3580:
553:
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
3498:
3305:
664:
392:
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
3599:, 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.
1798:, 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.
199:
479:
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.
623:
607:
1781:
652:
640:
3050:
429:. 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
187:
323:, 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 (
297:
595:
285:
3060:. 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
454:
513:
493:
3482:, 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
3353:), 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.
466:
33:
425:(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
1155:
1186:
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:
2177:, 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
1596:(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.
3416:
975:
445:
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.
3155:/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:
69:, 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.
2025:
3462:
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
2160:
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
1801:
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
1180:
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
478:
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
444:
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
391:
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
338:
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
3071:
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
2507:
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
560:
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
3558:
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,
1599:
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
412:
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
1185:
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
552:
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
179:
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
548:
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
315:
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
3032:
567:, 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.
1150:{\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}}}
2400:
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:
543:
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
845:
396:, 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
3532:
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.
3284:
403:
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
3571:. 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.
2497:
433:, 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
251:; 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
339:
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.
1870:
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
3289:
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.
1877:
2816:
219:
3652:
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.
3553:
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
663:
2395:
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
2390:
952:
1802:
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
2309:
2888:
225:
224:
221:
220:
1368:
2243:
226:
2709:
3142:
242:
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
2248:
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:
384:(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
2821:
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
719:
5069:
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.
2877:
2155:
80:, 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 (
2563:
2165:, 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.
2095:
3161:
3528:
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
223:
5783:
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".
266:, 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 (
2407:
980:
5078:
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.
198:
3545:
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
1865:
5182:
1236:
2634:
875:
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
1534:
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 (
296:
4130:
5088:
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".
3704:
1279:
606:
138:, 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
5060:
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.
2020:{\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}}}
167:(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
1402:
368:. 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 (
88:) 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.
622:
1172:
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
1442:
2731:
1600:
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.
400:, 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.
1489:
651:
2725:
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:
1592: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
1529:
1509:
1462:
1422:
186:
2324:
6454:
639:
6431:
965:, 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
889:
284:
2255:
3439:, 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
3027:{\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}}}
222:
3632:
Stephen P. Yanoviak and colleagues proposed in 2009 that the wing derives from directed aerial gliding descentâa preflight phenomenon found in some
3068:
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.
687:, which follows the conventions found in aerodynamics. The force component normal to the direction of the flow relative to the wing is called lift (
3579:
5502:
Kukalova-Peck, Jarmila (1978). "Origin and evolution of insect wings and their relation to metamorphosis, as documented by the fossil record".
2030:
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
1284:
4978:
4292:
3718:
3710:
2588:
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:
2187:
695:). 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
585:(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.
2657:
262:
work: these muscles, rather than attaching to the wings, attach to the thorax and deform it; since the wings are extensions of the thoracic
2639:
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
3086:
3037:
Since there are two wing strokes (the upstroke and downstroke) in each cycle of the wing movement, the kinetic energy is 2Ă43 = 86
3304:
840:{\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}}.}
372:) so that the leading edge is pointed backward. The upstroke then pushes the wing upward and backward. Then the wing is flipped again (
5958:
Prokop, Jakub; PecharovĂĄ, Martina; Nel, AndrĂ©; Hörnschemeyer, Thomas; KrzemiĆska, Ewa; KrzemiĆski, WiesĆaw; Engel, Michael S. (2017).
3497:
3790:
Josephson, Robert K.; Malamud, Jean G.; Stokes, Darrell R. (2001). "The efficiency of an asynchronous flight muscle from a beetle".
2173:
One can now compute the power required to maintain hovering by, considering again an insect with mass m 0.1 g, average force, F
2826:) along the wing path, the maximum velocity is twice as high as the average velocity. Therefore, the maximum angular velocity is:
4801:
4019:
2832:
2106:
3279:{\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}}}
2514:
594:
5034:
4832:
4636:
4585:
4495:
4380:
4076:
3839:
3792:
3517:
3331:
The more primitive groups have an enlarged lobe-like area near the basal posterior margin, i.e. at the base of the forewing, a
2040:
1584:
wing is approximately so, its motion relative to a fixed body can be described by three variables: the position of the tip in
4970:
3644:
Biologists including Averof, Niwa, Elias-Neto and their colleagues have begun to explore the origin of the insect wing using
335:). The overall effect is that many higher Neoptera can beat their wings much faster than insects with direct flight muscles.
3625:
and Ă
ke Norberg suggested in 2003 that wings may have evolved initially for sailing on the surface of water as seen in some
2492:{\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}}}
557:), tiny insects often have a higher stroke frequency to generate wing-tip velocities that are comparable to larger insects.
6153:
Lewin, G. C.; Haj-Hariri, H. (2003). "Modelling thrust generation of a two-dimensional heaving airfoil in a viscous flow".
880:
669:
Fling 3: new vortex forms at leading edge, trailing edge vortices cancel each other, perhaps helping flow to grow faster (
5415:
Crampton, G. (1916). "The Phylogenetic Origin and the Nature of the Wings of Insects According to the Paranotal Theory".
3724:
397:
6463:
5018:
Woiwod, I.P.; Reynolds, D.R.; Thomas, C.D. (Eds) 2001. Insect Movement: Mechanisms and Consequences. CAB International.
5398:
1585:
275:
5180:
Tillyard, R. J. (2009). "Some remarks on the Devonian fossil insects from the Rhynie chert beds, Old Red Sandstone".
1816:
6488:
5452:
4925:
4221:
3667:
545:
353:
There are two basic aerodynamic models of insect flight: creating a leading edge vortex, and using clap and fling.
6451:
6446:
6379:
Zbikowski, R. (2002). "On aerodynamic modelling of an insect-like flapping wing in hover for micro air vehicles".
6021:
Dickinson, M. H.; Lehmann, F. O.; Sane, S. P. (1999). "Wing rotation and the aerodynamic basis of insect flight".
4068:
6051:
5608:
3622:
3076:. This is not strictly true as the resilin is stretched by a considerable amount and therefore both the area and
1191:
561:
overall drag through the entire wing stroke when compared to rigid wings. Bristles on the wing edges, as seen in
4378:(1973). "Quick estimates of flight fitness in hovering animals, including novel mechanisms of lift production".
871:
around an airfoil can be approximated by a potential flow satisfying the no-penetration boundary condition. The
2594:
2181:. The total work done by the insect during each downward stroke is the product of force and distance; that is,
1786:
539:, is a lift generation method utilized during small insect flight. As insect sizes become less than 1 mm,
3064:. During the upstroke of the wing, the resilin is stretched. The kinetic energy of the wing is converted into
876:
5153:[A Lower Carboniferous insect from the Bitterfeld/Delitzsch area (Pterygota, Arnsbergian, Germany)].
127:
before shedding their wings after mating, while the members of other castes are wingless their entire lives.
872:
393:
259:
2100:
The frequency of the beats, f, meaning the number of wingbeats per second, is represented by the equation:
6493:
3324:
which render these taxa functionally two-winged. All but the most basal forms exhibit this wing-coupling.
966:
5272:"Evolutionary history of Polyneoptera and its implications for our understanding of early winged insects"
1564:, the former is often referred to as the advance ratio, and it is also related to the reduced frequency,
5724:
Averof, Michalis; Cohen, Stephen M. (1997). "Evolutionary origin of insect wings from ancestral gills".
5557:
5504:
4632:"The aerodynamic benefit of wing-wing interaction depends on stroke trajectory in flapping insect wings"
1780:
1752:
867:
may reach a steady state when it slices through the fluid at a small angle of attack. In this case, the
100:
5836:"Tergal and pleural structures contribute to the formation of ectopic prothoracic wings in cockroaches"
5151:"Ein unter-karbonisches Insekt aus dem Raum Bitterfeld/Delitzsch (Pterygota, Arnsbergium, Deutschland)"
3583:
Generalized arthropod biramous limb. Trueman proposed that an endite and an exite fused to form a wing.
3049:
6436:
1242:
6388:
6316:
6162:
6100:
6091:
Ellington, C. P. (1984). "The Aerodynamics of Hovering Insect Flight. I. The Quasi-Steady Analysis".
6063:
5973:
5847:
5733:
5620:
5350:
5283:
5099:
4766:
4701:
4467:
4349:
4139:
4028:
3835:
3756:
3608:
3529:
3436:
1795:
1648:
1589:
438:
4745:
Kasoju, V.; Santhanakrishnan, A. (2021). "Aerodynamic interaction of bristled wing pairs in fling".
4805:
4410:
Santhanakrishnan, A.; Robinson, A.; Jones, S.; Low, A.; Gadi, S.; Hendrick, T.; Miller, L. (2014).
4353:
3747:
3649:
958:
6381:
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
4869:
1375:
1164:(x, t) is the flow field, p the pressure, Ï the density of the fluid, Îœ the kinematic viscosity, u
6468:
6412:
6291:
6224:
6178:
6079:
5816:
5765:
5590:
5537:
5460:
5424:
5376:
5131:
4929:
4782:
4756:
4663:
4612:
4558:
4103:
4011:
3898:
3395:
to maintain and control flight. Research has demonstrated the role of sensory structures such as
3362:
The biochemistry of insect flight has been a focus of considerable study. While many insects use
4165:
3080:
change in the process of stretching. The potential energy U stored in the stretched resilin is:
3077:
4456:"Two- and three- dimensional numerical simulations of the clap-fling-sweep of hovering insects"
4188:
2811:{\displaystyle v_{av}={\frac {d}{\Delta t}}={\frac {0.57}{4.5\times 10^{-3}}}=127{\text{cm/s}}}
6404:
6367:
6347:
6216:
6141:
6121:
6038:
5999:
5991:
5940:
5922:
5881:
5863:
5808:
5800:
5757:
5749:
5706:
5636:
5582:
5574:
5529:
5521:
5396:
Trueman, J. W. H. (1990), Comment: evolution of insect wings: a limb exite plus endite model.
5368:
5319:
5301:
5252:
5199:
5123:
5115:
5090:
4974:
4851:
4747:
4727:
4655:
4604:
4550:
4433:
4331:
4288:
4121:
4095:
3962:
3890:
3882:
3817:
3809:
3772:
3714:
3446:
3424:
3396:
2585:
581:
575:
524:
409:
1427:
6396:
6359:
6332:
6324:
6283:
6249:
6208:
6170:
6133:
6108:
6071:
6030:
5981:
5930:
5912:
5871:
5855:
5792:
5741:
5696:
5688:
5654:
Marden, James (2003). "The Surface-Skimming Hypothesis for the Evolution of Insect Flight".
