Kinematic compensation for wing loss in flying damselflies

Flying insects can tolerate substantial wing wear before their ability to fly is entirely compromised. In order to keep flying with damaged wings, the entire flight apparatus needs to adjust its action to compensate for the reduced aerodynamic force and to balance the asymmetries in area and shape of the damaged wings. While several studies have shown that damaged wings change their flapping kinematics in response to partial loss of wing area, it is unclear how, in insects with four separate wings, the remaining three wings compensate for the loss of a fourth wing. We used high-speed video of flying blue-tailed damselflies (Ischnura elegans) to identify the wingbeat kinematics of the two wing pairs and compared it to the flapping kinematics after one of the hindwings was artificially removed. The insects remained capable of flying and precise maneuvering using only three wings. To compensate for the reduction in lift, they increased flapping frequency by 18 ± 15.4% on average. To achieve steady straight flight, the remaining intact hindwing reduced its flapping amplitude while the forewings changed their stroke plane angle so that the forewing of the manipulated side flapped at a shallower stroke plane angle. In addition, the angular position of the stroke reversal points became asymmetrical. When the wingbeat amplitude and frequency of the three wings were used as input in a simple aerodynamic model, the estimation of total aerodynamic force was not significantly different (paired t-test, p = 0.73) from the force produced by the four wings during normal flight. Thus, the removal of one wing resulted in adjustments of the motions of the remaining three wings, exemplifying the precision and plasticity of coordination between the operational wings. Such coordination is vital for precise maneuvering during normal flight but it also provides the means to maintain flight when some of the wings are severely damaged.     

Flight reconstruction of two European enantiornithines (Aves,Pygostylia) and the achievement of bounding flight in Early Cretaceous birds

Intermittent flight through flap‐gliding (alternating flapping phases and gliding phases with spread wings) or bounding (flapping and ballistic phases with wings folded against the body) are strategies to optimize aerial efficiency which are commonly used among small birds today. The broad morphological disparity of Mesozoic birds suggests that a range of aerial strategies could have evolved early in avian evolution. Based on biomechanics and aerodynamic theory, this study reconstructs the flight modes of two small enantiornithines from the Lower Cretaceous fossil site of Las Hoyas (Spain): Concornis lacustris and Eoalulavis hoyasi. Our results show that the short length of their wings in relation to their body masses were suitable for flying through strict flapping and intermittent bounds, but not through facultative glides. Aerodynamic models indicate that the power margins of these birds were sufficient to sustain bounding flight. Our results thus suggest that C. lacustris and E. hoyasi would have increased aerial efficiency through bounding flight, just as many small passerines and woodpeckers do today. Intermittent bounding appears to have evolved early in the evolutionary history of birds, at least 126 million years ago.     

Aerodynamic Interactions Between Wing and Body of a Model Insect in Forward Flight and Maneuvers

The aerodynamic interactions between the body and the wings of a model insect in forward flight and maneuvers are studied using the method of numerically solving the Navier-Stokes equations over moving overset grids. Three cases are considered, including a complete insect, wing pair only and body only. By comparing the results of these cases, the interaction effect between the body and the wing pair can be identified. The changes in the force and moment coefficients of the wing pair due to the presence of the body are less than 4.5% of the mean vertical force coefficient of the model insect; the changes in the aerodynamic force coefficients of the body due to the presence of the wings are less than 5.0% of the mean vertical force coefficient of the model insect. The results of this paper indicate that in studying the aerodynamics and flight dynamics of a flapping insect in forward flight or maneuver, separately computing (or measuring) the aerodynamic forces and moments on the wing pair and on the body could be a good approximation.     

Coordination of wingbeat and respiration in the Canada goose. I. Passive wing flapping.

The effects of passive wing flapping on respiratory pattern were examined in decerebrate Canada geese. The birds were suspended dorsally with two spine clamps while the extended wings were continuously moved up and down with a device designed to reproduce actual wing flapping. Passive wing motion entrained respiration over limited ranges by both increasing and decreasing the respiratory period relative to rest. All ratios of wingbeat frequency to respiratory frequency seen during free flight (Soc. Neurosci. Abstr. 15: 391, 1989) were produced during passive wing flapping. In addition, the phase relationship between wingbeat frequency and respiratory frequency, inspiration starting near the peak of wing upstroke, was similar to that seen during free flight and was unaffected by perturbations of the wing-flapping cycle. Removal of all afferent activity from the wings did not affect the ability of continuous passive wing movement to entrain respiration. However, feedback from the wings was required to produce rapid within-breath shifts in the respiratory period in response to single wing flaps. In conclusion, although feedback from the chest wall/lung may be more important in producing entrainment during the stable conditions of passive wing flapping, wing-related feedback may be critically involved in mediating the rapid adjustments in respiratory pattern required to maintain coordination between wing and respiratory movements during free flight.     

