The relationship between wingbeat kinematics and vortex wake of a thrush nightingale

Bio-inspired flapping wing robots with foldable or deformable wings: a review

Traditional flapping-wing robots (FWRs) obtain lift and thrust by relying on the passive deformation of their wings which cannot actively fold or deform. In contrast, flying creatures such as birds, bats, and insects can maneuver agilely through active folding or deforming their wings. Researchers have developed many bio-inspired foldable or deformable wings (FDWs) imitating the wings of flying creatures. The foldable wings refer to the wings like the creatures' wings that can fold in an orderly manner close to their bodies. Such wings have scattered feathers or distinct creases that can be stacked and folded to reduce the body envelope, which in nature is beneficial for these animals to prevent wing damage and ensure agility in crossing bushes. The deformable wings refer to the active deformation of the wings using active driving mechanisms and the passive deformation under the aerodynamic force, which functionally imitates the excellent hydrodynamic performance of the deformable body and wings of the creatures. However, the shape and external profile changes of deformable wings tend to be much smaller than that of folding wings. FDWs enable the FWRs to improve flight degree of flexibility, maneuverability, and efficiency and reduce flight energy consumption. However, FDWs still need to be studied, and a comprehensive review of the state-of-the-art progress of FDWs in FWR design is lacking. This paper analyzes the wing folding and deformation mechanisms of the creatures and reviews the latest progress of FWRs with FDWs. Furthermore, we summarize the current limitations and propose future directions in FDW design, which could help researchers to develop better FWRs for safe maneuvering in obstacle-dense environments.

Fluid dynamics, scaling laws and plesiosaur locomotion

The evolutionary success of plesiosaurs has led to much attention regarding the dynamics of their locomotion. They exhibit identical tandem flippers, which is unique among all living and extinct species. However, these tandem flippers have been a source of debate regarding plesiosaurs' locomotion and behavior. Here we propose a new approach to studying plesiosaur locomotion based on universal scaling laws in fluid dynamics, which were used to estimate reduced frequency to characterize unsteadiness of an airfoil. It was found that, while the reduced frequency of plesiosaurs with high-aspect ratio flippers is similar to that of sea turtles, the most commonly used living analog, lower aspect ratio plesiosaurs were more similar in reduced frequency to penguins. This implies that plesiosaurs may have had large variations in agility among themselves, depending in particular on the specimen's flipper aspect ratio. While our results are consistent with the previous literature indicating a relationship between plesiosaur neck length and agility, our work supports broad and diverse analogies to living animals. Moreover, based on our results, cruising reduced frequency has some predictive value into manoeuvring behavior, rather than simply cruising behavior.

The role of wingbeat frequency and amplitude in flight power

Body-mounted accelerometers provide a new prospect for estimating power use in flying birds, as the signal varies with the two major kinematic determinants of aerodynamic power: wingbeat frequency and amplitude. Yet wingbeat frequency is sometimes used as a proxy for power output in isolation. There is, therefore, a need to understand which kinematic parameter birds vary and whether this is predicted by flight mode (e.g. accelerating, ascending/descending flight), speed or morphology. We investigate this using high-frequency acceleration data from (i) 14 species flying in the wild, (ii) two species flying in controlled conditions in a wind tunnel and (iii) a review of experimental and field studies. While wingbeat frequency and amplitude were positively correlated, R² values were generally low, supporting the idea that parameters can vary independently. Indeed, birds were more likely to modulate wingbeat amplitude for more energy-demanding flight modes, including climbing and take-off. Nonetheless, the striking variability, even within species and flight types, highlights the complexity of describing the kinematic relationships, which appear sensitive to both the biological and physical context. Notwithstanding this, acceleration metrics that incorporate both kinematic parameters should be more robust proxies for power than wingbeat frequency alone.

A biomimetic robotic platform to study flight specializations of bats

Bats have long captured the imaginations of scientists and engineers with their unrivaled agility and maneuvering characteristics, achieved by functionally versatile dynamic wing conformations as well as more than 40 active and passive joints on the wings. Wing flexibility and complex wing kinematics not only bring a unique perspective to research in biology and aerial robotics but also pose substantial technological challenges for robot modeling, design, and control. We have created a fully self-contained, autonomous flying robot that weighs 93 grams, called Bat Bot (B2), to mimic such morphological properties of bat wings. Instead of using a large number of distributed control actuators, we implement highly stretchable silicone-based membrane wings that are controlled at a reduced number of dominant wing joints to best match the morphological characteristics of bat flight. First, the dominant degrees of freedom (DOFs) in the bat flight mechanism are identified and incorporated in B2's design by means of a series of mechanical constraints. These biologically meaningful DOFs include asynchronous and mediolateral movements of the armwings and dorsoventral movements of the legs. Second, the continuous surface and elastic properties of bat skin under wing morphing are realized by an ultrathin (56 micrometers) membranous skin that covers the skeleton of the morphing wings. We have successfully achieved autonomous flight of B2 using a series of virtual constraints to control the articulated, morphing wings.

