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.     

Structure of the vortex wake in hovering Anna's hummingbirds (Calypte anna)

Hummingbirds are specialized hoverers for which the vortex wake has been described as a series of single vortex rings shed primarily during the downstroke. Recent findings in bats and birds, as well as in a recent study on Anna''s hummingbirds, suggest that each wing may shed a discrete vortex ring, yielding a bilaterally paired wake. Here, we describe the presence of two discrete rings in the wake of hovering Anna''s hummingbirds, and also infer force production through a wingbeat with contributions to weight support. Using flow visualization, we found separate vortices at the tip and root of each wing, with 15% stronger circulation at the wingtip than at the root during the downstroke. The upstroke wake is more complex, with near-continuous shedding of vorticity, and circulation of approximately equal magnitude at tip and root. Force estimates suggest that the downstroke contributes 66% of required weight support, whereas the upstroke generates 35%. We also identified a secondary vortex structure yielding 8–26% of weight support. Lift production in Anna''s hummingbirds is more evenly distributed between the stroke phases than previously estimated for Rufous hummingbirds, in accordance with the generally symmetric down- and upstrokes that characterize hovering in these birds.     

Lift production in the hovering hummingbird

Aerodynamic theory and empirical observations of animals flying at similar Reynolds numbers (Re) predict that airflow over hummingbird wings will be dominated by a stable, attached leading edge vortex (LEV). In insects exhibiting similar kinematics, when the translational movement of the wing ceases (as at the end of the downstroke), the LEV is shed and lift production decreases until the energy of the LEV is re-captured in the subsequent half-cycle translation. We here show that while the hummingbird wing is strongly influenced by similar sharp-leading-edge aerodynamics, leading edge vorticity is inconsistent, varying from 0.7 to 26 per cent (mean 16%) of total lift production, is always generated within 3 mm of the dorsal surface of the wing, showing no retrograde (trailing to leading edge) flow, and does not increase from proximal to distal wing as would be expected with a conical vortex (class III LEV) described for hawkmoths. Further, the bound circulation is not shed as a vortex at the end of translation, but instead remains attached and persists after translation has ceased, augmented by the rotation (pronation, supination) of the wing that occurs between the wing-translation half-cycles. The result is a near-continuous lift production through wing turn-around, previously unknown in vertebrates, able to contribute to weight support as well as stability and control during hovering. Selection for a planform suited to creating this unique flow and nearly-uninterrupted lift production throughout the wingbeat cycle may help explain the relatively narrow hummingbird wing.     

A Review of Research on the Mechanical Design of Hoverable Flapping Wing Micro-Air Vehicles

Most insects and hummingbirds can generate lift during both upstroke and downstroke with a nearly horizontal flapping stroke plane,and perform precise hovering flight.Further,most birds can utilize tails and muscles in wings to actively control the flight performance,while insects control their flight with muscles based on wing root along with wing's passive deformation.Based on the above flight principles of birds and insects,Flapping Wing Micro Air Vehicles(FWMAVs)are classified as either bird-inspired or insect-inspired FWMAVs.In this review,the research achievements on mechanisms of insect-inspired,hoverable FWMAVs over the last ten years(2011-2020)are provided.We also provide the definition,func-tion,research status and development prospect of hoverable FWMAVs.Then discuss it from three aspects:bio-inspiration,motor-driving mechanisms and intelligent actuator-driving mechanisms.Following this,research groups involved in insect-inspired,hoverable FWMAV research and their major achievements are summarized and classified in tables.Problems,trends and challenges about the mechanism are compiled and presented.Finally,this paper presents conclusions about research on mechanical structure,and the future is discussed to enable further research interests.     

Flow Visualization of Rhinoceros Beetle (Trypoxylus dichotomus) in Free Flight

Aerodynamic characteristics of the beetle,Trypoxylus dichotomus,which has a pair of elytra (forewings) and flexible hind wings,are investigated.Visualization experiments were conducted for various flight conditions of a beetle,Trypoxylus dichotomus:free,tethered,hovering,forward and climbing flights.Leading edge,trailing edge and tip vortices on both wings were observed clearly.The leading edge vortex was stable and remained on the top surface of the elytron for a wide interval during the downstroke of free forward flight.Hence,the elytron may have a considerable role in lift force generation of the beetle.In addition,we reveal a suction phenomenon between the gaps of the hind wing and the elytron in upstroke that may improve the positive lift force on the hind wing.We also found the reverse clap-fling mechanism of the T.dichotomus beetle in hovering flight.The hind wings touch together at the beginning of the upstroke.The vortex generation,shedding and interaction give a better understanding of the detailed aerodynamic mechanism of beetle flight.     