A two-dimensional aerodynamic model of freely flying insects

Possible free flights of insects by a single flapping motion were studied. It is well-known that insects utilize vortices generated by flapping, by which they generate larger lift than that evaluated by the ordinary aerodynamic theory. However, the effect of the motion of the center of mass (CM) of the insect on its flight has not been clarified. To clarify the effect, numerical simulation was performed for a simple model considering the coupling between the vertical CM motion and the separation vortices generated by flapping wing. As a result, it is shown that the flapping flight has the following interesting features. First, despite a single flapping motion, the model exhibits two types of flapping flight: a steady flight in which the CM velocity oscillates and a wandering flight in which the CM velocity varies irregularly. These two types of flights are selected by the initial conditions even when all the parameters are the same. Second, at a certain critical parameter value, the steady flight loses its stability and undergoes an abrupt transition to the wandering flight. Interestingly, at this critical value, the steady flight can be regarded as hovering. The possible flights are analyzed in terms of bifurcation, and the bifurcation structure is qualitatively explained based on a simple assumption. These results suggest the significance of the effect of CM motion.     

A wing-assisted running robot and implications for avian flight evolution

DASH+Wings is a small hexapedal winged robot that uses flapping wings to increase its locomotion capabilities. To examine the effects of flapping wings, multiple experimental controls for the same locomotor platform are provided by wing removal, by the use of inertially similar lateral spars, and by passive rather than actively flapping wings. We used accelerometers and high-speed cameras to measure the performance of this hybrid robot in both horizontal running and while ascending inclines. To examine consequences of wing flapping for aerial performance, we measured lift and drag forces on the robot at constant airspeeds and body orientations in a wind tunnel; we also determined equilibrium glide performance in free flight. The addition of flapping wings increased the maximum horizontal running speed from 0.68 to 1.29 m s?1, and also increased the maximum incline angle of ascent from 5.6° to 16.9°. Free flight measurements show a decrease of 10.3° in equilibrium glide slope between the flapping and gliding robot. In air, flapping improved the mean lift:drag ratio of the robot compared to gliding at all measured body orientations and airspeeds. Low-amplitude wing flapping thus provides advantages in both cursorial and aerial locomotion. We note that current support for the diverse theories of avian flight origins derive from limited fossil evidence, the adult behavior of extant flying birds, and developmental stages of already volant taxa. By contrast, addition of wings to a cursorial robot allows direct evaluation of the consequences of wing flapping for locomotor performance in both running and flying.     

Wing‐beat characteristics of birds recorded with tracking radar and cine camera

This study presents wing‐beat frequency data measured mainly by radar, complemented by video and cinematic recordings, for 153 western Palaearctic and two African species. Data on a further 45 Palaearctic species from other sources are provided in an electronic appendix. For 41 species with passerine‐type flight, the duration of flapping and pausing phases is given. The graphical presentations of frequency ranges and wing‐beat patterns show within‐species variation and allow easy comparison between species, taxonomic groups and types of flight. Wing‐beat frequency is described by Pennycuick (J. Exp. Biol. 2001; 204: 3283–3294) as a function of body‐mass, wing‐span, wing‐area, gravity and air density; for birds with passerine‐type flight the power‐fraction has also to be considered. We tested Pennycuick’s general allometric model and estimated the coefficients based on our data. The general model explained a high proportion of variation in wing‐beat frequency and the coefficients differed only slightly from Pennycuick’s original values. Modelling continuous‐flapping flyers alone resulted in coefficients not different from those predicted (within 95% intervals). Doing so for passerine‐type birds resulted in a model with non‐significant contributions of body‐mass and wing‐span to the model. This was mainly due to the very high correlation between body‐mass, wing‐span and wing‐area, revealing similar relative scaling properties within this flight type. However, wing‐beat frequency increased less than expected with respect to power‐fraction, indicating that the drop in flight level during the non‐flapping phases, compensated by the factor (g/q)^0.5 in Pennycuick’s model, is smaller than presumed. This may be due to lift produced by the body during the bounding phase or by only partial folding of the wings.     

