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For many insects in hovering flight, the stroke amplitude is relatively large (above ) and the lift is mainly produced by the leading-edge vortex (LEV) attaching to the wing (the delayed-stall mechanism). Mosquitoes have a very small stroke amplitude ( ) and the LEV does not have enough time to form before a stroke ends; thus, the delayed-stall mechanism can not be used. In the present study, we show that their lift is produced by different aerodynamic mechanisms from those of insects with a large stroke amplitude: in a downstroke and upstroke, two large lift peaks and a relatively small one are generated. The first large lift peak (at the beginning of the stroke) mainly comes from the added-mass force caused by the large acceleration of the wing. The second large lift peak (in the mid-portion of the stroke) is produced by the ‘fast-pitching-up rotation’ mechanism: the wing fast pitches up while moving forward, generating a large-magnitude, opposite-sign vorticity at the trailing edge of the wing and near the leading edge of the wing; the rapid generation of opposite-sign vorticity at different locations of the wing results in a large time rate of change in the first moment of vorticity, hence a large aerodynamic force. The third lift peak, which is near the end of the stroke and is small, is a result of the fast-pitching-up rotation of a rapidly decelerating wing. Note that although the added-mass force contributes positive lift in the beginning part of the stroke when the wing is in acceleration, it gives negative lift in the next part of the stroke when the wing is in deceleration; i.e. the added-mass force has no effect on the time-average lift, but it greatly changes the time distribution of the lift.

To investigate the way in which very small insects compensate for unilateral wing damage, we measured the wing kinematics of a very small insect, a phorid fly (Megaselia scalaris), with $16.7%$ wing area loss in the outer part of the left wing and a normal counterpart, and we computed the aerodynamic forces and power expenditures of the phorid flies. Our major findings are the following. The phorid fly compensates for unilateral wing damage by increasing the stroke amplitude and the deviation angle of the damaged wing (the large deviation angle gives the wing a deep U-shaped wing path), unlike the medium and large insects studied previously, which compensate for the unilateral wing damage mainly by increasing the stroke amplitude of the damaged wing. The increased stroke amplitude and the deep U-shaped wing path give the damaged wing a larger wing velocity during its flapping motion and a rapid downward acceleration in the beginning of the upstroke, which enable the damaged wing to generate the required vertical force for weight support. However, the larger wing velocity of the damaged wing also generates larger horizontal and side forces, increasing the resultant aerodynamic force of the damaged wing. Due to the larger aerodynamic force and the smaller wing area, the wing loading of the damaged wing is 25% larger than that of the wings of the normal phorid fly; this may greatly shorten the life of the damaged wing. Furthermore, because the damaged wing has much larger angular velocity and produces larger aerodynamic moment compared with the intact wing of the damaged phorid fly, the aerodynamic power consumed by the damaged wing is $38%$ larger than that by the intact wing, i.e., the energy distribution between the damaged and intact wings is highly asymmetrical; this may greatly increase the muscle wastage of the damaged side.

The added mass forces of three-dimensional (3D) flapping wings of some representative insects, and the accuracy of the often used simple two-dimensional (2D) method, are studied. The added mass force of a flapping wing is calculated by both 3D and 2D methods, and the total aerodynamic force of the wing is calculated by the CFD method. Our findings are as following. The added mass force has a significant contribution to the total aerodynamic force of the flapping wings during and near the stroke reversals, and the shorter the stroke amplitude is, the larger the added mass force becomes. Thus the added mass force could not be neglected when using the simple models to estimate the aerodynamics force, especially for insects with relatively small stroke amplitudes. The accuracy of the often used simple 2D method is reasonably good: when the aspect ratio of the wing is greater than about 3.3, error in the added mass force calculation due to the 2D assumption is less than 9%; even when the aspect ratio is 2.8 (approximately the smallest for an insect), the error is no more than 13%.