Biomechanics and physiology of gait selection in flying birds

Two wing-beat gaits, distinguished by the presence or absence of lift production during the upstroke, are currently used to describe avian flight. Vortex-visualization studies indicate that lift is produced only during the downstroke in the vortex-ring gait and that lift is produced continuously in the continuous-vortex gait. Tip-reversal and feathered upstrokes represent different forms of vortex-ring gait distinguished by wing kinematics. Useful aerodynamic forces may be produced during tip-reversal upstroke in slow flight and during a feathered upstroke in fast flight, but it is probable that downstroke forces are much greater in magnitude. Uncertainty about the function of these types of upstroke may be resolved when more data are available on wake structure in different flight speeds and modes. Inferring from wing kinematics and available data on wake structure, birds with long wings or wings of high aspect ratio use a vortex-ring gait with tip-reversal upstroke at slow speeds, a vortex-ring gait with a feathered upstroke at intermediate speeds, and a continuous-vortex gait at fast speeds. Birds with short wings or wings of low aspect ratio use a vortex-ring gait with a feathered upstroke at all speeds. Regardless of wing shape, species tend to use a vortex-ring gait for acceleration and a continuous-vortex gait for deceleration. Some correlations may exist between gait selection and the function of the muscular and respiratory system. However, overall variation in wing kinematics, muscle activity, and respiratory activity is continuous rather than categorical. To further our understanding of gait selection in flying birds, it is important to test whether upstroke function varies in a similar manner. Transitions between lifting and nonlifting upstrokes may be more subtle and gradual than implied by a binomial scheme of classification.     

Animal flight dynamics II. Longitudinal stability in flapping flight

Stability is essential to flying and is usually assumed to be especially problematic in flapping flight. If so, problems of stability may have presented a particular hurdle to the evolution of flapping flight. In spite of this, the stability of flapping flight has never been properly analysed. Here we use quasi-static and blade element approaches to analyse the stability provided by a flapping wing. By using reduced order approximations to the natural modes of motion, we show that wing beat frequencies are generally high enough compared to the natural frequencies of motion for a quasi-static approach to be valid as a first approximation. Contrary to expectations, we find that there is noting inherently destabilizing about flapping: beating the wings faster simply amplifies any existing stability or instability, and flapping can even enhance stability compared to gliding at the same air speed. This suggests that aerodynamic stability may not have been a particular hurdle in the evolution of flapping flight. Hovering animals, like hovering helicopters, are predicted to possess neutral static stability. Flapping animals, like fixed wing aircraft, are predicted to be stable in forward flight if the mean flight force acts above and/or behind the centre of gravity. In this case, the downstroke will always be stabilizing. The stabilizing contribution may be diminished by an active upstroke with a low advance ratio and more horizontal stroke plane; other forms of the upstroke may make a small positive contribution to stability. An active upstroke could, therefore, be used to lower stability and enhance manoeuvrability. Translatory mechanisms of unsteady lift production are predicted to amplify the stability predicted by a quasi-static analysis. Non-translatory mechanisms will make little or no contribution to stability. This may be one reason why flies, and other animals which rely upon non-translatory aerodynamic mechanisms, often appear inherently unstable.     

Morphological and kinematic basis of the hummingbird flight stroke: scaling of flight muscle transmission ratio

Hummingbirds (Trochilidae) are widely known for their insect-like flight strokes characterized by high wing beat frequency, small muscle strains and a highly supinated wing orientation during upstroke that allows for lift production in both halves of the stroke cycle. Here, we show that hummingbirds achieve these functional traits within the limits imposed by a vertebrate endoskeleton and muscle physiology by accentuating a wing inversion mechanism found in other birds and using long-axis rotational movement of the humerus. In hummingbirds, long-axis rotation of the humerus creates additional wing translational movement, supplementing that produced by the humeral elevation and depression movements of a typical avian flight stroke. This adaptation increases the wing-to-muscle-transmission ratio, and is emblematic of a widespread scaling trend among flying animals whereby wing-to-muscle-transmission ratio varies inversely with mass, allowing animals of vastly different sizes to accommodate aerodynamic, biomechanical and physiological constraints on muscle-powered flapping flight.     

