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 rater, 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.
"Analysis of The Pivot Point for a Turning Ship,"
Journal of Marine Science and Technology: Vol. 6
, Article 5.
Available at: https://jmstt.ntou.edu.tw/journal/vol6/iss1/5