90

N. Chari et al.

Definition

Moment of Inertia is the measure of the resistance offered by a body to change the

rotational motion about an axis. It forms the basis for the calculation of the kinetic

energy of moving bodies. The general equation for the moment of inertia can be

written as follows:

I =

n



i=1

mir²

i

(7.1)

where

mi

is the mass of the individual strip of the wings (gm).

ri

is the distance between wing fulcrum and centre of mass of the strip.

i

Is the Strip Number.

n

is the total number of strips.

Expression for Moment of Inertia

During a rotary or oscillatory motion, the expression from Eq. 7.1 gets modified to

include the rotational effects. Then the kinetic energy of the oscillating or moving

wing can be expressed as

KE = ¹

2^Iw2

(7.2)

and

w = 2πϑ

(7.3)

where

I

is the moment of inertia of the wing.

w

is the angular velocity of wingbeat indicating angular movement during flapping

(rad/s).

ϑ

is the wingbeat frequency of the flier (cps).

∴KE = ¹

2^{I(2πϑ)2 = 2π2Iϑ2}

(7.4)

Note that I and MI are synonymous in this chapter/book.