Vortex trapping recaptures energy in flying fruit flies

Flapping flight is one of the most costly forms of locomotion in animals. To limit energetic expenditures, flying insects thus developed multiple strategies. An effective mechanism to reduce flight power expenditures is the harvesting of kinetic energy from motion of the surrounding air. We here show an unusual mechanism of energy harvesting in an insect that recaptures the rotational energy of air vortices. The mechanism requires pronounced chordwise wing bending during which the wing surface momentary traps the vortex and transfers its kinetic energy to the wing within less than a millisecond. Numerical and robotic controls show that the decrease in vortex strength is minimal without the nearby wing surface. The measured energy recycling might slightly reduce the power requirements needed for body weight support in flight, lowering the flight costs in animals flying at elevated power demands. An increase in flight efficiency improves flight during aversive manoeuvring in response to predation and long-distance migration, and thus factors that determine the worldwide abundance and distribution of insect populations.

Flapping flight is one of the most costly forms of locomotion in animals. To limit energetic expenditures, flying insects thus developed multiple strategies. An effective mechanism to reduce flight power expenditures is the harvesting of kinetic energy from motion of the surrounding air. We here show an unusual mechanism of energy harvesting in an insect that recaptures the rotational energy of air vortices. The mechanism requires pronounced chordwise wing bending during which the wing surface momentary traps the vortex and transfers its kinetic energy to the wing within less than a millisecond. Numerical and robotic controls show that the decrease in vortex strength is minimal without the nearby wing surface. The measured energy recycling might slightly reduce the power requirements needed for body weight support in flight, lowering the flight costs in animals flying at elevated power demands. An increase in flight efficiency improves flight during aversive manoeuvring in response to predation and long-distance migration, and thus factors that determine the worldwide abundance and distribution of insect populations.
To allocate low energy investment for big gains is an universal rule in nature [1][2][3][4][5][6][7][8] . The reduction of energy spent during locomotion is thus key to the ecological success of many flying animals. During wing flapping of insects, the energy for propulsion stems from the contraction of flight muscles. The majority of muscle energy during flight appears as kinetic energy in the surrounding air but part of it is also stored as elastic potential energy in the muscle tissue 9 , as elastic deformations of the thorax 10 and wings 11 , and as kinetic energy in the movement of wings. Energy loss in deforming structures are common in flight. Fly wings, for example, elastically recycle only ~ 80-90% of their deformation energy during wing flapping 11,12 , making flight less efficient. Many animals thus benefit from a reduction of energy needed to accelerate the surrounding fluid by extracting kinetic energy from their environment. Birds in flocks, for example, take advantage of flight formations using vortices shed from the wing tips of the heading animals [13][14][15][16] and trouts save muscle power by exploiting rotational energy from vortices generated by bodies upstream 17 .
Vortices at the wing may enhance the production of locomotor forces in flight. Elevated leading edge suction in birds 18,19 , bats 20,21 and insects 4,5,22,23 is generated by the wing's leading edge vortex (LEV) that boosts lift production for weight support and increases locomotor capacity during flight manoeuvres. The cyclic changes in wing flapping direction within the stroke cycle, however, force insects to periodically shed these vortices into the wake. Thus, at each stroke reversal, a large amount the kinetic energy and thus muscle power is wasted, lowering propulsion efficiency owing to energy conservation laws 4 . To cope with these constraints, many insects developed strategies to simultaneously increase lift production and locomotor efficiency during wing flapping. Dragonfly hindwings, for example, utilize energy-rich vortex flows shed from the forewings that increases aerodynamic efficiency 24 and butterfly wings lower the kinetic energy of stopping vortices by slicing through it 5 . While physical and numerical modelling of flight in small insects showed that a single wing recaptures vortex flows from the wake of a previous halfstroke 4,22,25,26 , two-winged models apparently miss this ability 27-30 . This study identifies that the 1.3 mg fruit fly Drosophila virilis harvests energy from trapped vortices during clap-and-fling wing kinematics 27,[30][31][32][33][34] , at which the flapping wings physically touch and chordwise bend during the dorsal stroke reversal (Fig. 1). Experiments previously showed that clap-and-fling kinematics alters vortex development 35,36 and also lowers the energetic costs for lift production per unit flight muscle mass compared to flight without clap-and-fling kinematics 29,37,38 . In freely flying fruit flies, high-speed video recording shows that full and partial dorsal wing-wing contact occurs in ~ 33% of 144 tested wing strokes (N = 24 flies, supplementary text S1), suggesting that this kinematic manoeuvre is frequent in fruit flies. Figure 1b  www.nature.com/scientificreports/ cycle. We estimated the wing's chordwise deformation using high-speed videography and a laser sheet (Fig. 1a,c), illuminating wing profiles at 4 equally distant wing sections. Figure 1d shows the evolution of the chordwise deformation at the centre of aerodynamic force production at ~ 0.6 wing length 29 .
