Photogrammetric reconstruction of high-resolution surface topographies and deformable wing kinematics of tethered locusts and free-flying hoverflies

Wing deformation improves aerodynamic performance of forward flight of bluebottle flies flying in a flight mill

Insect wings are flexible structures that exhibit deformations of complex spatiotemporal patterns. Existing studies on wing deformation underscore the indispensable role of wing deformation in enhancing aerodynamic performance. Here, we investigated forward flight in bluebottle flies, flying semi-freely in a magnetic flight mill; we quantified wing surface deformation using high-speed videography and marker-less surface reconstruction and studied the effects on aerodynamic forces, power and efficiency using computational fluid dynamics. The results showed that flies' wings exhibited substantial camber near the wing root and twisted along the wingspan, as they were coupled effects of deflection primarily about the claval flexion line. Such deflection was more substantial for supination during the upstroke when most thrust was produced. Compared with deformed wings, the undeformed wings generated 59-98% of thrust and 54-87% of thrust efficiency (i.e. ratio of thrust and power). Wing twist moved the aerodynamic centre of pressure proximally and posteriorly, likely improving aerodynamic efficiency.

The spatiotemporal richness of hummingbird wing deformations

Animals exhibit an abundant diversity of forms, and this diversity is even more evident when considering animals that can change shape on demand. The evolution of flexibility contributes to aspects of performance from propulsive efficiency to environmental navigation. It is, however, challenging to quantify and compare body parts that, by their nature, dynamically vary in shape over many time scales. Commonly, body configurations are tracked by labelled markers and quantified parametrically through conventional measures of size and shape (descriptor approach) or non-parametrically through data-driven analyses that broadly capture spatiotemporal deformation patterns (shape variable approach). We developed a weightless marker tracking technique and combined these analytic approaches to study wing morphological flexibility in hoverfeeding Anna's hummingbirds (Calypte anna). Four shape variables explained >95% of typical stroke cycle wing shape variation and were broadly correlated with specific conventional descriptors such as wing twist and area. Moreover, shape variables decomposed wing deformations into pairs of in-plane and out-of-plane components at integer multiples of the stroke frequency. This property allowed us to identify spatiotemporal deformation profiles characteristic of hoverfeeding with experimentally imposed kinematic constraints, including through shape variables explaining <10% of typical shape variation. Hoverfeeding in front of a visual barrier restricted stroke amplitude and elicited increased stroke frequencies together with in-plane and out-of-plane deformations throughout the stroke cycle. Lifting submaximal loads increased stroke amplitudes at similar stroke frequencies together with prominent in-plane deformations during the upstroke and pronation. Our study highlights how spatially and temporally distinct changes in wing shape can contribute to agile fluidic locomotion.

A hull reconstruction-reprojection method for pose estimation of free-flying fruit flies

Understanding the mechanisms of insect flight requires high-quality data of free-flight kinematics, e.g. for comparative studies or genetic screens. Although recent improvements in high-speed videography allow us to acquire large amounts of free-flight data, a significant bottleneck is automatically extracting accurate body and wing kinematics. Here, we present an experimental system and a hull reconstruction-reprojection algorithm for measuring the flight kinematics of fruit flies. The experimental system can automatically record hundreds of flight events per day. Our algorithm resolves a significant portion of the occlusions in this system by a reconstruction-reprojection scheme that integrates information from all cameras. Wing and body kinematics, including wing deformation, are then extracted from the hulls of the wing boundaries and body. This model-free method is fully automatic, accurate and open source, and can be readily adjusted for different camera configurations or insect species.

Functional compliance and protective stiffness: cross-veins in the hind wing of locust Locusta migratoria

Locusts (Locusta migratoria) have outstanding flying abilities, and most of their lift is provided by their hind wings. Insect aerodynamic performance is strongly affected by wing deformation during stroke, which is closely related to its functional morphology (particularly its mechanical properties). The cross-vein is one of the main morphologies in the hind wing of locusts. However, few studies on the mechanical properties of cross-veins have been conducted. This study evaluated the cross-veins of the locust hind wing using uniaxial tensile tester, scanning electron microscope, and finite element methods. Four cross-vein types were identified at different locations on the hind wing, including periodical semi- and full-ellipsoidal humps and periodical semi- and full-conical humps. The four cross-veins showed similar tensile stiffness but differed in bending compliance. We suggest that the mechanical properties of the four cross-veins can be attributed to their physiological functions. This study elucidates cross-veins of locust hind wing and contributes our understanding of the flapping flight mechanism in locusts.

Experimental identification of individual insect visual tracking delays in free flight and their effects on visual swarm patterns

Insects are model systems for swarming robotic agents, yet engineered descriptions do not fully explain the mechanisms by which they provide onboard sensing and feedback to support such motions; in particular, the exact value and population distribution of visuomotor processing delays are not yet quantified, nor the effect of such delays on a visually-interconnected swarm. This study measures untethered insects performing a solo in-flight visual tracking task and applies system identification techniques to build an experimentally-consistent model of the visual tracking behaviors, and then integrates the measured experimental delay and its variation into a visually interconnected swarm model to develop theoretical and simulated solutions and stability limits. The experimental techniques include the development of a moving visual stimulus and real-time multi camera based tracking system called VISIONS (Visual Input System Identification from Outputs of Naturalistic Swarms) providing the capability to recognize and simultaneously track both a visual stimulus (input) and an insect at a frame rate of 60-120 Hz. A frequency domain analysis of honeybee tracking trajectories is conducted via fast Fourier and Chirp Z transforms, identifying a coherent linear region and its model structure. The model output is compared in time and frequency domain simulations. The experimentally measured delays are then related to probability density functions, and both the measured delays and their distribution are incorporated as inter-agent interaction delays in a second order swarming dynamics model. Linear stability and bifurcation analysis on the long range asymptotic behavior is used to identify delay distributions leading to a family of solutions with stable and unstable swarm center of mass (barycenter) locations. Numerical simulations are used to verify these results with both continuous and measured distributions. The results of this experiment quantify a model structure and temporal lag (transport delay) in the closed loop dynamics, and show that this delay varies across 50 individuals from 5-110ms, with an average delay of 22ms and a standard deviation of 40ms. When analyzed within the swarm model, the measured delays support a diversity of solutions and indicate an unstable barycenter.

Raptors avoid the confusion effect by targeting fixed points in dense aerial prey aggregations

Collective behaviours are widely assumed to confuse predators, but empirical support for a confusion effect is often lacking, and its importance must depend on the predator’s targeting mechanism. Here we show that Swainson’s Hawks Buteo swainsoni and other raptors attacking swarming Mexican Free-tailed Bats Tadarida brasiliensis steer by turning towards a fixed point in space within the swarm, rather than by using closed-loop pursuit of any one individual. Any prey with which the predator is on a collision course will appear to remain on a constant bearing, so target selection emerges naturally from the geometry of a collision. Our results show how predators can simplify the demands on their sensory system by decoupling steering from target acquisition when capturing prey from a dense swarm. We anticipate that the same tactic will be used against flocks and schools across a wide range of taxa, in which case a confusion effect is paradoxically more likely to occur in attacks on sparse groups, for which steering and target acquisition cannot be decoupled.

