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 ψ ψ ( Y_ψ Y ψ , N_ψ N ψ ) appear, which have not been considered in existing studies. Y_ψ Y ψ and N_ψ N ψ 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_ψ Y ψ and N_ψ N ψ , and the course stability was investigated. As a result, we found that the effect of Y_ψ Y ψ and N_ψ N ψ on course stability cannot be neglected when the water depth becomes shallower. In case of the studied container ship, the consideration of Y_ψ Y ψ and N_ψ N ψ causes the ship to shift to the course stable direction.