Time-varying span efficiency through the wingbeat of desert locusts

Hovering flight in hummingbird hawkmoths: kinematics, wake dynamics and aerodynamic power

Hovering insects are divided into two categories: 'normal' hoverers that move the wing symmetrically in a horizontal stroke plane, and those with an inclined stroke plane. Normal hoverers have been suggested to support their weight during both downstroke and upstroke, shedding vortex rings each half-stroke. Insects with an inclined stroke plane should, according to theory, produce flight forces only during downstroke, and only generate one set of vortices. The type of hovering is thus linked to the power required to hover. Previous efforts to characterize the wake of hovering insects have used low-resolution experimental techniques or simulated the flow using computational fluid dynamics, and so it remains to be determined whether insect wakes can be represented by any of the suggested models. Here, we used tomographic particle image velocimetry, with a horizontal measurement volume placed below the animals, to show that the wake shed by hovering hawkmoths is best described as a series of bilateral, stacked vortex 'rings'. While the upstroke is aerodynamically active, despite an inclined stroke plane, it produces weaker vortices than the downstroke. In addition, compared with the near wake, the far wake lacks structure and is less concentrated. Both near and far wakes are clearly affected by vortex interactions, suggesting caution is required when interpreting wake topologies. We also estimated induced power (Pind) from downwash velocities in the wake. Standard models predicted a Pind more than double that from our wake measurements. Our results thus question some model assumptions and we propose a reevaluation of the model parameters.

The Aerodynamics and Power Requirements of Forward Flapping Flight in the Mango Stem Borer Beetle (Batocera rufomaculata)

The need for long dispersal flights can drive selection for behavioral, physiological, and biomechanical mechanisms to reduce the energy spent flying. However, some energy loss during the transfer of momentum from the wing to the fluid is inevitable, and inherent to the fluid-wing interaction. Here, we analyzed these losses during the forward flight of the mango stem borer (Batocera rufomaculata). This relatively large beetle can disperse substantial distances in search of new host trees, and laboratory experiments have demonstrated continuous tethered flights that can last for up to an hour. We flew the beetles tethered in a wind tunnel and used high-speed videography to estimate the aerodynamic power from their flapping kinematics and particle image velocimetry (PIV) to evaluate drag and kinetic energy from their unsteady wakes. To account for tethering effects, we measured the forces applied by the beetles on the tether arm holding them in place. The drag of the flying beetle over the flapping cycle, estimated from the flow fields in the unsteady wake, showed good agreement with direct measurement of mean horizontal force. Both measurements showed that total drag during flight is ∼5-fold higher than the parasite drag on the body. The aerodynamic power estimated from both the motion of the wings, using a quasi-steady blade-element model, and the kinetic energy in the wake, gave mean values of flight-muscle mass-specific power of 87 and 65 W kg muscle^-1, respectively. A comparison of the two values suggests that ∼25% of the energy is lost within the fluid due to turbulence and heat. The muscle mass-specific power found here is low relative to the maximal power output reported for insect flight muscles. This can be attributed to reduce weight support during tethered flight or to operation at submaximal output that may ensure a supply of metabolic substrates to the flight muscles, thus delaying their fatigue during long-distance flights.

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.

Lift and power in fruitflies in vertically-ascending flight

We measured the wing kinematics of fruitflies in both vertically-ascending and hovering flights and studied the aerodynamic forces and power in the two flight modes. The average ascending velocity is 0.45 m s^-1; the stroke plane angle and the stroke frequency are the same as that in hovering flight, whilst the stroke amplitude is increased by 12% and the wing angle of attack in the latter half of a down- and upstroke both increased by 10%. Flow analysis shows that during ascending, the flies experience a downward inflow which reduces the effective angle of attack considerably. This problem is overcome by the increases in the stroke amplitude and the angle of attack, which result in a larger wing drag. As a result, the power at ascending is increased by 36% over that at hovering. Two very interesting observations were made. (1) Using the same power, level-forward flight can be about four times as fast as ascending flight. (2) Power for ascending flight is the same as that for carrying a load about 27% of the insect's weight at hovering.

Flight of the dragonflies and damselflies

This work is a synthesis of our current understanding of the mechanics, aerodynamics and visually mediated control of dragonfly and damselfly flight, with the addition of new experimental and computational data in several key areas. These are: the diversity of dragonfly wing morphologies, the aerodynamics of gliding flight, force generation in flapping flight, aerodynamic efficiency, comparative flight performance and pursuit strategies during predatory and territorial flights. New data are set in context by brief reviews covering anatomy at several scales, insect aerodynamics, neuromechanics and behaviour. We achieve a new perspective by means of a diverse range of techniques, including laser-line mapping of wing topographies, computational fluid dynamics simulations of finely detailed wing geometries, quantitative imaging using particle image velocimetry of on-wing and wake flow patterns, classical aerodynamic theory, photography in the field, infrared motion capture and multi-camera optical tracking of free flight trajectories in laboratory environments. Our comprehensive approach enables a novel synthesis of datasets and subfields that integrates many aspects of flight from the neurobiology of the compound eye, through the aeromechanical interface with the surrounding fluid, to flight performance under cruising and higher-energy behavioural modes.

