3

Aerodynamic Considerations

29

D = ¹

2^{ρV 2SCD}

(3.4)

where

CL and CD

are dimensionless and denoted as coefficients¹ of lift and drag.

ρ

density of air.

V

Velocity of the insect.

S

Area of the two wings.

In an insect, the wing profile shape and viscosity of air influence the amount of

total drag on the wing, which in turn develops a certain amount of lift depending on

the Angle of Attack (AOA, ∝) [23]. The insect wings are thin chitinous membranes.

Hence, the non-dimensional coefficients of lift and drag (i.e. CL and CD) are the

functions of AOA.

From Eq. 3.3 and 3.4, we get

CL

CD

=



2L

ρV ²S





2D

ρV ²S

 = ^L

D ^.

(3.5)

However, by considering the balance between lift and weight during steady state,

we can write L = W, and also by considering the surface area (S) of the wing over a

functional parameter, we can write

L

D ⁼

W

S × K ^,

(3.6)

where K is the specific resistance value for individual species. The value of K depends

on the surface pattern/texture of the wing, wing position and angle of attack; thus,

this may be considered as a species-specific character. However, to know the exact

values of K, we need further experimental studies.

The flow around the insects is considered to be incompressible for which the

Mach number will be less than 0.3 and hence, there is no density variation and ρ

is considered to be constant. Considering the Navier–Stokes equation subjected to

no-slip boundary conditions, we can write

∂u

∂t ^{+ (u.∇)u = −∇p}

ρ

+ v∇²u

(3.7)

u.∇= 0

(3.8)

ubd = us

(3.9)

1 A coefficient can be considered as a number or symbol with a variable or unknown quantity.