5628:
5566:
5513:
5358:
5309:
5291:
5242:
5232:
5191:
5162:
5107:
5043:
4841:
4774:
4717:
4709:
4645:
4594:
4540:
4504:
4475:
4423:
4389:
4375:
4321:
4147:
4085:
4036:
3952:
3944:
3872:
3801:
3764:
3677:
3338:
Other groups have a frenulum on the hindwing that hooks under a retinaculum on the forewing.
3065:
2581:
670:
634:
Black (curved) arrows: flow; Blue arrows: induced velocity; Orange arrows: net force on wing
563:
536:
365:
38:
4040:
1467:
512:
492:
32:
6458:
6237:
5964:
5679:
5472:
4895:
3595:, also called the pleural hypothesis. This was based on a study by Goldschmidt in 1945 on
3513:
3489:; or that they arose from modifications of leg segments, which already contained muscles.
3471:
3327:
The mechanisms are of three different types â jugal, frenulo-retinacular and amplexiform:
1593:
519:
453:
414:
96:
5485:
3542:
3377:
as their energy source. Some species also use a combination of sources and moths such as
2161:
to its original vertical position, the average upward force during the downward stroke, F
6441:
6392:
6320:
6166:
6104:
6067:
5977:
5851:
5737:
5624:
5354:
5339:"Jumping and the aerial behavior of aquatic mayfly larvae (Myobaetis ellenae, Baetidae)"
5287:
5103:
4770:
4705:
4479:
4471:
4143:
4032:
3957:
3760:
2385:{\displaystyle {\text{E}}={\text{mgh}}=0.1\times 980\times 10^{-2}=0.98{\text{erg}}\,\!}
6337:
6304:
5935:
5900:
5876:
5835:
5701:
5674:
5314:
5271:
5247:
5218:
5195:
4722:
4689:
4284:
3525:
3456:
3073:
2397:
1514:
1494:
1447:
1407:
684:
540:
503:
465:
124:
6473:
6238:"The role of vortices and unsteady effects during the hovering flight of dragon flies"
3768:
3316:
Some four-winged insect orders, such as the Lepidoptera, have developed morphological
6482:
6182:
5796:
5632:
5611:; Norberg, R. Ă
ke (1996). "Skimming the surface â the origin of flight in insects?".
5555:
Rasnitsyn, Alexander P. (1981). "A modified paranotal theory of insect wing origin".
5380:
5166:
5150:
4786:
3902:
3592:
3588:
3546:
3420:
3379:
3363:
3317:
3309:
3299:
947:{\displaystyle C_{\text{L}}=2\pi \sin \alpha \quad {\text{and}}\quad C_{\text{D}}=0.}
868:
405:
143:
66:
6228:
5820:
5594:
5541:
5135:
4667:
4562:
4220:
Himmelskamp, H. (1945) "Profile investigations on a rotating airscrew". PhD thesis,
4107:
6416:
6083:
5917:
5769:
4690:"Wing-kinematics measurement and aerodynamics in a small insect in hovering flight"
4616:
4007:
3521:
3509:
3479:
3451:
3441:
1182:
613:
554:
422:
362:
348:
244:
131:
54:
6034:
2304:{\displaystyle {\text{Work}}=2\times 0.1\times 980\times 0.57=112{\text{erg}}\,\!}
6271:
4964:
4278:
2714:
During each stroke the center of the wings moves with an average linear velocity
6272:"Recordings of high wing-stroke and thoracic vibration frequency in some midges"
3672:
3662:
3560:
3428:
3346:
3342:
2318:
required to raise the mass of the insect 0.1 mm during each downstroke is:
1739:
1177:
962:
430:
332:
307:
263:
252:
176:
172:
108:
58:
4493:
Bennett, L. (1977). "Clap and fling aerodynamics- an experimental evaluation".
3936:
535:
Clap and fling, or the Weis-Fogh mechanism, discovered by the Danish zoologist
6174:
5986:
5959:
5363:
5338:
3948:
3633:
3371:
3350:
3151:
is the Young's modulus for resilin, which has been measured to be 1.8Ă10
3057:
2823:
1580:
426:
418:
369:
324:
104:
17:
6122:"The novel aerodynamics of insect flight: Applications to micro-air vehicles"
5995:
5926:
5867:
5804:
5753:
5578:
5525:
5305:
5203:
5119:
4412:"Clap and fling mechanism with interacting porous wing in tiny insect flight"
4335:
4326:
4309:
4151:
3886:
3813:
863:
are constants only if the flow is steady. A special class of objects such as
270:) to bow upward, making the wings flip down. Another set of muscles from the
6363:
6137:
5570:
5517:
5296:
5111:
5000:(pp. 631-664) in Resh, & Cardé (Eds). "Encyclopedia of Insects". 2003.
3805:
3555:
3464:
1726:
1687:
1661:
1622:
434:
380:
range in insects with synchronous flight muscles typically is 5 to 200
377:
373:
320:
316:
evolution of asynchronous flight muscles in several separate insect clades.
43:
6442:
The Novel Aerodynamics Of Insect Flight: Applications To Micro-Air Vehicles
6408:
6400:
6371:
6328:
6220:
6145:
6112:
6042:
6003:
5944:
5899:
Tomoyasu, Yoshinori; Ohde, Takahiro; Clark-Hachtel, Courtney (2017-03-14).
5885:
5812:
5710:
5692:
5640:
5586:
5533:
5372:
5323:
5256:
5127:
4933:
4855:
4731:
4659:
4608:
4581:"The aerodynamic effects of wing-wing interaction in flapping insect wings"
4554:
4437:
4099:
3966:
3894:
3821:
3776:
3407:
in controlling flight posture, wingbeat amplitude, and wingbeat frequency.
5761:
5047:
4310:"Investigation into Reynolds number effects on a biomimetic flapping wing"
3415:
691:), and the force component in the opposite direction of the flow is drag (
4508:
4393:
3937:"Machine learning reveals the control mechanics of the insect wing hinge"
3645:
3626:
3616:
3483:
3475:
3400:
3392:
2644:
1713:
1700:
1674:
303:
248:
77:
6253:
5859:
5428:
3591:, appendages on the respective inner and outer aspects of the primitive
3541:
The paranotal lobe or tergal (dorsal body wall) hypothesis, proposed by
1363:{\displaystyle r_{g}={\sqrt {{\frac {1}{s}}\int _{0}^{R}{r^{2}c(R)dr}}}}
6295:
5960:"Paleozoic Nymphal Wing Pads Support Dual Model of Insect Wing Origins"
5237:
4846:
4827:
4545:
4528:
4428:
4411:
3877:
3860:
3648:
in addition to palaeontological evidence. This suggests that wings are
3564:
3374:
3061:
2573:
2238:{\displaystyle {\text{Work}}=F_{av}\times d={\text{2W}}_{\text{d}}\,\!}
1181:
corresponding Reynolds number about 103. At the smaller end, a typical
864:
571:
328:
205:
164:
116:
73:
6309:
Philosophical Transactions of the Royal Society B: Biological Sciences
6212:
6093:
Philosophical Transactions of the Royal Society B: Biological Sciences
4778:
4713:
4650:
4631:
4599:
4580:
4090:
3916:
Heide, G.G. (1983). "Neural mechanisms of flight control in Diptera".
2704:{\displaystyle \omega _{\text{max}}={\frac {v_{\text{max}}}{\ell /2}}}
628:
Clap 3: trailing edges close, vortices shed, wings close giving thrust
417:
that is typical of insect flight. The Reynolds number is a measure of
6075:
5745:
4125:
3612:
3568:
3550:
3501:
3367:
3056:
Insects gain kinetic energy, provided by the muscles, when the wings
1765:
1635:
499:
385:
271:
209:
168:
160:
92:
85:
62:
50:
6287:
208:(dragonflies and damselflies) have direct flight musculature, as do
6050:
Ellington, Charles P.; Van Den Berg, Coen; Willmott, Alexander P.;
5901:"What serial homologs can tell us about the origin of insect wings"
4761:
3137:{\displaystyle U={\frac {1}{2}}{\frac {EA\Delta \ell ^{2}}{\ell }}}
2314:
The energy is used to raise the insect against gravity. The energy
6261:
Smyth, T. Jr. (1985). "Muscle systems". In Blum, M.S. Blum (ed.).
5223:
4455:
3836:"Definition of Asynchronous muscle in the Entomologists' glossary"
3587:
In 1990, J. W. H. Trueman proposed that the wing was adapted from
3578:
3496:
3486:
3414:
3321:
3048:
3041:. This is about as much energy as is consumed in hovering itself.
1779:
969:
being subject to the no-slip boundary condition, the equation is:
579:, a sea butterfly. Some insects, such as the vegetable leaf miner
381:
278:
pulls the notum downward again, causing the wings to flip upward.
267:
120:
81:
5009:
Gorb, S. (2001) Ch 4.1.5 "Inter-locking of body parts". pp 46â50.
4308:
Hope, Daniel K; DeLuca, Anthony M.; O'Hara, Ryan P (2018-01-03).
3370:
as the energy source for flight, many beetles and flies use the
4126:"Ăber die Entstehung des dynamischen Auftriebes von TragflĂŒgeln"
3467:
3459:, but it is uncertain if it had wings, or indeed was an insect.
3404:
3152:
657:
Fling 2: leading edge moves away, air rushes in, increasing lift
258:
What all Neoptera share, however, is the way the muscles in the
139:
4454:
Kolomenskiy, D; Moffatt, H.; Farge, M.; Schneider, K. (2011).
3859:
Deora, Tanvi; Gundiah, Namrata; Sane, Sanjay P. (2017-04-15).
3038:
290:
Indirect flight: muscles make thorax oscillate in most insects
112:
5675:"Gliding hexapods and the origins of insect aerial behaviour"
6348:"Rotational lift: something difference or more of the same?"
5219:"The presumed oldest flying insect: more likely a myriapod?"
5028:
Joos, B. (1987). "Carbohydrate use in the flight muscles of
4922:
The Biomechanics of Insect Flight: Form, Function, Evolution
4189:"The Behaviour and Performance of Leading-Edge Vortex Flaps"
570:
The clap and fling mechanism is also employed by the marine
192:
Direct flight: muscles attached to wings. Large insects only
5155:
Neues Jahrbuch fĂŒr Geologie und PalĂ€ontologie - Monatshefte
2872:{\displaystyle \omega _{\text{max}}={\frac {254}{\ell /2}}}
2150:{\displaystyle f={\frac {1}{T}}\approx 110{\text{ s}}^{-1}}
502:
are unsuitable for leading edge vortex flight, but support
5732:(6617). Springer Science and Business Media LLC: 627â630.
