Hello, just wondering if there are any aerodynamic specialist who may be able to answer few questions on aerodynamic center (AC)
Q1. Formula for Moment about the aerodynamic center = Cmac q s c (Cmac = moment coefficient, q = dynamic pressure, s = surface area, c = chord). I understand that moment = f x d so, distance has to be there hence why chord is in the formula. However, why is it not the distance from the AC to the center of pressure (COP)? I've noticed the same thing with Moment about the leading edge = Cmle q s c. My understanding of Moment about AC is as follows:
Q2. I've been using the A.C Kermode to study, and in the book, it says that Moment about AC = Moment about LE + Moment about AC after TR is moved to the leading edge. (This formula was used to calculate the position of aerodynamic center). The question I have with this formula is, why is the TR force moved randomly onto the leading edge? And on what basis has that formula been derived from? There wasn't much explanation in the book, it just stated that it was the formula and ended there.
If anyone can help it would be much appreciated! Many thanks in advance
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Re: Question on Aerodynamic Center
The chord length is merely a reference length. The actual symbol used in Moment coefficient is l. The reference length is chosen to pertain to the given geometric shape. For an airplane wing, l is the mean chord length.
Re: Question on Aerodynamic Center
The concept of Center of Pressure if fictitious. In a college course on statics, one of the first things you are taught about is a couple, which is two equal and opposite forces producing a moment with no net force. Most engineers seem to forget about this after the final exam. I was among the guilty until I went back and looked at my college notes ten years later.
Most pressure distributions when integrated can be found to produce a couple, plus a lift dependent pitching moment. The only exception is a 2D symmetric airfoil.
Hence, you can't find any point where there is a lift force, but no pitching moment. It just plain does not exist.
Don't believe me? Look in The Theory of Wing Sections. Cambered airfoils all have a non-zero pitching moment at zero lift. This non-zero pitching moment is a couple. Symmetric airfoils are the exception, as they have a zero pitching moment at zero lift.
Most pressure distributions when integrated can be found to produce a couple, plus a lift dependent pitching moment. The only exception is a 2D symmetric airfoil.
Hence, you can't find any point where there is a lift force, but no pitching moment. It just plain does not exist.
Don't believe me? Look in The Theory of Wing Sections. Cambered airfoils all have a non-zero pitching moment at zero lift. This non-zero pitching moment is a couple. Symmetric airfoils are the exception, as they have a zero pitching moment at zero lift.
Re: Question on Aerodynamic Center
kgh8616 wrote:Q1. Formula for Moment about the aerodynamic center = Cmac q s c (Cmac = moment coefficient, q = dynamic pressure, s = surface area, c = chord). I understand that moment = f x d so, distance has to be there hence why chord is in the formula. However, why is it not the distance from the AC to the center of pressure (COP)? I've noticed the same thing with Moment about the leading edge = Cmle q s c. My understanding of Moment about AC is as follows:
I think you're looking at this backwards. There is a convention for defining certain coefficients (lift, drag, moment), which says you take the actual quantity and divide it by the dynamic pressure * wing area, which renders the coefficient dimensionless.
For moment, because it is force x distance, you need an extra distance in the denominator to make it dimensionless, so you throw in chord.
The actual distance used in the Cm formula has nothing to do with the distance of the moment; it's rather a convenient number that is based on the wing.
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