28

P. Mukkavilli et al.

The insect wingbeat frequencies are variable from synchronous (2–100 Hz) to

asynchronous frequencies (100–1000 Hz) as mentioned earlier. During hovering,

upward stroke time slightly increases compared to that in normal flight, but still

about 10–15% less than downstroke time. The lift generated during each wingbeat

cycle is more or less equal to the weight of the flier.

The effects on a flapping wing can be summarized into three major aerodynamic

phenomena as follows:

• Leading edge vortex

• Steady-state aerodynamic forces on the wing and

• Wing interaction with its wake from previous strokes (wing-wake capture

reaction).

Generally, the weight of many flying insects ranges from 20 μg to 150 g. The

Reynolds number (Re) also changes from insect to insect and will be proportional to

the size of the insect. For smaller insects, it will be as low as 10 and may increase

to a value of 10⁴ based on the size of the insect and the velocity of the flier. Low Re

values of insects play a vital role in understanding insect flight and may contribute

better in inferring its flight design. In this flight regime, the flow physics is not fully

understood. A thorough knowledge of the flapping wing dynamics is vital in the

appropriate design of the bio-mimicking MAVs.

The Governing Equations for an Insect Flight

Considering a wing cross section, the force component normal to the flow direction

can be named as lift (L) and the force component acting along the flow direction is

a drag (D). The lift and drag components (Fig. 3.4) can be expressed as follows.

L = ¹

2^{ρV 2SC L}

(3.3)

Fig. 3.4 Aerodynamic forces on an airfoil