2558:{\displaystyle KE={\frac {1}{2}}I\omega _{\text{max}}^{2}}
699:
the wing speed. The dimensionless forces are called lift (
6432:
An Insect's Role In The Development Of Micro Air Vehicles
6199:
Sane, S. P. (2003). "The aerodynamics of insect flight".
5183:
Transactions of the Royal Entomological Society of London
4202:. International Council of Aeronautical Sciences: 758â765
4128:[On the origin of the dynamic lift of airfoils].
645:
Fling 1: wings rotate around trailing edge to fling apart
4802:"Swim Like a Butterfly? Sea Snail 'Flies' Through Water"
2090:{\displaystyle T=2\,\Delta t=9\times 10^{-3}{\text{ s}}}
1549:). The ratios of them form two dimensionless variables,
319:
Insects that beat their wings more rapidly, such as the
310:
and most other insects, have indirect flight musculature
4953:
in Capinera (Ed) (2008) "Encyc. Entom.", Vol 4. p. 4266
4826:
Murphy, D.; Adhikari, D.; Webster, D.; Yen, J. (2016).
6464:
Flow visualization of butterfly aerodynamic mechanisms
5673:
Yanoviak, Stephen P.; Kaspari, M.; Dudley, R. (2009).
3935:
Melis, Johan M.; Dickinson, Michael H. (2023-06-30).
3164:
3089:
2891:
2835:
2734:
2660:
2597:
2517:
2410:
2327:
2258:
2190:
2109:
2043:
1880:
1819:
1517:
1497:
1470:
1450:
1430:
1410:
1378:
1287:
1245:
1194:
1176:=uL/Μ . There are two obvious differences between an
978:
957:
The flows around birds and insects can be considered
892:
722:
130:
Some very small insects make use not of steady-state
3706:
Numbers of living species in Australia and the World
1806:
of the upward wingbeat, the insect drops a distance
361:
Most insects use a method that creates a spiralling
5270:Wipfler, Benjamin; et al. (19 February 2019).
4828:"Underwater flight by the planktonic sea butterfly"
91:Not all insects are capable of flight. A number of
6236:Savage, S. B.; Newman, B.G.; Wong, D.T.M. (1979).
6054:(1996). "Leading-edge vortices in insect flight".
5337:Yanoviak, Stephen P.; Dudley, Robert (July 2018).
4131:Zeitschrift fĂŒr Angewandte Mathematik und Mechanik
3278:
3136:
3026:
2871:
2810:
2703:
2628:
2557:
2491:
2384:
2303:
2237:
2149:
2089:
2019:
1859:
1523:
1503:
1483:
1456:
1436:
1416:
1396:
1362:
1273:
1230:
1149:
946:
839:
46:has flight muscles attached directly to its wings.
4683:
4681:
4679:
4677:
3745:Smith, D.S. (1965). "Flight muscles of insects".
3636:, a wingless sister taxon to the winged insects.
2381:
2300:
2234:
612:Clap 2: leading edges touch, wing rotates around
6305:"The vortex wake of a 'hovering' model hawkmoth"
5410:
5408:
4579:Lehmann, F.-O.; Sane, S.; Dickinson, M. (2005).
5276:Proceedings of the National Academy of Sciences
4529:"Flexible clap and fling in tiny insect flight"
1531:is the length of wing, including the wing tip.
589:Clap and fling flight mechanism after Sane 2003
5149:Brauckmann, Carsten; Schneider, Joerg (1996).
4062:
4060:
4058:
4056:
4054:
4052:
4050:
1860:{\displaystyle h={\frac {g(\Delta t^{2})}{2}}}
159:Unlike other insects, the wing muscles of the
146:to the hindwings so these can work in unison.
97:secondarily lost their wings through evolution
5417:Journal of the New York Entomological Society
4966:The Lepidoptera: Form, Function and Diversity
4896:"Butterflies in the Pieridae family (whites)"
3611:'s 1973 suggestion that wings developed from
123:reproductive castes develop wings during the
8:
6437:Insect-like Flapping-Wing Micro Air Vehicles
4915:
4913:
2643:, can be calculated from the maximum linear
6303:Van Den Berg, C.; Ellington, C. P. (1997).
5834:Elias-Neto, Moysés; Belles, Xavier (2016).
5447:Grimaldi, David; Engel, Michael S. (2005).
5442:
5440:
5438:
4992:
4990:
4314:International Journal of Micro Air Vehicles
4272:
4270:
4268:
4266:
4264:
4262:
4260:
4258:
4256:
4254:
4252:
4250:
1578:If an insect wing is rigid, for example, a
1231:{\displaystyle Re={\frac {{\bar {c}}U}{v}}}
5392:
5390:
4248:
4246:
4244:
4242:
4240:
4238:
4236:
4234:
4232:
4230:
4002:
3478:. Phylogenomic analysis suggests that the
3383:use carbohydrates for pre-flight warm-up.
3335:, that folds under the hindwing in flight.
1607:
413:this effect is negligible for flow with a
6336:
5985:
5934:
5916:
5875:
5700:
5362:
5313:
5295:
5246:
5236:
4945:
4943:
4845:
4760:
4721:
4649:
4598:
4544:
4427:
4325:
4089:
4000:
3998:
3996:
3994:
3992:
3990:
3988:
3986:
3984:
3982:
3956:
3876:
3698:
3696:
3694:
3692:
3271:
3250:
3229:
3213:
3194:
3181:
3171:
3163:
3122:
3106:
3096:
3088:
3019:
3007:
2992:
2983:
2962:
2956:
2947:
2929:
2918:
2901:
2890:
2858:
2849:
2840:
2834:
2803:
2785:
2769:
2751:
2739:
2733:
2690:
2680:
2674:
2665:
2659:
2629:{\displaystyle I={\frac {m\ell ^{2}}{3}}}
2614:
2604:
2596:
2549:
2544:
2527:
2516:
2484:
2475:
2457:
2451:
2433:
2422:
2411:
2409:
2380:
2375:
2360:
2336:
2328:
2326:
2299:
2294:
2259:
2257:
2233:
2227:
2222:
2203:
2191:
2189:
2138:
2133:
2116:
2108:
2082:
2073:
2053:
2042:
2012:
2003:
1980:
1975:
1969:
1964:
1954:
1945:
1931:
1918:
1914:
1895:
1879:
1842:
1826:
1818:
1516:
1496:
1475:
1469:
1449:
1429:
1409:
1380:
1379:
1377:
1333:
1328:
1322:
1317:
1303:
1301:
1292:
1286:
1265:
1244:
1208:
1207:
1204:
1193:
1134:
1129:
1115:
1110:
1090:
1075:
1069:
1044:
1029:
1013:
989:
983:
979:
977:
932:
922:
897:
891:
822:
804:
786:
776:
763:
745:
727:
721:
27:Mechanisms and evolution of insect flight
6265:. John Wiley and Sons. pp. 227â286.
5217:Carolin Haug & Joachim Haug (2017).
3941:BioRxiv: The Preprint Server for Biology
3303:
376:) and another downstroke can occur. The
31:
6194:. Oxford Biology Readers. Vol. 52.
3688:
632:
587:
280:
182:
5468:
5458:
4800:Weisberger, Mindy (19 February 2016).
4187:Ellis, D. G.; Stollery, J. L. (1988).
4041:10.1146/annurev.fluid.36.050802.121940
2584:during the wing stroke. To obtain the
683:A wing moving in fluids experiences a
5343:Arthropod Structure & Development
4574:
4572:
4522:
4520:
4518:
4449:
4447:
4405:
4403:
3711:Australian Biological Resources Study
2882:And the kinetic energy therefore is:
1538:), the forward velocity of the body (
7:
3493:Epicoxal (abdominal gill) hypothesis
6352:The Journal of Experimental Biology
6242:The Journal of Experimental Biology
6201:The Journal of Experimental Biology
6126:The Journal of Experimental Biology
4688:Cheng, Xin; Sun, Mao (2016-05-11).
4533:The Journal of Experimental Biology
4480:10.1016/j.jfluidstructs.2011.05.002
4069:"The aerodynamics of insect flight"
1168:the velocity at the boundary, and u
135:
5196:10.1111/j.1365-2311.1928.tb01188.x
3861:"Mechanics of the thorax in flies"
3115:
2757:
2054:
1881:
1835:
1790:) has indirect flight musculature.
1431:
1255:
1084:
1066:
1047:
1021:
996:
986:
136:Weis-Fogh clap and fling mechanism
25:
6447:The aerodynamics of insect flight
6263:Fundamentals of insect physiology
5613:Trends in Ecology & Evolution
5490:Jena. Zeitung Naturwissenschaften
4630:Lehmann, F.-O.; Pick, S. (2007).
3769:10.1038/scientificamerican0665-76
3575:Endite-exite (pleural) hypothesis
3504:nymph with paired abdominal gills
6346:Walker, J. A. (September 2002).
5846:(8). The Royal Society: 160347.
5797:10.1111/j.1525-142x.2010.00402.x
4460:Journal of Fluids and Structures
4020:Annual Review of Fluid Mechanics
1810:under the influence of gravity.
1274:{\displaystyle U=2\Theta fr_{g}}
1130:
1111:
1091:
1076:
1030:
1014:
990:
662:
650:
638:
621:
605:
593:
511:
491:
464:
452:
295:
283:
217:
197:
185:
5035:Journal of Experimental Biology
4833:Journal of Experimental Biology
4637:Journal of Experimental Biology
4586:Journal of Experimental Biology
4527:Miller, L.; Peskin, S. (2009).
4496:Journal of Experimental Biology
4416:Journal of Experimental Biology
4381:Journal of Experimental Biology
4280:Physics in Biology and Medicine
4077:Journal of Experimental Biology
3865:Journal of Experimental Biology
3840:North Carolina State University
3793:Journal of Experimental Biology
1545:), and the pitching velocity (Ω
927:
921:
781:
775:
232:Slow motion flight of dragonfly
180:hunted other airborne insects.
