We measure the wing kinematics and morphological parameters of seven freely hovering fruitflies and numerically compute the flows of the flapping wings. The computed mean lift approximately equals to the measured weight and the mean horizontal force is approximately zero, validating the computational model. Because of the very small relative velocity of the wing, the mean lift coefficient required to support the weight is rather large, around 1.8, and the Reynolds number of the wing is low, around 100. How such a large lift is produced at such a low Reynolds number is explained by combining the wing motion data, the computed vortical structures, and the theory of vorticity dynamics. It has been shown that two unsteady mechanisms are responsible for the high lift. One is referred as to "fast pitching-up rotation": at the start of an up-or downstroke when the wing has very small speed, it fast pitches down to a small angle of attack, and then, when its speed is higher, it fast pitches up to the angle it normally uses. When the wing pitches up while moving forward, large vorticity is produced and sheds at the trailing edge, and vorticity of opposite sign is produced near the leading edge and on the upper surface, resulting in a large time rate of change of the first moment of vorticity (or fluid impulse), hence a large aerodynamic force. The other is the well known "delayed stall" mechanism: in the mid-portion of the up-or downstroke the wing moves at large angle of attack (about 45 deg) and the leading-edge-vortex (LEV) moves with the wing; thus, the vortex ring, formed by the LEV, the tip vortices, and the starting vortex, expands in size continuously, producing a large time rate of change of fluid impulse or a large aerodynamic force. C 2015 AIP Publishing LLC. [http://dx.dynamic stall vortex (they called it the leading edge vortex, LEV) did not shed in a downstroke or upstroke, even if the wing traveled more than five chord lengths in a downstroke. Their analysis of the momentum imparted to the fluid by the vortex wake showed that the LEV could produce enough lift for weight support. The above studies identified delayed stall (or maintaining the LEV on the wing) as a high-lift mechanism of insects. This was confirmed by subsequent experimental and numerical studies on rotating and flapping wings (e.g., Refs. 6-15). Furthermore, in these studies, 6-15 the development of the LEV was studied in detail and how the LEV attachment was maintained was explained.The wing stroke of an insect is typically divided into four portions: two translations (upstroke translation and downstroke translation) and two rotations around stroke reversal (pronation and supination). 7,16 The above delayed stall mechanism operates during the translational phases. 5,6 Dickinson et al. 7 explored the rotational phases by measuring the aerodynamic forces of a dynamically scaled model fruitfly. On the basis of wing kinematics measured in tethered fruitflies, they assumed the following wing motion pattern: the translational velocity varied accor...

Here, we present a detailed analysis of the wing and body kinematics in drone-flies in free flight over a range of speeds from hovering to about 8.5 m s(-1). The kinematics was measured by high-speed video techniques. As the speed increased, the body angle decreased and the stroke plane angle increased; the wingbeat frequency changed little; the stroke amplitude first decreased and then increased; the ratio of the downstroke duration to the upstroke duration increased; the mean positional angle increased at lower speeds but changed little at speeds above 3 m s(-1). At a speed above about 1.5 m s(-1), wing rotation at supination was delayed and that at pronation was advanced, and consequently the wing rotations were mostly performed in the upstroke. In the downstroke, the relative velocity of the wing increased and the effective angle of attack decreased with speed; in the upstroke, they both decreased with speed at lower speeds, and at higher speeds, the relative velocity became larger but the effective angle of attack became very small. As speed increased, the increasing inclination of the stroke plane ensured that the effective angle of attack in the upstroke would not become negative, and that the wing was in suitable orientations for vertical-force and thrust production.

SUMMARYWe 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.

Corrugation gives an insect-wing the advantages of low mass, high stiffness, and low membrane stress. Researchers are interested to know if it is also advantageous aerodynamically. Previous works reported that corrugation enhanced the aerodynamic performance of wings at gliding flight. However, Reynolds numbers considered in these studies were higher than that of gliding insects. The present study showed that in the Reynolds number range of gliding insects, corrugation had negative aerodynamic effects. We studied aerodynamic effects of corrugation at gliding motion using the method of computational fluid dynamics, in the Reynolds number range of Re = 200–2400. Different corrugation patterns were considered. The effect of corrugation on aerodynamic performance was identified by comparing the aerodynamic forces between the corrugated and flat-plate wings, and the underlying flow mechanisms of the corrugation effects were revealed by analyzing the flow fields and surface pressure distributions. The findings are as follows: (1) the effect of corrugation is to decrease the lift, and change the drag only slightly (at 15°–25° angles of attack, lift is decreased by about 16%; at smaller angles of attack, the percentage of lift reduction is even larger because the lift is small). (2) Two mechanisms are responsible for the lift reduction. One is that the pleats at the lower surface of the corrugated wing produce relatively strong vortices, resulting in local low-pressure regions on the lower surface of the wing. The other is that corrugation near the leading edge pushes the leading-edge-separation layer slightly upwards and increases the size of the separation bubble above the upper surface, reducing the “suction pressure,” or increasing the pressure, on the upper surface.

Previous studies on forward flight stability in insects are for low to medium flight-speeds. In the present work, we investigated the stability problem for the full range of flight speeds (0-8.6 m/s) of a drone-fly. Our results show the following: The longitudinal derivatives due to the lateral motion are approximately 3 orders of magnitude smaller than the other longitudinal derivatives. Thus, we can decouple these two motions of the insect, as commonly done for a conventional airplane. At hovering flight, the motion of the dronefly is weakly unstable owing to two unstable natural modes of motion, a longitudinal one and a lateral one. At low (1.6 m/s) and medium (3.1 m/s) flight-speeds, the unstable modes become even weaker and the flight is approximately neutral. At high flight-speeds (4.6 m/s, 6.9 m/s and 8.6 m/s), the flight becomes more and more unstable due to an unstable longitudinal mode. At the highest flight speed, 8.6 m/s, the instability is so strong that the time constant representing the growth rate of the instability (disturbance-doubling time) is only 10.1 ms, which is close to the sensory reaction time of a fly (approximately 11 ms). This indicates that strong instability may play a role in limiting the flight speed of the insect.