Moment

The moment about the leading edge is given by

xdFz — -1 pU2 (cp (x) – C + (xxdx

(4.49)

Using again Ackeret results, the moment coefficient can be written

2 c /_ /, x dx

Cm, o — (f (x) – a + f +(x) – a)-

0

c / / x dx (f (x) + f +(x)) 0 c c
a2 – 2- + – в в
(4.50)
Let (Cm, o) 0 be the integral term. Introducing camber and thickness reduces the
equation to
	4 c d (x) dx в 0 c c
4 в
(4.51)

where we have performed an integration by parts and used d(0) — d(c) — 0. The integral represents the dimensionless area under the camberline. It is worth noting that, although lift does not depend on camber, the aerodynamic moment in general does.

Application:

• moment coefficient of a flat plate or symmetric profile: Cm, o — -2^

• moment coefficient of aparabolic plate of camber d; Cm, o — -2 ^-35 d.