Show that as varies, the point z = a(h + cos ) + ja(k + sin

Show that as θ varies, the point z = a(h + cos θ) + ja(k + sin θ) describes a circle. The Joukowski transformation u + jv = z + l²/z is applied to this circle to produce an aerofoil shape in the u–v plane. Show that the coordinates of the aerofoil can be written in the form

Taking the case a = 1 and l² = 8, trace the aerofoil where

(a) h = k = 0, and show that it is an ellipse;

(b) h = 0.04, k = 0 and show that it is a symmetrical aerofoil with a blunt leading and trailing edge;

(c) h = 0, k = 0.1 and show that it is a symmetrical aerofoil (about the v axis) with camber;

(d) h = 0.04, k = 0.1 and show that it is a nonsymmetrical aerofoil with camber and rounded leading and trailing edges.

Transcribed Image Text:

U a 2 a (h + cos 0) x 1 + 1 a(1 + h+k + 2h cos 0 + 2k sin )) = (k+ sin 0) x 1 1 a(1 + h+k + 2h cos 0 + 2k sin 0)