Very small insects use novel wing flapping and drag principle to generate the weight-supporting vertical force

Abstract

The effect of air viscosity on the flow around an insect wing increases as insect size decreases. For the smallest insects (wing length R below 1 mm), the viscous effect is so large that lift-generation mechanisms used by their larger counterparts become ineffective. How the weight-supporting vertical force is generated is unknown. To elucidate the aerodynamic mechanisms responsible, we measure the wing kinematics of the tiny wasp Encarsia formosa (0.6 mm R) in hovering or very slow ascending flight and compute and analyze the aerodynamic forces. We find that the insects perform two unusual wing-motions. One is "rowing": the wings move fast downward and backward, like stroking oars; the other is the previously discovered Weis-Fogh 'fling'. The rowing produces 70% of the required vertical force and the Weis-Fogh 'fling' the other 30%. The oaring wing mainly produces an approximately up-pointing drag, resulting in the vertical force. Because each oaring produces a starting flow, the drag is unsteady in nature and much greater than that in steady motion at the same velocities and angles of attack. Furthermore, our computation shows that if the tiny wasps employed the usual wing kinematics of the larger insects (flapping back and forth in a horizontal plane), vertical force produced would be only 1/3 of that by the real wing kinematics; i.e. they must use the special wing movements to overcome the problem of large viscous effects encountered by the commonly used flapping kinematics. We for the first time observe very small insects using drag to support their weight and explain how a net vertical force is generated when the drag principle is applied.Although the wing of an insect beats at high frequency (usually above 100 Hz), the velocity of the wing relative the undisturbed air is small, owing to the small wing-length. As a result, the vertical force coefficient of the wing required to balance the weight is relatively high; the mean vertical force coefficient required is around 2

Aerodynamic performance of a bristled wing of a very small insect

“…An idealized twodimensional computational study (Jones et al 2015) demonstrated such possibility of drag-based mean force generation by a cyclic motion of a flat plate. Three-dimensional numerical simulations of Encarsia formosa (Cheng and Sun 2018) and thrips Frankliniella occidentalis (Lyu et al 2019) with realistic wing kinematics also show cycle-average forces sufficient for body weight support, under the assumption that the wings are impermeable plates. However, until now, the force-generation capacity and aerodynamic function of the bristled wing morphology remains a largely open question.…”

“…The drag-based flight mode in insects (Jones et al 2015) requires reciprocating motion of the wings: the drag should be larger when the wings move down than when they move up. It can be referred to as the "rowing mechanism" (Cheng and Sun 2018;Lyu et al 2019), for its similarity with swimming or paddling action that was already noticed in an early work by Horridge (1956).…”

“…thrips (Thysanoptera). They are active fliers, which implies that bristled wings produce enough force to support the animal body weight and propel it through the air (Yavorskaya et al 2019;Cheng and Sun 2018;Zhao et al 2019). Considering the bristled morphology as a biological adaptation, it is important to look into the potential benefits and penalties from the mechanical standpoint.…”

“…Kuethe (1975) extended upon the idea about the key role of elastic deformation. However, recent high-speed videography in free flight, e.g., of a featherwing beetle Nephanes titan (Yavorskaya et al 2019), a chalcid wasp Encarsia formosa (Cheng and Sun 2018) and a thrips (Zhao et al 2019;Lyu et al 2019) shows large variation in the wing orientation during one stroke cycle, and relatively little bending of the setae.…”

Forward flight stability in a drone-fly

“…Moving overset grids are employed owing to the relative motion of the wings and body. The flow solver is the same as that employed in several previous works of our group 14,19,20 and the description of the method is presented in the Supplementary Material, Supplementary S1. Tests of the computational grid are also given in the Supplementary Material, Supplementary S2.…”