The effects of wing twist in slow-speed flapping flight of birds: trading brute force against efficiency

In aircraft propellers that are used to propel aircraft forward at some speed, propeller blade twist is important to make the individual propeller 'wings' operate at a relatively constant effective angle of attack over the full span. Wing twist is sometimes also assumed to be essential in flapping flight, especially in bird flight. For small insects, it has however been shown that wing twist has little effect on the forces generated by a flapping wing. The unimportance of twist was attributed to the prominent role of unsteady aerodynamic mechanisms. These were recently also shown to be important in bird flight. It has therefore become necessary to verify the role of wing twist in the flapping flight of birds. The aim of the study is to compare the efficiency and the aerodynamic forces of twisted and non-twisted wings that mimic the slow-speed flapping flight of birds. The analyses were performed by using physical models with different amounts of spanwise twist (0°, 10°, 40°). The flow was mapped in three-dimensions using digital particle image velocimetry. The spanwise circulation, the induced drag, the lift-to-drag ratio and the span efficiency were determined. Twist and Strouhal number (St) both determine the local effective angles of attack of the flapping wing. Wings with low average effective angles of attack (resulting from high twist and/or low St) are more efficient, but generate significantly lower aerodynamic forces. High average effective angles of attack result in lower efficiency and high aerodynamic forces. Efficiency and the magnitude of aerodynamic forces are competing parameters. Wing twist is beneficial only in the cases where efficiency is most important-e.g. in cruising flight. Take-off, landing and maneuvering, however, require large and robust aerodynamic forces to be generated. The additional force comes at the cost of efficiency, but it enables birds to perform extreme manoeuvres, increasing their overall fitness.

Flow pattern similarities in the near wake of three bird species suggest a common role for unsteady aerodynamic effects in lift generation

Analysis of the aerodynamics of flapping wings has yielded a general understanding of how birds generate lift and thrust during flight. However, the role of unsteady aerodynamics in avian flight due to the flapping motion still holds open questions in respect to performance and efficiency. We studied the flight of three distinctive bird species: western sandpiper (Calidris mauri), European starling (Sturnus vulgaris) and American robin (Turdus migratorius) using long-duration, time-resolved particle image velocimetry, to better characterize and advance our understanding of how birds use unsteady flow features to enhance their aerodynamic performances during flapping flight. We show that during transitions between downstroke and upstroke phases of the wing cycle, the near wake-flow structures vary and generate unique sets of vortices. These structures appear as quadruple layers of concentrated vorticity aligned at an angle with respect to the horizon (named 'double branch'). They occur where the circulation gradient changes sign, which implies that the forces exerted by the flapping wings of birds are modified during the transition phases. The flow patterns are similar in (non-dimensional) size and magnitude for the different birds suggesting that there are common mechanisms operating during flapping flight across species. These flow patterns occur at the same phase where drag reduction of about 5% per cycle and lift enhancement were observed in our prior studies. We propose that these flow structures should be considered in wake flow models that seek to account for the contribution of unsteady flow to lift and drag.

Physiological, aerodynamic and geometric constraints of flapping account for bird gaits, and bounding and flap-gliding flight strategies

Aerodynamically economical flight is steady and level. The high-amplitude flapping and bounding flight style of many small birds departs considerably from any aerodynamic or purely mechanical optimum. Further, many large birds adopt a flap-glide flight style in cruising flight which is not consistent with purely aerodynamic economy. Here, an account is made for such strategies by noting a well-described, general, physiological cost parameter of muscle: the cost of activation. Small birds, with brief downstrokes, experience disproportionately high costs due to muscle activation for power during contraction as opposed to work. Bounding flight may be an adaptation to modulate mean aerodynamic force production in response to (1) physiological pressure to extend the duration of downstroke to reduce power demands during contraction; (2) the prevention of a low-speed downstroke due to the geometric constraints of producing thrust; (3) an aerodynamic cost to flapping with very low lift coefficients. In contrast, flap-gliding birds, which tend to be larger, adopt a strategy that reduces the physiological cost of work due both to activation and contraction efficiency. Flap-gliding allows, despite constraints to modulation of aerodynamic force lever-arm, (1) adoption of moderately large wing-stroke amplitudes to achieve suitable muscle strains, thereby reducing the activation costs for work; (2) reasonably quick downstrokes, enabling muscle contraction at efficient velocities, while being (3) prevented from very slow weight-supporting upstrokes due to the cost of performing 'negative' muscle work.

