Page 198 - Aerodynamics for Engineering Students

Two-dimensional wing theory 181

With the usual substitution

since

sin
lT ne sin me dB = 0 when n # rn, or

(4.44)

In terms of the lift coefficient, CM, becomes
CM, = -5[1+w] A1 - A2
4
Then the centre of pressure coefficient is

(4.45)

and again the centre of pressure moves as the lift or incidence is changed. Now, from
Section 1.5.4,

(4.46)

and comparing Eqns (4.44) and (4.45) gives
7r
-CM,p = - (A1 - A2) (4.47)
4
This shows that, theoretically, the pitching moment about the quarter chord point for
a thin aerofoil is constant, depending on the camber parameters only, and the quarter
chord point is therefore the aerodynamic centre.
It is apparent from this analysis that no matter what the camber-line shape, only
the first three terms of the cosine series describing the camber-line slope have any
influence on the usual aerodynamic characteristics. This is indeed the case, but the
terms corresponding to n > 2 contribute to the pressure distribution over the chord.
Owing to the quality of the basic approximations used in the theory it is found
that the theoretical chordwise pressure distribution p does not agree closely with