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542:
rushes into the created gap and generates a strong leading edge vortex, and a second one developing at the wingtips. A third, weaker, vortex develops on the trailing edge. The strength of the developing vortices relies, in-part, on the initial gap of the inter-wing separation at the start of the flinging motion. With a decreased gap inter-wing gap indicating a larger lift generation, at the cost of larger drag forces. The implementation of a heaving motion during fling, flexible wings, and a delayed stall mechanism were found to reinforce vortex stability and attachment. Finally, to compensate the overall lower lift production during low
Reynolds number flight (with
3487:
3294:
653:
381:
wing at the same angle of attack. By dividing the flapping wing into a large number of motionless positions and then analyzing each position, it would be possible to create a timeline of the instantaneous forces on the wing at every moment. The calculated lift was found to be too small by a factor of three, so researchers realized that there must be unsteady phenomena providing aerodynamic forces. There were several developing analytical models attempting to approximate flow close to a flapping wing. Some researchers predicted force peaks at supination. With a dynamically scaled model of a
3588:, in which a variation called "pod" (for podomeres, limb segments) displayed a mutation that transformed normal wings. The result was interpreted as a triple-jointed leg arrangement with some additional appendages but lacking the tarsus, where the wing's costal surface would normally be. This mutation was reinterpreted as strong evidence for a dorsal exite and endite fusion, rather than a leg, with the appendages fitting in much better with this hypothesis. The innervation, articulation and musculature required for the evolution of wings are already present in the limb segments.
1787:, or stay in one spot in the air, doing so by beating their wings rapidly. Doing so requires sideways stabilization as well as the production of lift. The lifting force is mainly produced by the downstroke. As the wings push down on the surrounding air, the resulting reaction force of the air on the wings pushes the insect up. The wings of most insects are evolved so that, during the upward stroke, the force on the wing is small. Since the downbeat and return stroke force the insect up and down respectively, the insect oscillates and winds up staying in the same position.
188:
468:
flight more efficient as this efficiency becomes more necessary. Additionally, by changing the geometric angle of attack on the downstroke, the insect is able to keep its flight at an optimal efficiency through as many manoeuvres as possible. The development of general thrust is relatively small compared with lift forces. Lift forces may be more than three times the insect's weight, while thrust at even the highest speeds may be as low as 20% of the weight. This force is developed primarily through the less powerful upstroke of the flapping motion.
612:
596:
1770:
641:
629:
3039:
418:. At high angles of attack, the flow separates over the leading edge, but reattaches before reaching the trailing edge. Within this bubble of separated flow is a vortex. Because the angle of attack is so high, a lot of momentum is transferred downward into the flow. These two features create a large amount of lift force as well as some additional drag. The important feature, however, is the lift. Because the flow has separated, yet it still provides large amounts of lift, this phenomenon is called
176:
312:, use asynchronous muscle; this is a type of muscle that contracts more than once per nerve impulse. This is achieved by the muscle being stimulated to contract again by a release in tension in the muscle, which can happen more rapidly than through simple nerve stimulation alone. This allows the frequency of wing beats to exceed the rate at which the nervous system can send impulses. The asynchronous muscle is one of the final refinements that has appeared in some of the higher Neoptera (
286:
584:
274:
3049:. When the wings begin to decelerate toward the end of the stroke, this energy must dissipate. During the downstroke, the kinetic energy is dissipated by the muscles themselves and is converted into heat (this heat is sometimes used to maintain core body temperature). Some insects are able to utilize the kinetic energy in the upward movement of the wings to aid in their flight. The wing joints of these insects contain a pad of elastic, rubber-like protein called
443:
502:
482:
3471:, the group of winged insects that includes grasshoppers, evolved from a terrestrial ancestor, making the evolution of wings from gills unlikely. Additional study of the jumping behavior of mayfly larvae has determined that tracheal gills play no role in guiding insect descent, providing further evidence against this evolutionary hypothesis. This leaves two major historic theories: that wings developed from paranotal lobes, extensions of the
3342:), there is no arrangement of frenulum and retinaculum to couple the wings. Instead, an enlarged humeral area of the hindwing is broadly overlapped by the forewing. Despite the absence of a specific mechanical connection, the wings overlap and operate in phase. The power stroke of the forewing pushes down the hindwing in unison. This type of coupling is a variation of frenate type but where the frenulum and retinaculum are completely lost.
455:
22:
414:(smooth) when the Reynolds number is low, and turbulent when it is high. The Wagner effect was ignored, consciously, in at least one model. One of the most important phenomena that occurs during insect flight is leading edge suction. This force is significant to the calculation of efficiency. The concept of leading edge suction first was put forth by D. G. Ellis and J. L. Stollery in 1988 to describe vortex lift on sharp-edged
1144:
1175:
around an airfoil and Stokes flow experienced by a swimming bacterium. For this reason, this intermediate range is not well understood. On the other hand, it is perhaps the most ubiquitous regime among the things we see. Falling leaves and seeds, fishes, and birds all encounter unsteady flows similar to that seen around an insect. The chordwise
Reynolds number can be described by:
2166:, applied by the two wings during the downward stroke is two times the weight. Because the pressure applied by the wings is uniformly distributed over the total wing area, that means one can assume the force generated by each wing acts through a single point at the midsection of the wings. During the downward stroke, the center of the wings traverses a vertical distance
1585:(α). The typical angle of attack at 70% wingspan ranges from 25° to 45° in hovering insects (15° in hummingbirds). Despite the wealth of data available for many insects, relatively few experiments report the time variation of α during a stroke. Among these are wind tunnel experiments of a tethered locust and a tethered fly, and free hovering flight of a fruit fly.
3405:
964:
434:
to about 3 grams. As insect body mass increases, wing area increases and wing beat frequency decreases. For larger insects, the
Reynolds number (Re) may be as high as 10000, where flow is starting to become turbulent. For smaller insects, it may be as low as 10. This means that viscous effects are much more important to the smaller insects.
3144:/cm. Typically in an insect the size of a bee, the volume of the resilin may be equivalent to a cylinder 2Ă10 cm long and 4Ă10 cm in area. In the example given, the length of the resilin rod is increased by 50% when stretched. That is, Îâ is 10 cm. Therefore, in this case the potential energy stored in the resilin of each wing is:
58:, some 300 to 350 million years ago, making them the first animals to evolve flight. Wings may have evolved from appendages on the sides of existing limbs, which already had nerves, joints, and muscles used for other purposes. These may initially have been used for sailing on water, or to slow the rate of descent when gliding.
2014:
3451:
How and why insect wings developed is not well understood, largely due to the scarcity of appropriate fossils from the period of their development in the Lower
Carboniferous. There have historically been three main theories on the origins of insect flight. The first was that they are modifications of
2149:
In the examples used the frequency used is 110 beats/s, which is the typical frequency found in insects. Butterflies have a much slower frequency with about 10 beats/s, which means that they can't hover. Other insects may be able to produce a frequency of 1000 beats/s. To restore the insect
1790:
The distance the insect falls between wingbeats depends on how rapidly its wings are beating: the slower it flaps, the longer the interval in which it falls, and the farther it falls between each wingbeat. One can calculate the wingbeat frequency necessary for the insect to maintain a given stability
1169:
and an airfoil: An insect wing is much smaller and it flaps. Using a dragonfly as an example, Its chord (c) is about 1 cm (0.39 in), its wing length (l) about 4 cm (1.6 in), and its wing frequency (f) about 40 Hz. The tip speed (u) is about 1 m/s (3.3 ft/s), and the
467:
Another interesting feature of insect flight is the body tilt. As flight speed increases, the insect body tends to tilt nose-down and become more horizontal. This reduces the frontal area and therefore, the body drag. Since drag also increases as forward velocity increases, the insect is making its
433:
All of the effects on a flapping wing may be reduced to three major sources of aerodynamic phenomena: the leading edge vortex, the steady-state aerodynamic forces on the wing, and the wing's contact with its wake from previous strokes. The size of flying insects ranges from about 20 micrograms
380:
Identification of major forces is critical to understanding insect flight. The first attempts to understand flapping wings assumed a quasi-steady state. This means that the air flow over the wing at any given time was assumed to be the same as how the flow would be over a non-flapping, steady-state
327:
Asynchronous muscle is, by definition, under relatively coarse control by the nervous system. To balance this evolutionary trade-off, insects that evolved indirect flight have also developed a separate neuromuscular system for fine-grained control of the wingstroke. Known as "direct muscles", these
3060:
Using a few simplifying assumptions, we can calculate the amount of energy stored in the stretched resilin. Although the resilin is bent into a complex shape, the example given shows the calculation as a straight rod of area A and length. Furthermore, we will assume that throughout the stretch the
2496:
In the calculation of the power used in hovering, the examples used neglected the kinetic energy of the moving wings. The wings of insects, light as they are, have a finite mass; therefore, as they move they possess kinetic energy. Because the wings are in rotary motion, the maximum kinetic energy
549:
The overall largest expected drag forces occur during the dorsal fling motion, as the wings need to separate and rotate. The attenuation of the large drag forces occurs through several mechanisms. Flexible wings were found to decrease the drag in flinging motion by up to 50% and further reduce the
3547:
and enable the insect to land more softly. The theory suggests that these lobes gradually grew larger and in a later stage developed a joint with the thorax. Even later would appear the muscles to move these crude wings. This model implies a progressive increase in the effectiveness of the wings,
1588:
Because they are relatively easy to measure, the wing-tip trajectories have been reported more frequently. For example, selecting only flight sequences that produced enough lift to support a weight, will show that the wing tip follows an elliptical shape. Noncrossing shapes were also reported for
401:
in 1925, says that circulation rises slowly to its steady-state due to viscosity when an inclined wing is accelerated from rest. This phenomenon would explain a lift value that is less than what is predicted. Typically, the case has been to find sources for the added lift. It has been argued that
1174:
has a wing length of about 0.5â0.7 mm (0.020â0.028 in) and beats its wing at about 400 Hz. Its
Reynolds number is about 25. The range of Reynolds number in insect flight is about 10 to 10, which lies in between the two limits that are convenient for theories: inviscid steady flows
541:
Lift generation from the clap and fling mechanism occurs during several processes throughout the motion. First, the mechanism relies on a wing-wing interaction, as a single wing motion does not produce sufficient lift. As the wings rotate about the trailing edge in the flinging motion, air
168:
have fore and hind wings similar in shape and size. Each operates independently, which gives a degree of fine control and mobility in terms of the abruptness with which they can change direction and speed, not seen in other flying insects. Odonates are all aerial predators, and they have always
537:
and utilize the leading edge during an upstroke rowing motion. As the clap motion begins, the leading edges meet and rotate together until the gap vanishes. Initially, it was thought that the wings were touching, but several incidents indicate a gap between the wings and suggest it provides an
304:
Insects that beat their wings fewer than one hundred times a second use synchronous muscle. Synchronous muscle is a type of muscle that contracts once for every nerve impulse. This generally produces less power and is less efficient than asynchronous muscle, which accounts for the independent
3021:
556:, cause a porosity in the flow which augments and reduces the drag forces, at the cost of lower lift generation. Further, the inter-wing separation before fling plays an important role in the overall effect of drag. As the distance increases between the wings, the overall drag decreases.
1139:{\displaystyle {\begin{aligned}{\frac {\partial \mathbf {u} }{\partial t}}+\left(\mathbf {u} \cdot \nabla \right)\mathbf {u} &=-{\frac {\nabla p}{\rho }}+v\nabla ^{2}\mathbf {u} \\\nabla \cdot \mathbf {u} &=0\\\mathbf {u} _{\text{bd}}&=\mathbf {u} _{\text{s}}.\end{aligned}}}
2389:
of the air that is accelerated by the downward stroke of the wings. The power is the amount of work done in 1 s; in the insect used as an example, makes 110 downward strokes per second. Therefore, its power output P is, strokes per second, and that means its power output P is:
532:
become dominant and the efficacy of lift generation from an airfoil decreases drastically. Starting from the clap position, the two wings fling apart and rotate about the trailing edge. The wings then separate and sweep horizontally until the end of the downstroke. Next, the wings
834:
385:, these predicted forces later were confirmed. Others argued that the force peaks during supination and pronation are caused by an unknown rotational effect that fundamentally is different from the translational phenomena. There is some disagreement with this argument. Through
3521:
gills, which started their way as exits of the respiratory system and over time were modified into locomotive purposes, eventually developed into wings. The tracheal gills are equipped with little winglets that perpetually vibrate and have their own tiny straight muscles.
3273:
392:
Similar to the rotational effect mentioned above, the phenomena associated with flapping wings are not completely understood or agreed upon. Because every model is an approximation, different models leave out effects that are presumed to be negligible. For example, the
3560:. Still, lack of substantial fossil evidence of the development of the wing joints and muscles poses a major difficulty to the theory, as does the seemingly spontaneous development of articulation and venation, and it has been largely rejected by experts in the field.
