1. I learnt that for a symmetric airfoil, the pitch moment around the aerodynamic center should be null:


$\hspace{11pt}$ How could I intuitively explain this statement?

  1. I also learnt that for an airfoil with positive curvature, $M_{AC}<0$ and for an airfoil with negative curvature, $M_{AC}>0$. I'm new at my Flight Stability course, and I don't know how to achieve these conclusions. I do know the definition of aerodynamic center, but it isn't enough for me to make such observations.

    How could I deduce these statements?

  • $\begingroup$ This answer should help. Let me know if it doesn't. $\endgroup$ Oct 8 '16 at 15:13
  1. Per definition the moment coefficient in the Aerodynamic Centre is independent of the angle of attack.

  2. Since the airfoil is symmetrical, the moment around the a.c., $M_{a.c.}$ for an angle of attack $\alpha $ will be of equal magnitude and opposite sign at angle of attack $-\alpha $: $M_{a.c.}(\alpha)=-M_{a.c.}(-\alpha)$

The two statements can only hold if $M_{a.c.} = 0$

  • $\begingroup$ So, the second statement is true because the symmetry of the airfoil implies that the Aerodynamic Center is on symmetry axis. If the airfoil wasn't symmetric we would have two problems: locate the a.c. at horizontal axis and at the vertical axis. Without knowing one of these two coordinates it's hard to know the other. So, the answer to my second probem can't be so intuitive! Am I right? $\endgroup$ Oct 8 '16 at 14:52
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    $\begingroup$ After thinking about the question again, I should say that this answer as it is, can be considered self-contradictory. Since $M_{a.c.}$, by definition, doesn't depend on $\alpha$, it will always have the same value regardless of the signal of $\alpha$. Therefore the statement "$M_{a.c.}$ for an angle of attack $\alpha$ will be of equal magnitude and opposite sign at angle of attack $-\alpha$" is wrong. (To be continued) $\endgroup$ Oct 7 '19 at 12:07
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    $\begingroup$ (Continuation) "Opposite sign" should be replaced by "same sign'', and no important conclusion can be taken from this. However, in reality $M_{a.c.}$ is defined for small angles, where the linearisation of the dynamic equations may be performed. The truth is that $M_{a.c.}$ doesn't exist in exact terms. But if "$a.c.$" in "$M_{a.c.}$"' were substituted by some point in the chord of the airfoil near the "$a.c.$" point that would be obtained in a linear world, then the answer can be considered right. $\endgroup$ Oct 7 '19 at 12:07

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