The smallest flying insects commonly possess bristled wings and use drag to provide flight forces. A bristled wing, with a wing area about 10% of that of a flat-plate wing, operating at the relevant Reynolds number of 5–15, produces a drag close to the plate wing. How this is done is not well understood. Here, detailed flows around each of the bristles are investigated numerically using simple model wings, and the following results are shown. (1) The drag production mechanism of the bristled wing is different from that of the plate wing: For the plate wing, the flow is blocked by the wing, giving a small positive pressure on the windward surface, and there exists a pair of weak vortices on the wing back, giving a small negative pressure on the leeward surface; the drag is due to the pressure forces (the frictional stress has almost no contribution). For the bristled wing, each bristle operates in a creeping flow and produces thick and strong shear layers. Strong viscous force generates a very large pressure difference between the windward and leeward surfaces of each bristle and very large frictional stress on the bristle surface, resulting in a large drag on each bristle, and the drag is equally contributed by the pressure and frictional forces. (2) Due to the flow-interference effect, when the bristle number reaches a certain value, a further increase in bristles has little effect on force production but has the disadvantage of increasing wing mass; this means that for a bristled wing of miniature insects, the distribution density of the bristles will not be too large, which agrees with observations.

As a very basic flight mode, ascending flight is obviously of great importance to all kinds of manmade and natural fliers. Yet, for the most commonly seen fliers - insects, researches on this flight mode are rare. In this paper, we combined both experimental measurements and numerical simulations to investigate the kinematical characteristics, aerodynamic performance and power requirement of ascending flight in fruit flies (Drosophila virilis). The flies ascend at an advance ratio of about 0.12. The most significant characteristic of ascending flight is larger stroke amplitude compared to hovering, while the other kinematics is very similar. From an aerodynamics point of view, this increased stroke amplitude is needed to overcome the negative effects of “downwash flow”, caused by the upward motion of the fly. Same as hovering, the ascending fruit flies utilize delayed stall and fast pitching-up mechanisms to generate the majority of the lift required for balancing the weight and body drag. By using a larger stroke-amplitude to overcome the negative effects of “downwash flow”, larger energy cost (about 20%) than that of equivalent hovering is required.

Miniature insects fly at very low Reynolds number (Re); low Re means large viscous effect. If flapping as larger insects, sufficient vertical force cannot be produced. We measure the wing kinematics for miniature-insect species of different sizes and compute the aerodynamic forces. The planar upstroke commonly used by larger insects changes to a U-shaped upstroke, which becomes deeper as size or Re decreases. For relatively large miniature insects, the U-shaped upstroke produces a larger vertical force than a planar upstroke by having a larger wing velocity and, for very small ones, the deep U-shaped upstroke produces a large transient drag directed upwards, providing the required vertical force.

The flight of mosquitoes is unusual compared with many other insects, such as fruit-flies and honey bees: mosquitoes fly with their legs spread; they also have rather short stroke amplitude, hence use different aerodynamic mechanisms to produce lift. Could their flight-stability properties be different from those of other insects? Here, we first measured wing kinematics and morphological parameters of two hovering mosquitoes, and then use the method of computational fluid dynamics to compute the aerodynamic derivatives and the techniques of eigenvalue and eigenvector analysis to study their stability properties. We found that their natural-mode structure is the same as that of many other insects: for the longitudinal motion, one unstable oscillatory mode, one stable fast subsidence mode and one stable slow subsidence mode; for the lateral motion: an unstable divergence mode, a stable oscillatory mode and a stable subsidence mode. The different aerodynamic mechanisms of mosquitoes do not change the major aerodynamic derivatives. The spread legs of mosquitoes have great effect on the moments of inertia and make the eigenvalue of the stable lateral mode much smaller. However, the leg-spreading has only a small quantitative effect on the unstable eigenvalues: the magnitudes of the eigenvalues in the two unstable modes, or the growth rate of the disturbances, are reduced by approximately 11%, compared to those calculated without considering the spread legs.

In the development of MAVs, small sized flapping wing designs mimicking insects have appeared recently and lot of studies have been carried out for various aspects of insect flight. The study of aerodynamics of ground effect is an important venue. In this paper CFD studies has been done to simulate the ground effect in hover flight for a rectangular wing. Various heights from very near to the ground till free stream condition where the ground effect is absent are investigated. Incompressible 3D NS equations are numerically solved and results are presented. Aerodynamic vertical force and aerodynamic power variation has been presented. The study indicates that during hover very near to the ground, average vertical force during a wing beat cycle increases largely as compared to its free stream condition in the absence of ground effect. For the typical case taken a 26% increase in average cycle vertical force and 11% decrease in average specific power is noted near the ground. Maximum vertical force increase is found below three quarters of wing length distance from the ground. The ground effect on aerodynamic force or power vanishes after 2.5 times the wing length height above the ground.

