Example 4.  Consider the modified Joukowski airfoil when    is used to map the Z plane onto the W plane.  Refer to Figure 11.69 and discuss why the angle of the trailing edge of the modified Joukowski airfoil forms an angle of radians.  

Figure 11.69  The images of the circles and under the modified Joukowski airfoil.

Solution 4.

    The image of the circle is the line , then two rays and , and then two arcs and in the respective Z,  W, and w planes.  The image of the circle is the circle , then the "cardioid like" curve , and then the modified Joukowski airfoil .  The details are left as an exercise for the reader in the book.

Complex Analysis for Mathematics and Engineering

(c) 2006 John H. Mathews, Russell W. Howell