In this study, ship turning in regular waves is investigated after sufficient time has passed after steering. At that time, the ship reaches the so-called periodic steady turning condition, under which the ship turns periodically with a constant drift in waves. The analytical formulas for the turning trajectory in waves are derived using the Fourier series expansion of the surge velocity, lateral velocity, and yaw rate under periodic steady turning conditions. From the obtained formulas, it is found that the ship turning in waves has the following characteristics. The turning trajectory in waves is deformed by ship drift in proportion to time. The drift velocity and the drift direction during turning are then determined by a combination of the average velocity components and first-order velocity components with the turning frequency. Furthermore, the turning trajectory in waves is composed of periodic circular motions with various frequencies in addition to the drift motion, and it is generally not a perfect circle. As a concrete example, using the derived analytical formulas, the turning trajectory for the KCS model in regular waves is analyzed. For the analysis, two turning trajectories obtained using a simulation method based on a two-time scale concept and a free-running model test are used under the same wave conditions. The reasons for the difference between the two are then clarified analytically.

在这项研究中，船舶在转向后经过足够的时间后在规则波浪中转向进行了研究。此时，船舶达到所谓的周期性稳定转向状态，即船舶在波浪中不断漂移的情况下周期性转向。利用周期性稳定转弯条件下的喘振速度、侧向速度和偏航角速度的傅里叶级数展开，推导了波浪中转弯轨迹的解析公式。由所得公式可知，船舶在波浪中转弯具有以下特点。波浪中的转弯轨迹因船舶漂移而与时间成比例地变形。然后，通过平均速度分量和一阶速度分量与转弯频率的组合来确定转弯期间的漂移​​速度和漂移方向。此外，波浪中的转动轨迹除漂移运动外，还由各种频率的周期性圆周运动组成，一般不是完美的圆。作为具体例子，利用推导的解析公式，对KCS模型在规则波中的转弯轨迹进行了分析。为了进行分析，在相同的波浪条件下使用基于两倍尺度概念的模拟方法和自由运行模型试验获得的两条转弯轨迹。然后分析阐明两者差异的原因。分析了KCS模型在规则波浪中的转弯轨迹。为了进行分析，在相同的波浪条件下使用基于两倍尺度概念的模拟方法和自由运行模型试验获得的两条转弯轨迹。然后分析阐明两者差异的原因。分析了KCS模型在规则波浪中的转弯轨迹。为了进行分析，在相同的波浪条件下使用基于两倍尺度概念的模拟方法和自由运行模型试验获得的两条转弯轨迹。然后分析阐明两者差异的原因。