6

Theories on Hovering Flight of Insects

83

where

K = ¹

2



981x1000

4x3.1416x1.125 ^{= 263.4}

Hence, the value of K is 263.4.

Newton’s formula is basically based on the mass flow concept. However, larger

samples of fliers have to be tested by using for generalization of this formula.

Deakin’s Theory

Deakin [12] has suggested the following formula for the calculation of wingbeat

frequency of insects.

ϑh = ^317√m

s

(6.19)

where s is the combined area of the two wings. This theory is applicable to a large

number of insects. Hence, this can be universal in its application to insect frequency

calculations.

The above seven theories and their formulae have been briefly mentioned from

Bio-Aerodynamics of Avian Flight [11].

Earlier Work on Hovering

Ellington [13] studied the kinematic changes with the flight speed of bumblebee.

Other insects like fruitfly and hawk moth were also studied. He derived the mass ‘m’

that can be supported during hovering as

m = ^{0.387ϕ2n2R4CL}

AR

(6.20)

where

ϕ

is wingbeat amplitude (peak to peak in radians).

AR

is the aspect ratio of the wing.

m

is mass of insect (kg).

n

is strokes/seconds of wingbeat, (Hz).

R

is wing length (m).