The vortex wake of a 'hovering' model hawkmoth

Visualization experiments with Manduca sexta have revealed the presence of a leading-edge vortex and a highly three-dimensional flow pattern. To further investigate this important discovery, a scaled-up robotic insect was built (the ''flapper'') which could mimic the complex movements of the wings of a hovering hawkmoth. Smoke released from the leading edge of the flapper wing revealed a small but strong leading-edge vortex on the downstroke. This vortex had a high axial flow velocity and was stable, separating from the wing at approximately 75 per cent of the wing length. It connected to a large, tangled tip vortex, extending back to a combining stopping and starting vortex from pronation. At the end of the downstroke, the wake could be approximated as one vortex ring per wing. Based on the size and velocity of the vortex rings, the mean lift force during the downstroke was estimated to be about 1.5 times the body weight of a hawkmoth, confirming that the downstroke is the main provider of lift force.     

The three-dimensional leading-edge vortex of a 'hovering' model hawkmoth

Recent flow visualisation experiments with the hawkmoth, Manduca sexta, revealed small but clear leading-edge vortex and a pronounced three-dimensional flow. Details of this flow pattern were studied with a scaled-up, robotic insect (''the flapper'') that accurately mimicked the wing movements of a hovering hawkmoth. Smoke released from the leading edge of the flapper wing confirmed the existence of a small, strong and stable leading-edge vortex, increasing in size from wingbase to wingtip. Between 25 and 75 per cent of the wing length, its diameter increased approximately from 10 to 50 per cent of the wing chord. The leading-edge vortex had a strong axial flow veolocity, which stabilized it and reduced its diamater. The vortex separated from the wing at approximately 75 per cent of the wing length and thus fed vorticity into a large, tangled tip vortex. If the circulation of the leading-edge vortex were fully used for lift generation, it could support up to two-thirds of the hawkmoth''s weight during the downstroke. The growth of this circulation with time and spanwise position clearly identify dynamic stall as the unsteady aerodynamic mechanism responsible for high lift production by hovering hawkmoths and possibly also by many other insect species.     

The Role of Elytra in Beetle Flight: I. Generation of Quasi-Static Aerodynamic Forces

We conducted a comprehensive study to investigate the aerodynamic characteristics and force generation of the elytra of abeetle,Allomyrina dichotoma.Our analysis included wind tunnel experiments and three-dimensional computational fluiddynamics simulations using ANSYS-CFX software.Our first approach was a quasi-static study that considered the effect ofinduced flapping flow due to the flapping motion of the fore-wings (elytra) at a frequency of around 30 Hz to 40 Hz.The dihedralangle was varied to represent flapping motion during the upstroke and downstroke.We found that an elytron producespositive lift at 0° geometric angle of attack,negative lift during the upstroke,and always produces drag during both the upstrokeand downstroke.We also found that the lift coefficient of an elytron does not drop even at a very high geometric angle of attack.For a beetle with a body weight of 5 g,based on the quasi-static method,the fore-wings (elytra) can produce lift of less than 1%of its body weight.     

The physiology and biomechanics of avian flight at high altitude

Many birds fly at high altitude, either during long-distanceflights or by virtue of residence in high-elevation habitats.Among the many environmental features that vary systematicallywith altitude, five have significant consequences for avianflight performance: ambient wind speeds, air temperature, humidity,oxygen availability, and air density. During migratory flights,birds select flight altitudes that minimize energy expenditurevia selection of advantageous tail- and cross-winds. Oxygenpartial pressure decreases substantially to as little as 26%of sea-level values for the highest altitudes at which birdsmigrate, whereas many taxa reside above 3000 meters in hypoxicair. Birds exhibit numerous adaptations in pulmonary, cardiovascular,and muscular systems to alleviate such hypoxia. The systematicdecrease in air density with altitude can lead to a benefitfor forward flight through reduced drag but imposes an increasedaerodynamic demand for hovering by degrading lift productionand simultaneously elevating the induced power requirementsof flight. This effect has been well-studied in the hoveringflight of hummingbirds, which occur throughout high-elevationhabitats in the western hemisphere. Phylogenetically controlledstudies have shown that hummingbirds compensate morphologicallyfor such hypodense air through relative increases in wing size,and kinematically via increased stroke amplitude during thewingbeat. Such compensatory mechanisms result in fairly constantpower requirements for hovering at different elevations, butdecrease the margin of excess power available for other flightbehaviors.     

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.     

The flight mechanism of the pigeon Columbia livia during take-off

High-speed film analysis of the mechanism of take-off of a pigeon ascending nearly vertically reveals the pattern of movements of the wing segments and the bones within them during each of the five phases of the wingbeat cycle. Differences in the type and extent of wing movements between the upstroke and downstroke portions of the first and successive wingbeat cycles are explained with reference to the upward vertical jump made during the first wingbeat cycle. The presence during pigeon take-off of a non-steady state pattern of airfoil action similar to that seen in some insects at the beginning of the downstroke was verified.     

