra (forewings) and flexible hind wings,are investigated.Visualization experiments were conducted for various flight conditions of a beetle,Trypoxylus dichotomus:free,tethered,hovering,forward and climbing flights.Leading edge,trailing edge and tip vortices on both wings were observed clearly.The leading edge vortex was stable and remained on the top surface of the elytron for a wide interval during the downstroke of free forward flight.Hence,the elytron may have a considerable role in lift force generation of the beetle.In addition,we reveal a suction phenomenon between the gaps of the hind wing and the elytron in upstroke that may improve the positive lift force on the hind wing.We also found the reverse clap-fling mechanism of the T.dichotomus beetle in hovering flight.The hind wings touch together at the beginning of the upstroke.The vortex generation,shedding and interaction give a better understanding of the detailed aerodynamic mechanism of beetle flight.     

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.     

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.     

Lift production in the hovering hummingbird

Aerodynamic theory and empirical observations of animals flying at similar Reynolds numbers (Re) predict that airflow over hummingbird wings will be dominated by a stable, attached leading edge vortex (LEV). In insects exhibiting similar kinematics, when the translational movement of the wing ceases (as at the end of the downstroke), the LEV is shed and lift production decreases until the energy of the LEV is re-captured in the subsequent half-cycle translation. We here show that while the hummingbird wing is strongly influenced by similar sharp-leading-edge aerodynamics, leading edge vorticity is inconsistent, varying from 0.7 to 26 per cent (mean 16%) of total lift production, is always generated within 3 mm of the dorsal surface of the wing, showing no retrograde (trailing to leading edge) flow, and does not increase from proximal to distal wing as would be expected with a conical vortex (class III LEV) described for hawkmoths. Further, the bound circulation is not shed as a vortex at the end of translation, but instead remains attached and persists after translation has ceased, augmented by the rotation (pronation, supination) of the wing that occurs between the wing-translation half-cycles. The result is a near-continuous lift production through wing turn-around, previously unknown in vertebrates, able to contribute to weight support as well as stability and control during hovering. Selection for a planform suited to creating this unique flow and nearly-uninterrupted lift production throughout the wingbeat cycle may help explain the relatively narrow hummingbird wing.     

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.     

On the Estimation of Time Dependent Lift of a European Starling (Sturnus vulgaris) during Flapping Flight

We study the role of unsteady lift in the context of flapping wing bird flight. Both aerodynamicists and biologists have attempted to address this subject, yet it seems that the contribution of unsteady lift still holds many open questions. The current study deals with the estimation of unsteady aerodynamic forces on a freely flying bird through analysis of wingbeat kinematics and near wake flow measurements using time resolved particle image velocimetry. The aerodynamic forces are obtained through two approaches, the unsteady thin airfoil theory and using the momentum equation for viscous flows. The unsteady lift is comprised of circulatory and non-circulatory components. Both approaches are presented over the duration of wingbeat cycles. Using long-time sampling data, several wingbeat cycles have been analyzed in order to cover both the downstroke and upstroke phases. It appears that the unsteady lift varies over the wingbeat cycle emphasizing its contribution to the total lift and its role in power estimations. It is suggested that the circulatory lift component cannot assumed to be negligible and should be considered when estimating lift or power of birds in flapping motion.     

Spatial distribution and aggregation of Xenobalanus globicipitis on the flukes of striped dolphins,Stenella coeruleoalba: An indicator of host hydrodynamics?

We analyzed patterns of aggregation and spatial distribution of the epizoic barnacle Xenobalanus globicipitis on the flukes of Mediterranean striped dolphins, Stenella coeruleoalba, assessing its potential use as an indicator of the host's hydrodynamics based on data from 55 dolphins. Barnacles occurred along the trailing edge with the cirri oriented towards the oncoming flow. Nearest neighbor analyses suggested that new recruits actively seek placement next to already settled barnacles, forming aggregations possibly to facilitate copulation. The probability of spanwise settlement strongly increased with fluke width (presumably enabling prolonged leading-edge vorticity), and with chordwise length where pressure is predicted to be positive. Consequently, clustering tended to increase nonlinearly towards the fluke notch. Furthermore, it was three times more likely for barnacles to occur on the dorsal vs. ventral side of flukes, at an average abundance ca. 12 times higher. This difference could result from a host's asymmetric oscillation of the tail, which would alter leading-edge vorticity, and/or an interaction between the wake produced by the dorsal fin and the flow associated with flukes. Both processes could primarily enhance cyprid contact and/or attachment on the dorsal side. This study offers a starting point for future comparison with other cetaceans.     

