Moment

The elementary moment of a small aerodynamic force located at x about the leading edge reads (Fig.3.19)

dM o = – dF’ x = —pU Г ‘(x )xdx (3.74)

the minus sign is needed for the “nose up” moment to be positive. Replacing Г’ by its expansion and integrating in t from zero to n gives

Rearranging and using orthogonality of sine modes one gets

1 П П 1 П

M’o = — pU 2c2 A0 sin2 tdt + Ai sin2 tdt — A2 sin22tdt

’ 2 0 0 2 0

The moment coefficient is

Note that the moment depends on one more mode, mode 2, than lift. Application:

• moment coefficient for the flat plate: Cmo = – f a

• moment coefficient for the parabolic plate: Cm, o = – f (a + 4 f )