Flocking, schooling, and swarming prey are thought to benefit from a confusion effect. However, here the authors show that hawks attacking swarming bats avoid confusion by steering towards a fixed point in the swarm instead of targeting any one individual.

Auditory sensory range of male mosquitoes for the detection of female flight sound

Male mosquitoes detect and localize conspecific females by their flight-tones using the Johnston's organ (JO), which detects antennal deflections under the influence of local particle motion. Acoustic behaviours of mosquitoes and their JO physiology have been investigated extensively within the frequency domain, yet the auditory sensory range and the behaviour of males at the initiation of phonotactic flights are not well known. In this study, we predict a maximum spatial sensory envelope for flying Culex quinquefasciatus by integrating the physiological tuning response of the male JO with female aeroacoustic signatures derived from numerical simulations. Our sensory envelope predictions were tested with a behavioural assay of free-flying males responding to a female-like artificial pure tone. The minimum detectable particle velocity observed during flight tests was in good agreement with our theoretical prediction formed by the peak JO sensitivity measured in previous studies. The iso-surface describing the minimal detectable particle velocity represents the quantitative auditory sensory range of males and is directional with respect to the female body orientation. Our results illuminate the intricacy of the mating behaviour and point to the importance of observing the body orientation of flying mosquitoes to understand fully the sensory ecology of conspecific communication.

High speed visual insect swarm tracker (Hi-VISTA) used to identify the effects of confinement on individual insect flight

Individual insects flying in crowded assemblies perform complex aerial maneuvers by sensing and feeding back neighbor measurements to small changes in their wing motions. To understand the individual feedback rules that permit these fast, adaptive behaviors in group flight, both experimental preparations inducing crowded flight and high-speed tracking systems capable of tracking both body motions and more subtle wing motion changes for multiple insects in simultaneous flight are needed. This measurement capability extends tracking beyond the previous focus on individual insects to multiple insects. This paper describes an experimental preparation that induces crowded insect flight in more naturalistic conditions (a laboratory-outdoor transition tunnel) and directly compares the resulting flight performance to traditional flight enclosures. Measurements are made possible via the introduction of a multi-agent high speed insect tracker called Hi-VISTA, which provides a capability to track wing and body motions of multiple insects using high speed cameras (9000-12 500 fps). Processing steps consist of automatic background identification, data association, hull reconstruction, segmentation, and feature measurement. To improve the biological relevance of laboratory experiments and develop a platform for interaction studies, this paper applies the Hi-VISTA measurement system toApis melliferaforagers habituated to transit flights through the transparent transition environment. Binary statistical analysis (Welch's t-test, Cohen's d effect size) of 95 flight trajectories is presented, quantifying the differences between flights in an unobstructed environment and in a confined tunnel volume. The results indicate that body pitch angle, heading rate, flapping frequency, and vertical speed (heave) are each affected by confinement, and other flight variables show minor or statistically insignificant changes. These results form a baseline as swarm tracking and analysis begins to isolate the effects of neighbors from environmental enclosures, and improve the connection of high speed insect laboratory experiments to outdoor field experiments.

A semi-empirical model of the aerodynamics of manoeuvring insect flight

Blade element modelling provides a quick analytical method for estimating the aerodynamic forces produced during insect flight, but such models have yet to be tested rigorously using kinematic data recorded from free-flying insects. This is largely because of the paucity of detailed free-flight kinematic data, but also because analytical limitations in existing blade element models mean that they cannot incorporate the complex three-dimensional movements of the wings and body that occur during insect flight. Here, we present a blade element model with empirically fitted aerodynamic force coefficients that incorporates the full three-dimensional wing kinematics of manoeuvring Eristalis hoverflies, including torsional deformation of their wings. The two free parameters were fitted to a large free-flight dataset comprising N = 26 541 wingbeats, and the fitted model captured approximately 80% of the variation in the stroke-averaged forces in the sagittal plane. We tested the robustness of the model by subsampling the data, and found little variation in the parameter estimates across subsamples comprising 10% of the flight sequences. The simplicity and generality of the model that we present is such that it can be readily applied to kinematic datasets from other insects, and also used for the study of insect flight dynamics.

Butterflies fly using efficient propulsive clap mechanism owing to flexible wings

Butterflies look like no other flying animal, with unusually short, broad and large wings relative to their body size. Previous studies have suggested butterflies use several unsteady aerodynamic mechanisms to boost force production with upstroke wing clap being a prominent feature. When the wings clap together at the end of upstroke the air between the wings is pressed out, creating a jet, pushing the animal in the opposite direction. Although viewed, for the last 50 years, as a crucial mechanism in insect flight, quantitative aerodynamic measurements of the clap in freely flying animals are lacking. Using quantitative flow measurements behind freely flying butterflies during take-off and a mechanical clapper, we provide aerodynamic performance estimates for the wing clap. We show that flexible butterfly wings, forming a cupped shape during the upstroke and clap, thrust the butterfly forwards, while the downstroke is used for weight support. We further show that flexible wings dramatically increase the useful impulse (+22%) and efficiency (+28%) of the clap compared to rigid wings. Combined, our results suggest butterflies evolved a highly effective clap, which provides a mechanistic hypothesis for their unique wing morphology. Furthermore, our findings could aid the design of man-made flapping drones, boosting propulsive performance.

Reconstructing full-field flapping wing dynamics from sparse measurements

Flapping insect wings deform during flight. This deformation benefits the insect's aerodynamic force production as well as energetic efficiency. However, it is challenging to measure wing displacement field in flying insects. Many points must be tracked over the wing's surface to resolve its instantaneous shape. To reduce the number of points one is required to track, we propose a physics-based reconstruction method called system equivalent reduction expansion processes to estimate wing deformation and strain from sparse measurements. Measurement locations are determined using a weighted normalized modal displacement method. We experimentally validate the reconstruction technique by flapping a paper wing from 5-9 Hz with 45° and measuring strain at three locations. Two measurements are used for the reconstruction and the third for validation. Strain reconstructions had a maximal error of 30% in amplitude. We extend this methodology to a more realistic insect wing through numerical simulation. We show that wing displacement can be estimated from sparse displacement or strain measurements, and that additional sensors spatially average measurement noise to improve reconstruction accuracy. This research helps overcome some of the challenges of measuring full-field dynamics in flying insects and provides a framework for strain-based sensing in insect-inspired flapping robots.

The impact of dragonfly wing deformations on aerodynamic performance during forward flight

Bulk wing kinematics and wing deformations of free-flying dragonflies of the species Pachydiplax longipennis were measured in a controlled environment. Both upright and inverted straight flights were recorded and analyzed. The inverted dragonflies exhibited similar bulk kinematics to the upright specimens in the global frame, but wing deformations were generally consistent in the body-relative frame. The deformations primarily comprised camber during the body-relative downstroke and twist during the body-relative upstroke. Based on these data, models were developed to incorporate the measured kinematics and deformations into computational fluid dynamics simulations. Both isolated and tandem wings were simulated (rigid and deforming in each case), allowing the effects of deformations and wing-wing interactions to be examined independently. During the upstroke the addition of deformation reduced flow separation on the outboard sections of the wing, whereas the impact of the deformation during the downstroke was found to be dependent on the wing kinematics. The simulations of tandem wings indicated that they produce more force than isolated wings, but the wing deformations reduced the impact of this wing-wing interaction. The changes in average lift and thrust induced by the wing deformations were relatively minor and dependent on the flight orientation, but the aerodynamic efficiency of the deforming wings was significantly higher than that of the rigid wings for all examined cases, including the inverted flights for which the deformations were in the opposite (global) sense to the upright flights.

