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.

Aerodynamics of gliding flight in common swifts.

Gliding flight performance and wake topology of a common swift (Apus apus L.) were examined in a wind tunnel at speeds between 7 and 11 m s(-1). The tunnel was tilted to simulate descending flight at different sink speeds. The swift varied its wingspan, wing area and tail span over the speed range. Wingspan decreased linearly with speed, whereas tail span decreased in a nonlinear manner. For each airspeed, the minimum glide angle was found. The corresponding sink speeds showed a curvilinear relationship with airspeed, with a minimum sink speed at 8.1 m s(-1) and a speed of best glide at 9.4 m s(-1). Lift-to-drag ratio was calculated for each airspeed and tilt angle combinations and the maximum for each speed showed a curvilinear relationship with airspeed, with a maximum of 12.5 at an airspeed of 9.5 m s(-1). Wake was sampled in the transverse plane using stereo digital particle image velocimetry (DPIV). The main structures of the wake were a pair of trailing wingtip vortices and a pair of trailing tail vortices. Circulation of these was measured and a model was constructed that showed good weight support. Parasite drag was estimated from the wake defect measured in the wake behind the body. Parasite drag coefficient ranged from 0.30 to 0.22 over the range of airspeeds. Induced drag was calculated and used to estimate profile drag coefficient, which was found to be in the same range as that previously measured on a Harris' hawk.

Time-resolved vortex wake of a common swift flying over a range of flight speeds.

The wake of a freely flying common swift (Apus apus L.) is examined in a wind tunnel at three different flight speeds, 5.7, 7.7 and 9.9 m s(-1). The wake of the bird is visualized using high-speed stereo digital particle image velocimetry (DPIV). Wake images are recorded in the transverse plane, perpendicular to the airflow. The wake of a swift has been studied previously using DPIV and recording wake images in the longitudinal plane, parallel to the airflow. The high-speed DPIV system allows for time-resolved wake sampling and the result shows features that were not discovered in the previous study, but there was approximately a 40 per cent vertical force deficit. As the earlier study also revealed, a pair of wingtip vortices are trailing behind the wingtips, but in addition, a pair of tail vortices and a pair of 'wing root vortices' are found that appear to originate from the wing/body junction. The existence of wing root vortices suggests that the two wings are not acting as a single wing, but are to some extent aerodynamically detached from each other. It is proposed that this is due to the body disrupting the lift distribution over the wing by generating less lift than the wings.

The vortex wake of blackcaps (Sylvia atricapilla L.) measured using high-speed digital particle image velocimetry (DPIV).

Reconstructing the vortex wake of freely flying birds is challenging, but in the past few years, direct measurements of the wake circulation have become available for a number of species. Streamwise circulation has been measured at different positions along the span of the birds, but no measurements have been performed in the transverse plane. Recent findings from studies of bat wakes have pointed to the importance of transverse plane data for reconstructing the wake topology because important structures may be missed otherwise. We present results of high-speed DPIV measurements in the transverse plane behind freely flying blackcaps. We found novel wake structures previously not shown in birds, including wing root vortices of opposite as well as the same sign as the wing tip vortices. This suggests a more complex wake structure in birds than previously assumed and calls for more detailed studies of the flow over the wings and body, respectively. Based on measurements on birds with and without a tail we also tested hypotheses regarding the function of the tail during steady flight. We were unable to detect any differences in the wake pattern between birds with and without a tail. We conclude that the birds do not use their tail to exploit vortices shed at the wing root during the downstroke. Neither did we find support for the hypothesis that the tail should reduce the drag of the bird. The function of the tail during steady flight thus remains unclear and calls for further investigation in future studies.

Flight speeds of swifts (Apus apus): seasonal differences smaller than expected.

We have studied the nocturnal flight behaviour of the common swift (Apus apus L.), by the use of a tracking radar. Birds were tracked from Lund University in southern Sweden during spring migration, summer roosting flights and autumn migration. Flight speeds were compared with predictions from flight mechanical and optimal migration theories. During spring, flight speeds were predicted to be higher than during both summer and autumn due to time restriction. In such cases, birds fly at a flight speed that maximizes the overall speed of migration. For summer roosting flights, speeds were predicted to be lower than during both spring and autumn since the predicted flight speed is the minimum power speed that involves the lowest energy consumption per unit time. During autumn, we expected flight speeds to be higher than during summer but lower than during spring since the expected flight speed is the maximum range speed, which involves the lowest energy consumption per unit distance. Flight speeds during spring were indeed higher than during both summer and autumn, which indicates time-selected spring migration. Speeds during autumn migration were very similar to those recorded during summer roosting flights. The general result shows that swifts change their flight speed between different flight behaviours to a smaller extent than expected. Furthermore, the difference between flight speeds during migration and roosting among swifts was found to be less pronounced than previously recorded.

