Falling with Style: Bats Perform Complex Aerial Rotations by Adjusting Wing Inertia

The remarkable maneuverability of flying animals results from precise movements of their highly specialized wings. Bats have evolved an impressive capacity to control their flight, in large part due to their ability to modulate wing shape, area, and angle of attack through many independently controlled joints. Bat wings, however, also contain many bones and relatively large muscles, and thus the ratio of bats’ wing mass to their body mass is larger than it is for all other extant flyers. Although the inertia in bat wings would typically be associated with decreased aerial maneuverability, we show that bat maneuvers challenge this notion. We use a model-based tracking algorithm to measure the wing and body kinematics of bats performing complex aerial rotations. Using a minimal model of a bat with only six degrees of kinematic freedom, we show that bats can perform body rolls by selectively retracting one wing during the flapping cycle. We also show that this maneuver does not rely on aerodynamic forces, and furthermore that a fruit fly, with nearly massless wings, would not exhibit this effect. Similar results are shown for a pitching maneuver. Finally, we combine high-resolution kinematics of wing and body movements during landing and falling maneuvers with a 52-degree-of-freedom dynamical model of a bat to show that modulation of wing inertia plays the dominant role in reorienting the bat during landing and falling maneuvers, with minimal contribution from aerodynamic forces. Bats can, therefore, use their wings as multifunctional organs, capable of sophisticated aerodynamic and inertial dynamics not previously observed in other flying animals. This may also have implications for the control of aerial robotic vehicles.     

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.     

Strouhal number for flying and swimming in rhinoceros auklets Cerorhinca monocerata

Alcids propel themselves by flapping wings in air and water that have vastly different densities. We hypothesized that alcids change wing kinematics and maintain Strouhal numbers (St = fA/U, where f is wingbeat frequency, A is the wingbeat amplitude, and U is forward speed) within a certain range, to achieve efficient locomotion during both flying and swimming. We used acceleration and GPS loggers to measure the wingbeat frequency and forward speed of free‐ranging rhinoceros auklets Cerorhinca monocerata during both flying and swimming. We also measured wingbeat amplitude from video footage taken in the wild. On average, wingbeat frequency, forward speed, and wingbeat amplitude were 8.9 Hz, 15.3 m s^?1, and 0.39 m, respectively, during flying, and 2.6 Hz, 1.3 m s^?1, and 0.18 m, respectively, during swimming. The smaller wingbeat amplitude during swimming was achieved by partially folding the wings, while maintaining the dorso‐ventral wingbeat angle. Mean St was 0.23 during flying and 0.36 during swimming. The higher St value for swimming might be related to the higher thrust force required for propulsion in water. Our results suggest that rhinoceros auklets maintain St for both flying and swimming within the range (0.2–0.4) that propulsive efficiency is known to be high and St in both flying specialists and swimming specialists are known to converge.     

Hovering and intermittent flight in birds

Two styles of bird locomotion, hovering and intermittent flight, have great potential to inform future development of autonomous flying vehicles. Hummingbirds are the smallest flying vertebrates, and they are the only birds that can sustain hovering. Their ability to hover is due to their small size, high wingbeat frequency, relatively large margin of mass-specific power available for flight and a suite of anatomical features that include proportionally massive major flight muscles (pectoralis and supracoracoideus) and wing anatomy that enables them to leave their wings extended yet turned over (supinated) during upstroke so that they can generate lift to support their weight. Hummingbirds generate three times more lift during downstroke compared with upstroke, with the disparity due to wing twist during upstroke. Much like insects, hummingbirds exploit unsteady mechanisms during hovering including delayed stall during wing translation that is manifest as a leading-edge vortex (LEV) on the wing and rotational circulation at the end of each half stroke. Intermittent flight is common in small- and medium-sized birds and consists of pauses during which the wings are flexed (bound) or extended (glide). Flap-bounding appears to be an energy-saving style when flying relatively fast, with the production of lift by the body and tail critical to this saving. Flap-gliding is thought to be less costly than continuous flapping during flight at most speeds. Some species are known to shift from flap-gliding at slow speeds to flap-bounding at fast speeds, but there is an upper size limit for the ability to bound (~0.3 kg) and small birds with rounded wings do not use intermittent glides.     

