Wave drag and wave patterns by ships moving in a single-file formation

Abstract

To minimize energy expenditure for each individual, animals adopt distinctive formations, such as fish schooling, “V” formation by flying birds, and single-file formation by waterfowls. The phenomenon of ducklings following their mothers in a single-file configuration has been revealed by the mechanisms of wave-riding and wave-passing. Drawing inspiration from this phenomenon, an investigation is undertaken on ships moving in a single-file formation. The objective is to quantify how much energy can be saved in different configurations. In this study, a three-dimensional boundary element method incorporating linear free-surface boundary conditions is used to obtain the wave drag and wave patterns. It is found that when constructive wave interference occurs in a two-ship formation, the wave resistance of the trailing ship increases and the leading ship experiences a decrease in its wave drags, especially when the two ships are in close proximity. Mutual benefit arises when destructive wave interference occurs between two ships. In addition, increasing the size of the trailing vessel facilitates the effect of wave-riding by the leading ship, but this effect becomes less pronounced as the speed increases. In a multi-ship formation configuration, changing the size of the leading ship will have a localized effect on the wave-passing, but the fleet will eventually tend to a dynamic equilibrium. When the position of the first trailing vessel is changed, there is similarly a localized effect on the wave-passing. Adjusting the first trailing ship to the position of the constructive wave interference is not favorable to reducing its own drag but enhances the wave-riding effect of its close follower. Finally, to achieve wave-passing, the trailing ship does not necessarily have to occupy an optimum position. This can still be accomplished if the trailing ship moves backward by an integer multiple of wavelength.