# But how exactly do you calculate the Joukowsky Airfoil, within a minimal margin of error?

After reading a fair bit of theory around the uses of conformal mapping to solve for the forces of lift acting on a wing, or a 2D cross section of the wing, in relation to the angle of attack. However I haven't been able to find much on numerical tools I can use to actually calculate the parameters for the transform. For example how could I convert a .dat file filled with the coordinates on the perimeter of the airfoil into its representation as a circle before undergoing the Joukowsky Transformation.

• The Joukowsky transform is an interesting application of conformal mapping and was historically important for understanding the relation between lift and circulation in the flow around airfoils, but it doesn't correspond to any practical airfoil shapes. So you are probably looking for something that can't done, if your data points define the shape of a "real" airfoil. – alephzero Jan 20 '19 at 10:10
• I know that it will not be exact, but if you look at this paper - evoq-eval.siam.org/Portals/0/Publications/SIURO/Vol1_Issue2/… . In Fig. 9 they seem to get fairly close to actual airfoils. I'm just wondering what numerical tools (applications) they used to get these results. – John Miller Jan 20 '19 at 10:12
• If not maybe you can recommend some other transforms used currently, I was hoping to eventually calculate the forces for a Boeing-737 on the midspan. – John Miller Jan 20 '19 at 10:15
• – alephzero Jan 20 '19 at 10:31
• The total lift of the wing and other lifting components is equal to the weight. I don't know why you would need the forces at midspan, but if you did, it would require a 3-D calculation to derive it from the total. So, you don't need the transformation (or any other 2D analysis). – D. Halsey Jan 21 '19 at 1:25