Direct measurements of the kinematics and dynamics of bat flight

Experimental measurements and analysis of the flight of bats are presented, including kinematic analysis of high-speed stereo videography of straight and turning flight, and measurements of the wake velocity field behind the bat. The kinematic data reveal that, at relatively slow flight speeds, wing motion is quite complex, including a sharp retraction of the wing during the upstroke and a broad sweep of the partially extended wing during the downstroke. The data also indicate that the flight speed and elevation are not constant, but oscillate in synchrony with both the horizontal and vertical movements of the wing. PIV measurements in the transverse (Trefftz) plane of the wake indicate a complex 'wake vortex' structure dominated by a strong wing tip vortex shed from the wing tip during the downstroke and either the wing tip or a more proximal joint during the upstroke. Data synthesis of several discrete realizations suggests a 'cartoon' of the wake structure during the entire wing beat cycle. Considerable work remains to be done to confirm and amplify these results.     

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.     

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

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

ON THE RECONSTRUCTION OF PTEROSAURS AND THEIR MANNER OF FLIGHT, WITH NOTES ON VORTEX WAKES

Classical pterosaur reconstructions are variants on a ‘bat-analogy’, whereby the wing is conceived as a simple membrane with no inherent bending strength, stretched between the arm and leg skeletons. The legs are considered to be splayed out to the sides, as in bats, so that the animal would have to adopt a quadrupedal stance on the ground, supported on its feet and the metacarpo-phalangeal joints. In recent years an alternative ‘bird-analogy’ has come to be generally accepted. This hypothesis, most elements of which are due to Padian (1983 a, b) calls for the animal to stand upright on its legs like a bird. The wings are independent of the legs, as in birds, are stiffened by skeletal fibres in the membrane, and have a very narrow, sharply pointed shape. There are difficulties in reconciling the bird-analogy with the evidence. The long-tailed rhamphorhynchs might conceivably have balanced their weight about their hip joints but this would not have been possible for the short-tailed pterodactyls. The bird pelvis shows modifications which permit bipedal standing in spite of the reduction of the tail, but no equivalent adaptations are seen in pterodactyls. Besides, all known pterosaur pelvises, except that of the giant pterodactyl Pteranodon were open ventrally, which would have precluded the legs from being brought to a parasagittal position, as required for bipedal walking. The notion that the wing was not attached to the legs is based on negative evidence, in that no clear impressions of the inner end of the wing membrane are preserved in the fossils. However one pterodactyl fossil shows a membrane edge approaching the ankle joint. In fossils that are preserved with the wings forward, the legs have been pulled forwards by the ankles. A tendon connecting the ankle to the wing tip is consistent with the evidence. The ‘fibres’ in the wing membranes are actually impressions of surface ridges, with no internal structure, and are better interpreted as surface wrinkles in the skin, caused by contraction of elastic fibres within the membrane. The bird analogy also results in a very unsatisfactory wing from an aerodynamic point of view. The structure of an animal wing is best understood in terms of the type of vortex wake it is adapted to generate. Hummingbirds, and insects capable of economical hovering, have wings that can be inverted on the upstroke, and when hovering, generate a wake consisting of two vortex rings per wingbeat cycle. The span of such wings is fixed, which implies that they create a ‘ladder wake’ in cruising flight, consisting of a pair of undulating wing-tip vortices, joined by a transverse vortex at each transition from downstroke to upstroke and back. Normal birds cannot invert their wings, and so are less efficient in hovering, but they can shorten the wing during the upstroke in cruising flight. This creates a ‘concertina wake’, with no transverse vortices. Hummingbirds show very limited migration performance, compared with normal birds, with the implication that a wing capable of creating a concertina wake is more economical in cruising flight than one creating a ladder wake, and is an essential adaptation for long-distance migration. A revised reconstruction of the pterosaur wing starts from the observations that, contrary to the currently popular bird-analogy, pterosaurs were not bipedal, their wings did not contain stiffening fibres but did contain elastic fibres, and the trailing edge of the membrane was supported by a tendon joining the tip of the wing finger to the ankle. A hypothetical arrangement of elastic fibres, that accounts well for the observed pattern of wrinkles in contracted wings, also allows the planform shape of the wing to be adjusted in much the same way as seen in birds, although using a completely different mechanism. It opens the possibility that pterosaurs could fly with a concertina wake, and thus could have been long-distance migrators like modern birds. Although this hypothetical wing is mechanically somewhat bat-like, it is not a return to the classical bat-analogy. It would not have the high degree of control over profile shape, which gives bats their outstanding manoeuvrability. On the other hand bats do not have the degree of control over their wingspan that is suggested here for pterosaurs, and consequently are not notable for migration performance.     

