On the Steady Turn of a Ship

Abstract

A wing of zero thickness and small aspect ratio is used as a mathematical model for a ship in steady turn. The shape of the wing is given by the projection of the hull on the vertical plane of symmetry and the aspect_ratio by the relation draft/length of the ship. As the ship moves in a turn, the angle of attack in each section is different; this fact is approximately simulated in the model by adding a camber to the wing and letting the wing follow a straight course. &&Near the ship three regions are identified: the region downstream of the section of maximum draft (span), in which the Kutta condition is required to be satisfied, the region near midship, and the region near the bow. In the first region, the condition on the free surface is a rigid wall condition, thus permitting a reflection into the upper space. The acceleration potential concept is used in order to describe the flow in this region. In the region near midship, a reflection into the upper space is also possible. The method of solution is similar to the usual slender body theory for ships. In the region near the bow, where the free surface suffers large deformations, the rigid_wall condition at the free surface is no longer valid. A different problem is formulated here, and Fourier transform approach is used to solve the problem in this region. &&The method of matched asymptotic expansions was used to solve the problem. Therefore, the condition at [ ] in each of the problems mentioned in the preceding paragraph is given by the far_field expansion, which describes the flow far from the ship. &&For a simple case, when the ship has a constant draft in the bow region, the shape of the free surface near the ship in the bow region has been calculated.