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Slope of Cm vs alpha graph is negative, why it is so? The attached graph is from https://en.m.wikipedia.org/wiki/Pitching_moment , this graph is for cambered airfoil, as pitching moment is zero for symmetrical airfoil, as center of pressure remains constant for symmetrical airfoil.

My question is different from suggested question Should the pitching moment be up or down? as my question is talking about pitching moment coffecient which depend on pitching moment, dynamic pressure, and other parameter.

Cm= M/qSc

Where M is pitching moment, q is dynamic pressure, S is the wing area, c is the length of chord of airfoil. But I am not able to get it correctly how Cm decreases with increases in angel of coffecient. If we see pitching moment value then I think it should increases with increase in angle of attack as centre of pressure shifts away from center of gravity with increase in angle of attack. Cm vs alpha graph, source:Wikipedia (source: wikipedia)

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  • $\begingroup$ Where does you graph comes from? to what aircraft type does it apply? $\endgroup$
    – Manu H
    Jun 1, 2020 at 17:06
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    $\begingroup$ That looks like the Cm of the whole aircraft. Is that right? $\endgroup$
    – JZYL
    Jun 1, 2020 at 17:38
  • $\begingroup$ @Manu sir source of graph is en.m.wikipedia.org/wiki/Pitching_moment $\endgroup$
    – Rajakr
    Jun 2, 2020 at 1:14
  • $\begingroup$ @JZYL sir, I also think it's for whole aircraft. $\endgroup$
    – Rajakr
    Jun 2, 2020 at 1:16
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    $\begingroup$ Does this answer your question? Should the pitching moment be up or down? $\endgroup$
    – JZYL
    Jun 2, 2020 at 2:04

1 Answer 1

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There are several, equivalent explanations:

  1. The airplane has positive static longitudinal stability.
  2. As the angle of attack increases, wing lift grows more slowly relative to tail lift because the coefficient of lift on the wing is larger than that on the tail.
  3. The airplane exhibits a growing nose-down pitching moment as the angle of attack increases in order to return to its trimmed angle of attack of -3°.

The increasing slope of the moment curve at 12° angle of attack indicates stall onset on the inner wing. Here, the flow starts to separate on the rear upper wing root which reduces local circulation and, consequently, the downwash angle at the tail so the lift increase on the tail becomes disproportionally large. This is typical for a straight wing with a moderately high aspect ratio.

The two lines show the behavior at two different Reynolds numbers which seem to belong to a model airplane or a low-speed tunnel measurement. They also show the behavior of a full airplane, not an isolated airfoil.

If we see pitching moment value then I think it should increases with increase in angle of attack as centre of pressure shifts away from center of gravity with increase in angle of attack.

It does grow, but in the negative direction. This is because a nose-up pitching moment is defined as positive and what we see here is an increasing nose-down pitching moment. The center of pressure of the wing-tail combination is shifting backwards with increasing angle of attack and the pilot would need to trim a negative elevator deflection to bring it back to the center of gravity.

My question is different from suggested question Should the pitching moment be up or down? as my question is talking about pitching moment coffecient which depend on pitching moment, dynamic pressure, and other parameter.

No, it's not. As the constant Reynolds number indicates, this has been measured at constant speed and it does not matter if it is a coefficient or the "real" moment because both only differ by a constant factor.

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