Page 206 - Aerodynamics for Engineering Students

Two-dimensional wing theory 189

which can be rearranged in terms of a function of coefficients An plus a term
involving q, thus:

(4.68)

The contribution of the wings to 2, or zq thus becomes

by differentiating Eqn (4.64) with respect to q.
Therefore for a rectangular wing, defining zq by Zq/(pVSlt),
-a 3
zq = (; - h) (4.69)

For other than rectangular wings an approximate expression can be obtained by
using the strip theory, e.g.

Z, = -pV/'- a3 (-- h)c2dy
+2 4

giving
(4.70)

In a similar fashion the contribution to Mq and mq can be found by differentiating
the expression for MCG, with respect to q, i.e.

from Eqn (4.68)
2K-alvsc2
+- 32 (4.71)

giving for a rectangular wing

(4.72)

For other than rectangular wings the contribution becomes, by strip theory:

Mq = -pv/-s(;(l - 2h)2 +- 27r - ") c3 dy (4.73)
--s 32
and

mq = (4.74)