Motor output and control input in flapping flight: a compact model of the deforming wing kinematics of manoeuvring hoverflies

Insects are conventionally modelled as controlling flight by varying a few summary kinematic parameters that are defined on a per-wingbeat basis, such as the stroke amplitude, mean stroke angle and mean wing pitch angle. Nevertheless, as insects have tens of flight muscles and vary their kinematics continuously, the true dimension of their control input space is likely to be much higher. Here, we present a compact description of the deforming wing kinematics of 36 manoeuvring Eristalis hoverflies, applying functional principal components analysis to Fourier series fits of the wingtip position and wing twist measured over 26 541 wingbeats. This analysis offers a high degree of data reduction, in addition to insight into the natural kinematic couplings. We used statistical resampling techniques to verify that the principal components (PCs) were repeatable features of the data, and analysed their coefficient vectors to provide insight into the form of these natural couplings. Conceptually, the dominant PCs provide a natural set of control input variables that span the control input subspace utilized by this species, but they can also be thought of as output states of the flight motor. This functional description of the wing kinematics is appropriate to modelling insect flight as a form of limit cycle control.

Avian surface reconstruction in free flight with application to flight stability analysis of a barn owl and peregrine falcon

Birds primarily create and control the forces necessary for flight through changing the shape and orientation of their wings and tail. Their wing geometry is characterised by complex variation in parameters such as camber, twist, sweep and dihedral. To characterise this complexity, a multi-view stereo-photogrammetry setup was developed for accurately measuring surface geometry in high resolution during free flight. The natural patterning of the birds was used as the basis for phase correlation-based image matching, allowing indoor or outdoor use while being non-intrusive for the birds. The accuracy of the method was quantified and shown to be sufficient for characterising the geometric parameters of interest, but with a reduction in accuracy close to the wing edge and in some localised regions. To demonstrate the method's utility, surface reconstructions are presented for a barn owl (Tyto alba) and peregrine falcon (Falco peregrinus) during three instants of gliding flight per bird. The barn owl flew with a consistent geometry, with positive wing camber and longitudinal anhedral. Based on flight dynamics theory, this suggests it was longitudinally statically unstable during these flights. The peregrine falcon flew with a consistent glide angle, but at a range of air speeds with varying geometry. Unlike the barn owl, its glide configuration did not provide a clear indication of longitudinal static stability/instability. Aspects of the geometries adopted by both birds appeared to be related to control corrections and this method would be well suited for future investigations in this area, as well as for other quantitative studies into avian flight dynamics.

Local deformation and stiffness distribution in fly wings

Mechanical properties of insect wings are essential for insect flight aerodynamics. During wing flapping, wings may undergo tremendous deformations, depending on the wings’ spatial stiffness distribution. We here show an experimental evaluation of wing stiffness in three species of flies using a micro-force probe and an imaging method for wing surface reconstruction. Vertical deflection in response to point loads at 11 characteristic points on the wing surface reveals that average spring stiffness of bending lines between wing hinge and point loads varies ∼77-fold in small fruit flies and up to ∼28-fold in large blowflies. The latter result suggests that local wing deformation depends to a considerable degree on how inertial and aerodynamic forces are distributed on the wing surface during wing flapping. Stiffness increases with an increasing body mass, amounting to ∼0.6 Nm⁻¹ in fruit flies, ∼0.7 Nm⁻¹ in house flies and ∼2.6 Nm⁻¹ in blowflies for bending lines, running from the wing base to areas near the center of aerodynamic pressure. Wings of house flies have a ∼1.4-fold anisotropy in mean stiffness for ventral versus dorsal loading, while anisotropy is absent in fruit flies and blowflies. We present two numerical methods for calculation of local surface deformation based on surface symmetry and wing curvature. These data demonstrate spatial deformation patterns under load and highlight how veins subdivide wings into functional areas. Our results on wings of living animals differ from previous experiments on detached, desiccated wings and help to construct more realistic mechanical models for testing the aerodynamic consequences of specific wing deformations.

Summary: We determined mechanical properties of wings under load in three fly species. Fly wings broadly deform similar to homogenous beams. Veins and joints shape wing mechanics and govern wing deformation during flapping flight.

Flight in Ground Effect Dramatically Reduces Aerodynamic Costs in Bats

Most flying animals, from insects to seabirds [1], perform flights close to ground or water when taking off or landing [2], drinking, and feeding [3-5] or when traveling near water surfaces [1, 6, 7]. When flying close to a surface within approximately one wingspan, the surface acts as an aerodynamic mirror, interrupting the downwash [8, 9], resulting in increased pressure underneath the wing and suppression of wingtip vortex development [10]. This aerodynamic interaction lowers the energy added to the air by the animal, reducing the cost of flying. Modeling suggests that flapping wings in ground effect can affect the expected power savings compared to gliding flight, either positively or negatively, depending on the wing motion [11-13]. Although aerodynamic theory predicts substantial power reductions when animals fly in ground effect [4-6, 9, 11, 12], quantitative measurements of savings are lacking. Here, we show, through wake-based power measurements, that Daubenton's bats utilize 29% less aerodynamic power when flying in compared to out of ground effect, which is twice the predicted savings. Contrary to theoretical predictions [4-6, 9, 11, 12] we find no variation in savings with distance above ground when in ground effect. Given alterations in kinematics with ground proximity, we hypothesize that modulation of wing kinematics raises the achievable benefit from ground effect relative to current model predictions. The savings from ground effect are comparable to formation flight [14, 15] but are not limited to large bird species. Instead, ground effect is experienced by most flying animals and may have facilitated the evolution of powered animal flight.

Measurement of shape and deformation of insect wing

To measure the shape and deformation of an insect wing, a scanning setup adopting laser triangulation and image matching was developed. Only one industry camera with two light sources was employed to scan the transparent insect wings. 3D shape and point to point full field deformation of the wings could be obtained even when the wingspan is less than 3 mm. The venation and corrugation could be significantly identified from the results. The deformation of the wing under pin loading could be seen clearly from the results as well. Calibration shows that the shape and deformation measurement accuracies are no lower than 0.01 mm. Laser triangulation and image matching were combined dexterously to adapt wings' complex shape, size, and transparency. It is suitable for insect flight research or flapping wing micro-air vehicle development.

Superfast high-resolution absolute 3D recovery of a stabilized flapping flight process

Scientific research of a stabilized flapping flight process (e.g. hovering) has been of great interest to a variety of fields including biology, aerodynamics, and bio-inspired robotics. Different from the current passive photogrammetry based methods, the digital fringe projection (DFP) technique has the capability of performing dense superfast (e.g. kHz) 3D topological reconstructions with the projection of defocused binary patterns, yet it is still a challenge to measure a flapping flight process with the presence of rapid flapping wings. This paper presents a novel absolute 3D reconstruction method for a stabilized flapping flight process. Essentially, the slow motion parts (e.g. body) and the fast-motion parts (e.g. wings) are segmented and separately reconstructed with phase shifting techniques and the Fourier transform, respectively. The topological relations between the wings and the body are utilized to ensure absolute 3D reconstruction. Experiments demonstrate the success of our computational framework by testing a flapping wing robot at different flapping speeds.