Biomechanics and biomimetics in insect-inspired flight systems

Insect- and bird-size drones—micro air vehicles (MAV) that can perform autonomous flight in natural and man-made environments are now an active and well-integrated research area. MAVs normally operate at a low speed in a Reynolds number regime of 10⁴–10⁵ or lower, in which most flying animals of insects, birds and bats fly, and encounter unconventional challenges in generating sufficient aerodynamic forces to stay airborne and in controlling flight autonomy to achieve complex manoeuvres. Flying insects that power and control flight by flapping wings are capable of sophisticated aerodynamic force production and precise, agile manoeuvring, through an integrated system consisting of wings to generate aerodynamic force, muscles to move the wings and a control system to modulate power output from the muscles. In this article, we give a selective review on the state of the art of biomechanics in bioinspired flight systems in terms of flapping and flexible wing aerodynamics, flight dynamics and stability, passive and active mechanisms in stabilization and control, as well as flapping flight in unsteady environments. We further highlight recent advances in biomimetics of flapping-wing MAVs with a specific focus on insect-inspired wing design and fabrication, as well as sensing systems.This article is part of the themed issue ‘Moving in a moving medium: new perspectives on flight’.     

Computation of Unsteady Flow Past a Biomimetic Fin

The unsteady hydrodynamics of a biomimetic fin attached to a cylindrical body has been studied numerically using a computational fluid dynamic (CFD) simulator based on an in-house solver of the Navier-Stokes equations, combined with a recently developed multi-block, overset grid method. The fin-body CFD model is based on a mechanical pectoral fin device, which consists of a cylindrical body and an asymmetric fin and can mimic flapping, rowing and feathering motions of the pectoral fins in fishes. First the multi-block, overset grid method incorporated into the NS solver was verified through an extensive study of unsteady flows past a single fin undergoing rowing and feathering motion. Then unsteady flows past the biomimetic fin-body model undergoing the same motions were computed and compared with the measurements of forces of the mechanical pectoral fin, which shows good agreement in both time-varying and time-averaged hydrodynamic forces. The relationship between force generation and vortex dynamics points to the importance of the match in fin kinematics between power and recovery strokes and implies that an optimal selection of parameters of phase lags between and amplitudes of rowing and feathering motions can improve the performance of labriform propulsion in terms of either maximum force generation or minimum mechanical power.     

How Could Beetle＇s Elytra Support Their Own Weight during Forward Flight？

The aerodynamic role of the elytra during a beetle＇s flapping motion is not well-elucidated, although it is well-recognized that the evolution of elytra has been a key in the success of coleopteran insects due to their protective function. An experimental study on wing kinematics reveals that for almost concurrent flapping with the hind wings, the flapping angle of the elytra is 5 times smaller than that of the hind wings. Then, we explore the aerodynamic forces on elytra in free forward flight with and without an effect of elytron-hind wing interaction by three-dimensional numerical simulation. The numerical results show that vertical force generated by the elytra without interaction is not sufficient to support even its own weight. However, the elytron-hind wing interaction improves the vertical force on the elytra up to 80%; thus, the total vertical force could fully support its own weight. The interaction slightly increases the vertical force on the hind wind by 6% as well.     

Two-and Three-Dimensional Simulations of Beetle Hind Wing Flapping during Free Forward Flight

Aerodynamic characteristic of the beetle, Trypoxylus dichotomus, which has a pair of elytra (forewings) and hind wings, is numerically investigated. Based on the experimental results of wing kinematics, two-dimensional (2D) and three-dimensional (3D) computational fluid dynamic simulations were carried out to reveal aerodynamic performance of the hind wing. The roles of the spiral Leading Edge Vortex (LEV) and the spanwise flow were clarified by comparing 2D and 3D simulations. Mainly due to pitching down of chord line during downstroke in highly inclined stroke plane, relatively high averaged thrust was produced in the free forward flight of the beetle. The effects of the local corrugation and the camber variation were also investigated for the beetle's hind wings. Our results show that the camber variation plays a significant role in improving both lift and thrust in the flapping. On the other hand, the local corrugation pattern has no significant effect on the aerodynamic force due to large angle of attack during flapping.     

Periodic Tail Motion Linked to Wing Motion Affects the Longitudinal Stability of Ornithopter Flight

During slow level flight of a pigeon,a caudal muscle involved in tail movement,the levator caudae pars vertebralis,is activated at a particular phase with the pectoralis wing muscle.Inspired by mechanisms for the control of stability in flying animals,especially the role of the tail in avian flight,we investigated how periodic tail motion linked to motion of the wings affects the longitudinal stability of omithopter flight.This was achieved by using an integrative ornithopter flight simulator that included aeroelastic behaviour of the flexible wings and tail.Trim flight trajectories of the simulated ornithopter model were calculated by time integration of the nonlinear equations of a flexible multi-body dynamics coupled with a semi-empirical flapping-wing and tail aerodynamic models.The unique trim flight characteristics of ornithopter,Limit-Cycle Oscillation,were found under the sets of wingbeat frequency and tail elevation angle,and the appropriate phase angle of tail motion was determined by parameter studies minimizing the amplitude of the oscillations.The numerical simulation results show that tail actuation synchronized with wing motion suppresses the oscillation of body pitch angle over a wide range of wingbeat frequencies.     

