Page 197 - Aerodynamics for Engineering Students

180 Aemdynamics for Engineering Students

Therefore

(4.41)

Multiplying both sides of Eqn (4.35) by cos me, where m is an integer, and integrating
with respect to e

LnAn cos nf3 cos me de = 0 except when n = m

Then the first term on the right-hand side vanishes, and also the second term, except
for n = m, i.e.

whence

A, = z/TgcosnBd6' (4.42)
n-0

Lift and moment coefficients for a general thin aerofoil
From Eqn (4.7)

I= pUkdx= pUEksinBd0
1= 1" 2

?T 1
- Ao) +-AI] = CL-~U~C
2 2
Since

1 *sin ne dB = 0 when n # 1, giving

dCL
CL = (Cb) + - 01 = r(A1- 2Ao) + 27ra (4.43)
da
The first term on the right-hand side of Eqn (4.43) is the coefficient of lift at zero
incidence. It contains the effects of camber and is zero for a symmetrical aerofoil. It is
also worth noting that, according to general thin aerofoil theory, the lift curve slope
takes the same value 2n- for all aerofoils.