Short-amplitude high-frequency wing strokes determine the aerodynamics of honeybee flight

Abstract

Most insects are thought to fly by creating a leading-edge vortex that remains attached to the wing as it translates through a stroke. In the species examined so far, stroke amplitude is large, and most of the aerodynamic force is produced halfway through a stroke when translation velocities are highest. Here we demonstrate that honeybees use an alternative strategy, hovering with relatively low stroke amplitude (Ϸ90°) and high wingbeat frequency (Ϸ230 Hz). When measured on a dynamically scaled robot, the kinematics of honeybee wings generate prominent force peaks during the beginning, middle, and end of each stroke, indicating the importance of additional unsteady mechanisms at stroke reversal. When challenged to fly in low-density heliox, bees responded by maintaining nearly constant wingbeat frequency while increasing stroke amplitude by nearly 50%. We examined the aerodynamic consequences of this change in wing motion by using artificial kinematic patterns in which amplitude was systematically increased in 5°increments. To separate the aerodynamic effects of stroke velocity from those due to amplitude, we performed this analysis under both constant frequency and constant velocity conditions. The results indicate that unsteady forces during stroke reversal make a large contribution to net upward force during hovering but play a diminished role as the animal increases stroke amplitude and flight power. We suggest that the peculiar kinematics of bees may reflect either a specialization for increasing load capacity or a physiological limitation of their flight muscles.bee flight ͉ flight in heliox ͉ stroke amplitude ͉ unsteady mechanisms ͉ wingbeat kinematics I n 1934, August Magnan and André Sainte-Lague (1) concluded from a simple mathematical analysis that the flight of bees was ''impossible.'' Since this time, bees have symbolized both the inadequacy of aerodynamic theory as applied to animals and the hubris with which theoreticians analyze the natural world. Although the assumptions used by Magnan and SainteLague have since proven erroneous (2), conventional fixed-wing aerodynamic theory is indeed insufficient to explain the flapping flight of bees and other small insects. In particular, the performance of insect wings, when tested under steady conditions in wind tunnels, is too low to account for the forces required to sustain flight (3). However, a number of more recent studies have demonstrated that wings perform much better when started from rest or rotated continuously around their base (4-6) due to the formation of a leading-edge vortex (LEV). Instead of shedding to initiate stall, the LEV remains attached throughout each stroke, presumably because of the transport of vorticity by span-wise flow (7-9). Whereas the delayed stall forces are greatest at midstroke, flapping wings generate additional forces during stroke reversals. These forces, which result from the rapid rotation of the wing, added mass effects, and the influence of the wake shed from previous strokes, are very sensitive to the precise p...

Scaling law and enhancement of lift generation of an insect-size hovering flexible wing

“…When k is lowered, the aerodynamic force induced by vorticity in the flow field, such as translational forces (equation (B 2)) and nonlinear wing-wake interactions [3,4], starts to dominate the lift [22,23]. These nonlinearities in the unsteady aerodynamics lead to intriguing consequences caused by small differences in the resulting nonlinear wing motion and the camber deformation, which will be discussed further in §3.5.…”

“…As g increases, wing deformations become larger and will eventually cause the observed differences. The dependence on k 2 can be explained by considering the relative contribution of the added mass force and the forces induced by the vorticity in the flow field [22,23], which scale as k and 1/k, respectively, for hover [23]. The ratio between these two forces is then k/(1/k) ¼ k 2 [22,23] and the added mass gains its relative contribution to the total lift with increasing k.…”

“…The simple representation a FH in the study of flapping wings is a popular approximation for rigid wings [19,28], despite the observations of hovering fruit flies and honeybees [21,22] using wing strokes that are clearly far from sinusoidal. Similar to the stroke used by these insects, the resulting flexible wing motion significantly deviates from being a sinusoid, depending on the wing properties (figure 5a).…”

“…The superscript asterisk (*) indicates non-dimensional variables. In absence of a freestream in hovering wings, we take the maximum translation velocity U of the flat plate at the LE as the reference velocity, such that U ¼ 2pfh a ¼ 1 [19,22]. Note that reduced frequency in hover becomes a geometric quantity: k ¼ c/(2h a ) [19].…”

“…Moreover, tethered flying Drosophila actively control left/right wing rotation timing to initiate yaw turns [20]. However, hovering fruit flies [21] and honeybees [22], beetles [11] and hymenopterans in general exhibit symmetric rotation [11], which means that they rotate their wings around the same time as they reverse the stroke.…”