During wing rotation at the dorsal reversal, the wings deform only little until they clap together (0 ms stroke cycle, Fig. 1b). However, they strongly deform within only ~ 0.5 ms during wing separation (peel motion), increasing the wings' rise-to-chord ratio up to ~ 18% (Fig. 1d). The flexing motion of the wing chord accordingly reduces the elevated drag on the wing that results from both the viscous forces between the wing surfaces and wing acceleration during wing separation 30,31 . Figure 1d shows that wing rotation occurs symmetrical in fruit flies with respect to the up-and downstroke, producing elevated lift for weight support compared to a delayed rotation 4 . At wing clap, instantaneous translational wing velocity is minimum but quickly accelerates to ~ 2.4 ms −1 within only ~ 1.5 ms during wing separation (Fig. 1e). The wings' rotational motion peaks at ~ 1579 rad s −1 during wing clapping and decelerates to zero at the beginning of the downstroke within less than a millisecond (Fig. 1f). In contrast to the negative wing camber as used in computer simulations 30,39 , the wings in fruit flies have a small positive camber at the beginning of the downstroke. This positive camber contributes to lift production at the initial phase of the downstroke 40 because it increases the wing's angle of attack and thus fluid momentum 41 . The fate of vortical structures at the end of the wings' upstroke is key for aerodynamic recapture mechanisms (movie S1). Figure 2 shows the evolution of leading and trailing edge vortices during the dorsal stroke reversal in 5 equally-spaced out of 17 moments sampled at 10 kHz. At the beginning of wing rotation, vorticity of LEV at the ventral wing surface increases due to the wing's increasing angle of attack. As a consequence of wing rotation and wing deceleration, the wing also produces counter-balancing vorticity at the trailing edge (Fig. 2a). At wing clapping, both vortices have gained maximum strength but remain attached at the ventral wing surface www.nature.com/scientificreports/ (Fig. 2b). The stretched shape of LEV and trailing edge vortices results from air viscosity at low Reynolds number of ~ 214 for wing flapping in conjunction with the vortex shear velocity relative to the air. Throughout wing peel motion (Fig. 2c), the LEV does not separate from the wing as reported for robotic wings 28 and computer simulation models 29,30 . Instead, it remains close to the wing's ventral surface and consequentially travels downstream from the leading towards the trailing wing edge (Fig. 2d). The ability of fruit fly wings to trap the LEV from the upstroke results from the combined effect of chordwise wing bending during peel and upward heaving motion 27 . The two wing surfaces effectively separate left and right LEV, avoiding that both vortices cancel each other out owing to their opposite spins. This factor saves the LEV's kinetic energy for later use. The positive wing camber generates a curvature with finite radius, which increases the tangential contact area between wing and LEV and inevitably facilitates vortex trapping. For comparison, in rigid wings of robotic Drosophila wing flapping models, leading edge vorticies are shed during the fling phase into the opening cleft between both wings 28 (Fig. 2f-j) that forces vortex extinction according the Kelvin's law rather than energy recycling. The time, at which the moving upstroke LEV reaches the wing's trailing edge (~ 1 ms after wing clap, Fig. 2d,e), the wings start to separate and to produce start vortices that balance the wings' bound circulation. At this moment, upstroke LEV and downstroke start vortex fuse because of equal spin, and are subsequently shed as a single structure into the wake (Fig. 2e). The latter process is quantified in Fig. 2m, showing that the LEV gains ~ 2.9 times its vorticity (~ 1442 ± 568 s −1 to ~ 4112 ± 314 s −1 ) during fusion. While travelling chordwise, the trapped LEV keeps its orientation relative to ventral wing surface (Fig. 2k). This potentially allows to transfer the LEV's kinetic energy to the wing by surface friction (Fig. 2l). Due to the horizontal stroke plane in flying fruit flies, the resulting shear force vector at the wing may contribute to both vertical lift support and nose down pitching moments on the fly body for posture control. Notably, Fig. 2m shows that while travelling, the LEV looses ~ 74.2% or ~ 4356 ± 738 s −1 of its initial peak vorticity (~ 5873 ± 909 s −1 , N = 15 stroke cycles, 12 animals) within less than a millisecond. The LEV's sectional kinetic energy decreases likewise by ~ 71% from ~ 718 ± 93 nJm −1 before peel to ~ 212 ± 126 nJm −1 after peel (Fig. 2n). At absence of steering manoeuvres elicited by visual stimulation of the fly's compound eyes, the difference in vortex decay is negligible between both wings.
