78

N. Chari et al.

Table 6.1 Seven classical theories

1

Mechanical oscillator theory

[1]

2

Crawfords theory

[2]

3

Norberg’s theory

[3, 4]

4

Pennycuick theory

[6]

5

Theory based on Newton’s laws

–

6

Mass flow theory

Puranik and Ahmed [7]

7

Deakin’s theory based on dimensional analysis

[12]

of the flier. The buoyant nature of the air also would help in keeping afloat the tiny

insects in the hovering state. Birds like certain hawks, kingfishers and hummingbirds

also hover for survey and feeding. Hummingbirds are the masters of hovering flight

in nature. Among the insects, the hovering flight is found in honey bees, bumblebees,

moths, butterflies, some plant bugs and moths during sucking of juice from the plant

or nectar from the flowers. In normal hovering, the wing moves in a horizontal

plane. Seven classical theories have been mentioned below to predict the hovering

capabilities of the various fliers in terms of frequency (Table 6.1).

Out of these seven theories, we are discussing Mass Flow Theory and its related

formulae in greater detail because it forms the basis for the interpretation of other

theories. Murthy [8] in his Ph.D. Thesis has discussed hovering parameters and

hovering of Carpenter Bee.

Mass Flow Theory of Hovering

Puranik and Ahmed [7] suggested a theory for wingbeat frequency of a flier on the

basis of mass flow of air displaced by wings.

During the hovering state, the reaction force of a flier is proportional to its weight.

According to mass flow theory, during the hovering state, the insect is in dynamic

equilibrium and the reacting force is proportional to the rate of mass flow of air where

R = W

(6.1)

where,

W = M f.g

∴R = M f.g

(6.2)

Rα ^dm

dt