Dragondrop: a novel passive mechanism for aerial righting in the dragonfly

Dragonflies perform dramatic aerial manoeuvres when chasing targets but glide for periods during cruising flights. This makes dragonflies a great system to explore the role of passive stabilizing mechanisms that do not compromise manoeuvrability. We challenged dragonflies by dropping them from selected inverted attitudes and collected 6-degrees-of-freedom aerial recovery kinematics via custom motion capture techniques. From these kinematic data, we performed rigid-body inverse dynamics to reconstruct the forces and torques involved in righting behaviour. We found that inverted dragonflies typically recover themselves with the shortest rotation from the initial body inclination. Additionally, they exhibited a strong tendency to pitch-up with their head leading out of the manoeuvre, despite the lower moment of inertia in the roll axis. Surprisingly, anaesthetized dragonflies could also complete aerial righting reliably. Such passive righting disappeared in recently dead dragonflies but could be partially recovered by waxing their wings to the anaesthetised posture. Our kinematics data, inverse dynamics model and wind-tunnel experiments suggest that the dragonfly''s long abdomen and wing posture generate a rotational tendency and passive attitude recovery mechanism during falling. This work demonstrates an aerodynamically stable body configuration in a flying insect and raises new questions in sensorimotor control for small flying systems.     

Tuning of Strouhal number for high propulsive efficiency accurately predicts how wingbeat frequency and stroke amplitude relate and scale with size and flight speed in birds

The wing kinematics of birds vary systematically with body size, but we still, after several decades of research, lack a clear mechanistic understanding of the aerodynamic selection pressures that shape them. Swimming and flying animals have recently been shown to cruise at Strouhal numbers (St) corresponding to a regime of vortex growth and shedding in which the propulsive efficiency of flapping foils peaks (St approximately fA/U, where f is wingbeat frequency, U is cruising speed and A approximately bsin(theta/2) is stroke amplitude, in which b is wingspan and theta is stroke angle). We show that St is a simple and accurate predictor of wingbeat frequency in birds. The Strouhal numbers of cruising birds have converged on the lower end of the range 0.2 < St < 0.4 associated with high propulsive efficiency. Stroke angle scales as theta approximately 67b-0.24, so wingbeat frequency can be predicted as f approximately St.U/bsin(33.5b-0.24), with St0.21 and St0.25 for direct and intermittent fliers, respectively. This simple aerodynamic model predicts wingbeat frequency better than any other relationship proposed to date, explaining 90% of the observed variance in a sample of 60 bird species. Avian wing kinematics therefore appear to have been tuned by natural selection for high aerodynamic efficiency: physical and physiological constraints upon wing kinematics must be reconsidered in this light.     

On the Estimation of Time Dependent Lift of a European Starling (Sturnus vulgaris) during Flapping Flight

We study the role of unsteady lift in the context of flapping wing bird flight. Both aerodynamicists and biologists have attempted to address this subject, yet it seems that the contribution of unsteady lift still holds many open questions. The current study deals with the estimation of unsteady aerodynamic forces on a freely flying bird through analysis of wingbeat kinematics and near wake flow measurements using time resolved particle image velocimetry. The aerodynamic forces are obtained through two approaches, the unsteady thin airfoil theory and using the momentum equation for viscous flows. The unsteady lift is comprised of circulatory and non-circulatory components. Both approaches are presented over the duration of wingbeat cycles. Using long-time sampling data, several wingbeat cycles have been analyzed in order to cover both the downstroke and upstroke phases. It appears that the unsteady lift varies over the wingbeat cycle emphasizing its contribution to the total lift and its role in power estimations. It is suggested that the circulatory lift component cannot assumed to be negligible and should be considered when estimating lift or power of birds in flapping motion.     

The constraints of body size on aerodynamics and energetics in flying fruit flies: an integrative view

Reynolds number and thus body size may potentially limit aerodynamic force production in flying insects due to relative changes of viscous forces on the beating wings. By comparing four different species of fruit flies similar in shape but with different body mass, we have investigated how small insects cope with changes in fluid mechanical constraints on power requirements for flight and the efficiency with which chemical energy is turned into aerodynamic flight forces. The animals were flown in a flight arena in which stroke kinematics, aerodynamic force production, and carbon dioxide release were measured within the entire working range of the flight motor. The data suggest that during hovering performance mean lift coefficient for flight is higher in smaller animals than in their larger relatives. This result runs counter to predictions based on conventional aerodynamic theory and suggests subtle differences in stroke kinematics between the animals. Estimates in profile power requirements based on high drag coefficient suggest that among all tested species of fruit flies elastic energy storage might not be required to minimize energetic expenditures during flight. Moreover, muscle efficiency significantly increases with increasing body size whereas aerodynamic efficiency tends to decrease with increasing size or Reynolds number. As a consequence of these two opposite trends, total flight efficiency tends to increase only slightly within the 6-fold range of body sizes. Surprisingly, total flight efficiency in fruit flies is broadly independent of different profile power estimates and typically yields mean values between 2–4%.     