Leading-edge vortex improves lift in slow-flying bats.

Staying aloft when hovering and flying slowly is demanding. According to quasi-steady-state aerodynamic theory, slow-flying vertebrates should not be able to generate enough lift to remain aloft. Therefore, unsteady aerodynamic mechanisms to enhance lift production have been proposed. Using digital particle image velocimetry, we showed that a small nectar-feeding bat is able to increase lift by as much as 40% using attached leading-edge vortices (LEVs) during slow forward flight, resulting in a maximum lift coefficient of 4.8. The airflow passing over the LEV reattaches behind the LEV smoothly to the wing, despite the exceptionally large local angles of attack and wing camber. Our results show that the use of unsteady aerodynamic mechanisms in flapping flight is not limited to insects but is also used by larger and heavier animals.

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.

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.

Bat flight generates complex aerodynamic tracks.

The flapping flight of animals generates an aerodynamic footprint as a time-varying vortex wake in which the rate of momentum change represents the aerodynamic force. We showed that the wakes of a small bat species differ from those of birds in some important respects. In our bats, each wing generated its own vortex loop. Also, at moderate and high flight speeds, the circulation on the outer (hand) wing and the arm wing differed in sign during the upstroke, resulting in negative lift on the hand wing and positive lift on the arm wing. Our interpretations of the unsteady aerodynamic performance and function of membranous-winged, flapping flight should change modeling strategies for the study of equivalent natural and engineered flying devices.

How swifts control their glide performance with morphing wings.

Gliding birds continually change the shape and size of their wings, presumably to exploit the profound effect of wing morphology on aerodynamic performance. That birds should adjust wing sweep to suit glide speed has been predicted qualitatively by analytical glide models, which extrapolated the wing's performance envelope from aerodynamic theory. Here we describe the aerodynamic and structural performance of actual swift wings, as measured in a wind tunnel, and on this basis build a semi-empirical glide model. By measuring inside and outside swifts' behavioural envelope, we show that choosing the most suitable sweep can halve sink speed or triple turning rate. Extended wings are superior for slow glides and turns; swept wings are superior for fast glides and turns. This superiority is due to better aerodynamic performance-with the exception of fast turns. Swept wings are less effective at generating lift while turning at high speeds, but can bear the extreme loads. Finally, our glide model predicts that cost-effective gliding occurs at speeds of 8-10 m s(-1), whereas agility-related figures of merit peak at 15-25 m s(-1). In fact, swifts spend the night ('roost') in flight at 8-10 m s(-1) (ref. 11), thus our model can explain this choice for a resting behaviour. Morphing not only adjusts birds' wing performance to the task at hand, but could also control the flight of future aircraft.

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.

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

The wingbeat kinematics of a thrush nightingale Luscinia luscinia were measured for steady flight in a wind tunnel over a range of flight speeds (5-10 m s(-1)), and the results are interpreted and discussed in the context of a detailed, previously published, wake analysis of the same bird. Neither the wingbeat frequency nor wingbeat amplitude change significantly over the investigated speed range and consequently dimensionless measures that compare timescales of flapping vs. timescales due to the mean flow vary in direct proportion to the mean flow itself, with no constant or slowly varying intervals. The only significant kinematic variations come from changes in the upstroke timing (downstroke fraction) and the upstroke wing folding (span ratio), consistent with the gradual variations, primarily in the upstroke wake, previously reported. The relationship between measured wake geometry and wingbeat kinematics can be qualitatively explained by presumed self-induced convection and deformation of the wake between its initial formation and later measurement, and varies in a predictable way with flight speed. Although coarse details of the wake geometry accord well with the kinematic measurements, there is no simple explanation based on these observed kinematics alone that accounts for the measured asymmetries of circulation magnitude in starting and stopping vortex structures. More complex interactions between the wake and wings and/or body are implied.

A family of vortex wakes generated by a thrush nightingale in free flight in a wind tunnel over its entire natural range of flight speeds.

