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.     

Flow visualization and unsteady aerodynamics in the flight of the hawkmoth,Manduca sexta

The aerodynamic mechanisms employed durng the flight of the hawkmoth, Manduca sexta, have been investigated through smoke visualization studies with tethered moths. Details of the flow around the wings and of the overall wake structure were recorded as stereophotographs and high-speed video sequences. The changes in flow which accompanied increases in flight speed from 0.4 to 5.7 m s^-1 were analysed. The wake consists of an alternating series of horizontal and vertical vortex rings which are generated by successive down- and upstrokes, respectively. The downstroke produces significantly more lift than the upstroke due to a leading-edge vortex which is stabilized by a radia flow moving out towards the wingtip. The leading-edge vortex grew in size with increasing forward flight velocity. Such a phenomenon is proposed as a likely mechanism for lift enhancement in many insect groups. During supination, vorticity is shed from the leading edge as postulated in the ''flex'' mechanism. This vorticity would enhance upstroke lift if it was recaptured diring subsequent translation, but it is not. Instead, the vorticity is left behind and the upstroke circulation builds up slowly. A small jet provides additional thrust as the trailing edges approach at the end of the upstroke. The stereophotographs also suggest that the bound circulation may not be reversed between half strokes at the fastest flight speeds.     

Centripetal Acceleration Reaction: An Effective and Robust Mechanism for Flapping Flight in Insects

Despite intense study by physicists and biologists, we do not fully understand the unsteady aerodynamics that relate insect wing morphology and kinematics to lift generation. Here, we formulate a force partitioning method (FPM) and implement it within a computational fluid dynamic model to provide an unambiguous and physically insightful division of aerodynamic force into components associated with wing kinematics, vorticity, and viscosity. Application of the FPM to hawkmoth and fruit fly flight shows that the leading-edge vortex is the dominant mechanism for lift generation for both these insects and contributes between 72–85% of the net lift. However, there is another, previously unidentified mechanism, the centripetal acceleration reaction, which generates up to 17% of the net lift. The centripetal acceleration reaction is similar to the classical inviscid added-mass in that it depends only on the kinematics (i.e. accelerations) of the body, but is different in that it requires the satisfaction of the no-slip condition, and a combination of tangential motion and rotation of the wing surface. Furthermore, the classical added-mass force is identically zero for cyclic motion but this is not true of the centripetal acceleration reaction. Furthermore, unlike the lift due to vorticity, centripetal acceleration reaction lift is insensitive to Reynolds number and to environmental flow perturbations, making it an important contributor to insect flight stability and miniaturization. This force mechanism also has broad implications for flow-induced deformation and vibration, underwater locomotion and flows involving bubbles and droplets.     

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.     

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.     

Particle-Image Velocimetry and Force Measurements of Leading-Edge Serrations on Owl-Based Wing Models

High-resolution Particle-Image Velocimetry （PIV） and time-resolved force measurements were performed to analyze the impact of the comb-like structure on the leading edge of barn owl wings on the flow field and overall aerodynamic performance. The Reynolds number was varied in the range of 40,000 to 120,000 and the range of angle of attack was 0° to 6° for the PIV and -15° to ＋20° for the force measurements to cover the full flight envelope of the owl. As a reference, a wind-tunnel model which possessed a geometry based on the shape of a typical barn owl wing without any owl-specific adaptations was built, and measurements were performed in the aforementioned Reynolds number and angle of attack： range. This clean wing model shows a separation bubble in the distal part of the wing at higher angles of attack. Two types of comb-like structures, i.e., artificial serrations, were manufactured to model the owl＇s leading edge with respect to its length, thickness, and material properties. The artificial structures were able to reduce the size of the separation region and additionally cause a more uniform size of the vortical structures shed by the separation bubble within the Reynolds number range investigated, resulting in stable gliding flight independent of the flight velocity. However, due to increased drag coefficients in conjunction with similar lift coefficients, the overall aerodynamic performance, i.e., lift-to-drag ratio is reduced for the serrated models. Nevertheless, especially at lower Reynolds numbers the stabilizing effect of the uniform vortex size outperforms the lower aerodynamic performance.     

