Creating alternative airfoil by conformal mapping

Abstract

In recent years the field of research to design more and more efficient airplanes has been growing, considering the rising need for fuel efficiency. In this thesis, we aim to develop a new mathematical formula to model a cross section of an airplane wing what is called an airfoil, by conformal mapping. The resulting flow pattern around this airfoil will be calculated using the same transformation, and implications will be outlined. The main goal is to come up with an improved airfoil geometry then the one that is common be used in modern aeronautics using the lift coefficient. A well-known devise for generating airfoil structures and the resulting flow pattern is the Joukowski transformation. Motivated by this, we come up with a new transformation and calculate the lift exerted on the airfoil. We then compare the results of both transformations and hence the efficiency of the two airfoils, and test whether the new transformation improve existing airfoils.