In view of the complexity of the wing-beat kinematics and geometry, an important class of theoretical models for analysis and prediction of bird flight performance entirely, or almost entirely, ignores the action of the wing itself and considers only the resulting motions in the air behind the bird. These motions can also be complicated, but some success has previously been recorded in detecting and measuring relatively simple wake structures that can sometimes account for required quantities used to estimate aerodynamic power consumption. To date, all bird wakes, measured or presumed, seem to fall into one of two classes: the closed-loop, discrete vortex model at low flight speeds, and the constant-circulation, continuous vortex model at moderate to high speeds. Here, novel and accurate quantitative measurements of velocity fields in vertical planes aligned with the freestream are used to investigate the wake structure of a thrush nightingale over its entire range of natural flight speeds. At most flight speeds, the wake cannot be categorised as one of the two standard types, but has an intermediate structure, with approximations to the closed-loop and constant-circulation models at the extremes. A careful accounting for all vortical structures revealed with the high-resolution technique permits resolution of the previously unexplained wake momentum paradox. All the measured wake structures have sufficient momentum to provide weight support over the wingbeat. A simple model is formulated and explained that mimics the correct, measured balance of forces in the downstroke- and upstroke-generated wake over the entire range of flight speeds. Pending further work on different bird species, this might form the basis for a generalisable flight model.

Flight kinematics of the barn swallow (Hirundo rustica) over a wide range of speeds in a wind tunnel.

Two barn swallows (Hirundo rustica) flying in the Lund wind tunnel were filmed using synchronised high-speed cameras to obtain posterior, ventral and lateral views of the birds in horizontal flapping flight. We investigated wingbeat kinematics, body tilt angle, tail spread and angle of attack at speeds of 4-14 ms(-1). Wingbeat frequency showed a clear U-shaped relationship with air speed with minima at 8.9 ms(-1)(bird 1) and 8.7 ms(-1) (bird 2). A method previously used by other authors of estimating the body drag coefficient (C(D,par)) by obtaining agreement between the calculated minimum power (V(min)) and the observed minimum wingbeat frequency does not appear to be valid in this species, possibly due to upstroke pauses that occur at intermediate and high speeds, causing the apparent wingbeat frequency to be lower. These upstroke pauses represent flap-gliding, which is possibly a way of adjusting the force generated to the requirements at medium and high speeds, similar to the flap-bound mode of flight in other species. Body tilt angle, tail spread and angle of attack all increase with decreasing speed, thereby providing an additional lift surface and suggesting an important aerodynamic function for the tail at low speeds in forward flight. Results from this study indicate the high plasticity in the wingbeat kinematics and use of the tail that birds have available to them in order to adjust the lift and power output required for flight.

Migration along orthodromic sun compass routes by arctic birds.

Flight directions of birds migrating at high geographic and magnetic latitudes can be used to test bird orientation by celestial or geomagnetic compass systems under polar conditions. Migration patterns of arctic shorebirds, revealed by tracking radar studies during an icebreaker expedition along the Northwest Passage in 1999, support predicted sun compass trajectories but cannot be reconciled with orientation along either geographic or magnetic loxodromes (rhumb lines). Sun compass routes are similar to orthodromes (great circle routes) at high latitudes, showing changing geographic courses as the birds traverse longitudes and their internal clock gets out of phase with local time. These routes bring the shorebirds from high arctic Canada to the east coast of North America, from which they make transoceanic flights to South America. The observations are also consistent with a migration link between Siberia and the Beaufort Sea region by way of sun compass routes across the Arctic Ocean.

Gliding flight in a jackdaw: a wind tunnel study.

We examined the gliding flight performance of a jackdaw Corvus monedula in a wind tunnel. The jackdaw was able to glide steadily at speeds between 6 and 11 m s(-1). The bird changed its wingspan and wing area over this speed range, and we measured the so-called glide super-polar, which is the envelope of fixed-wing glide polars over a range of forward speeds and sinking speeds. The glide super-polar was an inverted U-shape with a minimum sinking speed (V(ms)) at 7.4 m s(-1) and a speed for best glide (V(bg)) at 8.3 m s(-)). At the minimum sinking speed, the associated vertical sinking speed was 0.62 m s(-1). The relationship between the ratio of lift to drag (L:D) and airspeed showed an inverted U-shape with a maximum of 12.6 at 8.5 m s(-1). Wingspan decreased linearly with speed over the whole speed range investigated. The tail was spread extensively at low and moderate speeds; at speeds between 6 and 9 m s(-1), the tail area decreased linearly with speed, and at speeds above 9 m s(-1) the tail was fully furled. Reynolds number calculated with the mean chord as the reference length ranged from 38 000 to 76 000 over the speed range 6-11 m s(-1). Comparisons of the jackdaw flight performance were made with existing theory of gliding flight. We also re-analysed data on span ratios with respect to speed in two other bird species previously studied in wind tunnels. These data indicate that an equation for calculating the span ratio, which minimises the sum of induced and profile drag, does not predict the actual span ratios observed in these birds. We derive an alternative equation on the basis of the observed span ratios for calculating wingspan and wing area with respect to forward speed in gliding birds from information about body mass, maximum wingspan, maximum wing area and maximum coefficient of lift. These alternative equations can be used in combination with any model of gliding flight where wing area and wingspan are considered to calculate sinking rate with respect to forward speed.

