Page 205 - Aerodynamics for Engineering Students

188 Aerodynamics for Engineering Students

where the coefficients are changed because of the relative flow changes, while the
camber-line shape remains constant, i.e. the form of the function remains the same
but the coefficients change. Thus in the pitching case

-- (4.62)
dy
dx
Equations (4.60) and (4.62) give:

and B,, = A,

In analogy to the derivation of Eqn (4.40), the vorticity distribution here can be
written

and following similar steps for those of the derivation of Eqn (4.43), this leads to

(4.63)

It should be remembered that this is for a two-dimensional wing. However, the
effect of the curvature of the trailing vortex sheet is negligible in three dimensions, so
it remains to replace the ideal aC,/& = 27r by a reasonable value, Q, that accounts
for the aspect ratio change (see Chapter 5). The lift coefficient of a pitching rect-
angular wing then becomes

(4.64)

Similarly the pitching-moment coefficient about the leading edge is found from
Eqn (4.44):

7r
=-(A2-A1)---- 7rqC 1 (4.65)
4 8V 4cL
which for a rectangular wing, on substituting for CL, becomes

The moment coefficient of importance in the derivative is that about the CG and
this is found from
CM,, = CMm + hCL (4.67)

and substituting appropriate values