Power requirements in vertical flight in the dronefly (Eristarlis tenax; also known as hoverfly) are studied using the method of computational fluid dynamics. The flow solution provides the aerodynamic forces and torques; the inertial torques due to the acceleration of the wing-mass are computed analytically. From the aerodynamic and inertial torques, the mechanical power is obtained. It has been shown that at hovering flight, the specific power with 100% elastic energy storage is 43.51 W·kg−1 and that without elastic energy storage is 60.12 W·kg−1. During vertical flight, the specific power increases with the ascending ratio K (ratio of the ascending velocity to the tip velocity); it is proportional to K to the power of about 1.37. When flying upward at an ascending ratio of about 0.3, the power required is the same as that when the insect carries a load of about 50% of its weight.

Insects can hover, fly forward, climb, and descend with ease while demonstrating amazing stability, and they can also maneuver in impressive ways as no other organisms can. Is their flight inherently stable? If so, how can they maneuver so well? In recent years, significant progress has been made in revealing the dynamic flight stability and flight control mechanisms of insects and has partially answered these questions. Here the most recent advances in this active area are reviewed. The aim is to provide the background necessary to do research in the area and raise questions that need to be addressed in the future. This review begins with an overview of the flapping kinematics and aerodynamics of insect flight. It is followed by a summary of the governing equations of insect motion and the simplified theoretical models used for analysis of dynamic stability and control. Next, the stability properties of hovering flight and forward flight are scrutinized. Then the flight control properties are explored, dealing in turn with flight stabilization control, steady-state control for changing from hovering to forward flight and from one forward-flight speed to another, and control for maneuvers near hovering. Finally, remarks are given on the state of the art of this research field and speculation is made on its outlook in the near future.

The longitudinal dynamic flight stability of a model dragonfly at hovering flight is studied, using the method of computational fluid dynamics to compute the stability derivatives and the techniques of eigenvalue and eigenvector analysis for solving the equations of motion. Three natural modes of motion are identified for the hovering flight: one unstable oscillatory mode, one stable fast subsidence mode and one stable slow subsidence mode. The flight is dynamically unstable owing to the unstable oscillatory mode. The instability is caused by a pitch-moment derivative with respect to horizontal velocity. The damping force and moment derivatives (with respect to horizontal and vertical velocities and pitch-rotational velocity, respectively) weaken the instability considerably. The aerodynamic interaction between the forewing and the hindwing does not have significant effect on the stability properties. The dragonfly has similar stability derivatives, hence stability properties, to that of a one-wing-pair insect at normal hovering, but there are differences in how the derivatives are produced because of the highly inclined stroke plane of the dragonfly.

The aerodynamic interactions between the body and the wings of a model insect in forward flight and maneuvers are studied using the method of numerically solving the Navier-Stokes equations over moving overset grids. Three cases are considered, including a complete insect, wing pair only and body only. By comparing the results of these cases, the interaction effect between the body and the wing pair can be identified. The changes in the force and moment coefficients of the wing pair due to the presence of the body are less than 4.5% of the mean vertical force coefficient of the model insect; the changes in the aerodynamic force coefficients of the body due to the presence of the wings are less than 5.0% of the mean vertical force coefficient of the model insect. The results of this paper indicate that in studying the aerodynamics and flight dynamics of a flapping insect in forward flight or maneuver, separately computing (or measuring) the aerodynamic forces and moments on the wing pair and on the body could be a good approximation.