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

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

Wing structure and neural encoding jointly determine sensing strategies in insect flight

Animals rely on sensory feedback to generate accurate, reliable movements. In many flying insects, strain-sensitive neurons on the wings provide rapid feedback that is critical for stable flight control. While the impacts of wing structure on aerodynamic performance have been widely studied, the impacts of wing structure on sensing are largely unexplored. In this paper, we show how the structural properties of the wing and encoding by mechanosensory neurons interact to jointly determine optimal sensing strategies and performance. Specifically, we examine how neural sensors can be placed effectively on a flapping wing to detect body rotation about different axes, using a computational wing model with varying flexural stiffness. A small set of mechanosensors, conveying strain information at key locations with a single action potential per wingbeat, enable accurate detection of body rotation. Optimal sensor locations are concentrated at either the wing base or the wing tip, and they transition sharply as a function of both wing stiffness and neural threshold. Moreover, the sensing strategy and performance is robust to both external disturbances and sensor loss. Typically, only five sensors are needed to achieve near-peak accuracy, with a single sensor often providing accuracy well above chance. Our results show that small-amplitude, dynamic signals can be extracted efficiently with spatially and temporally sparse sensors in the context of flight. The demonstrated interaction of wing structure and neural encoding properties points to the importance of understanding each in the context of their joint evolution.     

A modified blade element theory for estimation of forces generated by a beetle-mimicking flapping wing system

We present an unsteady blade element theory (BET) model to estimate the aerodynamic forces produced by a freely flying beetle and a beetle-mimicking flapping wing system. Added mass and rotational forces are included to accommodate the unsteady force. In addition to the aerodynamic forces needed to accurately estimate the time history of the forces, the inertial forces of the wings are also calculated. All of the force components are considered based on the full three-dimensional (3D) motion of the wing. The result obtained by the present BET model is validated with the data which were presented in a reference paper. The difference between the averages of the estimated forces (lift and drag) and the measured forces in the reference is about 5.7%. The BET model is also used to estimate the force produced by a freely flying beetle and a beetle-mimicking flapping wing system. The wing kinematics used in the BET calculation of a real beetle and the flapping wing system are captured using high-speed cameras. The results show that the average estimated vertical force of the beetle is reasonably close to the weight of the beetle, and the average estimated thrust of the beetle-mimicking flapping wing system is in good agreement with the measured value. Our results show that the unsteady lift and drag coefficients measured by Dickinson et al are still useful for relatively higher Reynolds number cases, and the proposed BET can be a good way to estimate the force produced by a flapping wing system.     

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.     

In Vivo Time-Resolved Microtomography Reveals the Mechanics of the Blowfly Flight Motor

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.     

Wing flexibility enhances load-lifting capacity in bumblebees

The effect of wing flexibility on aerodynamic force production has emerged as a central question in insect flight research. However, physical and computational models have yielded conflicting results regarding whether wing deformations enhance or diminish flight forces. By experimentally stiffening the wings of live bumblebees, we demonstrate that wing flexibility affects aerodynamic force production in a natural behavioural context. Bumblebee wings were artificially stiffened in vivo by applying a micro-splint to a single flexible vein joint, and the bees were subjected to load-lifting tests. Bees with stiffened wings showed an 8.6 per cent reduction in maximum vertical aerodynamic force production, which cannot be accounted for by changes in gross wing kinematics, as stroke amplitude and flapping frequency were unchanged. Our results reveal that flexible wing design and the resulting passive deformations enhance vertical force production and load-lifting capacity in bumblebees, locomotory traits with important ecological implications.     

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.     

Kinematic and aerodynamic aspects of ultrasound-induced negative phonotaxis in flying Australian field crickets (Teleogryllus oceanicus)

