Wingbeat kinematics and motor control of yaw turns in Anna's hummingbirds (Calypte anna)

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.

Hummingbirds use distinct control strategies for forward and hovering flight

The detection of optic flow is important for generating optomotor responses to mediate retinal image stabilization, and it can also be used during ongoing locomotion for centring and velocity control. Previous work in hummingbirds has separately examined the roles of optic flow during hovering and when centring through a narrow passage during forward flight. To develop a hypothesis for the visual control of forward flight velocity, we examined the behaviour of hummingbirds in a flight tunnel where optic flow could be systematically manipulated. In all treatments, the animals exhibited periods of forward flight interspersed with bouts of spontaneous hovering. Hummingbirds flew fastest when they had a reliable signal of optic flow. All optic flow manipulations caused slower flight, suggesting that hummingbirds had an expected optic flow magnitude that was disrupted. In addition, upward and downward optic flow drove optomotor responses for maintaining altitude during forward flight. When hummingbirds made voluntary transitions to hovering, optomotor responses were observed to all directions. Collectively, these results are consistent with hummingbirds controlling flight speed via mechanisms that use an internal forward model to predict expected optic flow whereas flight altitude and hovering position are controlled more directly by sensory feedback from the environment.

Sideways maneuvers enable narrow aperture negotiation by free-flying hummingbirds

Many birds routinely fly fast through dense vegetation characterized by variably sized structures and voids. Successfully negotiating these cluttered environments requires maneuvering through narrow constrictions between obstacles. We show that Anna's hummingbirds (Calypte anna) can negotiate apertures less than one wingspan in diameter using a novel sideways maneuver that incorporates continuous, bilaterally asymmetric wing motions. Crucially, this maneuver allows hummingbirds to continue flapping as they negotiate the constriction. Even smaller openings are negotiated via a faster ballistic trajectory characterized by tucked and thus non-flapping wings, which reduces force production and increases descent rate relative to the asymmetric technique. Hummingbirds progressively shift to the swept method as they perform hundreds of consecutive transits, suggesting increased locomotor performance with task familiarity. Initial use of the slower asymmetric transit technique may allow birds to better assess upcoming obstacles and voids, thereby reducing the likelihood of subsequent collisions. Repeated disruptions of normal wing kinematics as birds negotiate tight apertures may determine the limits of flight performance in structurally complex environments. These strategies for aperture transit and associated flight trajectories can inform designs and algorithms for small aerial vehicles flying within cluttered environments.

From the eye to the wing: neural circuits for transforming optic flow into motor output in avian flight

Avian flight is guided by optic flow-the movement across the retina of images of surfaces and edges in the environment due to self-motion. In all vertebrates, there is a short pathway for optic flow information to reach pre-motor areas: retinal-recipient regions in the midbrain encode optic flow, which is then sent to the cerebellum. One well-known role for optic flow pathways to the cerebellum is the control of stabilizing eye movements (the optokinetic response). However, the role of this pathway in controlling locomotion is less well understood. Electrophysiological and tract tracing studies are revealing the functional connectivity of a more elaborate circuit through the avian cerebellum, which integrates optic flow with other sensory signals. Here we review the research supporting this framework and identify the cerebellar output centres, the lateral (CbL) and medial (CbM) cerebellar nuclei, as two key nodes with potentially distinct roles in flight control. The CbM receives bilateral optic flow information and projects to sites in the brainstem that suggest a primary role for flight control over time, such as during forward flight. The CbL receives monocular optic flow and other types of visual information. This site provides feedback to sensory areas throughout the brain and has a strong projection the nucleus ruber, which is known to have a dominant role in forelimb muscle control. This arrangement suggests primary roles for the CbL in the control of wing morphing and for rapid maneuvers.

Musculoskeletal wing-actuation model of hummingbirds predicts diverse effects of primary flight muscles in hovering flight

Hummingbirds have evolved to hover and manoeuvre with exceptional flight control. This is enabled by their musculoskeletal system that successfully exploits the agile motion of flapping wings. Here, we synthesize existing empirical and modelling data to generate novel hypotheses for principles of hummingbird wing actuation. These may help guide future experimental work and provide insights into the evolution and robotic emulation of hummingbird flight. We develop a functional model of the hummingbird musculoskeletal system, which predicts instantaneous, three-dimensional torque produced by primary (pectoralis and supracoracoideus) and combined secondary muscles. The model also predicts primary muscle contractile behaviour, including stress, strain, elasticity and work. Results suggest that the primary muscles (i.e. the flight 'engine') function as diverse effectors, as they do not simply power the stroke, but also actively deviate and pitch the wing with comparable actuation torque. The results also suggest that the secondary muscles produce controlled-tightening effects by acting against primary muscles in deviation and pitching. The diverse effects of the pectoralis are associated with the evolution of a comparatively enormous bicipital crest on the humerus.

