Kinematics Measurement and Power Requirements of Fruitflies At

energies

Article Kinematics Measurement and Power Requirements of Fruitﬂies at Various Flight Speeds

Hao Jie Zhu * and Mao Sun Ministry-of-Education Key Laboratory of Fluid Mechanics, Beihang University, Beijing 100191, China; [email protected] * Correspondence: [email protected]

Received: 22 June 2020; Accepted: 11 August 2020; Published: 18 August 2020

Abstract: Energy expenditure is a critical characteristic in evaluating the flight performance of flying insects. To investigate how the energy cost of small-sized insects varies with flight speed, we measured the detailed wing and body kinematics in the full speed range of fruitflies and computed the aerodynamic forces and power requirements of the flies. As flight speed increases, the body angle decreases and the stroke plane angle increases; the wingbeat frequency only changes slightly; the geometrical angle of attack in the middle upstroke increases; the stroke amplitude first decreases and then increases. The mechanical power of the fruitflies at all flight speeds is dominated by aerodynamic power (inertial power is very small), and the magnitude of aerodynamic power in upstroke increases significantly at high flight speeds due to the increase of the drag and the flapping velocity of the wing. The specific power (power required for flight divided by insect weigh) changes little when the advance ratio is below about 0.45 and afterwards increases sharply. That is, the specific power varies with flight speed according to a J-shaped curve, unlike those of aircrafts, birds and large-sized insects which vary with flight speed according to a U-shaped curve.

Keywords: forward ﬂight; kinematics; power requirement; fruitﬂy; insect

1. Introduction Hovering and level-forward flight are the most common flight modes of insects. To accomplish various flight tasks in different scenarios, insects adjust the generation mechanisms of aerodynamic forces by sophisticatedly controlling the flapping motion of their wings [1]. Since flight is an energetically demanding mode of locomotion [2], there is an optimization pressure for insects to select the appropriate flight speed to economize energy consumption according to specific tasks. Previous studies have shown that the power-speed curve of flying vertebrates such as birds and bats [3,4], similar to that of helicopters, is U-shaped, which means the migration distance can be reached at its maximum when flying at some intermediate speed. However, whether the U-shaped model is suitable for insects remains unclear, because the wings of insects operate at relatively low Reynolds number and the flows around are strongly unsteady during flight, which is quite different from that of vertebrates and helicopters. To remain airborne, the mechanical power output of insects’ flight muscles must match the requirement for flapping the wings [5]. In order to investigate the variation of mechanical power with flight speed increasing, several experimental measurements have been conducted during insects’ freely forward flight. Ellington et al. [6] measured the oxygen consumption rates of bumblebees flying in a wind tunnel at the speeds up to 4 m/s; it was shown that the metabolic rate only changed slightly with flight speed, suggesting that the U-shaped model may be inadequate for bumblebees. Warfvinge et al. [7] reconstructed the wake of hawkmoth flying in a wind tunnel over a speed range of 1–3.8 m/s by using the tomographic particle image velocimetry technique, and calculated the

Energies 2020, 13, 4271; doi:10.3390/en13164271 www.mdpi.com/journal/energies Energies 2020, 13, 4271 2 of 23 mechanical power as the rate of energy added into the wake by the flapping wings; the result suggested that the power curve of hawkmoths is U-shaped. Benefit from the measurement and calculation methods used in the above two studies, total mechanical power can be obtained without measuring the wing kinematics of insects; but these methods also have some limitations, e.g., they are difficult to acquire the time courses of instantaneous power in a wingbeat cycle. One approach to improve this situation is that using the method of computational fluid dynamics (CFD) to study the power requirement of insect flight, which requires the wing and body kinematics were accurately measured at first. However, present experimental measurements were mostly focused on hovering or single-speed flight [8–19]; there only exist three studies that measured the wing and body kinematics of an individual insect in multiple-speed forward flight [20–22]. Dudley and Ellington [20] filmed and measured the forward flight of three bumblebees using a wind tunnel and each individual had 3–4 flight speeds; since only one high-speed camera was used, the pitching angle of flapping wings could just be estimated. Willmott and Ellington [21] further measured the complete kinematics of three hawkmoths using the same wind tunnel and two high-speed cameras and each individual had 5–6 flight speeds. In these two studies, the measured maximum flight speeds were 4.5 and 5 m/s for bumblebees and hawkmoths, respectively, which may not reach the limit of flight capability of these two insects. Recently, Meng and Sun [22] measured the wing and body kinematics in the full flight speed range of three droneflies, each had 6 flight speeds, from hovering to 8.6 m/s with the usage of three orthogonally aligned high-speed cameras and a customized low-speed wind tunnel. Based on the measured kinematic data of bumblebees from Dudley and Ellington [20], Wu and Sun [23] studied the trend of mechanical power with flight speed. The results demonstrated that the power required at medium speeds only decreased slightly from that at hovering and became relatively large at the measured highest speed, i.e., the power curve was approximately J-shaped. However, due to the absence of the kinematics at the potential maximum flight speed, the conceivably last rapid-growth phase of the curve was lacking. The above brief review shows that presently there are only three species of insects (bumblebee, hawkmoth and dronefly) whose kinematic data at multiple flight speeds were measured [20–22], and previous energetic researches were all based on the data that were measured over a partial speed range [6,7,23]. And it has been shown that, for the medium-sized bumblebee whose wing length is about 13 mm, the power-speed curve is probably J-shaped [23]; for the large-sized hawkmoth whose wing length is about 50 mm, the curve is more likely U-shaped [7]. But for other insects, especially for small-sized insects (e.g., fruitfly), no research based on measured kinematics has been conducted to explore how their power cost changes with flight speed. Therefore, the shape of the power-speed curve of insects is still not yet fully understood. In the present paper, first, the wing and body kinematics of fruitflies in forward flight were quantitatively measured using three-dimensional high-speed cinematography technique. The experiments were carried out in a wind tunnel and hence the measured speeds could be distributed in the full range of possible speeds. Then, the aerodynamic forces and torques exerted on the wings were computed by numerically solving the Navier-Stokes equations, and the inertial torques were computed analytically. On the basis of the aerodynamic and inertial torques, the mechanical power required for each flight was calculated. Therefore, what the shape of the power-speed curve is for this small-sized insect, whose wing length is about 3 mm, can be known. Selecting fruitfly is not only due to that it is a valuable model insect which has excellent ability to hover or fly forward stably and has been extensively used in flight mechanics and other biological fields, also due to that its wing kinematics in forward flight are still quite lacking. Although the body motions in freely forward flight have been tracked when studying the flight behaviors of fruitflies under visual control [24–26], there is still no measured wing kinematics of fruitfly flying at high speed; the measured largest flight speed for fruitfly (fruitfly F1 in Meng and Sun [14]) with detailed wing motion obtained was about 1.0 m/s, which is only a medium flight speed for fruitfly. Energies 2020, 13, 4271 3 of 23

2. Materials and Methods

2.1. Insects and Experimental Setup Experiments were performed on 3–5 days old fruitflies (Drosophila virilis), which were obtained from the Laboratory of Genetics of the School of Life Science of Peking University. These flies were descendants of wild-caught females and were reared under a 12 h light: 12 h dark cycle. Each fly was starved at least 5 h before being used in experiments, and the laboratory temperature was controlled at about 25 ◦C. Measurement of freely forward flight of insects is much difficult than hovering, especially for large-speed situation. In measuring hovering flight of fruitflies, an enclosed cubic chamber was always used [13,27]. While in measuring forward flight, larger chamber size is needed but also restricted by, on one hand, the operating space of experimental platform, and on the other hand, the measurement accuracy. If chamber size is not large enough, the flight of insect in it would be full of acceleration and deceleration, and the flight speed was also greatly restricted. However, increasing the length of flight chamber, which is necessary to provide sufficient space for the insect to fly forward stably, would in turn pose difficulties for setting up an experimental platform and reduce the success rate of filming. In the study of Meng and Sun [14], a large-aspect-ratio chamber and light brightness control was used to induce fruitflies to fly forward. Even so, the average flight speed of the six fruitflies they measured was only about 0.7 m/s, far less than the flight speed limit (about 2.0 m/s) of fruitflies [28]. Another problem for this method of measuring insects’ autonomous flight in still air is that if the flight speed is relatively large, the length of the measured arena in the flying direction is much longer than those in the other two directions, resulting in many problems for high-speed camera filming, such as the reduction of imaging quality and insufficiency of depth-of-field. Thus, it was concluded that a wind tunnel must be used in measuring high-speed forward flight of insects. In this paper, to acquire the forward flights of fruitflies, experiments were conducted with a low-speed open-jet wind tunnel, which is customized for insect flight tests. This wind tunnel has a 15 cm diameter circular opening and a 0.5–10 m/s speed range. The turbulence intensity is below 1.5% and air velocities uniformity is below 2% in the test section where flights were filmed. As shown in Figure1, the working section of the wind tunnel was enclosed by a 20 20 60 cm3 plexiglass × × flight chamber whose upstream and downstream ends were open. And a square piece of weave fabric net was used to block the downstream end to keep the insect within the flight chamber. To film the forward flight of fruitflies, three orthogonally aligned synchronized high-speed cameras (FASTCAM Mini UX100, Photron Inc., San Diego, CA, USA; 6250 frames per second, shutter speed 20 µs, resolution 1280 800 pixels) were used. The view of each camera was backlit by a 50 W integrated red-light × emitting diode (LED; PT-121-R-C11-MPD, Luminus Devices Inc., Sunnyvale, CA, USA; luminous flux, 4000 lm; wavelength, 632 nm), and two lenses (a CCTV lens with 25 mm focal length and a convex lens with 50 mm focal length) were used to make the light uniform. When tested insect was observed flying steadily in the filming area (intersecting field of views of the three cameras, approximately 3.5 3.5 3.5 cm3), the synchronized cameras were manually triggered. The filming area was set at × × the position that 11 cm from the opening and on the central line of the wind tunnel. Taking advantage of phototaxis of insects, Dudley and Ellington [20] and Meng and Sun [22] both used an ultraviolet fluorescent light to elicit bumblebees and droneflies to fly in a wind tunnel and successfully measured the forward flight kinematics. Thus, in the present paper, we also employed this approach to induce fruitflies by position a 40 W ultraviolet fluorescent light on the roof of the chamber and near the opening of the wind tunnel (Figure1). Most of the light tube was masked out, leaving only a small part, about 3 cm in length, to be visible. Through observation, we found that fruitfly indeed flied in the wind tunnel toward the location of ultraviolet light, but the flight was always unstable and not keeping on the center line of the flight chamber, such that other means were needed to stabilize the flight. Energies 2020, 13, x FOR PEER REVIEW 4 of 23 Energies 2020, 13, 4271 4 of 23 Energies 2020, 13, x FOR PEER REVIEW 4 of 23

