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

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PF_Help_Bot

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"Pitching Moment Acting on a Wing"

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