Moment

The moment about the leading edge is given by

Подпись: dM o — -x

xdFz — -1 pU2 (cp (x) – C + (xxdx

Moment

(4.49)

 

Using again Ackeret results, the moment coefficient can be written

2 c /_ /, x dx

Подпись: ccCm, 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

 

Moment

4 c d (x) dx в 0 c c

 

4

в

 

(4.51)

 

Moment

Moment

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.