On the hydrodynamic derivatives with respect to heading angle for ship maneuvering in a canal

This study focused on the equation of motion, hydrodynamic derivatives, and course stability with respect to ship maneuvering in a canal. Based on the potential theory, a consistent linearized equation of motion was derived when a ship maneuvers near the center line of a canal with a symmetrical cross-section and uniform length. In the new equation of motion, hydrodynamic derivatives for the lateral force and yaw moment with respect to ship heading angle \(\psi\) $\psi$ ( \(Y_\psi\) $Y_{\psi }$ , \(N_\psi\) $N_{\psi }$ ) appear, which have not been considered in existing studies. \(Y_\psi\) $Y_{\psi }$ and \(N_\psi\) $N_{\psi }$ are measured by captive tests using a container ship model in a canal model, and they are significant. Furthermore, the course stability criterion for ships in the canal was derived by considering the \(Y_\psi\) $Y_{\psi }$ and \(N_\psi\) $N_{\psi }$ , and the course stability was investigated. As a result, we found that the effect of \(Y_\psi\) $Y_{\psi }$ and \(N_\psi\) $N_{\psi }$ on course stability cannot be neglected when the water depth becomes shallower. In case of the studied container ship, the consideration of \(Y_\psi\) $Y_{\psi }$ and \(N_\psi\) $N_{\psi }$ causes the ship to shift to the course stable direction.