Power of the wingbeat: modelling the effects of flapping wings in vertebrate flight

Animal flight performance has been studied using models developed for man-made aircraft. For an aeroplane with fixed wings, the energetic cost as a function of flight speed can be expressed in terms of weight, wing span, wing area and body area, where more details are included in proportionality coefficients. Flying animals flap their wings to produce thrust. Adopting the fixed wing flight model implicitly incorporates the effects of wing flapping in the coefficients. However, in practice, these effects have been ignored. In this paper, the effects of reciprocating wing motion on the coefficients of the fixed wing aerodynamic power model for forward flight are explicitly formulated in terms of thrust requirement, wingbeat frequency and stroke-plane angle, for optimized wingbeat amplitudes. The expressions are obtained by simulating flights over a large parameter range using an optimal vortex wake method combined with a low-level blade element method. The results imply that previously assumed acceptable values for the induced power factor might be strongly underestimated. The results also show the dependence of profile power on wing kinematics. The expressions introduced in this paper can be used to significantly improve animal flight models.

In vivo recording of aerodynamic force with an aerodynamic force platform: from drones to birds

Flapping wings enable flying animals and biomimetic robots to generate elevated aerodynamic forces. Measurements that demonstrate this capability are based on experiments with tethered robots and animals, and indirect force calculations based on measured kinematics or airflow during free flight. Remarkably, there exists no method to measure these forces directly during free flight. Such in vivo recordings in freely behaving animals are essential to better understand the precise aerodynamic function of their flapping wings, in particular during the downstroke versus upstroke. Here, we demonstrate a new aerodynamic force platform (AFP) for non-intrusive aerodynamic force measurement in freely flying animals and robots. The platform encloses the animal or object that generates fluid force with a physical control surface, which mechanically integrates the net aerodynamic force that is transferred to the earth. Using a straightforward analytical solution of the Navier-Stokes equation, we verified that the method is accurate. We subsequently validated the method with a quadcopter that is suspended in the AFP and generates unsteady thrust profiles. These independent measurements confirm that the AFP is indeed accurate. We demonstrate the effectiveness of the AFP by studying aerodynamic weight support of a freely flying bird in vivo. These measurements confirm earlier findings based on kinematics and flow measurements, which suggest that the avian downstroke, not the upstroke, is primarily responsible for body weight support during take-off and landing.

Wake development behind paired wings with tip and root trailing vortices: consequences for animal flight force estimates

Recent experiments on flapping flight in animals have shown that a variety of unrelated species shed a wake behind left and right wings consisting of both tip and root vortices. Here we present an investigation using Particle Image Velocimetry (PIV) of the behaviour and interaction of trailing vortices shed by paired, fixed wings that simplify and mimic the wake of a flying animal with a non-lifting body. We measured flow velocities at five positions downstream of two adjacent NACA 0012 aerofoils and systematically varied aspect ratio, the gap between the wings (corresponding to the width of a non-lifting body), angle of attack, and the Reynolds number. The range of aspect ratios and Reynolds number where chosen to be relevant to natural fliers and swimmers, and insect flight in particular. We show that the wake behind the paired wings deformed as a consequence of the induced flow distribution such that the wingtip vortices convected downwards while the root vortices twist around each other. Vortex interaction and wake deformation became more pronounced further downstream of the wing, so the positioning of PIV measurement planes in experiments on flying animals has an important effect on subsequent force estimates due to rotating induced flow vectors. Wake deformation was most severe behind wings with lower aspect ratios and when the distance between the wings was small, suggesting that animals that match this description constitute high-risk groups in terms of measurement error. Our results, therefore, have significant implications for experimental design where wake measurements are used to estimate forces generated in animal flight. In particular, the downstream distance of the measurement plane should be minimised, notwithstanding the animal welfare constraints when measuring the wake behind flying animals.

Estimation of unsteady aerodynamics in the wake of a freely flying European starling (Sturnus vulgaris)

Wing flapping is one of the most widespread propulsion methods found in nature; however, the current understanding of the aerodynamics in bird wakes is incomplete. The role of the unsteady motion in the flow and its contribution to the aerodynamics is still an open question. In the current study, the wake of a freely flying European starling has been investigated using long-duration high-speed Particle Image Velocimetry (PIV) in the near wake. Kinematic analysis of the wings and body of the bird has been performed using additional high-speed cameras that recorded the bird movement simultaneously with the PIV measurements. The wake evolution of four complete wingbeats has been characterized through reconstruction of the time-resolved data, and the aerodynamics in the wake have been analyzed in terms of the streamwise forces acting on the bird. The profile drag from classical aerodynamics was found to be positive during most of the wingbeat cycle, yet kinematic images show that the bird does not decelerate. It is shown that unsteady aerodynamics are necessary to satisfy the drag/thrust balance by approximating the unsteady drag term. These findings may shed light on the flight efficiency of birds by providing a partial answer to how they minimize drag during flapping flight.