Quantifying the dynamic wing morphing of hovering hummingbird

Animal wings are lightweight and flexible; hence, during flapping flight their shapes change. It has been known that such dynamic wing morphing reduces aerodynamic cost in insects, but the consequences in vertebrate flyers, particularly birds, are not well understood. We have developed a method to reconstruct a three-dimensional wing model of a bird from the wing outline and the feather shafts (rachides). The morphological and kinematic parameters can be obtained using the wing model, and the numerical or mechanical simulations may also be carried out. To test the effectiveness of the method, we recorded the hovering flight of a hummingbird (Amazilia amazilia) using high-speed cameras and reconstructed the right wing. The wing shape varied substantially within a stroke cycle. Specifically, the maximum and minimum wing areas differed by 18%, presumably due to feather sliding; the wing was bent near the wrist joint, towards the upward direction and opposite to the stroke direction; positive upward camber and the 'washout' twist (monotonic decrease in the angle of incidence from the proximal to distal wing) were observed during both half-strokes; the spanwise distribution of the twist was uniform during downstroke, but an abrupt increase near the wrist joint was found during upstroke.

Smart wing rotation and trailing-edge vortices enable high frequency mosquito flight

Mosquitoes exhibit unusual wing kinematics; their long, slender wings flap at remarkably high frequencies for their size (>800 Hz)and with lower stroke amplitudes than any other insect group. This shifts weight support away from the translation-dominated, aerodynamic mechanisms used by most insects, as well as by helicopters and aeroplanes, towards poorly understood rotational mechanisms that occur when pitching at the end of each half-stroke. Here we report free-flight mosquito wing kinematics, solve the full Navier-Stokes equations using computational fluid dynamics with overset grids, and validate our results with in vivo flow measurements. We show that, although mosquitoes use familiar separated flow patterns, much of the aerodynamic force that supports their weight is generated in a manner unlike any previously described for a flying animal. There are three key features: leading-edge vortices (a well-known mechanism that appears to be almost ubiquitous in insect flight), trailing-edge vortices caused by a form of wake capture at stroke reversal, and rotational drag. The two new elements are largely independent of the wing velocity, instead relying on rapid changes in the pitch angle (wing rotation) at the end of each half-stroke, and they are therefore relatively immune to the shallow flapping amplitude. Moreover, these mechanisms are particularly well suited to high aspect ratio mosquito wings.

Aerodynamic forces and flows of the full and partial clap-fling motions in insects

Most of the previous studies on Weis-Fogh clap-fling mechanism have focused on the vortex structures and velocity fields. Detailed pressure distribution results are provided for the first time in this study to reveal the differences between the full and the partial clap-fling motions. The two motions are studied by numerically solving the Navier-Stokes equations in moving overset grids. The Reynolds number is set to 20, relevant to the tiny flying insects. The following has been shown: (1) During the clap phase, the wings clap together and create a high pressure region in the closing gap between wings, greatly increasing the positive pressure on the lower surface of wing, while pressure on the upper surface is almost unchanged by the interaction; during the fling phase, the wings fling apart and create a low pressure region in the opening gap between wings, greatly increasing the suction pressure on the upper surface of wing, while pressure on the lower surface is almost unchanged by the interaction; (2) The interference effect between wings is most severe at the end of clap phase and the start of the fling phase: two sharp force peaks (8-9 times larger than that of the one-winged case) are generated. But the total force peaks are manifested mostly as drag and barely as lift of the wing, owing to the vertical orientation of the wing section; (3) The wing-wing interaction effect in the partial clap-fling case is much weaker than that in the full clap-fling case, avoiding the generation of huge drag. Compared with a single wing flapping with the same motion, mean lift in the partial case is enhanced by 12% without suffering any efficiency degradation, indicating that partial clap-fling is a more practical choice for tiny insects to employ.

Beneficial aerodynamic effect of wing scales on the climbing flight of butterflies

It is hypothesized that butterfly wing scale geometry and surface patterning may function to improve aerodynamic efficiency. In order to investigate this hypothesis, a method to measure butterfly flapping kinematics optically over long uninhibited flapping sequences was developed. Statistical results for the climbing flight flapping kinematics of 11 butterflies, based on a total of 236 individual flights, both with and without their wing scales, are presented. Results show, that for each of the 11 butterflies, the mean climbing efficiency decreased after scales were removed. Data was reduced to a single set of differences of climbing efficiency using are paired t-test. Results show a mean decrease in climbing efficiency of 32.2% occurred with a 95% confidence interval of 45.6%-18.8%. Similar analysis showed that the flapping amplitude decreased by 7% while the flapping frequency did not show a significant difference. Results provide strong evidence that butterfly wing scale geometry and surface patterning improve butterfly climbing efficiency. The authors hypothesize that the wing scale's effect in measured climbing efficiency may be due to an improved aerodynamic efficiency of the butterfly and could similarly be used on flapping wing micro air vehicles to potentially achieve similar gains in efficiency.

Validating two-dimensional leadership models on three-dimensionally structured fish schools

Identifying leader-follower interactions is crucial for understanding how a group decides where or when to move, and how this information is transferred between members. Although many animal groups have a three-dimensional structure, previous studies investigating leader-follower interactions have often ignored vertical information. This raises the question of whether commonly used two-dimensional leader-follower analyses can be used justifiably on groups that interact in three dimensions. To address this, we quantified the individual movements of banded tetra fish (Astyanax mexicanus) within shoals by computing the three-dimensional trajectories of all individuals using a stereo-camera technique. We used these data firstly to identify and compare leader-follower interactions in two and three dimensions, and secondly to analyse leadership with respect to an individual's spatial position in three dimensions. We show that for 95% of all pairwise interactions leadership identified through two-dimensional analysis matches that identified through three-dimensional analysis, and we reveal that fish attend to the same shoalmates for vertical information as they do for horizontal information. Our results therefore highlight that three-dimensional analyses are not always required to identify leader-follower relationships in species that move freely in three dimensions. We discuss our results in terms of the importance of taking species' sensory capacities into account when studying interaction networks within groups.

Wing and body kinematics of forward flight in drone-flies

Here, we present a detailed analysis of the wing and body kinematics in drone-flies in free flight over a range of speeds from hovering to about 8.5 m s(-1). The kinematics was measured by high-speed video techniques. As the speed increased, the body angle decreased and the stroke plane angle increased; the wingbeat frequency changed little; the stroke amplitude first decreased and then increased; the ratio of the downstroke duration to the upstroke duration increased; the mean positional angle increased at lower speeds but changed little at speeds above 3 m s(-1). At a speed above about 1.5 m s(-1), wing rotation at supination was delayed and that at pronation was advanced, and consequently the wing rotations were mostly performed in the upstroke. In the downstroke, the relative velocity of the wing increased and the effective angle of attack decreased with speed; in the upstroke, they both decreased with speed at lower speeds, and at higher speeds, the relative velocity became larger but the effective angle of attack became very small. As speed increased, the increasing inclination of the stroke plane ensured that the effective angle of attack in the upstroke would not become negative, and that the wing was in suitable orientations for vertical-force and thrust production.