Figure 1. Sketch of filming system. FigureFigure 1.1. SketchSketch of filming filming system. system. Alternatively, moving background of sine grating or random dot patterns were usually applied in the Alternatively,investigationAlternatively, of moving movingvision-based background background control of in sine sine banked grating grating maneuvering or or random random dot [29] dot patterns and patterns forward were were usually flight usually [26].applied appliedIn thisin inpaper, the investigation we applied of ofthis vision-based vision-based visual speed co controlntrol control in in banked bankedmethod maneuvering, maneuvering using moving [29] [29 sineand] and gratingsforward forward flightto flight provide [26]. [26 In]. optical Inthis this paper,flowpaper, corresponding we we applied applied this thisto visual the visual preferred speed speed control speedcontrol method, of method fruitflies, using, using to moving controlmoving sine their sine gratings upwindgratings to speed provideto provide and optical opticalstabilize flow correspondingthemflow on corresponding the center to the linepreferred to ofthe the preferred wind speed tunnel. ofspeed fruitflies, An of opfrui toen-sourcetflies, control to control theirpsychophysics upwind their upwind speed toolbox andspeed (Psychtoolbox stabilize and stabilize them 3.0) on theonthem centerMatlab on line the platform ofcenter the wind line(Matlab of tunnel. the v. wind 9.0, An Thetunnel. open-source Mathworks, An open-source psychophysics Inc., Natick, psychophysics toolbox MA, USA) (Psychtoolbox toolbox was (Psychtoolboxused 3.0)to accurately on Matlab 3.0) platformgenerateon Matlab (Matlaband platform control v. 9.0, (Matlab the The visual Mathworks,v. 9.0, stimuli. The Mathworks, Inc.,Then Natick, via Inc.,two MA, Natick,digital USA) MA,light was USA) processing used was to accuratelyused (DLP) to accurately projectors generate and(ViewSonicgenerate control and thePJD7831HDL, visualcontrol stimuli.the ViewSonic visual Then stimuli. Ch viaina, twoThen Shanghai, digital via twolight China), digital processing the light rendered processing (DLP) sine projectors grating (DLP) stripesprojectors (ViewSonic were PJD7831HDL,displayed(ViewSonic onto PJD7831HDL, ViewSonic the sidewalls China, ViewSonic of the Shanghai, flight China, chamber China), Shanghai, (Figure the China), rendered 1). The the sinevelorendered gratingcity of sine sine stripes grating grating were stripes stripes displayed were was ontosetdisplayed at the 0.2 sidewalls m/s, onto because the of sidewalls the under flight thisof chamberthe visual flight surround, (Figurechamber1 the).(Figure The flight velocity1). speed The velo relative of sinecity of gratingto sine the gratingground stripes stripesof was fruitfly setwas atis 0.2veryset m / ats,small 0.2 because m/s, [25]. because under Finally, thisunder with visual this ultraviolet visual surround, surround, light the flightstimulating the flight speed speed relativeto flyrelative upwind to the to groundthe and ground moving of fruitflyof fruitfly patterns is veryis smallcontrollingvery [25 small]. Finally, the [25]. speed withFinally, and ultraviolet stabilizingwith ultraviolet light the stimulating flight, light the stimulating me to flyasurement upwind to flyof and forwardupwind moving flightand patterns movingof fruitflies controlling patterns can be the controlling the speed and stabilizing the flight, the measurement of forward flight of fruitflies can be speedachieved. and stabilizing the flight, the measurement of forward flight of fruitflies can be achieved. achieved. 2.2.2.2. Filming Filming ProceduresProcedures 2.2. Filming Procedures AtAt the the beginning beginning ofof eacheach experiment,experiment, thethe high-speedhigh-speed cameras were switched switched on on and and kept kept in in the the At the beginning of each experiment, the high-speed cameras were switched on and kept in the recordingrecording mode. mode. Then Then the the wind wind tunnel tunnel was was turned turned on and on waitingand waiting for about for about half a minutehalf a minute to stabilize to recording mode. Then the wind tunnel was turned on and waiting for about half a minute to thestabilize wind beforethe wind a fruitfly before was a fruitfly introduced was introduced into the flight into chamber the flight at chamber the downstream at the downstream end (Figure end2). stabilize the wind before a fruitfly was introduced into the flight chamber at the downstream end (Figure 2). (Figure 2).

FigureFigureFigure 2.2. 2. DiagramDiagram Diagram of of the the fullfull forward-flightforward-flightforward-flight procproc processessess ofof fruitfliesfruitflies fruitflies in in in the the the flight flight flight chamber. chamber. chamber.

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Energies 2020, 13, x FOR PEER REVIEW 5 of 23 The ultraviolet light was flickered on and off until the fruitfly began to take off from the rear of theThe flight ultraviolet chamber, light and was then flickered the light on and was off left until on the to avoidfruitfly disturbing began to take the off flight. from Meanwhile,the rear of thethe moving flight chamber, grating stripes and then were the projected light was onto left the on sideto avoid walls disturbing of the flight the chamber. flight. Meanwhile, Since enticed the by themoving ultraviolet grating light stripes and were oriented projected by the onto moving the side gratings, walls of the the tested flight fruitfly chamber. flew Since forward enticed steadily by the at ultraviolet light and oriented by the moving gratings, the tested fruitfly flew forward steadily at a a low ground-speed in the working section (Figure2). low ground-speed in the working section (Figure 2). The closer to the ultraviolet light the insect is, the lower the flight speed. When the insect reached The closer to the ultraviolet light the insect is, the lower the flight speed. When the insect the filming area that beneath the ultraviolet light, it stayed for several seconds (Figure2); this is the reached the filming area that beneath the ultraviolet light, it stayed for several seconds (Figure 2); best time to trigger the cameras so that steady forward flight can be filmed. As the flight was coming this is the best time to trigger the cameras so that steady forward flight can be filmed. As the flight to an end, the insect adjusted its flying attitude and flew upward towards the location of the ultraviolet was coming to an end, the insect adjusted its flying attitude and flew upward towards the location of light to land (Figure2). Immediately after the filming process had finished (approximately 0.89 s), the ultraviolet light to land (Figure 2). Immediately after the filming process had finished the ultraviolet light was turned off and the moving grating stripes were stopped. After ensuring the (approximately 0.89 s), the ultraviolet light was turned off and the moving grating stripes were insect was returned to the rear of the flight chamber to rest, the filmed images were downloaded from stopped. After ensuring the insect was returned to the rear of the flight chamber to rest, the filmed theimages high-speed were downloaded cameras to computer.from the high-speed cameras to computer. TheThe key key point point to to the the achievement achievement of of the the filming filming was was the the existence existence of the of stayingthe staying stage. stage. Based Based upon thisupon behavioral this behavioral observation, observation, the filming the filming area of area high-speed of high-speed cameras cameras could becould preset be preset at the stayingat the locationstaying accordinglylocation accordingly (Figure2 ),(Figure which 2), can which greatly can improvegreatly improve the success the success rate of filming.rate of filming. The fruitfly The wasfruitfly almost was stationary almost stationary relative torelative the flight to the chamber flight whenchamber it was when staying, it was thus staying, the flightthus the speed flight was approximatelyspeed was approximately equal to the equal wind to speed. the wind speed. AtAt least least three three flight flight speeds speeds distributed distributed in in the the full full speed speed range range were were filmed filmed for for each each fruitfly, fruitfly, and and the experimentsthe experiments were were begun begun with with the measurementthe measurement of theof the flight flight at theat the maximum maximum speed. speed. According According to Vogelto Vogel [28], [28], the maximum the maximum flight flight speed speed of fruitflies of fruitflies is about is about 2.0 m /2.0s,such m/s, thatsuch the that wind the speedwind speed was first was set aroundfirst set this around value this to check value whether to check the whether tested fruitflies the tested could fruitflies take o ffcouldand flytake forward off and steadily fly forward or not; ifsteadily not, the or wind not; speed if not, was the continuouslywind speed was lowered continuously until it can. lowered Thus, until the filmedit can. flightThus, couldthe filmed be regarded flight ascould at the be maximum regarded speedas at the of maximum the tested fruitfly.speed of Next, the te thested wind fruitfly. speed Next, was the set wind to an speed intermediate was set to speed an (e.g.,intermediate about 1.0 speed m/s) and (e.g., the about entire 1.0 filming m/s) processand the wasentire repeated. filming Last,process the was near-hovering repeated. Last, flight the was filmednear-hovering with the visualflight was control filmed system with and the windvisual tunnel control turned system o ffand. The wind total tunnel experimental turned off. time The for total each fruitflyexperimental was generally time for less each than fruitfly 40 min. was generally less than 40 min.

2.3.2.3. Measurement Measurement of of Morphological Morphological andand KinematicKinematic Data TheThe method method of of measuringmeasuring morphologicalmorphological parameters parameters was was same same as as that that given given in in Mou Mou et etal. al. [30]. [30 ]. OnceOnce the the filming filming events events hadhad finished,finished, the tested fr fruitflyuitfly was was anaesthetized anaesthetized with with ethyl ethyl acetate acetate vapor. vapor. TheThe total total massmass ((mm)) ofof the insect insect was was measured measured to to an an accuracy accuracy of ±0.01 of 0.01 mg. mg.The wing The wingplanform planform and ± andthe thebody body in indorsoventral dorsoventral and and lateral lateral views views were were scanned scanned using using a ascanner scanner (Epson (Epson Scanner Scanner V370; V370; EpsonEpson (China) (China) Co.,Co., Ltd.,Ltd., Beijing,Beijing, China; resolution resolution 3600 3600 × 36003600 dpi) dpi) and and hence hence the the wing wing and and body body × shapesshapes can can be be extracted, extracted, as asshown shown inin FigureFigure3 3..

FigureFigure3. 3. MorphologicalMorphological parameters of the wing wing and and body body of of an an insect. insect.

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Then, the morphological parameters of the insect can be measured or computed based on the Then, the morphological parameters of the insect can be measured or computed based on the measured data, including wing length (R, the distance between wing base and wing tip), area of one measured data, including wing length (R, the distance between wing base and wing tip), area of one wing (S), mean wing chord (c), radius of the second moment of wing area (r2), body length (lb), wing (S), mean wing chord (c), radius of the second moment of wing area (r2), body length (lb), distance distance between the wing roots (lr), distance between the wing-root axis and the center of mass (l1, between the wing roots (lr), distance between the wing-root axis and the center of mass (l , the center the center of mass is determined by assuming the body of the insect is a body of revolution1 with of mass is determined by assuming the body of the insect is a body of revolution with uniform density), uniform density), distance between the wing-root axis and the body axis (h1), distance from the distance between the wing-root axis and the body axis (h1), distance from the anterior end of the body anterior end of the body to the center of mass (l2). to the center of mass (l ). After all the required2 morphological parameters were obtained, the wing was modeled as a After all the required morphological parameters were obtained, the wing was modeled as flat-plate with the outline extracted from the scanned cut-off wing (Figure 3), and the body was a ﬂat-plate with the outline extracted from the scanned cut-oﬀ wing (Figure3), and the body was modeled as a rigid-body represented by two perpendicular lines (the line linking the head and the modeled as a rigid-body represented by two perpendicular lines (the line linking the head and the end of the abdomen and the line linking the two wing hinges, see Figure 4). Then the wing and body end of the abdomen and the line linking the two wing hinges, see Figure4). Then the wing and models were used in a self-developed MatLab toolbox, which is a realization of the method of body models were used in a self-developed MatLab toolbox, which is a realization of the method three-dimensional reconstruction (see Mou et al. [30] for detailed description and error analysis), to of three-dimensional reconstruction (see Mou et al. [30] for detailed description and error analysis), measure the wing and body kinematics. Within the interactive graphic user interface of this toolbox, to measure the wing and body kinematics. Within the interactive graphic user interface of this toolbox, the positions and orientations of the models of the body and two wings were adjusted manually the positions and orientations of the models of the body and two wings were adjusted manually until until the best overlap between their projections and the displayed frames recorded by three cameras the best overlap between their projections and the displayed frames recorded by three cameras was was achieved (Figure 4); at this point, the positions and orientations of these models could be achieved (Figure4); at this point, the positions and orientations of these models could be regarded as regarded as that of their real counterparts. that of their real counterparts.

