Page 262 - Aerodynamics for Engineering Students

Finite wing theory 245

harmonics are symmetrical. Even harmonics, on the other hand, return to zero again
at 7r/2 where in addition there is always a change in sign. For any asymmetry in the
loading one or more even harmonics are necessary.
With the number and magnitude of harmonics effectively giving all possibilities the
general spanwise loading can be expressed as

W
r = 4sV A, sin ne (5.45)
1
It should be noted that since I = pFT the spanwise lift distribution can be expressed
as

W
I = 4p~~sC~,sinne (5.46)
1
The aerodynamic characteristics for symmetrical general loading are derived in the
next subsection. The case of asymmetrical loading is not included. However, it may
be dealt with in a very similar manner, and in this way expressions derived for such
quantities as rolling and yawing moment.

5.5.5 Aerodynamic characteristics for symmetrical
general loading
The operations to obtain lift, downwash and drag vary only in detail from the
previous cases.

Lift on the wing

and changing the variable z = -scos 8,
r?F
L = lo pVI'ssinf3dO

and substituting for the general series expression

sin(n - i)e sin(n + 1)e
-

The sum within the squared bracket equals zero for all values of n other than unity
when it becomes

[ lim =Air
(n-l)+O