2486:
422:, first noticed on aircraft propellers by H. Himmelskamp in 1945. This effect was observed in flapping insect flight and it was proven to be capable of providing enough lift to account for the deficiency in the quasi-steady-state models. This effect is used by
240:; it corresponds, probably not coincidentally, with the appearance of a wing-folding mechanism, which allows Neopteran insects to fold the wings back over the abdomen when at rest (though this ability has been lost secondarily in some groups, such as in the
328:
muscles attach directly to the sclerites that make up the wing hinge and are contract with 1:1 impulses from motor neurons. Recent work has begun to address the complex non-linear muscular dynamics at the wing hinge and its effects on the wingtip path.
1859:
The upward stroke then restores the insect to its original position. Typically, it may be required that the vertical position of the insect changes by no more than 0.1 mm (i.e., h = 0.1 mm). The maximum allowable time for free fall is then
3278:
The stored energy in the two wings for a bee-sized insect is 36 erg, which is comparable to the kinetic energy in the upstroke of the wings. Experiments show that as much as 80% of the kinetic energy of the wing may be stored in the resilin.
1866:
2805:
208:
3641:
with both tergal and pleural structures, potentially resolving the centuries-old debate. Jakub Prokop and colleagues have in 2017 found palaeontological evidence from
Paleozoic nymphal wing pads that wings indeed had such a dual origin.
3542:
that would have assisted stabilization while hopping or falling. In favor of this hypothesis is the tendency of most insects, when startled while climbing on branches, to escape by dropping to the ground. Such lobes would have served as
652:
2384:
This is a negligible fraction of the total energy expended which clearly, most of the energy is expended in other processes. A more detailed analysis of the problem shows that the work done by the wings is converted primarily into
2379:
941:
1791:
in its amplitude. To simplify the calculations, one must assume that the lifting force is at a finite constant value while the wings are moving down and that it is zero while the wings are moving up. During the time interval Î
2298:
2877:
214:
213:
210:
209:
1357:
2232:
215:
2698:
3131:
231:
Other than the two orders with direct flight muscles, all other living winged insects fly using a different mechanism, involving indirect flight muscles. This mechanism evolved once and is the defining feature
2237:
If the wings swing through the beat at an angle of 70°, then in the case presented for the insect with 1 cm long wings, d is 0.57 cm. Therefore, the work done during each stroke by the two wings is:
373:(Hz). In those with asynchronous flight muscles, wing beat frequency may exceed 1000 Hz. When the insect is hovering, the two strokes take the same amount of time. A slower downstroke, however, provides
2810:
The velocity of the wings is zero both at the beginning and at the end of the wing stroke, meaning the maximum linear velocity is higher than the average velocity. If we assume that the velocity oscillates
708:
5058:
Dickerson, Bradley H., Alysha M. de Souza, Ainul Huda, and
Michael H. Dickinson. "Flies regulate wing motion via active control of a dual-function gyroscope." Current Biology 29, no. 20 (2019): 3517-3524.
2866:
2144:
69:, have flight muscles attached directly to the wings. In other winged insects, flight muscles attach to the thorax, which make it oscillate in order to induce the wings to beat. Of these insects, some (
2552:
2154:, must be equal to twice the weight of the insect. Note that since the upward force on the insect body is applied only for half the time, the average upward force on the insect is simply its weight.
2084:
3150:
3517:
in 1905 have suggested that a possible origin for insect wings might have been movable abdominal gills found in many aquatic insects, such as on naiads of mayflies. According to this theory these
212:
5772:
Niwa, Nao; Akimoto-Kato, Ai; Niimi, Teruyuki; Tojo, Koji; Machida, Ryuichiro; Hayashi, Shigeo (2010-03-17). "Evolutionary origin of the insect wing via integration of two developmental modules".
255:, the deformations of the thorax cause the wings to move as well. A set of longitudinal muscles along the back compresses the thorax from front to back, causing the dorsal surface of the thorax (
2396:
969:
5067:
Wolf, Harald. "The locust tegula: significance for flight rhythm generation, wing movement control and aerodynamic force production." Journal of
Experimental Biology 182, no. 1 (1993): 229-253.
187:
3534:
in 1875 and reworked by G. Crampton in 1916, Jarmila
Kukalova-Peck in 1978 and Alexander P. Rasnitsyn in 1981 among others, suggests that the insect's wings developed from paranotal lobes, a
1854:
5171:
1225:
2623:
864:
of a 2D airfoil further assumes that the flow leaves the sharp trailing edge smoothly, and this determines the total circulation around an airfoil. The corresponding lift is given by
1523:
In addition to the
Reynolds number, there are at least two other relevant dimensionless parameters. A wing has three velocity scales: the flapping velocity with respect to the body (
285:
4119:
5077:
Misof, B.; Liu, S.; Meusemann, K.; Peters, R. S.; Donath, A.; Mayer, C.; Frandsen, P.; et al. (2014). "Phylogenomics resolves the timing and pattern of insect evolution".
3693:
1268:
595:
127:, generating large lift forces at the expense of wear and tear on the wings. Many insects can hover, maintaining height and controlling their position. Some insects such as
5049:
Sane, Sanjay P., Alexandre Dieudonné, Mark A. Willis, and Thomas L. Daniel. "Antennal mechanosensors mediate flight control in moths." science 315, no. 5813 (2007): 863-866.
2009:{\displaystyle \Delta t=\left({\frac {2h}{g}}\right)^{1/2}={\sqrt {\frac {2\times 10^{-2}{\text{ cm}}}{980{\text{ cm}}/{\text{s}}^{2}}}}\approx 4.5\times 10^{-3}{\text{ s}}}
156:(dragonflies and damselflies) insert directly at the wing bases, which are hinged so that a small downward movement of the wing base lifts the wing itself upward, much like
1391:
357:. These flapping wings move through two basic half-strokes. The downstroke starts up and back and is plunged downward and forward. Then the wing is quickly flipped over (
77:) achieve very high wingbeat frequencies through the evolution of an "asynchronous" nervous system, in which the thorax oscillates faster than the rate of nerve impulses.
611:
1161:
the velocity of the solid. By choosing a length scale, L, and velocity scale, U, the equation can be expressed in nondimensional form containing the Reynolds number, R
1431:
2720:
1589:
other insects. Regardless of their exact shapes, the plugging-down motion indicates that insects may use aerodynamic drag in addition to lift to support its weight.
389:, some researchers argue that there is no rotational effect. They claim that the high forces are caused by an interaction with the wake shed by the previous stroke.
1478:
640:
2714:
traversed by the center of the wing divided by the duration Ît of the wing stroke. From our previous example, d = 0.57 cm and Ît = 4.5Ă10 s. Therefore:
1581:Ï(t), about the axis connecting the root and the tip. To estimate the aerodynamic forces based on blade-element analysis, it is also necessary to determine the
1518:
1498:
1451:
1411:
175:
2313:
6443:
628:
6420:
954:, or velocity relative to the speed of sound in air, is typically 1/300 and the wing frequency is about 10â103 Hz. Using the governing equation as the
878:
273:
2244:
3428:, some 350 to 300 million years ago, when there were only two major land masses, insects began flying. Among the oldest winged insect fossils is
3016:{\displaystyle KE={\frac {1}{2}}I\omega _{max}^{2}=\left(10^{-3}{\frac {\ell ^{2}}{3}}\right)\left({\frac {254}{\ell /2}}\right)^{2}=43{\text{ erg}}}
211:
3621:
Stephen P. Yanoviak and colleagues proposed in 2009 that the wing derives from directed aerial gliding descentâa preflight phenomenon found in some
3057:
in the stretched resilin, which stores the energy much like a spring. When the wing moves down, this energy is released and aids in the downstroke.
676:, which follows the conventions found in aerodynamics. The force component normal to the direction of the flow relative to the wing is called lift (
3568:
5491:
Kukalova-Peck, Jarmila (1978). "Origin and evolution of insect wings and their relation to metamorphosis, as documented by the fossil record".
2019:
Since the up movements and the down movements of the wings are about equal in duration, the period T for a complete up-and-down wing is twice Î
1273:
4967:
4281:
3707:
3699:
2577:
for the wing, we will assume that the wing can be approximated by a thin rod pivoted at one end. The moment of inertia for the wing is then:
2176:
684:). At the Reynolds numbers considered here, an appropriate force unit is 1/2(ÏUS), where Ï is the density of the fluid, S the wing area, and
574:(a fly), exploit a partial clap and fling, using the mechanism only on the outer part of the wing to increase lift by some 7% when hovering.
2646:
251:
work: these muscles, rather than attaching to the wings, attach to the thorax and deform it; since the wings are extensions of the thoracic
2628:
Where l is the length of the wing (1 cm) and m is the mass of two wings, which may be typically 10 g. The maximum angular velocity, Ï
3075:
3026:
Since there are two wing strokes (the upstroke and downstroke) in each cycle of the wing movement, the kinetic energy is 2Ă43 = 86
3293:
829:{\displaystyle C_{\text{L}}(\alpha )={\frac {2L}{\rho U^{2}S}}\quad {\text{and}}\quad C_{\text{D}}(\alpha )={\frac {2D}{\rho U^{2}S}}.}
361:) so that the leading edge is pointed backward. The upstroke then pushes the wing upward and backward. Then the wing is flipped again (
5947:
Prokop, Jakub; PecharovĂĄ, Martina; Nel, AndrĂ©; Hörnschemeyer, Thomas; KrzemiĆska, Ewa; KrzemiĆski, WiesĆaw; Engel, Michael S. (2017).
3486:
3779:
Josephson, Robert K.; Malamud, Jean G.; Stokes, Darrell R. (2001). "The efficiency of an asynchronous flight muscle from a beetle".
2162:
One can now compute the power required to maintain hovering by, considering again an insect with mass m 0.1 g, average force, F
2815:) along the wing path, the maximum velocity is twice as high as the average velocity. Therefore, the maximum angular velocity is:
4790:
4008:
2821:
2095:
3268:{\displaystyle U={\frac {1}{2}}{\frac {1.8\times 10^{7}\times 4\times 10^{-4}\times 10^{-4}}{2\times 10^{-2}}}=18\ {\text{erg}}}
2503:
583:
5023:
4821:
4625:
4574:
4484:
4369:
4065:
3828:
3781:
3506:
3320:
The more primitive groups have an enlarged lobe-like area near the basal posterior margin, i.e. at the base of the forewing, a
2029:
1573:
wing is approximately so, its motion relative to a fixed body can be described by three variables: the position of the tip in
4959:
3633:
Biologists including Averof, Niwa, Elias-Neto and their colleagues have begun to explore the origin of the insect wing using
324:). The overall effect is that many higher Neoptera can beat their wings much faster than insects with direct flight muscles.
3614:
and Ă
ke Norberg suggested in 2003 that wings may have evolved initially for sailing on the surface of water as seen in some
2481:{\displaystyle {\text{P}}=112{\text{erg}}\times 110{\text{/s}}=1.23\times 10^{4}{\text{erg/s}}=1.23\times 10^{-3}{\text{W}}}
546:), tiny insects often have a higher stroke frequency to generate wing-tip velocities that are comparable to larger insects.
6142:
Lewin, G. C.; Haj-Hariri, H. (2003). "Modelling thrust generation of a two-dimensional heaving airfoil in a viscous flow".
869:
658:
Fling 3: new vortex forms at leading edge, trailing edge vortices cancel each other, perhaps helping flow to grow faster (
5404:
Crampton, G. (1916). "The Phylogenetic Origin and the Nature of the Wings of Insects According to the Paranotal Theory".
3713:
386:
6452:
5007:
Woiwod, I.P.; Reynolds, D.R.; Thomas, C.D. (Eds) 2001. Insect Movement: Mechanisms and Consequences. CAB International.
5387:
1574:
264:
5169:
Tillyard, R. J. (2009). "Some remarks on the Devonian fossil insects from the Rhynie chert beds, Old Red Sandstone".
1805:
6477:
5441:
4914:
4210:
3656:
534:
342:
There are two basic aerodynamic models of insect flight: creating a leading edge vortex, and using clap and fling.
6440:
6435:
6368:
Zbikowski, R. (2002). "On aerodynamic modelling of an insect-like flapping wing in hover for micro air vehicles".
6010:
Dickinson, M. H.; Lehmann, F. O.; Sane, S. P. (1999). "Wing rotation and the aerodynamic basis of insect flight".
4057:
6040:
5597:
3611:
3065:. This is not strictly true as the resilin is stretched by a considerable amount and therefore both the area and
1180:
550:
overall drag through the entire wing stroke when compared to rigid wings. Bristles on the wing edges, as seen in
4367:(1973). "Quick estimates of flight fitness in hovering animals, including novel mechanisms of lift production".
