Wing drag minimization by using measure theory

Abstract

In this article, the problem of determining the shape of a thin wing for minimum drag has been<br><br>examined. In order to determine the optimal shape, we have extended a measure theory-based method.<br><br>Using an embedding procedure, the problem of finding the optimal shape is reduced to one consisting<br><br>of minimizing a linear form over a set of positive measures. The resulting problem can be approximated<br><br>by a finite dimensional linear programming problem. The solution of this problem is used to construct<br><br>a nearly optimal shape. A numerical example is given to illustrate the method.