5918:10.12688/f1000research.10285.1
3449:from the Lower Carboniferous;
1848:
1832:
1424:is the speed of the wing tip,
1385:
1348:
1342:
1213:
798:
792:
739:
733:
1:
6035:10.1126/science.284.5422.1954
3537:Paranotal (tergal) hypothesis
2651:, at the center of the wing:
1404:is the average chord length,
600:Clap 1: wings close over back
107:never evolved wings. In some
5633:10.1016/0169-5347(96)30022-0
5032:during pre-flight warm-up".
3838:. Department of Entomology,
2508:during each wing stroke is:
1397:{\displaystyle {\bar {c}}\ }
398:computational fluid dynamics
65:. Insects first flew in the
6469:The Flight Of The Bumblebee
5785:Evolution & Development
5656:Acta Zoologica Cracoviensia
5399:Canadian Journal of Zoology
4963:Scoble, Malcolm J. (1995).
4166:"Transition and Turbulence"
1491:is the radius of gyration,
528:to "fly" through the water.
6510:
6190:Pringle, J. W. S. (1975).
6155:Journal of Fluid Mechanics
5840:Royal Society Open Science
5453:Cambridge University Press
5167:10.1127/njgpm/1996/1996/17
4926:Princeton University Press
4876:. Cislunar Aerospace. 1997
4012:"Dissecting Insect Flight"
3668:Flying and gliding animals
3297:
518:Clap and fling is used in
346:
6175:10.1017/S0022112003005743
6120:Ellington, C. P. (1999).
5987:10.1016/j.cub.2016.11.021
5449:Insects take to the skies
5364:10.1016/j.asd.2017.06.005
4949:Stocks, Ian. (2008). Sec.
4924:. Princeton, New Jersey:
4870:"Insect Wings in General"
4277:Davidovits, Paul (2008).
3949:10.1101/2023.06.29.547116
3607:Other hypotheses include
1764:
1751:
1738:
1725:
1712:
1699:
1686:
1673:
1660:
1647:
1634:
1621:
1616:
1613:
1610:
1444:is the stroke amplitude,
713:) coefficients, that is:
4327:10.1177/1756829317745319
4152:10.1002/zamm.19250050103
4067:Sane, Sanjay P. (2003).
3411:Evolution and adaptation
3312:in male and female moths
498:The feathery wings of a
161:Ephemeroptera (mayflies)
6364:10.1242/jeb.205.24.3783
6138:10.1242/jeb.202.23.3439
5571:10.1002/jmor.1051680309
5518:10.1002/jmor.1051560104
5297:10.1073/pnas.1817794116
5112:10.1126/science.1257570
4920:Dudley, Robert (2000).
4874:Aerodynamics of Insects
4222:University of Göttingen
3806:10.1242/jeb.204.23.4125
3703:Chapman, A. D. (2006).
3597:Drosophila melanogaster
1588:, (Î(t),Ί(t)), and the
1511:is the wing area, and
1464:is the beat frequency,
1437:{\displaystyle \Theta }
873:Kutta-Joukowski theorem
72:Two insect groups, the
6401:10.1098/rsta.2001.0930
6329:10.1098/rstb.1997.0023
6276:Biol. Bull. Woods Hole
6270:Sotavalta, O. (1953).
6113:10.1098/rstb.1984.0049
5693:10.1098/rsbl.2009.0029
4971:Natural History Museum
4168:. Princeton University
3584:
3505:
3470:, as found on aquatic
3432:
3313:
3280:
3138:
3053:
3028:
2873:
2812:
2721:given by the distance
2705:
2630:
2559:
2493:
2386:
2305:
2239:
2151:
2091:
2021:
1861:
1791:
1787:Philhelius pedissequum
1525:
1505:
1485:
1458:
1438:
1418:
1398:
1364:
1275:
1232:
1151:
967:Navier-Stokes equation
948:
841:
53:are the only group of
47:
5558:Journal of Morphology
5505:Journal of Morphology
5048:10.1242/jeb.133.1.317
4996:Powell, Jerry A. Ch.
3582:
3500:
3418:
3307:
3281:
3139:
3052:
3029:
2874:
2813:
2706:
2631:
2560:
2494:
2387:
2306:
2240:
2152:
2092:
2022:
1862:
1783:
1753:Large white butterfly
1586:spherical coordinates
1526:
1506:
1486:
1484:{\displaystyle r_{g}}
1459:
1439:
1419:
1399:
1365:
1276:
1233:
1152:
949:
877:Bernoulli's principle
842:
549:aerodynamic benefit.
347:Further information:
247:) for the infraclass
35:
6358:(Pt 24): 3783â3792.
6132:(Pt 23): 3439â3448.
6052:Thomas, Adrian L. R.
5609:Thomas, Adrian L. R.
5512:(1). Wiley: 53â125.
4593:(Pt 16): 3075â3092.
4509:10.1242/jeb.69.1.261
4422:(Pt 21): 3898â4709.
4394:10.1242/jeb.59.1.169
3615:protrusions used as
3609:Vincent Wigglesworth
3437:Carboniferous Period
3419:Reconstruction of a
3308:Frenulo-retinacular
3162:
3087:
2889:
2833:
2732:
2658:
2595:
2515:
2408:
2325:
2256:
2188:
2107:
2041:
1878:
1817:
1649:Hummingbird hawkmoth
1515:
1495:
1468:
1448:
1428:
1408:
1376:
1285:
1243:
1192:
976:
890:
720:
439:sculling draw stroke
6393:2002RSPTA.360..273Z
6321:1997RSPTB.352..317V
6254:10.1242/jeb.83.1.59
6207:(Pt 23): 4191â208.
6167:2003JFM...492..339L
6105:1984RSPTB.305....1E
6068:1996Natur.384..626E
5978:2017CBio...27..263P
5860:10.1098/rsos.160347
5852:2016RSOS....360347E
5738:1997Natur.385..627A
5625:1996TEcoE..11..187T
5455:. pp. 155â159.
5355:2018ArtSD..47..370Y
5288:2019PNAS..116.3024W
5104:2014Sci...346..763M
4806:Scientific American
4771:2021PhFl...33c1901K
4706:2016NatSR...625706C
4644:(Pt 8): 1362â1377.
4472:2011JFS....27..784K
4354:Scientific American
4350:"Catching the Wake"
4196:ICAS 1988 Jerusalem
4144:1925ZaMM....5...17W
4033:2005AnRFM..37..183W
3761:1965SciAm.212f..76S
3748:Scientific American
3650:serially homologous
3567:and finally active
3455:is older, from the
2934:
2554:
1327:
679:Governing equations
357:Leading edge vortex
142:have the forewings
99:, while other more
6457:2004-08-22 at the
5238:10.7717/peerj.3402
4973:. pp. 56â60.
4847:10.1242/jeb.129205
4694:Scientific Reports
4546:10.1242/jeb.028662
4429:10.1242/jeb.084897
4287:. pp. 78â79.
3878:10.1242/jeb.128363
3589:endites and exites
3585:
3506:
3447:Palaeodictyopteran
3433:
3425:palaeodictyopteran
3320:mechanisms in the
3314:
3276:
3134:
3054:
3024:
2914:
2869:
2808:
2701:
2626:
2555:
2540:
2489:
2382:
2301:
2235:
2147:
2087:
2017:
1857:
1792:
1611:Flight parameters
1521:
1501:
1481:
1454:
1434:
1414:
1394:
1360:
1313:
1271:
1228:
1147:
1145:
944:
837:
57:that have evolved
48:
6489:Insect physiology
6387:(1791): 273â290.
6315:(1351): 317â328.
6213:10.1242/jeb.00663
6062:(6610): 626â630.
6029:(5422): 1954â60.
5098:(6210): 763â767.
4980:978-0-19-854952-9
4779:10.1063/5.0036018
4748:Physics of Fluids
4714:10.1038/srep25706
4651:10.1242/jeb.02746
4600:10.1242/jeb.01744
4539:(19): 3076â3090.
4376:Weis-Fogh, Torkel
4294:978-0-12-369411-9
4091:10.1242/jeb.00663
4084:(23): 4191â4208.
3800:(23): 4125â4139.
3720:978-0-642-56850-2
3713:. pp. 60pp.
3274:
3270:
3260:
3179:
3132:
3104:
3022:
3001:
2971:
2909:
2867:
2843:
2806:
2795:
2764:
2699:
2683:
2668:
2624:
2586:moment of inertia
2576:of the wing and Ï
2572:is the moment of
2547:
2535:
2487:
2460:
2436:
2425:
2414:
2378:
2339:
2331:
2297:
2262:
2230:
2225:
2194:
2136:
2124:
2085:
2015:
1988:
1987:
1978:
1967:
1957:
1908:
1855:
1794:Many insects can
1778:
1777:
1768:(clap and fling)
1623:Aeshnid dragonfly
1524:{\displaystyle R}
1504:{\displaystyle s}
1457:{\displaystyle f}
1417:{\displaystyle U}
1393:
1388:
1358:
1311:
1226:
1216:
1137:
1118:
1057:
1003:
935:
925:
900:
832:
789:
779:
773:
730:
582:Liriomyza sativae
576:Limacina helicina
525:Limacina helicina
410:Herbert A. Wagner
408:, as proposed by
227:
171:through the air.
16:(Redirected from
6501:
6420:
6375:
6342:
6340:
6299:
6266:
6257:
6232:
6195:
6186:
6149:
6116:
6087:
6076:10.1038/384626a0
6046:
6008:
6007:
5989:
5955:
5949:
5948:
5938:
5920:
5896:
5890:
5889:
5879:
5831:
5825:
5824:
5780:
5774:
5773:
5746:10.1038/385627a0
5721:
5715:
5714:
5704:
5670:
5664:
5663:
5651:
5645:
5644:
5605:
5599:
5598:
5552:
5546:
5545:
5499:
5493:
5483:
5477:
5476:
5470:
5466:
5464:
5456:
5444:
5433:
5432:
5412:
5403:
5394:
5385:
5384:
5366:
5334:
5328:
5327:
5317:
5299:
5282:(8): 3024â3029.