A coupled kinematics-energetics model for predicting energy efficient flapping flight

A new computational model based on an optimal power, wake-only aerodynamics method is presented to predict the interdependency of energetics and kinematics in bird and bat flight. The model is divided into offline, intermediate and online modules. In the offline module, a four-dimensional design space sweep is performed (lift, thrust, flapping amplitude and flapping frequency). In the intermediate stage, the physical characteristics of the animal are introduced (wing span, mass, wing area, aspect ratio, etc.), and a series of amplitude-frequency response surfaces are constructed for all viable flight speeds. In the online component, the amplitude-frequency response surfaces are mined for the specific flapping motions being considered. The method is applied to several biological examples including a medium sized fruit bat (Cynopterus brachyotis), and two birds: a thrush nightingale (Luscinia luscinia) and a budgerigar (Melopsittacus undulatus). For each of these animals, the power and kinematics predictions are compared with available experimental data. These examples demonstrate that this new method can reasonably predict animal flight energetics and kinematics.

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.

Changes in kinematics and aerodynamics over a range of speeds in Tadarida brasiliensis, the Brazilian free-tailed bat

To date, wake measurements using particle image velocimetry (PIV) of bats in flight have studied only three bat species, all fruit and nectar feeders. In this study, we present the first wake structure analysis for an insectivorous bat. Tadarida brasiliensis, the Brazilian free-tailed bat, is an aerial hunter that annually migrates long distances and also differs strikingly from the previously investigated species morphologically. We compare the aerodynamics of T. brasiliensis with those of other, frugivorous bats and with common swifts, Apus apus, a bird with wing morphology, kinematics and flight ecology similar to that of these bats. The comparison reveals that, for the range of speeds evaluated, the cyclical pattern of aerodynamic forces associated with a wingbeat shows more similarities between T. brasiliensis and A. apus than between T. brasiliensis and other frugivorous bats.

Fluid–structure interaction simulation of an avian flight model

A three-dimensional numerical avian model was developed to investigate the unsteady and turbulent aerodynamic performance of flapping wings for varying wingbeat frequencies and flow velocities (up to 12 Hz and 9 m s–1), corresponding to a reduced frequency range of k=0.22 to k=1.0 and a Reynolds number range of Re=16,000 to Re=50,000. The wings of the bird-inspired model consist of an elastic membrane. Simplifying the complicated locomotion kinematics to a sinusoidal wing rotation about two axes, the main features of dynamic avian flight were approximated. Numerical simulation techniques of fluid–structure interaction (FSI) providing a fully resolved flow field were applied to calculate the aerodynamic performance of the flapping elastic wings with the Reynolds averaged Navier–Stokes (RANS) approach. The results were used to characterize and describe the macroscopic flow configurations in terms of starting, stopping, trailing and bound vortices. For high reduced frequencies up to k=0.67 it was shown that the wake does not consist of individual vortex rings known as the discrete vortex ring gait. Rather, the wake is dominated by a chain of elliptical vortex rings on each wing. The structures are interlocked at the starting and stopping vortices, which are shed in pairs at the reversal points of the wingbeat cycle. For decreasing reduced frequency, the results indicate a transition to a continuous vortex gait. The upstroke becomes more aerodynamically active, leading to a consistent circulation of the bound vortex on the wing and a continuous spanwise shedding of small scale vortices. The formation of the vortices shed spanwise in pairs at the reversal points is reduced and the wake is dominated by the tip and root vortices, which form long drawn-out vortex structures.

Wing and body kinematics of takeoff and landing flight in the pigeon (Columba livia)