Morphomechanical Innovation Drives Explosive Seed Dispersal

How mechanical and biological processes are coordinated across cells, tissues, and organs to produce complex traits is a key question in biology. Cardamine hirsuta, a relative of Arabidopsis thaliana, uses an explosive mechanism to disperse its seeds. We show that this trait evolved through morphomechanical innovations at different spatial scales. At the organ scale, tension within the fruit wall generates the elastic energy required for explosion. This tension is produced by differential contraction of fruit wall tissues through an active mechanism involving turgor pressure, cell geometry, and wall properties of the epidermis. Explosive release of this tension is controlled at the cellular scale by asymmetric lignin deposition within endocarp b cells-a striking pattern that is strictly associated with explosive pod shatter across the Brassicaceae plant family. By bridging these different scales, we present an integrated mechanism for explosive seed dispersal that links evolutionary novelty with complex trait innovation. VIDEO ABSTRACT.

Force generation and wing deformation characteristics of a flapping-wing micro air vehicle 'DelFly II' in hovering flight

The study investigates the aerodynamic performance and the relation between wing deformation and unsteady force generation of a flapping-wing micro air vehicle in hovering flight configuration. Different experiments were performed where fluid forces were acquired with a force sensor, while the three-dimensional wing deformation was measured with a stereo-vision system. In these measurements, time-resolved power consumption and flapping-wing kinematics were also obtained under both in-air and in-vacuum conditions. Comparison of the results for different flapping frequencies reveals different wing kinematics and deformation characteristics. The high flapping frequency case produces higher forces throughout the complete flapping cycle. Moreover, a phase difference occurs in the variation of the forces, such that the low flapping frequency case precedes the high frequency case. A similar phase lag is observed in the temporal evolution of the wing deformation characteristics, suggesting that there is a direct link between the two phenomena. A considerable camber formation occurs during stroke reversals, which is mainly determined by the stiffener orientation. The wing with the thinner surface membrane displays very similar characteristics to the baseline wing, which implies the dominance of the stiffeners in terms of providing rigidity to the wing. Wing span has a significant effect on the aerodynamic efficiency such that increasing the span length by 4 cm results in a 6% enhancement in the cycle-averaged X-force to power consumption ratio compared to the standard DelFly II wings with a span length of 28 cm.

Wing-kinematics measurement and aerodynamics in a small insect in hovering flight

Wing-motion of hovering small fly Liriomyza sativae was measured using high-speed video and flows of the wings calculated numerically. The fly used high wingbeat frequency (≈265 Hz) and large stroke amplitude (≈182°); therefore, even if its wing-length (R) was small (R ≈ 1.4 mm), the mean velocity of wing reached ≈1.5 m/s, the same as that of an average-size insect (R ≈ 3 mm). But the Reynolds number (Re) of wing was still low (≈40), owing to the small wing-size. In increasing the stroke amplitude, the outer parts of the wings had a "clap and fling" motion. The mean-lift coefficient was high, ≈1.85, several times larger than that of a cruising airplane. The partial "clap and fling" motion increased the lift by ≈7%, compared with the case of no aerodynamic interaction between the wings. The fly mainly used the delayed stall mechanism to generate the high-lift. The lift-to-drag ratio is only 0.7 (for larger insects, Re being about 100 or higher, the ratio is 1-1.2); that is, although the small fly can produce enough lift to support its weight, it needs to overcome a larger drag to do so.

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.

Recent developments in the study of insect flight

Here we review recent contributions to the study of insect flight, in particular those brought about by advances in experimental techniques. We focus particularly on the following areas: wing flexibility and deformation, the physiology and biophysics of asynchronous insect flight muscle, the aerodynamics of flight, and stability and maneuverability. This recent research reveals the importance of wing flexibility to insect flight, provides a detailed model of how asynchronous flight muscle functions and how it may have evolved, synthesizes many recent studies of insect flight aerodynamics into a broad-reaching summary of unsteady flight aerodynamics, and highlights new insights into the sources of flight stability in insects. The focus on experimental techniques and recently developed apparatus shows how these advancements have occurred and point the way towards future experiments.

Simultaneous measurement of aerodynamic forces and kinematics in flapping wings of tethered locust

Aerodynamic and inertial forces and corresponding kinematics of flapping wings of locusts, Schistocerca americana, were investigated in a low-speed wind tunnel. The experimental setup included live locusts mounted on microbalance synchronized with a high-speed video system. Simultaneous measurements of wing kinematics and forces were carried out on three locusts at 7° angle of attack and velocities of 0 m s(-1) and 4 m s(-1). Time variations of flapping and pitching angles exhibit similar patterns in fore- and hindwings and among the animals. Significant tip to root variations in pitching angle are found in both wings. The locusts have much larger flapping and pitching amplitudes in still air causing larger oscillations in inertial forces. Inertial forces are added to the lift and thrust on one part of the stroke, resulting in higher reaction forces and subtracted on the other part. Plots of the lift demonstrate similar trends with and without the wind. The global maxima and peak-to-peak amplitudes in lift are about the same in both tests. However, local minima are significantly lower in still air, resulting in much smaller stroke-averaged lift. Amplitudes of thrust force oscillations are much higher in still air; consequently, the stroke-averaged thrust is higher compared to the non-zero freestream velocity case.

Refraction corrected calibration for aquatic locomotion research: application of Snell's law improves spatial accuracy

Images of underwater objects are distorted by refraction at the water-glass-air interfaces and these distortions can lead to substantial errors when reconstructing the objects' position and shape. So far, aquatic locomotion studies have minimized refraction in their experimental setups and used the direct linear transform algorithm (DLT) to reconstruct position information, which does not model refraction explicitly. Here we present a refraction corrected ray-tracing algorithm (RCRT) that reconstructs position information using Snell's law. We validated this reconstruction by calculating 3D reconstruction error-the difference between actual and reconstructed position of a marker. We found that reconstruction error is small (typically less than 1%). Compared with the DLT algorithm, the RCRT has overall lower reconstruction errors, especially outside the calibration volume, and errors are essentially insensitive to camera position and orientation and the number and position of the calibration points. To demonstrate the effectiveness of the RCRT, we tracked an anatomical marker on a seahorse recorded with four cameras to reconstruct the swimming trajectory for six different camera configurations. The RCRT algorithm is accurate and robust and it allows cameras to be oriented at large angles of incidence and facilitates the development of accurate tracking algorithms to quantify aquatic manoeuvers.

In vivo time-resolved microtomography reveals the mechanics of the blowfly flight motor

Time-resolved X-ray microtomography permits a real-time view of the blowfly in flight at a previously unprecedented level of detail, revealing how the tiny steering muscles work.

