Confusion about Aerodynamic center

Question

suppose, i assume Aerodynamic Center lies at Center of gravity. Then apparently moment by lift will be zero about CoG. But in reality Centre of Pressure may be behind aerodynamic center and still be producing a moment. So isn’t using aerodynamic center absurd?

Answer 1

It's easy if we clarify your statement a bit.

When aerodynamicists say "moment by lift", this means the derivative of moment by lift. That is, the change of moment per change of lift, $\partial M/\partial L$, or shorthand $M_L$ (or their coefficients more commonly: $C_{M_{C_L}}$). Stability analysis (that's where the aerodynamic center is most useful) is all about derivatives rather than actual forces and moments: we are interested what changes when conditions change.

In this light, "moment by lift" will be zero, true, but "just moment" won't be.

Answer 2

First of all, I am going to comment on your statement

Then apparently moment by lift will be zero about CoG.

This is not apparent and not necessarily true, as your next comment also implies you know about.

But in reality Centre of Pressure may be behind aerodynamic center and still be producing a moment. So isn’t using aerodynamic center absurd?

I cannot answer whether or not the aerodynamic center is absurd. I will instead give an explanation of why it is reasonable to define the aerodynamic center.

You are right in the fact that the center of pressure may be behind the aerodynamic center and hence produces a moment around the center of gravity which you assume equal to the aerodynamic center. In fact, a lifting force through the center of pressure produces a moment around any point not equal to itself, hence also the aerodynamic center.

Consider an airfoil at a given angle of attack and fix the airfoil in some arbitrary point p along the chord line. We can now (at least theoretically) determine the pressure distribution around the airfoil and use that to calculate the aerodynamic force from these pressure variations and the center of pressure. The force acting through the center of pressure gives rise to a moment around p proportional to the arm, i.e. the distance between the center of pressure and p.

If we change the angle of attack, the pressure distribution changes. Therefore, the aerodynamic force and the location of the center of pressure and the moment all change. If we had still fixed the wing at p, the size of the moment would most likely have changed by now.

We see that determining the aerodynamic behavior of an airfoil is very complicated if we use the center of pressure to analyze the forces because all variables (leverage, force and moment) change when we change the angle of attack.

We could have computed the moment about any point on the airfoil. Given a pressure distribution, the aerodynamic force will be the same, but the value of the moment depends on the point where that force is applied. It has been found both experimentally and theoretically that, if the aerodynamic force is applied at a location roughly 1/4 chord aft the leading edge on most low speed airfoils, the magnitude of the aerodynamic moment remains nearly constant with angle of attack. Engineers call the location where the aerodynamic moment remains constant the aerodynamic center of the airfoil. Using the aerodynamic center as the location where the aerodynamic force is applied eliminates the problem of the movement of the center of pressure with angle of attack in aerodynamic analysis. The aerodynamic center is important when determining the longitudinal stability of an aircraft.

You can think of the aerodynamic center as the point through which the part of lift, which is dependent on the angle of attack, acts.

A figure showing the constant aerodynamic center for angles of attack equal to 8, 4, 0 and -4 degrees. Notice the negative lift on the forward part of the wing at negative angles of attack compensating for the large leverage of the center of pressure (here denoted TC).