Bio-inspired flapping wing robots with foldable or deformable wings: a review

Traditional flapping-wing robots (FWRs) obtain lift and thrust by relying on the passive deformation of their wings which cannot actively fold or deform. In contrast, flying creatures such as birds, bats, and insects can maneuver agilely through active folding or deforming their wings. Researchers have developed many bio-inspired foldable or deformable wings (FDWs) imitating the wings of flying creatures. The foldable wings refer to the wings like the creatures' wings that can fold in an orderly manner close to their bodies. Such wings have scattered feathers or distinct creases that can be stacked and folded to reduce the body envelope, which in nature is beneficial for these animals to prevent wing damage and ensure agility in crossing bushes. The deformable wings refer to the active deformation of the wings using active driving mechanisms and the passive deformation under the aerodynamic force, which functionally imitates the excellent hydrodynamic performance of the deformable body and wings of the creatures. However, the shape and external profile changes of deformable wings tend to be much smaller than that of folding wings. FDWs enable the FWRs to improve flight degree of flexibility, maneuverability, and efficiency and reduce flight energy consumption. However, FDWs still need to be studied, and a comprehensive review of the state-of-the-art progress of FDWs in FWR design is lacking. This paper analyzes the wing folding and deformation mechanisms of the creatures and reviews the latest progress of FWRs with FDWs. Furthermore, we summarize the current limitations and propose future directions in FDW design, which could help researchers to develop better FWRs for safe maneuvering in obstacle-dense environments.

Wing Kinematics and Unsteady Aerodynamics of a Hummingbird Pure Yawing Maneuver

As one of few animals with the capability to execute agile yawing maneuvers, it is quite desirable to take inspiration from hummingbird flight aerodynamics. To understand the wing and body kinematics and associated aerodynamics of a hummingbird performing a free yawing maneuver, a crucial step in mimicking the biological motion in robotic systems, we paired accurate digital reconstruction techniques with high-fidelity computational fluid dynamics (CFD) simulations. Results of the body and wing kinematics reveal that to achieve the pure yaw maneuver, the hummingbird utilizes very little body pitching, rolling, vertical, or horizontal motion. Wing angle of incidence, stroke, and twist angles are found to be higher for the inner wing (IW) than the outer wing (OW). Unsteady aerodynamic calculations reveal that drag-based asymmetric force generation during the downstroke (DS) and upstroke (US) serves to control the speed of the turn, a characteristic that allows for great maneuvering precision. A dual-loop vortex formation during each half-stroke is found to contribute to asymmetric drag production. Wake analysis revealed that asymmetric wing kinematics led to leading-edge vortex strength differences of around 59% between the IW and OW. Finally, analysis of the role of wing flexibility revealed that flexibility is essential for generating the large torque necessary for completing the turn as well as producing sufficient lift for weight support.

Birds both avoid and control collisions by harnessing visually guided force vectoring

Birds frequently manoeuvre around plant clutter in complex-structured habitats. To understand how they rapidly negotiate obstacles while flying between branches, we measured how foraging Pacific parrotlets avoid horizontal strings obstructing their preferred flight path. Informed by visual cues, the birds redirect forces with their legs and wings to manoeuvre around the obstacle and make a controlled collision with the goal perch. The birds accomplish aerodynamic force vectoring by adjusting their body pitch, stroke plane angle and lift-to-drag ratios beat-by-beat, resulting in a range of about 100° relative to the horizontal plane. The key role of drag in force vectoring revises earlier ideas on how the avian stroke plane and body angle correspond to aerodynamic force direction-providing new mechanistic insight into avian manoeuvring-and how the evolution of flight may have relied on harnessing drag.

Effect of Ducted Multi-Propeller Configuration on Aerodynamic Performance in Quadrotor Drone

Motivated by a bioinspired optimal aerodynamic design of a multi-propeller configuration, here we propose a ducted multi-propeller design to explore the improvement of lift force production and FM efficiency in quadrotor drones through optimizing the ducted multi-propeller configuration. We first conducted a CFD-based study to explore a high-performance duct morphology in a ducted single-propeller model in terms of aerodynamic performance and duct volume. The effect of a ducted multi-propeller configuration on aerodynamic performance is then investigated in terms of the tip distance and the height difference of propellers under a hovering state. Our results indicate that the tip distance-induced interactions have a noticeable effect in impairing the lift force production and FM efficiency but are limited to small tip distances, whereas the height difference-induced interactions have an impact on enhancing the aerodynamic performance over a certain range. An optimal ducted multi-propeller configuration with a minimal tip distance and an appropriate height difference was further examined through a combination of CFD simulations and a surrogate model in a broad-parameter space, which enables a significant improvement in both lift force production and FM efficiency for the multirotor, and thus provides a potential optimal design for ducted multirotor UAVs.