This article is part of the themed issue ‘Moving in a moving medium: new perspectives on flight’.

Petiolate wings: effects on the leading-edge vortex in flapping flight

The wings of many insect species including crane flies and damselflies are petiolate (on stalks), with the wing planform beginning some distance away from the wing hinge, rather than at the hinge. The aerodynamic impact of flapping petiolate wings is relatively unknown, particularly on the formation of the lift-augmenting leading-edge vortex (LEV): a key flow structure exploited by many insects, birds and bats to enhance their lift coefficient. We investigated the aerodynamic implications of petiolation P using particle image velocimetry flow field measurements on an array of rectangular wings of aspect ratio 3 and petiolation values of P = 1-3. The wings were driven using a mechanical device, the 'Flapperatus', to produce highly repeatable insect-like kinematics. The wings maintained a constant Reynolds number of 1400 and dimensionless stroke amplitude Λ* (number of chords traversed by the wingtip) of 6.5 across all test cases. Our results showed that for more petiolate wings the LEV is generally larger, stronger in circulation, and covers a greater area of the wing surface, particularly at the mid-span and inboard locations early in the wing stroke cycle. In each case, the LEV was initially arch-like in form with its outboard end terminating in a focus-sink on the wing surface, before transitioning to become continuous with the tip vortex thereafter. In the second half of the wing stroke, more petiolate wings exhibit a more detached LEV, with detachment initiating at approximately 70% and 50% span for P = 1 and 3, respectively. As a consequence, lift coefficients based on the LEV are higher in the first half of the wing stroke for petiolate wings, but more comparable in the second half. Time-averaged LEV lift coefficients show a general rise with petiolation over the range tested.

Lift calculations based on accepted wake models for animal flight are inconsistent and sensitive to vortex dynamics

There are three common methods for calculating the lift generated by a flying animal based on the measured airflow in the wake. However, these methods might not be accurate according to computational and robot-based studies of flapping wings. Here we test this hypothesis for the first time for a slowly flying Pacific parrotlet in still air using stereo particle image velocimetry recorded at 1000 Hz. The bird was trained to fly between two perches through a laser sheet wearing laser safety goggles. We found that the wingtip vortices generated during mid-downstroke advected down and broke up quickly, contradicting the frozen turbulence hypothesis typically assumed in animal flight experiments. The quasi-steady lift at mid-downstroke was estimated based on the velocity field by applying the widely used Kutta-Joukowski theorem, vortex ring model, and actuator disk model. The calculated lift was found to be sensitive to the applied model and its different parameters, including vortex span and distance between the bird and laser sheet-rendering these three accepted ways of calculating weight support inconsistent. The three models predict different aerodynamic force values mid-downstroke compared to independent direct measurements with an aerodynamic force platform that we had available for the same species flying over a similar distance. Whereas the lift predictions of the Kutta-Joukowski theorem and the vortex ring model stayed relatively constant despite vortex breakdown, their values were too low. In contrast, the actuator disk model predicted lift reasonably accurately before vortex breakdown, but predicted almost no lift during and after vortex breakdown. Some of these limitations might be better understood, and partially reconciled, if future animal flight studies report lift calculations based on all three quasi-steady lift models instead. This would also enable much needed meta studies of animal flight to derive bioinspired design principles for quasi-steady lift generation with flapping wings.

Optimum hovering wing planform

Theoretical analysis is used to identify the optimum wing planform of a flapping/revolving wing in hover. This solution is of interest as a benchmark to which hovering wing geometries driven by broader multidisciplinary evolutionary or engineering constraints can be compared. Furthermore, useful insights into the aerodynamic performance of untwisted hovering wings are delivered. It is shown that profile power is minimised by using an untwisted elliptical planform whereas induced power is minimised by a more highly tapered planform similar to that of a hummingbird.

Three-dimensional simulation for fast forward flight of a calliope hummingbird

We present a computational study of flapping-wing aerodynamics of a calliope hummingbird (Selasphorus calliope) during fast forward flight. Three-dimensional wing kinematics were incorporated into the model by extracting time-dependent wing position from high-speed videos of the bird flying in a wind tunnel at 8.3 m s(-1). The advance ratio, i.e. the ratio between flight speed and average wingtip speed, is around one. An immersed-boundary method was used to simulate flow around the wings and bird body. The result shows that both downstroke and upstroke in a wingbeat cycle produce significant thrust for the bird to overcome drag on the body, and such thrust production comes at price of negative lift induced during upstroke. This feature might be shared with bats, while being distinct from insects and other birds, including closely related swifts.

