190

G. Shailaja and N. Chari

Table 14.1 Comparative account of theories on wing beat frequency

S. No.

Name of theory

Formula

Proportionality

constant (K)

Mass (M)

Wing dimensions

Remarks

1

Greenwalt’s Theory

(1960)

vhln = 3540

n = 1 to 1.5

ln

Considering as

mechanical oscillator

applied damped

hormonic oscillator,

derived formula for

frequency

2

Crawford’s Theory

(1971)

vh = Kc ×

 m f

Sw

Kc =

 g

4πρ =

252

M1/2

f

Sw

Wing swift area is taken

into account. Disc area

is considered, to

calculate frequency as

in massflow theory.

Suitable in calculating

frequency of small

insects

3

Norberg’s Theory

(1990)

vh = KNr(m)−0.27

KNr = 0.19

or 0.24

M−0.27

L

Norberg related

frequency to the Mass

raised to the power

(−1/3), wing span (L)

4

Pennyquick’s Theory

(1996)

vh = m3/8g1/2b−23/24S−1/3ρ−3/8

or

vh =



g1/2ρ−3/8 m3/8b−23/24

s−1/3

K p = g1/2

ρ3/8 = 390

M3/8

S1/3b23/24

Adopted dimensional

analysis method similar

to Deakins

(continued)