Individual variation and the biomechanics of maneuvering flight in hummingbirds

An animal's maneuverability will determine the outcome of many of its most important interactions. A common approach to studying maneuverability is to force the animal to perform a specific maneuver or to try to elicit maximal performance. Recently, the availability of wider-field tracking technology has allowed for high-throughput measurements of voluntary behavior, an approach that produces large volumes of data. Here, we show how these data allow for measures of inter-individual variation that are necessary to evaluate how performance depends on other traits, both within and among species. We use simulated data to illustrate best practices when sampling a large number of voluntary maneuvers. Our results show how the sample average can be the best measure of inter-individual variation, whereas the sample maximum is neither repeatable nor a useful metric of the true variation among individuals. Our studies with flying hummingbirds reveal that their maneuvers fall into three major categories: simple translations, simple rotations and complex turns. Simple maneuvers are largely governed by distinct morphological and/or physiological traits. Complex turns involve both translations and rotations, and are more subject to inter-individual differences that are not explained by morphology. This three-part framework suggests that different wingbeat kinematics can be used to maximize specific aspects of maneuverability. Thus, a broad explanatory framework has emerged for interpreting hummingbird maneuverability. This framework is general enough to be applied to other types of locomotion, and informative enough to explain mechanisms of maneuverability that could be applied to both animals and bio-inspired robots.

Humming hummingbirds, insect flight tones and a model of animal flight sound

Why do hummingbirds hum and insects whine when their wings flap in flight? Gutin proposed that a spinning propeller produces tonal sound because the location of the center of aerodynamic pressure on each blade oscillates relative to an external receiver. Animal wings also move, and in addition, aerodynamic force produced by animal wings fluctuates in magnitude and direction over the course of the wingbeat. Here, we modeled animal wing tone as the equal, opposite reaction to aerodynamic forces on the wing, using Lowson's equation for the sound field produced by a moving point force. Two assumptions of Lowson's equation were met: animal flight is low (<0.3) Mach and animals from albatrosses to mosquitoes are acoustically compact, meaning they have a small spatial extent relative to the wavelength of their wingbeat frequency. This model predicted the acoustic waveform of a hovering Costa's hummingbird (Calypte costae), which varies in the x, y and z directions around the animal. We modeled the wing forces of a hovering animal as a sinusoid with an amplitude equal to body weight. This model predicted wing sound pressure levels below a hovering hummingbird and mosquito to within 2 dB; and that far-field mosquito wing tone attenuates to 20 dB within about 0.2 m of the animal, while hummingbird humming attenuates to 20 dB at about 10 m. Wing tone plays a role in communication of certain insects, such as mosquitoes, and influences predator-prey interactions, because it potentially reveals the predator's presence to its intended prey.

Kinematic control of male Allen's hummingbird wing trill over a range of flight speeds

Wing trills are pulsed sounds produced by modified wing feathers at one or more specific points in time during a wingbeat. Male Allen's hummingbirds (Selasphorus sasin) produce a sexually dimorphic 9 kHz wing trill in flight. Here, we investigated the kinematic basis for trill production. The wingtip velocity hypothesis posits that trill production is modulated by the airspeed of the wingtip at some point during the wingbeat, whereas the wing rotation hypothesis posits that trill production is instead modulated by wing rotation kinematics. To test these hypotheses, we flew six male Allen's hummingbirds in an open-jet wind tunnel at flight speeds of 0, 3, 6, 9, 12 and 14 m s^-1, and recorded their flight with two 'acoustic cameras' placed below and behind, or below and lateral to the flying bird. The acoustic cameras are phased arrays of 40 microphones that used beamforming to spatially locate sound sources within a camera image. Trill sound pressure level (SPL) exhibited a U-shaped relationship with flight speed in all three camera positions. SPL was greatest perpendicular to the stroke plane. Acoustic camera videos suggest that the trill is produced during supination. The trill was up to 20 dB louder during maneuvers than it was during steady-state flight in the wind tunnel, across all airspeeds tested. These data provide partial support for the wing rotation hypothesis. Altered wing rotation kinematics could allow male Allen's hummingbirds to modulate trill production in social contexts such as courtship displays.

Hovering hummingbird wing aerodynamics during the annual cycle. II. Implications of wing feather moult

Birds usually moult their feathers in a particular sequence which may incur aerodynamic, physiological and behavioural implications. Among birds, hummingbirds are unique species in their sustained hovering flight. Because hummingbirds frequently hover-feed, they must maintain sufficiently high flight capacities even when moulting their flight feathers. A hummingbird wing consists of 10 primary flight feathers whose absence during moult may strongly affect wing performance. Using dynamic similarity rules, we compared time-accurate aerodynamic loads and flow field measurements over several wing geometries that follow the natural feather moult sequence of Calypte anna, a common hummingbird species in western North America. Our results suggest a drop of more than 20% in lift production during the early stages of the moult sequence in which mid-wing flight feathers are moulted. We also found that the wing's ability to generate lift strongly depended on the morphological integrity of the outer primaries and leading-edge. These findings may explain the evolution of wing morphology and moult attributes. Specifically, the high overlap between adjacent wing feathers, especially at the wing tip, and the slow sequential replacement of the wing feathers result in a relatively small reduction in wing surface area during moult with limited aerodynamic implications. We present power and efficiency analyses for hover flight during moult under several plausible scenarios, suggesting that body mass reduction could be a compensatory mechanism that preserves the energetic costs of hover flight.