FigureFigure 4. 4. ExampleExample of of three-dime three-dimensionalnsional reconstruction. reconstruction. For a fruitfly flying at a given speed, about 35 pictures were taken during each wingbeat. For a fruitfly flying at a given speed, about 35 pictures were taken during each wingbeat. After After measuring frame by frame, the wing and body motions in about five wing strokes were digitized. measuring frame by frame, the wing and body motions in about five wing strokes were digitized. In In order to clearly describe the wing kinematics of the fruitflies, the method given by Ellington [8] order to clearly describe the wing kinematics of the fruitflies, the method given by Ellington [8] was was employed, and two coordinate systems and following definitions were introduced. In a reference employed, and two coordinate systems and following definitions were introduced. In a reference frame that moved with the body of the fly, the discrete wing-tip trace of both of the left and right wings frame that moved with the body of the fly, the discrete wing-tip trace of both of the left and right were projected onto the symmetric plane of the body, and a linear regression line of the projections wings were projected onto the symmetric plane of the body, and a linear regression line of the could be determined using least square method. The plane paralleled to the above regression line and projections could be determined using least square method. The plane paralleled to the above passed the wing base is defined as the stroke plane. Thereafter, two coordinate systems, oxyz and regression line and passed the wing base is defined as the stroke plane. Thereafter, two coordinate o1x1y1z1, are brought in. For the lab-fixed coordinate system oxyz, the origin locates at the center of the systems, oxyz and o1x1y1z1, are brought in. For the lab-fixed coordinate system oxyz, the origin locates body initially, x-axis points forward horizontally, y-axis points to the right of the body horizontally and at the center of the body initially, x-axis points forward horizontally, y-axis points to the right of the z-axis points downward vertically (Figure5). For the body-fixed coordinate system o x y z , the origin body horizontally and z-axis points downward vertically (Figure 5). For the body-fixed1 1 1 1coordinate locates at the wing base, the x1-y1 plane coincides with the stroke plane and y1-axis coincides with system o1x1y1z1, the origin locates at the wing base, the x1-y1 plane coincides with the stroke plane and y-axis, and z1-axis is normal to the stroke plane (Figure5). The inclination angle of the stroke plane y1-axis coincides with y-axis, and z1-axis is normal to the stroke plane (Figure 5). The inclination about the horizontal is referred to as the stroke plane angle (β), and the angle between the body axis angle of the stroke plane about the horizontal is referred to as the stroke plane angle (β), and the and the horizontal is referred to as the body angle (χ), thus β + χ represents the included angle of the angle between the body axis and the horizontal is referred to as the body angle (χ), thus β + χ body axis and the stroke plane (Figure5a). represents the included angle of the body axis and the stroke plane (Figure 5a). The orientation of a flat-plate wing relative to the stroke plane can be determined by three Euler angles: the stroke angle (φ), the deviation angle (θ) and the pitch angle (ψ). As shown in Figure5b, φ is defined as the angle between the projection of the wing axis (the line passing wing base and wing tip) onto the stroke plane and y1-axis; θ is defined as the angle between the wing axis and its projection onto the stroke plane; ψ is defined as the angle between the local wing chord and l (a line which is perpendicular to the wing axis and parallel to the stroke plane).

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Then, the morphological parameters of the insect can be measured or computed based on the measured data, including wing length (R, the distance between wing base and wing tip), area of one wing (S), mean wing chord (c), radius of the second moment of wing area (r2), body length (lb), distance between the wing roots (lr), distance between the wing-root axis and the center of mass (l1, the center of mass is determined by assuming the body of the insect is a body of revolution with uniform density), distance between the wing-root axis and the body axis (h1), distance from the anterior end of the body to the center of mass (l2). After all the required morphological parameters were obtained, the wing was modeled as a flat-plate with the outline extracted from the scanned cut-off wing (Figure 3), and the body was modeled as a rigid-body represented by two perpendicular lines (the line linking the head and the end of the abdomen and the line linking the two wing hinges, see Figure 4). Then the wing and body models were used in a self-developed MatLab toolbox, which is a realization of the method of three-dimensional reconstruction (see Mou et al. [30] for detailed description and error analysis), to measure the wing and body kinematics. Within the interactive graphic user interface of this toolbox, the positions and orientations of the models of the body and two wings were adjusted manually until the best overlap between their projections and the displayed frames recorded by three cameras was achieved (Figure 4); at this point, the positions and orientations of these models could be regarded as that of their real counterparts.

Figure 4. Example of three-dimensional reconstruction.

For a fruitfly flying at a given speed, about 35 pictures were taken during each wingbeat. After measuring frame by frame, the wing and body motions in about five wing strokes were digitized. In order to clearly describe the wing kinematics of the fruitflies, the method given by Ellington [8] was employed, and two coordinate systems and following definitions were introduced. In a reference frame that moved with the body of the fly, the discrete wing-tip trace of both of the left and right wings were projected onto the symmetric plane of the body, and a linear regression line of the projections could be determined using least square method. The plane paralleled to the above regression line and passed the wing base is defined as the stroke plane. Thereafter, two coordinate systems, oxyz and o1x1y1z1, are brought in. For the lab-fixed coordinate system oxyz, the origin locates at the center of the body initially, x-axis points forward horizontally, y-axis points to the right of the body horizontally and z-axis points downward vertically (Figure 5). For the body-fixed coordinate system o1x1y1z1, the origin locates at the wing base, the x1-y1 plane coincides with the stroke plane and y1-axis coincides with y-axis, and z1-axis is normal to the stroke plane (Figure 5). The inclination angle of the stroke plane about the horizontal is referred to as the stroke plane angle (β), and the angle between the body axis and the horizontal is referred to as the body angle (χ), thus β + χ Energies 2020, 13, 4271 7 of 23 represents the included angle of the body axis and the stroke plane (Figure 5a).

Figure 5. Coordinate systems and Euler angles of a flapping wing. (a) The lab-fixed coordinate system; (b) The body-fixed coordinate system and Euler angles.

Some other kinematic parameters of the flapping wing are as follows: f, the wingbeat frequency; Φ, the stroke amplitude, defined as Φ = φmax φ (φmax and φ are the maximum and minimum − min min values of φ, respectively); φ, the mean stroke angle, defined as φ= (φmax + φmin)/2; d/u, the ratio of downstroke duration to upstroke duration (when φ changes from φmax to φmin, the wing is referred to be in downstroke; in reverse, in upstroke). For forward flight, the advance ratio is defined as the ratio of the flight speed to the mean flapping velocity at wing tip, i.e., J = V /2ΦfR, where V is the ∞ ∞ flight speed.

2.4. Evaluation of the Aerodynamic Forces and Mechanical Power The unsteady flow around the flapping wings was computed by numerically solving the incompressible Navier-Stokes equations. Previous studies have shown that for fruitfly, the aerodynamic interaction effect between the wings and the body was very small: the changes of aerodynamic forces acting on the wings with or without the presence of the body was less than 2% at hovering [31,32] and 4.5% at forward flight (J was up to 0.67 with idealized wing motions) [33]. Therefore, only two wings were considered in the present CFD model, and the wing was modeled as a flat-plate with rounded leading and trailing edges. The thickness of the wing model is set at 3% of the wing chord length. Selecting c, U (the mean flapping velocity at r2 for near hovering flight, defined as U = 2Φ0f 0r2, where the subscript ‘0’ denotes the near hovering flight) and c/U as reference length, velocity and time, respectively, the dimensionless Navier-Stokes equations are as follows:

u = 0 (1) ∇ · ∂u 1 + u u = p + 2u (2) ∂t∗ · ∇ −∇ Re ∇ where u is the non-dimensional fluid velocity field, t* is the non-dimensional time, p is the non-dimensional fluid pressure, Re is the Reynolds number, is the gradient operator and 2 ∇ ∇ is the Laplacian operator. The flow solver is the same as that in some previous studies of our group [14,16], which is based on the method of artificial compressibility developed by Rogers et al. [34,35]. In solving the equations, the method of moving overset grids is used. As shown in Figure6, there is a body-fitted curvilinear grid for each wing which extends a relatively short distance (2.5c in the normal direction), and a background Cartesian grid which extends to the far field boundary of the domain (20c in all of the x, y, z directions at near-hovering, and extends to 30c along the downstream (negative x) direction at the maximum-speed flight). The wing grids capture such as boundary layers, separated vortices and vortex/wing interactions, and the background grid carries the solution to the far field. The two grids exchange flow information through their overlapped regions. The wing grid is O-H type and generated using a Poisson solver which is based on the algorithm of Hilgenstock [36]. The background Cartesian grid is generated algebraically. Energies 2020, 13, 4271 8 of 23 EnergiesEnergies 20202020,, 1313,, xx FORFOR PEERPEER REVIEWREVIEW 88 ofof 2323

FigureFigure 6. 6. PortionsPortions ofof computationalcomputational grids.grids.

OnceOnce the the Navier-Stokes Navier-Stokes equationsequations werewere solved,solved, thethe aerodynamic aerodynamic forcesforces andand moments moments acting acting on on thethe wingwing wing werewere were calculatedcalculated calculated byby by integratingintegrating integrating thethe the pressurepressure pressure andand and thethe the viscousviscous viscous stressstress stress overover over thethe wing thewing wing surfacesurface surface atat aa timeattime a time step.step. step. VerticalVertical Vertical forceforce force ((VV)) (andandV) and thrustthrust thrust ((TT)) (ofTof) ofaa wingwing a wing areare are defineddefined defined asas as thethe the componentscomponents components ofof of thethe total totaltotal aerodynamicaerodynamic forceforce alongalong thethe negative negative zz andand positive positive xx direction,direction, respectively; respectively; liftlift (( LL)) isis defined defineddefined as as the the componentcomponent perpendicularperpendicular toto to thethe the strokestroke stroke planeplane plane andand alongalong thethe zz11 direction;direction; dragdrag drag (( (DDD))) isis defined defineddefined as as the the . componentcomponent inin in thethe strokestroke planeplane andand and alongalong along thethe the directiondirection direction thatthat that oppositeopposite opposite toto to thethe the flappingflapping flapping movementmovement movement ((φ (φφ).).). 2 TheThe corresponding corresponding forceforce force coefficients,coefficients, coefficients, denoteddenoted denoted byby by CCCVV,V, CC, TCT,, TCC,LLC andandL and CCDDC areareD are defineddefined defined as:as: as:CCVV = =C V/0.5V/0.5V = Vρρ/U0.5U22SSρ,, U etc.,etc.,S , whereetc.,where where ρρ isis ρthetheis fluid thefluid fluid density.density. density. TheThe The relationshiprelationship relationship betweebetwee betweennn thesethese these forcesforces forces isis isshownshown shown inin in FigureFigure Figure 77 andand theirtheir transformationtransformation formulasformulas formulas areare are asas as follows:follows: follows: CCCC=⋅=⋅coscosββββ +⋅ +⋅ C C sin sin C =LVLVC cos β + C T Tsin β (3)(3) L V · T · C CCCC= =⋅(=⋅C()()sinsinsinβββφββφ −⋅ −⋅C C Ccos cos cosβ) ⋅ ⋅cos cosφ (4) D DVDVV · − T T T· · (4)(4)

FigureFigure 7.7. RelationshipRelationshipRelationship betweenbetween aerodynamicaerodynamic forceforce coefficients. coecoefficients.ﬃcients.

TheThe aerodynamic aerodynamic andand inertial inertial momentsmoments aroundaround thethe wing-root wing-root areare denoted denoted as as MMaa andand MMi,i, , respectively.respectively. TheThe The mechanicalmechanical mechanical powerpower power ((PP (P)) )ofof of aa a flappingflapping flapping wingwing wing isis is producedproduced byby by thethe flight flightflight muscles muscles to to overcomeovercome MMaaa andandand MMMi,i, i and,and and itit it cancan can bebe be calculatedcalculated calculated by:by: by: =+⋅=+⋅()() P P=P (MMMMMa ai+aiM ) ΩΩΩ i · ==⋅=⋅MMMa ΩΩΩ+++MMMi ⋅ ⋅ΩΩΩ (5)(5) ai·ai· ==+=+Pa + Pi PPPPaiai wherewhere ΩΩΩ isis thethe angularangular velocityvelocityvelocity vectorvectorvector of ofof the thethe wing, wing,wing,P PPaaa = == M MMaaa∙∙ΩΩΩ andand PPi i == MMi∙i∙ΩΩΩ areareare thethe the aerodynamicaerodynamic aerodynamic andand · i i· inertialinertial powerpower power ofof of thethe the wing,wing, wing, respectively.respectively. respectively. AsAs MMMaaa has hashas already alreadyalready been beenbeen computed computedcomputed using usingusing the force thethe distribution forcforcee distributiondistribution obtained fromobtainedobtained the flow fromfrom computation thethe flowflow computationandcomputationΩ is also knownandand ΩΩ is fromis alsoalso the knownknown measured fromfrom kinematics, thethe measuredmeasured the aerodynamic kinematics,kinematics, thethe power aerodynamicaerodynamicPa can be readily powerpower calculated. PPaa cancan bebe readilyHowever,readily calculated.calculated. the inertial However,However, power P thethei still inertialinertial cannot powerpower be straightforwardly PPi i stillstill cannotcannot bebe calculated, straightforwardlystraightforwardly because calculated,calculated, the mass ( m becausebecausew) and thethe massmass ((mmww)) andand thethe radiusradius ofof gyrationgyration ((rr2,m2,m)) ofof thethe wingwing requiredrequired toto determinedetermine MMi i areare unknownunknown forfor thethe testedtested fruitflies.fruitflies. ToTo dealdeal withwith thisthis problem,problem, thethe wing-to-bodywing-to-body massmass ratioratio ((mmww//mm == 0.24%)0.24%) andand thethe

Energies 2020, 13, 4271 9 of 23

the radius of gyration (r2,m) of the wing required to determine Mi are unknown for the tested fruitflies. To deal with this problem, the wing-to-body mass ratio (mw/m = 0.24%) and the non-dimensional radius of gyration (r2,m/R = 0.48) that had been measured in Vogel[28] for the same species, Drosophila virilis, are used in the present paper. Because the venation is typically denser near the leading edge, the wing-mass mostly distributed near the axis of flip-rotation which is close to the leading edge; thus, it is reasonable to neglect the moment of inertia of the wing-mass about the axis of flip rotation. The moments of inertial about the other two axes (denoted as Iw) are approximately the same and can be computed 2 by Iw = emphmwr2,m . With Iw obtained and wing acceleration computed from Ω, Mi thus Pi can be calculated. The coefficients of the aerodynamic and inertial power of a flapping wing are defined as 3 3 CPa = Pa/0.5ρU S and CPi = Pi/0.5ρU S, respectively.

