Analysis of the pivot point for a turning ship

An approximate method based on the steady state linearized sway-yaw equations is proposed to estimate the pivot point of a turning ship. The location of the pivot point is directly related to the ratio of the `sway-rudder' and `yaw-rudder' gain coefficients, which can be readily computed from six linear hydrodynamic coefficients. Hence, estimation of the pivot point for a ship at the design stage is made possible with minimum hydrodynamic coefficients information required. Numerical results indicate that based on the proposed method, the estimated pivot point position for a turning ship correlates well with the solution obtained from a full nonlinear differential equations of motion-based analysis, where some forty hydrodynamic coefficients are involved. Existence of similar pattern in the sway speed v and yaw rate r, known as the cancellation effect in a turning maneuver significantly extends the applicability of the proposed steady condition-based approach. Specifically, the ratio v/r that defines the pivot point reaches a steady value long before the ship reaches the steady state phase of the turning.