Into rude air: hummingbird flight performance in variable aerial environments

Hummingbirds are well known for their ability to sustain hovering flight, but many other remarkable features of manoeuvrability characterize the more than 330 species of trochilid. Most research on hummingbird flight has been focused on either forward flight or hovering in otherwise non-perturbed air. In nature, however, hummingbirds fly through and must compensate for substantial environmental perturbation, including heavy rain, unpredictable updraughts and turbulent eddies. Here, we review recent studies on hummingbirds flying within challenging aerial environments, and discuss both the direct and indirect effects of unsteady environmental flows such as rain and von Kármán vortex streets. Both perturbation intensity and the spatio-temporal scale of disturbance (expressed with respect to characteristic body size) will influence mechanical responses of volant taxa. Most features of hummingbird manoeuvrability remain undescribed, as do evolutionary patterns of flight-related adaptation within the lineage. Trochilid flight performance under natural conditions far exceeds that of microair vehicles at similar scales, and the group as a whole presents many research opportunities for understanding aerial manoeuvrability.This article is part of the themed issue 'Moving in a moving medium: new perspectives on flight'.

Evolution of avian flight: muscles and constraints on performance

Competing hypotheses about evolutionary origins of flight are the 'fundamental wing-stroke' and 'directed aerial descent' hypotheses. Support for the fundamental wing-stroke hypothesis is that extant birds use flapping of their wings to climb even before they are able to fly; there are no reported examples of incrementally increasing use of wing movements in gliding transitioning to flapping. An open question is whether locomotor styles must evolve initially for efficiency or if they might instead arrive due to efficacy. The proximal muscles of the avian wing output work and power for flight, and new research is exploring functions of the distal muscles in relation to dynamic changes in wing shape. It will be useful to test the relative contributions of the muscles of the forearm compared with inertial and aerodynamic loading of the wing upon dynamic morphing. Body size has dramatic effects upon flight performance. New research has revealed that mass-specific muscle power declines with increasing body mass among species. This explains the constraints associated with being large. Hummingbirds are the only species that can sustain hovering. Their ability to generate force, work and power appears to be limited by time for activation and deactivation within their wingbeats of high frequency. Most small birds use flap-bounding flight, and this flight style may offer an energetic advantage over continuous flapping during fast flight or during flight into a headwind. The use of flap-bounding during slow flight remains enigmatic. Flap-bounding birds do not appear to be constrained to use their primary flight muscles in a fixed manner. To improve understanding of the functional significance of flap-bounding, the energetic costs and the relative use of alternative styles by a given species in nature merit study.This article is part of the themed issue 'Moving in a moving medium: new perspectives on flight'.

Visual Sensory Signals Dominate Tactile Cues during Docked Feeding in Hummingbirds

Animals living in and interacting with natural environments must monitor and respond to changing conditions and unpredictable situations. Using information from multiple sensory systems allows them to modify their behavior in response to their dynamic environment but also creates the challenge of integrating different, and potentially contradictory, sources of information for behavior control. Understanding how multiple information streams are integrated to produce flexible and reliable behavior is key to understanding how behavior is controlled in natural settings. Natural settings are rarely still, which challenges animals that require precise body position control, like hummingbirds, which hover while feeding from flowers. Tactile feedback, available only once the hummingbird is docked at the flower, could provide additional information to help maintain its position at the flower. To investigate the role of tactile information for hovering control during feeding, we first asked whether hummingbirds physically interact with a feeder once docked. We quantified physical interactions between docked hummingbirds and a feeder placed in front of a stationary background pattern. Force sensors on the feeder measured a complex time course of loading that reflects the wingbeat frequency and bill movement of feeding hummingbirds, and suggests that they sometimes push against the feeder with their bill. Next, we asked whether the measured tactile interactions were used by feeding hummingbirds to maintain position relative to the feeder. We created two experimental scenarios-one in which the feeder was stationary and the visual background moved and the other where the feeder moved laterally in front of a white background. When the visual background pattern moved, docked hummingbirds pushed significantly harder in the direction of horizontal visual motion. When the feeder moved, and the background was stationary, hummingbirds generated aerodynamic force in the opposite direction of the feeder motion. These results suggest that docked hummingbirds are using visual information about the environment to maintain body position and orientation, and not actively tracking the motion of the feeder. The absence of flower tracking behavior in hummingbirds contrasts with the behavior of hawkmoths, and provides evidence that they rely primarily on the visual background rather than flower-based cues while feeding.

Hovering hummingbird wing aerodynamics during the annual cycle. I. Complete wing

The diverse hummingbird family (Trochilidae) has unique adaptations for nectarivory, among which is the ability to sustain hover-feeding. As hummingbirds mainly feed while hovering, it is crucial to maintain this ability throughout the annual cycle-especially during flight-feather moult, in which wing area is reduced. To quantify the aerodynamic characteristics and flow mechanisms of a hummingbird wing throughout the annual cycle, time-accurate aerodynamic loads and flow field measurements were correlated over a dynamically scaled wing model of Anna's hummingbird (Calypte anna). We present measurements recorded over a model of a complete wing to evaluate the baseline aerodynamic characteristics and flow mechanisms. We found that the vorticity concentration that had developed from the wing's leading-edge differs from the attached vorticity structure that was typically found over insects' wings; firstly, it is more elongated along the wing chord, and secondly, it encounters high levels of fluctuations rather than a steady vortex. Lift characteristics resemble those of insects; however, a 20% increase in the lift-to-torque ratio was obtained for the hummingbird wing model. Time-accurate aerodynamic loads were also used to evaluate the time-evolution of the specific power required from the flight muscles, and the overall wingbeat power requirements nicely matched previous studies.