Takeoff and landing are critical phases in a flight. To better understand the functional importance of the kinematic adjustments birds use to execute these flight modes, we studied the wing and body movements of pigeons (Columba livia) during short-distance free-flights between two perches. The greatest accelerations were observed during the second wingbeat of takeoff. The wings were responsible for the majority of acceleration during takeoff and landing, with the legs contributing only one-quarter of the acceleration. Parameters relating to aerodynamic power output such as downstroke amplitude, wingbeat frequency and downstroke velocity were all greatest during takeoff flight and decreased with each successive takeoff wingbeat. This pattern indicates that downstroke velocity must be greater for accelerating flight to increase the amount of air accelerated by the wings. Pigeons used multiple mechanisms to adjust thrust and drag to accelerate during takeoff and decelerate during landing. Body angle, tail angle and wing plane angles all shifted from more horizontal orientations during takeoff to near-vertical orientations during landing, thereby reducing drag during takeoff and increasing drag during landing. The stroke plane was tilted steeply downward throughout takeoff (increasing from -60+/-5 deg. to -47+/-1 deg.), supporting our hypothesis that a downward-tilted stroke plane pushes more air rearward to accelerate the bird forward. Similarly, the stroke plane tilted upward during landing (increasing from -1+/-2 deg. to 17+/-7 deg.), implying that an upward-tilted stroke plane pushes more air forward to slow the bird down. Rotations of the stroke plane, wing planes and tail were all strongly correlated with rotation of the body angle, suggesting that pigeons are able to redirect aerodynamic force and shift between flight modes through modulation of body angle alone.

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

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

The importance of leading edge vortices under simplified flapping flight conditions at the size scale of birds

Over the last decade, interest in animal flight has grown, in part due to the possible use of flapping propulsion for micro air vehicles. The importance of unsteady lift-enhancing mechanisms in insect flight has been recognized, but unsteady effects were generally thought to be absent for the flapping flight of larger animals. Only recently has the existence of LEVs (leading edge vortices) in small vertebrates such as swifts, small bats and hummingbirds been confirmed. To study the relevance of unsteady effects at the scale of large birds [reduced frequency k between 0.05 and 0.3, k=(πfc)/U∞; f is wingbeat frequency, U∞ is free-stream velocity, and c is the average wing chord], and the consequences of the lack of kinematic and morphological refinements, we have designed a simplified goose-sized flapping model for wind tunnel testing. The 2-D flow patterns along the wing span were quantitatively visualized using particle image velocimetry (PIV), and a three-component balance was used to measure the forces generated by the wings. The flow visualization on the wing showed the appearance of LEVs, which is typically associated with a delayed stall effect, and the transition into flow separation. Also, the influence of the delayed stall and flow separation was clearly visible in measurements of instantaneous net force over the wingbeat cycle. Here, we show that, even at reduced frequencies as low as those of large bird flight, unsteady effects are present and non-negligible and have to be addressed by kinematic and morphological adaptations.

Bird or bat: comparing airframe design and flight performance

Birds and bats have evolved powered flight independently, which makes a comparison of evolutionary 'design' solutions potentially interesting. In this paper we highlight similarities and differences with respect to flight characteristics, including morphology, flight kinematics, aerodynamics, energetics and flight performance. Birds' size range is 0.002-15 kg and bats' size range is 0.002-1.5 kg. The wingbeat kinematics differ between birds and bats, which is mainly due to the different flexing of the wing during the upstroke and constraints by having a wing of feathers and a skin membrane, respectively. Aerodynamically, bats appear to generate a more complex wake than birds. Bats may be more closely adapted for slow maneuvering flight than birds, as required by their aerial hawking foraging habits. The metabolic rate and power required to fly are similar among birds and bats. Both groups share many characteristics associated with flight, such as for example low amounts of DNA in cells, the ability to accumulate fat as fuel for hibernation and migration, and parallel habitat-related wing shape adaptations.

Vortex wake and flight kinematics of a swift in cruising flight in a wind tunnel

In this paper we describe the flight characteristics of a swift (Apus apus) in cruising flight at three different flight speeds (8.0, 8.4 and 9.2 m s(-1)) in a low turbulence wind tunnel. The wingbeat kinematics were recorded by high-speed filming and the wake of the bird was visualized by digital particle image velocimetry (DPIV). Certain flight characteristics of the swift differ from those of previously studied species. As the flight speed increases, the angular velocity of the wingbeat remains constant, and so as the wingbeat amplitude increases, the frequency decreases accordingly, as though the flight muscles were contracting at a fixed rate. The wings are also comparatively inflexible and are flexed or retracted rather little during the upstroke. The upstroke is always aerodynamically active and this is reflected in the wake, where shedding of spanwise vorticity occurs throughout the wingbeat. Although the wake superficially resembles those of other birds in cruising flight, with a pair of trailing wingtip vortices connected by spanwise vortices, the continuous shedding of first positive vorticity during the downstroke and then negative vorticity during the upstroke suggests a wing whose circulation is gradually increasing and then decreasing during the wingbeat cycle. The wake (and implied wing aerodynamics) are not well described by discrete vortex loop models, but a new wake-based model, where incremental spanwise and streamwise variations of the wake impulse are integrated over the wingbeat, shows good agreement of the vertical momentum flux with the required weight support. The total drag was also estimated from the wake alone, and the calculated lift:drag ratio of approximately 13 for flapping flight is the highest measured yet for birds.