The assumption that vortex energy is transferred to the wing is supported by comparison of slopes for vorticity decay time between leading and trailing edge vortices (TEV) in the fly (supplementary text S2). These data show that vortex circulation decreases ~ 6.4 to ~ 9.0 times and sectional energy ~ 6.1 to ~ 7.8 times faster in the LEV than the TEV (supplemental text S3). We further confirmed this finding by comparing the time evolution of vorticity in vortices modelled by a Lamb-Oseen vortex model (supplementary text S3) and by estimation of vorticity decay times of free vortices shed from a robotic fruit fly wing (supplementary text S4 and S5). There is also no evidence for vortex-splitting at the wing surface that could cause vorticity decrement 42 . We also tested the idea that spanwise axial flow on the wing surface pulls the LEV outward, in turn changing both sectional vorticity and energy of the LEV over time (supplementary text S4). Due the LEV's conical vorticity profile, a change in LEV's longitudinal position relative to the wing surface might appear as a change in vorticity in the 2-dimensional measurement plane during particle image velocimetry. Data measured in a fruit fly model wing, however, suggest that spanwise displacement of a vortex may account for not more than ~ 21.9% change in circulation and ~ 36.6% change in sectional kinetic energy (supplementary text S4). These findings rule out the hypothesis that spanwise drift causes the measured attenuation in LEV strength in the fruit fly during peel motion. We also carefully considered vortex stretching as a possible explanation for vortex decay using computational fluid dynamics (supplementary text S6). Vortex stretching is a pure 3-dimensional effect and cannot be captured considering our 2-dimensional slices of the flow field. Both, enstrophy dissipation and vortex stretching determine the time evolution of enstrophy. The numerical simulations show that vortex stretching is several orders of magnitude smaller than enstrophy dissipation (supplementary text S6). The excessive dissipation observed in leading edge vortices near the wings can thus not be explained by vortex stretching and supports the hypothesis that energy is transferred to the wing. In addition, negligible vortex stretching also implies that 2-dimensional measurements are sufficient to characterize the decay of vortex enstrophy. Altogether, the controls suggest that the LEV's loss of kinetic energy during peel motion cannot be fully explained by enstrophy dissipation, vortex stretching or axial displacement.
To answer the question on how much muscle mechanical power a fruit fly might maximally save by vortex trapping, we determined total energy loss in both the fly's LEV and a corresponding Lamb-Oseen vortex model, included the LEV's spanwise conical vorticity profile and calculated the transferred power with respect to the flapping cycle (supplementary text S3). We found that the LEV might maximally transfer ~ 1.08 nJ kinetic energy to the wing surface. The potential kinetic energy transfer converts to ~ 0.66 Wkg -1 flight muscle mass and further to ~ 1.1% the total aerodynamic power requirements for flight (~ 59.8 W kg −1 flight muscle mass) 43 or ~ 3.0% the total induced power requirements (~ 21.4 W kg −1 flight muscle mass) 43 for vertical lift production 44 during hovering flight. However, if we compare with mean induced power during peel time (supplementary text S3), LEV trapping might lower induced power during peel by ~ 20.6%. Moreover, in a horizontal stroke plane, the transferred energy likely accelerates the wings upward, which might further augment lift production due to augmentation of the transient unilateral asymmetry in vorticity distribution during fling motion 30 . As the leading edge vortices merge with trailing edge vortices at the end of wing separation, the proximity of LEVs to the wing surfaces does not hinder the generation of bound circulation during wing translation. Thus, despite vortex trapping, Weis-Fogh's original clap-and-fling mechanism 32 still applies, as two strong new downstroke LEVs are generated at the leading edge during fling motion (Fig. 2e). The latter enhance the wing's total circulation and thus lift production during the early phase of the downstroke.
Worldwide, small insects are of significant ecological 45,46 and agricultural 47 importance. Savings in muscle power by recycling of kinetic energy from the wake extends the locomotor capacity of these animals. An increase in locomotor capacity is highly relevant for the abundance of insect populations and their migration 7,8 but also in behavioural contexts, in which an insect requires elevated aerodynamic forces such as during take-off 48 49 , climbing flight 50 , evasive manoeuvring during predation 6 , and chasing flight [51][52][53] . Assuming that insect flight is primarily limited by the production of muscle power and not the production of aerodynamic forces, any increase in locomotor efficiency should provide a benefit for a species flying at elevated power demands 54 . This conclusion is evident considering the low total flight efficiency in insects, ranging from ~ 2.3% to ~ 3.5% 55 .
Our study, moreover, provides an explanation on how flies utilize elastic deformation of their wings for energy harvesting and thus sheds light on the general function of wing elasticity in flapping flight of insects. The latter aspect is currently under extended controversial debate, not only for wing flapping motion in animals 56-60 but also for bioinspired man-made flight devices [61][62][63] .

Data availability
All data is available in the main text or the supplementary materials.