Page 211 - Aerodynamics for Engineering Students

194 Aerodynamics for Engineering bdents

wing sections such as the Gottingen 398 and the Clark Y were nearly the same when
the maximum thicknesses were set equal to the same value. The thickness distribution
for the NACA four-digit sections was selected to correspond closely to those for
these earlier wing sections and is given by the following equation:

yt = f5ct[0.2969& - 0.12605 - 0.3516$ + 0.2843J3 - 0.101554] (4.84)

where t is the maximum thickness expressed as a fraction of the chord and 5 = x/c.
The leading-edge radius is

rt = 1.1019ctz (4.85)
It will be noted from Eqns (4.84) and (4.85) that the ordinate at any point is
directly proportional to the thickness ratio and that the leading-edge radius varies as
the square of the thickness ratio.
In order to study systematically the effect of variation in the amount of camber
and the shape of the camber line, the shapes of the camber lines were expressed
analytically as two parabolic arcs tangent at the position of the maximum camber-
line ordinate. The equations used to define the camber line are:
mc
Yc = p2 (2P5 - P> ESP
mc
Yc = - + 2PE - c21 5 1 (4.86)
[(I
2P)
P
-
2
(1 -P>
where m is the maximum value of yc expressed as a fraction of the chord c, and p is
the value of x/c corresponding to this maximum.
The numbering system for the NACA four-digit wing sections is based on the
section geometry. The first integer equals loom, the second equals lop, and the final
two taken together equal 100t. Thus the NACA 4412 wing section has 4 per cent
camber at x = 0.4~ from the leading edge and is 12 per cent thick.
To determine the lifting characteristics using thin-aerofoil theory the camber-line
slope has to be expressed as a Fourier series. Differentiating Eqn (4.86) with respect
to x gives

Changing variables from 5 to 8 where 5 = (1 - cos 8)/2 gives

(4.87)

where 6, is the value of 0 corresponding to x = pc.