Avian furcula morphology may indicate relationships of flight requirements among birds

This study examined furcula (wishbone) shape relative to flight requirements. The furculae from 53 museum specimens in eight orders were measured: 1) three-dimensional shape (SR) as indicated by the ratio of the direct distance between the synostosis interclavicularis and the ligamentous attachment of one of its clavicles to the actual length of the clavicle between those same two points, and 2) curvature within the primary plane (LR) as indicated by the ratio of the length of the clavicle to the sum of the orthogonal distances between the same points using a projected image. Canonical discriminant analysis of these ratios placed the individuals into a) one of four general flight categories and b) one of eight taxonomic orders. The four flight categories were defined as: i) soaring with no flapping, ii) flapping with no soaring, iii) subaqueous (i.e., all wingbeats taking place under water), and iv) partial subaqueous (i.e., wingbeats used for both aerial and submerged flapping). The error rate for placement of the specimens in flight categories was only 26.4%, about half of the error rate for placement in taxonomic orders (51.3%). Subaqueous fliers (penguins, great auks) have furculae that are the most V-shaped. Partial subaqueous fliers (alcids, storm petrels) have furculae that are more U-shaped than the subaqueous fliers but more V-shaped than the aerial flapping fliers. The partial subaqueous fliers have furculae that are also the most anteriorly curved, possibly increasing protraction capability by changing the angle of applied force and increasing attachment area for the origin of the sternobrachialis pectoralis. The increased protraction capability can counteract profile drag, which is greater in water than in air due to the greater density of water. Soaring birds have furculae that are more U-shaped or circular than those of flapping birds and have the smallest range of variation. These results indicate that the shape of the furcula is functionally related to general differences in flight requirements and may be used to infer relationships of these requirements among birds.     

Design and Demonstration of Insect Mimicking Foldable Artificial Wing Using Four-Bar Linkage Systems

In this work, we develop an artificial foldable wing that mimics the hind wing of a beetle （Allomyrina dichotoma）. In real flight, the beetle unfolds forewings and hind wings, and maintains the unfolded configuration unless it is exhausted. The artificial wing has to be able to maintain a fully unfolded configuration while flapping at a desirable flapping frequency. The artificial foldable hind wing developed in this work is based on two four-bar linkages which adapt the behaviors of the beetle＇s hind wing. The four-bar-linkages are designed to mimic rotational motion of the wing base and the vein folding/unfolding motion of the beetle＇s hind wing. The behavior of the artificial wings, which are installed in a flapping-wing system, is observed using a high-speed camera. The observation shows that the wing could maintain a fully unfolded configuration during flapping motion. A series of thrust measurements are also conducted to estimate the force generated by the flapping-wing system with foldable artificial wings. Although the artificial foldable wings give added burden to the flapping-wing system because of its weight, the thrust measurement results show that the flapping-wing system could still generate reasonable thrust.     

Perturbation analysis of 6DoF flight dynamics and passive dynamic stability of hovering fruit fly Drosophila melanogaster

Insects exhibit exquisite control of their flapping flight, capable of performing precise stability and steering maneuverability. Here we develop an integrated computational model to investigate flight dynamics of insect hovering based on coupling the equations of 6 degree of freedom (6DoF) motion with the Navier-Stokes (NS) equations. Unsteady aerodynamics is resolved by using a biology-inspired dynamic flight simulator that integrates models of realistic wing-body morphology and kinematics, and a NS solver. We further develop a dynamic model to solve the rigid body equations of 6DoF motion by using a 4th-order Runge-Kutta method. In this model, instantaneous forces and moments based on the NS-solutions are represented in terms of Fourier series. With this model, we perform a systematic simulation-based analysis on the passive dynamic stability of a hovering fruit fly, Drosophila melanogaster, with a specific focus on responses of state variables to six one-directional perturbation conditions during latency period. Our results reveal that the flight dynamics of fruit fly hovering does not have a straightforward dynamic stability in a conventional sense that perturbations damp out in a manner of monotonous convergence. However, it is found to exist a transient interval containing an initial converging response observed for all the six perturbation variables and a terminal instability that at least one state variable subsequently tends to diverge after several wing beat cycles. Furthermore, our results illustrate that a fruit fly does have sufficient time to apply some active mediation to sustain a steady hovering before losing body attitudes.     

