Page 204 - Aerodynamics for Engineering Students

Two-dimensional wing theory 187

Fig. 4.18

normal force derivative due to pitching z,, and the non-dimensional pitching moment
derivative due to pitching m,.
The contributions to these two, due to the mainplanes, can be considered by
replacing the wing by the equivalent thin aerofoil. In Fig. 4.19, the centre of rotation
(CG) is a distance hc behind the leading edge where c is the chord. At some point x
from the leading edge of the aerofoil the velocity induced by the rotation of the
aerofoil about the CG is d = -q(hc - x). Owing to the vorticity replacing the camber
line a velocity v is induced. The incident flow velocity is V inclined at a to the chord
line, and from the condition that the local velocity at x must be tangential to the
aerofoil (camber line) (see Section 4.3) Eqn (4.14) becomes for this case
(2 )
v --a =v-v’

or

(4.59)

C
and with the substitution x = -(1 - cos 0)
2

From the general case in steady straight flight, Eqn (4.35), gives

-- a=Ao-a++A,cosne (4.60)
d~
dx
but in the pitching case the loading distribution would be altered to some general
form given by, say,
V
- = B~ + CB, cosne (4.61)
V

Fig. 4.19