Limitations of rotational manoeuvrability in insects and hummingbirds: evaluating the effects of neuro-biomechanical delays and muscle mechanical power

Flying animals ranging in size from fruit flies to hummingbirds are nimble fliers with remarkable rotational manoeuvrability. The degrees of manoeuvrability among these animals, however, are noticeably diverse and do not simply follow scaling rules of flight dynamics or muscle power capacity. As all manoeuvres emerge from the complex interactions of neural, physiological and biomechanical processes of an animal's flight control system, these processes give rise to multiple limiting factors that dictate the maximal manoeuvrability attainable by an animal. Here using functional models of an animal's flight control system, we investigate the effects of three such limiting factors, including neural and biomechanical (from limited flapping frequency) delays and muscle mechanical power, for two insect species and two hummingbird species, undergoing roll, pitch and yaw rotations. The results show that for animals with similar degree of manoeuvrability, for example, fruit flies and hummingbirds, the underlying limiting factors are different, as the manoeuvrability of fruit flies is only limited by neural delays and that of hummingbirds could be limited by all three factors. In addition, the manoeuvrability also appears to be the highest about the roll axis as it requires the least muscle mechanical power and can tolerate the largest neural delays.

Wing kinematics measurement and aerodynamics of a dragonfly in turning flight

This study integrates high-speed photogrammetry, 3D surface reconstruction, and computational fluid dynamics to explore a dragonfly (Erythemis Simplicicollis) in free flight. Asymmetric wing kinematics and the associated aerodynamic characteristics of a turning dragonfly are analyzed in detail. Quantitative measurements of wing kinematics show that compared to the outer wings, the inner wings sweep more slowly with a higher angle of attack during the downstroke, whereas they flap faster with a lower angle of attack during the upstroke. The inner-outer asymmetries of wing deviations result in an oval wingtip trajectory for the inner wings and a figure-eight wingtip trajectory for the outer wings. Unsteady aerodynamics calculations indicate significantly asymmetrical force production between the inner and outer wings, especially for the forewings. Specifically, the magnitude of the drag force on the inner forewing is approximately 2.8 times greater than that on the outer forewing during the downstroke. In the upstroke, the outer forewing generates approximately 1.9 times greater peak thrust than the inner forewing. To keep the body aloft, the forewings contribute approximately 64% of the total lift, whereas the hindwings provide 36%. The effect of forewing-hindwing interaction on the aerodynamic performance is also examined. It is found that the hindwings can benefit from this interaction by decreasing power consumption by 13% without sacrificing force generation.

Hummingbirds control turning velocity using body orientation and turning radius using asymmetrical wingbeat kinematics

Turning in flight requires reorientation of force, which birds, bats and insects accomplish either by shifting body position and total force in concert or by using left-right asymmetries in wingbeat kinematics. Although both mechanisms have been observed in multiple species, it is currently unknown how each is used to control changes in trajectory. We addressed this problem by measuring body and wingbeat kinematics as hummingbirds tracked a revolving feeder, and estimating aerodynamic forces using a quasi-steady model. During arcing turns, hummingbirds symmetrically banked the stroke plane of both wings, and the body, into turns, supporting a body-dependent mechanism. However, several wingbeat asymmetries were present during turning, including a higher and flatter outer wingtip path and a lower more deviated inner wingtip path. A quasi-steady analysis of arcing turns performed with different trajectories revealed that changes in radius were associated with asymmetrical kinematics and forces, and changes in velocity were associated with symmetrical kinematics and forces. Collectively, our results indicate that both body-dependent and -independent force orientation mechanisms are available to hummingbirds, and that these kinematic strategies are used to meet the separate aerodynamic challenges posed by changes in velocity and turning radius.

Direct lateral maneuvers in hawkmoths

We used videography to investigate direct lateral maneuvers, i.e. ‘sideslips’, of the hawkmoth Manduca sexta. M. sexta sideslip by rolling their entire body and wings to reorient their net force vector. During sideslip they increase net aerodynamic force by flapping with greater amplitude, (in both wing elevation and sweep), allowing them to continue to support body weight while rolled. To execute the roll maneuver we observed in sideslips, they use an asymmetric wing stroke; increasing the pitch of the roll-contralateral wing pair, while decreasing that of the roll-ipsilateral pair. They also increase the wing sweep amplitude of, and decrease the elevation amplitude of, the contralateral wing pair relative to the ipsilateral pair. The roll maneuver unfolds in a stairstep manner, with orientation changing more during downstroke than upstroke. This is due to smaller upstroke wing pitch angle asymmetries as well as increased upstroke flapping counter-torque from left-right differences in global reference frame wing velocity about the moth's roll axis. Rolls are also opposed by stabilizing aerodynamic moments from lateral motion, such that rightward roll velocity will be opposed by rightward motion. Computational modeling using blade-element approaches confirm the plausibility of a causal linkage between the previously mentioned wing kinematics and roll/sideslip. Model results also predict high degrees of axial and lateral damping. On the time scale of whole and half wing strokes, left-right wing pair asymmetries directly relate to the first, but not second, derivative of roll. Collectively, these results strongly support a roll-based sideslip with a high degree of roll damping in M. sexta.

