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P. Mukkavilli et al.

Resilin

The wing joints of insects contain a pad of elastic (rubber-like) protein called as

resilin. It helps insects in moving their wings in upward and downward directions.

During upstroke, resilin is stretched and KE of the wing is converted into potential

energy. During the downward position of the wing, energy is released which helps

in completing the downstroke.

Insects will gain KE during the acceleration by the contraction of the flight

muscles. During deceleration at the end of the stroke, energy must be dissipated

and KE will be converted into heat energy. Sometimes, this heat will be utilized by

the insects to maintain their core body temperatures.

Based on some simplified assumptions, the amount of energy stored in the resilin

can be calculated. In reality, the resilin will be bent into complex shapes. However,

in this case, it is considered as a straight rod with area A and length l.

Considering resilin obeying Hooke’s law, which in general is not exactly true as

resilin is stretched by a considerable amount, considering area and Young’s Modulus

do not change in the process of stretching, the energy E stored in resilin can be

estimated as below [25]:

E = ¹

2

Y A l²

l

,

(3.16)

where Y is Young’s Modulus for resilin (≈1.8 × 10⁷ dyne/cm²).

Typically for a honey bee weighing 0.1 gm, the stored energy in the two wings

was calculated to be 40 ergs approximately, where the value of l is about 10^–2 cm.

Similar values can be calculated for plant bugs and carpenter bees which weigh above

1 gm. A further discussion on resilin and the relevant equations is given in Chap. 8.

Actuator Disc Concept (Disc Area Concept)

The actuator disc theory is the oldest mathematical representation of a propeller or

a wind turbine. This concept was first developed for evaluating ship propellers by

Rankine in 1865 and Froude in 1885. Later on, Betz in 1926 developed a simple

model of actuator disc concept for turbine rotors. ‘Actuator Disc Theory’ is also

known as ‘Momentum Theory’. The analysis of the aerodynamic behaviour of rotary

wings, wind turbines and flapping wings can be started by considering the energy

extraction process, without any specific design considerations. Froude derived the

energy balance as “the work done by the disc equal to the thrust times the velocity

through the disc, which in turn equals mass flow times the change in velocity”.

Therefore, the velocity at the disc is the average of the velocities for upstream and

downstream flows (Fig. 3.5).