7

Moment of Inertia and Mutilation Studies of an Insect Wing

91

Expression for Rotational Kinetic Energy

In the case of a flapping wing, the kinetic energy possessed by the wing is due to the

rotational energy.

Rotational Kinetic Energy (KE) = ¹

2^m1v2

1 ^{+ 1}

2^m2v2

2 ^{+ 1}

2^m3v2

3 ^{+ · · ·}

where v = r.w

KE = ¹

2^m1w2r2

1 ^{+ 1}

2^m2w2r2

2 ^{+ 1}

2^m3w2r2

3 ^{+ . . .}

= ¹

2^w2

m1r²

1 ^{+ m2r2}

2 ^{+ m3r2}

3 ^{+ . . .}



= ¹

2^w2

n

i=1

mi.r²

i ^{= 1}

2^{w2.I (from Eq. 7.1)}

∴KE = ¹

2^I.w2

(7.5)

The quantity I is called the moment of inertia. The moment of inertia is calculated

about the fulcrum of the moving bodies. Usually, a single unfolded wing is considered

for the calculation purpose. The wingspan (wing length) of the insect has a bearing

on the disc area and also influences the wing loading.

Computation of Moment of Inertia of an Insect Wing

The kinetic energy is required basically to accelerate the wings at each stroke. This

is also known as the inertial power which can be calculated. The inertial power helps

in understanding the energy expended by the insect for flight. In order to determine

the inertial power, the MI of the wing is calculated about an axis parallel to the wing

surface passing through the point of articulation of the wing with the body.

The moment of inertia about a given axis takes into account the distribution of

mass and area about the axis of rotation or oscillations and plays a vital role in the

angular movement of the flexible wings. In the context of Entomology, these are

conventionally termed as the linear and rotational motion of the wings. It should be

clearly stated that the inertial power is that component of power which is associated

with the acceleration and retardation of wing movements. In most of the insects

when they are flying slowly, the angular velocity may not change significantly. Due

to the movement of the wing, a force field is generated which consists of a resultant

force and a couple. This force is responsible for the lift and thrust and the couple is