Flight speeds among bird species: allometric and phylogenetic effects

Flight speed is expected to increase with mass and wing loading among flying animals and aircraft for fundamental aerodynamic reasons. Assuming geometrical and dynamical similarity, cruising flight speed is predicted to vary as (body mass)^1/6 and (wing loading)^1/2 among bird species. To test these scaling rules and the general importance of mass and wing loading for bird flight speeds, we used tracking radar to measure flapping flight speeds of individuals or flocks of migrating birds visually identified to species as well as their altitude and winds at the altitudes where the birds were flying. Equivalent airspeeds (airspeeds corrected to sea level air density, U_e) of 138 species, ranging 0.01–10 kg in mass, were analysed in relation to biometry and phylogeny. Scaling exponents in relation to mass and wing loading were significantly smaller than predicted (about 0.12 and 0.32, respectively, with similar results for analyses based on species and independent phylogenetic contrasts). These low scaling exponents may be the result of evolutionary restrictions on bird flight-speed range, counteracting too slow flight speeds among species with low wing loading and too fast speeds among species with high wing loading. This compression of speed range is partly attained through geometric differences, with aspect ratio showing a positive relationship with body mass and wing loading, but additional factors are required to fully explain the small scaling exponent of U_e in relation to wing loading. Furthermore, mass and wing loading accounted for only a limited proportion of the variation in U_e. Phylogeny was a powerful factor, in combination with wing loading, to account for the variation in U_e. These results demonstrate that functional flight adaptations and constraints associated with different evolutionary lineages have an important influence on cruising flapping flight speed that goes beyond the general aerodynamic scaling effects of mass and wing loading.

Analysing the variation in flight speed among bird species is important in understanding flight. We tested if the cruising speed of different migrating bird species in flapping flight scales with body mass and wing loading according to predictions from aerodynamic theory and to what extent phylogeny provides an additional explanation for variation in speed. Flight speeds were measured by tracking radar for bird species ranging in size from 0.01 kg (small passerines) to 10 kg (swans). Equivalent airspeeds of 138 species ranged between 8 and 23 m/s and did not scale as steeply in relation to mass and wing loading as predicted. This suggests that there are evolutionary restrictions to the range of flight speeds that birds obtain, which counteract too slow and too fast speeds among bird species with low and high wing loading, respectively. In addition to the effects of body size and wing morphology on flight speed, we also show that phylogeny accounted for an important part of the remaining speed variation between species. Differences in flight apparatus and behaviour among species of different evolutionary origin, and with different ecology and flight styles, are likely to influence cruising flight performance in important ways.

Measurement of flight speeds of 138 species of bird reveals that mass and wing loading do not scale according to aerodynamic theory but vary significantly depending on phylogeny.

The implications of low-speed fixed-wing aerofoil measurements on the analysis and performance of flapping bird wings

Bird flight occurs over a range of Reynolds numbers (Re; 10(4) < or = Re < or = 10(5), where Re is a measure of the relative importance of inertia and viscosity) that includes regimes where standard aerofoil performance is difficult to predict, compute or measure, with large performance jumps in response to small changes in geometry or environmental conditions. A comparison of measurements of fixed wing performance as a function of Re, combined with quantitative flow visualisation techniques, shows that, surprisingly, wakes of flapping bird wings at moderate flight speeds admit to certain simplifications where their basic properties can be understood through quasi-steady analysis. Indeed, a commonly cited measure of the relative flapping frequency, or wake unsteadiness, the Strouhal number, is seen to be approximately constant in accordance with a simple requirement for maintaining a moderate local angle of attack on the wing. Together, the measurements imply a fine control of boundary layer separation on the wings, with implications for control strategies and wing shape selection by natural and artificial fliers.

Automatic aeroelastic devices in the wings of a steppe eagleAquila nipalensis

Here we analyse aeroelastic devices in the wings of a steppe eagle Aquila nipalensis during manoeuvres. Chaotic deflections of the upperwing coverts observed using video cameras carried by the bird (50 frames s–1) indicate trailing-edge separation but attached flow near the leading edge during flapping and gust response, and completely stalled flows upon landing. The underwing coverts deflect automatically along the leading edge at high angle of attack. We use high-speed digital video (500 frames s–1) to analyse these deflections in greater detail during perching sequences indoors and outdoors. Outdoor perching sequences usually follow a stereotyped three-phase sequence comprising a glide, pitch-up manoeuvre and deep stall. During deep stall, the spread-eagled bird has aerodynamics reminiscent of a cross-parachute. Deployment of the underwing coverts is closely phased with wing sweeping during the pitch-up manoeuvre,and is accompanied by alula protraction. Surprisingly, active alula protraction is preceded by passive peeling from its tip. Indoor flights follow a stereotyped flapping perching sequence, with deployment of the underwing coverts closely phased with alula protraction and the end of the downstroke. We propose that the underwing coverts operate as an automatic high-lift device, analogous to a Kruger flap. We suggest that the alula operates as a strake, promoting formation of a leading-edge vortex on the swept hand-wing when the arm-wing is completely stalled, and hypothesise that its active protraction is stimulated by its initial passive deflection. These aeroelastic devices appear to be used for flow control to enhance unsteady manoeuvres, and may also provide sensory feedback.