3. Results and Discussion

3.1. Measured Morphological Parameters and Wing and Body Motions In the filming experiments, the flight sequences of 24 fruitflies with at least three flight speeds were recorded. After carefully scrutinizing all the flight films of these fruitflies, we found that some fruitflies were unable to maintain steady flight under large wind-speed condition and hence their flights were accompanied with rolling or yawing motion; and some fruitflies were performing climbing flight towards the location of the ultraviolet light, not performing desired level-forward flight, when the wind speed was not very large. Therefore, for most of these fruitflies, at least one forward flight was inadequately steady or was not performing level-forward flight. Eventually, four individuals which had three steady flights were selected for further kinematic measurement. They are denoted as FF1, FF2, FF3 and FF4, respectively, and their morphological parameters are listed in Table1.

Table 1. Morphological parameters of the fruitﬂies.

Individual m (mg) c (mm) R (mm) r2/R lb (mm) lr/lb l1/lb h1/lb l2/lb FF1 1.75 0.93 3.31 0.59 3.31 0.24 0.17 0.12 0.47 FF2 1.22 0.89 3.05 0.59 3.33 0.28 0.15 0.10 0.45 FF3 1.79 1.04 3.35 0.58 3.60 0.25 0.18 0.14 0.47 FF4 2.07 0.98 3.30 0.58 3.68 0.27 0.21 0.15 0.47

It is noteworthy that the above steady and balanced flights are the controlled results of insects’ sensory-motor system. Previous studies [37–40] have shown that the hovering and forward flights of insects are inherently unstable, and as flight speed increases, the longitudinal instability of insect flight becomes stronger and stronger, but the inherently unstable flights of insects are controllable [37,41], counting on the fast response of sensory-motor system. That is the reason why we could capture steady forward flights of fruitflies in our experiments. The image sequences at several instants in a flapping cycle filmed by one high-speed camera for FF1 flying at three speeds are demonstrated in Figure8 (the corresponding video sequences are provided in the Supplementary Materials). It can be seen that the flying attitude changes with flight speed obviously: at V = 0.16 m/s (near hovering), the body tilted at a relatively large angle and the ∞ wing tip position when the wing flaps to its farthest behind the body is approximately at the same altitude with that ahead the body; while as the flight speed increases, the inclined angle of the body becomes smaller and the farthest position of the wing tip behind the body becomes much higher than that ahead the body. Energies 2020, 13, 4271 10 of 23 EnergiesEnergies 2020 2020, ,13 13, ,x x FOR FOR PEER PEER REVIEW REVIEW 1010 of of 23 23

FigureFigure 8. 8. TheThe The filmed filmedfilmed image image sequences sequences of of FF1 FF1 flyingflying flying at at three three flight flight flight speeds. speeds.

TheseThese observations observations are are consistent consistent with with the the measured measured data data of of the the body body angle angle ( χ(χ) )and and the the stroke stroke planeplane angle angle ( β(β) ) for for all all the the four four fruitfliesfruitflies fruitflies plotted plotted in in Figure Figure9 9. .9. FromFrom From thethe the scattersscatters scatters plotplot plot inin in FigureFigure Figure9 9a,a, 9a, it it it can can can bebe clearly clearly observed observed that that χ χ decreases decreases and and β β increases increases with with flightflight flight speed speed increasing increasing in in the the speed speed range range ofof thethe presentpresent studystudy ( V(V∞∞ ≈ ≈ 0–2 0–20–2 m/s), m/s), m/s), and and and the the reduction reduction rate rate of of χ χ and andand the thethe and andand growth growthgrowth rate raterate of ofof β β are are ∞ ≈ significantlysignificantlysignificantly decreased decreased when when the the flight flightflight speed speed exceed exceedsexceedss about about 1.3 1.3 m/s. mm/s./s. While WhileWhile as asas seen seenseen from fromfrom Figure FigureFigure 99b, b,9b, anotheranother obvious obviousobvious feature featurefeature is is thatis thatthat the the anglethe angleangle between betweenbetween the stroke thethe strokestroke plane andplaneplane body andand axis, bodybodyβ + axis,χaxis,, only ββ + fluctuates+ χχ, , onlyonly fluctuatesslightly,fluctuates indicating slightly,slightly, that indicatingindicating the position thatthat of thethe the positionposition stroke plane ofof thethe relative strokestroke to theplaneplane body relativerelative almost toto remains thethe bodybody unchanged almostalmost remainsinremains the full unchanged speedunchanged range in forin the fruitflies.the fullfull speedspeed These resultsrangerange areforfor similar fruifruitflies.tflies. to that TheseThese of bumblebees resultsresults areare [ 20 similarsimilar], hawkmoths toto thatthat [ 21 ofof] bumblebeesandbumblebees droneflies [20], [20], [22 hawkmoths ]hawkmoths in their own [21] [21] measured and and droneflies droneflies speed ranges.[22] [22] in in thei theirr own own measured measured speed speed ranges. ranges.

FigureFigure 9. 9. The The variations variations of of ( a(a) )β β and and χ χ and and ( b(b) )β β + + χχ χ ofof of FF1-FF4 FF1-FF4FF1-FF4 at atat various variousvarious flight ﬂightflight speeds. speeds.

TheThe variationvariation variation ofof of thethe the stroke stroke stroke plane plane plane angle angle angle as as functionsas functi functionsons of flightof of flight flight speed speed speed is highly is is highly highly correlated correlated correlated to the to to wing the the wingmovementswing movements movements at each at at flight each each speed. flight flight speed. Inspeed. order In In to order order examine to to examine examine the wing the the motions, wing wing motions, wemotions, take the we we flight take take ofthe the FF1 flight flight flying of of at V = 1.07 m/s as an example. The measured time histories of the three Euler angles, φ, θ and ψ, FF1FF1 flying∞ flying at at V V∞∞ = = 1.07 1.07 m/s m/s as as an an example. example. The The measured measured time time histories histories of of the the three three Euler Euler angles, angles, ϕ ϕ, ,θ θ andofand the ψψ, left , ofof and thethe right leftleft andand wings rightright during wingswings a period duringduringof aa about periodperiod 26 ofof ms aboutabout are plotted 2626 msms in areare Figure plottedplotted 10 a. ininTo FigureFigure eliminate 10a.10a. the ToTo eliminatehigh-ordereliminate the noisethe high-orderhigh-order and obtain noise thenoise smooth andand obtain dataobtain that thethe can smoothsmooth be used datadata for numerical thatthat cancan computation, bebe usedused forfor the numericalnumerical original computation,datacomputation, of φ, θ and the theψ areoriginal original first averaged data data of of ϕ betweenϕ, ,θ θ and and leftψ ψ are andare first rightfirst averaged averaged wings, and between between then are left left phase-averaged and and right right wings, wings, over and fiveand wingbeatthenthen are are phase-averaged phase-averaged cycles; finally, the over over phase-averaged five five wingbeat wingbeat cycles; data cycles; are finally, finally, filtered the the with phase-averaged phase-averaged a fifth-orderlow-pass data data are are filtered Butterworthfiltered with with afiltera fifth-order fifth-order (the cut-o low-pass low-passff frequency Butterworth Butterworth are 400, filter 800filter and (the (the 1600 cut-off cut-off Hz forfrequency frequencyφ, θ and are areψ ,400, respectively).400, 800 800 and and 1600 1600 For Hz convenienceHz for for ϕ ϕ, ,θ θ and and of ψdescription,ψ, ,respectively). respectively). we defineFor For convenience convenience a non-dimensional of of descri description, time,ption, weτ we, in define define a wingbeat a a non-dimensional non-dimensional cycle that τ = time, time,0 is theτ τ, ,in in start a a wingbeat wingbeat time of cycleacycle downstroke that that τ τ = = 0 and0 is is the theτ = start start1 is thetime time end of of timea a downstroke downstroke of the subsequent and and τ τ = = 1 upstroke.1 is is the the end end The time time filtered of of the the Euler subsequent subsequent angles withupstroke. upstroke. error bands (mean s.d.) as functions of τ are given in Figure 10b. TheThe filtered filtered Euler Euler± angles angles with with error error bands bands (mean (mean ± ± s.d.) s.d.) as as functions functions of of τ τ are are given given in in Figure Figure 10b. 10b.

Energies 2020, 13, x FOR PEER REVIEW 11 of 23 Energies 2020, 13, 4271 11 of 23 Energies 2020, 13, x FOR PEER REVIEW 11 of 23

Figure 10. The measured wing kinematics of FF1 in forward flight at V∞ = 1.07 m/s. (a) The original data of instantaneous Euler angles. ϕ, the stroke angle; θ, the deviation angle; ψ, the pitch angle. (b) FigureThe filtered 10.10. The values measuredmeasured of ϕ wing,wing θ and kinematicskinematics ψ as function ofof FF1FF1 in inof forward forwardnon-dimensio flight flight at nalatV V period∞ = 1.07 (meanm/s. m/s. ( a )± Thes.d.; originaloriginal n = 5 ∞ datawingbeats). ofof instantaneousinstantaneous Euler Euler angles. angles.φ ϕ, the, the stroke stroke angle; angle;θ, theθ, the deviation deviation angle; angle;ψ, the ψ, pitchthe pitch angle. angle. (b) The (b) filteredThe filtered values values of φ, θ ofand ϕ,ψ θas and function ψ as offunction non-dimensional of non-dimensio period (meannal periods.d.; (mean n = 5 wingbeats).± s.d.; n = 5 ± wingbeats).The wing kinematic results of FF1 at all three flight speeds are given in Figure 11 (the correspondingThe wing kinematic results of results FF2–FF4 of FF1are atgiven all three in Figure flight speedsA1–A3are in Appendix given in Figure A, respectively). 11 (the corresponding It can be resultsseen Thethat of thewing FF2–FF4 magnitude kinematic are given of results stroke in Figures angleof FF1 A1 is –atmuchA3 all in lathre Appendixrgere thanflightA deviation ,speeds respectively). are angle given It(Figure can in be Figure11a), seen such that11 (thethat the magnitudecorrespondingthe wing-tip of paths stroke results are angle of generally FF2–FF4 is much areflat larger givenopen than inloops Figure deviation (Figure A1–A3 angle11c). in Appendix (FigureIn most 11 of a),A, the suchrespectively). wingbeat that the cycle, wing-tipIt can the be pathsseentrajectory that are generally theof upstrokemagnitude flat openis belowof loopsstroke that (Figure angle of downstroke is11 muchc). In mostlarger at ofeach than the wingbeatflight deviation speed, cycle, angle except the (Figure trajectory at the 11a), beginning of such upstroke that of istheupstroke below wing-tip thatthat ofpathsone-time downstroke are crossovergenerally at each occursflat flight open due speed, loops to th excepte(Figure wing at first11c). the elevates beginningIn most a oflittle of the upstroke and wingbeat then that descends cycle, one-time the (θ crossovertrajectoryincreases slightly occursof upstroke due and to thenis the below wingdecreases that first of elevatesin downstroke Figure a 11a little). at andThe each thencorresponding flight descends speed,( θresults exceptincreases of at other the slightly beginningthree and insects then of decreasesupstrokeare similar. that in Figure one-time 11a). crossover The corresponding occurs due results to the ofwing other first three elevates insects a arelittle similar. and then descends (θ increases slightly and then decreases in Figure 11a). The corresponding results of other three insects are similar.