860:
around an airfoil can be approximated by a potential flow satisfying the no-penetration boundary condition. The
2583:
2170:. The total work done by the insect during each downward stroke is the product of force and distance; that is,
1775:
528:, is a lift generation method utilized during small insect flight. As insect sizes become less than 1 mm,
3053:. During the upstroke of the wing, the resilin is stretched. The kinetic energy of the wing is converted into
865:
5142:[A Lower Carboniferous insect from the Bitterfeld/Delitzsch area (Pterygota, Arnsbergian, Germany)].
116:
before shedding their wings after mating, while the members of other castes are wingless their entire lives.
861:
382:
248:
2089:
The frequency of the beats, f, meaning the number of wingbeats per second, is represented by the equation:
6482:
3313:
which render these taxa functionally two-winged. All but the most basal forms exhibit this wing-coupling.
955:
5261:"Evolutionary history of Polyneoptera and its implications for our understanding of early winged insects"
1553:, the former is often referred to as the advance ratio, and it is also related to the reduced frequency,
5713:
Averof, Michalis; Cohen, Stephen M. (1997). "Evolutionary origin of insect wings from ancestral gills".
5546:
5493:
4621:"The aerodynamic benefit of wing-wing interaction depends on stroke trajectory in flapping insect wings"
1769:
1741:
856:
may reach a steady state when it slices through the fluid at a small angle of attack. In this case, the
89:
5825:"Tergal and pleural structures contribute to the formation of ectopic prothoracic wings in cockroaches"
5140:"Ein unter-karbonisches Insekt aus dem Raum Bitterfeld/Delitzsch (Pterygota, Arnsbergium, Deutschland)"
3572:
Generalized arthropod biramous limb. Trueman proposed that an endite and an exite fused to form a wing.
3038:
6425:
1231:
6377:
6305:
6151:
6089:
6080:
Ellington, C. P. (1984). "The Aerodynamics of Hovering Insect Flight. I. The Quasi-Steady Analysis".
6052:
5962:
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4690:
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4338:
4128:
4017:
3824:
3745:
3597:
3518:
3425:
1784:
1637:
1578:
427:
4734:
Kasoju, V.; Santhanakrishnan, A. (2021). "Aerodynamic interaction of bristled wing pairs in fling".
4794:
4399:
Santhanakrishnan, A.; Robinson, A.; Jones, S.; Low, A.; Gadi, S.; Hendrick, T.; Miller, L. (2014).
4342:
3736:
3638:
947:
6370:
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
4858:
1364:
1153:(x, t) is the flow field, p the pressure, Ï the density of the fluid, Îœ the kinematic viscosity, u
6457:
6401:
6280:
6213:
6167:
6068:
5805:
5754:
5579:
5526:
5449:
5413:
5365:
5120:
4918:
4771:
4745:
4652:
4601:
4547:
4092:
4000:
3887:
3384:
to maintain and control flight. Research has demonstrated the role of sensory structures such as
3351:
The biochemistry of insect flight has been a focus of considerable study. While many insects use
4154:
3069:
change in the process of stretching. The potential energy U stored in the stretched resilin is:
3066:
4445:"Two- and three- dimensional numerical simulations of the clap-fling-sweep of hovering insects"
4177:
2800:{\displaystyle v_{av}={\frac {d}{\Delta t}}={\frac {0.57}{4.5\times 10^{-3}}}=127{\text{cm/s}}}
6393:
6356:
6336:
6205:
6130:
6110:
6027:
5988:
5980:
5929:
5911:
5870:
5852:
5797:
5789:
5746:
5738:
5695:
5625:
5571:
5563:
5518:
5510:
5385:
Trueman, J. W. H. (1990), Comment: evolution of insect wings: a limb exite plus endite model.
5357:
5308:
5290:
5241:
5188:
5112:
5104:
5079:
4963:
4840:
4736:
4716:
4644:
4593:
4539:
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4320:
4277:
4110:
4084:
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3879:
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3703:
3435:
3413:
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2574:
570:
564:
513:
398:
1416:
6385:
6348:
6321:
6313:
6272:
6238:
6197:
6159:
6122:
6097:
6060:
6019:
5970:
5919:
5901:
5860:
5844:
5781:
5730:
5685:
5677:
5643:
Marden, James (2003). "The Surface-Skimming Hypothesis for the Evolution of Insect Flight".
5617:
5555:
5502:
5347:
5298:
5280:
5231:
5221:
5180:
5151:
5096:
5032:
4830:
4763:
4706:
4698:
4634:
4583:
4529:
4493:
4464:
4412:
4378:
4364:
4310:
4136:
4074:
4025:
3941:
3933:
3861:
3790:
3753:
3666:
3327:
Other groups have a frenulum on the hindwing that hooks under a retinaculum on the forewing.
3054:
2570:
659:
623:
Black (curved) arrows: flow; Blue arrows: induced velocity; Orange arrows: net force on wing
552:
525:
354:
27:
4029:
1456:
501:
481:
21:
6447:
6226:
5953:
5668:
5461:
4884:
3584:, also called the pleural hypothesis. This was based on a study by Goldschmidt in 1945 on
3502:
3478:; or that they arose from modifications of leg segments, which already contained muscles.
3460:
3316:
The mechanisms are of three different types â jugal, frenulo-retinacular and amplexiform:
1582:
508:
442:
403:
85:
5474:
3531:
3366:
as their energy source. Some species also use a combination of sources and moths such as
2150:
to its original vertical position, the average upward force during the downward stroke, F
6430:
6381:
6309:
6155:
6093:
6056:
5966:
5840:
5726:
5613:
5343:
5328:"Jumping and the aerial behavior of aquatic mayfly larvae (Myobaetis ellenae, Baetidae)"
5276:
5092:
4759:
4694:
4468:
4460:
4132:
4021:
3946:
3749:
2374:{\displaystyle {\text{E}}={\text{mgh}}=0.1\times 980\times 10^{-2}=0.98{\text{erg}}\,\!}
6326:
6293:
5924:
5889:
5865:
5824:
5690:
5663:
5303:
5260:
5236:
5207:
5184:
4711:
4678:
4273:
3514:
3445:
3062:
2386:
1503:
1483:
1436:
1396:
673:
529:
492:
454:
113:
6462:
6227:"The role of vortices and unsteady effects during the hovering flight of dragon flies"
3757:
3305:
Some four-winged insect orders, such as the Lepidoptera, have developed morphological
6471:
6171:
5785:
5621:
5600:; Norberg, R. Ă
ke (1996). "Skimming the surface â the origin of flight in insects?".
5544:
Rasnitsyn, Alexander P. (1981). "A modified paranotal theory of insect wing origin".
5369:
5155:
5139:
4775:
3891:
3581:
3577:
3535:
3409:
3368:
3352:
3306:
3298:
3288:
936:{\displaystyle C_{\text{L}}=2\pi \sin \alpha \quad {\text{and}}\quad C_{\text{D}}=0.}
857:
394:
132:
55:
6217:
5809:
5583:
5530:
5124:
4656:
4551:
4209:
Himmelskamp, H. (1945) "Profile investigations on a rotating airscrew". PhD thesis,
4096:
6405:
6072:
5906:
5758:
4679:"Wing-kinematics measurement and aerodynamics in a small insect in hovering flight"
4605:
3996:
3510:
3498:
3468:
3440:
3430:
1171:
602:
543:
411:
351:
337:
233:
120:
43:
6023:
2293:{\displaystyle {\text{Work}}=2\times 0.1\times 980\times 0.57=112{\text{erg}}\,\!}
6260:
4953:
4267:
2703:
During each stroke the center of the wings moves with an average linear velocity
6261:"Recordings of high wing-stroke and thoracic vibration frequency in some midges"
3661:
3651:
3549:
3417:
3335:
3331:
2307:
required to raise the mass of the insect 0.1 mm during each downstroke is:
1728:
1166:
951:
419:
321:
296:
252:
241:
165:
161:
97:
47:
4482:
Bennett, L. (1977). "Clap and fling aerodynamics- an experimental evaluation".
3925:
524:
Clap and fling, or the Weis-Fogh mechanism, discovered by the Danish zoologist
6163:
5975:
5948:
5352:
5327:
3937:
3622:
3360:
3339:
3140:
is the Young's modulus for resilin, which has been measured to be 1.8Ă10
3046:
2812:
1569:
415:
407:
358:
313:
93:
6111:"The novel aerodynamics of insect flight: Applications to micro-air vehicles"
5984:
5915:
5856:
5793:
5742:
5567:
5514:
5294:
5192:
5108:
4401:"Clap and fling mechanism with interacting porous wing in tiny insect flight"
4324:
4315:
4298:
4140:
3875:
3802:
852:
are constants only if the flow is steady. A special class of objects such as
259:) to bow upward, making the wings flip down. Another set of muscles from the
6352:
6126:
5559:
5506:
5285:
5100:
4989:(pp. 631-664) in Resh, & Cardé (Eds). "Encyclopedia of Insects". 2003.
3794:
3544:
3453:
1715:
1676:
1650:
1611:
423:
369:
range in insects with synchronous flight muscles typically is 5 to 200
366:
362:
309:
305:
evolution of asynchronous flight muscles in several separate insect clades.
32:
6431:
The Novel Aerodynamics Of Insect Flight: Applications To Micro-Air Vehicles
6397:
6389:
6360:
6317:
6209:
6134:
6101:
6031:
5992:
5933:
5888:
Tomoyasu, Yoshinori; Ohde, Takahiro; Clark-Hachtel, Courtney (2017-03-14).
5874:
5801:
5699:
5681:
5629:
5575:
5522:
5361:
5312:
5245:
5116:
4922:
4844:
4720:
4648:
4597:
4570:"The aerodynamic effects of wing-wing interaction in flapping insect wings"
4543:
4426:
4088:
3955:
3883:
3810:
3765:
3396:
in controlling flight posture, wingbeat amplitude, and wingbeat frequency.
5750:
5036:
4299:"Investigation into Reynolds number effects on a biomimetic flapping wing"
3404:
680:), and the force component in the opposite direction of the flow is drag (
4497:
4382:
3926:"Machine learning reveals the control mechanics of the insect wing hinge"
3634:
3615:
3605:
3472:
3464:
3389:
3381:
2633:
1702:
1689:
1663:
292:
237:
66:
6242:
5848:
5417:
3580:, appendages on the respective inner and outer aspects of the primitive
3530:
The paranotal lobe or tergal (dorsal body wall) hypothesis, proposed by
1352:{\displaystyle r_{g}={\sqrt {{\frac {1}{s}}\int _{0}^{R}{r^{2}c(R)dr}}}}
6284:
5949:"Paleozoic Nymphal Wing Pads Support Dual Model of Insect Wing Origins"
5226:
4835:
4816:
4534:
4517:
4417:
4400:
3866:
3849:
3637:
in addition to palaeontological evidence. This suggests that wings are
3553:
3363:
3050:
2562:
2227:{\displaystyle {\text{Work}}=F_{av}\times d={\text{2W}}_{\text{d}}\,\!}
1170:
corresponding Reynolds number about 103. At the smaller end, a typical
853:
560:
317:
194:
153:
105:
62:
6298:
Philosophical Transactions of the Royal Society B: Biological Sciences
6201:
6082:
Philosophical Transactions of the Royal Society B: Biological Sciences
4767:
4702:
4639:
4620:
4588:
4569:
4079:
3905:
Heide, G.G. (1983). "Neural mechanisms of flight control in Diptera".
2693:{\displaystyle \omega _{\text{max}}={\frac {v_{\text{max}}}{\ell /2}}}
617:
Clap 3: trailing edges close, vortices shed, wings close giving thrust
406:
that is typical of insect flight. The Reynolds number is a measure of
6064:
5734:
4114:
3601:
3557:
3539:
3490:
3356:
3045:
Insects gain kinetic energy, provided by the muscles, when the wings
1754:
1624:
488:
374:
260:
198:
157:
149:
81:
74:
51:
39:
6276:
197:(dragonflies and damselflies) have direct flight musculature, as do
6039:
Ellington, Charles P.; Van Den Berg, Coen; Willmott, Alexander P.;
5890:"What serial homologs can tell us about the origin of insect wings"
4750:
3126:{\displaystyle U={\frac {1}{2}}{\frac {EA\Delta \ell ^{2}}{\ell }}}
2303:
The energy is used to raise the insect against gravity. The energy
6250:
Smyth, T. Jr. (1985). "Muscle systems". In Blum, M.S. Blum (ed.).
5212:
4444:
3825:"Definition of Asynchronous muscle in the Entomologists' glossary"
3576:
In 1990, J. W. H. Trueman proposed that the wing was adapted from
3567:
3485:
3475:
3403:
3310:
3037:
3030:. This is about as much energy as is consumed in hovering itself.
1768:
958:
being subject to the no-slip boundary condition, the equation is:
568:, a sea butterfly. Some insects, such as the vegetable leaf miner
370:
267:
pulls the notum downward again, causing the wings to flip upward.