The forward flight of a model butterfly was studied by simulation using the equations of motion coupled with the Navier-Stokes equations. The model butterfly moved under the action of aerodynamic and gravitational forces, where the aerodynamic forces were generated by flapping wings which moved with the body, allowing the body oscillations of the model butterfly to be simulated. The main results are as follows: (1) The aerodynamic force produced by the wings is approximately perpendicular to the long-axis of body and is much larger in the downstroke than in the upstroke. In the downstroke the body pitch angle is small and the large aerodynamic force points up and slightly backward, giving the weight-supporting vertical force and a small negative horizontal force, whilst in the upstroke, the body angle is large and the relatively small aerodynamic force points forward and slightly downward, giving a positive horizontal force which overcomes the body drag and the negative horizontal force generated in the downstroke. (2) Pitching oscillation of the butterfly body plays an equivalent role of the wing-rotation of many other insects. (3) The body-massspecific power of the model butterfly is 33.3 W/kg, not very different from that of many other insects, e.g., fruitflies and dragonflies.

In the present paper, the controlled flight of fruitflies after voluntary takeoff is studied. Wing and body kinematics of the insects after takeoff are measured using high-speed video techniques, and the aerodynamic force and moment are calculated by the computational fluid dynamics method based on the measured data. How the control moments are generated is analyzed by correlating the computed moments with the wing kinematics. A fruit-fly has a large pitch-up angular velocity owing to the takeoff jump and the fly controls its body attitude by producing pitching moments. It is found that the pitching moment is produced by changes in both the aerodynamic force and the moment arm. The change in the aerodynamic force is mainly due to the change in angle of attack. The change in the moment arm is mainly due to the change in the mean stroke angle and deviation angle, and the deviation angle plays a more important role than the mean stroke angle in changing the moment arm (note that change in deviation angle implies variation in the position of the aerodynamic stroke plane with respect to the anatomical stroke plane). This is unlike the case of fruitflies correcting pitch perturbations in steady free flight, where they produce pitching moment mainly by changes in mean stroke angle.

Wing-motion of hovering small fly Liriomyza sativae was measured using high-speed video and flows of the wings calculated numerically. The fly used high wingbeat frequency (≈265 Hz) and large stroke amplitude (≈182°); therefore, even if its wing-length (R) was small (R ≈ 1.4 mm), the mean velocity of wing reached ≈1.5 m/s, the same as that of an average-size insect (R ≈ 3 mm). But the Reynolds number (Re) of wing was still low (≈40), owing to the small wing-size. In increasing the stroke amplitude, the outer parts of the wings had a “clap and fling” motion. The mean-lift coefficient was high, ≈1.85, several times larger than that of a cruising airplane. The partial “clap and fling” motion increased the lift by ≈7%, compared with the case of no aerodynamic interaction between the wings. The fly mainly used the delayed stall mechanism to generate the high-lift. The lift-to-drag ratio is only 0.7 (for larger insects, Re being about 100 or higher, the ratio is 1–1.2); that is, although the small fly can produce enough lift to support its weight, it needs to overcome a larger drag to do so.

Because of the periodically varying aerodynamic and inertial forces of the flapping wings, a hovering or constant-speed flying insect is a cyclically forcing system, and, generally, the flight is not in a fixed-point equilibrium, but in a cyclic-motion equilibrium. Current stability theory of insect flight is based on the averaged model and treats the flight as a fixed-point equilibrium. In the present study, we treated the flight as a cyclic-motion equilibrium and used the Floquet theory to analyse the longitudinal stability of insect flight. Two hovering model insects were considered—a dronefly and a hawkmoth. The former had relatively high wingbeat frequency and small wing-mass to body-mass ratio, and hence very small amplitude of body oscillation; while the latter had relatively low wingbeat frequency and large wing-mass to body-mass ratio, and hence relatively large amplitude of body oscillation. For comparison, analysis using the averaged-model theory (fixed-point stability analysis) was also made. Results of both the cyclic-motion stability analysis and the fixed-point stability analysis were tested by numerical simulation using complete equations of motion coupled with the Navier–Stokes equations. The Floquet theory (cyclic-motion stability analysis) agreed well with the simulation for both the model dronefly and the model hawkmoth; but the averaged-model theory gave good results only for the dronefly. Thus, for an insect with relatively large body oscillation at wingbeat frequency, cyclic-motion stability analysis is required, and for their control analysis, the existing well-developed control theories for systems of fixed-point equilibrium are no longer applicable and new methods that take the cyclic variation of the flight dynamics into account are needed.

