The stability of a freely floating ship

The paper presents the problem of calculating the righting arms (GZ-curve) for a freely floating ship, longitudinally balanced at each heel angle. In such cases the GZ-curve is ambiguous, as it depends on the way the ship is balanced. Three cases are discussed: when the ship is balanced by rotating her around the trace of water in the midships, around a normal to the ship plane of symmetry (PS), and around a normal to the initial waterplane, fixed to the ship, identical with the curve of minimum stability. In all these cases the direction of the righting moment in space and area under the GZ-curves, which is the lowest possible, are preserved. Angular displacements (heel and trim) are the Euler's angles related to the relevant reference axis. The most important features of the GZ-curve with free trim are provided. Exemplary calculations illustrate how the way of balancing affects the GZ-curves. © 2017: The Royal Institution of Naval Architects.