Figure 11. Time courses of (a) φϕ and θ and (b) ψ for FF1 in one wingbeat cycle at three flight ﬂight speeds.

((cc)) TheThe wing-tipwing-tip paths paths relative relative to to the the stroke stroke plane plane determined determined by φ byand ϕ θandat eachθ at flighteach speedflight speed (the stroke (the planeFigurestroke is plane11. indicated Time is indicated courses by the of dash-dotby ( athe) ϕ dash-dot and line θ andand line the(b )and wing-rootψ for the FF1 wing-root in is indicatedone wingbeat is indicated by a cycle red by dot). ata redthree dot). flight speeds. (c) The wing-tip paths relative to the stroke plane determined by ϕ and θ at each flight speed (the Asstroke shown plane in is Figureindicated 1111b, byb, the dash-dot wing pitches line and up the (supination)(sup wing-rootination) is in indicated the end by of a downstroke red dot). and in the beginning ofof thethe subsequentsubsequent upstroke upstroke and and pitches pitches down down (pronation) (pronation) in in the the end end of upstrokeof upstroke and and in the in beginningthe beginningAs shown of the of in subsequentthe Figure subsequent 11b, downstroke.the downstroke.wing pitches To clearlyTo up clea (sup describerlyination) describe the in variationthe variationend of of downstroke the of pitchthe pitch angle and angle inin onethe in cycle,beginningone cycle, the geometricaltheof thegeometrical subsequent angle angle ofupstro attackof attackke (andα) ( ofα )pitches theof the wing-section wing-sectiondown (pronation) is is defined: defined: in theα α =end =ψ ψin inof downstrokedownstrokeupstroke and andand in αthe = 180°beginning180 − ψψ in in ofupstroke. upstroke.the subsequent Figure Figure 12 downstroke. 12gives gives the thetime To time coursesclea coursesrly describeof α of in αa theinwingbeat a variation wingbeat cycle of cycle forthe FF1 pitch for at FF1 angleall atthree allin ◦ − threeoneflight cycle, flightspeeds the speeds geometrical(the same (the samesets angle of sets ofdata attack of datafor ( αthe for) of othe thethe otherrwing-section three three fruitflies fruitflies is defined: are arepresented α presented = ψ in downstrokein Figure in Figure A4 and A4 in inαAppendix = Appendix 180° − ψA). inA ). upstroke. Figure 12 gives the time courses of α in a wingbeat cycle for FF1 at all three flight speeds (the same sets of data for the other three fruitflies are presented in Figure A4 in Appendix A).

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Figure 12. TimeTime courses of α inin a a wingbeat wingbeat cycle for FF1 at three ﬂightflight speeds.

From Figure 1212,, wewe cancan seesee that,that, whenwhen nearnear hoveringhovering ( V(V∞ == 0.160.16 m/s), m/s), the the wing wing first first fast pitches ∞ down to a small α (from(from aboutabout 100100°◦ toto aboutabout 1010°)◦) atat thethe beginningbeginning ofof upstrokeupstroke ((ττ ≈ 0.53–0.66);0.53-0.66); then it ≈ rapidly pitches up to a large αα (about(about 4545°)◦) inin aa relativelyrelatively shortshort timetime ((ττ ≈ 0.66–0.75)0.66-0.75) and maintains this ≈ angle in the mid-portion of upstroke (τ ≈ 0.75–0.9); near the end of upstroke (τ ≈ 0.9–1), the wing ≈ ≈ continues toto pitchpitch up up to to that thatα reaches α reaches about about 110◦ .110°. Similarly, Similarly, the pitch-down the pitch-down and the and pitch-up the pitch-up motions motionsalso exist also in downstrokeexist in downstroke but the magnitudes but the magnitudes that α changes that α arechanges smaller are (Figure smaller 12 (Figure). In addition, 12). In addition,at medium at (Vmedium= 1.07 (V m∞ /=s) 1.07 and m/s) high and (V high= 1.69 (V m∞ =/s) 1.69 flight m/s) speeds, flight thespeeds, variation the variation of α in a wingbeatof α in a ∞ ∞ wingbeatcycle are similar cycle are to that similar at near-hovering to that at near-hovering flight (Figure flight12). It (Figure can be observed 12). It can that be the observed value of thatα in the valuemiddle of upstroke α in the ismiddle generally upstroke larger is than generally that in thelarger middle thandownstroke that in the middle at all flight downstroke speeds of at FF1, all andflightα speedsin the middle of FF1, upstroke and α in increases the middle with upstroke flight speed increases greatly with (about flight 45◦ ,speed 60◦ and greatly 68◦ at (aboutV = 0.16, 45°, 1.0760° and ∞ 1.6968° at m V/s,∞ = respectively) 0.16, 1.07 and while 1.69 thatm/s, inrespectively) the middle while downstroke that in almostthe middle remains downstroke unchanged almost (about remains 30◦). Theunchanged above results (about are 30°). also The true above for theresults other ar threee also insects. true for the other three insects. According to the definitionsdefinitions in Section 2.32.3,, somesome periodical parameters of the wing motions computed from the kinematic data (Figures(Figure 11 11 and and Fi A1gures, Figures A1–A3 A2 in and Appendix A3 in Appendix A) are listedA) are in listedTable 2,in including Table2, including the wingbeat the wingbeat frequency frequency (f), the (strokef ), the strokeamplitude amplitude (Φ), the (Φ mean), the meanstroke stroke angle angle(φ ), (theφ), ratiothe ratio of downstroke of downstroke duration duration to upstroke to upstroke duration duration (d/ (ud/)u and) and the the advance advance ratio ratio (J ().J). For For convenience, convenience, the stroke plane angle (β) and the body angle ((χ)) areare alsoalso listedlisted inin TableTable2 2..

Table 2. Kinematic parameters of the fruitﬂies. Table 2. Kinematic parameters of the fruitflies. ¯ Individual V (m/s) f (Hz) Φ (◦) φ β (◦) χ (◦) d/u J Individual ∞ V∞ (m/s) f (Hz) Φ (°) φ (◦) (°) β (°) χ (°) d/u J 0.16 187.9 0.2 126.3 2.4 8.2 1.1 0.1 54.6 1.12 0.06 0.16 187.9± ± 0.2 126.3± ± 2.4 ± 8.2 ± 1.1 0.1 54.6 1.12 0.06 FF1 1.07 171.4 0.1 126.8 0.9 18.0 0.8 21.9 39.1 1.38 0.45 ± ± ± FF1 1.691.07 182.0 171.40.1 ± 0.1 147.1 126.81.1 ± 0.9 15.2 18.0.80 ± 0.8 34.921.9 27.039.1 1.571.38 0.45 0.53 ± ± ± 014 161.2 0.1 146.0 2.2 5.1 0.7 1.1 59.3 1.19 0.06 1.69 182.0± ± 0.1 147.1± ± 1.1 15.± 2 ± 0.8 − 34.9 27.0 1.57 0.53 FF2 0.68 156.3 0.2 140.9 1.4 14.5 1.2 11.9 51.1 1.33 0.27 ± ± ± 1.70014 156.9 161.20.1 ± 0.1 161.9 146.01.6 ± 2.2 11.3 5.10.6 ± 0.7 36.6 -1.1 25.859.3 1.591.19 0.06 0.65 ± ± ± FF2 0.100.68 184.0 156.30.2 ± 0.2 122.2 140.91.6 ± 1.4 6.7 14.1.15 ± 1.2 1.211.9 54.951.1 1.081.33 0.27 0.04 ± ± ± FF3 1.28 189.1 0.1 134.3 1.0 12.1 0.5 32.9 29.9 1.27 0.44 ± ± ± 1.631.70 181.3 156.90.1 ± 0.1 144.2 161.91.2 ± 1.6 13.4 11.0.83 ± 0.6 35.236.6 22.625.8 1.341.59 0.65 0.54 ± ± ± 0.220.10 172.5 184.00.3 ± 0.2 142.8 122.22.8 ± 1.6 10.8 6.71.4 ± 1.1 0.4 1.2 51.5 54.9 1.14 1.08 0.04 0.08 ± ± ± FF4 0.64 170.7 0.1 133.5 1.3 14.8 1.3 15.4 41.8 1.18 0.25 FF3 1.28 189.1± ± 0.1 134.3± ± 1.0 12.± 1 ± 0.5 32.9 29.9 1.27 0.44 1.98 174.2 0.2 164.0 0.9 14.4 0.9 30.4 26.6 1.44 0.62 ± ± ± 1.63 181.3 ± 0.1 144.2 ± 1.2 13.4 ± 0.8 35.2 22.6 1.34 0.54

It can be seen that0.22f only changes 172.5 ± 0.3 slightly, 142.8 within± 2.8 10.9%,8 ± with 1.4 flight 0.4 speed 51.5 increasing, 1.14 0.08 which is same as thatFF4 of bumblebees0.64 [20] 170.7 and ± hawkmoths 0.1 133.5 ± [ 211.3]. Based 14.8 ± on1.3 the15.4 results 41.8 of the1.18 stroke 0.25 amplitude listed in Table2, increments1.98 of the 174.2 stroke ± 0.2 amplitude 164.0 ± 0.9 ( ∆Φ 14.) can4 ± 0.9 be computed30.4 26.6 by subtracting1.44 0.62 the Φ at near-hovering from that at other flight speeds for each fruitfly. Plotted in Figure 13 are ∆Φ and φ of all the fourIt can fruitflies be seen as that function f only of changes flight speed. slightly, From within the overall 9%, with data flight in Figure speed 13 a,increasing, a clear trend which of ∆ Φis samecan be as observed that of bumblebees that ∆Φ thus [20]Φ andfirst hawkmoths decreases (Φ [21].is about Based 8% on smaller the results at V of the0.7 stroke m/s than amplitude that at ∞ ≈ listednear-hovering in Table case)2, increments and then increasesof the stroke (Φ is amplitude about 16% (ΔΦ larger) can at thebe computed maximum by flight subtracting speed than the that Φ at near-hovering case)from withthat flightat other speed flight increasing. speeds for From each the fruitfly. overall Plotted data in in Figure Figure 13 13b, itare can ΔΦ be and seen φ thatof all the four fruitflies as function of flight speed. From the overall data in Figure 13a, a clear trend of ΔΦ can be observed that ΔΦ thus Φ first decreases (Φ is about 8% smaller at V∞ ≈ 0.7 m/s than that at

Energies 2020, 13, x FOR PEER REVIEW 13 of 23 Energies 2020, 13, 4271 13 of 23 near-hovering case) and then increases (Φ is about 16% larger at the maximum flight speed than that φatincreases near-hovering with flight case) speed with increasingflight speed in theincreasing. speed range From of theV overall0–0.7 data m/s, in but Figure remains 13b, unchanged it can be φ ∞ ≈ andseen even that decreases increases a little with at flight higher speed flight increasing speeds. Inin addition,the speed drange/u (Table of V2∞) ≈ is 0–0.7 approximately m/s, but remains 1.1 at near-hoveringunchanged and and even gradually decreases increases a little with flightat higher speed flight increasing. speeds. At theIn addition, highest flight d/u speeds(Tableof 2) FF1 is andapproximately FF2, d/u are 1.1 close at tonear-hovering 1.6, resulting inand a relativelygradually large increases flapping with velocity flight ofspeed the wing increasing. relative At to thethe bodyhighest in upstrokeflight speeds in comparison of FF1 and to FF2, that ind/u downstroke. are close to 1.6, resulting in a relatively large flapping velocity of the wing relative to the body in upstroke in comparison to that in downstroke.