Field estimates of body drag coefficient on the basis of dives in passerine birds.

During forward flight, a bird's body generates drag that tends to decelerate its speed. By flapping its wings, or by converting potential energy into work if gliding, the bird produces both lift and thrust to balance the pull of gravity and drag. In flight mechanics, a dimensionless number, the body drag coefficient (C(D,par)), describes the magnitude of the drag caused by the body. The drag coefficient depends on the shape (or streamlining), the surface texture of the body and the Reynolds number. It is an important variable when using flight mechanical models to estimate the potential migratory flight range and characteristic flight speeds of birds. Previous wind tunnel measurements on dead, frozen bird bodies indicated that C(D,par) is 0.4 for small birds, while large birds should have lower values of approximately 0.2. More recent studies of a few birds flying in a wind tunnel suggested that previous values probably overestimated C(D,par). We measured maximum dive speeds of passerine birds during the spring migration across the western Mediterranean. When the birds reach their top speed, the pull of gravity should balance the drag of the body (and wings), giving us an opportunity to estimate C(D,par). Our results indicate that C(D,par) decreases with increasing Reynolds number within the range 0.17-0.77, with a mean C(D,par) of 0.37 for small passerines. A somewhat lower mean value could not be excluded because diving birds may control their speed below the theoretical maximum. Our measurements therefore support the notion that 0.4 (the 'old' default value) is a realistic value of C(D,par) for small passerines.

Optimal stopover decisions under wind influence: the effects of correlated winds.

Wind speed and direction have a significant effect on a flying bird's ground speed. Migrants are therefore expected to be sensitive to wind conditions and this should have consequences for optimal strategies of stopover and refuelling. Based on an earlier model of time-minimizing migration which includes wind condition, we investigate the consequences of the temporal correlation of wind conditions. Day-to-day changes in wind conditions are modelled with a two-state Markov process and an expression for the expected speed of migration is derived. The policy of the migrants is described by two parameters: a day t(g) when the birds start to leave whenever favourable conditions occur and a later day t(b)when they leave even in unfavourable winds. The model predicts that in most cases departures should be close to the date which is predicted by a wind-free deterministic model and that the birds should never leave without wind assistance. Only if the probability that the condition remains the same on the following day is close to 1 should the birds leave even in unfavourable conditions shortly after the deterministic optimal date. If the transition matrix is highly asymmetrical, i.e. if it is very probable that unfavourable conditions remain and that favourable conditions will change into unfavourable, then the birds are predicted to start using good winds several days before the deterministic optimal date. An analysis of six years of wind data from two sites in Sweden shows that wind directions on successive days are in fact correlated in all years.

Energetics, cost reduction and functional consequences of fish morphology.

Cost reduction strategies are often invoked as explanations when studies of adaptation fail to find predicted costs. This might seem discouraging, offering little opportunity for further investigation. In this paper, we demonstrate that cost reduction strategies can themselves be investigated by arguments from design. Recent work on inducible morphological defences has shown that hydrodynamical disadvantages (e.g. high drag) in fishes can be compensated for by standard metabolic rate (SMR) adjustments. Here, we theoretically investigate the possibilities and limitations for swimming cost compensation through SMR adjustment. We continue by modelling how intraspecific power curve variation affects the optimal swimming velocity between food patches. Our results show that, even though SMR modifications may compensate for hydrodynamical disadvantages, low-drag fishes will nevertheless have a marked advantage under high food abundance. The relative advantage will decrease with decreasing food levels. We also show that hydrodynamical properties of fishes can be used to predict their propensity to become foraging (or swimming) specialists. Low-drag fishes can use a broad range of swimming velocities without substantial increases in swimming cost, whereas the cost of deviating from the optimal swimming velocity increases markedly in high-drag fishes. The results have important implications for the evolution of morphological diversity in fishes.