The functional anatomy of the shoulder in the European starling (Sturnus vulgaris)

The excursions of wing elements and the activity of eleven shoulder muscles were studied by cineradiography and electromyography in European starlings (Sturnus vulgaris) flying in a wind tunnel at speeds of 9–20 m s^?1. At the beginning of downstroke the humerus is elevated 80–90° above horizontal, and both elbow and wrist are extended to 90° or less. During downstroke, protraction of the humerus (55°) remains constant; elbow and wrist are maximally extended (120° and 160°, respectively) as the humerus passes through a horizontal orientation. During the downstroke-upstroke transition humeral depression ceases (at about 20° below horizontal) and the humerus begins to retract. However, depression of the distal wing continues by rotation of the humerus and adduction of the carpometacarpus. Humeral retraction (to within about 30° of the body axis) is completed early in upstroke, accompanied by flexion of the elbow and carpometacarpus. Thereafter the humerus begins to protract as elevation continues. At mid-upstroke a rapid counterrotation of the humerus reorients the ventral surface of the wing to face laterad; extension of the elbow and carpometacarpus are initiated sequentially. The upstroke-downstroke transition is characterized by further extension of the elbow and carpometacarpus, and the completion of humeral protraction. Patterns of electromyographic activity primarily coincide with the transitional phases of the wingbeat cycle rather than being confined to downstroke or upstroke. Thus, the major downstroke muscles (pectoralis, coracobrachialis caudalis, sternocoracoideus, subscapularis, and humerotriceps) are activated in late upstroke to decelerate, extend, and reaccelerate the wing for the subsequent downstroke; electromyographic activity ends well before the downstroke is completed. Similarly, the upstroke muscles (supracoracoideus, deltoideus major) are activated in late downstroke to decelerate and then reaccelerate the wing into the upstroke; these muscles are deactivated by mid-upstroke. Only two muscles (scapulohumeralis caudalis, scapulotriceps) exhibit electromyographic activity exclusively during the downstroke. Starlings exhibit a functional partitioning of the two heads of the triceps (the humerotriceps acts with the pectoralis group, and does not overlap with the scapulotriceps). The biphasic pattern of the biceps brachii appears to correspond to this partitioning.     

Hindlimb Motion during Steady Flight of the Lesser Dog-Faced Fruit Bat,Cynopterus brachyotis

In bats, the wing membrane is anchored not only to the body and forelimb, but also to the hindlimb. This attachment configuration gives bats the potential to modulate wing shape by moving the hindlimb, such as by joint movement at the hip or knee. Such movements could modulate lift, drag, or the pitching moment. In this study we address: 1) how the ankle translates through space during the wingbeat cycle; 2) whether amplitude of ankle motion is dependent upon flight speed; 3) how tension in the wing membrane pulls the ankle; and 4) whether wing membrane tension is responsible for driving ankle motion. We flew five individuals of the lesser dog-faced fruit bat, Cynopterus brachyotis (Family: Pteropodidae), in a wind tunnel and documented kinematics of the forelimb, hip, ankle, and trailing edge of the wing membrane. Based on kinematic analysis of hindlimb and forelimb movements, we found that: 1) during downstroke, the ankle moved ventrally and during upstroke the ankle moved dorsally; 2) there was considerable variation in amplitude of ankle motion, but amplitude did not correlate significantly with flight speed; 3) during downstroke, tension generated by the wing membrane acted to pull the ankle dorsally, and during upstroke, the wing membrane pulled laterally when taut and dorsally when relatively slack; and 4) wing membrane tension generally opposed dorsoventral ankle motion. We conclude that during forward flight in C. brachyotis, wing membrane tension does not power hindlimb motion; instead, we propose that hindlimb movements arise from muscle activity and/or inertial effects.     

Effect of outer wing separation on lift and thrust generation in a flapping wing system

We explore the implementation of wing feather separation and lead-lagging motion to a flapping wing. A biomimetic flapping wing system with separated outer wings is designed and demonstrated. The artificial wing feather separation is implemented in the biomimetic wing by dividing the wing into inner and outer wings. The features of flapping, lead-lagging, and outer wing separation of the flapping wing system are captured by a high-speed camera for evaluation. The performance of the flapping wing system with separated outer wings is compared to that of a flapping wing system with closed outer wings in terms of forward force and downward force production. For a low flapping frequency ranging from 2.47 to 3.90 Hz, the proposed biomimetic flapping wing system shows a higher thrust and lift generation capability as demonstrated by a series of experiments. For 1.6 V application (lower frequency operation), the flapping wing system with separated wings could generate about 56% higher forward force and about 61% less downward force compared to that with closed wings, which is enough to demonstrate larger thrust and lift production capability of the separated outer wings. The experiments show that the outer parts of the separated wings are able to deform, resulting in a smaller amount of drag production during the upstroke, while still producing relatively greater lift and thrust during the downstroke.     

