## 4 Results and Discussion
### Free-Decay Test  
Free-decay tests for the surge, sway, heave, roll, pitch and yaw DOFs are performed using both the MAP++ and the MoorDyn packages. Details of the simulation settings are shown in Table 6. The LCs (Load Cases) considered here correspond to LCs 1.3a\(\sim\)d in the OC4, Phase II Project. All the \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Line Number**} & \multicolumn{2}{c}{**SPM Configuration**} & \multicolumn{2}{c}{**MPM Configuration**} \\ \cline{2-5}  & **Anchor Node** & **Fairlead Node** & **Anchor Node** & **Fairlead Node** \\ \hline I & 1 & 4 & 1 & 4 \\ II & 2 & 4 & 2 & 5 \\ III & 3 & 4 & 3 & 6 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The composition of line nodes in two different configurations. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Node Number**} & \multirow{2}{*}{**Node Type**} & \multicolumn{4}{c}{**SPM Node Coordinates**} & \multicolumn{4}{c}{**MPM Node Coordinates**} \\ \cline{3-8}  & & **X** & **Y** & **Z** & **X** & **Y** & **Z** \\ \hline
1 & Fix & 398.366 & 689.99 & \(-\)206.00 & 418.800 & 725.38 & \(-\)200.00 \\
2 & Fix & \(-\)796.732 & 0.00 & \(-\)206.00 & \(-\)837.600 & 0.00 & \(-\)200.00 \\
3 & Fix & 398.366 & \(-\)689.99 & \(-\)206.00 & 418.800 & \(-\)725.38 & \(-\)200.00 \\
4 & Vessel & 0.00 & 0.00 & \(-\)20.00 & 20.434 & 35.393 & \(-\)14.00 \\
5 & Vessel & - & - & - & \(-\)40.868 & 0.00 & \(-\)14.00 \\
6 & Vessel & - & - & - & 20.434 & \(-\)35.393 & \(-\)14.00 \\ \hline \hline \end{tabular} Note: in the node type, “Fix” means the anchors, and “Vessel” means the fairleads.  
\end{table} 
Table 3: Global coordinates of the anchor points and the fairlead points in the single-point mooring system and the multi-point mooring system; SPM: Single-Point Mooring, MPM: Multiple-Point Mooring. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Line Properties**} & \multirow{2}{*}{**Value**} \\ \hline Mooring Line Diameter & 0.0766 m \\ Equivalent Line Mass Density in Air & 113.35 kg/m \\ Equivalent Line Mass Density in Water & 108.63 kg/m \\ Equivalent Mooring Line Extensional Stiffness & 753.6 \(\times\) 10\({}^{6}\) N \\ Seabed Drag Coefficient & 1.0 \\ Unstretched Mooring Line Length & 835.5 m \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Major line-properties of the two mooring system configurations. platform and mooring DOFs are enabled while the generator DOFs are disabled. Computations for the inflow wind velocities and aerodynamic loads are disabled, while computations for the hydrodynamic loads, the structural dynamics and the mooring system are enabled. This is because, although there is no wind and wave, the motion of floating wind turbine generates radiated waves that can induce hydrodynamic loads on the platform and the mooring lines. In the free-decay test, the floating system was offset an initial displacement and allowed to damp out until reaching the equilibrium position. From the time-series of the simulation results, as shown in Figure 3, it is found that while the natural periods of the translational modes (surge, sway and heave) do not change due to the SPM layout, the natural periods of the rotational modes (roll, pitch and yaw) are elongated noticeably. This is because the diagonal rotational terms of the mooring stiffness matrix are decreased in the SPM layout, as shown in Equation (6), leading to the slower of the rotational natural periods (natural periods are inversely proportional to the square root of the corresponding mooring stiffness). Furthermore, natural periods and damping ratios of those computed by MoorDyn are slightly larger than those of MAP++, especially for the surge and the sway modes. This is proved clearly by the analysis results of the natural periods and the damping ratios of all the free-decay time-series data (see Table 7). The reason is that MoorDyn includes the effect of line damping and line drag force while MAP++ has not yet considered it.