The complex aerodynamic footprint of desert locusts revealed by large-volume tomographic particle image velocimetry

Particle image velocimetry has been the preferred experimental technique with which to study the aerodynamics of animal flight for over a decade. In that time, hardware has become more accessible and the software has progressed from the acquisition of planes through the flow field to the reconstruction of small volumetric measurements. Until now, it has not been possible to capture large volumes that incorporate the full wavelength of the aerodynamic track left behind during a complete wingbeat cycle. Here, we use a unique apparatus to acquire the first instantaneous wake volume of a flying animal's entire wingbeat. We confirm the presence of wake deformation behind desert locusts and quantify the effect of that deformation on estimates of aerodynamic force and the efficiency of lift generation. We present previously undescribed vortex wake phenomena, including entrainment around the wing-tip vortices of a set of secondary vortices borne of Kelvin–Helmholtz instability in the shear layer behind the flapping wings.

Enhanced flight performance by genetic manipulation of wing shape in Drosophila

Insect wing shapes are remarkably diverse and the combination of shape and kinematics determines both aerial capabilities and power requirements. However, the contribution of any specific morphological feature to performance is not known. Using targeted RNA interference to modify wing shape far beyond the natural variation found within the population of a single species, we show a direct effect on flight performance that can be explained by physical modelling of the novel wing geometry. Our data show that altering the expression of a single gene can significantly enhance aerial agility and that the Drosophila wing shape is not, therefore, optimized for certain flight performance characteristics that are known to be important. Our technique points in a new direction for experiments on the evolution of performance specialities in animals.

Insect wings are under multiple competing selection pressures, but which are important in natural populations is not clear. Using RNAi to modify wing shape, Ray et al. show that aerial agility can be significantly enhanced in Drosophila, suggesting that natural variation does not reflect an optimization solely for flight agility.

Kinematics and aerodynamics of avian upstrokes during slow flight

Slow flight is extremely energetically costly per unit time, yet highly important for takeoff and survival. However, at slow speeds it is presently thought that most birds do not produce beneficial aerodynamic forces during the entire wingbeat: instead they fold or flex their wings during upstroke, prompting the long-standing prediction that the upstroke produces trivial forces. There is increasing evidence that the upstroke contributes to force production, but the aerodynamic and kinematic mechanisms remain unknown. Here, we examine the wingbeat cycle of two species: the diamond dove (Geopelia cuneata) and zebra finch (Taeniopygia guttata), that exhibit different upstroke styles, a wingtip-reversal and flexed-wing upstroke, respectively. We used a combination of particle image velocimetry and near-wake streamline measures alongside detailed 3D-kinematics. We show during the middle of the wingtip-reversal upstroke, the hand-wing has a high angular velocity (15.3±0.8 deg/ms) and translational speed (8.4±0.6 m/s). The flexed-wing upstroke, in contrast, has low wingtip speed during mid-upstroke. Instead, later in the stroke cycle, during the transition from upstroke to downstroke, it exhibits higher angular velocities (45.5±13.8 deg/ms) and translational speeds (11.0±1.9 m/s). Aerodynamically, the wingtip-reversal upstroke imparts momentum to the wake, with entrained air shed backward (visible as circulation of 14.4±0.09 m2/s). In contrast, the flexed-wing upstroke imparts minimal momentum. Clap and peel in the dove enhances the time course for circulation production on the wings, and provides new evidence of convergent evolution on time-varying aerodynamic mechanisms during flapping in insects and birds.

Leading edge vortices in lesser long-nosed bats occurring at slow but not fast flight speeds

Slow and hovering animal flight creates high demands on the lift production of animal wings. Steady state aerodynamics is unable to explain the forces required and the most commonly used mechanism to enhance the lift production is a leading edge vortex (LEV). Although LEVs increase the lift, they come at the cost of high drag. Here we determine the flow above the wing of lesser long-nosed bats at slow and cruising speed using particle image velocimetry (PIV). We find that a prominent LEV is present during the downstroke at slow speed, but not at cruising speed. Comparison with previously published LEV data from a robotic flapper inspired by lesser long-nosed bats suggests that bats should be able to generate LEVs at cruising speeds, but that they avoid doing so, probably to increase flight efficiency. In addition, at slow flight speeds we find LEVs of opposite spin at the inner and outer wing during the upstroke, potentially providing a control challenge to the animal. We also note that the LEV stays attached to the wing throughout the downstoke and does not show the complex structures found in insects. This suggests that bats are able to control the development of the LEV and potential control mechanisms are discussed.

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.

