Newton’s Problem of the Optimal Forebody: History of the Solution

Abstract

Newton’s problem of constructing an axisymmetric forebody part of minimum drag is considered. The solution to this problem, although without any explanation, was given by Newton himself in the main work of his life, Philosophiae Naturalis Principia Mathematica. However, Newton’s prefabricated solution was not understood by aerodynamicists who turned to solving Newton’s problem and some of its generalizations in the middle of the twentieth century. A.N. Krylov translated Newton’s Principia into Russian, giving detailed explanations of many of Newton’s statements, including the discussed problem. Moreover, having explained one of these statements, Krylov formulated the necessary condition for the drag minimum, missed by all Newton readers, not just aerodynamicists, but also such an authority on the variational calculus as Legendre. However, even Krylov’s explanations did not help to understand Newton’s solution to the only who had access to them—Soviet aerodynamicists. The main goal of this article is to describe the history of the Newton problem solution, in which the author happened to participate.