Within-wingbeat damping: dynamics of continuous free-flight yaw turns in Manduca sexta

Free-flight body dynamics and wing kinematics were collected from recordings of continuous, low-speed, multi-wingbeat yaw turns in hawkmoths (Manduca sexta) using stereo videography. These data were used to examine the effects of rotational damping arising from interactions between the body rotation and flapping motion (flapping counter-torque, FCT) on continuous turning. The moths were found to accelerate during downstroke, then decelerate during upstroke by an amount consistent with FCT damping. Wing kinematics related to turning were then analysed in a simulation of hawkmoth flight; results were consistent with the observed acceleration–deceleration pattern. However, an alternative wing kinematic which produced more continuous and less damped accelerations was found in the simulation. These findings demonstrate that (i) FCT damping is detectable in the dynamics of continuously turning animals and (ii) FCT-reducing kinematics do exist but were not employed by turning moths, possibly because within-wingbeat damping simplifies control of turning by allowing control systems to target angular velocity rather than acceleration.     

Skipping flights in Ypthima butterflies (Lepidoptera: Nymphalidae)

The skipping flight patterns of three species of Ypthima (Lepidoptera: Nymphalidae) were analyzed using high‐speed video recordings to clarify how wings move and how driving forces are produced. All three species showed a flight pattern that includes a pause that accounts for about 50% of a flap cycle when their wings completely close after each upstroke. The observed pause causes the “skipping” flight trajectory based on the clap–fling mechanism. Pause duration was correlated with upstroke wing motion, suggesting the contribution of the latter to a long pause duration. This is also supported by the temporal relationship between the wing and body motions. The aerodynamic power necessary for the pause flight was calculated for the three species.     

Flexible Wing Kinematics of a Free-Flying Beetle (Rhinoceros Beetle Trypoxylus Dichotomus)

Detailed 3-Dimensional (3D) wing kinematics was experimentally presented in free flight of a beetle,Trypoxylus dichotomus,which has a pair of elytra (forewings) and flexible hind wings.The kinematic parameters such as the wing tip trajectory,angle of attack and camber deformation were obtained from a 3D reconstruction technique that involves the use of two synchronized high-speed cameras to digitize various points marked on the wings.Our data showed outstanding characteristics of deformation and flexibility of the beetle's hind wing compared with other measured insects,especially in the chordwise and spanwise directions during flapping motion.The hind wing produced 16％ maximum positive camber deformation during the downstroke.It also experienced twisted shape showing large variation of the angle of attack from the root to the tip during the upstroke.     

Pitching Moment Generation in an Insect-Mimicking Flapping-Wing System

Unlike birds, insects lack control surfaces at the tail and hence most insects modify their wing kinematics to produce control forces or moments while flapping their wings. Change of the flapping angle range is one of the ways to modify wing kinematics, resulting in relocation of the mean Aerodynamic force Center （mean AC） and finally creating control moments. In an attempt to mimic this feature, we developed a flapping-wing system that generates a desired pitching moment during flap- ping-wing motion. The system comprises a flapping mechanism that creates a large and symmetric flapping motion in a pair of wings, a flapping angle change mechanism that modifies the flapping angle range, artificial wings, and a power source. From the measured wing kinematics, we have found that the flapping-wing system can properly modify the flapping angle ranges. The measured pitching moments show that the flapping-wing system generates a pitching moment in a desired direction by shifting the flapping angle range. We also demonstrated that the system can in practice change the longitudinal attitude by generating a nonzero pitching moment.     

Flight mode affects allometry of migration range in birds

Billions of birds migrate to exploit seasonally available resources. The ranges of migration vary greatly among species, but the underlying mechanisms are poorly understood. I hypothesise that flight mode (flapping or soaring) and body mass affect migration range through their influence on flight energetics. Here, I compiled the tracks of migratory birds (196 species, weighing 12–10 350 g) recorded by electronic tags in the last few decades. In flapping birds, migration ranges decreased with body mass, as predicted from rapidly increasing flight cost with increasing body mass. The species with higher aspect ratio and lower wing loading had larger migration ranges. In soaring birds, migration ranges were mass‐independent and larger than those of flapping birds, reflecting their low flight costs irrespective of body mass. This study demonstrates that many animal‐tracking studies are now available to explore the general patterns and the underlying mechanisms of animal migration.