Efficiency of lift production in flapping and gliding flight of swifts

Many flying animals use both flapping and gliding flight as part of their routine behaviour. These two kinematic patterns impose conflicting requirements on wing design for aerodynamic efficiency and, in the absence of extreme morphing, wings cannot be optimised for both flight modes. In gliding flight, the wing experiences uniform incident flow and the optimal shape is a high aspect ratio wing with an elliptical planform. In flapping flight, on the other hand, the wing tip travels faster than the root, creating a spanwise velocity gradient. To compensate, the optimal wing shape should taper towards the tip (reducing the local chord) and/or twist from root to tip (reducing local angle of attack). We hypothesised that, if a bird is limited in its ability to morph its wings and adapt its wing shape to suit both flight modes, then a preference towards flapping flight optimization will be expected since this is the most energetically demanding flight mode. We tested this by studying a well-known flap-gliding species, the common swift, by measuring the wakes generated by two birds, one in gliding and one in flapping flight in a wind tunnel. We calculated span efficiency, the efficiency of lift production, and found that the flapping swift had consistently higher span efficiency than the gliding swift. This supports our hypothesis and suggests that even though swifts have been shown previously to increase their lift-to-drag ratio substantially when gliding, the wing morphology is tuned to be more aerodynamically efficient in generating lift during flapping. Since body drag can be assumed to be similar for both flapping and gliding, it follows that the higher total drag in flapping flight compared with gliding flight is primarily a consequence of an increase in wing profile drag due to the flapping motion, exceeding the reduction in induced drag.

On the quasi-steady aerodynamics of normal hovering flight part I: the induced power factor

An analytical treatment to quantify the losses captured in the induced power factor, k, is provided for flapping wings in normal hover, including the effects of non-uniform downwash, tip losses and finite flapping amplitude. The method is based on a novel combination of actuator disc and lifting line blade theories that also takes into account the effect of advance ratio. The model has been evaluated against experimental results from the literature and qualitative agreement obtained for the effect of advance ratio on the lift coefficient of revolving wings. Comparison with quantitative experimental data for the circulation as a function of span for a fruitfly wing shows that the model is able to correctly predict the circulation shape of variation, including both the magnitude of the peak circulation and the rate of decay in circulation towards zero. An evaluation of the contributions to induced power factor in normal hover for eight insects is provided. It is also shown how Reynolds number can be accounted for in the induced power factor, and good agreement is obtained between predicted span efficiency as a function of Reynolds number and numerical results from the literature. Lastly, it is shown that for a flapping wing in hover k owing to the non-uniform downwash effect can be reduced to 1.02 using an arcsech chord distribution. For morphologically realistic wing shapes based on beta distributions, it is shown that a value of 1.07 can be achieved for a radius of first moment of wing area at 40% of wing length.

Span efficiency in hawkmoths

Flight in animals is the result of aerodynamic forces generated as flight muscles drive the wings through air. Aerial performance is therefore limited by the efficiency with which momentum is imparted to the air, a property that can be measured using modern techniques. We measured the induced flow fields around six hawkmoth species flying tethered in a wind tunnel to assess span efficiency, ei, and from these measurements, determined the morphological and kinematic characters that predict efficient flight. The species were selected to represent a range in wingspan from 40 to 110 mm (2.75 times) and in mass from 0.2 to 1.5 g (7.5 times) but they were similar in their overall shape and their ecology. From high spatio-temporal resolution quantitative wake images, we extracted time-resolved downwash distributions behind the hawkmoths, calculating instantaneous values of ei throughout the wingbeat cycle as well as multi-wingbeat averages. Span efficiency correlated positively with normalized lift and negatively with advance ratio. Average span efficiencies for the moths ranged from 0.31 to 0.60 showing that the standard generic value of 0.83 used in previous studies of animal flight is not a suitable approximation of aerodynamic performance in insects.

Tomographic particle image velocimetry of desert locust wakes: instantaneous volumes combine to reveal hidden vortex elements and rapid wake deformation

Aerodynamic structures generated by animals in flight are unstable and complex. Recent progress in quantitative flow visualization has advanced our understanding of animal aerodynamics, but measurements have hitherto been limited to flow velocities at a plane through the wake. We applied an emergent, high-speed, volumetric fluid imaging technique (tomographic particle image velocimetry) to examine segments of the wake of desert locusts, capturing fully three-dimensional instantaneous flow fields. We used those flow fields to characterize the aerodynamic footprint in unprecedented detail and revealed previously unseen wake elements that would have gone undetected by two-dimensional or stereo-imaging technology. Vortex iso-surface topographies show the spatio-temporal signature of aerodynamic force generation manifest in the wake of locusts, and expose the extent to which animal wakes can deform, potentially leading to unreliable calculations of lift and thrust when using conventional diagnostic methods. We discuss implications for experimental design and analysis as volumetric flow imaging becomes more widespread.

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

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