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.     

Particle-Image Velocimetry and Force Measurements of Leading-Edge Serrations on Owl-Based Wing Models

High-resolution Particle-Image Velocimetry （PIV） and time-resolved force measurements were performed to analyze the impact of the comb-like structure on the leading edge of barn owl wings on the flow field and overall aerodynamic performance. The Reynolds number was varied in the range of 40,000 to 120,000 and the range of angle of attack was 0° to 6° for the PIV and -15° to ＋20° for the force measurements to cover the full flight envelope of the owl. As a reference, a wind-tunnel model which possessed a geometry based on the shape of a typical barn owl wing without any owl-specific adaptations was built, and measurements were performed in the aforementioned Reynolds number and angle of attack： range. This clean wing model shows a separation bubble in the distal part of the wing at higher angles of attack. Two types of comb-like structures, i.e., artificial serrations, were manufactured to model the owl＇s leading edge with respect to its length, thickness, and material properties. The artificial structures were able to reduce the size of the separation region and additionally cause a more uniform size of the vortical structures shed by the separation bubble within the Reynolds number range investigated, resulting in stable gliding flight independent of the flight velocity. However, due to increased drag coefficients in conjunction with similar lift coefficients, the overall aerodynamic performance, i.e., lift-to-drag ratio is reduced for the serrated models. Nevertheless, especially at lower Reynolds numbers the stabilizing effect of the uniform vortex size outperforms the lower aerodynamic performance.     

Into turbulent air: size-dependent effects of von Kármán vortex streets on hummingbird flight kinematics and energetics

Animal fliers frequently move through a variety of perturbed flows during their daily aerial routines. However, the extent to which these perturbations influence flight control and energetic expenditure is essentially unknown. Here, we evaluate the kinematic and metabolic consequences of flight within variably sized vortex shedding flows using five Anna''s hummingbirds feeding from an artificial flower in steady control flow and within vortex wakes produced behind vertical cylinders. Tests were conducted at three horizontal airspeeds (3, 6 and 9 m s⁻¹) and using three different wake-generating cylinders (with diameters equal to 38, 77 and 173% of birds'' wing length). Only minimal effects on wing and body kinematics were demonstrated for flight behind the smallest cylinder, whereas flight behind the medium-sized cylinder resulted in significant increases in the variances of wingbeat frequency, and variances of body orientation, especially at higher airspeeds. Metabolic rate was, however, unchanged relative to that of unperturbed flight. Hummingbirds flying within the vortex street behind the largest cylinder exhibited highest increases in variances of wingbeat frequency, and of body roll, pitch and yaw amplitudes at all measured airspeeds. Impressively, metabolic rate under this last condition increased by up to 25% compared with control flights. Cylinder wakes sufficiently large to interact with both wings can thus strongly affect stability in flight, eliciting compensatory kinematic changes with a consequent increase in flight metabolic costs. Our findings suggest that vortical flows frequently encountered by aerial taxa in diverse environments may impose substantial energetic costs.     

Volumetric imaging of shark tail hydrodynamics reveals a three-dimensional dual-ring vortex wake structure

Understanding how moving organisms generate locomotor forces is fundamental to the analysis of aerodynamic and hydrodynamic flow patterns that are generated during body and appendage oscillation. In the past, this has been accomplished using two-dimensional planar techniques that require reconstruction of three-dimensional flow patterns. We have applied a new, fully three-dimensional, volumetric imaging technique that allows instantaneous capture of wake flow patterns, to a classic problem in functional vertebrate biology: the function of the asymmetrical (heterocercal) tail of swimming sharks to capture the vorticity field within the volume swept by the tail. These data were used to test a previous three-dimensional reconstruction of the shark vortex wake estimated from two-dimensional flow analyses, and show that the volumetric approach reveals a different vortex wake not previously reconstructed from two-dimensional slices. The hydrodynamic wake consists of one set of dual-linked vortex rings produced per half tail beat. In addition, we use a simple passive shark-tail model under robotic control to show that the three-dimensional wake flows of the robotic tail differ from the active tail motion of a live shark, suggesting that active control of kinematics and tail stiffness plays a substantial role in the production of wake vortical patterns.     