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.     

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.     

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.     

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

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

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.     

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.     

Leading edge vortex in a slow-flying passerine

Most hovering animals, such as insects and hummingbirds, enhance lift by producing leading edge vortices (LEVs) and by using both the downstroke and upstroke for lift production. By contrast, most hovering passerine birds primarily use the downstroke to generate lift. To compensate for the nearly inactive upstroke, weight support during the downstroke needs to be relatively higher in passerines when compared with, e.g. hummingbirds. Here we show, by capturing the airflow around the wing of a freely flying pied flycatcher, that passerines may use LEVs during the downstroke to increase lift. The LEV contributes up to 49 per cent to weight support, which is three times higher than in hummingbirds, suggesting that avian hoverers compensate for the nearly inactive upstroke by generating stronger LEVs. Contrary to other animals, the LEV strength in the flycatcher is lowest near the wing tip, instead of highest. This is correlated with a spanwise reduction of the wing's angle-of-attack, partly owing to upward bending of primary feathers. We suggest that this helps to delay bursting and shedding of the particularly strong LEV in passerines.     

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.     

Der Vorderflügel großer Heuschrecken als Luftkrafterzeuger

Summary The mode is demonstrated in which the three regions of the forewings of large grasshoppers, i.e. the costal, radial and anal parts (Fig. 2) are folded against each other during up- and downstroke (Fig. 1; measurements made by W. Zarnack). The aerodynamic effects of this wing folding are determined from the measurements of lift carried out on wing models in parallel air stream (Fig. 3) and on rotating wing models (Fig. 4). Accordingly wing bending during downstroke generates distinctly higher lift at small and medium angles of attack than a flat wing having the same dimensions and moving at the same speed. It generates less lift at high angles of attack. Wing bending during upstroke generates higher lift only at>15°. Lift remains greater than that of a flat wing up to the highest angles of attack. These conclusions are supported by measurements of downstroke wind velocity (Fig. 5). Therefore it is possible to change the lift of right and left wings in order to generate moments for flight control around all three axes of the animal's system of co-ordinates without changing the rough kinematics of the beating wings.

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Der Verfasser dankt Dr. H.K. Pfau für die Einstellung der Flügelmodelle auf typische Mittelpositionen nach funktionsmorphologischen Gesichtspunkten (Abb. 2a) und Dr. W. Zarnack für die Vorpublikationserlaubnis der in Abb. 1 zusammengefaßten Meßdaten. Für meßtechnische Mitarbeit dankt er Frl. cand. rer. nat. U. Britz.     

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.     

In vivo strain in the humerus of pigeons (Columba livia) during flight

Longitudinal and principal strain recordings were made in vivo at three sites (dorsal, anterior, and ventral) on the humeral midshaft of pigeons executing five modes of free flight: Take-off, level flight, landing, vertical ascent, and near-vertical descent. Strains were also recorded while the birds flew carrying weights that were 33%, 50%, or 100% of their body weight. The relative distribution of strain measured at the three surface midshaft sites and across the bone's cortex was found to be similar for all flight modes. Principal strains recorded in the dorsal and ventral humerus indicated considerable torsion produced by aerodynamic loading of the wing surface posterior to the bone. Measured torsional shear strains (maximum: 2,700–4,150 μ ε during level flight) were 1.5 times greater than longitudinal strains. In addition to torsion, the humerus is also subjected to significant dorsoventral bending owing to lift forces acting on the wing during the downstroke. Analysis of the cross-sectional distribution of longitudinal strains at the humeral midshaft cortex shows that the orientation of bending shifts in a regular manner during the downstroke, indicating that the wing generates progressively more thurst (vs. lift) later in the downstroke. This shift is less during take-off and vertical ascent when greater lift is required. Peak principal and longitudinal strains increased by an average of only 50% from landing to vertical ascending flight and take-off (e.g., dorsal humerus: ?1,503 to ?2,329 μ ε) and did not exceed ?2,600 μ epsiv; at any site, even when the birds flew carrying twice their body weight. Strains recorded when birds flew at two times their body weight (100% BW load) were similar in magnitude to those recorded during vertical ascent and take-off and likely represent those developed during maximal performance. Strains developed within the midshaft were maximal in the anterodorsal and posteroventral cortices, not at the dorsal, ventral, and anterior sites at which strain was recorded. Consequently, maximum strains experienced by the bone are probably 20–25% greater than those recorded (ca. 3,200 μ ε), indicating a safety factor of about 3.5 for compressive strain failure. The much higher shear strains, however, indicate a lower safety factor (1.9), in which the bone's torsional strength is its most critical design feature. Finally, the magnitude and distribution of strains developed in the humerus of pigeons are generally similar to those recorded in the humerus of large fruit-eating bats during flight. © 1995 Wiley-Liss, Inc.     

