At the early design stage of a submarine, it is necessary to have a good estimate of the linear manoeuvring coefficients, or derivatives. These are necessary to determine the required size of any appendages to achieve the desired level of motion stability and controllability. Various empirical methods exist to make such estimates, including the influence of appendages. However, methods do not exist to predict the linear rotary coefficients (i.e. \({Y}_{r}^{^{\prime}}\) and \({N}_{r}^{^{\prime}}\)) for a bare hull. Thus, the aim of this work was to determine the values of the linear rotary coefficients for an axisymmetric underwater body as functions of Length to Diameter (L/D) ratio to improve the empirical estimate of these values for a fully appended submarine. The work was performed using validated Reynolds Averaged Navier Stokes (RANS) based simulations to obtain forces and moments on the body. It is considered that the developed expressions for the linear rotary coefficients are adequate for an unappended axisymmetric underwater body at the design stage over the range: 6 ≤ L/D ≤ 14, which can then be used to size and locate the appendages.

在潜艇的早期设计阶段，有必要对线性机动系数或导数进行良好的估计。这些对于确定任何附件所需的大小以实现所需的运动稳定性和可控性水平是必要的。存在各种经验方法来进行此类估计，包括附属物的影响。然而，不存在预测线性旋转系数的方法（即\({Y}_{r}^{^{\prime}}\)和\({N}_{r}^{^{\prime} }\) ) 用于裸露的船体。因此，这项工作的目的是确定轴对称水下体的线性旋转系数值作为长度与直径 ( L/D)的函数) 比率，以改进对完全附加潜艇的这些值的经验估计。这项工作是使用经过验证的基于雷诺平均纳维斯托克斯 (RANS) 的模拟进行的，以获得身体上的力和力矩。据认为，线性旋转系数的开发表达式适用于设计阶段在以下范围内的无附加轴对称水下主体：6 ≤  L/D  ≤ 14，然后可用于确定附件的尺寸和定位。