The fish tail motion forms an attached leading edge vortex

The tail (caudal fin) is one of the most prominent characteristics of fishes, and the analysis of the flow pattern it creates is fundamental to understanding how its motion generates locomotor forces. A mechanism that is known to greatly enhance locomotor forces in insect and bird flight is the leading edge vortex (LEV) reattachment, i.e. a vortex (separation bubble) that stays attached at the leading edge of a wing. However, this mechanism has not been reported in fish-like swimming probably owing to the overemphasis on the trailing wake, and the fact that the flow does not separate along the body of undulating swimmers. We provide, to our knowledge, the first evidence of the vortex reattachment at the leading edge of the fish tail using three-dimensional high-resolution numerical simulations of self-propelled virtual swimmers with different tail shapes. We show that at Strouhal numbers (a measure of lateral velocity to the axial velocity) at which most fish swim in nature (approx. 0.25) an attached LEV is formed, whereas at a higher Strouhal number of approximately 0.6 the LEV does not reattach. We show that the evolution of the LEV drastically alters the pressure distribution on the tail and the force it generates. We also show that the tail''s delta shape is not necessary for the LEV reattachment and fish-like kinematics is capable of stabilising the LEV. Our results suggest the need for a paradigm shift in fish-like swimming research to turn the focus from the trailing edge to the leading edge of the tail.     

Computational hydrodynamics of animal swimming: boundary element method and three-dimensional vortex wake structure.

The slender body theory, lifting surface theories, and more recently panel methods and Navier-Stokes solvers have been used to study the hydrodynamics of fish swimming. This paper presents progress on swimming hydrodynamics using a boundary integral equation method (or boundary element method) based on potential flow model. The unsteady three-dimensional BEM code 3DynaFS that we developed and used is able to model realistic body geometries, arbitrary movements, and resulting wake evolution. Pressure distribution over the body surface, vorticity in the wake, and the velocity field around the body can be computed. The structure and dynamic behavior of the vortex wakes generated by the swimming body are responsible for the underlying fluid dynamic mechanisms to realize the high-efficiency propulsion and high-agility maneuvering. Three-dimensional vortex wake structures are not well known, although two-dimensional structures termed 'reverse Karman Vortex Street' have been observed and studied. In this paper, simulations about a swimming saithe (Pollachius virens) using our BEM code have demonstrated that undulatory swimming reduces three-dimensional effects due to substantially weakened tail tip vortex, resulting in a reverse Karman Vortex Street as the major flow pattern in the three-dimensional wake of an undulating swimming fish.     

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.     

Modulation of leading edge vorticity and aerodynamic forces in flexible flapping wings

In diverse biological flight systems, the leading edge vortex has been implicated as a flow feature of key importance in the generation of flight forces. Unlike fixed wings, flapping wings can translate at higher angles of attack without stalling because their leading edge vorticity is more stable than the corresponding fixed wing case. Hence, the leading edge vorticity has often been suggested as the primary determinant of the high forces generated by flapping wings. To test this hypothesis, it is necessary to modulate the size and strength of the leading edge vorticity independently of the gross kinematics while simultaneously monitoring the forces generated by the wing. In a recent study, we observed that forces generated by wings with flexible trailing margins showed a direct dependence on the flexural stiffness of the wing. Based on that study, we hypothesized that trailing edge flexion directly influences leading edge vorticity, and thereby the magnitude of aerodynamic forces on the flexible flapping wings. To test this hypothesis, we visualized the flows on wings of varying flexural stiffness using a custom 2D digital particle image velocimetry system, while simultaneously monitoring the magnitude of the aerodynamic forces. Our data show that as flexion decreases, the magnitude of the leading edge vorticity increases and enhances aerodynamic forces, thus confirming that the leading edge vortex is indeed a key feature for aerodynamic force generation in flapping flight. The data shown here thus support the hypothesis that camber influences instantaneous aerodynamic forces through modulation of the leading edge vorticity.