# Where am I wrong at aerodynamic center calculation?

I'm currently taking aerodynmics course.In the classical thin airfoil theory. we saw that both for symmetric and non-symmetric airfoils the term $$dc_l/d\alpha= 2\pi$$. But in the preceding chapter, calculation of aerodynamic center, if we calculate aerodynamic center with using values of Lift and Moment about the quarter chord, there appear the following equation:

0=$$\dfrac{dc_l}{d\alpha}(x_{ac}-0.25)+\dfrac{d{c_{m,c/4}}}{d\alpha}$$

However, the problem is that, in the example question, the solution is like the following:

• There are given two values of $$c_l$$ and $$c_{m,c/4}$$ for different angle of attacks.
• $$\dfrac{dc_l}{d\alpha}$$ calculation is being done by applying finite difference for these two values.

Finally, I don't understand why we do not use the value of $$2\pi$$ directly.

Thanks for advance :)

• You might be better off asking this on Physics.SE. – ZeroOne Jan 14 at 16:56