In this paper, we study the aerodynamic interactions between the contralateral wings and between the body and wings of a model insect, when the insect is hovering and has various translational and rotational motions, using the method numerically solving the Navier-Stokes equations over moving overset grids. The aerodynamic interactional effects are identified by comparing the results of a complete model insect, the corresponding wing pair, single wing and body without the wings. Horizontal, vertical and lateral translations and roll, pitch and yaw rotations at small speeds are considered. The results indicate that for the motions considered, both the interaction between the contralateral wings and the interaction between the body and wings are weak. The changes in the forces and moments of a wing due to the contralateral wing interaction, of the wings due to the presence of the body, and of the body due to the presence of the wings are generally less than 4.5%. Results show that aerodynamic forces of wings and body can be measured or computed separately in the analysis of flight stability and control of hovering insects.

We have examined the aerodynamic effects of corrugation in model wings that closely mimic the wing movements of a forward flight bumblebee using the method of computational fluid dynamics. Various corrugated wing models were tested (care was taken to ensure that the corrugation introduced zero camber). Advance ratio ranging from 0 to 0.57 was considered. The results shown that at all flight speeds considered, the time courses of aerodynamic force of the corrugated wing are very close to those of the flat-plate wing. The corrugation decreases aerodynamic force slightly. The changes in the mean location of center of pressure in the spanwise and chordwise directions resulting from the corrugation are no more than 3% of the wing chord length. The possible reason for the small aerodynamic effects of wing corrugation is that the wing operates at a large angle of attack and the flow is separated: the large angle of incidence dominates the corrugation in determining the flow around the wing, and for separated flow, the flow is much less sensitive to wing shape variation.

SUMMARY We have examined the aerodynamic effects of corrugation in model insect wings that closely mimic the wing movements of hovering insects. Computational fluid dynamics were used with Reynolds numbers ranging from 35 to 3400, stroke amplitudes from 70 to 180 deg and mid-stroke angles of incidence from 15 to 60 deg. Various corrugated wing models were tested (care was taken to ensure that the corrugation introduced zero camber). The main results are as follows. At typical mid-stroke angles of incidence of hovering insects (35–50 deg), the time courses of the lift, drag, pitching moment and aerodynamic power coefficients of the corrugated wings are very close to those of the flat-plate wing, and compared with the flat-plate wing, the corrugation changes (decreases) the mean lift by less than 5% and has almost no effect on the mean drag, the location of the center of pressure and the aerodynamic power required. A possible reason for the small aerodynamic effects of wing corrugation is that the wing operates at a large angle of incidence and the flow is separated: the large angle of incidence dominates the corrugation in determining the flow around the wing, and for separated flow, the flow is much less sensitive to wing shape variation. The present results show that for hovering insects, using a flat-plate wing to model the corrugated wing is a good approximation.

Hovering insects require a rather large lift coefficient. Many insects hover with a large stroke amplitude (120°-170°), and it has been found that the high lift is mainly produced by the delayed-stall mechanism. However, some insects hover with a small stroke amplitude (e.g., 65°). The delayed-stall mechanism might not work for these insects because the wings travel only a very short distance in a stroke, and other aerodynamic mechanisms must be operating. Here we explore the aerodynamic mechanisms of a hoverfly hovering with an inclined stroke plane and a small stroke amplitude (65.6°). The Navier-Stokes equations are numerically solved to give the flows and forces and the theory of vorticity dynamics used to reveal the aerodynamic mechanisms. The majority of the weight-supporting vertical force is produced in the mid portion of the downstroke, a short period (about 26% of the stroke cycle) in which the vertical force coefficient is larger than 4. The force is produced using a new mechanism, the “paddlin...

