Application point of the lift force and pitching moment

  • Thread starter fog37
  • Start date
806
40
Hello

As the angle of attack of an airfoil changes, the lift force ##L## changes both in magnitude and position (not in direction, always upward). The force location is a point called the center of pressure ##x_{cp}##. It is possible to transfer the force to any another different point along the chord (even if it is always physically applied to ##x_{cp}##). But that transfer implies that we add a pure couple moment ##M##. However, as we change the AoA, the pure couple moment ##M## varies, i.e. it is dependent on the AoA even if we keep the reference point about which we calculate the moment fixed.

However, there is a special point called the aerodynamic center ##x_{ac}##, located at a quarter chord distance from the leading edge ##LE##. If the lift force ##L## is transferred to ##x_{ac}## as its application point, this pure couple moment ##M_{ac}## does NOT vary with AoA. Is that correct? This pure couple moment is always nonzero, even when ##L=0##, for any AoA, and always equal to zero for a symmetric airfoil.

246356


I believe, not sure if correct though, that if we leave the lift force ##L## at the center of pressure ##x_{cp}## and calculate the moment of the lift force ##L## about the aerodynamic center, with the lever arm being the distance ##|x_{cp} - x_{ac}|##, the resulting moment
##|M|## = ##L |x_{cp} - x_{ac}|## remains constant and is independent of the angle of attack even if both the distance ##|x_{cp} - x_{ac}|## and ##|L|## change with AoA . Is that correct? Also, this moment happens to be equal to the constant pure couple moment ##M=M_{ac}## described in the first paragraph...

Thanks and any clarification and validation!!
 
806
40
Hopefully, just to add clarity to my question, here another picture illustrating the lift force ##L## applied at the center of pressure ##CP##, which varies with AoA. If the pitching moment due to ##L## is calculated about the aerodynamic center ##AC##, the moment remains constant: even if the magnitude of ##L## increases from ##L_1## to ##L_2##, the lever arm ##d## decreases from ##d_1## to ##d_2## keeping the moment constant...

246452


The second figure shows how the force can be moved to different points of applications causing the moment ##M## to change depending on the application point. But only when the force is applied at c/4 the moment remains constant with AoA.
246451
 

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