256:
109:
70:
4998:
Gorb, S. (2001) Ch 4.1.5 "Inter-locking of body parts". pp 46â50.
4297:
Hope, Daniel K; DeLuca, Anthony M.; O'Hara, Ryan P (2018-01-03).
3359:
as the energy source for flight, many beetles and flies use the
4115:"Ăber die Entstehung des dynamischen Auftriebes von TragflĂŒgeln"
3456:
3448:, but it is uncertain if it had wings, or indeed was an insect.
3393:
3141:
646:
Fling 2: leading edge moves away, air rushes in, increasing lift
247:
What all Neoptera share, however, is the way the muscles in the
128:
4443:
Kolomenskiy, D; Moffatt, H.; Farge, M.; Schneider, K. (2011).
3848:
Deora, Tanvi; Gundiah, Namrata; Sane, Sanjay P. (2017-04-15).
3027:
279:
Indirect flight: muscles make thorax oscillate in most insects
101:
5664:"Gliding hexapods and the origins of insect aerial behaviour"
6337:"Rotational lift: something difference or more of the same?"
5208:"The presumed oldest flying insect: more likely a myriapod?"
5017:
Joos, B. (1987). "Carbohydrate use in the flight muscles of
4911:
The Biomechanics of Insect Flight: Form, Function, Evolution
4178:"The Behaviour and Performance of Leading-Edge Vortex Flaps"
559:
The clap and fling mechanism is also employed by the marine
181:
Direct flight: muscles attached to wings. Large insects only
5144:
Neues Jahrbuch fĂŒr Geologie und PalĂ€ontologie - Monatshefte
2861:{\displaystyle \omega _{\text{max}}={\frac {254}{\ell /2}}}
2139:{\displaystyle f={\frac {1}{T}}\approx 110{\text{ s}}^{-1}}
491:
are unsuitable for leading edge vortex flight, but support
5721:(6617). Springer Science and Business Media LLC: 627â630.
2547:{\displaystyle KE={\frac {1}{2}}I\omega _{\text{max}}^{2}}
688:
the wing speed. The dimensionless forces are called lift (
6421:
An Insect's Role In The Development Of Micro Air Vehicles
6188:
Sane, S. P. (2003). "The aerodynamics of insect flight".
5172:
Transactions of the Royal Entomological Society of London
4191:. International Council of Aeronautical Sciences: 758â765
4117:[On the origin of the dynamic lift of airfoils].
634:
Fling 1: wings rotate around trailing edge to fling apart
4791:"Swim Like a Butterfly? Sea Snail 'Flies' Through Water"
2079:{\displaystyle T=2\,\Delta t=9\times 10^{-3}{\text{ s}}}
1538:). The ratios of them form two dimensionless variables,
308:
Insects that beat their wings more rapidly, such as the
299:
and most other insects, have indirect flight musculature
4942:
in Capinera (Ed) (2008) "Encyc. Entom.", Vol 4. p. 4266
4815:
Murphy, D.; Adhikari, D.; Webster, D.; Yen, J. (2016).
6453:
Flow visualization of butterfly aerodynamic mechanisms
5662:
Yanoviak, Stephen P.; Kaspari, M.; Dudley, R. (2009).
3924:
Melis, Johan M.; Dickinson, Michael H. (2023-06-30).
3153:
3078:
2880:
2824:
2723:
2649:
2586:
2506:
2399:
2316:
2247:
2179:
2098:
2032:
1869:
1808:
1506:
1486:
1459:
1439:
1419:
1399:
1367:
1276:
1234:
1183:
1165:=uL/Μ . There are two obvious differences between an
967:
946:
The flows around birds and insects can be considered
881:
711:
119:
Some very small insects make use not of steady-state
3695:
Numbers of living species in Australia and the World
1795:
of the upward wingbeat, the insect drops a distance
350:
Most insects use a method that creates a spiralling
5259:Wipfler, Benjamin; et al. (19 February 2019).
4817:"Underwater flight by the planktonic sea butterfly"
80:Not all insects are capable of flight. A number of
6225:Savage, S. B.; Newman, B.G.; Wong, D.T.M. (1979).
6043:(1996). "Leading-edge vortices in insect flight".
5326:Yanoviak, Stephen P.; Dudley, Robert (July 2018).
4120:Zeitschrift fĂŒr Angewandte Mathematik und Mechanik
3267:
3125:
3015:
2860:
2799:
2692:
2617:
2546:
2480:
2373:
2292:
2226:
2138:
2078:
2008:
1848:
1512:
1492:
1472:
1445:
1425:
1405:
1385:
1351:
1262:
1219:
1138:
935:
828:
35:has flight muscles attached directly to its wings.
4672:
4670:
4668:
4666:
3734:Smith, D.S. (1965). "Flight muscles of insects".
3625:, a wingless sister taxon to the winged insects.
2370:
2289:
2223:
601:Clap 2: leading edges touch, wing rotates around
6294:"The vortex wake of a 'hovering' model hawkmoth"
5399:
5397:
4568:Lehmann, F.-O.; Sane, S.; Dickinson, M. (2005).
5265:Proceedings of the National Academy of Sciences
4518:"Flexible clap and fling in tiny insect flight"
1520:is the length of wing, including the wing tip.
578:Clap and fling flight mechanism after Sane 2003
5138:Brauckmann, Carsten; Schneider, Joerg (1996).
4051:
4049:
4047:
4045:
4043:
4041:
4039:
1849:{\displaystyle h={\frac {g(\Delta t^{2})}{2}}}
148:Unlike other insects, the wing muscles of the
135:to the hindwings so these can work in unison.
86:secondarily lost their wings through evolution
5406:Journal of the New York Entomological Society
4955:The Lepidoptera: Form, Function and Diversity
4885:"Butterflies in the Pieridae family (whites)"
3600:'s 1973 suggestion that wings developed from
112:reproductive castes develop wings during the
8:
6426:Insect-like Flapping-Wing Micro Air Vehicles
4904:
4902:
2632:, can be calculated from the maximum linear
6292:Van Den Berg, C.; Ellington, C. P. (1997).
5823:Elias-Neto, Moysés; Belles, Xavier (2016).
5436:Grimaldi, David; Engel, Michael S. (2005).
5431:
5429:
5427:
4981:
4979:
4303:International Journal of Micro Air Vehicles
4261:
4259:
4257:
4255:
4253:
4251:
4249:
4247:
4245:
4243:
4241:
4239:
1567:If an insect wing is rigid, for example, a
1220:{\displaystyle Re={\frac {{\bar {c}}U}{v}}}
5381:
5379:
4237:
4235:
4233:
4231:
4229:
4227:
4225:
4223:
4221:
4219:
3991:
3467:. Phylogenomic analysis suggests that the
3372:use carbohydrates for pre-flight warm-up.
3324:, that folds under the hindwing in flight.
1596:
402:this effect is negligible for flow with a
6325:
5974:
5923:
5905:
5864:
5689:
5351:
5302:
5284:
5235:
5225:
4934:
4932:
4834:
4749:
4710:
4638:
4587:
4533:
4416:
4314:
4078:
3989:
3987:
3985:
3983:
3981:
3979:
3977:
3975:
3973:
3971:
3945:
3865:
3687:
3685:
3683:
3681:
3260:
3239:
3218:
3202:
3183:
3170:
3160:
3152:
3111:
3095:
3085:
3077:
3008:
2996:
2981:
2972:
2951:
2945:
2936:
2918:
2907:
2890:
2879:
2847:
2838:
2829:
2823:
2792:
2774:
2758:
2740:
2728:
2722:
2679:
2669:
2663:
2654:
2648:
2618:{\displaystyle I={\frac {m\ell ^{2}}{3}}}
2603:
2593:
2585:
2538:
2533:
2516:
2505:
2473:
2464:
2446:
2440:
2422:
2411:
2400:
2398:
2369:
2364:
2349:
2325:
2317:
2315:
2288:
2283:
2248:
2246:
2222:
2216:
2211:
2192:
2180:
2178:
2127:
2122:
2105:
2097:
2071:
2062:
2042:
2031:
2001:
1992:
1969:
1964:
1958:
1953:
1943:
1934:
1920:
1907:
1903:
1884:
1868:
1831:
1815:
1807:
1505:
1485:
1464:
1458:
1438:
1418:
1398:
1369:
1368:
1366:
1322:
1317:
1311:
1306:
1292:
1290:
1281:
1275:
1254:
1233:
1197:
1196:
1193:
1182:
1123:
1118:
1104:
1099:
1079:
1064:
1058:
1033:
1018:
1002:
978:
972:
968:
966:
921:
911:
886:
880:
811:
793:
775:
765:
752:
734:
716:
710:
16:Mechanisms and evolution of insect flight
6254:. John Wiley and Sons. pp. 227â286.
5206:Carolin Haug & Joachim Haug (2017).
3930:BioRxiv: The Preprint Server for Biology
3292:
365:) and another downstroke can occur. The
20:
6183:. Oxford Biology Readers. Vol. 52.
3677:
621:
576:
269:
171:
5457:
5447:
4789:Weisberger, Mindy (19 February 2016).
4176:Ellis, D. G.; Stollery, J. L. (1988).
4030:10.1146/annurev.fluid.36.050802.121940
2573:during the wing stroke. To obtain the
672:A wing moving in fluids experiences a
5332:Arthropod Structure & Development
4563:
4561:
4511:
4509:
4507:
4438:
4436:
4394:
4392:
3700:Australian Biological Resources Study
2871:And the kinetic energy therefore is:
1527:), the forward velocity of the body (
7:
3482:Epicoxal (abdominal gill) hypothesis
6341:The Journal of Experimental Biology
6231:The Journal of Experimental Biology
6190:The Journal of Experimental Biology
6115:The Journal of Experimental Biology
4677:Cheng, Xin; Sun, Mao (2016-05-11).
4522:The Journal of Experimental Biology
4469:10.1016/j.jfluidstructs.2011.05.002
4058:"The aerodynamics of insect flight"
1157:the velocity at the boundary, and u
124:
5185:10.1111/j.1365-2311.1928.tb01188.x
3850:"Mechanics of the thorax in flies"
3104:
2746:
2043:
1870:
1824:
1779:) has indirect flight musculature.
1420:
1244:
1073:
1055:
1036:
1010:
985:
975:
125:Weis-Fogh clap and fling mechanism
14:
6436:The aerodynamics of insect flight
6252:Fundamentals of insect physiology
5602:Trends in Ecology & Evolution
5479:Jena. Zeitung Naturwissenschaften
4619:Lehmann, F.-O.; Pick, S. (2007).
3758:10.1038/scientificamerican0665-76
3564:Endite-exite (pleural) hypothesis
3493:nymph with paired abdominal gills
6335:Walker, J. A. (September 2002).
5835:(8). The Royal Society: 160347.
5786:10.1111/j.1525-142x.2010.00402.x
4449:Journal of Fluids and Structures
4009:Annual Review of Fluid Mechanics
1799:under the influence of gravity.
1263:{\displaystyle U=2\Theta fr_{g}}
1119:
1100:
1080:
1065:
1019:
1003:
979:
651:
639:
627:
610:
594:
582:
500:
480:
453:
441:
284:
272:
206:
186:
174:
5024:Journal of Experimental Biology
4822:Journal of Experimental Biology
4626:Journal of Experimental Biology
4575:Journal of Experimental Biology
4516:Miller, L.; Peskin, S. (2009).
4485:Journal of Experimental Biology
4405:Journal of Experimental Biology
4370:Journal of Experimental Biology
4269:Physics in Biology and Medicine
4066:Journal of Experimental Biology
3854:Journal of Experimental Biology
3829:North Carolina State University
3782:Journal of Experimental Biology
1534:), and the pitching velocity (Ω
916:
910:
770:
764:
221:Slow motion flight of dragonfly
169:hunted other airborne insects.
5907:10.12688/f1000research.10285.1
3438:from the Lower Carboniferous;
1837:
1821:
1413:is the speed of the wing tip,
1374:
1337:
1331:
1202:
787:
781:
728:
722:
1:
6024:10.1126/science.284.5422.1954
3526:Paranotal (tergal) hypothesis
2640:, at the center of the wing:
1393:is the average chord length,
589:Clap 1: wings close over back
96:never evolved wings. In some
5622:10.1016/0169-5347(96)30022-0
5021:during pre-flight warm-up".
3827:. Department of Entomology,
2497:during each wing stroke is:
1386:{\displaystyle {\bar {c}}\ }
387:computational fluid dynamics
54:. Insects first flew in the
6458:The Flight Of The Bumblebee
5774:Evolution & Development
5645:Acta Zoologica Cracoviensia
5388:Canadian Journal of Zoology
4952:Scoble, Malcolm J. (1995).