D RAGONFLIES are accomplished fliers. Scientists have always been fascinated by theirflight. Experimental and computational studies on a single airfoil in dragonfly hovering mode were conducted by Freymuth [1] and Wang [2], respectively. They showed that large vertical force was produced during each downstroke. In each downstroke, a vortex pair was created; the large vertical force was explained by the downward two-dimensional jet induced by the vortex pair [2]. Recently, due to the advances in computational and experimental techniques and facilities, researchers are beginning to study dragonfly aerodynamics and forewing–hindwing interactions using three-dimensional model wings [3–5]. Sun and Lan [3] studied the aerodynamics and the forewing–hindwing interaction of a dragonfly in hover flight, using the method of computational fluid dynamics (CFD). Maybury and Lehmann [4] and Yamamoto and Isogai [5] conducted experimental studies on the forewing–hindwing interaction at hovering conditions. Wang and Sun [6] extended the computational study of Sun and Lan [3] to the case of forward flight. Inmost of these studies, only hovering flight was considered. Only Wang and Sun [6] investigated the effects of forward flight speed, but the investigation was limited to a few phase differences ( d 0, 60, 90, and 180 deg; d denotes the difference in phase angle between the forewing and the hindwing stroke cycles, positive when the hindwing leads the forewing and negative when the forewing leads the hindwing). Because the distance of a wing from the wake of another wing depends on the flight speed and the relative motion of the foreand hindwings, it is expected that the forewing–hindwing interaction is strongly influenced by the flight speed and the relative phase difference. Therefore, it is desirable to study the forewing–hindwing interaction by systematically varying the flight speed and the phase angle. Moreover, in the above studies [3–6], attention was mainly paid on whether or not the aerodynamic forces were changed by the forewing–hindwing interaction, while how the interaction occurred was not well understood. It is of interest tomake further investigation on the flow field of the wing wake to reveal how the forewing– hindwing interaction occurs. In the present study, we address the above questions by numerical simulation of the flows of model dragonfly wings. The phasing and the flight speed are systematically varied. Advance ratio (the nondimensional flight speed) ranges form 0 to 0.6. At each advance ratio, eight phase differences, 180, 135, 90, 45, 0, 45, 90, and 135 deg, are considered.

SUMMARYThe aerodynamics and forewing-hindwing interaction of a model dragonfly in forward flight are studied, using the method of numerically solving the Navier-Stokes equations. Available morphological and stroke-kinematic parameters of dragonfly (Aeshna juncea) are used for the model dragonfly. Six advance ratios (J; ranging from 0 to 0.75) and, at each J, four forewing-hindwing phase angle differences(γd; 180°, 90°, 60° and 0°) are considered. The mean vertical force and thrust are made to balance the weight and body-drag, respectively, by adjusting the angles of attack of the wings, so that the flight could better approximate the real flight.At hovering and low J (J=0, 0.15), the model dragonfly uses separated flows or leading-edge vortices (LEV) on both the fore- and hindwing downstrokes; at medium J (J=0.30, 0.45), it uses the LEV on the forewing downstroke and attached flow on the hindwing downstroke; at high J (J=0.6, 0.75), it uses attached flows on both fore- and hindwing downstrokes. (The upstrokes are very lightly loaded and, in general, the flows are attached.)At a given J, at γd=180°, there are two vertical force peaks in a cycle, one in the first half of the cycle, produced mainly by the hindwing downstroke, and the other in the second half of the cycle, produced mainly by the forewing downstroke; atγ d=90°, 60° and 0°, the two force peaks merge into one peak. The vertical force is close to the resultant aerodynamic force[because the thrust (or body-drag) is much smaller than vertical force (or the weight)]. 55-65% of the vertical force is contributed by the drag of the wings.The forewing-hindwing interaction is detrimental to the vertical force (and resultant force) generation. At hovering, the interaction reduces the mean vertical force (and resultant force) by 8-15%, compared with that without interaction; as J increases, the reduction generally decreases (e.g. at J=0.6 and γd=90°, it becomes 1.6%). A possible reason for the detrimental interaction is as follows: each of the wings produces a mean vertical force coefficient close to half that needed for weight support, and a downward flow is generated in producing the vertical force; thus, in general, a wing moves in the downwash-velocity field induced by the other wing, reducing its aerodynamic forces.

