Pitching Moment Acting on a Wing

[fog37]

Hello, I am learning about the pitching moment acting on a wing that is immersed in an airflow hoping to clarify some key concepts. In general, the moment of a force depends on:

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

A 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 $F_{lift} \neq 0$...

 

[Aaron Barnard]

Is it correct?

Yes, that is correct. When the lift force $F_{lift}=0$, the total pitching moment $M_o$ about a reference point $o$ is equal to the camber moment $M_{camber}$. Even when $F_{lift}\neq 0$, the camber moment contribution $M_{camber}\neq 0$ must be included in the total pitching moment $M_o$ and the total pitching moment $M_o$ is equal to the sum of the camber moment and lift-induced moment: $$M_o = M_{camber}+M_{lift}$$

 

[NatSusan]

Yes, your understanding is correct. The total pitching moment is always a combination of the camber moment and the lift moment, and the lift moment is only present when the lift force is non-zero. When the lift force is zero, the total pitching moment is equal to the camber moment. Additionally, the location of the force application point (aerodynamic center or center of pressure) does not affect the total moment when the lift force is zero. However, it does affect the total moment when the lift force is non-zero, as it changes the lever arm of the lift force.