SUMMARYMost hovering insects flap their wings in a horizontal plane (body having a large angle from the horizontal), called 'normal hovering'. But some of the best hoverers, e.g. true hoverflies, hover with an inclined stroke plane (body being approximately horizontal). In the present paper, wing and body kinematics of four freely hovering true hoverflies were measured using threedimensional high-speed video. The measured wing kinematics was used in a Navier-Stokes solver to compute the aerodynamic forces of the insects. The stroke amplitude of the hoverflies was relatively small, ranging from 65 to 85deg, compared with that of normal hovering. The angle of attack in the downstroke (~50deg) was much larger that in the upstroke (~20deg), unlike normalhovering insects, whose downstroke and upstroke angles of attack are not very different. The major part of the weight-supporting force (approximately 86%) was produced in the downstroke and it was contributed by both the lift and the drag of the wing, unlike the normal-hovering case in which the weight-supporting force is approximately equally contributed by the two half-strokes and the lift principle is mainly used to produce the force. The mass-specific power was 38.59-46.3 and 27.5-35.4Wkg -1 in the cases of 0 and 100% elastic energy storage, respectively. Comparisons with previously published results of a normal-hovering true hoverfly and with results obtained by artificially making the insects' stroke planes horizontal show that for the true hoverflies, the power requirement for inclined stroke-plane hover is only a little (<10%) larger than that of normal hovering. Supplementary material available online at

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.

Tiny insects with bristled wings perform the “rowing” motion: the wings accelerate rapidly from zero-velocity to certain reference velocity at 90° angle-of-attack, and the drag produced in this motion provides the weight-supporting force. A flat-plate wing will produce a large drag in such a motion, but it is unknown whether a bristled wing could do so. Here, we study this problem using numerical simulation and simple model wings. The acceleration is large: the wing translates only about half the wing chord length to reach the reference velocity. The following is shown. The bristled wing can produce a very large unsteady drag peak and large time-averaged drag as a flat-plate wing does; the time-averaged drag is about 2.5 times as large as the quasi-steady value. The force production mechanisms are different between the two wings: for the flat-plate wing, because of the large acceleration, the added-mass and the strong free vorticity in the flow produce a large pressure difference between the windward and leeward surfaces of the plate, resulting in large drag (surface frictional force has negligible contribution). Yet for the bristled wing, although the acceleration of the wing is large, a bristle needs to translate about 80 diameters to reach the reference velocity; thus, the effect of acceleration is very weak. Each bristle operates in a quasi-steady Stokes flow and the large drag of the bristled wing is due to the very large surface pressure and frictional forces on each bristle, generated by the strong viscous effect of the Stokes flow (the drag is equally contributed by the surface pressure and frictional forces).

Most of the smallest flying insects use bristled wings. It was observed that during the second half of their upstroke, the left and right wings become parallel and close to each other at the back, and move upward at zero angle of attack. In this period, the wings may produce drag (negative vertical force) and side forces which tend to push two wings apart. Here we study the aerodynamic forces and flows of two simplified bristled wings experiencing such a motion, compared with the case of membrane wings (flat-plate wings), to see if there is any advantage in using the bristled wings. The method of computational fluid dynamics is used in the study. The results are as follows. In the motion of two bristled wings, the drag acting on each wing is 40% smaller than the case of a single bristled wing conducting the same motion, and only a very small side force is produced. But in the case of the flat-plate wings, although there is similar drag reduction, the side force on each wing is larger than that of the bristled wing by an order of magnitude (the underlying physical reason is discussed in the paper). Thus, if the smallest insects use membrane wings, their flight muscles need to overcome large side forces in order to maintain the intended motion for less negative lift, whereas using bristled wings do not have this problem. Therefore, the adoption of bristled wings can be beneficial during upward movement of the wings near the end of the upstroke, which may be one reason why most of the smallest insects adopt them.