Steaming on Convex Hulls

Abstract

This is a sea story about using a simple classroom example to save a great deal of money, as well as to convince beginning Postgraduate Naval School operations research students—experienced, skeptical military officers—that mathematical analysis can yield immediate results. The application is planning a ship’s transit from one point to another in a fixed amount of time, given that the ship can operate with one or more of its propulsion plants idled to save fuel. Simple analysis yields nonintuitive results that US Navy shipboard energy-conservation guides overlook. One of the authors (Kline) solved this homework problem as a student and subsequently applied this example when he took command of USS AQUILA, a patrol hydrofoil missile ship. AQUILA achieved results so striking in comparison to her sister ships that the squadron material officer inspected her engineering plant to ensure that no safety settings were being overridden to achieve this record. Kline’s spreadsheet decision-support tool was provided to other hydrofoil commanders. A more general version has been conveyed to the US Navy. Considering that our navy spends about a billion dollars per year on fuel for surface-combatant ships alone, this development promises substantial, long-term returns. “But thou, contracted to thine own bright eyes, Feed'st thy light'st flame with self-substantial fuel.” Shakespeare, Sonnet I