SUMMARY A computational fluid-dynamic analysis was conducted to study the unsteady aerodynamics of a model fruit fly wing. The wing performs an idealized flapping motion that emulates the wing motion of a fruit fly in normal hovering flight. The Navier–Stokes equations are solved numerically. The solution provides the flow and pressure fields, from which the aerodynamic forces and vorticity wake structure are obtained. Insights into the unsteady aerodynamic force generation process are gained from the force and flow-structure information. Considerable lift can be produced when the majority of the wing rotation is conducted near the end of a stroke or wing rotation precedes stroke reversal (rotation advanced), and the mean lift coefficient can be more than twice the quasi-steady value. Three mechanisms are responsible for the large lift: the rapid acceleration of the wing at the beginning of a stroke, the absence of stall during the stroke and the fast pitching-up rotation of the wing near the end of the stroke. When half the wing rotation is conducted near the end of a stroke and half at the beginning of the next stroke (symmetrical rotation), the lift at the beginning and near the end of a stroke becomes smaller because the effects of the first and third mechanisms above are reduced. The mean lift coefficient is smaller than that of the rotation-advanced case, but is still 80 % larger than the quasi-steady value. When the majority of the rotation is delayed until the beginning of the next stroke (rotation delayed), the lift at the beginning and near the end of a stroke becomes very small or even negative because the effect of the first mechanism above is cancelled and the third mechanism does not apply in this case. The mean lift coefficient is much smaller than in the other two cases.

Here, we present a detailed analysis of the take-off mechanics in droneflies performing voluntary take-offs. Wing and body kinematics of the insects during take-off were measured using high-speed video techniques. Based on the measured data, the inertia force acting on the insect was computed and the aerodynamic force of the wings was calculated by the method of computational fluid dynamics. Subtracting the aerodynamic force and the weight from the inertia force gave the leg force. In take-off, a dronefly increases its stroke amplitude gradually in the first 10–14 wingbeats and becomes airborne at about the 12th wingbeat. The aerodynamic force increases monotonously from zero to a value a little larger than its weight, and the leg force decreases monotonously from a value equal to its weight to zero, showing that the droneflies do not jump and only use aerodynamic force of flapping wings to lift themselves into the air. Compared with take-offs in insects in previous studies, in which a very large force (5–10 times of the weight) generated either by jumping legs (locusts, milkweed bugs and fruit flies) or by the ‘fling’ mechanism of the wing pair (butterflies) is used in a short time, the take-off in the droneflies is relatively slow but smoother.

We investigated the aerodynamic effects of wing deformation and corrugation of a three-dimensional model hoverfly wing at a hovering condition by solving the Navier-Stokes equations on a dynamically deforming grid. Various corrugated wing models were tested. Insight into whether or not there existed significant aerodynamic coupling between wing deformation (camber and twist) and wing corrugation was obtained by comparing aerodynamic forces of four cases: a smooth-plate wing in flapping motion without deformation (i.e. a rigid flat-plate wing in flapping motion); a smooth-plate wing in flapping motion with deformation; a corrugated wing in flapping motion without deformation (i.e. a rigid corrugated wing in flapping motion); a corrugated wing in flapping motion with deformation. There was little aerodynamic coupling between wing deformation and corrugation: the aerodynamic effect of wing deformation and corrugation acting together was approximately a superposition of those of deformation and corrugation acting separately. When acting alone, the effect of wing deformation was to increase the lift by 9.7% and decrease the torque (or aerodynamic power) by 5.2%, and that of wing corrugation was to decrease the lift by 6.5% and increase the torque by 2.2%. But when acting together, the wing deformation and corrugation only increased the lift by ~3% and decreased the torque by ~3%. That is, the combined aerodynamic effect of deformation and corrugation is rather small. Thus, wing corrugation is mainly for structural, not aerodynamic, purpose, and in computing or measuring the aerodynamic forces, using a rigid flat-plate wing to model the corrugated deforming wing at hovering condition can be a good approximation.