Dipteran flies are amongst the smallest and most agile of flying animals. Their wings are driven indirectly by large power muscles, which cause cyclical deformations of the thorax that are amplified through the intricate wing hinge. Asymmetric flight manoeuvres are controlled by 13 pairs of steering muscles acting directly on the wing articulations. Collectively the steering muscles account for <3% of total flight muscle mass, raising the question of how they can modulate the vastly greater output of the power muscles during manoeuvres. Here we present the results of a synchrotron-based study performing micrometre-resolution, time-resolved microtomography on the 145 Hz wingbeat of blowflies. These data represent the first four-dimensional visualizations of an organism's internal movements on sub-millisecond and micrometre scales. This technique allows us to visualize and measure the three-dimensional movements of five of the largest steering muscles, and to place these in the context of the deforming thoracic mechanism that the muscles actuate. Our visualizations show that the steering muscles operate through a diverse range of nonlinear mechanisms, revealing several unexpected features that could not have been identified using any other technique. The tendons of some steering muscles buckle on every wingbeat to accommodate high amplitude movements of the wing hinge. Other steering muscles absorb kinetic energy from an oscillating control linkage, which rotates at low wingbeat amplitude but translates at high wingbeat amplitude. Kinetic energy is distributed differently in these two modes of oscillation, which may play a role in asymmetric power management during flight control. Structural flexibility is known to be important to the aerodynamic efficiency of insect wings, and to the function of their indirect power muscles. We show that it is integral also to the operation of the steering muscles, and so to the functional flexibility of the insect flight motor.

A blowfly's wingbeat is 50 times shorter than a blink of a human eye, and is controlled by numerous tiny steering muscles—some of which are as thin as a human hair. To visualize the movements of these muscles and the deformations of the surrounding exoskeleton, we developed a technique to allow us to look inside the insects during tethered flight. We used a particle accelerator to record high-speed X-ray images of the flying blowflies, which we used to reconstruct three-dimensional tomograms of their flight motor at ten different stages of the wingbeat. We measured the asymmetric movements of the steering muscles associated with turning flight, together with the accompanying movements of the wing hinge—arguably the most complex joint in nature. The steering muscles represent <3% of total flight muscle mass, so a key question has been how they can modulate the output of the much larger power muscles. We show that by shifting the flight motor between different modes of oscillation, the fly is able to divert mechanical energy into a steering muscle that is specialized to absorb mechanical energy. In general, we find that deformations of the muscles and thorax are key to understanding this remarkable mechanism.

A protocol and calibration method for accurate multi-camera field videography

Stereo videography is a powerful technique for quantifying the kinematics and behavior of animals, but it can be challenging to use in an outdoor field setting. We here present a workflow and associated software for performing calibration of cameras placed in a field setting and estimating the accuracy of the resulting stereoscopic reconstructions. We demonstrate the workflow through example stereoscopic reconstructions of bat and bird flight. We provide software tools for planning experiments and processing the resulting calibrations that other researchers may use to calibrate their own cameras. Our field protocol can be deployed in a single afternoon, requiring only short video clips of light, portable calibration objects.

Relationship between wingbeat frequency and resonant frequency of the wing in insects

In this study, we experimentally studied the relationship between wingbeat frequency and resonant frequency of 30 individuals of eight insect species from five orders: Odonata (Sympetrum flaveolum), Lepidoptera (Pieris rapae, Plusia gamma and Ochlodes), Hymenoptera (Xylocopa pubescens and Bombus rupestric), Hemiptera (Tibicen linnei) and Coleoptera (Allomyrina dichotoma). The wingbeat frequency of free-flying insects was measured using a high-speed camera while the natural frequency was determined using a laser displacement sensor along with a Bruel and Kjaer fast Fourier transform analyzer based on the base excitation method. The results showed that the wingbeat frequency was related to body mass (m) and forewing area (Af), following the proportionality f ~ m(1/2)/Af, while the natural frequency was significantly correlated with area density (f0 ~ mw/Af, mw is the wing mass). In addition, from the comparison of wingbeat frequency to natural frequency, the ratio between wingbeat frequency and natural frequency was found to be, in general, between 0.13 and 0.67 for the insects flapping at a lower wingbeat frequency (less than 100 Hz) and higher than 1.22 for the insects flapping at a higher wingbeat frequency (higher than 100 Hz). These results suggest that wingbeat frequency does not have a strong relation with resonance frequency: in other words, insects have not been evolved sufficiently to flap at their wings' structural resonant frequency. This contradicts the general conclusion of other reports--that insects flap at their wings' resonant frequency to take advantage of passive deformation to save energy.

Wing and body motion and aerodynamic and leg forces during take-off in droneflies

Here, we present a detailed analysis of the take-off mechanics in droneflies performing voluntary take-offs. Wing and body kinematics of the insects during take-off were measured using high-speed video techniques. Based on the measured data, the inertia force acting on the insect was computed and the aerodynamic force of the wings was calculated by the method of computational fluid dynamics. Subtracting the aerodynamic force and the weight from the inertia force gave the leg force. In take-off, a dronefly increases its stroke amplitude gradually in the first 10-14 wingbeats and becomes airborne at about the 12th wingbeat. The aerodynamic force increases monotonously from zero to a value a little larger than its weight, and the leg force decreases monotonously from a value equal to its weight to zero, showing that the droneflies do not jump and only use aerodynamic force of flapping wings to lift themselves into the air. Compared with take-offs in insects in previous studies, in which a very large force (5-10 times of the weight) generated either by jumping legs (locusts, milkweed bugs and fruit flies) or by the 'fling' mechanism of the wing pair (butterflies) is used in a short time, the take-off in the droneflies is relatively slow but smoother.

Force balance in the take-off of a pierid butterfly: relative importance and timing of leg impulsion and aerodynamic forces

Up to now, the take-off stage has remained an elusive phase of insect flight that was relatively poorly explored compared with other maneuvers. An overall assessment of the different mechanisms involved in force production during take-off has never been explored. Focusing on the first downstroke, we have addressed this problem from a force balance perspective in butterflies taking off from the ground. In order to determine whether the sole aerodynamic wing force could explain the observed motion of the insect, we have firstly compared a simple analytical model of the wing force with the acceleration of the insect's center of mass estimated from video tracking of the wing and body motions. Secondly, wing kinematics were also used for numerical simulations of the aerodynamic flow field. Similar wing aerodynamic forces were obtained by the two methods. However, neither are sufficient, nor is the inclusion of the ground effect, to predict faithfully the body acceleration. We have to resort to the leg forces to obtain a model that best fits the data. We show that the median and hind legs display an active extension responsible for the initiation of the upward motion of the insect's body, occurring before the onset of the wing downstroke. We estimate that legs generate, at various times, an upward force that can be much larger than all other forces applied to the insect's body. The relative timing of leg and wing forces explains the large variability of trajectories observed during the maneuvers.

Collision-avoidance behaviors of minimally restrained flying locusts to looming stimuli

Visually guided collision avoidance is of paramount importance in flight, for instance to allow escape from potential predators. Yet, little is known about the types of collision-avoidance behaviors that may be generated by flying animals in response to an impending visual threat. We studied the behavior of minimally restrained locusts flying in a wind tunnel as they were subjected to looming stimuli presented to the side of the animal, simulating the approach of an object on a collision course. Using high-speed movie recordings, we observed a wide variety of collision-avoidance behaviors including climbs and dives away from - but also towards - the stimulus. In a more restrained setting, we were able to relate kinematic parameters of the flapping wings with yaw changes in the trajectory of the animal. Asymmetric wing flapping was most strongly correlated with changes in yaw, but we also observed a substantial effect of wing deformations. Additionally, the effect of wing deformations on yaw was relatively independent of that of wing asymmetries. Thus, flying locusts exhibit a rich range of collision-avoidance behaviors that depend on several distinct aerodynamic characteristics of wing flapping flight.

