Two theories are developed for predicting the hydrodynamic sway force and yaw moment acting on each of two ships while they are moving along parallel paths. In the first case, the two ship hulls are assumed slender, and moving with constant velocities which may differ. This case therefore includes examples such as steady parallel motion in a re-fuelling maneuver, passing of a slow vessel by a faster-moving vessel, passing in opposite directions, and passing of a moored vesel by a moving vessel. In the second case, the effects of shallow water are considered, but now with the restriction that the two vessels must be moving at the same velocity, so that the resulting hydrodynamic interaction is analogous to a two-dimensional bi-plane problem. In both theories, the fluid is assumed to be ideal, and free-surface effects are ignored. Numerical examples are developed for both cases, and encouraging comparisons with existing experiments are noted.
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