5267:
5261:
5260:
5250:
5240:
5214:
5208:
5207:
5177:
5171:
5170:
5146:
5140:
5139:
5085:
5079:
5076:
5070:
5067:
5061:
5058:
5052:
5051:
5025:
5019:
5016:
5010:
5007:
5001:
4994:
4985:
4984:
4960:
4954:
4947:
4938:
4937:
4917:
4908:
4907:
4905:
4903:
4892:
4886:
4885:
4883:
4881:
4866:
4860:
4859:
4849:
4823:
4817:
4816:
4814:
4812:
4797:
4791:
4790:
4764:
4742:
4736:
4735:
4725:
4685:
4672:
4671:
4653:
4627:
4621:
4620:
4602:
4576:
4567:
4566:
4548:
4524:
4513:
4512:
4490:
4484:
4483:
4451:
4442:
4441:
4431:
4407:
4398:
4397:
4372:
4366:
4365:
4363:
4361:
4346:
4340:
4339:
4329:
4305:
4299:
4298:
4274:
4225:
4218:
4212:
4211:
4209:
4207:
4193:
4184:
4178:
4177:
4175:
4173:
4162:
4156:
4155:
4118:
4112:
4111:
4093:
4073:
4064:
4045:
4044:
4016:
4004:
3977:
3976:
3974:
3973:
3960:
3932:
3926:
3925:
3913:
3907:
3906:
3880:
3871:(8): 1382â1395.
3856:
3850:
3849:
3847:
3846:
3832:
3826:
3825:
3787:
3781:
3780:
3742:
3736:
3735:
3733:
3732:
3723:. Archived from
3700:
3678:Insect migration
3603:Other hypotheses
3549:found in insect
3435:Sometime in the
3393:sensory feedback
3387:Sensory feedback
3285:
3283:
3282:
3277:
3275:
3272:
3268:
3261:
3259:
3258:
3257:
3238:
3237:
3236:
3221:
3220:
3199:
3198:
3182:
3180:
3172:
3143:
3141:
3140:
3135:
3133:
3128:
3127:
3126:
3107:
3105:
3097:
3066:potential energy
3033:
3031:
3030:
3025:
3023:
3020:
3012:
3011:
3006:
3002:
3000:
2996:
2984:
2977:
2973:
2972:
2967:
2966:
2957:
2955:
2954:
2933:
2928:
2910:
2902:
2878:
2876:
2875:
2870:
2868:
2866:
2862:
2850:
2845:
2844:
2841:
2817:
2815:
2814:
2809:
2807:
2804:
2796:
2794:
2793:
2792:
2770:
2765:
2763:
2752:
2747:
2746:
2710:
2708:
2707:
2702:
2700:
2698:
2694:
2685:
2684:
2681:
2675:
2670:
2669:
2666:
2635:
2633:
2632:
2627:
2625:
2620:
2619:
2618:
2605:
2582:angular velocity
2564:
2562:
2561:
2556:
2553:
2548:
2545:
2536:
2528:
2498:
2496:
2495:
2490:
2488:
2485:
2483:
2482:
2461:
2458:
2456:
2455:
2437:
2434:
2426:
2423:
2415:
2412:
2391:
2389:
2388:
2383:
2379:
2376:
2368:
2367:
2340:
2337:
2332:
2329:
2310:
2308:
2307:
2302:
2298:
2295:
2263:
2260:
2244:
2242:
2241:
2236:
2232:
2231:
2228:
2226:
2223:
2211:
2210:
2195:
2192:
2156:
2154:
2153:
2148:
2146:
2145:
2137:
2134:
2125:
2117:
2096:
2094:
2093:
2088:
2086:
2083:
2081:
2080:
2026:
2024:
2023:
2018:
2016:
2013:
2011:
2010:
1989:
1986:
1985:
1984:
1979:
1976:
1973:
1968:
1965:
1959:
1958:
1955:
1953:
1952:
1933:
1932:
1927:
1926:
1922:
1913:
1909:
1904:
1896:
1866:
1864:
1863:
1858:
1856:
1851:
1847:
1846:
1827:
1608:
1530:
1528:
1527:
1522:
1510:
1508:
1507:
1502:
1490:
1488:
1487:
1482:
1480:
1479:
1463:
1461:
1460:
1455:
1443:
1441:
1440:
1435:
1423:
1421:
1420:
1415:
1403:
1401:
1400:
1395:
1391:
1390:
1389:
1381:
1369:
1367:
1366:
1361:
1359:
1357:
1338:
1337:
1326:
1321:
1312:
1304:
1302:
1297:
1296:
1280:
1278:
1277:
1272:
1270:
1269:
1237:
1235:
1234:
1229:
1227:
1222:
1218:
1217:
1209:
1205:
1156:
1154:
1153:
1148:
1146:
1139:
1138:
1135:
1133:
1120:
1119:
1116:
1114:
1094:
1079:
1074:
1073:
1058:
1053:
1045:
1033:
1028:
1024:
1017:
1004:
1002:
994:
993:
984:
953:
951:
950:
945:
937:
936:
933:
926:
923:
902:
901:
898:
846:
844:
843:
838:
833:
831:
827:
826:
813:
805:
791:
790:
787:
780:
777:
774:
772:
768:
767:
754:
746:
732:
731:
728:
666:
654:
642:
625:
609:
597:
564:Encarsia formosa
537:Torkel Weis-Fogh
515:
495:
468:
456:
299:
287:
229:
228:
201:
189:
39:Hemicordulia tau
21:
6509:
6508:
6504:
6503:
6502:
6500:
6499:
6498:
6479:
6478:
6459:Wayback Machine
6428:
6423:
6378:
6345:
6302:
6288:10.2307/1538496
6269:
6260:
6235:
6198:
6189:
6152:
6119:
6090:
6049:
6020:
6016:
6014:Further reading
6011:
5965:Current Biology
5957:
5956:
5952:
5898:
5897:
5893:
5833:
5832:
5828:
5782:
5781:
5777:
5723:
5722:
5718:
5680:Biology Letters
5672:
5671:
5667:
5653:
5652:
5648:
5607:
5606:
5602:
5554:
5553:
5549:
5501:
5500:
5496:
5484:
5480:
5467:
5457:
5446:
5445:
5436:
5414:
5413:
5406:
5395:
5388:
5336:
5335:
5331:
5269:
5268:
5264:
5216:
5215:
5211:
5179:
5178:
5174:
5148:
5147:
5143:
5087:
5086:
5082:
5077:
5073:
5068:
5064:
5059:
5055:
5027:
5026:
5022:
5017:
5013:
5008:
5004:
4995:
4988:
4981:
4962:
4961:
4957:
4948:
4941:
4919:
4918:
4911:
4901:
4899:
4898:. Bumblebee.org
4894:
4893:
4889:
4879:
4877:
4868:
4867:
4863:
4825:
4824:
4820:
4810:
4808:
4799:
4798:
4794:
4744:
4743:
4739:
4687:
4686:
4675:
4629:
4628:
4624:
4578:
4577:
4570:
4526:
4525:
4516:
4492:
4491:
4487:
4453:
4452:
4445:
4409:
4408:
4401:
4374:
4373:
4369:
4359:
4357:
4356:. June 28, 1999
4348:
4347:
4343:
4307:
4306:
4302:
4295:
4276:
4275:
4228:
4219:
4215:
4205:
4203:
4191:
4186:
4185:
4181:
4171:
4169:
4164:
4163:
4159:
4122:Wagner, Herbert
4120:
4119:
4115:
4071:
4066:
4065:
4048:
4014:
4006:
4005:
3980:
3971:
3969:
3934:
3933:
3929:
3915:
3914:
3910:
3858:
3857:
3853:
3844:
3842:
3834:
3833:
3829:
3789:
3788:
3784:
3744:
3743:
3739:
3730:
3728:
3721:
3702:
3701:
3690:
3686:
3659:
3642:
3605:
3577:
3539:
3495:
3413:
3389:
3360:
3302:
3296:
3246:
3239:
3225:
3209:
3190:
3183:
3160:
3159:
3118:
3108:
3085:
3084:
3078:Young's modulus
3047:
2988:
2979:
2978:
2958:
2943:
2942:
2938:
2887:
2886:
2854:
2836:
2831:
2830:
2781:
2774:
2756:
2735:
2730:
2729:
2720:
2686:
2676:
2661:
2656:
2655:
2650:
2642:
2610:
2606:
2593:
2592:
2580:is the maximum
2579:
2513:
2512:
2505:
2471:
2447:
2406:
2405:
2356:
2323:
2322:
2254:
2253:
2221:
2199:
2186:
2185:
2176:
2171:
2164:
2132:
2105:
2104:
2069:
2039:
2038:
1999:
1974:
1960:
1941:
1934:
1897:
1891:
1890:
1876:
1875:
1838:
1828:
1815:
1814:
1606:
1594:angle of attack
1574:
1555:
1544:
1513:
1512:
1493:
1492:
1471:
1466:
1465:
1446:
1445:
1426:
1425:
1406:
1405:
1374:
1373:
1329:
1288:
1283:
1282:
1261:
1241:
1240:
1206:
1190:
1189:
1183:chalcidoid wasp
1175:
1171:
1167:
1144:
1143:
1128:
1121:
1109:
1106:
1105:
1095:
1081:
1080:
1065:
1046:
1034:
1012:
1008:
995:
985:
974:
973:
928:
893:
888:
887:
881:Blasius theorem
861:
854:
818:
814:
806:
782:
759:
755:
747:
723:
718:
717:
711:
704:
681:
674:
667:
658:
655:
646:
643:
629:
626:
617:
616:, vortices form
610:
601:
598:
533:
532:
531:
530:
529:
520:sea butterflies
516:
508:
507:
496:
485:
476:
475:
474:
473:
472:
469:
461:
460:
457:
423:flow is laminar
415:Reynolds number
359:
351:
345:
311:
300:
291:
288:
240:
238:Indirect flight
233:
230:
218:
213:
202:
193:
190:
157:
152:
36:A tau emerald (
28:
23:
22:
15:
12:
11:
5:
6507:
6505:
6497:
6496:
6491:
6481:
6480:
6477:
6476:
6471:
6466:
6461:
6452:Flight muscles
6449:
6444:
6439:
6434:
6427:
6426:External links
6424:
6422:
6421:
6376:
6343:
6300:
6282:(3): 439â444.
6267:
6258:
6233:
6196:
6187:
6150:
6117:
6099:(1122): 1â15.
6088:
6047:
6017:
6015:
6012:
6010:
6009:
5972:(2): 263â269.
5950:
5891:
5826:
5791:(2): 168â176.
5775:
5716:
5665:
5646:
5619:(5): 187â188.
5600:
5565:(3): 331â338.
5547:
5494:
5478:
5434:
5404:
5386:
5349:(4): 370â374.
5329:
5262:
5209:
5172:
5141:
5080:
5071:
5062:
5053:
5020:
5011:
5002:
4986:
4979:
4955:
4939:
4928:. p. 69.
4909:
4887:
4861:
4840:(4): 535â543.
