Wing drag minimization by using measure theory

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