FigureFigure 13.13. TheThe incrementsincrements ofof ((aa)) thethe strokestroke amplitudeamplitude andand ((bb)) meanmean strokestroke angleangle asas functionfunction ofof ﬂightflight speedspeed forfor allall thethe fourfour fruitﬂies.fruitflies.

3.2.3.2. Aerodynamic ForcesForces 3.2.1. Code Validation and Grid Test 3.2.1. Code Validation and Grid Test The flow solver had been validated in our previous studies by comparing the computed unsteady The flow solver had been validated in our previous studies by comparing the computed aerodynamic forces with the measured results of model insect wings in translating [42], revolving and unsteady aerodynamic forces with the measured results of model insect wings in translating [42], flapping motions [43]. These tests all showed that the computed aerodynamic forces by the present revolving and flapping motions [43]. These tests all showed that the computed aerodynamic forces solver were in good agreement with the corresponding experimental measurements. by the present solver were in good agreement with the corresponding experimental measurements. To further ensure the computation is grid-independent, a grid resolution test was conducted using To further ensure the computation is grid-independent, a grid resolution test was conducted the wing models and wing kinematics of FF1 flying at medium speed (V = 1.07 m/s). Three grid using the wing models and wing kinematics of FF1 flying at medium speed∞ (V∞ = 1.07 m/s). Three systems were considered. For the grid system 1, the dimensions of the wing grid were 31 45 37 grid systems were considered. For the grid system 1, the dimensions of the wing grid were× 31 ×× 45 × in the normal direction, around the wing and in the spanwise direction, respectively (the first-layer 37 in the normal direction, around the wing and in the spanwise direction, respectively (the thickness was 0.002c); the dimensions of the background grid were 101 61 61 in the x, y and z first-layer thickness was 0.002c); the dimensions of the background grid were× 101× × 61 × 61 in the x, y directions, respectively. For grid system 2, the corresponding grid dimensions were 45 67 57 and z directions, respectively. For grid system 2, the corresponding grid dimensions were× 45 ×× 67 × (0.0015c) and 155 95 95. For grid system 3, the corresponding grid dimensions were 66 101 83 57 (0.0015c) and 155× × ×95 × 95. For grid system 3, the corresponding grid dimensions were× 66 × 101× × (0.001c) and 234 141 141. For the wing grids in these grid systems, the grid points were densely 83 (0.001c) and 234× × 141× × 141. For the wing grids in these grid systems, the grid points were densely distributed toward the wing surface and toward the wake area; for the background grids, the grid distributed toward the wing surface and toward the wake area; for the background grids, the grid points were concentrated in the near field of the wings. The non-dimensional time step was 0.02. points were concentrated in the near field of the wings. The non-dimensional time step was 0.02. Shown in Figure 14a,b are the vertical force and thrust coefficients in a wingbeat cycle, computed Shown in Figure 14a,b are the vertical force and thrust coefficients in a wingbeat cycle, with the above three grid systems. Plotted in Figure 14c are the iso-vorticity surfaces of the computed with the above three grid systems. Plotted in Figure 14c are the iso-vorticity surfaces of non-dimensional vorticity at τ = 0.42. It can be found that there is almost no difference between the the non-dimensional vorticity at τ = 0.42. It can be found that there is almost no difference between aerodynamic force coefficients calculated by the three grid systems; and some discrepancies exist in the the aerodynamic force coefficients calculated by the three grid systems; and some discrepancies exist iso-surface plots of vorticity between grid system 2 and grid system 1, but there are only very small in the iso-surface plots of vorticity between grid system 2 and grid system 1, but there are only very discrepancies between grid system 2 and grid system 3. This indicates that good solution accuracy can small discrepancies between grid system 2 and grid system 3. This indicates that good solution be achieved with grid system 2 or 3. Here, grid system 3 was used in the present paper. accuracy can be achieved with grid system 2 or 3. Here, grid system 3 was used in the present paper.

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Figure 14. Grid resolution test. Time courses of the (a) vertical force and (b) thrust coefficients of the Figure 14. Grid resolution test. Time courses of the (a) vertical force and (b) thrust coefficients of wingsFigure in14. a Grid wingbeat resolution cycle test. computed Time courses with ofthree the (grida) vertical systems. force ( cand) The (b ) iso-surfacethrust coefficients plots of of thethe the wings in a wingbeat cycle computed with three grid systems. (c) The iso-surface plots of the non-dimensionalwings in a wingbeat vorticity cycle at τcomputed = 0.42 (the withmagnitude three gridof the systems. non-dimensional (c) The iso-surfacevorticity is 1).plots of the non-dimensional vorticity at τ = 0.42 (the magnitude of the non-dimensional vorticity is 1). non-dimensional vorticity at τ = 0.42 (the magnitude of the non-dimensional vorticity is 1). 3.2.2. Computed Aerodynamic forces 3.2.2. Computed Aerodynamic forces 3.2.2.Using Computed the numericalAerodynamic method forces described above and the measured wing kinematics, the Using the numerical method described above and the measured wing kinematics, the aerodynamic aerodynamicUsing the forces numerical at each flightmethod of the described fruitflies canabove be computed.and the measuredFigure 15 showswing thekinematics, vertical force the forces at each flight of the fruitflies can be computed. Figure 15 shows the vertical force (CV) and thrust (aerodynamicCV) and thrust forces (CT) coefficientsat each flight on of the the wings fruitflies in acan wingbeat be computed. cycle of Figure FF1 at 15 three shows flight the speeds,vertical afterforce (CT) coefficients on the wings in a wingbeat cycle of FF1 at three flight speeds, after periodical state has periodical state has been achieved (the corresponding results of the other three fruitflies are been(CV) achievedand thrust (the (CT corresponding) coefficients on results the wings of the in other a wingbeat three fruitflies cycle of are FF1 presented at three inflight Figure speeds, A5 in after the presented in Figure A5 in the Appendix A). AppendixperiodicalA ).state has been achieved (the corresponding results of the other three fruitflies are presented in Figure A5 in the Appendix A).

FigureFigure 15.15. TimeTime coursescourses ofof thethe computedcomputed ((aa)) verticalvertical forceforce andand ((bb)) thrustthrust coecoefficientsfficients inin aa wingbeatwingbeat cyclecycleFigure ofof FF115.FF1 Time atat threethree courses flightflight of speeds.speeds. the computed (a) vertical force and (b) thrust coefficients in a wingbeat cycle of FF1 at three flight speeds. FigureFigure 1616 showsshows thethe instantaneousinstantaneous forceforce vectorsvectors atat severalseveral momentsmoments inin oneone cyclecycle superimposedsuperimposed onon thetheFigure wing-tipwing-tip 16 shows pathspaths the forfor FF1instantaneousFF1 atat threethree flightflight force speeds.speed vectorss. TheTheat several followingfollowing moments observationsobservations in one cycle cancan bebesuperimposed mademade fromfrom FiguresFigureson the wing-tip1515 andand 1616. paths. for FF1 at three flight speeds. The following observations can be made from AtAt near-hoveringnear-hovering(V (V∞= =0.16 0.16 m /s),m/s), positive positiveCV is C producedV is produced in downstroke in downstroke and upstroke and to upstroke support theto Figures 15 and 16. ∞ weight (Figures 15a and 16a), and the contribution of downstroke is about 53%, only slightly larger than that supportAt thenear-hovering weight (Figures (V∞ = 15a 0.16 and m/s), 16a), positive and the C Vcontribution is produced of indownstroke downstroke is aboutand upstroke 53%, only to ofslightlysupport upstroke. larger the Negative weight than that (FiguresCT producedof upstroke. 15a inand downstrokeNegative 16a), and C andTthe produced contribution positive in in downstroke upstroke of downstroke (Figures and positive is15 aboutb and in 53%,16 upstrokea) haveonly almost the same magnitude that cancel each other out, resulting in an approximately zero mean thrust, (Figuresslightly larger15b and than 16a) that have of upstroke. almost the Negative same magnitude CT produced that in cancel downstroke each other and positiveout, resulting in upstroke in an asapproximately required for thezero hovering mean thrust, flight. as At required medium for flight the speedhovering (V flight.= 1.07 At m/ s),medium positive flightCV producedspeed (V∞in = (Figures 15b and 16a) have almost the same magnitude that∞ cancel each other out, resulting in an downstroke is about 86% of the total C in the entire cycle, much larger than its counterpart in upstroke 1.07approximately m/s), positive zero C Vmean produced thrust, in asdownstroke Vrequired for is aboutthe hovering 86% of theflight. total At C mediumV in the entire flight cycle,speed much (V∞ = (Figure 15a). Thus, the weight-supporting force is mainly generated during downstroke (Figure 16b). larger1.07 m/s), than positive its counterpart CV produced in upstroke in downstroke (Figure is 15a). about Thus, 86% theof the weight-supporting total CV in the entire force cycle, is mainly much Thegeneratedlarger magnitudes than during its counterpart of downstroke positive CinT upstrokeproduced(Figure 16b). (Figure in upstrokeThe 15a).magnitudes andThus, negative the of weight-supportingpositiveCT produced CT produced in downstrokeforce in isupstroke mainly are both decreased, but the magnitude of the positive C in upstroke is much larger than its negative andgenerated negative during CT produced downstroke in downstroke (Figure 16b). are bothThe decreamagnitudesT sed, but of thepositive magnitude CT produced of the positive in upstroke CT in counterpart in downstroke (Figure 15b), resulting in a positive cycle-averaged thrust. Thus, the thrust upstrokeand negative is much CT produced larger than in downstroke its negative are counte both rpartdecrea insed, downstroke but the magnitude (Figure 15b),of the resulting positive CinT ina thatpositiveupstroke required cycle-averaged is much for overcoming larger thrust. than the its Thus, body negative dragthe thrust iscounte mainly thatrpart generated required in downstroke in for upstroke overcoming (Figure (Figure 15b), the 16 b).bodyresulting drag in isa mainlypositive generated cycle-averaged in upstroke thrust. (Figure Thus, 16b). the thrust that required for overcoming the body drag is mainly generated in upstroke (Figure 16b).