Effects of structural flexibility of wings in flapping flight of butterfly

The objective of this paper is to clarify the effects of structural flexibility of wings of a butterfly in flapping flight. For this purpose, a dynamics model of a butterfly is derived by Lagrange's method, where the butterfly is considered as a rigid multi-body system. The panel method is employed to simulate the flow field and the aerodynamic forces acting on the wings. The mathematical model is validated by the agreement of the numerical result with the experimentally measured data. Then, periodic orbits of flapping-of-wings flights are parametrically searched in order to fly the butterfly models. Almost periodic orbits are found, but they are unstable. Deformation of the wings is modeled in two ways. One is bending and its effect on the aerodynamic forces is discussed. The other is passive wing torsion caused by structural flexibility. Numerical simulations demonstrate that flexible torsion reduces the flight instability.

3D reconstruction and analysis of wing deformation in free-flying dragonflies

Insect wings demonstrate elaborate three-dimensional deformations and kinematics. These deformations are key to understanding many aspects of insect flight including aerodynamics, structural dynamics and control. In this paper, we propose a template-based subdivision surface reconstruction method that is capable of reconstructing the wing deformations and kinematics of free-flying insects based on the output of a high-speed camera system. The reconstruction method makes no rigid wing assumptions and allows for an arbitrary arrangement of marker points on the interior and edges of each wing. The resulting wing surfaces are projected back into image space and compared with expert segmentations to validate reconstruction accuracy. A least squares plane is then proposed as a universal reference to aid in making repeatable measurements of the reconstructed wing deformations. Using an Eastern Pondhawk, Erythimus simplicicollis dragonfly as a demonstration, we quantify and visualize the wing twist and camber in both the chord-wise and span-wise directions, and discuss the implications of the results. In particular, a detailed analysis of the subtle deformation in the dragonfly's right hindwing suggests that the muscles near the wing root could be used to induce chord-wise camber in the portion of the wing nearest the specimen's body. We conclude by proposing a novel technique for modeling wing corrugation in the reconstructed flapping wings. In this method, displacement mapping is used to combine wing surface details measured from static wings with the reconstructed flapping wings, while not requiring any additional information be tracked in the high speed camera output.

Neuromuscular and biomechanical compensation for wing asymmetry in insect hovering flight

Wing damage is common in flying insects and has been studied using a variety of approaches to assess its biomechanical and fitness consequences. Results of these studies range from strong to nil effect among the variety of species, fitness measurements and damage modes studied, suggesting that not all damage modes are equal and that insects may be well adapted to compensate for some types of damage. Here, we examine the biomechanical and neuromuscular means by which flying insects compensate for asymmetric wing damage, which is expected to produce asymmetric flight forces and torques and thus destabilize the animal in addition to reducing its total wing size. We measured the kinematic and neuromuscular responses of hawkmoths (Manduca sexta) hovering in free flight with asymmetrically damaged wings via high-speed videography and extracellular neuromuscular activity recordings. The animals responded to asymmetric wing damage with asymmetric changes to wing stroke amplitude sufficient to restore symmetry in lift production. These asymmetries in stroke amplitude were significantly correlated with bilateral asymmetries in the timing of activation of the dorsal ventral muscle among and within trials. Correspondingly, the magnitude of wing asymmetry was significantly although non-linearly correlated with the magnitude of the neuromuscular response among individuals. The strongly non-linear nature of the relationship suggests that active neural compensation for asymmetric wing damage may only be necessary above a threshold, &gt;12% asymmetry in wing second moment of area in this case, below which passive mechanisms may be adequate to maintain flight stability.

Operation of the alula as an indicator of gear change in hoverflies

The alula is a hinged flap found at the base of the wings of most brachyceran Diptera. The alula accounts for up to 10 per cent of the total wing area in hoverflies (Syrphidae), and its hinged arrangement allows the wings to be swept back over the thorax and abdomen at rest. The alula is actuated via the third axillary sclerite, which is a component of the wing hinge that is involved in wing retraction and control. The third axillary sclerite has also been implicated in the gear change mechanism of flies. This mechanism allows rapid switching between different modes of wing kinematics, by imposing or removing contact with a mechanical stop limiting movement of the wing during the lower half of the downstroke. The alula operates in two distinct states during flight-flipped or flat-and we hypothesize that its state indicates switching between different flight modes. We used high-speed digital video of free-flying hoverflies (Eristalis tenax and Eristalis pertinax) to investigate whether flipping of the alula was associated with changes in wing and body kinematics. We found that alula state was associated with different distributions of multiple wing kinematic parameters, including stroke amplitude, stroke deviation angle, downstroke angle of incidence and timing of supination. Changes in all of these parameters have previously been linked to gear change in flies. Symmetric flipping of the alulae was associated with changes in the symmetric linear acceleration of the body, while asymmetric flipping of the alulae was associated with asymmetric angular acceleration of the body. We conclude that the wings produce less aerodynamic force when the alula is flipped, largely as a result of the accompanying changes in wing kinematics. The alula changes state at mid-downstroke, which is the point at which the gear change mechanism is known to come into effect. This transition is accompanied by changes in the other wing kinematic parameters. We therefore find that the state of the alula is linked to the same parameters as are affected by the gear change mechanism. We conclude that the state of the alula does indeed indicate the operation of different flight modes in Eristalis, and infer that a likely mechanism for these changes in flight mode is the gear change mechanism.

Wing motion measurement and aerodynamics of hovering true hoverflies

Most hovering insects flap their wings in a horizontal plane (body having a large angle from the horizontal), called `normal hovering'. But some of the best hoverers, e.g. true hoverflies, hover with an inclined stroke plane (body being approximately horizontal). In the present paper, wing and body kinematics of four freely hovering true hoverflies were measured using three-dimensional high-speed video. The measured wing kinematics was used in a Navier–Stokes solver to compute the aerodynamic forces of the insects. The stroke amplitude of the hoverflies was relatively small, ranging from 65 to 85 deg, compared with that of normal hovering. The angle of attack in the downstroke (∼50 deg) was much larger that in the upstroke (∼20 deg), unlike normal-hovering insects, whose downstroke and upstroke angles of attack are not very different. The major part of the weight-supporting force (approximately 86%) was produced in the downstroke and it was contributed by both the lift and the drag of the wing, unlike the normal-hovering case in which the weight-supporting force is approximately equally contributed by the two half-strokes and the lift principle is mainly used to produce the force. The mass-specific power was 38.59–46.3 and 27.5–35.4 W kg–1 in the cases of 0 and 100% elastic energy storage, respectively. Comparisons with previously published results of a normal-hovering true hoverfly and with results obtained by artificially making the insects' stroke planes horizontal show that for the true hoverflies, the power requirement for inclined stroke-plane hover is only a little (&lt;10%) larger than that of normal hovering.