4818:
4792:
4737:
4673:
4622:
4568:
4514:
4485:
4443:
4399:
4367:
4341:
4320:(1): 106â122.
4300:
4293:
4285:Academic Press
4226:
4213:
4179:
4157:
4113:
4046:
4027:(1): 183â210.
3978:
3927:
3908:
3851:
3827:
3782:
3737:
3719:
3687:
3685:
3682:
3681:
3680:
3675:
3670:
3665:
3658:
3655:
3641:
3638:
3604:
3601:
3593:arthropod limb
3576:
3573:
3559:starting with
3538:
3535:
3494:
3491:
3457:Early Devonian
3412:
3409:
3388:
3385:
3359:
3356:
3355:
3354:
3341:In almost all
3339:
3336:
3298:Main article:
3295:
3292:
3287:
3286:
3267:
3264:
3256:
3253:
3249:
3245:
3242:
3235:
3232:
3228:
3224:
3219:
3216:
3212:
3208:
3205:
3202:
3197:
3193:
3189:
3186:
3178:
3175:
3170:
3167:
3145:
3144:
3131:
3125:
3121:
3117:
3114:
3111:
3103:
3100:
3095:
3092:
3072:resilin obeys
3046:
3043:
3035:
3034:
3018:
3015:
3010:
3005:
2999:
2995:
2991:
2987:
2982:
2976:
2970:
2965:
2961:
2953:
2950:
2946:
2941:
2937:
2932:
2927:
2924:
2921:
2917:
2913:
2908:
2905:
2900:
2897:
2894:
2880:
2879:
2865:
2861:
2857:
2853:
2848:
2839:
2819:
2818:
2802:
2799:
2791:
2788:
2784:
2780:
2777:
2773:
2768:
2762:
2759:
2755:
2750:
2745:
2742:
2738:
2718:
2712:
2711:
2697:
2693:
2689:
2679:
2673:
2664:
2648:
2640:
2637:
2636:
2623:
2617:
2613:
2609:
2603:
2600:
2577:
2566:
2565:
2552:
2543:
2539:
2534:
2531:
2526:
2523:
2520:
2504:
2501:
2500:
2499:
2481:
2478:
2474:
2470:
2467:
2464:
2454:
2450:
2446:
2443:
2440:
2432:
2429:
2421:
2418:
2398:kinetic energy
2393:
2392:
2374:
2371:
2366:
2363:
2359:
2355:
2352:
2349:
2346:
2343:
2335:
2312:
2311:
2293:
2290:
2287:
2284:
2281:
2278:
2275:
2272:
2269:
2266:
2246:
2245:
2220:
2217:
2214:
2209:
2206:
2202:
2198:
2174:
2170:
2167:
2162:
2158:
2157:
2144:
2141:
2131:
2128:
2123:
2120:
2115:
2112:
2098:
2097:
2079:
2076:
2072:
2068:
2065:
2062:
2059:
2056:
2052:
2049:
2046:
2028:
2027:
2009:
2006:
2002:
1998:
1995:
1992:
1983:
1972:
1963:
1951:
1948:
1944:
1940:
1937:
1930:
1925:
1921:
1917:
1912:
1907:
1903:
1900:
1894:
1889:
1886:
1883:
1868:
1867:
1854:
1850:
1845:
1841:
1837:
1834:
1831:
1825:
1822:
1776:
1775:
1772:
1769:
1762:
1761:
1758:
1755:
1749:
1748:
1745:
1742:
1736:
1735:
1732:
1729:
1723:
1722:
1719:
1716:
1710:
1709:
1706:
1703:
1697:
1696:
1693:
1690:
1684:
1683:
1680:
1677:
1671:
1670:
1667:
1664:
1658:
1657:
1654:
1651:
1645:
1644:
1641:
1638:
1632:
1631:
1628:
1625:
1619:
1618:
1615:
1612:
1605:
1602:
1590:pitching angle
1572:
1553:
1542:
1520:
1500:
1478:
1474:
1453:
1433:
1413:
1387:
1384:
1356:
1353:
1350:
1347:
1344:
1341:
1336:
1332:
1325:
1320:
1316:
1310:
1307:
1300:
1295:
1291:
1268:
1264:
1260:
1257:
1254:
1251:
1248:
1225:
1221:
1215:
1212:
1203:
1200:
1197:
1173:
1169:
1165:
1158:
1157:
1142:
1132:
1127:
1124:
1122:
1113:
1108:
1107:
1104:
1101:
1098:
1096:
1093:
1089:
1086:
1083:
1082:
1078:
1072:
1068:
1064:
1061:
1056:
1052:
1049:
1043:
1040:
1037:
1035:
1032:
1027:
1023:
1020:
1016:
1011:
1007:
1001:
998:
992:
988:
982:
981:
959:incompressible
955:
954:
943:
940:
931:
920:
917:
914:
911:
908:
905:
896:
859:
852:
848:
847:
836:
830:
825:
821:
817:
812:
809:
803:
800:
797:
794:
785:
771:
766:
762:
758:
753:
750:
744:
741:
738:
735:
726:
709:
702:
680:
677:
676:
675:
668:
661:
659:
656:
649:
647:
644:
637:
635:
631:
630:
627:
620:
618:
611:
604:
602:
599:
592:
590:
541:viscous forces
517:
510:
509:
504:clap and fling
497:
490:
489:
488:
487:
486:
484:
483:Clap and fling
481:
470:
463:
462:
458:
451:
450:
449:
448:
447:
358:
355:
344:
341:
313:
312:
301:
294:
292:
289:
282:
239:
236:
235:
234:
231:
216:
214:
203:
196:
194:
191:
184:
156:
153:
151:
148:
26:
24:
18:Clap and fling
14:
13:
10:
9:
6:
4:
3:
2:
6506:
6495:
6494:Animal flight
6492:
6490:
6487:
6486:
6484:
6475:
6474:Insect Flight
6472:
6470:
6467:
6465:
6462:
6460:
6456:
6453:
6450:
6448:
6445:
6443:
6440:
6438:
6435:
6433:
6430:
6429:
6425:
6418:
6414:
6410:
6406:
6402:
6398:
6394:
6390:
6386:
6382:
6377:
6373:
6369:
6365:
6361:
6357:
6353:
6349:
6344:
6339:
6334:
6330:
6326:
6322:
6318:
6314:
6310:
6306:
6301:
6297:
6293:
6289:
6285:
6281:
6277:
6273:
6268:
6264:
6259:
6255:
6251:
6247:
6243:
6239:
6234:
6230:
6226:
6222:
6218:
6214:
6210:
6206:
6202:
6197:
6193:
6192:Insect flight
6188:
6184:
6180:
6176:
6172:
6168:
6164:
6160:
6156:
6151:
6147:
6143:
6139:
6135:
6131:
6127:
6123:
6118:
6114:
6110:
6106:
6102:
6098:
6094:
6089:
6085:
6081:
6077:
6073:
6069:
6065:
6061:
6057:
6053:
6048:
6044:
6040:
6036:
6032:
6028:
6024:
6019:
6018:
6013:
6005:
6001:
5997:
5993:
5988:
5983:
5979:
5975:
5971:
5967:
5966:
5961:
5954:
5951:
5946:
5942:
5937:
5932:
5928:
5924:
5919:
5914:
5910:
5906:
5905:F1000Research
5902:
5895:
5892:
5887:
5883:
5878:
5873:
5869:
5865:
5861:
5857:
5853:
5849:
5845:
5841:
5837:
5830:
5827:
5822:
5818:
5814:
5810:
5806:
5802:
5798:
5794:
5790:
5786:
5779:
5776:
5771:
5767:
5763:
5759:
5755:
5751:
5747:
5743:
5739:
5735:
5731:
5727:
5720:
5717:
5712:
5708:
5703:
5698:
5694:
5690:
5686:
5682:
5681:
5676:
5669:
5666:
5661:
5657:
5650:
5647:
5642:
5638:
5634:
5630:
5626:
5622:
5618:
5614:
5610:
5604:
5601:
5596:
5592:
5588:
5584:
5580:
5576:
5572:
5568:
5564:
5560:
5559:
5551:
5548:
5543:
5539:
5535:
5531:
5527:
5523:
5519:
5515:
5511:
5507:
5506:
5498:
5495:
5491:
5487:
5486:MĂŒller, Fritz
5482:
5479:
5474:
5462:
5454:
5450:
5443:
5441:
5439:
5435:
5430:
5426:
5422:
5418:
5411:
5409:
5405:
5401:
5400:
5393:
5391:
5387:
5382:
5378:
5374:
5370:
5365:
5360:
5356:
5352:
5348:
5344:
5340:
5333:
5330:
5325:
5321:
5316:
5311:
5307:
5303:
5298:
5293:
5289:
5285:
5281:
5277:
5273:
5266:
5263:
5258:
5254:
5249:
5244:
5239:
5234:
5230:
5226:
5225:
5220:
5213:
5210:
5205:
5201:
5197:
5193:
5189:
5185:
5184:
5176:
5173:
5168:
5164:
5160:
5157:(in German).
5156:
5152:
5145:
5142:
5137:
5133:
5129:
5125:
5121:
5117:
5113:
5109:
5105:
5101:
5097:
5093:
5092:
5084:
5081:
5075:
5072:
5066:
5063:
5057:
5054:
5049:
5045:
5041:
5037:
5036:
5031:
5030:Manduca sexta
5024:
5021:
5015:
5012:
5006:
5003:
4999:
4993:
4991:
4987:
4982:
4976:
4972:
4968:
4967:
4959:
4956:
4952:
4951:Wing Coupling
4946:
4944:
4940:
4935:
4931:
4927:
4923:
4916:
4914:
4910:
4897:
4891:
4888:
4875:
4871:
4865:
4862:
4857:
4853:
4848:
4843:
4839:
4835:
4834:
4829:
4822:
4819:
4807:
4803:
4796:
4793:
4788:
4784:
4780:
4776:
4772:
4768:
4763:
4758:
4755:(3): 031901.