Limb disparity and wing shape in pterosaurs

The limb proportions of the extinct flying pterosaurs were clearly distinct from their living counterparts, birds and bats. Within pterosaurs, however, we show that further differences in limb proportions exist between the two main groups: the clade of short-tailed Pterodactyloidea and the paraphyletic clades of long-tailed rhamphorhynchoids. The hindlimb to forelimb ratios of rhamphorhynchoid pterosaurs are similar to that seen in bats, whereas those of pterodactyloids are much higher. Such a clear difference in limb ratios indicates that the extent of the wing membrane in rhamphorhynchoids and pterodactyloids may also have differed; this is borne out by simple ternary analyses. Further, analyses also indicate that the limbs of Sordes pilosus, a well-preserved small taxon used as key evidence for inferring the extent and shape of the wing membrane in all pterosaurs, are not typical even of its closest relatives, other rhamphorhynchoids. Thus, a bat-like extensive hindlimb flight membrane, integrated with the feet and tail may be applicable only to a small subset of pterosaur diversity. The range of flight morphologies seen in these extinct reptiles may prove much broader than previously thought.     

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.     

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.     

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

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

The kinematics of Heteroptera in free flight

The kinematics of six species of Heteroptera in free flight are analysed and compared.

• (1) 

  Using nested analysis of variance techniques, statistically significant variation was detected between species for several of the flight parameters measured: mean angular velocity; pronation/supination ratio; upstroke/downstroke ratio; and wing beat frequency. In each case this is discussed in terms of variation in flight behaviour.
• (2) 

  Beneficial aerodynamic forces are generated during the upstroke and the downstroke, in both fast forward and rising flight.
• (3). 

  When the insects change from level, forward flight to near vertical, rising flight, the following parameters are altered in most of the sequences analysed:

• (a). 

  the stroke plane angle becomes steeply, negatively inclined, associated with an increase in body angle;
• (b). 

  the stroke amplitude is reduced;
• (c). 

  wing beat frequency is lowered, associated with a drop in mean angular velocity;
• (d). 

  the speed of stroke reversal (rotational velocity) is increased. This may be associated with increased wing torsion and tip flexion which in turn could improve any beneficial unsteady aerodynamic effects generated at stroke reversal.

The reasons for this change in flight performance and the deviations from that seen in other insects are discussed.
It is shown that Heteroptera may make use of wing drag in flight, particularly during rising flight.     

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

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

Mechanical properties of the avian acrocoracohumeral ligament and its role in shoulder stabilization in flight

Control of movement in the avian shoulder joint is fundamental to understanding the avian wingstroke. The acrocoracohumeral ligament (AHL) is thought to play a key role in stabilizing the glenoid and balancing the pectoralis in gliding flight. If the AHL has to be taut to balance the pectoralis, then it must constrain glenohumeral motion during flapping flight as well. However, birds vary wing kinematics depending on flight speed and behavior. How can a passive ligament accommodate such varying joint movements? Herein, mechanical testing and 3-D modeling are used to link the mechanical properties and morphology of the AHL to its functional role during flapping flight. The bone-ligament-bone complex of the pigeon (Columba livia) fails at a tensile loading of 141 ± 18 N (± s .D., n = 10) or 39 times body weight, which corresponds to a failure stress of 51 MPa, well above expected loads during flight. Simulated AHL length changes, comparisons to glenohumeral kinematics from the literature, and manipulations of partially dissected pigeon specimens all support the hypothesis that the AHL remains taut through downstroke and most of upstroke while becoming slack during the downstroke/upstroke transition. The digital AHL model provides a mechanism for explaining how the AHL can stabilize the shoulder joint under a broad array of humeral paths by constraining the coordination of glenohumeral degrees of freedom.     