4155:"Transition and Turbulence"
1480:is the radius of gyration,
517:to "fly" through the water.
6499:
6179:Pringle, J. W. S. (1975).
6144:Journal of Fluid Mechanics
5829:Royal Society Open Science
5442:Cambridge University Press
5156:10.1127/njgpm/1996/1996/17
4915:Princeton University Press
4865:. Cislunar Aerospace. 1997
4001:"Dissecting Insect Flight"
3657:Flying and gliding animals
3286:
507:Clap and fling is used in
335:
6164:10.1017/S0022112003005743
6109:Ellington, C. P. (1999).
5976:10.1016/j.cub.2016.11.021
5438:Insects take to the skies
5353:10.1016/j.asd.2017.06.005
4938:Stocks, Ian. (2008). Sec.
4913:. Princeton, New Jersey:
4859:"Insect Wings in General"
4266:Davidovits, Paul (2008).
3938:10.1101/2023.06.29.547116
3596:Other hypotheses include
1753:
1740:
1727:
1714:
1701:
1688:
1675:
1662:
1649:
1636:
1623:
1610:
1605:
1602:
1599:
1433:is the stroke amplitude,
702:) coefficients, that is:
4316:10.1177/1756829317745319
4141:10.1002/zamm.19250050103
4056:Sane, Sanjay P. (2003).
3400:Evolution and adaptation
3301:in male and female moths
487:The feathery wings of a
150:Ephemeroptera (mayflies)
6353:10.1242/jeb.205.24.3783
6127:10.1242/jeb.202.23.3439
5560:10.1002/jmor.1051680309
5507:10.1002/jmor.1051560104
5286:10.1073/pnas.1817794116
5101:10.1126/science.1257570
4909:Dudley, Robert (2000).
4863:Aerodynamics of Insects
4211:University of Göttingen
3795:10.1242/jeb.204.23.4125
3692:Chapman, A. D. (2006).
3586:Drosophila melanogaster
1577:, (Î(t),Ί(t)), and the
1500:is the wing area, and
1453:is the beat frequency,
1426:{\displaystyle \Theta }
862:Kutta-Joukowski theorem
61:Two insect groups, the
6390:10.1098/rsta.2001.0930
6318:10.1098/rstb.1997.0023
6265:Biol. Bull. Woods Hole
6259:Sotavalta, O. (1953).
6102:10.1098/rstb.1984.0049
5682:10.1098/rsbl.2009.0029
4960:Natural History Museum
4157:. Princeton University
3573:
3494:
3459:, as found on aquatic
3421:
3302:
3269:
3127:
3042:
3017:
2862:
2801:
2710:given by the distance
2694:
2619:
2548:
2482:
2375:
2294:
2228:
2140:
2080:
2010:
1850:
1780:
1776:Philhelius pedissequum
1514:
1494:
1474:
1447:
1427:
1407:
1387:
1353:
1264:
1221:
1140:
956:Navier-Stokes equation
937:
830:
42:are the only group of
36:
5547:Journal of Morphology
5494:Journal of Morphology
5037:10.1242/jeb.133.1.317
4985:Powell, Jerry A. Ch.
3571:
3489:
3407:
3296:
3270:
3128:
3041:
3018:
2863:
2802:
2695:
2620:
2549:
2483:
2376:
2295:
2229:
2141:
2081:
2011:
1851:
1772:
1742:Large white butterfly
1575:spherical coordinates
1515:
1495:
1475:
1473:{\displaystyle r_{g}}
1448:
1428:
1408:
1388:
1354:
1265:
1222:
1141:
938:
866:Bernoulli's principle
831:
538:aerodynamic benefit.
336:Further information:
236:) for the infraclass
24:
6347:(Pt 24): 3783â3792.
6121:(Pt 23): 3439â3448.
6041:Thomas, Adrian L. R.
5598:Thomas, Adrian L. R.
5501:(1). Wiley: 53â125.
4582:(Pt 16): 3075â3092.
4498:10.1242/jeb.69.1.261
4411:(Pt 21): 3898â4709.
4383:10.1242/jeb.59.1.169
3604:protrusions used as
3598:Vincent Wigglesworth
3426:Carboniferous Period
3408:Reconstruction of a
3297:Frenulo-retinacular
3151:
3076:
2878:
2822:
2721:
2647:
2584:
2504:
2397:
2314:
2245:
2177:
2096:
2030:
1867:
1806:
1638:Hummingbird hawkmoth
1504:
1484:
1457:
1437:
1417:
1397:
1365:
1274:
1232:
1181:
965:
879:
709:
428:sculling draw stroke
6382:2002RSPTA.360..273Z
6310:1997RSPTB.352..317V
6243:10.1242/jeb.83.1.59
6196:(Pt 23): 4191â208.
6156:2003JFM...492..339L
6094:1984RSPTB.305....1E
6057:1996Natur.384..626E
5967:2017CBio...27..263P
5849:10.1098/rsos.160347
5841:2016RSOS....360347E
5727:1997Natur.385..627A
5614:1996TEcoE..11..187T
5444:. pp. 155â159.
5344:2018ArtSD..47..370Y
5277:2019PNAS..116.3024W
5093:2014Sci...346..763M
4795:Scientific American
4760:2021PhFl...33c1901K
4695:2016NatSR...625706C
4633:(Pt 8): 1362â1377.
4461:2011JFS....27..784K
4343:Scientific American
4339:"Catching the Wake"
4185:ICAS 1988 Jerusalem
4133:1925ZaMM....5...17W
4022:2005AnRFM..37..183W
3750:1965SciAm.212f..76S
3737:Scientific American
3639:serially homologous
3556:and finally active
3444:is older, from the
2923:
2543:
1316:
668:Governing equations
346:Leading edge vortex
131:have the forewings
88:, while other more
6446:2004-08-22 at the
5227:10.7717/peerj.3402
4962:. pp. 56â60.
4836:10.1242/jeb.129205
4683:Scientific Reports
4535:10.1242/jeb.028662
4418:10.1242/jeb.084897
4276:. pp. 78â79.
3867:10.1242/jeb.128363
3578:endites and exites
3574:
3495:
3436:Palaeodictyopteran
3422:
3414:palaeodictyopteran
3309:mechanisms in the
3303:
3265:
3123:
3043:
3013:
2903:
2858:
2797:
2690:
2615:
2544:
2529:
2478:
2371:
2290:
2224:
2136:
2076:
2006:
1846:
1781:
1600:Flight parameters
1510:
1490:
1470:
1443:
1423:
1403:
1383:
1349:
1302:
1260:
1217:
1136:
1134:
933:
826:
46:that have evolved
37:
6478:Insect physiology
6376:(1791): 273â290.
6304:(1351): 317â328.
6202:10.1242/jeb.00663
6051:(6610): 626â630.
6018:(5422): 1954â60.
5087:(6210): 763â767.
4969:978-0-19-854952-9
4768:10.1063/5.0036018
4737:Physics of Fluids
4703:10.1038/srep25706
4640:10.1242/jeb.02746
4589:10.1242/jeb.01744
4528:(19): 3076â3090.
4365:Weis-Fogh, Torkel
4283:978-0-12-369411-9
4080:10.1242/jeb.00663
4073:(23): 4191â4208.
3789:(23): 4125â4139.
3709:978-0-642-56850-2
3702:. pp. 60pp.
3263:
3259:
3249:
3168:
3121:
3093:
3011:
2990:
2960:
2898:
2856:
2832:
2795:
2784:
2753:
2688:
2672:
2657:
2613:
2575:moment of inertia
2565:of the wing and Ï
2561:is the moment of
2536:
2524:
2476:
2449:
2425:
2414:
2403:
2367:
2328:
2320:
2286:
2251:
2219:
2214:
2183:
2125:
2113:
2074:
2004:
1977:
1976:
1967:
1956:
1946:
1897:
1844:
1783:Many insects can
1767:
1766:
1757:(clap and fling)
1612:Aeshnid dragonfly
1513:{\displaystyle R}
1493:{\displaystyle s}
1446:{\displaystyle f}
1406:{\displaystyle U}
1382:
1377:
1347:
1300:
1215:
1205:
1126:
1107:
1046:
992:
924:
914:
889:
821:
778:
768:
762:
719:
571:Liriomyza sativae
565:Limacina helicina
514:Limacina helicina
399:Herbert A. Wagner
397:, as proposed by
216:
160:through the air.
6490:
6409:
6364:
6331:
6329:
6288:
6255:
6246:
6221:
6184:
6175:
6138:
6105:
6076:
6065:10.1038/384626a0
6035:
5997:
5996:
5978:
5944:
5938:
5937:
5927:
5909:
5885:
5879:
5878:
5868:
5820:
5814:
5813:
5769:
5763:
5762:
5735:10.1038/385627a0
5710:
5704:
5703:
5693:
5659:
5653:
5652:
5640:
5634:
5633:
5594:
5588:
5587:
5541:
5535:
5534:
5488:
5482:
5472:
5466:
5465:
5459:
5455:
5453:
5445:
5433:
5422:
5421:
5401:
5392:
5383:
5374:
5373:
5355:
5323:
5317:
5316:
5306:
5288:
5271:(8): 3024â3029.
5256:
5250:
5249:
5239:
5229:
5203:
5197:
5196:
5166:
5160:
5159:
5135:
5129:
5128:
5074:
5068:
5065:
5059:
5056:
5050:
5047:
5041:
5040:
5014:
5008:
5005:
4999:
4996:
4990:
4983:
4974:
4973:
4949:
4943:
4936:
4927:
4926:
4906:
4897:
4896:
4894:
4892:
4881:
4875:
4874:
4872:
4870:
4855:
4849:
4848:
4838:
4812:
4806:
4805:
4803:
4801:
4786:
4780:
4779:
4753:
4731:
4725:
4724:
4714:
4674:
4661:
4660:
4642:
4616:
4610:
4609:
4591:
4565:
4556:
4555:
4537:
4513:
4502:
4501:
4479:
4473:
4472:
4440:
4431:
4430:
4420:
4396:
4387:
4386:
4361:
4355:
4354:
4352:
4350:
4335:
4329:
4328:
4318:
4294:
4288:
4287:
4263:
4214:
4207:
4201:
4200:
4198:
4196:
4182:
4173:
4167:
4166:
4164:
4162:
4151:
4145:
4144:
4107:
4101:
4100:
4082:
4062:
4053:
4034:
4033:
4005:
3993:
3966:
3965:
3963:
3962:
3949:
3921:
3915:
3914:
3902:
3896:
3895:
3869:
3860:(8): 1382â1395.