Biomechanics of bird flight

Power output is a unifying theme for bird flight and considerable progress has been accomplished recently in measuring muscular, metabolic and aerodynamic power in birds. The primary flight muscles of birds, the pectoralis and supracoracoideus, are designed for work and power output, with large stress (force per unit cross-sectional area) and strain (relative length change) per contraction. U-shaped curves describe how mechanical power output varies with flight speed, but the specific shapes and characteristic speeds of these curves differ according to morphology and flight style. New measures of induced, profile and parasite power should help to update existing mathematical models of flight. In turn, these improved models may serve to test behavioral and ecological processes. Unlike terrestrial locomotion that is generally characterized by discrete gaits, changes in wing kinematics and aerodynamics across flight speeds are gradual. Take-off flight performance scales with body size, but fully revealing the mechanisms responsible for this pattern awaits new study. Intermittent flight appears to reduce the power cost for flight, as some species flap–glide at slow speeds and flap–bound at fast speeds. It is vital to test the metabolic costs of intermittent flight to understand why some birds use intermittent bounds during slow flight. Maneuvering and stability are critical for flying birds,and design for maneuvering may impinge upon other aspects of flight performance. The tail contributes to lift and drag; it is also integral to maneuvering and stability. Recent studies have revealed that maneuvers are typically initiated during downstroke and involve bilateral asymmetry of force production in the pectoralis. Future study of maneuvering and stability should measure inertial and aerodynamic forces. It is critical for continued progress into the biomechanics of bird flight that experimental designs are developed in an ecological and evolutionary context.

Three-dimensional kinematics of hummingbird flight

Hummingbirds are specialized for hovering flight, and substantial research has explored this behavior. Forward flight is also important to hummingbirds, but the manner in which they perform forward flight is not well documented. Previous research suggests that hummingbirds increase flight velocity by simultaneously tilting their body angle and stroke-plane angle of the wings, without varying wingbeat frequency and upstroke: downstroke span ratio. We hypothesized that other wing kinematics besides stroke-plane angle would vary in hummingbirds. To test this, we used synchronized high-speed (500 Hz) video cameras and measured the three-dimensional wing and body kinematics of rufous hummingbirds (Selasphorus rufus, 3 g, N=5) as they flew at velocities of 0-12 m s(-1) in a wind tunnel. Consistent with earlier research, the angles of the body and the stroke plane changed with velocity, and the effect of velocity on wingbeat frequency was not significant. However, hummingbirds significantly altered other wing kinematics including chord angle, angle of attack, anatomical stroke-plane angle relative to their body, percent of wingbeat in downstroke, wingbeat amplitude, angular velocity of the wing, wingspan at mid-downstroke, and span ratio of the wingtips and wrists. This variation in bird-centered kinematics led to significant effects of flight velocity on the angle of attack of the wing and the area and angles of the global stroke planes during downstroke and upstroke. We provide new evidence that the paths of the wingtips and wrists change gradually but consistently with velocity, as in other bird species that possess pointed wings. Although hummingbirds flex their wings slightly at the wrist during upstroke, their average wingtip-span ratio of 93% revealed that they have kinematically ;rigid' wings compared with other avian species.

Wake structure and wingbeat kinematics of a house-martin Delichon urbica

The wingbeat kinematics and wake structure of a trained house martin in free, steady flight in a wind tunnel have been studied over a range of flight speeds, and compared and contrasted with similar measurements for a thrush nightingale and a pair of robins. The house martin has a higher aspect ratio (more slender) wing, and is a more obviously agile and aerobatic flyer, catching insects on the wing. The wingbeat is notable for the presence at higher flight speeds of a characteristic pause in the upstroke. The essential characteristics of the wing motions can be reconstructed with a simple two-frequency model derived from Fourier analysis. At slow speeds, the distribution of wake vorticity is more simple than for the other previously measured birds, and the upstroke does not contribute to weight support. The upstroke becomes gradually more significant as the flight speed increases, and although the vortex wake shows a signature of the pause phase, the global circulation measurements are otherwise in good agreement with surprisingly simple aerodynamic models, and with predictions across the different species, implying quite similar aerodynamic performance of the wing sections. The local Reynolds numbers of the wing sections are sufficiently low that the well-known instabilities of attached laminar flows over lifting surfaces, which are known to occur at two to three times this value, may not develop.