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FigureFigure 16. 16. InstantaneousInstantaneous force force vectors vectors (red (red arrows) arrows) superimposed superimposed on on the the side side view view of of the the wing-tip wing-tip pathspaths for for FF1 FF1 at atthree three flight flight speeds. speeds. The The blue blue and and purple purple lines lines indicate indicate the orientation the orientation of the of wing the wing in downstrokein downstroke and andupstroke, upstroke, respective respectively,ly, at several at several times times in a in flapping a flapping cycle, cycle, with with dots dots marking marking the the leadingleading edge. edge. (a ()a At) At near-hovering near-hovering (V (V∞ = 0.16= 0.16 m/s); m/s); (b ()b At) At medium medium flight flight speed speed (V (V∞ = 1.07= 1.07 m/s); m/s); (c) ( cAt) At ∞ ∞ highhigh flight flight speed speed (V (∞V = 1.69= 1.69 m/s). m/ s). ∞

At high flight speed (∞V = 1.69 m/s), positiveV CV produced in downstroke is rather larger and At high flight speed (V =∞ 1.69 m/s), positive C produced in downstroke is rather larger and in upstrokein upstroke is rather is rather smaller smaller (Figures (Figures 15a 15 anda and 16c). 16 c).About About 89% 89% of ofthe the weight-supporting weight-supporting vertical vertical force force isis produced produced duringduring downstroke.downstroke. Same Same as theas medium-speedthe medium-speed case, thecase, thrust the required thrust forrequired overcoming for overcomingthe larger body the larger drag isbody mainly drag generated is mainly in generated upstroke in (Figures upstroke 15b (Figures and 16c). 15b The and similar 16c). The observations similar observationsof FF2–FF4 areof FF2–FF4 given in are Appendix given inA .Appendix A. ForFor steady steady forward forward flight, flight, the the aerodynamic aerodynamic forces forces acting acting on on the the wings wings and and the the body body should should be be approximatelyapproximately equal equal to to the the insect-weight insect-weight in in the the vertical vertical direction direction and and should should be be close close to to zero zero in in the the 2 horizontalhorizontal direction. direction. The The non-dimensional non-dimensional weight weight (CG == mg/0.5mg/0.5ρρUU2(2S)(2S),, in in which g isis thethe accelerationacceleration of ofgravity) gravity) of of FF1 FF1 is is about about 1.76. 1.76. The The computed computed non-dimensional non-dimensional mean mean vertical vertical force force of the of the wings wings at three at threeflight flight speeds speeds for FF1 for are FF1 1.80, are 1.75 1.80, and 1.75 1.62, and respectively. 1.62, respectively. At V = At0.16 V∞ and = 0.16 1.07 and m/s, 1.07 the dim/s,fferences the ∞ differencesof the computed of the computed vertical forces vertical on theforces wings, on the compared wings, compared with CG, arewith less CG than, are 2%,less whichthan 2%, means which the meanscomputed the computed vertical forces vertical on forces the wings on the are wing suffiscient are sufficient for supporting for supporting the weight. the Atweight.V = At1.69 V∞ m =/ s, ∞ 1.69as them/s, body as the angle body is angle about is 27 about◦, the 27°, small the vertical small vertical force on force the body on the would body compensate would compensate the shortage, the shortage,about 8%, about between 8%, between the computed the computed vertical force vertical acting force on theacting wings on andthe wingsCG. Therefore, and CG. Therefore, the equilibrium the equilibriumconditions thatconditions the vertical that the forces vertical balance forces the weightbalance at the all weight three flight at all speeds three flight of FF1 speeds are approximately of FF1 are approximatelysatisfied. The satisfied. similar results The similar of FF2–FF4 results are of presented FF2–FF4 are in the presented Appendix in Athe. Appendix A.

3.3.3.3. Power Power Requirements Requirements 3.3.1. Computed Mechanical Power 3.3.1. Computed Mechanical Power Power requirement is a crucial parameter to quantify the flight performance of insect. Based upon Power requirement is a crucial parameter to quantify the flight performance of insect. Based the measured wing kinematics and the computed aerodynamic forces, the aerodynamic and inertial upon the measured wing kinematics and the computed aerodynamic forces, the aerodynamic and powers can be calculated using the computational method described in Section 2.4. Figure 17 shows the inertial powers can be calculated using the computational method described in Section 2.4. Figure time histories of the instantaneous non-dimensional aerodynamic (CPa), inertial (CPi) and mechanical 17 shows the time histories of the instantaneous non-dimensional aerodynamic (CPa), inertial (CPi) (CP) powers in one stroke cycle of FF1-FF4 at various flight speeds. It can be seen that at all flight and mechanical (CP) powers in one stroke cycle of FF1-FF4 at various flight speeds. It can be seen speeds of these fruitflies, CPi is much smaller than CPa in most of the flapping cycle, and hence the that at all flight speeds of these fruitflies, CPi is much smaller than CPa in most of the flapping cycle, curves of CP are approximately the same as that of CPa. Moreover, the value of CPi is very small (close and hence the curves of CP are approximately the same as that of CPa. Moreover, the value of CPi is to zero) in downstroke and is positive in the first half of upstroke and is negative in the next half of very small (close to zero) in downstroke and is positive in the first half of upstroke and is negative upstroke. This indicates that for fruitflies in near-hovering or forward flights, the influence of inertial in the next half of upstroke. This indicates that for fruitflies in near-hovering or forward flights, the power on power consumption (the cycle-averaged mechanical power) is very small. influence of inertial power on power consumption (the cycle-averaged mechanical power) is very small.

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Figure 17. Time histories of (a,c,e,g) CPa and CPi and (b,d,f,h) CP in one stroke cycle of FF1-FF4 at Figure 17. Time histories of (a,c,e,g) CPa and CPi and (b,d,f,h) CP in one stroke cycle of FF1-FF4 at various ﬂight speeds. various flight speeds.

As seen from Figure 17, the magnitude of CP changes slightly in downstroke and significantly As seen from Figure 17, the magnitude of CP changes slightly in downstroke and significantly inin upstroke upstroke for for all all the the fruitflies fruitflies withwith flightflight speedspeed increasing.increasing. Compared Compared with with their their respective respective near-hovering cases, the peak values of C in upstroke at low or medium flight speeds (e.g., FF1 at near-hovering cases, the peak values of CP in upstroke at low or medium flight speeds (e.g., FF1 at V = 1.07 m/s, FF2 at V = 0.68 m/s and FF4 at V = 0.64 m/s) are a little smaller but at higher flight ∞V∞ = 1.07 m/s, FF2 at V∞∞ = 0.68 m/s and FF4 at V∞ ∞= 0.64 m/s) are a little smaller but at higher flight speedsspeeds are are much much larger. larger. Thus, Thus, it can it becan concluded be concluded that thethat magnitude the magnitude of CP inof upstrokeCP in upstroke first decreases first anddecreases then increases and then with increases flight with speed flight increasing. speed increasing. InIn order order to to analyze analyze how howC CPaPa (or(or CP)) is is generated, generated, here here we we take take the the flights flights of ofFF1 FF1 as asexamples examples andand the the interpretation interpretation isis asas follows. As As seen seen from from Equation Equation (5), (5), CPaC isPa theis inner the inner product product of Ma of andM aΩand. Ω.Since Since the the wings wings of of FF1 FF1 are are approximately approximately flapping flapping back back and and forth forth in inthe the stroke stroke plane plane at all at allthree three flightflight speeds, speeds, the the aerodynamic aerodynamic powerpower consumed by by a a wing wing is is mainly mainly used used to toovercome overcome the the drag drag exertedexerted on on it (theit (the wing wing drag drag is the is forcethe force that thethat insect the insect must overcomemust overcome for moving for moving its wing). its Therefore,wing). . φ theTherefore, aerodynamic the aerodynamic power must power be positive must be (Figure positive 17) (Figure and is closely17) and related is closely to CrelatedD and toφ (whereCD and “dot” . φ denotes(where a “dot” time derivative). denotes a time Figure derivative). 18 shows theFigure time 18 histories shows oftheC Dtimeand historiesφ in a wingbeat of CD and cycle of in FF1 a at threewingbeat flight speeds.cycle of AsFF1 illustrated at three flight in Figures speeds. 17 andAs illustrated18, in the firstin Figure half downstroke, 17 and FigureCPa 18,at near-hoveringin the first (Vhalf= downstroke,0.16 m/s) is aC littlePa at near-hovering larger than that (V∞ at = medium0.16 m/s) (isV a little= 1.07 larger m/s )than and that high at ( Vmedium= 1.69 (V m∞ =/s) 1.07 flight . ∞ ∞ φ ∞ speedsm/s ) dueand high to the (V larger∞ = 1.69 magnitude m/s) flightof speedsφ; while due in to thethe nextlarger half magnitude downstroke, of ;C whilePa increases in the next with half flight .  speeddownstroke, due to the CPa increasing increases with of the flight magnitudes speed due of toCD theand increasingφ. During of upstroke,the magnitudes from near-hovering of CD and φ . to medium flight speed, the magnitude of CD decreases a little, thus CPa decreases a little; whereas at Energies 2020, 13, x FOR PEER REVIEW 17 of 23

Energies 2020, 13, 4271 17 of 23 During upstroke, from near-hovering to medium flight speed, the magnitude of CD decreases a little,  thus CPa decreases a little; whereas at high flight speeds, both of the magnitudes of CD and φ . highincrease flight speeds,significantly, both ofthus the C magnitudesPa becomes very of C Dlarge.and Aφdditionally,increase significantly, because of d/u thus isC increasingPa becomes with very  large.flight Additionally, speed, the becausepeak position of d/u isof increasingCP in upstroke, with flight where speed, the values the peak of positionCD and φ of CareP inmaximal, upstroke, . wherecontinues the values to be ofdelayed.CD and Throughφ are maximal, the same continues method of to analysis, be delayed. the similar Through results the of same FF2–FF4 method can of analysis,also be the obtained. similar results of FF2–FF4 can also be obtained.

FigureFigure 18. 18.Time Time histories histories of of drag drag coe coefficientfficient and andflapping flapping angularangular velocity of of the the wing wing in in a awingbeat wingbeat cyclecycle of FF1of FF1 at threeat three flight flight speeds. speeds. (a ()a Drag) Drag coe coefficient;fficient; ((bb)) FlappingFlapping angular velocity. velocity.

3.3.2.3.3.2. Speciﬁc Specific power power

ToTo evaluate evaluate the the power power requirement requirement of of insect insect flight, flight, thethe body-mass-specificbody-mass-specific power power (P (P*, *defined, defined as as thethe cycle-averaged cycle-averaged mechanical mechanical power power divided divided by by the the massmass ofof thethe insect) is is usually usually used: used:

*3=×ρ * P 0.53US（）2 () CTW / / m (6) P∗ = 0.5ρU (2S) (C /T∗)/m (6) × W where CW is the non-dimensional work in a wingbeat cycle and T* is the non-dimensional period where C is the non-dimensional work in a wingbeat cycle and T* is the non-dimensional period (definedW as T* = U/cf). (defined as T* = U/cf ). Commonly, when computing CW, two limiting cases are considered [44]: in the case of zero C elasticCommonly, energy whenstorage, computing with the addedW, two assumption limiting cases that the are cost considered for dissipating [44]: in the casenegative of zero work elastic is energy storage, with the added assumption that the cost for dissipating the negative work is negligible, negligible, CW is calculated by integrating CP over the part of a wingbeat cycle where it is positive; in CWtheis calculatedcase of 100% by elastic integrating energyC Pstorage,over the with part the of added a wingbeat assumption cycle wherethat the it negative is positive; work in can the casebe of 100%stored elastic by an energyelastic storage,element and with then the addedcan be assumptionreleased when that the the wing negative does workpositive can work, be stored CW is by an elasticcalculated element by integrating and then C canP over be releasedthe entire when wingbeat the wingcycle. does The real positive CW lies work, betweenCW is the calculated values of by integratingthese twoC Plimitingover the cases. entire However, wingbeat for cycle. all the The flig realhts CofW thelies four between fruitflies the valuesin the present of these paper, two limiting CP is cases.positive However, in almost for all the the entire flights flapping of the four cycle fruitflies because in the the presentvalue of paper, negativeCP isCPi positive is very in small. almost theConsequently, entire flapping CW cycle calculated because by the these value two of considered negative C limitingPi is very cases small. will Consequently, be approximatelyCW thecalculated same byand these any two of consideredthem is a good limiting approximation cases will of be the approximately real CW. This theresult same is similar and any to ofthat them in previous is a good approximationstudies [45,46]. of theHere, real theC Wcase. This of 100% result elastic is similar energy to thatstorage in previous is adopted. studies [45,46]. Here, the case of 100% elasticWith energyCW known, storage P* at iseach adopted. flight of FF1-FF4 can be calculated using Equation (6), and the results as function of advance* ratio (J) are plotted in Figure 19. The specific powers at near-hovering of With CW known, P at each flight of FF1-FF4 can be calculated using Equation (6), and the results * as functionFF1-FF4 of(the advance first data ratio point (J) areof each plotted fruitfly) in Figure are about 19. The 26.6 specific W/kg. And powers the atvariations near-hovering of P with of FF1-FF4 flight (thespeed first dataof the point four of fruitflies each fruitfly) are consistent. are about From 26.6 Wth/ekg. overall And thedata variations of the specific of P* withpowers, flight it speedcan be of * theobserved four fruitflies that P are only consistent. changes very From little the overallwhen the data advance of the ratio specific changes powers, from it 0 can to beabout observed 0.45, and that afterwards P* increases sharply. P* only changes very little when the advance ratio changes from 0 to about 0.45, and afterwards P* increases sharply. Energies 2020, 13, 4271 18 of 23 Energies 2020, 13, x FOR PEER REVIEW 18 of 23

FigureFigure 19. 19.Speciﬁc Specificpower power versusversus advance ratio ratio of of fruitflies. fruitﬂies.