3845:
3839:
3838:
3836:
3835:
3821:
3815:
3814:
3776:
3770:
3769:
3731:
3725:
3724:
3722:
3721:
3712:. Archived from
3689:
3667:Insect migration
3592:Other hypotheses
3538:found in insect
3424:Sometime in the
3382:sensory feedback
3376:Sensory feedback
3274:
3272:
3271:
3266:
3264:
3261:
3257:
3250:
3248:
3247:
3246:
3227:
3226:
3225:
3210:
3209:
3188:
3187:
3171:
3169:
3161:
3132:
3130:
3129:
3124:
3122:
3117:
3116:
3115:
3096:
3094:
3086:
3055:potential energy
3022:
3020:
3019:
3014:
3012:
3009:
3001:
3000:
2995:
2991:
2989:
2985:
2973:
2966:
2962:
2961:
2956:
2955:
2946:
2944:
2943:
2922:
2917:
2899:
2891:
2867:
2865:
2864:
2859:
2857:
2855:
2851:
2839:
2834:
2833:
2830:
2806:
2804:
2803:
2798:
2796:
2793:
2785:
2783:
2782:
2781:
2759:
2754:
2752:
2741:
2736:
2735:
2699:
2697:
2696:
2691:
2689:
2687:
2683:
2674:
2673:
2670:
2664:
2659:
2658:
2655:
2624:
2622:
2621:
2616:
2614:
2609:
2608:
2607:
2594:
2571:angular velocity
2553:
2551:
2550:
2545:
2542:
2537:
2534:
2525:
2517:
2487:
2485:
2484:
2479:
2477:
2474:
2472:
2471:
2450:
2447:
2445:
2444:
2426:
2423:
2415:
2412:
2404:
2401:
2380:
2378:
2377:
2372:
2368:
2365:
2357:
2356:
2329:
2326:
2321:
2318:
2299:
2297:
2296:
2291:
2287:
2284:
2252:
2249:
2233:
2231:
2230:
2225:
2221:
2220:
2217:
2215:
2212:
2200:
2199:
2184:
2181:
2145:
2143:
2142:
2137:
2135:
2134:
2126:
2123:
2114:
2106:
2085:
2083:
2082:
2077:
2075:
2072:
2070:
2069:
2015:
2013:
2012:
2007:
2005:
2002:
2000:
1999:
1978:
1975:
1974:
1973:
1968:
1965:
1962:
1957:
1954:
1948:
1947:
1944:
1942:
1941:
1922:
1921:
1916:
1915:
1911:
1902:
1898:
1893:
1885:
1855:
1853:
1852:
1847:
1845:
1840:
1836:
1835:
1816:
1597:
1519:
1517:
1516:
1511:
1499:
1497:
1496:
1491:
1479:
1477:
1476:
1471:
1469:
1468:
1452:
1450:
1449:
1444:
1432:
1430:
1429:
1424:
1412:
1410:
1409:
1404:
1392:
1390:
1389:
1384:
1380:
1379:
1378:
1370:
1358:
1356:
1355:
1350:
1348:
1346:
1327:
1326:
1315:
1310:
1301:
1293:
1291:
1286:
1285:
1269:
1267:
1266:
1261:
1259:
1258:
1226:
1224:
1223:
1218:
1216:
1211:
1207:
1206:
1198:
1194:
1145:
1143:
1142:
1137:
1135:
1128:
1127:
1124:
1122:
1109:
1108:
1105:
1103:
1083:
1068:
1063:
1062:
1047:
1042:
1034:
1022:
1017:
1013:
1006:
993:
991:
983:
982:
973:
942:
940:
939:
934:
926:
925:
922:
915:
912:
891:
890:
887:
835:
833:
832:
827:
822:
820:
816:
815:
802:
794:
780:
779:
776:
769:
766:
763:
761:
757:
756:
743:
735:
721:
720:
717:
655:
643:
631:
614:
598:
586:
553:Encarsia formosa
526:Torkel Weis-Fogh
504:
484:
457:
445:
288:
276:
218:
217:
190:
178:
28:Hemicordulia tau
6498:
6497:
6493:
6492:
6491:
6489:
6488:
6487:
6468:
6467:
6448:Wayback Machine
6417:
6412:
6367:
6334:
6291:
6277:10.2307/1538496
6258:
6249:
6224:
6187:
6178:
6141:
6108:
6079:
6038:
6009:
6005:
6003:Further reading
6000:
5954:Current Biology
5946:
5945:
5941:
5887:
5886:
5882:
5822:
5821:
5817:
5771:
5770:
5766:
5712:
5711:
5707:
5669:Biology Letters
5661:
5660:
5656:
5642:
5641:
5637:
5596:
5595:
5591:
5543:
5542:
5538:
5490:
5489:
5485:
5473:
5469:
5456:
5446:
5435:
5434:
5425:
5403:
5402:
5395:
5384:
5377:
5325:
5324:
5320:
5258:
5257:
5253:
5205:
5204:
5200:
5168:
5167:
5163:
5137:
5136:
5132:
5076:
5075:
5071:
5066:
5062:
5057:
5053:
5048:
5044:
5016:
5015:
5011:
5006:
5002:
4997:
4993:
4984:
4977:
4970:
4951:
4950:
4946:
4937:
4930:
4908:
4907:
4900:
4890:
4888:
4887:. Bumblebee.org
4883:
4882:
4878:
4868:
4866:
4857:
4856:
4852:
4814:
4813:
4809:
4799:
4797:
4788:
4787:
4783:
4733:
4732:
4728:
4676:
4675:
4664:
4618:
4617:
4613:
4567:
4566:
4559:
4515:
4514:
4505:
4481:
4480:
4476:
4442:
4441:
4434:
4398:
4397:
4390:
4363:
4362:
4358:
4348:
4346:
4345:. June 28, 1999
4337:
4336:
4332:
4296:
4295:
4291:
4284:
4265:
4264:
4217:
4208:
4204:
4194:
4192:
4180:
4175:
4174:
4170:
4160:
4158:
4153:
4152:
4148:
4111:Wagner, Herbert
4109:
4108:
4104:
4060:
4055:
4054:
4037:
4003:
3995:
3994:
3969:
3960:
3958:
3923:
3922:
3918:
3904:
3903:
3899:
3847:
3846:
3842:
3833:
3831:
3823:
3822:
3818:
3778:
3777:
3773:
3733:
3732:
3728:
3719:
3717:
3710:
3691:
3690:
3679:
3675:
3648:
3631:
3594:
3566:
3528:
3484:
3402:
3378:
3349:
3291:
3285:
3235:
3228:
3214:
3198:
3179:
3172:
3149:
3148:
3107:
3097:
3074:
3073:
3067:Young's modulus
3036:
2977:
2968:
2967:
2947:
2932:
2931:
2927:
2876:
2875:
2843:
2825:
2820:
2819:
2770:
2763:
2745:
2724:
2719:
2718:
2709:
2675:
2665:
2650:
2645:
2644:
2639:
2631:
2599:
2595:
2582:
2581:
2569:is the maximum
2568:
2502:
2501:
2494:
2460:
2436:
2395:
2394:
2345:
2312:
2311:
2243:
2242:
2210:
2188:
2175:
2174:
2165:
2160:
2153:
2121:
2094:
2093:
2058:
2028:
2027:
1988:
1963:
1949:
1930:
1923:
1886:
1880:
1879:
1865:
1864:
1827:
1817:
1804:
1803:
1595:
1583:angle of attack
1563:
1544:
1533:
1502:
1501:
1482:
1481:
1460:
1455:
1454:
1435:
1434:
1415:
1414:
1395:
1394:
1363:
1362:
1318:
1277:
1272:
1271:
1250:
1230:
1229:
1195:
1179:
1178:
1172:chalcidoid wasp
1164:
1160:
1156:
1133:
1132:
1117:
1110:
1098:
1095:
1094:
1084:
1070:
1069:
1054:
1035:
1023:
1001:
997:
984:
974:
963:
962:
917:
882:
877:
876:
870:Blasius theorem
850:
843:
807:
803:
795:
771:
748:
744:
736:
712:
707:
706:
700:
693:
670:
663:
656:
647:
644:
635:
632:
618:
615:
606:
605:, vortices form
599:
590:
587:
522:
521:
520:
519:
518:
509:sea butterflies
505:
497:
496:
485:
474:
465:
464:
463:
462:
461:
458:
450:
449:
446:
412:flow is laminar
404:Reynolds number
348:
340:
334:
300:
289:
280:
277:
229:
227:Indirect flight
222:
219:
207:
202:
191:
182:
179:
146:
141:
25:A tau emerald (
17:
12:
11:
5:
6496:
6494:
6486:
6485:
6480:
6470:
6469:
6466:
6465:
6460:
6455:
6450:
6441:Flight muscles
6438:
6433:
6428:
6423:
6416:
6415:External links
6413:
6411:
6410:
6365:
6332:
6289:
6271:(3): 439â444.
6256:
6247:
6222:
6185:
6176:
6139:
6106:
6088:(1122): 1â15.
6077:
6036:
6006:
6004:
6001:
5999:
5998:
5961:(2): 263â269.
5939:
5880:
5815:
5780:(2): 168â176.
5764:
5705:
5654:
5635:
5608:(5): 187â188.
5589:
5554:(3): 331â338.
5536:
5483:
5467:
5423:
5393:
5375:
5338:(4): 370â374.
5318:
5251:
5198:
5161:
5130:
5069:
5060:
5051:
5042:
5009:
5000:
4991:
4975:
4968:
4944:
4928:
4917:. p. 69.
4898:
4876:
4850:
4829:(4): 535â543.
4807:
4781:
4726:
4662:
4611:
4557:
4503:
4474:
4432:
4388:
4356:
4330:
4309:(1): 106â122.
4289:
4282:
4274:Academic Press
4215:
4202:
4168:
4146:
4102:
4035:
4016:(1): 183â210.
3967:
3916:
3897:
3840:
3816:
3771:
3726:
3708:
3676:
3674:
3671:
3670:
3669:
3664:
3659:
3654:
3647:
3644:
3630:
3627:
3593:
3590:
3582:arthropod limb
3565:
3562:
3548:starting with
3527:
3524:
3483:
3480:
3446:Early Devonian
3401:
3398:
3377:
3374:
3348:
3345:
3344:
3343:
3330:In almost all
3328:
3325:
3287:Main article:
3284:
3281:
3276:
3275:
3256:
3253:
3245:
3242:
3238:
3234:
3231:
3224:
3221:
3217:
3213:
3208:
3205:
3201:
3197:
3194:
3191:
3186:
3182:
3178:
3175:
3167:
3164:
3159:
3156:
3134:
3133:
3120:
3114:
3110:
3106:
3103:
3100:
3092:
3089:
3084:
3081:
3061:resilin obeys
3035:
3032:
3024:
3023:
3007:
3004:
2999:
2994:
2988:
2984:
2980:
2976:
2971:
2965:
2959:
2954:
2950:
2942:
2939:
2935:
2930:
2926:
2921:
2916:
2913:
2910:
2906:
2902:
2897:
2894:
2889:
2886:
2883:
2869:
2868:
2854:
2850:
2846:
2842:
2837:
2828:
2808:
2807:
2791:
2788:
2780:
2777:
2773:
2769:
2766:
2762:
2757:
2751:
2748:
2744:
2739:
2734:
2731:
2727:
2707:
2701:
2700:
2686:
2682:
2678:
2668:
2662:
2653:
2637:
2629:
2626:
2625:
2612:
2606:
2602:
2598:
2592:
2589:
2566:
2555:
2554:
2541:
2532:
2528:
2523:
2520:
2515:
2512:
2509:
2493:
2490:
2489:
2488:
2470:
2467:
2463:
2459:
2456:
2453:
2443:
2439:
2435:
2432:
2429:
2421:
2418:
2410:
2407:
2387:kinetic energy
2382:
2381:
2363:
2360:
2355:
2352:
2348:
2344:
2341:
2338:
2335:
2332:
2324:
2301:
2300:
2282:
2279:
2276:
2273:
2270:
2267:
2264:
2261:
2258:
2255:
2235:
2234:
2209:
2206:
2203:
2198:
2195:
2191:
2187:
2163:
2159:
2156:
2151:
2147:
2146:
2133:
2130:
2120:
2117:
2112:
2109:
2104:
2101:
2087:
2086:
2068:
2065:
2061:
2057:
2054:
2051:
2048:
2045:
2041:
2038:
2035:
2017:
2016:
1998:
1995:
1991:
1987:
1984:
1981:
1972:
1961:
1952:
1940:
1937:
1933:
1929:
1926:
1919:
1914:
1910:
1906:
1901:
1896:
1892:
1889:
1883:
1878:
1875:
1872:
1857:
1856:
1843:
1839:
1834:
1830:
1826:
1823:
1820:
1814:
1811:
1765:
1764:
1761:
1758:
1751:
1750:
1747:
1744:
1738:
1737:
1734:
1731:
1725:
1724:
1721:
1718:
1712:
1711:
1708:
1705:
1699:
1698:
1695:
1692:
1686:
1685:
1682:
1679:
1673:
1672:
1669:
1666:
1660:
1659:
1656:
1653:
1647:
1646:
1643:
1640:
1634:
1633:
1630:
1627:
1621:
1620:
1617:
1614:
1608:
1607:
1604:
1601:
1594:
1591:
1579:pitching angle
1561:
1542:
1531:
1509:
1489:
1467:
1463:
1442:
1422:
1402:
1376:
1373:
1345:
1342:
1339:
1336:
1333:
1330:
1325:
1321:
1314:
1309:
1305:
1299:
1296:
1289:
1284:
1280:
1257:
1253:
1249:
1246:
1243:
1240:
1237:
1214:
1210:
1204:
1201:
1192:
1189:
1186:
1162:
1158:
1154:
1147:
1146:
1131:
1121:
1116:
1113:
1111:
1102:
1097:
1096:
1093:
1090:
1087:
1085:
1082:
1078:
1075:
1072:
1071:
1067:
1061:
1057:
1053:
1050:
1045:
1041:
1038:
1032:
1029:
1026:
1024:
1021:
1016:
1012:
1009:
1005:
1000:
996:
990:
987:
981:
977:
971:
970:
948:incompressible
944:
943:
932:
929:
920:
909:
906:
903:
900:
897:
894:
885:
848:
841:
837:
836:
825:
819:
814:
810:
806:
801:
798:
792:
789:
786:
783:
774:
760:
755:
751:
747:
742:
739:
733:
730:
727:
724:
715:
698:
691:
669:
666:
665:
664:
657:
650:
648:
645:
638:
636:
633:
626:
624:
620:
619:
616:
609:
607:
600:
593:
591:
588:
581:
579:
530:viscous forces
506:
499:
498:
493:clap and fling
486:
479:
478:
477:
476:
475:
473:
472:Clap and fling
470:
459:
452:
451:
447:
440:
439:
438:
437:
436:
347:
344:
333:
330:
302:
301:
290:
283:
281:
278:
271:
228:
225:
224:
223:
220:
205:
203:
192:
185:
183:
180:
173:
145:
142:
140:
137:
15:
13:
10:
9:
6:
4:
3:
2:
6495:
6484:
6483:Animal flight
6481:
6479:
6476:
6475:
6473:
6464:
6463:Insect Flight
6461:
6459:
6456:
6454:
6451:
6449:
6445:
6442:
6439:
6437:
6434:
6432:
6429:
6427:
6424:
6422:
6419:
6418:
6414:
6407:
6403:
6399:
6395:
6391:
6387:
6383:
6379:
6375:
6371:
6366:
6362:
6358:
6354:
6350:
6346:
6342:
6338:
6333:
6328:
6323:
6319:
6315:
6311:
6307:
6303:
6299:
6295:
6290:
6286:
6282:
6278:
6274:
6270:
6266:
6262:
6257:
6253:
6248:
6244:
6240:
6236:
6232:
6228:
6223:
6219:
6215:
6211:
6207:
6203:
6199:
6195:
6191:
6186:
6182:
6181:Insect flight
6177:
6173:
6169:
6165:
6161:
6157:
6153:
6149:
6145:
6140:
6136:
6132:
6128:
6124:
6120:
6116:
6112:
6107:
6103:
6099:
6095:
6091:
6087:
6083:
6078:
6074:
6070:
6066:
6062:
6058:
6054:
6050:
6046:
6042:
6037:
6033:
6029:
6025:
6021:
6017:
6013:
6008:
6007:
6002:
5994:
5990:
5986:
5982:
5977:
5972:
5968:
5964:
5960:
5956:
5955:
5950:
5943:
5940:
5935:
5931:
5926:
5921:
5917:
5913:
5908:
5903:
5899:
5895:
5894:F1000Research
5891:
5884:
5881:
5876:
5872:
5867:
5862:
5858:
5854:
5850:
5846:
5842:
5838:
5834:
5830:
5826:
5819:
5816:
5811:
5807:
5803:
5799:
5795:
5791:
5787:
5783:
5779:
5775:
5768:
5765:
5760:
5756:
5752:
5748:
5744:
5740:
5736:
5732:
5728:
5724:
5720:
5716:
5709:
5706:
5701:
5697:
5692:
5687:
5683:
5679:
5675:
5671:
5670:
5665:
5658:
5655:
5650:
5646:
5639:
5636:
5631:
5627:
5623:
5619:
5615:
5611:
5607:
5603:
5599:
5593:
5590:
5585:
5581:
5577:
5573:
5569:
5565:
5561:
5557:
5553:
5549:
5548:
5540:
5537:
5532:
5528:
5524:
5520:
5516:
5512:
5508:
5504:
5500:
5496:
5495:
5487:
5484:
5480:
5476:
5475:MĂŒller, Fritz
5471:
5468:
5463:
5451:
5443:
5439:
5432:
5430:
5428:
5424:
5419:
5415:
5411:
5407:
5400:
5398:
5394:
5390:
5389:
5382:
5380:
5376:
5371:
5367:
5363:
5359:
5354:
5349:
5345:
5341:
5337:
5333:
5329:
5322:
5319:
5314:
5310:
5305:
5300:
5296:
5292:
5287:
5282:
5278:
5274:
5270:
5266:
5262:
5255:
5252:
5247:
5243:
5238:
5233:
5228:
5223:
5219:
5215:
5214:
5209:
5202:
5199:
5194:
5190:
5186:
5182:
5178:
5174:
5173:
5165:
5162:
5157:
5153:
5149:
5146:(in German).