Aerodynamic performance of a hovering hawkmoth with flexible wings: a computational approach

Insect wings are deformable structures that change shape passively and dynamically owing to inertial and aerodynamic forces during flight. It is still unclear how the three-dimensional and passive change of wing kinematics owing to inherent wing flexibility contributes to unsteady aerodynamics and energetics in insect flapping flight. Here, we perform a systematic fluid-structure interaction based analysis on the aerodynamic performance of a hovering hawkmoth, Manduca, with an integrated computational model of a hovering insect with rigid and flexible wings. Aerodynamic performance of flapping wings with passive deformation or prescribed deformation is evaluated in terms of aerodynamic force, power and efficiency. Our results reveal that wing flexibility can increase downwash in wake and hence aerodynamic force: first, a dynamic wing bending is observed, which delays the breakdown of leading edge vortex near the wing tip, responsible for augmenting the aerodynamic force-production; second, a combination of the dynamic change of wing bending and twist favourably modifies the wing kinematics in the distal area, which leads to the aerodynamic force enhancement immediately before stroke reversal. Moreover, an increase in hovering efficiency of the flexible wing is achieved as a result of the wing twist. An extensive study of wing stiffness effect on aerodynamic performance is further conducted through a tuning of Young's modulus and thickness, indicating that insect wing structures may be optimized not only in terms of aerodynamic performance but also dependent on many factors, such as the wing strength, the circulation capability of wing veins and the control of wing movements.

Deformable wing kinematics in free-flying hoverflies

Here, we present a detailed analysis of the deforming wing kinematics of free-flying hoverflies (Eristalis tenax, Linnaeus) during hovering flight. We used four high-speed digital video cameras to reconstruct the motion of approximately 22 points on each wing using photogrammetric techniques. While the root-flapping motion of the wing is similar in both the downstroke and upstroke, and is well modelled as a simple harmonic motion, other wing kinematic parameters show substantial variation between the downstroke and upstroke. Whereas the magnitude of the angle of incidence varies considerably within and between different hoverflies, the twist distribution along the wing is highly stereotyped. The angle of incidence and camber both show a recoil effect as they change abruptly at stroke reversal. Pronation occurs consistently after stroke reversal, which is perhaps surprising, because this has been found to reduce lift production in modelling studies. We find that the alula, a hinged flap near the base of the wing, operates in two discrete states: either in plane with the wing, or flipped approximately normal to it. We hypothesize that the alula may be acting as a flow-control device.

Passive maintenance of high angle of attack and its lift generation during flapping translation in crane fly wing

We have studied the passive maintenance of high angle of attack and its lift generation during the crane fly's flapping translation using a dynamically scaled model. Since the wing and the surrounding fluid interact with each other, the dynamic similarity between the model flight and actual insect flight was measured using not only the non-dimensional numbers for the fluid (the Reynolds and Strouhal numbers) but also those for the fluid—structure interaction (the mass and Cauchy numbers). A difference was observed between the mass number of the model and that of the actual insect because of the limitation of available solid materials. However, the dynamic similarity during the flapping translation was not much affected by the mass number since the inertial force during the flapping translation is not dominant because of the small acceleration. In our model flight, a high angle of attack of the wing was maintained passively during the flapping translation and the wing generated sufficient lift force to support the insect weight. The mechanism of the maintenance is the equilibrium between the elastic reaction force resulting from the wing torsion and the fluid dynamic pressure. Our model wing rotated quickly at the stroke reversal in spite of the reduced inertial effect of the wing mass compared with that of the actual insect. This result could be explained by the added mass from the surrounding fluid. Our results suggest that the pitching motion can be passive in the crane fly's flapping flight.

Details of insect wing design and deformation enhance aerodynamic function and flight efficiency

Insect wings are complex structures that deform dramatically in flight. We analyzed the aerodynamic consequences of wing deformation in locusts using a three-dimensional computational fluid dynamics simulation based on detailed wing kinematics. We validated the simulation against smoke visualizations and digital particle image velocimetry on real locusts. We then used the validated model to explore the effects of wing topography and deformation, first by removing camber while keeping the same time-varying twist distribution, and second by removing camber and spanwise twist. The full-fidelity model achieved greater power economy than the uncambered model, which performed better than the untwisted model, showing that the details of insect wing topography and deformation are important aerodynamically. Such details are likely to be important in engineering applications of flapping flight.

Deformable wing kinematics in the desert locust: how and why do camber, twist and topography vary through the stroke?

Here, we present a detailed analysis of the wing kinematics and wing deformations of desert locusts (Schistocerca gregaria, Forskål) flying tethered in a wind tunnel. We filmed them using four high-speed digital video cameras, and used photogrammetry to reconstruct the motion of more than 100 identified points. Whereas the hindwing motions were highly stereotyped, the forewing motions showed considerable variation, consistent with a role in flight control. Both wings were positively cambered on the downstroke. The hindwing was cambered through an 'umbrella effect' whereby the trailing edge tension compressed the radial veins during the downstroke. Hindwing camber was reversed on the upstroke as the wing fan corrugated, reducing the projected area by 30 per cent, and releasing the tension in the trailing edge. Both the wings were strongly twisted from the root to the tip. The linear decrease in incidence along the hindwing on the downstroke precisely counteracts the linear increase in the angle of attack that would otherwise occur in root flapping for an untwisted wing. The consequent near-constant angle of attack is reminiscent of the optimum for a propeller of constant aerofoil section, wherein a linear twist distribution allows each section to operate at the unique angle of attack maximizing the lift to drag ratio. This implies tuning of the structural, morphological and kinematic parameters of the hindwing for efficient aerodynamic force production.

Aerodynamic effects of flexibility in flapping wings

Recent work on the aerodynamics of flapping flight reveals fundamental differences in the mechanisms of aerodynamic force generation between fixed and flapping wings. When fixed wings translate at high angles of attack, they periodically generate and shed leading and trailing edge vortices as reflected in their fluctuating aerodynamic force traces and associated flow visualization. In contrast, wings flapping at high angles of attack generate stable leading edge vorticity, which persists throughout the duration of the stroke and enhances mean aerodynamic forces. Here, we show that aerodynamic forces can be controlled by altering the trailing edge flexibility of a flapping wing. We used a dynamically scaled mechanical model of flapping flight (Re approximately 2000) to measure the aerodynamic forces on flapping wings of variable flexural stiffness (EI). For low to medium angles of attack, as flexibility of the wing increases, its ability to generate aerodynamic forces decreases monotonically but its lift-to-drag ratios remain approximately constant. The instantaneous force traces reveal no major differences in the underlying modes of force generation for flexible and rigid wings, but the magnitude of force, the angle of net force vector and centre of pressure all vary systematically with wing flexibility. Even a rudimentary framework of wing veins is sufficient to restore the ability of flexible wings to generate forces at near-rigid values. Thus, the magnitude of force generation can be controlled by modulating the trailing edge flexibility and thereby controlling the magnitude of the leading edge vorticity. To characterize this, we have generated a detailed database of aerodynamic forces as a function of several variables including material properties, kinematics, aerodynamic forces and centre of pressure, which can also be used to help validate computational models of aeroelastic flapping wings. These experiments will also be useful for wing design for small robotic insects and, to a limited extent, in understanding the aerodynamics of flapping insect wings.