82

N. Chari et al.

This theory is applicable where the wing swept area and mass of the insect are

relatively small as in the case of a mosquito and other very small insects with a high

wingbeat frequency. The value of K as calculated is 252.44.

Norberg’s Theory

Norberg [3] suggested the formula for the calculation of wingbeat frequency based

on the mass of the flier (M).

ϑh = 3.98 M^−0.27

(6.15)

This formula is applicable to fliers having medium speed and size. However, it

is not applicable to hummingbirds which are of specialized category; he proposed a

different formula as given below

ϑh = 1.32M^−0.60

(6.16)

Norberg has considered the mass of the flier alone as a criterion for the calculation

of wingbeat frequency and assumed that other parameters (flight) are related to it.

Pennycuick’s Theory

Pennycuick [5, 6] considered the following parameters to be influencing the wingbeat

frequency and suggested the final equation as follows:

ϑh = 1.08



m^3/8g^1/2b^−23/24S^−1/4ρ^3/8

(6.17)

As Pennycuick studied marine birds alone, therefore, the value of K is obtained to

be 253 as suggested by him. The density of air is 1.225 × 10^–3 gm/cm³. The universal

application of this formula to insects remains to be established by further studies.

Theory Based on Newton’s Laws

The hovering frequency formula suggested based on Newton’s theory is as follows:

The hovering frequency ϑh can be expressed as

ϑh = ^K√m

A

(6.18)