Lift and power requirements of hovering insect flight

Abstract

Lift and power requirements for hovering flight of eight species of insects are studied by solving the Navier-Stokes equation numerically. The solution provides velocity and pressure fields, from which unsteady aerodynamic forces and moments are obtained. The inertial torque of wing mass are computed analytically. The wing length of the insects ranges from 2 mm (fruit fly) to 52mm (hawkmoth); Reynolds numbersRe (based on mean flapping speed and mean chord length) ranges from 75 to 3 850. The primary findings are shown in the following: (1) Either small (R=2mm,Re=75), medium (R≈10mm,Re≈500) or large (R≈50 mm,Re≈4000) insects mainly employ the same high-lift mechanism, delayed stall, to produce lift in hovering flight. The midstroke angle of attack needed to produce a mean lift equal to the insect weight is approximately in the range of 25° to 45°, which is approximately in agreement with observation. (2) For the small insect (fruit fly) and for the medium and large insects with relatively small wingbeat frequency (cranefly, ladybird and hawkmoth), the specific power ranges from 18 to 39 W·kg−1, the major part of the power is due to aerodynamic force, and the elastic storage of negatige work does not change the specific power greatly. However for medium and large insects with relatively large wingbeat frequency (hoverfly, dronefly, honey bee and bumble bee), the specific power ranges from 39 to 61 W·kg−1, the major part of the power is due to wing inertia, and the elastic storage of negative work can decrease the specific power by approximately 33%. (3) For the case of power being mainly contributed by aerodynamic force (fruit fly, cranefly, ladybird and hawkmoth), the specific power is proportional to the product of the wingbeat frequency, the stroke amplitude, the wing length and the drag-to-lift ratio. For the case of power being mainly contributed by wing inertia (hoverfly, dronefly, honey bee and bumble bee), the specific power (without elastic storage) is proportional to the product of the cubic of wingbeat frequency, the square of the stroke amplitude, the square of the wing length and the ratio of wing mass to insect mass.