Sinkage and trim of two ships passing each other on parallel courses

A theoretical method is used to predict the sinkage and trim of two moving ships as they pass each other, either from opposite directions, or as one ship overtaking the other. The description is simplified to open water of shallow constant depth. The method is based on linear superposition of slender-body shallow-water flow solutions. It is shown that even for head-on encounters, oscillatory heave and pitch effects are small, and sinkage and trim can be calculated using hydrostatic balancing. Results are compared to available experimental results, and applied to an example situation of a containership and bulk carrier in a head-on or overtaking encounter. Using dimensional analysis, simple approximate formulae are then developed for estimating the maximum sinkage of two similar vessels in a passing encounter.