Summary: We show that hawkmoths fly sideways by rolling in the direction of movement, adding a left- or right-ward component to their net lift vector. The underlying roll maneuvers are produced from a suite of asymmetric wing kinematic changes and are heavily damped.

Flight mechanics and control of escape manoeuvres in hummingbirds II. Aerodynamic force production, flight control and performance limitations

The superior manoeuvrability of hummingbirds emerges from complex interactions of specialized neural and physiological processes with the unique flight dynamics of flapping wings. Escape manoeuvring is an ecologically relevant, natural behaviour of hummingbirds, from which we can gain understanding into the functional limits of vertebrate locomotor capacity. Here, we extend our kinematic analysis of escape manoeuvres from a companion paper to assess two potential limiting factors of manoeuvring performance of hummingbirds 1) muscle mechanical power output and 2) delays in the neural sensing and control system. We focused on the magnificent hummingbird, (Eugenes fulgens, 7.8g) and black-chinned hummingbird (Archilochus alexandri, 3.1 g), which represent large and small species, respectively. We first estimated the aerodynamic forces, moments and the mechanical power of escape manoeuvres using measured wing kinematics. Comparing active-manoeuvring and passive-damping aerodynamic moments, we found that pitch dynamics were lightly damped and dominated by effect of inertia while roll dynamics were highly damped. To achieve observed closed-loop performance, pitch manoeuvres required faster sensorimotor transduction, as hummingbirds can only tolerate half the delay allowed in roll manoeuvres. Accordingly, our results suggested that pitch control may require a more sophisticated control strategy, such as those based on prediction. For the magnificent hummingbird, we estimated escape manoeuvres required muscle mass-specific power 4.5 times that during hovering. Therefore, in addition to the limitation imposed by sensorimotor delays, muscle power could also limit the performance of escape manoeuvres.

Flight mechanics and control of escape manoeuvres in hummingbirds I. Flight kinematics

Hummingbirds are nature‘s masters of aerobatic manoeuvres. Previous research shows hummingbirds and insects converged evolutionarily upon similar aerodynamic mechanisms and kinematics in hovering. Herein, we use three-dimensional kinematic data to begin to test for similar convergence of kinematics used for escape flight and to explore the effects of body size upon manoeuvring. We studied four hummingbird species in North America including two large species (magnificent hummingbird, Eugenes fulgens, 7.8 g and blue-throated hummingbird, Lampornis clemenciae, 8.0 g) and two smaller species (broad-billed hummingbird, Cynanthus latirostris, 3.4 g and black-chinned hummingbirds Archilochus alexandri, 3.1 g). Starting from a steady hover, hummingbirds consistently manoeuvred away from perceived threats using a drastic escape response that featured body pitch and roll rotations coupled with a large linear acceleration. Hummingbirds changed their flapping frequency and wing trajectory in all three degrees-of-freedom on stroke-by-stroke basis, likely causing rapid and significant alteration of the magnitude and direction of aerodynamic forces. Thus it appears that the flight control of hummingbirds does not obey the “helicopter model” that is valid for similar escape manoeuvres in fruit flies. Except for broad-billed hummingbirds, the hummingbirds had faster reaction times than those reported for visual feedback control in insects. The two larger hummingbird species performed pitch rotations and global-yaw turns with considerably larger magnitude than the smaller species, but roll rates and cumulative roll angles were similar among the four species.

The biophysics of bird flight: functional relationships integrate aerodynamics, morphology, kinematics, muscles, and sensors

Bird flight is a remarkable adaptation that has allowed the approximately 10 000 extant species to colonize all terrestrial habitats on earth including high elevations, polar regions, distant islands, arid deserts, and many others. Birds exhibit numerous physiological and biomechanical adaptations for flight. Although bird flight is often studied at the level of aerodynamics, morphology, wingbeat kinematics, muscle activity, or sensory guidance independently, in reality these systems are naturally integrated. There has been an abundance of new studies in these mechanistic aspects of avian biology but comparatively less recent work on the physiological ecology of avian flight. Here we review research at the interface of the systems used in flight control and discuss several common themes. Modulation of aerodynamic forces to respond to different challenges is driven by three primary mechanisms: wing velocity about the shoulder, shape within the wing, and angle of attack. For birds that flap, the distinction between velocity and shape modulation synthesizes diverse studies in morphology, wing motion, and motor control. Recently developed tools for studying bird flight are influencing multiple areas of investigation, and in particular the role of sensory systems in flight control. How sensory information is transformed into motor commands in the avian brain remains, however, a largely unexplored frontier.

