7

Moment of Inertia and Mutilation Studies of an Insect Wing

101

Example 1—Case of an Insect Wing (T. Javanica)

Mass of the wing = 10 mg

Wingbeat Frequency ϑ = 50 cps

MaximumAmplitudeaboutthemeanis45⁰ = 45⁰× ^π

180 ^{= 0.7854 rad(Typically)}

Total Energy E = 2π²mϑ²a²

By considering θ = 30⁰ =

30

180 ^{× π = π}

6 ^{radians ; a = rθ = 1 × π}

6 ^{= 0.5236 cm.}

Here, we considered r = 1 cm as the distance of centre of mass of the wing from

the fulcrum.

= 2 × π² × 10 × 10⁻³ × 50² × (0.5236)²

∴Total Energy = 135 Ergs

Total energy values are computed for different amplitudes of θ ranging from 0⁰

to 60⁰ as shown plotted in Fig. 7.6. The total energy spent by the insect is seen to

increase with the rise in θ.

Fig. 7.6 Energy values for different amplitudes of θ