5145:
5141:
5134:
5131:
5126:
5122:
5118:
5114:
5110:
5106:
5102:
5098:
5094:
5090:
5086:
5082:
5081:
5073:
5070:
5064:
5061:
5055:
5052:
5046:
5043:
5038:
5034:
5030:
5026:
5025:
5020:
5019:Manduca sexta
5013:
5010:
5004:
5001:
4995:
4992:
4988:
4982:
4980:
4976:
4971:
4965:
4961:
4957:
4956:
4948:
4945:
4941:
4940:Wing Coupling
4935:
4933:
4929:
4924:
4920:
4916:
4912:
4905:
4903:
4899:
4886:
4880:
4877:
4864:
4860:
4854:
4851:
4846:
4842:
4837:
4832:
4828:
4824:
4823:
4818:
4811:
4808:
4796:
4792:
4785:
4782:
4777:
4773:
4769:
4765:
4761:
4757:
4752:
4747:
4744:(3): 031901.
4743:
4739:
4738:
4730:
4727:
4722:
4718:
4713:
4708:
4704:
4700:
4696:
4692:
4688:
4684:
4680:
4673:
4671:
4669:
4667:
4663:
4658:
4654:
4650:
4646:
4641:
4636:
4632:
4628:
4627:
4622:
4615:
4612:
4607:
4603:
4599:
4595:
4590:
4585:
4581:
4577:
4576:
4571:
4564:
4562:
4558:
4553:
4549:
4545:
4541:
4536:
4531:
4527:
4523:
4519:
4512:
4510:
4508:
4504:
4499:
4495:
4491:
4487:
4486:
4478:
4475:
4470:
4466:
4462:
4458:
4454:
4450:
4446:
4439:
4437:
4433:
4428:
4424:
4419:
4414:
4410:
4406:
4402:
4395:
4393:
4389:
4384:
4380:
4376:
4372:
4371:
4366:
4360:
4357:
4344:
4340:
4334:
4331:
4326:
4322:
4317:
4312:
4308:
4304:
4300:
4293:
4290:
4285:
4279:
4275:
4271:
4270:
4262:
4260:
4258:
4256:
4254:
4252:
4250:
4248:
4246:
4244:
4242:
4240:
4238:
4236:
4234:
4232:
4230:
4228:
4226:
4224:
4222:
4220:
4216:
4212:
4206:
4203:
4190:
4186:
4179:
4172:
4169:
4156:
4150:
4147:
4142:
4138:
4134:
4130:
4126:
4123:(in German).
4122:
4121:
4116:
4112:
4106:
4103:
4098:
4094:
4090:
4086:
4081:
4076:
4072:
4068:
4067:
4059:
4052:
4050:
4048:
4046:
4044:
4042:
4040:
4036:
4031:
4027:
4023:
4019:
4015:
4011:
4010:
4002:
3998:
3997:Wang, Z. Jane
3992:
3990:
3988:
3986:
3984:
3982:
3980:
3978:
3976:
3974:
3972:
3968:
3957:
3953:
3948:
3943:
3939:
3935:
3931:
3927:
3920:
3917:
3912:
3908:
3901:
3898:
3893:
3889:
3885:
3881:
3877:
3873:
3868:
3863:
3859:
3855:
3851:
3844:
3841:
3830:
3826:
3820:
3817:
3812:
3808:
3804:
3800:
3796:
3792:
3788:
3784:
3783:
3775:
3772:
3767:
3763:
3759:
3755:
3751:
3747:
3743:
3739:
3738:
3730:
3727:
3716:on 2009-05-19
3715:
3711:
3705:
3701:
3697:
3696:
3688:
3686:
3684:
3682:
3678:
3672:
3668:
3665:
3663:
3660:
3658:
3655:
3653:
3650:
3649:
3645:
3643:
3640:
3636:
3628:
3626:
3624:
3619:
3617:
3613:
3612:Adrian Thomas
3609:
3607:
3603:
3599:
3591:
3589:
3587:
3583:
3579:
3570:
3563:
3561:
3559:
3555:
3551:
3546:
3541:
3537:
3536:preadaptation
3533:
3525:
3523:
3520:
3516:
3513:in 1877, and
3512:
3508:
3504:
3500:
3499:entomologists
3492:
3488:
3481:
3479:
3477:
3474:
3470:
3466:
3462:
3458:
3455:
3449:
3447:
3443:
3442:
3437:
3433:
3432:
3427:
3420:
3419:
3415:
3411:
3410:Carboniferous
3406:
3399:
3397:
3395:
3391:
3387:
3383:
3375:
3373:
3371:
3370:
3369:Manduca sexta
3365:
3362:
3358:
3354:
3353:carbohydrates
3346:
3341:
3337:
3333:
3329:
3326:
3323:
3319:
3318:
3317:
3314:
3312:
3308:
3307:wing coupling
3300:
3299:wing coupling
3295:
3290:
3289:Wing coupling
3283:Wing coupling
3282:
3280:
3254:
3251:
3243:
3240:
3236:
3232:
3229:
3222:
3219:
3215:
3211:
3206:
3203:
3199:
3195:
3192:
3189:
3184:
3180:
3176:
3173:
3165:
3162:
3157:
3154:
3147:
3146:
3145:
3143:
3139:
3118:
3112:
3108:
3101:
3098:
3090:
3087:
3082:
3079:
3072:
3071:
3070:
3068:
3064:
3058:
3056:
3052:
3048:
3040:
3033:
3031:
3029:
3005:
3002:
2997:
2992:
2986:
2982:
2978:
2974:
2969:
2963:
2957:
2952:
2948:
2940:
2937:
2933:
2928:
2924:
2919:
2914:
2911:
2908:
2904:
2900:
2895:
2892:
2887:
2884:
2881:
2874:
2873:
2872:
2852:
2848:
2844:
2840:
2835:
2826:
2818:
2817:
2816:
2814:
2789:
2786:
2778:
2775:
2771:
2767:
2764:
2760:
2755:
2749:
2742:
2737:
2732:
2729:
2725:
2717:
2716:
2715:
2713:
2706:
2684:
2680:
2676:
2666:
2660:
2651:
2643:
2642:
2641:
2635:
2610:
2604:
2600:
2596:
2590:
2587:
2580:
2579:
2578:
2576:
2572:
2564:
2560:
2539:
2530:
2526:
2521:
2518:
2513:
2510:
2507:
2500:
2499:
2498:
2491:
2468:
2465:
2461:
2457:
2454:
2451:
2441:
2437:
2433:
2430:
2427:
2419:
2416:
2408:
2405:
2393:
2392:
2391:
2388:
2361:
2358:
2353:
2350:
2346:
2342:
2339:
2336:
2333:
2330:
2322:
2310:
2309:
2308:
2306:
2280:
2277:
2274:
2271:
2268:
2265:
2262:
2259:
2256:
2253:
2241:
2240:
2239:
2207:
2204:
2201:
2196:
2193:
2189:
2185:
2173:
2172:
2171:
2169:
2157:
2155:
2131:
2128:
2118:
2115:
2110:
2107:
2102:
2099:
2092:
2091:
2090:
2066:
2063:
2059:
2055:
2052:
2049:
2046:
2039:
2036:
2033:
2026:
2025:
2024:
2022:
1996:
1993:
1989:
1985:
1982:
1979:
1970:
1959:
1950:
1938:
1935:
1931:
1927:
1924:
1917:
1912:
1908:
1904:
1899:
1894:
1890:
1887:
1881:
1876:
1873:
1863:
1862:
1861:
1841:
1832:
1828:
1818:
1812:
1809:
1802:
1801:
1800:
1798:
1794:
1788:
1786:
1778:
1777:
1771:
1762:
1759:
1756:
1752:
1748:
1745:
1743:
1739:
1735:
1732:
1730:
1726:
1722:
1719:
1717:
1713:
1709:
1706:
1704:
1700:
1696:
1693:
1691:
1687:
1683:
1680:
1678:
1674:
1670:
1667:
1665:
1661:
1657:
1654:
1652:
1648:
1644:
1641:
1639:
1635:
1631:
1628:
1626:
1622:
1618:
1615:
1613:
1609:
1598:
1592:
1590:
1586:
1584:
1580:
1576:
1572:
1571:
1565:
1560:
1556:
1552:
1548:
1541:
1537:
1530:
1526:
1521:
1507:
1487:
1465:
1461:
1440:
1400:
1371:
1359:
1343:
1340:
1334:
1328:
1323:
1319:
1312:
1307:
1303:
1297:
1294:
1287:
1282:
1278:
1255:
1251:
1247:
1241:
1238:
1235:
1227:
1212:
1208:
1199:
1190:
1187:
1184:
1176:
1173:
1168:
1152:
1129:
1114:
1112:
1091:
1088:
1086:
1076:
1059:
1051:
1048:
1043:
1039:
1030:
1027:
1025:
1014:
1007:
998:
994:
988:
961:
960:
959:
957:
953:
949:
930:
927:
918:
907:
904:
901:
898:
895:
892:
883:
875:
874:
873:
871:
867:
863:
859:
858:inviscid flow
855:
851:
844:
823:
817:
812:
808:
804:
799:
796:
790:
784:
772:
758:
753:
749:
745:
740:
737:
731:
725:
713:
705:
704:
703:
701:
694:
687:
683:
679:
675:
667:
661:
654:
649:
642:
637:
630:
625:
622:
613:
608:
604:
597:
592:
585:
580:
577:
575:
573:
572:
567:
566:
562:
557:
555:
554:
547:
545:
539:
536:
531:
527:
516:
515:
510:
503:
494:
490:
483:
471:
469:
456:
444:
435:
431:
429:
425:
421:
417:
413:
409:
405:
400:
396:
395:Wagner effect
390:
388:
384:
378:
376:
372:
368:
364:
360:
356:
353:
345:
343:
339:
331:
329:
325:
323:
319:
315:
311:
306:
298:
294:
287:
282:
275:
270:
268:
266:
262:
258:
254:
250:
245:
243:
239:
235:
226:
204:
200:
196:
189:
184:
177:
172:
170:
167:
163:
159:
155:
151:
144:Direct flight
143:
138:
136:
134:
130:
126:
123:, but of the
122:
117:
115:
114:mating season
111:
107:
103:
100:insects like
99:
95:
92:insects like
91:
87:
84:insects have
83:
78:
76:
72:
68:
64:
59:
57:
56:Carboniferous
53:
49:
45:
44:invertebrates
41:
34:
30:
29:
23:
19:
6373:
6369:
6344:
6340:
6301:
6297:
6268:
6264:
6251:
6237:(1): 59â77.
