Flapping-pattern change in small and very small insects

TL;DR

This study investigates how small and very small insects adapt their wing flapping patterns, shifting from planar to U-shaped upstrokes, to generate sufficient lift in low Reynolds number conditions.

Contribution

It introduces a hypothesis that smaller insects use deeper U-shaped upstrokes to overcome viscous effects, supported by flight data and aerodynamic force calculations.

Findings

U-shaped upstrokes become deeper as insect size or Re decreases

Deeper U-shapes generate larger vertical forces in small insects

Fast downward wing acceleration produces upward-directed transient drag

Abstract

Medium and large insects in normal hovering have horizontal, planar up- and downstrokes1-4. The lift of the two half-strokes, generated by the leading-edge vortex, provides the weight-supporting vertical force. But for small insects (wing length R less than about 4 mm and Reynolds number Re very low, about 80 to 10), because of the large effect of air viscosity (as Re becomes very low, moving in air is like in oil), sufficient vertical force could not be produced if using the above wing kinematics. Small insects must use different flapping mode. Here, through analyzing flight data from our recent studies on a relatively-large small insect (fruitfly: R=3 mm, Re=80) and a very small insect (wasp: R=0.5 mm, Re=10), we put forward a hypothesis on how the flapping pattern will change: as insect-size or Re decreasing, a deeper and deeper U-shape upstroke will be used to overcome the viscous effect. And we test this hypothesis by measuring the wing kinematics for species of different sizes to obtain data for Re ranging from 80 to 10 and by computing the aerodynamic forces. The data and computation support our hypothesis: the planar upstroke changes to U-shape upstroke which becomes deeper as size or Re becomes smaller; for relatively-large small insects, the U-shape upstroke produces a larger vertical force than a planar upstroke by having a larger wing velocity, and for very small insects, the deep U-shape upstroke produces a large transient drag that points almost upwards by fast downward acceleration of the wing, providing the required vertical force.