Hummingbird wing efficacy depends on aspect ratio and compares with helicopter rotors

Hummingbirds are the only birds that can sustain hovering. This unique flight behaviour comes, however, at high energetic cost. Based on helicopter and aeroplane design theory, we expect that hummingbird wing aspect ratio (AR), which ranges from about 3.0 to 4.5, determines aerodynamic efficacy. Previous quasi-steady experiments with a wing spinner set-up provide no support for this prediction. To test this more carefully, we compare the quasi-steady hover performance of 26 wings, from 12 hummingbird taxa. We spun the wings at angular velocities and angles of attack that are representative for every species and measured lift and torque more precisely. The power (aerodynamic torque × angular velocity) required to lift weight depends on aerodynamic efficacy, which is measured by the power factor. Our comparative analysis shows that AR has a modest influence on lift and drag forces, as reported earlier, but interspecific differences in power factor are large. During the downstroke, the power required to hover decreases for larger AR wings at the angles of attack at which hummingbirds flap their wings (p < 0.05). Quantitative flow visualization demonstrates that variation in hover power among hummingbird wings is driven by similar stable leading edge vortices that delay stall during the down- and upstroke. A side-by-side aerodynamic performance comparison of hummingbird wings and an advanced micro helicopter rotor shows that they are remarkably similar.

How Lovebirds Maneuver Rapidly Using Super-Fast Head Saccades and Image Feature Stabilization

Diurnal flying animals such as birds depend primarily on vision to coordinate their flight path during goal-directed flight tasks. To extract the spatial structure of the surrounding environment, birds are thought to use retinal image motion (optical flow) that is primarily induced by motion of their head. It is unclear what gaze behaviors birds perform to support visuomotor control during rapid maneuvering flight in which they continuously switch between flight modes. To analyze this, we measured the gaze behavior of rapidly turning lovebirds in a goal-directed task: take-off and fly away from a perch, turn on a dime, and fly back and land on the same perch. High-speed flight recordings revealed that rapidly turning lovebirds perform a remarkable stereotypical gaze behavior with peak saccadic head turns up to 2700 degrees per second, as fast as insects, enabled by fast neck muscles. In between saccades, gaze orientation is held constant. By comparing saccade and wingbeat phase, we find that these super-fast saccades are coordinated with the downstroke when the lateral visual field is occluded by the wings. Lovebirds thus maximize visual perception by overlying behaviors that impair vision, which helps coordinate maneuvers. Before the turn, lovebirds keep a high contrast edge in their visual midline. Similarly, before landing, the lovebirds stabilize the center of the perch in their visual midline. The perch on which the birds land swings, like a branch in the wind, and we find that retinal size of the perch is the most parsimonious visual cue to initiate landing. Our observations show that rapidly maneuvering birds use precisely timed stereotypic gaze behaviors consisting of rapid head turns and frontal feature stabilization, which facilitates optical flow based flight control. Similar gaze behaviors have been reported for visually navigating humans. This finding can inspire more effective vision-based autopilots for drones.

Folding in and out: passive morphing in flapping wings

We present a new mechanism for passive wing morphing of flapping wings inspired by bat and bird wing morphology. The mechanism consists of an unactuated hand wing connected to the arm wing with a wrist joint. Flapping motion generates centrifugal accelerations in the hand wing, forcing it to unfold passively. Using a robotic model in hover, we made kinematic measurements of unfolding kinematics as functions of the non-dimensional wingspan fold ratio (2-2.5) and flapping frequency (5-17 Hz) using stereo high-speed cameras. We find that the wings unfold passively within one to two flaps and remain unfolded with only small amplitude oscillations. To better understand the passive dynamics, we constructed a computer model of the unfolding process based on rigid body dynamics, contact models, and aerodynamic correlations. This model predicts the measured passive unfolding within about one flap and shows that unfolding is driven by centrifugal acceleration induced by flapping. The simulations also predict that relative unfolding time only weakly depends on flapping frequency and can be reduced to less than half a wingbeat by increasing flapping amplitude. Subsequent dimensional analysis shows that the time required to unfold passively is of the same order of magnitude as the flapping period. This suggests that centrifugal acceleration can drive passive unfolding within approximately one wingbeat in small and large wings. Finally, we show experimentally that passive unfolding wings can withstand impact with a branch, by first folding and then unfolding passively. This mechanism enables flapping robots to squeeze through clutter without sophisticated control. Passive unfolding also provides a new avenue in morphing wing design that makes future flapping morphing wings possibly more energy efficient and light-weight. Simultaneously these results point to possible inertia driven, and therefore metabolically efficient, control strategies in bats and birds to morph or recover within a beat.

Automatic analysis and characterization of the hummingbird wings motion using dense optical flow features

A new method for automatic analysis and characterization of recorded hummingbird wing motion is proposed. The method starts by computing a multiscale dense optical flow field, which is used to segment the wings, i.e., pixels with larger velocities. Then, the kinematic and deformation of the wings were characterized as a temporal set of global and local measures: a global angular acceleration as a time function of each wing and a local acceleration profile that approximates the dynamics of the different wing segments. Additionally, the variance of the apparent velocity orientation estimates those wing foci with larger deformation. Finally a local measure of the orientation highlights those regions with maximal deformation. The approach was evaluated in a total of 91 flight cycles, captured using three different setups. The proposed measures follow the yaw turn hummingbird flight dynamics, with a strong correlation of all computed paths, reporting a standard deviation of [Formula: see text] and [Formula: see text] for the global angular acceleration and the global wing deformation respectively.

