The beautiful expression for lift of a two-dimensional airfoil, Eq. (8.59), arose from

Chapter 8, Problem p8.80

(choose chapter or problem)

The beautiful expression for lift of a two-dimensional airfoil, Eq. (8.59), arose from applying the Joukowski transformation, 5 z 1 a2 /z, where z 5x 1 iy and 5 1 i. The constant a is a length scale. The theory transforms a certain circle in the z plane into an airfoil in the plane. Taking a 5 1 unit for convenience, show that (a) a circle with center at the origin and radius . 1 will become an ellipse in the plane and (b) a circle with center at x 5 2 ! 1, y 5 0, and radius (1 1 ) will become an airfoil shape in the plane. [Hint: The Excel spreadsheet is excellent for solving this problem.]