4754:
4750:
4749:
4741:
4738:
4733:
4729:
4724:
4719:
4715:
4711:
4707:
4703:
4699:
4695:
4691:
4684:
4682:
4680:
4678:
4674:
4669:
4665:
4661:
4657:
4652:
4647:
4643:
4639:
4638:
4633:
4626:
4623:
4618:
4614:
4610:
4606:
4601:
4596:
4592:
4588:
4587:
4582:
4575:
4573:
4569:
4564:
4560:
4556:
4552:
4547:
4542:
4538:
4534:
4530:
4523:
4521:
4519:
4515:
4510:
4506:
4502:
4498:
4497:
4489:
4486:
4481:
4477:
4473:
4469:
4465:
4461:
4457:
4450:
4448:
4444:
4439:
4435:
4430:
4425:
4421:
4417:
4413:
4406:
4404:
4400:
4395:
4391:
4387:
4383:
4382:
4377:
4371:
4368:
4355:
4351:
4345:
4342:
4337:
4333:
4328:
4323:
4319:
4315:
4311:
4304:
4301:
4296:
4290:
4286:
4282:
4281:
4273:
4271:
4269:
4267:
4265:
4263:
4261:
4259:
4257:
4255:
4253:
4251:
4249:
4247:
4245:
4243:
4241:
4239:
4237:
4235:
4233:
4231:
4227:
4223:
4217:
4214:
4201:
4197:
4190:
4183:
4180:
4167:
4161:
4158:
4153:
4149:
4145:
4141:
4137:
4134:(in German).
4133:
4132:
4127:
4123:
4117:
4114:
4109:
4105:
4101:
4097:
4092:
4087:
4083:
4079:
4078:
4070:
4063:
4061:
4059:
4057:
4055:
4053:
4051:
4047:
4042:
4038:
4034:
4030:
4026:
4022:
4021:
4013:
4009:
4008:Wang, Z. Jane
4003:
4001:
3999:
3997:
3995:
3993:
3991:
3989:
3987:
3985:
3983:
3979:
3968:
3964:
3959:
3954:
3950:
3946:
3942:
3938:
3931:
3928:
3923:
3919:
3912:
3909:
3904:
3900:
3896:
3892:
3888:
3884:
3879:
3874:
3870:
3866:
3862:
3855:
3852:
3841:
3837:
3831:
3828:
3823:
3819:
3815:
3811:
3807:
3803:
3799:
3795:
3794:
3786:
3783:
3778:
3774:
3770:
3766:
3762:
3758:
3754:
3750:
3749:
3741:
3738:
3727:on 2009-05-19
3726:
3722:
3716:
3712:
3708:
3707:
3699:
3697:
3695:
3693:
3689:
3683:
3679:
3676:
3674:
3671:
3669:
3666:
3664:
3661:
3660:
3656:
3654:
3651:
3647:
3639:
3637:
3635:
3630:
3628:
3624:
3623:Adrian Thomas
3620:
3618:
3614:
3610:
3602:
3600:
3598:
3594:
3590:
3581:
3574:
3572:
3570:
3566:
3562:
3557:
3552:
3548:
3547:preadaptation
3544:
3536:
3534:
3531:
3527:
3524:in 1877, and
3523:
3519:
3515:
3511:
3510:entomologists
3503:
3499:
3492:
3490:
3488:
3485:
3481:
3477:
3473:
3469:
3466:
3460:
3458:
3454:
3453:
3448:
3444:
3443:
3438:
3431:
3430:
3426:
3422:
3421:Carboniferous
3417:
3410:
3408:
3406:
3402:
3398:
3394:
3386:
3384:
3382:
3381:
3380:Manduca sexta
3376:
3373:
3369:
3365:
3364:carbohydrates
3357:
3352:
3348:
3344:
3340:
3337:
3334:
3330:
3329:
3328:
3325:
3323:
3319:
3318:wing coupling
3311:
3310:wing coupling
3306:
3301:
3300:Wing coupling
3294:Wing coupling
3293:
3291:
3265:
3262:
3254:
3251:
3247:
3243:
3240:
3233:
3230:
3226:
3222:
3217:
3214:
3210:
3206:
3203:
3200:
3195:
3191:
3187:
3184:
3176:
3173:
3168:
3165:
3158:
3157:
3156:
3154:
3150:
3129:
3123:
3119:
3112:
3109:
3101:
3098:
3093:
3090:
3083:
3082:
3081:
3079:
3075:
3069:
3067:
3063:
3059:
3051:
3044:
3042:
3040:
3016:
3013:
3008:
3003:
2997:
2993:
2989:
2985:
2980:
2974:
2968:
2963:
2959:
2951:
2948:
2944:
2939:
2935:
2930:
2925:
2922:
2919:
2915:
2911:
2906:
2903:
2898:
2895:
2892:
2885:
2884:
2883:
2863:
2859:
2855:
2851:
2846:
2837:
2829:
2828:
2827:
2825:
2800:
2797:
2789:
2786:
2782:
2778:
2775:
2771:
2766:
2760:
2753:
2748:
2743:
2740:
2736:
2728:
2727:
2726:
2724:
2717:
2695:
2691:
2687:
2677:
2671:
2662:
2654:
2653:
2652:
2646:
2621:
2615:
2611:
2607:
2601:
2598:
2591:
2590:
2589:
2587:
2583:
2575:
2571:
2550:
2541:
2537:
2532:
2529:
2524:
2521:
2518:
2511:
2510:
2509:
2502:
2479:
2476:
2472:
2468:
2465:
2462:
2452:
2448:
2444:
2441:
2438:
2430:
2427:
2419:
2416:
2404:
2403:
2402:
2399:
2372:
2369:
2364:
2361:
2357:
2353:
2350:
2347:
2344:
2341:
2333:
2321:
2320:
2319:
2317:
2291:
2288:
2285:
2282:
2279:
2276:
2273:
2270:
2267:
2264:
2252:
2251:
2250:
2218:
2215:
2212:
2207:
2204:
2200:
2196:
2184:
2183:
2182:
2180:
2168:
2166:
2142:
2139:
2129:
2126:
2121:
2118:
2113:
2110:
2103:
2102:
2101:
2077:
2074:
2070:
2066:
2063:
2060:
2057:
2050:
2047:
2044:
2037:
2036:
2035:
2033:
2007:
2004:
2000:
1996:
1993:
1990:
1981:
1970:
1961:
1949:
1946:
1942:
1938:
1935:
1928:
1923:
1919:
1915:
1910:
1905:
1901:
1898:
1892:
1887:
1884:
1874:
1873:
1872:
1852:
1843:
1839:
1829:
1823:
1820:
1813:
1812:
1811:
1809:
1805:
1799:
1797:
1789:
1788:
1782:
1773:
1770:
1767:
1763:
1759:
1756:
1754:
1750:
1746:
1743:
1741:
1737:
1733:
1730:
1728:
1724:
1720:
1717:
1715:
1711:
1707:
1704:
1702:
1698:
1694:
1691:
1689:
1685:
1681:
1678:
1676:
1672:
1668:
1665:
1663:
1659:
1655:
1652:
1650:
1646:
1642:
1639:
1637:
1633:
1629:
1626:
1624:
1620:
1609:
1603:
1601:
1597:
1595:
1591:
1587:
1583:
1582:
1576:
1571:
1567:
1563:
1559:
1552:
1548:
1541:
1537:
1532:
1518:
1498:
1476:
1472:
1451:
1411:
1382:
1370:
1354:
1351:
1345:
1339:
1334:
1330:
1323:
1318:
1314:
1308:
1305:
1298:
1293:
1289:
1266:
1262:
1258:
1252:
1249:
1246:
1238:
1223:
1219:
1210:
1201:
1198:
1195:
1187:
1184:
1179:
1163:
1140:
1125:
1123:
1102:
1099:
1097:
1087:
1070:
1062:
1059:
1054:
1050:
1041:
1038:
1036:
1025:
1018:
1009:
1005:
999:
972:
971:
970:
968:
964:
960:
941:
938:
929:
918:
915:
912:
909:
906:
903:
894:
886:
885:
884:
882:
878:
874:
870:
869:inviscid flow
866:
862:
855:
834:
828:
823:
819:
815:
810:
807:
801:
795:
783:
769:
764:
760:
756:
751:
748:
742:
736:
724:
716:
715:
714:
712:
705:
698:
694:
690:
686:
678:
672:
665:
660:
653:
648:
641:
636:
633:
624:
619:
615:
608:
603:
596:
591:
588:
586:
584:
583:
578:
577:
573:
568:
566:
565:
558:
556:
550:
547:
542:
538:
527:
526:
521:
514:
505:
501:
494:
482:
480:
467:
455:
446:
442:
440:
436:
432:
428:
424:
420:
416:
411:
407:
406:Wagner effect
401:
399:
395:
389:
387:
383:
379:
375:
371:
367:
364:
356:
354:
350:
342:
340:
336:
334:
330:
326:
322:
317:
309:
305:
298:
293:
286:
281:
279:
277:
273:
269:
265:
261:
256:
254:
250:
246:
237:
215:
211:
207:
200:
195:
188:
183:
181:
178:
174:
170:
166:
162:
155:Direct flight
154:
149:
147:
145:
141:
137:
134:, but of the
133:
128:
126:
125:mating season
122:
118:
114:
111:insects like
110:
106:
103:insects like
102:
98:
95:insects have
94:
89:
87:
83:
79:
75:
70:
68:
67:Carboniferous
64:
60:
56:
55:invertebrates
52:
45:
41:
40:
34:
30:
19:
6384:
6380:
6355:
6351:
6312:
6308:
6279:
6275:
6262:
6248:(1): 59â77.
6245:
6241:
6204:
6200:
6191:
6158:
6154:
6129:
6125:
6096:
6092:
6059:
6055:
6026:
6022:
5969:
5963:
5953:
5908:
5904:
5894:
5843:
5839:
5829:
5788:
5784:
5778:
5729:
5725:
5719:
5687:(4): 510â2.
5684:
5678:
5668:
5659:
5655:
5649:
5616:
5612:
5603:
5562:
5556:
5550:
5509:
5503:
5497:
5489:
5481:
5451:. New York:
5448:
5420:
5416:
5397:
5346:
5342:
5332:
5279:
5275:
5265:
5228:
5222:
5212:
5190:(1): 65â71.
5187:
5181:
5175:
5161:(1): 17â30.
5158:
5154:
5144:
5095:
5089:
5083:
5074:
5065:
5056:
5039:
5033:
5029:
5023:
5014:
5005:
4997:
4965:
4958:
4950:
4921:
4900:. Retrieved
4890:
4878:. Retrieved
4873:
4864:
4837:
4831:
4821:
4809:. Retrieved
4795:
4752:
4746:
4740:
4700:(1): 25706.
