- #1

fog37

- 1,568

- 108

- Location of moment reference point ##o##
- Force magnitude
- Lever arm (distance between force application point and moment reference point ##o##)

__positively cambered wing__always experiences a nonzero, constant, pure and negative (nose-down) moment ##M_{camber}## even when the net lift force ##F_{lift}=0##. However, when the lift force ##F_{lift}\neq 0##, which happens for increasing angles of attack ##\alpha##, an extra moment ##M_{lift}\neq 0## due to ##F_{lift}\neq 0## must be included and the total pitching moment ##M_o## about the arbitrary point ##o## is equal to: $$M_o = M_{camber}+M_{lift}$$ When ##M_{lift}=0## then ##M_o = M_{camber}##.

**I think this discussion presumes that the lift force ##F_{lift}## is applied at the aerodynamic center ##a.c.##**and generates a moment ##M_{lift} = F_{lift} x## where ##x## wis the distance between the moment reference point ##o## and ##a.c.##. When the moment reference point ##o=a.c.##, the total pitching moment becomes $$M_O = M_{a.c.}= M_{camber}$$ since ##M_{lift}=0## because the lever arm ##x=0##. So ##M_{lift}## is always zero when either ##x=0## (which happens when ##o=a.c.##) and/or ##F_{lift}=0##. Is that correct?

The same total moment ##M_o## should be obtained when, for a certain angle of attack ##\alpha##, when we consider the force ##F_{lift} \neq 0## and to be applied at the center of pressure ##c.p.## instead of at the aerodynamic center ##a.c.##. I can see how the total moment ##M_o## about a reference point ##o## would be nonzero when ##F_{lift} \neq 0## since $$M_o =F_{lift} x^{*}$$ where ##x^{*}## is the distance between ##c.p.## and the point ##o##. The moment can be positive or negative depending on if ##o## is before or after ##c.p.##.

But when ##F_{lift} = 0##, the moment ##M_o=0## always regardless of the lever arm ##x^{*}##. However, the total moment ##M_o## should always be nonzero due to camber moment contribution ##M_{camber} \neq 0## existing even when ##F_{lift} \neq 0##...