Calculating polars from 2D airfoil coordinates...
 

Hey,

I've been trying, over the last few weeks, to write a relatively simple program that, given the airfoil coordinates, will generate the polar data for Cl, Cd, etc. Unfortunately, I continually run into a brick wall so I've come here in the hopes that someone can point me in the right direction.

So, given an airfoil, it seems possible to generate out polar data. I've seen several applications that do this (Xfoil, JavaFoil, etc come to mind) but I simply cannot find any information on how they do this.

Let's take the NACA 1408 airfoil, for example.

http://www.worldofkrauss.com/foils/1711

Plugging that 2D airfoil cross-section into JavaFoil allows me to see not only the pressure differential map but also an accurate (or, what seems to be a pretty accurate) Cl to angle of attack graphing.

How are they doing this? Everywhere I see that Cl for a 2D airfoil is calculated using the Thin Airfoil Theory (2 * Pi * angle of attack) which nets you strait slope instead of the more accurate "lightning bolt" upward slope with the drop-off as the wing stalls.

Are there formulas for getting accurate polar data (specifically, Cl) for a 2D airfoil if you know the Re, density, velocity but not the reference area?

I'm trying to do this from start-to-finish with no tools... just the math.