Hawkmoth flight performance in tornado-like whirlwind vortices

Vertical vortex systems such as tornadoes dramatically affect the flight control and stability of aircraft. However, the control implications of smaller scale vertically oriented vortex systems for small fliers such as animals or micro-air vehicles are unknown. Here we examined the flapping kinematics and body dynamics of hawkmoths performing hovering flights (controls) and maintaining position in three different whirlwind intensities with transverse horizontal velocities of 0.7, 0.9 and 1.2 m s(-1), respectively, generated in a vortex chamber. The average and standard deviation of yaw and pitch were respectively increased and reduced in comparison with hovering flights. Average roll orientation was unchanged in whirlwind flights but was more variable from wingbeat to wingbeat than in hovering. Flapping frequency remained unchanged. Wingbeat amplitude was lower and the average stroke plane angle was higher. Asymmetry was found in the angle of attack between right and left wings during both downstroke and upstroke at medium and high vortex intensities. Thus, hawkmoth flight control in tornado-like vortices is achieved by a suite of asymmetric and symmetric changes to wingbeat amplitude, stroke plane angle and principally angle of attack.

Into turbulent air: size-dependent effects of von Kármán vortex streets on hummingbird flight kinematics and energetics

Animal fliers frequently move through a variety of perturbed flows during their daily aerial routines. However, the extent to which these perturbations influence flight control and energetic expenditure is essentially unknown. Here, we evaluate the kinematic and metabolic consequences of flight within variably sized vortex shedding flows using five Anna's hummingbirds feeding from an artificial flower in steady control flow and within vortex wakes produced behind vertical cylinders. Tests were conducted at three horizontal airspeeds (3, 6 and 9 m s(-1)) and using three different wake-generating cylinders (with diameters equal to 38, 77 and 173% of birds' wing length). Only minimal effects on wing and body kinematics were demonstrated for flight behind the smallest cylinder, whereas flight behind the medium-sized cylinder resulted in significant increases in the variances of wingbeat frequency, and variances of body orientation, especially at higher airspeeds. Metabolic rate was, however, unchanged relative to that of unperturbed flight. Hummingbirds flying within the vortex street behind the largest cylinder exhibited highest increases in variances of wingbeat frequency, and of body roll, pitch and yaw amplitudes at all measured airspeeds. Impressively, metabolic rate under this last condition increased by up to 25% compared with control flights. Cylinder wakes sufficiently large to interact with both wings can thus strongly affect stability in flight, eliciting compensatory kinematic changes with a consequent increase in flight metabolic costs. Our findings suggest that vortical flows frequently encountered by aerial taxa in diverse environments may impose substantial energetic costs.

Neuromuscular control of hovering wingbeat kinematics in response to distinct flight challenges in the ruby-throated hummingbird, Archilochus colubris

While producing one of the highest sustained mass-specific power outputs of any vertebrate, hovering hummingbirds must also precisely modulate the activity of their primary flight muscles to vary wingbeat kinematics and modulate lift production. Although recent studies have begun to explore how pectoralis (the primary downstroke muscle) neuromuscular activation and wingbeat kinematics are linked in hummingbirds, it is unclear whether different species modulate these features in similar ways, or consistently in response to distinct flight challenges. In addition, little is known about how the antagonist, the supracoracoideus, is modulated to power the symmetrical hovering upstroke. We obtained simultaneous recordings of wingbeat kinematics and electromyograms from the pectoralis and supracoracoideus in ruby-throated hummingbirds (Archilochus colubris) hovering under the following conditions: (1) ambient air, (2) air density reduction trials, (3) submaximal load-lifting trials and (4) maximal load-lifting trials. Increased power output was achieved through increased stroke amplitude during air density reduction and load-lifting trials, but wingbeat frequency only increased at low air densities. Overall, relative electromyographic (EMG) intensity was the best predictor of stroke amplitude and is correlated with angular velocity of the wingtip. The relationship between muscle activation intensity and kinematics was independent of treatment type, indicating that reduced drag on the wings in hypodense air did not lead to high wingtip angular velocities independently of increased muscle work. EMG bursts consistently began and ended before muscle shortening under all conditions. During all sustained hovering, spike number per burst consistently averaged 1.2 in the pectoralis and 2.0 in the supracoracoideus. The number of spikes increased to 2.5-3 in both muscles during maximal load-lifting trials. Despite the relative kinematic symmetry of the hovering downstroke and upstroke, the supracoracoideus was activated ~1 ms earlier, EMG bursts were longer (~0.9 ms) and they exhibited 1.6 times as many spikes per burst. We hypothesize that earlier and more sustained activation of the supracoracoideus fibres is necessary to offset the greater compliance resulting from the presence of the supracoracoid tendon.