Normalized lift: an energy interpretation of the lift coefficient simplifies comparisons of the lifting ability of rotating and flapping surfaces

For a century, researchers have used the standard lift coefficient C(L) to evaluate the lift, L, generated by fixed wings over an area S against dynamic pressure, ?ρv(2), where v is the effective velocity of the wing. Because the lift coefficient was developed initially for fixed wings in steady flow, its application to other lifting systems requires either simplifying assumptions or complex adjustments as is the case for flapping wings and rotating cylinders.This paper interprets the standard lift coefficient of a fixed wing slightly differently, as the work exerted by the wing on the surrounding flow field (L/ρ·S), compared against the total kinetic energy required for generating said lift, ?v(2). This reinterpreted coefficient, the normalized lift, is derived from the work-energy theorem and compares the lifting capabilities of dissimilar lift systems on a similar energy footing. The normalized lift is the same as the standard lift coefficient for fixed wings, but differs for wings with more complex motions; it also accounts for such complex motions explicitly and without complex modifications or adjustments. We compare the normalized lift with the previously-reported values of lift coefficient for a rotating cylinder in Magnus effect, a bat during hovering and forward flight, and a hovering dipteran.The maximum standard lift coefficient for a fixed wing without flaps in steady flow is around 1.5, yet for a rotating cylinder it may exceed 9.0, a value that implies that a rotating cylinder generates nearly 6 times the maximum lift of a wing. The maximum normalized lift for a rotating cylinder is 1.5. We suggest that the normalized lift can be used to evaluate propellers, rotors, flapping wings of animals and micro air vehicles, and underwater thrust-generating fins in the same way the lift coefficient is currently used to evaluate fixed wings.     

Non-Jumping Take off Performance in Beetle Flight （Rhinoceros Beetle Trypoxylus dichotomus）

In recent decades, the take-off mechanisms of flying animals have received much attention in insect flight initiation. Most of previous works have focused on the jumping mechanism, which is the most common take-off mechanism found in flying animals. Here, we presented that the rhinoceros beetle, Trypoxylus dichotomus, takes offwithout jumping. In this study, we used 3-Dimensional （3D） high-speed video techniques to quantitatively analyze the wings and body kinematics during the initiation periods of flight. The details of the flapping angle, angle of attack of the wings and the roll, pitch and yaw angles of the body were investigated to understand the mechanism of take-off in T. dichotomus. The beetle took off gradually with a small velocity and small acceleration. The body kinematic analyses showed that the beetle exhibited stable take-off. To generate high lift force, the beetle modulated its hind wing to control the angle of attack; the angle of attack was large during the upstroke and small during the downstroke. The legs of beetle did not contract and strongly release like other insects. The hind wing could be con- sidered as a main source of lift for heavy beetle.     

Of hummingbirds and helicopters: hovering costs, competitive ability, and foraging strategies

Wing morphology and flight kinematics profoundly influence foraging costs and the overall behavioral ecology of hummingbirds. By analogy with helicopters, previous energetic studies have applied the momentum theory of aircraft propellers to estimate hovering costs from wing disc loading (WDL), a parameter incorporating wingspan (or length) and body mass. Variation in WDL has been used to elucidate differences either among hummingbird species in nectar-foraging strategies (e.g., territoriality, traplining) and dominance relations or among gender-age categories within species. We first demonstrate that WDL, as typically calculated, is an unreliable predictor of hovering (induced power) costs; predictive power is increased when calculations use wing length instead of wingspan and when actual wing stroke amplitudes are incorporated. We next evaluate the hypotheses that foraging strategy and competitive ability are functions of WDL, using our data in combination with those of published sources. Variation in hummingbird behavior cannot be easily classified using WDL and instead is correlated with a diversity of morphological and physiological traits. Evaluating selection pressures on hummingbird wings will require moving beyond wing and body mass measurements to include the assessment of the aerodynamic forces, power requirements, and power reserves of hovering, forward flight, and maneuvering. However, the WDL-helicopter dynamics model has been instrumental in calling attention to the importance of comparative wing morphology and related aerodynamics for understanding the behavioral ecology of hummingbirds.