I had a question regarding the direction of the pitching moment.

To make sure we are on the same page, here is what I know so far (please correct me if I am wrong).

  1. Lift acts through center of pressure
  2. Normally moment is taken around Aerodynamic Center because then the moment does not vary with angle of attack.
  3. In a cambered airfoil, the aerodynamic center and center of pressure are not at the same place, so the lift created also generates a moment at the aerodynamic center.
  4. In a symmetric airfoil, the aerodynamic center and the center of pressure are at the same place, so you do not have a pitching moment.
  5. Location of Aerodynamic Center is fixed for an airfoil, it does not change with speed.

I am trying to understand the concept of longitudinal static stability and in all the diagrams, the pitching moment is shown to be nose up.
enter image description here

But I would imagine that the center of pressure is further downstream on a airfoil than the aerodynamic center, so shouldn't the pitching moment be nose down? As shown in this picture enter image description here

Thanks for your help,

  • 1
    $\begingroup$ you can have a moment computed around any arbitrary point. There is a center of gravity, a center of pressure and aerodynamic center. 3 different things, but really, the rotation of an object depends on the moment computed around whatever is the hinge (in this case center of gravity) $\endgroup$ – Radu094 Oct 26 '16 at 18:19
  • $\begingroup$ @Radu094, you are right except that there is no 'hinge' on a flying aircraft. For our mathematical convenience, we may consider all motion as rotations around CG plus whatever translation there is, but if you try to isolate pure rotation, its centre could be anywhere. A delta wing airplane can have centre of controlled pitch rotation outside in front of the craft (which may confuse pilots), due to strong force from elevons. An isolated normal wing, with its initial lift (CP) at ¼chord and CG at ½, will start pitching up about a point midway between the two. $\endgroup$ – Zeus Oct 27 '16 at 2:25
  • $\begingroup$ The diagram above is for an aircraft with the Center of Pressure (CP) IN FRONT of the center of Gravity (CG). in this case the pitching moment is indeed Nose up. But this makes the aircraft statically unstable. Only one aircraft (AFAIK) is like this, (the F-16) and it is only like this when subsonic. It can deal with the instability because it is "fly by wire" - the computer constantly generates stabilator inputs to compensate. Most all other aircraft have the CP behind the CG and then the pitching moment is indeed nose down. $\endgroup$ – Charles Bretana Oct 30 '16 at 16:11

All points you mention are correct (for the nitpickers: Point 5 is only true below transsonic speeds). That the pitching moment of the wing is drawn nose-up is probably because it is positive this way - nothing more. The sketch you posted in your question is rather poor, with the center of gravity located behind mid-chord when it should be closer to the aerodynamic center.

Indeed, if you have positive camber, the center of pressure of the wing is behind the aerodynamic center, so the wing's pitching moment around the aerodynamic center should be nose-down. However, if you assume the center of gravity of the isolated wing to be at mid-chord, the aerodynamic center is normally between the quarter chord and mid points, so the wing all by itself will pitch up because it pitches around the center of gravity. The moment depends on the reference point.

Did you look at this answer for an explanation of static stability yet? Let me know if something is left unclear.

  • $\begingroup$ Thanks, for the reply, indeed if you want longitudinal stability, the change in lift at the rear has to be more than at the front! $\endgroup$ – T-REX Oct 27 '16 at 9:03
  • $\begingroup$ @T-REX: Yup. Simple, isn't it? $\endgroup$ – Peter Kämpf Oct 27 '16 at 9:32

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