## The Oshkosh Airfoil Transformation

The Oshkosh airfoil is a modification of the Joukowski airfoil transformation, developed by R. T. Jones in the 80's. The Joukowski airfoil is based on a conformal transformation of a circle with circulatory flow combined with a uniform flow field into an airfoil shape. This results in an exact solution to ideal fluid flow around an airfoil type shape. The Oshkosh airfoil first transforms the circle into an oval, and then transforms the oval into an airfoil. Selection of the transformation parameters can give an airfoil that is similar to a NACA 6 series.

The five parameters, X_{c}, X_{t}, Y_{c}, Y_{t}, and D control the airfoil transformation. If X_{t}, Y_{t}, and D are set to zero, the result is a Joukowski airfoil. The top five slider bars control the airfoil design parameters X_{c}, X_{t}, Y_{c}, Y_{t}, and D. The bottom slider bar alters the angle of attack and subsequent changes in the surface velocity.

The blue and red lines represent the air velocity over the upper and lower surfaces respectively and will vary with the angle of attack.