Stability of free-floating ship. Part I

Problem of calculation of righting arms of the free-floating ship, i.e. longitudinally balanced at any heel angle, was formulated. In such a case of particular interest for a ship in the damage condition, the righting arms are ambiguous as they depend on a way the heeling moment acts. Two cases were considered: when the heeling moment is parallel to the ship plane of symmetry, and the case when it performs the least work, i.e. when the moment is parallel to the main axis of ship waterplane. It was demonstrated that angular translations (heel and trim) are then the Euler angles associated with a relevant reference axis. Some cases of the incorrect defining and using of those angles in today design practice were indicated. The most important features of the curve of righting arms of free-floating ship were demonstrated.