Mathematical Modeling: Convoying Merchant Ships

Abstract

Few events of the twentieth century have had as much impact as who won World Wars I and II. In both wars, Great Britain reduced the sinkings of merchant ships by German submarines through sailing their ships in groups (convoying). Before instituting convoys, Great Britain suffered severe losses to attack by German submarines. In World War II, Japan allowed merchant ships to sail individually. Japan's losses to U.S. submarines were a critical element in Japan's defeat (Roscoe 1949). In a convoy, many merchant ships sail in a large group under the escort of naval warships to protect the poorly armed merchant ships. In World War I, the British admiralty opposed sending merchant ships grouped together in convoys for several reasons that proved to be false. I proposed the problem of whether or not the British should convoy their merchant ships to my preservice teachers in a course in mathematical modeling for middle school teachers. While working on this problem, the students analyze and rebut each of the admiralty's arguments against convoying. Mathematical models are used to support the rebuttals.