Page 242 - Aerodynamics for Engineering Students

Finite wing theory 225

Fig. 5.16

The downwash at the mid-span point P of the tailplane caused by the wing is the sum of that
caused by the bound vortex ac and that of each of the trailing vortices ab and cd. Using the
special form of BiotSavart equations (Section 5.2.2) the downwash at P:

r0
WP 1 =-2sinp+-(l 2ro +cos@)
47rx 47rd

From the sketch x = d cot /3 and x' = (7r/4)s

27rs'
2r0
=-(l+secp)
73s
Now by using the Kutta-Zhukovsky theorem, Eqn (4.10) and downwash angle
WP
E=-
V

or

The derivative

Thus

(5.19)

For cases when the distribution is non-elliptic or the tailplane is above or below the wing
centre of pressure, the arithmetic of the problem is altered from that above, which applies
only to this restricted problem. Again the mid-span point is taken as representative of the
whole tailplane.