6

Theories on Hovering Flight of Insects

85

• Figure of ‘8’ is formed in the vertical plane by the flapping flexible wing at the

tip.

• The wing is rigid and cambered and has no flexion except at the tip.

• Example: Cicada and Hummingbird.

• Lift produced in insects during downstroke is 50% and upstroke is about 40%. In

• hummingbirds downstroke is 70% and in upstroke is 30%.

• The hovering frequency is high and ranges between 10 and 80 cps.

Principles involved in hovering flight are as follows

1.

During hovering, the weight of the hovering insect is acting downward, and it is

balanced by a lift force given by the rate of change of momentum of air acting

in an upward direction due to wingbeat cycle. The mass of the insect is usually

small as compared to a bird or bat. The hovering equilibrium can be expressed

as follows:

R = W

W = Mf

R = Mf

Rα = dm/dt

R stands for reaction force.

W indicates the weight of the hovering insect. Mf is the mass of the flier.

dm/dt is the rate of the small mass of a quantity of air.

2.

In the hovering state, the forward velocity is almost zero and hence W = L.

The drag and thrust forces which are developed by the flapping flexible wings

almost become equal to each other, contributing to equilibrium conditions in

the hovering state.

3.

Most of the aerodynamic work is done during the downstroke of the wingbeat

cycle and the upstroke of the wing is assumed as more or less a recovery stroke

which needs relatively less power. However, the wingbeat cycle, in general,

depends on anatomy, physiology, elastic nature of the fulcrum (resilin), the

structure of the flapping flexible wing and muscle type.

4.

Biological flier which has higher body mass cannot hover for a longer time,

since high power is not available to the muscle.

5.

Hovering is a continuous power-on beating of the wings.

6.

The flow of air through stroke plane in hovering state is mainly due to induced

downward velocity.

7.

The hovering state of the flier is calculated on the assumption of steady state

of the air. Hovering in an unsteady state of air cannot be ruled out in nature.

True hovering is different from wind-assisted hovering.

8.

The wing tip during hovering flight traces a figure of ‘8’. The shape of figure of

‘8’ is variable in different groups of insects. The figure of ‘8’ can be explained

by wing Lissajou’s pattern.

9.

In the case of Cicada (or hummingbird) while hovering, the flapping pattern

is coupled with the wing pitch adjustment, leading to the formation of figure

of 8.