Minimizing fuel consumption in ocean vessels

The rate at which a ship consumes fuel is nonlinearly related to both speed and amount of fuel in the ship´s tanks. A model for this phenomenon is developed. The problem of finding the velocity pattern (as a function of time) necessary to move the ship between two fixed points in a fixed amount of time is then considered. It is determined that the optimal velocity pattern is a constant. A typical numerical example is presented to illustrate the savings in fuel which might result when compared to other possible velocity patterns.