ForFor example, example, the the specific specific power power ofof FF4FF4 atat thethe highesthighest flight flight speed speed is is approximately approximately 61% 61% larger larger thanthan that that at at near-hovering. near-hovering. That That is, is, the the energy energy consumptionconsumption of of the the fruitflies fruitflies varies varies with with flight flight speed speed accordingaccording to ato J-shaped a J-shaped curve. curve. This This is similar is similar to that to ofthat the of medium-sized the medium-sized bumblebee bumblebee [23] but [23] di ffbuterent to thatdifferent of the to large-sized that of the hawkmoth large-sized which hawkmoth is U-shaped which [is7 ].U-shaped One possible [7]. One reason possible for this reason difference for this may bedifference that the size may of be the that hawkmoth the size of is the much hawkmoth larger and is much flapping larger frequency and flapping much frequency lower than much those lower of the fruitflythan andthose bumblebee of the fruitfly (hawkmoth: and bumblebee wing-length (hawkm aboutoth: wing-length 50 mm and about frequency 50 mm about and 25frequency Hz; fruitfly about and bumblebee:25 Hz; fruitfly wing-length and bumblebee: 3–13 mm wing-length and frequency 3–13 mm 150–200 and frequency Hz). 150-200 Hz).

4. Conclusions4. Conclusions InIn this this paper, paper, an an elaborate elaborate filming filming system system consistingconsisting of three high-speed high-speed cameras, cameras, a acustomized customized low-speedlow-speed open-jet open-jet wind wind tunnel tunnel and and otherother visualvisual controllingcontrolling devices devices was was designed designed to to capture capture the the forward flight of fruitflies. The wing and body kinematics at multiple speeds of four fruitflies flying forward flight of fruitflies. The wing and body kinematics at multiple speeds of four fruitflies flying in their full speed range were successfully measured, and the maximum flight speed obtained was in their full speed range were successfully measured, and the maximum flight speed obtained was about 2 m/s, reaching the limiting flight speed of fruitfly. The kinematic results show that, as flight about 2 m/s, reaching the limiting flight speed of fruitfly. The kinematic results show that, as flight speed increases, the body angle decreases and the stroke plane angle increases; the fluctuation of the speed increases, the body angle decreases and the stroke plane angle increases; the fluctuation of wingbeat frequency is small; the geometrical angle of attack in the middle upstroke increases while thein wingbeat the middle frequency downstroke is small; almost the remains geometrical unchanged; angle the of stroke attack amplitude in the middle decreases upstroke first and increases then while in the middle downstroke almost remains unchanged; the stroke amplitude decreases first and increases; the mean stroke angle increases in the speed range of V∞ ≈ 0–0.7 m/s but remains then increases; the mean stroke angle increases in the speed range of V 0–0.7 m/s but remains unchanged and even decreases a little at higher flight speeds; the ratio of∞ downstroke≈ duration to unchangedupstroke duration and even increases. decreases The a little aerodynamic at higher forc flightes and speeds; power the requirement ratio of downstroke at each flight duration speed to upstrokewere computed duration increases.using CFD The method. aerodynamic It is shown forces andthat power the mechanical requirement power at each is flightdominated speed wereby computedaerodynamic using power, CFD method. and the magnitude It is shown of that aerodynami the mechanicalc power powerin upstroke is dominated increases bysignificantly aerodynamic at power,high andflight the speeds magnitude due to the of aerodynamicincrease of the power drag and in upstrokethe flapping increases velocity significantly of the wing. atThe high overall flight speedsdata dueof the to specific the increase powers of of the th drage four and fruitflies the flapping as function velocity of advance of the wing.ratio shows The overall that the data specific of the specificpower powers only changes of the foura little fruitflies when the as functionadvance ofratio advance is below ratio about shows 0.45 that and the afterwards specific powerincreases only changessharply. a little That when is, the the energy advance consumption ratio is below of the about fruitflies 0.45 andvaries afterwards with flight increases speed according sharply. Thatto a is, theJ-shaped energy consumptioncurve. of the fruitflies varies with flight speed according to a J-shaped curve.

SupplementarySupplementary Materials: Materials:The The following following are are available available online online at athttp: www.mdpi.com/xxx/s1,//www.mdpi.com/1996-1073 Video S1:/13 /FF116/4271 near/ s1, Videohovering, S1: FF1 Video near S2: hovering, FF1 medium Video speed, S2: FF1 Video medium S3: FF1 speed, high Videospeed. S3: FF1 high speed.

AuthorAuthor Contributions: Contributions:Conceptualization, Conceptualization, H.J.Z.H.J.Z. andand M.S.; Methodology, H.J.Z. H.J.Z. and and M.S.; M.S.; Software, Software, H.J.Z.; H.J.Z.; Validation,Validation, H.J.Z.; H.J.Z.; Formal Formal Analysis, Analysis, H.J.Z. H.J.Z. and and M.S.; M.S.; Investigation, Investigation, H.J.Z.; H.J.Z.; Resources, Resources, H.J.Z.; H.J.Z.; Data Data Curation, Curation, H.J.Z.; Writing—Original Draft Preparation, H.J.Z.; Writing—Review & Editing, M.S.; Visualization, H.J.Z.; Supervision, H.J.Z.; Writing—Original Draft Preparation, H.J.Z.; Writing—Review & Editing, M.S.; Visualization, H.J.Z.; M.S.; Project Administration, H.J.Z.; Funding Acquisition, M.S. All authors have read and agreed to the published versionSupervision, of the manuscript. M.S.; Project Administration, H.J.Z.; Funding Acquisition, M.S. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National Natural Science Foundation of China, grant numbers 11232030 andFunding: 11832004. This research was funded by the National Natural Science Foundation of China, grant numbers 11232030 and 11832004. Conﬂicts of Interest: The authors declare no conﬂict of interest.

Energies 2020, 13, x FOR PEER REVIEW 19 of 23 Energies 2020, 13, x FOR PEER REVIEW 19 of 23 Conflicts of Interest: The authors declare no conflict of interest. Conflicts of Interest: The authors declare no conflict of interest. Energies 2020, 13, 4271 19 of 23 Appendix A Appendix A AppendixThe measured A time courses of stroke angle, deviation angle and pitch angle in a wingbeat cycle and The measured time courses of stroke angle, deviation angle and pitch angle in a wingbeat cycle and the corresponding wing-tip path of FF2–FF4 at all flight speeds are given in Figures A1–A3, the correspondingThe measured timewing-tip courses path of stroke of FF2–FF4 angle, deviation at all flight angle speeds and pitch are angle given in ain wingbeat Figures cycle A1–A3, and respectively. therespectively. corresponding wing-tip path of FF2–FF4 at all ﬂight speeds are given in Figures A1–A3, respectively.

Figure A1. Time courses of (a) ϕ and θ and (b) ψ for FF2 in one wingbeat cycle at three flight speeds. Figure A1.A1. Time courses of (a) φϕ and θ and (b) ψ for FF2 in one wingbeat cycle at three flight ﬂight speeds. (c) The wing-tip paths relative to the stroke plane determined by ϕ and θ at each flight speed (the ((cc)) TheThe wing-tip wing-tip paths paths relative relative to to the the stroke stroke plane plane determined determined by φ byand ϕ θandat eachθ at ﬂighteach speedflight speed (the stroke (the stroke plane is indicated by the dash-dot line and the wing-root is indicated by a red dot). planestroke is plane indicated is indicated by the dash-dotby the dash-dot line and line the and wing-root the wing-root is indicated is indicated by a red by dot). a red dot).

Figure A2. Time courses of (a) φ and θ and (b) ψ for FF3 in one wingbeat cycle at three flight speeds. Figure A2. Time courses of (a) ϕ and θ and (b) ψ for FF3 in one wingbeat cycle at three flight speeds. (Figurec) The wing-tipA2. Time paths courses relative of (a) to ϕ the and stroke θ and plane (b) ψ determined for FF3 in one by φ wingbeatand θ at eachcycle flight at three speed flight (the speeds. stroke (c) The wing-tip paths relative to the stroke plane determined by ϕ and θ at each flight speed (the plane(c) The is wing-tip indicated paths by the relative dash-dot to linethe stroke and the plane wing-root determined is indicated by ϕ byand a redθ at dot). each flight speed (the stroke plane is indicated by the dash-dot line and the wing-root is indicated by a red dot). stroke plane is indicated by the dash-dot line and the wing-root is indicated by a red dot). Time courses of geometrical angle of attack in a wingbeat cycle of FF2–FF4 at all flight speeds are given in Figure A4. As flight speed increases, it can be observed that the variations of α of FF2–FF4 are similar to that of FF1 (described in Section 3.1).

Energies 2020, 13, x FOR PEER REVIEW 20 of 23

Energies 2020, 13, 4271 20 of 23 Energies 2020, 13, x FOR PEER REVIEW 20 of 23

Figure A3. Time courses of (a) ϕ and θ and (b) ψ for FF4 in one wingbeat cycle at three flight speeds. (c) The wing-tip paths relative to the stroke plane determined by ϕ and θ at each flight speed (the stroke plane is indicated by the dash-dot line and the wing-root is indicated by a red dot).

FigureTime courses A3. Time of courses geometrical of (a) φ angleand θ ofand attack (b) ψ forin a FF4 wingbeat in one wingbeat cycle of cycle FF2–FF4 at three at ﬂightall flight speeds. speeds Figure A3. Time courses of (a) ϕ and θ and (b) ψ for FF4 in one wingbeat cycle at three flight speeds. are given(c) The in wing-tip Figure paths A4. relativeAs flight to the speed stroke increases, plane determined it can bybeφ observedand θ at each that ﬂight the speed variations (the stroke of α of (c) The wing-tip paths relative to the stroke plane determined by ϕ and θ at each flight speed (the FF2–FF4plane are is indicatedsimilar to by that the of dash-dot FF1 (described line and the in wing-rootSection 3.1). is indicated by a red dot). stroke plane is indicated by the dash-dot line and the wing-root is indicated by a red dot).

Time courses of geometrical angle of attack in a wingbeat cycle of FF2–FF4 at all flight speeds are given in Figure A4. As flight speed increases, it can be observed that the variations of α of FF2–FF4 are similar to that of FF1 (described in Section 3.1).

Figure A4. Time courses of α in a wingbeat cycle for FF2–FF4 at various ﬂight speeds. (a) FF2; (b) FF3; (c) FF4.

The computed CV and CT on the wings in a ﬂapping cycle after periodical state has been established for FF2–FF4 at various ﬂight speeds are shown in Figure A5. The following observations which is

Energies 2020, 13, x FOR PEER REVIEW 21 of 23

Figure 4. Time courses of α in a wingbeat cycle for FF2–FF4 at various flight speeds. (a) FF2; (b) FF3; (c) FF4.

The computed CV and CT on the wings in a flapping cycle after periodical state has been Energies 2020, 13, 4271 21 of 23 established for FF2–FF4 at various flight speeds are shown in Figure A5. The following observations which is similar to that of FF1 can be made. At near hovering, both of downstroke and upstroke similarcontribute to that to ofthe FF1 weight-supporting can be made. At nearvertical hovering, force, bothand ofthe downstroke contributions and are upstroke approximately contribute the to thesame; weight-supporting positive CT in upstroke vertical force, and andnegative the contributions in downstroke are approximatelycancel each other the same;out, bringing positive CanT inequilibrium upstroke and state. negative As flight in downstroke speed increa cancelses, the each contribution other out, bringing of downstroke an equilibrium to CV to state. support As ﬂight the speedweight increases, is increasing, the contribution while the ofcontribution downstroke of to CupstrokeV to support to C theT to weight overcome is increasing, the body while drag the is contributionincreasing. of upstroke to CT to overcome the body drag is increasing.

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