Power requirements for the hovering flight of insects with different sizes

Winged insects vary greatly in size, from tiny wasps (0.015 mg) to large moths (1.6 g). Previous studies on the power requirements of insect flight focused on relatively large insects; those of miniature insects remain relatively unknown. In this study the power requirements of a series of miniature insects were calculated, and changes with size across a range of insect sizes were investigated. Aerodynamic power was computed by numerically solving the Navier-Stokes equation, and inertial power was computed analytically. Comparison analysis was then conducted on the power requirements of miniature and large insects. Despite a 100,000-fold weight difference, the required power per unit insect mass, referred to as mass-specific power, was approximately equal for all the insects examined. This finding is explained as follows. Power is approximately proportional to the product of the wing speed and the wing drag per unit weight (i.e., "drag-to-lift ratio"). When insect size decreased, wing speed decreased (due to reduced wing-length), while wing drag increased (due to increased air-viscosity), resulting in an approximately unchanged mass-specific power. For large or small insects, flight power is derived from the same type of muscles (striated). Assuming that the mean power per unit muscle mass is the same under the same type of muscle, the above size/specific-power relation indicates that the ratio of flight-muscle mass to insect mass is the same for different sized insects.