FORELIMB POSTURE IN DINOSAURS AND THE EVOLUTION OF THE AVIAN FLAPPING FLIGHT-STROKE

Ontogenetic and behavioral studies using birds currently do not document the early evolution of flight because birds (including juveniles) used in such studies employ forelimb oscillation frequencies over 10 Hz, forelimb stroke-angles in excess of 130°, and possess uniquely avian flight musculatures. Living birds are an advanced morphological stage in the development of flapping flight. To gain insight into the early stages of flight evolution (i.e., prebird), in the absence of a living analogue, a new approach using Strouhal number     was used. Strouhal number is a nondimensional number that describes the relationship between wing-stroke amplitude ( A ), wing-beat frequency ( f ), and flight speed ( U ). Calculations indicated that even moderate wing movements are enough to generate rudimentary thrust and that a propulsive flapping flight-stroke could have evolved via gradual incremental changes in wing movement and wing morphology. More fundamental to the origin of the avian flapping flight-stroke is the question of how a symmetrical forelimb posture—required for gliding and flapping flight—evolved from an alternating forelimb motion, evident in all extant bipeds when running except birds.     

Proprioceptive activity of the wing-hinge stretch receptor in Manduca sexta and other atympanate moths: a study of the noctuoid moth ear B cell homologue

A multiterminal neurone, recently identified at the wing-hinge of the atympanate moth Manduca sexta, is shown to respond as a proprioceptor monitoring elevatory movements of the hind wing. Extracellular recordings from the individual receptor axon confirm this cell to be the source of the spontaneous and regular discharge observed in previous recordings of peripheral nerve 3N1b1. When the wing is raised, this tonic discharge rate increases proportionally with the angle of elevation. When the wing is displaced sinusoidally at a low frequency, the receptor discharge is modulated throughout the wing beat, increasing steadily to a maximum at the top of the upstroke, then slowly decreasing to a minimum at the bottom of the downstroke. At higher wing-beat frequencies, a phasic burst of activity occurs near the top of the upstroke, followed by a silent period during the down-stroke. Video-microscopic observations of the wing-hinge during active, stationary flight suggest that the receptor is stimulated by the stretching of its peripheral attachment, the subalar membrane. Stretch receptor sensitivity to wing movement is demonstrated in representatives of 4 lepidopteran families, suggesting that the proprioceptive response is widespread among the Lepidoptera. The functional role of the wing-hinge receptor, and its proposed homologous relationship to both the B cell of the noctuoid moth ear, and the locust wing-hinge stretch receptor are discussed.Abbreviations CO chordotonal organ - EGAA Enhanced Graphics Acquisition and Analysis System - HP hair plate - 3N1b1 tympanal nerve - SR stretch receptor     

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.     

Flight of the honey bee. VIII. Functional elements and mechanics of the “flight motor” and the wing joint – one of the most complicated gear-mechanisms in the animal kingdom

The form and position of the sclerites and important parts of the thorax, as well as the insertion points of the flight muscles, are described in this study with the help of three-dimensional drawings and electron micrographs. Morphological studies are used for functional analysis of the wing joint and flight muscles, and a three-dimensional model of the wing joint of a honey bee is used to demonstrate the automatic forced guidance of the forewings during the upstroke and downstroke. Accepted: 4 February 1998     

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.     

Wing kinematics during natural leaping in the mantids Mantis religiosa and Iris oratoria

High-speed flash photography was used to analyse wing movements of Mantis religiosa and Iris oratoria at the moment of take-off during natural leaping. Wing kinematics are compared with those of the similarly designed locust wing. Iris oratoria showed strong coupling between leg extensor and wing depressor muscle activity immediately prior to take-off, with a possible enhancement of jump momentum. A 'clap and peel' was observed in the hind wings of both species during the first downstroke. Supination in the mantid forewing is accomplished by a backward rotation of the whole of the main wing plate about the claval furrow. Both fore- and hind wings show pronounced ventral flexure at the lower point of stroke reversal. Camber was developed in the hind wing during the upstroke as well as the downstroke. Possible roles of the claval furrow and transverse flexion in protecting the forewing base against torsional forces generated at stroke reversal are discussed.     

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.     

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.