4697:
4693:
4641:
4635:
4625:
4590:
4584:
4536:
4532:
4500:
4494:
4488:
4463:
4459:
4419:
4415:
4385:
4379:
4370:
4358:. Retrieved
4344:
4317:
4313:
4303:
4279:
4216:
4204:. Retrieved
4199:
4195:
4182:
4170:. Retrieved
4160:
4138:(1): 17â35.
4135:
4129:
4116:
4081:
4075:
4024:
4018:
3970:. Retrieved
3940:
3930:
3921:
3918:BIONA Report
3917:
3911:
3868:
3864:
3854:
3843:. Retrieved
3830:
3797:
3791:
3785:
3755:(6): 76â88.
3752:
3746:
3740:
3729:. Retrieved
3725:the original
3709:. Canberra:
3705:
3643:
3631:
3621:
3606:
3596:
3586:
3543:Fritz MĂŒller
3540:
3507:
3480:Polyneoptera
3461:
3452:Rhyniognatha
3450:
3442:Delitzschala
3440:
3434:
3427:
3423:insect, the
3391:Insects use
3390:
3378:
3361:
3358:Biochemistry
3349:(except the
3332:
3326:
3315:
3288:
3148:
3146:
3070:
3055:
3036:
2881:
2824:sinusoidally
2820:
2722:
2715:
2713:
2638:
2569:
2567:
2506:
2503:Power output
2394:
2315:
2313:
2247:
2178:
2172:
2159:
2099:
2031:
2029:
1869:
1807:
1803:
1800:
1793:
1785:
1614:Speed (m/s)
1598:
1579:
1577:
1569:
1565:
1561:
1557:
1550:
1546:
1539:
1535:
1533:
1371:
1239:
1188:
1161:
1159:
956:
857:
850:
849:
707:
706:) and drag (
700:
696:
692:
688:
682:
614:leading edge
580:
574:
569:
562:
559:
555:laminar flow
551:
534:
523:
477:
443:
402:
390:
363:leading edge
360:
352:
349:Aerodynamics
343:Aerodynamics
337:
318:
314:
306:, including
257:
245:synapomorphy
241:
158:
132:aerodynamics
129:
90:
71:
49:
37:
29:
6161:: 339â362.
5469:|work=
5423:(1): 1â39.
5042:: 317â327.
4998:Lepidoptera
4934:j.ctv301g2x
4811:20 February
4503:: 261â272.
4388:: 169â230.
3673:Gliding ant
3663:Bird flight
3640:Dual origin
3561:parachuting
3429:Mazothairos
3347:Bombycoidea
3345:and in the
3343:butterflies
3074:Hooke's law
2169:Power input
2034:, that is,
1740:Scorpionfly
1178:insect wing
963:Mach number
685:fluid force
431:stall delay
427:delta wings
333:Hymenoptera
308:butterflies
264:exoskeleton
253:butterflies
177:damselflies
173:Dragonflies
119:, only the
74:dragonflies
6483:Categories
4762:2011.00939
4466:(5): 784.
3972:2023-08-23
3845:2011-03-21
3731:2015-09-15
3684:References
3634:apterygota
3627:stoneflies
3556:parachutes
3512:including
3372:amino acid
3351:Sphingidae
3058:accelerate
3045:Elasticity
1784:Hoverfly (
1581:Drosophila
459:downstroke
419:turbulence
370:supination
325:Coleoptera
150:Mechanisms
105:silverfish
6183:122077834
5996:0960-9822
5927:2046-1402
5868:2054-5703
5805:1520-541X
5754:0028-0836
5579:0362-2525
5526:0362-2525
5492:, 9, 241.
5471:ignored (
5461:cite book
5381:205697025
5306:0027-8424
5231:: e3402.
5204:0035-8894
5120:0036-8075
4880:March 28,
4787:226227261
4360:March 31,
4336:1756-8293
3903:207172023
3887:1477-9145
3814:0022-0949
3617:radiators
3520:in 1873,
3516:in 1871,
3508:Numerous
3465:abdominal
3252:−
3244:×
3231:−
3223:×
3215:−
3207:×
3201:×
3188:×
3130:ℓ
3120:ℓ
3116:Δ
3021: erg
2990:ℓ
2960:ℓ
2949:−
2916:ω
2856:ℓ
2838:ω
2787:−
2779:×
2758:Δ
2688:ℓ
2663:ω
2612:ℓ
2542:ω
2477:−
2469:×
2445:×
2428:×
2362:−
2354:×
2348:×
2283:×
2277:×
2271:×
2213:×
2140:−
2127:≈
2075:−
2067:×
2055:Δ
2005:−
1997:×
1991:≈
1947:−
1939:×
1882:Δ
1836:Δ
1727:Damselfly
1688:Bumblebee
1432:Θ
1386:¯
1315:∫
1256:Θ
1214:¯
1088:⋅
1085:∇
1067:∇
1055:ρ
1048:∇
1042:−
1022:∇
1019:⋅
997:∂
987:∂
919:α
916:
910:π
816:ρ
796:α
757:ρ
737:α
671:Weis-Fogh
435:canoeists
394:fruit fly
378:frequency
374:pronation
321:bumblebee
84:and some
44:dragonfly
6455:Archived
6409:16210181
6372:12432002
6229:17453426
6221:14581590
6146:10562527
6043:10373107
6004:28089512
5945:28357056
5886:27853616
5821:15838166
5813:20433457
5711:19324632
5662:: 73â84.
5641:21237803
5595:52010764
5587:30110990
5542:52301138
5534:30231597
5429:25003692
5373:28684306
5324:30642969
5257:28584727
5136:36008925
5128:25378627
4902:18 March
4856:26889002
4732:27168523
4668:23330782
4660:17401119
4609:16081606
4563:29711043
4555:19749100
4438:25189374
4124:(1925).
4108:17453426
4100:14581590
4010:(2005).
3967:37425804
3958:10327165
3924:: 33â52.
3895:28424311
3822:11809787
3777:14327957
3657:See also
3646:evo-devo
3613:thoracic
3530:tracheal
3484:thoracic
3476:mayflies
3463:movable
3401:halteres
3397:antennae
2645:velocity
1966: cm
1956: cm
1714:Housefly
1701:Honeybee
1675:Hoverfly
1662:horsefly
1617:Beats/s
1604:Hovering
865:airfoils
471:upstroke
304:Neoptera
249:Neoptera
210:mayflies
117:termites
109:eusocial
93:apterous
78:mayflies
76:and the
6417:2430367
6389:Bibcode
6338:1691928
6317:Bibcode
6296:1538496
6163:Bibcode
6101:Bibcode
6084:4358428
6064:Bibcode
6023:Science
5974:Bibcode
5936:5357031
5911:: 268.
5877:5108966
5848:Bibcode
5770:4257270
5762:9024659
5734:Bibcode
5702:2781901
5621:Bibcode
5488:(1875)
5351:Bibcode
5315:6386694
5284:Bibcode
5248:5452959
5100:Bibcode
5091:Science
4767:Bibcode
4723:4863373
4702:Bibcode
4617:7750411
4468:Bibcode
4140:Bibcode
4029:Bibcode
3757:Bibcode
3565:gliding
3563:, then
3551:fossils
3518:Lubbock
3514:Landois
3375:proline
3062:resilin
2574:inertia
2135: s
2084: s
2014: s
1560:and Ωc/
572:mollusc
546:pronate
329:Diptera
276:sternum
274:to the
206:Odonata
165:Odonata
144:coupled
86:beetles
51:Insects
6415:
6407:
6370:
6335:
6294:
6227:
6219:
6181:
6144:
6082:
6056:Nature
6041:
6002:
5994:
5943:
5933:
5925:
5884:
5874:
5866:
5819:
5811:
5803:
5768:
5760:
5752:
5726:Nature
5709:
5699:
5639:
5593:
5585:
5577:
5540:
5532:
5524:
5427:
5379:
5371:
5322:
5312:
5304:
5255:
5245:
5202:
5134:
5126:
5118:
4977:
4932:
4854:
4785:
4730:
4720:
4666:
4658:
4615:
4607:
4561:
4553:
4436:
4334:
4291:
4206:8 July
4172:8 July
4106:
4098:
3965:
3955:
3901:
3893:
3885:
3820:
3812:
3775:
3717:
3569:flight
3526:Osborn
3522:Graber
3502:Mayfly
3472:naiads
3368:lipids
3269:
1766:Thrips
1636:Hornet
1392:
1372:Where
1160:Where
961:: The
500:thrips
386:thrust
366:vortex
331:, and
272:tergum
260:thorax
169:rowing
63:flight
6413:S2CID
6292:JSTOR
6225:S2CID
6179:S2CID
6080:S2CID
5817:S2CID
5766:S2CID
5591:S2CID
5538:S2CID
5425:JSTOR
5377:S2CID
5224:PeerJ
5132:S2CID
4930:JSTOR
4783:S2CID
4757:arXiv
4664:S2CID
4613:S2CID
4559:S2CID
4192:(PDF)
4104:S2CID
4072:(PDF)
4015:(PDF)
3899:S2CID
3487:terga
3468:gills
3405:wings
3333:jugum
3322:imago
3147:Here
2568:Here
2459:erg/s
1796:hover
1744:0.49
673:1973)
522:like
437:in a
382:hertz
268:notum
140:moths
121:alate
101:basal
82:flies
59:wings
6405:PMID
6368:PMID
6217:PMID
6142:PMID
6039:PMID
6000:PMID
5992:ISSN
5941:PMID
5923:ISSN
5882:PMID
5864:ISSN
5809:PMID
5801:ISSN
5758:PMID
5750:ISSN
5707:PMID
5637:PMID
5583:PMID
5575:ISSN
5530:PMID
5522:ISSN
5473:help
5369:PMID
5320:PMID
5302:ISSN
5253:PMID
5200:ISSN
5159:1996
5124:PMID
5116:ISSN
4975:ISBN
4904:2018
4882:2011
4852:PMID
4813:2016
4728:PMID
4656:PMID
4605:PMID
4551:PMID
4434:PMID
4362:2011
4332:ISSN
4289:ISBN
4208:2021
4200:1988
4174:2021
4096:PMID
3963:PMID
3891:PMID
3883:ISSN
3818:PMID
3810:ISSN
3773:PMID
3715:ISBN
3445:, a
3403:and
3366:and
2805:cm/s
2772:0.57
2466:1.23
2442:1.23
2373:0.98
2286:0.57
2261:Work
2193:Work
1774:254
1771:0.3
1757:2.5
1731:1.5
1721:190
1718:2.0
1708:250
1705:2.5
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