Flight Characteristics of Two Plume Moths, Alucita pentadacty/a L. and Orneodes hexadactyla L. (Microlepidoptera)

Norberg, R. Å. (Department of Zoology, University of Gothenburg, Göteborg, Sweden.) Flight characteristics of two plume moths, Alucita pentadactyla L. and Orneodes hexadactyla L. (Microlepidoptera). Zool. Scripta 1 (6): 241–246,1972.–Multiple exposure photographs of up to 100 exposures/sec were taken on two plume moth species in free, unrestrained flight, in order to determine approximate lift/drag ratios and other functional characteristics of their wings, which are of a remarkable structure for insects of this size. In Alucita the forewing is cleft in two fringed lobes, the hind-wing in three, while in Orneodes both forewing and hindwing are deeply cleft in six very narrow, fringed lobes. Wing stroke frequencies are ca. 33 Hz in A. pentadactyla and ca. 40 Hz in O. hexadactyla. During both the downstroke and the upstroke the fringed wing lobes lie edge against edge, thus forming a continuous wing surface. The upstroke seems to contribute no useful forces in A. pentadactyla, possibly some propulsive force in O. hexadactyla. The wings are strongly supinated in the upstroke to minimize drag. From relative wind diagrams, lift/drag ratios of 1.1 and 1.4 (minimum values) can be read for A. pentadactyla and O. hexadactyla, respectively. It is thus clear that these species do not make more use of drag forces than of lift forces. However, in A. pentadactyla the drag force in the downstroke may be almost as large as the lift force. Since drag certainly is small in the upstroke, the drag force probably contributes significantly to useful forces for flight in A. pentadactyla. These plume moths operate at Reynolds numbers of ca. 700. Reynolds numbers are calculated for very small insects. It is obvious that the wings of the smallest insects must be operating at Reynolds numbers of about 1. The fringed wings of small insects are briefly discussed.     

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 fish tail motion forms an attached leading edge vortex

The tail (caudal fin) is one of the most prominent characteristics of fishes, and the analysis of the flow pattern it creates is fundamental to understanding how its motion generates locomotor forces. A mechanism that is known to greatly enhance locomotor forces in insect and bird flight is the leading edge vortex (LEV) reattachment, i.e. a vortex (separation bubble) that stays attached at the leading edge of a wing. However, this mechanism has not been reported in fish-like swimming probably owing to the overemphasis on the trailing wake, and the fact that the flow does not separate along the body of undulating swimmers. We provide, to our knowledge, the first evidence of the vortex reattachment at the leading edge of the fish tail using three-dimensional high-resolution numerical simulations of self-propelled virtual swimmers with different tail shapes. We show that at Strouhal numbers (a measure of lateral velocity to the axial velocity) at which most fish swim in nature (approx. 0.25) an attached LEV is formed, whereas at a higher Strouhal number of approximately 0.6 the LEV does not reattach. We show that the evolution of the LEV drastically alters the pressure distribution on the tail and the force it generates. We also show that the tail''s delta shape is not necessary for the LEV reattachment and fish-like kinematics is capable of stabilising the LEV. Our results suggest the need for a paradigm shift in fish-like swimming research to turn the focus from the trailing edge to the leading edge of the tail.