6234:
6230:
6193:
6189:
6180:
6147:
6143:
6118:
6114:
6085:
6081:
6048:
6044:
6015:
6011:
5958:
5952:
5942:
5897:
5893:
5883:
5832:
5828:
5818:
5777:
5773:
5767:
5718:
5714:
5708:
5676:(4): 510â2.
5673:
5667:
5657:
5648:
5644:
5638:
5605:
5601:
5592:
5551:
5545:
5539:
5498:
5492:
5486:
5478:
5470:
5440:. New York:
5437:
5409:
5405:
5386:
5335:
5331:
5321:
5268:
5264:
5254:
5217:
5211:
5201:
5179:(1): 65â71.
5176:
5170:
5164:
5150:(1): 17â30.
5147:
5143:
5133:
5084:
5078:
5072:
5063:
5054:
5045:
5028:
5022:
5018:
5012:
5003:
4994:
4986:
4954:
4947:
4939:
4910:
4889:. Retrieved
4879:
4867:. Retrieved
4862:
4853:
4826:
4820:
4810:
4798:. Retrieved
4784:
4741:
4735:
4729:
4689:(1): 25706.
4686:
4682:
4630:
4624:
4614:
4579:
4573:
4525:
4521:
4489:
4483:
4477:
4452:
4448:
4408:
4404:
4374:
4368:
4359:
4347:. Retrieved
4333:
4306:
4302:
4292:
4268:
4205:
4193:. Retrieved
4188:
4184:
4171:
4159:. Retrieved
4149:
4127:(1): 17â35.
4124:
4118:
4105:
4070:
4064:
4013:
4007:
3959:. Retrieved
3929:
3919:
3910:
3907:BIONA Report
3906:
3900:
3857:
3853:
3843:
3832:. Retrieved
3819:
3786:
3780:
3774:
3744:(6): 76â88.
3741:
3735:
3729:
3718:. Retrieved
3714:the original
3698:. Canberra:
3694:
3632:
3620:
3610:
3595:
3585:
3575:
3532:Fritz MĂŒller
3529:
3496:
3469:Polyneoptera
3450:
3441:Rhyniognatha
3439:
3431:Delitzschala
3429:
3423:
3416:
3412:insect, the
3380:Insects use
3379:
3367:
3350:
3347:Biochemistry
3338:(except the
3321:
3315:
3304:
3277:
3137:
3135:
3059:
3044:
3025:
2870:
2813:sinusoidally
2809:
2711:
2704:
2702:
2627:
2558:
2556:
2495:
2492:Power output
2383:
2304:
2302:
2236:
2167:
2161:
2148:
2088:
2020:
2018:
1858:
1796:
1792:
1789:
1782:
1774:
1603:Speed (m/s)
1587:
1568:
1566:
1558:
1554:
1550:
1546:
1539:
1535:
1528:
1524:
1522:
1360:
1228:
1177:
1150:
1148:
945:
846:
839:
838:
696:
695:) and drag (
689:
685:
681:
677:
671:
603:leading edge
569:
563:
558:
551:
548:
544:laminar flow
540:
523:
512:
466:
432:
391:
379:
352:leading edge
349:
341:
338:Aerodynamics
332:Aerodynamics
326:
307:
303:
295:, including
246:
234:synapomorphy
230:
147:
121:aerodynamics
118:
79:
60:
38:
26:
18:
6150:: 339â362.
5458:|work=
5412:(1): 1â39.
5031:: 317â327.
4987:Lepidoptera
4923:j.ctv301g2x
4800:20 February
4492:: 261â272.
4377:: 169â230.
3662:Gliding ant
3652:Bird flight
3629:Dual origin
3550:parachuting
3418:Mazothairos
3336:Bombycoidea
3334:and in the
3332:butterflies
3063:Hooke's law
2158:Power input
2023:, that is,
1729:Scorpionfly
1167:insect wing
952:Mach number
674:fluid force
420:stall delay
416:delta wings
322:Hymenoptera
297:butterflies
253:exoskeleton
242:butterflies
166:damselflies
162:Dragonflies
108:, only the
63:dragonflies
6472:Categories
4751:2011.00939
4455:(5): 784.
3961:2023-08-23
3834:2011-03-21
3720:2015-09-15
3673:References
3623:apterygota
3616:stoneflies
3545:parachutes
3501:including
3361:amino acid
3340:Sphingidae
3047:accelerate
3034:Elasticity
1773:Hoverfly (
1570:Drosophila
448:downstroke
408:turbulence
359:supination
314:Coleoptera
139:Mechanisms
94:silverfish
6172:122077834
5985:0960-9822
5916:2046-1402
5857:2054-5703
5794:1520-541X
5743:0028-0836
5568:0362-2525
5515:0362-2525
5481:, 9, 241.
5460:ignored (
5450:cite book
5370:205697025
5295:0027-8424
5220:: e3402.
5193:0035-8894
5109:0036-8075
4869:March 28,
4776:226227261
4349:March 31,
4325:1756-8293
3892:207172023
3876:1477-9145
3803:0022-0949
3606:radiators
3509:in 1873,
3505:in 1871,
3497:Numerous
3454:abdominal
3241:−
3233:×
3220:−
3212:×
3204:−
3196:×
3190:×
3177:×
3119:ℓ
3109:ℓ
3105:Δ
3010: erg
2979:ℓ
2949:ℓ
2938:−
2905:ω
2845:ℓ
2827:ω
2776:−
2768:×
2747:Δ
2677:ℓ
2652:ω
2601:ℓ
2531:ω
2466:−
2458:×
2434:×
2417:×
2351:−
2343:×
2337:×
2272:×
2266:×
2260:×
2202:×
2129:−
2116:≈
2064:−
2056:×
2044:Δ
1994:−
1986:×
1980:≈
1936:−
1928:×
1871:Δ
1825:Δ
1716:Damselfly
1677:Bumblebee
1421:Θ
1375:¯
1304:∫
1245:Θ
1203:¯
1077:⋅
1074:∇
1056:∇
1044:ρ
1037:∇
1031:−
1011:∇
1008:⋅
986:∂
976:∂
908:α
905:
899:π
805:ρ
785:α
746:ρ
726:α
660:Weis-Fogh
424:canoeists
383:fruit fly
367:frequency
363:pronation
310:bumblebee
73:and some
33:dragonfly
6444:Archived
6398:16210181
6361:12432002
6218:17453426
6210:14581590
6135:10562527
6032:10373107
5993:28089512
5934:28357056
5875:27853616
5810:15838166
5802:20433457
5700:19324632
5651:: 73â84.
5630:21237803
5584:52010764
5576:30110990
5531:52301138
5523:30231597
5418:25003692
5362:28684306
5313:30642969
5246:28584727
5125:36008925
5117:25378627
4891:18 March
4845:26889002
4721:27168523
4657:23330782
4649:17401119
4598:16081606
4552:29711043
4544:19749100
4427:25189374
4113:(1925).
4097:17453426
4089:14581590
3999:(2005).
3956:37425804
3947:10327165
3913:: 33â52.
3884:28424311
3811:11809787
3766:14327957
3646:See also
3635:evo-devo
3602:thoracic
3519:tracheal
3473:thoracic
3465:mayflies
3452:movable
3390:halteres
3386:antennae
2634:velocity
1955: cm
1945: cm
1703:Housefly
1690:Honeybee
1664:Hoverfly
1651:horsefly
1606:Beats/s
1593:Hovering
854:airfoils
460:upstroke
293:Neoptera
238:Neoptera
199:mayflies
106:termites
98:eusocial
82:apterous
67:mayflies
65:and the
6406:2430367
6378:Bibcode
6327:1691928
6306:Bibcode
6285:1538496
6152:Bibcode
6090:Bibcode
6073:4358428
6053:Bibcode
6012:Science
5963:Bibcode
5925:5357031
5900:: 268.
5866:5108966
5837:Bibcode
5759:4257270
5751:9024659
5723:Bibcode
5691:2781901
5610:Bibcode
5477:(1875)
5340:Bibcode
5304:6386694
5273:Bibcode
5237:5452959
5089:Bibcode
5080:Science
4756:Bibcode
4712:4863373
4691:Bibcode
4606:7750411
4457:Bibcode
4129:Bibcode
4018:Bibcode
3746:Bibcode
3554:gliding
3552:, then
3540:fossils
3507:Lubbock
3503:Landois
3364:proline
3051:resilin
2563:inertia
2124: s
2073: s
2003: s
1549:and Ωc/
561:mollusc
535:pronate
318:Diptera
265:sternum
263:to the
195:Odonata
154:Odonata
133:coupled
75:beetles
40:Insects
6404:
6396:
6359:
6324:
6283:
6216:
6208:
6170:
6133:
6071:
6045:Nature
6030:
5991:
5983:
5932:
5922:
5914:
5873:
5863:
5855:
5808:
5800:
5792:
5757:
5749:
5741:
5715:Nature
5698:
5688:
5628:
5582:
5574:
5566:
5529:
5521:
5513:
5416:
5368:
5360:
5311:
5301:
5293:
5244:
5234:
5191:
5123:
5115:
5107:
4966:
4921:
4843:
4774:
4719:
4709:
4655:
4647:
4604:
4596:
4550:
4542:
4425:
4323:
4280:
4195:8 July
4161:8 July
4095:
4087:
3954:
3944:
3890:
3882:
3874:
3809:
3801:
3764:
3706:
3558:flight
3515:Osborn
3511:Graber
3491:Mayfly
3461:naiads
3357:lipids
3258:
1755:Thrips
1625:Hornet
1381:
1361:Where
1149:Where
950:: The
489:thrips
375:thrust
355:vortex
320:, and
261:tergum
249:thorax
158:rowing
52:flight
6402:S2CID
6281:JSTOR
6214:S2CID
6168:S2CID
6069:S2CID
5806:S2CID
5755:S2CID
5580:S2CID
5527:S2CID
5414:JSTOR
5366:S2CID
5213:PeerJ
5121:S2CID
4919:JSTOR
4772:S2CID
4746:arXiv
4653:S2CID
4602:S2CID
4548:S2CID
4181:(PDF)
4093:S2CID
4061:(PDF)
4004:(PDF)
3888:S2CID
3476:terga
3457:gills
3394:wings
3322:jugum
3311:imago
3136:Here
2557:Here
2448:erg/s
1785:hover
1733:0.49
662:1973)
511:like
426:in a
371:hertz
257:notum
129:moths
110:alate
90:basal
71:flies
48:wings
6394:PMID
6357:PMID
6206:PMID
6131:PMID
6028:PMID
5989:PMID
5981:ISSN
5930:PMID
5912:ISSN
5871:PMID
5853:ISSN
5798:PMID
5790:ISSN
5747:PMID
5739:ISSN
5696:PMID
5626:PMID
5572:PMID
5564:ISSN
5519:PMID
5511:ISSN
5462:help
5358:PMID
5309:PMID
5291:ISSN
5242:PMID
5189:ISSN
5148:1996
5113:PMID
5105:ISSN
4964:ISBN
4893:2018
4871:2011
4841:PMID
4802:2016
4717:PMID
4645:PMID
4594:PMID
4540:PMID
4423:PMID
4351:2011
4321:ISSN
4278:ISBN
4197:2021
4189:1988
4163:2021
4085:PMID
3952:PMID
3880:PMID
3872:ISSN
3807:PMID
3799:ISSN
3762:PMID
3704:ISBN
3434:, a
3392:and
3355:and
2794:cm/s
2761:0.57
2455:1.23
2431:1.23
2362:0.98
2275:0.57
2250:Work
2182:Work
1763:254
1760:0.3
1746:2.5
1720:1.5
1710:190
1707:2.0
1697:250
1694:2.5
1684:130
1681:2.9
1671:120
1668:3.5
1655:3.9
1642:5.0
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