Eccentric effect of a circle on the transformation of symmetric hydrofoil using Zhukovsky mapping

In this study, effect of eccentricity of a circle along the x-axis on the transformation of symmetric hydrofoil has been investigated using Zhukovsky mapping. The circle under study has a radius of 2 units, which is located at the origin of coordinates in the first case. In the first case, where the center of circle corresponds to origin of coordinates, the circle becomes a line and an ellipse and by moving the circle along the x-axis, a hydrofoil is obtained. The eccentricity of 0.4,0.2, 0.6, 1 and 1.5 have been studied and symmetric hydrofoils are calculated based on this mapping. The results indicate that as the eccentricity of the circle increases, the length of the hydrofoil decreases and the hydrofoil thickness increases. Up to eccentricity of a circle of 0.5, the maximum thickness occurs at a corresponding angle of 45 degrees and after this value occurs at the angle of 90 degrees.