Question: A flat-plate airfoil is aligned along the x-axis with the origin at the leading edge and trailing edge at x = c. The plate is at an angle of incidence α to a free stream of air speed U. A vortex of strength 0v is located at (xv, yv). Show that the distribution k(x) of vorticity along the airfoil from x = 0 to x = c satisfies the integral equation
where x = x1 is a particular location on the chord of the airfoil. If xv = c/2 and yv = h >> xv, show that the additional increment of lift produced by the vortex (which can represent a nearby airfoil) is given approximately by