SUMMARYThe time courses of wing and body kinematics of three freely hovering droneflies (Eristalis tenax) were measured using 3D high-speed video,and the morphological parameters of the wings and body of the insects were also measured. The measured wing kinematics was used in a Navier–Stokes solver to compute the aerodynamic forces and moments acting on the insects. The time courses of the geometrical angle of attack and the deviation angle of the wing are considerably different from that of fruit flies recently measured using the same approach. The angle of attack is approximately constant in the mid portions of a half-stroke (a downstroke or upstroke) and varies rapidly during the stroke reversal. The deviation angle is relatively small and is higher at the beginning and the end of a half-stroke and lower at the middle of the half-stroke, giving a shallow U-shaped wing-tip trajectory. For all three insects considered, the computed vertical force is approximately equal to the insect weight (the difference is less than 6% of the weight) and the computed horizontal force and pitching moment about the center of mass of the insect are approximately zero. The computed results satisfying the equilibrium flight conditions, especially the moment balance condition, validate the computation model. The lift principle is mainly used to produce the weight-supporting vertical force, unlike the fruit flies who use both lift and drag principles to generate the vertical force; the vertical force is mainly due to the delayed stall mechanism. The magnitude of the inertia power is larger than that of the aerodynamic power, and the largest possible effect of elastic storage amounts to a reduction of flight power by around 40%, much larger than in the case of the fruit fly.

Recently, much progress has been made in revealing aerodynamic force mechanisms and predicting power requirements in insect flight. In this study we have experimentally measured the wing kinematics of a hovering hoverfly (Episyrphus balteatus) and numerically analyzed the flapping mechanism of it. Using multi-digital high speed cameras, we photographed the continuous images of flapping wings and body from different viewpoints, and then we captured kinematics data and modeled the flight motion of the hovering hoverfly. Three-dimensional unsteady computations of the flow past the hoverfly under hovering flight conditions prescribed from above experimental observations were computed. The computed time average force and moment coefficients were validated with expected equilibrium values and were in well agreement. The computational result shows that the major part of the mean lift comes from the mid-portions of the down- and upstrokes.

SUMMARYAerodynamic force generation and power requirements in forward flight in a fruit fly with modeled wing motion were studied using the method of computational fluid dynamics. The Navier-Stokes equations were solved numerically. The solution provided the flow velocity and pressure fields, from which the vorticity wake structure and the unsteady aerodynamic forces and torques were obtained (the inertial torques due to the acceleration of the wing-mass were computed analytically). From the flow-structure and force information, insights were gained into the unsteady aerodynamic force generation. On the basis of the aerodynamic and inertial torques, the mechanical power was obtained, and its properties were investigated.The unsteady force mechanisms revealed previously for hovering (i.e. delayed stall, rapid acceleration at the beginning of the strokes and fast pitching-up rotation at the end of the strokes) apply to forward flight. Even at high advance ratios, e.g. J=0.53-0.66 (J is the advance ratio), the leading edge vortex does not shed (at such advance ratios, the wing travels approximately 6.5 chord lengths during the downstroke).At low speeds (J≈0.13), the lift (vertical force) for weight support is produced during both the down- and upstrokes (the downstroke producing approximately 80% and the upstroke producing approximately 20% of the mean lift), and the lift is contributed mainly by the wing lift; the thrust that overcomes the body drag is produced during the upstroke, and it is contributed mainly by the wing drag. At medium speeds (J≈0.27),the lift is mainly produced during the downstroke and the thrust mainly during the upstroke; both of them are contributed almost equally by the wing lift and wing drag. At high speeds (J≈0.53), the lift is mainly produced during the downstroke and is mainly contributed by the wing drag; the thrust is produced during both the down- and upstrokes, and in the downstroke, is contributed by the wing lift and in the upstroke, by the wing drag.In forward flight, especially at medium and high flight speeds, the work done during the downstroke is significantly greater than during the upstroke. At advance ratios J≈0.13, 0.27 and 0.53, the work done during the downstroke is approximately 1.6, 2.8 and 4.2 times as much as that during the upstroke, respectively.At J=0 (hovering), the body-mass-specific power is approximately 29 W kg-1; at J=0.13 and 0.27, the power is approximately 10% less than that of hovering; at J=0.40, the power is approximately the same as that of hovering; when J is further increased, the power increases sharply. The graph of power against flying speeds is approximately J-shaped.From the graph of power against flying speeds, it is predicted that the insect usually flies at advance ratios between zero and 0.4, and for fast flight, it would fly at an advance ratio between 0.4 and 0.53.