Negative phonotaxis is elicited in flying Australian field crickets, Teleogryllus oceanicus, by ultrasonic stimuli. Using upright tethered flying crickets, we quantitatively examined several kinematic and aerodynamic factors which accompany ultrasound-induced negative phonotactic behavior. These factors included three kinematic effects (hindwing wingbeat frequency, hindwing elevation and depression, and forewing tilt) and two aerodynamic effects (pitch and roll). 1. Within two cycles following a 20 dB suprathreshold ultrasonic stimulus, the hindwing wingbeat frequency increases by 3-4 Hz and outlasts the duration of the stimulus. Moreover, the relationship between the maximum increase in wingbeat frequency and stimulus intensity is a two-stage response. At lower suprathreshold intensities the maximum wingbeat frequency increases by approximately 1 Hz; but, at higher intensities, the maximum increase is 3-4 Hz. 2. The maximum hindwing elevation angle increases on the side ipsilateral to the stimulus, while there was no change in upstroke elevation on the side contralateral to the stimulus. 3. An ultrasonic stimulus affects forewing tilt such that the forewings bank into the turn. The forewing ipsilateral to the stimulus tilts upward while the contralateral forewing tilts downward. Both the ipsilateral and contralateral forewing tilt change linearly with stimulus intensity. 4. Flying crickets pitch downward when presented with a laterally located ultrasonic stimulus. Amputation experiments indicate that both the fore and hindwings contribute to changes in pitch but the pitch response in an intact cricket exceeds the simple addition of fore and hindwing contributions. With the speaker placed above or below the flying cricket, the change is downward or upward, respectively.(ABSTRACT TRUNCATED AT 250 WORDS)     

Movements of the hindwings ofLocusta migratoria,measured with miniature coils

Summary Tethered migratory locusts were induced to fly in an airstream for hours at a time, carrying on their extremely delicate hindwings miniature induction coils by which the hindwing movements were recorded in three dimensions.The two coils were mounted at right angles to one another on the central field of the hindwing, which is in close aerodynamic contact with the forewing. Each coil emitted three signals to define the components of a 3-dimensional vector. The movements of the central field can be described completely by the rotations of the two vectors. The main component of the hindwing movement thus becomes accessible to detailed kinematic analysis (Figs. 2, 3).The results obtained with this inductive method are consistent with the few published data based on photogrammetric samples of the movement.The various forms of movement can all be observed during the flight experiment. The movement spectrum is very broad even in an undisturbed flying animal (Figs. 4, 5).Various wingbeat parameters were calculated, including oscillation period, the durations of upstroke and downstroke, and their ratio (Fig. 6).Simultaneous measurement of the movements of the fore- and hindwings has provided the first documentation of the varying interactions of the wings on side of the body during a long flight. Even small changes in the relative positions of the two wings are measurable (Fig. 7).     

Upstroke wing flexion and the inertial cost of bat flight

Flying vertebrates change the shapes of their wings during the upstroke, thereby decreasing wing surface area and bringing the wings closer to the body than during downstroke. These, and other wing deformations, might reduce the inertial cost of the upstroke compared with what it would be if the wings remained fully extended. However, wing deformations themselves entail energetic costs that could exceed any inertial energy savings. Using a model that incorporates detailed three-dimensional wing kinematics, we estimated the inertial cost of flapping flight for six bat species spanning a 40-fold range of body masses. We estimate that folding and unfolding comprises roughly 44 per cent of the inertial cost, but that the total inertial cost is only approximately 65 per cent of what it would be if the wing remained extended and rigid throughout the wingbeat cycle. Folding and unfolding occurred mostly during the upstroke; hence, our model suggests inertial cost of the upstroke is not less than that of downstroke. The cost of accelerating the metacarpals and phalanges accounted for around 44 per cent of inertial costs, although those elements constitute only 12 per cent of wing weight. This highlights the energetic benefit afforded to bats by the decreased mineralization of the distal wing bones.     

Simulating avian wingbeat kinematics

Inverse dynamics methods are used to simulate avian wingbeats in varying flight conditions. A geometrically scalable multi-segment bird model is constructed, and optimisation techniques are employed to determine segment motions that generate desired aerodynamic force coefficients with minimal mechanical power output. The results show that wingbeat kinematics vary gradually with changes in cruise speed, which is consistent with experimental data. Optimised solutions for cruising flight of the pigeon suggest that upstroke wing retraction is used as a method of saving energy. Analysis of the aerodynamic force coefficient variation in high and low speed cruise leads to the proposal that a suitable gait metric should include both thrust and lift generation during each half-stroke.     

Numerical investigation of the aerodynamic characteristics of a hovering Coleopteran insect

The aerodynamic characteristics of the Coleopteran beetle species Epilachna quadricollis, a species with flexible hind wings and stiff elytra (fore wings), are investigated in terms of hovering flight. The flapping wing kinematics of the Coleopteran insect are modeled through experimental observations with a digital high-speed camera and curve fitting from an ideal harmonic kinematics model. This model numerically simulates flight by estimating a cross section of the wing as a two-dimensional elliptical plane. There is currently no detailed study on the role of the elytron or how the elytron-hind wing interaction affects aerodynamic performance. In the case of hovering flight, the relatively small vertical or horizontal forces generated by the elytron suggest that the elytron makes no significant contribution to aerodynamic force.