Wing beat kinematics of a nectar-feeding bat,Glossophaga soricina,flying at different flight speeds and Strouhal numbers

High-speed film analysis showed that the wing beat kinematics in Glossophaga soricina change gradually with increasing flight speed,indicating that there is no sudden gait change at any particular, critical,flight speed. The flight of two adult specimens was studied over a range of flight speeds (1.23-7.52 ms-1) in a 30 m long flight tunnel. During the upstroke in hovering and slow flight there is a tip-reversal or supination of the handwings, which thus produce a backward flick. This backward motion successively disappears at speeds V≈3.2 ms-1, above which the wingtip path becomes more vertical or directed upwards-forwards relative to the still air (the stroke plane angle increasing with flight speed as α=44.8V0.29). We found no correlations between either span ratio SR (the ratio of the wing span on the upstroke to that on the downstroke) and V, or downstroke ratio (the duration of the downstroke divided by the total stroke period) and V.On the other hand, SR decreases significantly with increasing wing beat frequency f, SR∝f-0.40. The Strouhal number (St=f×amplitude/V), a dimensionless parameter describing oscillating flow mechanisms and being a predictor of the unsteadiness of the flow, decreases with the speed as St∝V-1.37. Close to the theoretical minimum power speed (4-6 m s-1) G. soricina operates with a Strouhal number in the region 0.17&lt;St&lt;0.22, which is associated with efficient lift and thrust production. At slower speeds, 3.4-4 m s-1, St is 0.25-0.4, which is still within the favourable region. But at speeds below 3 m s-1St becomes higher(0.5&lt;St&lt;0.68), indicating that unsteady effects become important, with unfavourable lift and thrust production as a result. Only at these speeds do the bats perform the backward flick during the upstroke, which may produce thrust. This may serve as a compensation in some bats and birds to increase aerodynamic performance.

Vortex wakes generated by robins Erithacus rubecula during free flight in a wind tunnel

The wakes of two individual robins were measured in digital particle image velocimetry (DPIV) experiments conducted in the Lund wind tunnel. Wake measurements were compared with each other, and with previous studies in the same facility. There was no significant individual variation in any of the measured quantities. Qualitatively, the wake structure and its gradual variation with flight speed were exactly as previously measured for the thrush nightingale. A procedure that accounts for the disparate sources of circulation spread over the complex wake structure nevertheless can account for the vertical momentum flux required to support the weight, and an example calculation is given for estimating drag from the components of horizontal momentum flux (whose net value is zero). The measured circulations of the largest structures in the wake can be predicted quite well by simple models, and expressions are given to predict these and other measurable quantities in future bird flight experiments.

The aerodynamic effects of wing–wing interaction in flapping insect wings

We employed a dynamically scaled mechanical model of the small fruit fly Drosophila melanogaster (Reynolds number 100–200) to investigate force enhancement due to contralateral wing interactions during stroke reversal (the `clap-and-fling'). The results suggest that lift enhancement during clap-and-fling requires an angular separation between the two wings of no more than 10–12°. Within the limitations of the robotic apparatus, the clap-and-fling augmented total lift production by up to 17%, but depended strongly on stroke kinematics. The time course of the interaction between the wings was quite complex. For example, wing interaction attenuated total force during the initial part of the wing clap, but slightly enhanced force at the end of the clap phase. We measured two temporally transient peaks of both lift and drag enhancement during the fling phase: a prominent peak during the initial phase of the fling motion, which accounts for most of the benefit in lift production, and a smaller peak of force enhancement at the end fling when the wings started to move apart. A detailed digital particle image velocimetry (DPIV) analysis during clap-and-fling showed that the most obvious effect of the bilateral `image' wing on flow occurs during the early phase of the fling, due to a strong fluid influx between the wings as they separate. The DPIV analysis revealed, moreover, that circulation induced by a leading edge vortex (LEV) during the early fling phase was smaller than predicted by inviscid two-dimensional analytical models, whereas circulation of LEV nearly matched the predictions of Weis-Fogh's inviscid model at late fling phase. In addition, the presence of the image wing presumably causes subtle modifications in both the wake capture and viscous forces. Collectively, these effects explain some of the changes in total force and lift production during the fling. Quite surprisingly, the effect of clap-and-fling is not restricted to the dorsal part of the stroke cycle but extends to the beginning of upstroke, suggesting that the presence of the image wing distorts the gross wake structure throughout the stroke cycle.