# Numerical Study on Hydrodynamic Performance of a New Semi-Submersible Aquaculture Platform
## 4 Results and Discussion
### Dynamic Response in Waves, Winds, and Currents
#### 4.3.2 Six-Degree-of-Freedom Motion  
Table 11 presents the statistics of the motion of six-degree-of-freedom at the center of gravity (the average value of the results obtained from five different seed numbers) under various loading cases for survival conditions. The statistics of motion for operation conditions are omitted to reduce the length of this paper. It is observed that the motion of six-degree-of-freedom is acceptable for the platform operated in the specific sea area. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & & **LC1** & **LC2** & **LC3** & **LC4** & **LC5** & **LC6** & **LC7** & **LC8** & **LC9** & **LC10** \\ \hline \multirow{4}{*}{Surge} & Mean (m) & \(-5.20\) & \(-4.77\) & \(-4.26\) & \(-2.34\) & \(0.00\) & \(-5.69\) & \(-5.23\) & \(-4.37\) & \(-2.07\) & \(0.15\) \\  & Std. Dev. & \(0.18\) & \(0.16\) & \(0.23\) & \(0.29\) & \(0.02\) & \(0.18\) & \(0.17\) & \(0.25\) & \(0.27\) & \(0.06\) \\  & Max (m) & \(-4.61\) & \(-4.22\) & \(-3.41\) & \(-1.45\) & \(0.12\) & \(-5.09\) & \(-4.68\) & \(-3.46\) & \(-1.24\) & \(0.47\) \\  & Min (m) & \(-6.24\) & \(-5.69\) & \(-5.26\) & \(-3.68\) & \(-0.10\) & \(-6.74\) & \(-6.19\) & \(-5.41\) & \(-3.32\) & \(-0.19\) \\ \hline \multirow{4}{*}{Sway} & Mean (m) & \(0.00\) & \(4.18\) & \(5.13\) & \(5.98\) & \(6.33\) & \(0.32\) & \(4.53\) & \(5.56\) & \(6.68\) & \(7.07\) \\  & Std. Dev. & \(0.00\) & \(0.16\) & \(0.16\) & \(0.27\) & \(0.38\) & \(0.01\) & \(0.16\) & \(0.21\) & \(0.31\) & \(0.39\) \\  & Max (m) & \(0.00\) & \(4.82\) & \(5.82\) & \(7.19\) & \(8.22\) & \(0.37\) & \(5.17\) & \(6.51\) & \(8.15\) & \(9.13\) \\  & Min (m) & \(-0.01\) & \(3.61\) & \(4.56\) & \(4.90\) & \(4.79\) & \(0.29\) & \(3.94\) & \(4.88\) & \(5.54\) & \(5.59\) \\ \hline \multirow{4}{*}{Heave} & Mean (m) & \(-6.03\) & \(-6.06\) & \(-6.09\) & \(-6.10\) & \(-6.12\) & \(-6.00\) & \(-6.02\) & \(-6.04\) & \(-6.06\) & \(-6.08\) \\  & Std. Dev. & \(0.09\) & \(0.09\) & \(0.09\) & \(0.15\) & \(0.25\) & \(0.09\) & \(0.09\) & \(0.09\) & \(0.16\) & \(0.24\) \\  & Max (m) & \(-5.56\) & \(-5.60\) & \(-5.63\) & \(-5.43\) & \(-4.95\) & \(-5.52\) & \(-5.55\) & \(-5.57\) & \(-5.33\) & \(-4.91\) \\  & Min (m) & \(-6.44\) & \(-6.47\) & \(-6.48\) & \(-6.77\) & \(-7.15\) & \(-6.41\) & \(-6.42\) & \(-6.43\) & \(-6.77\) & \(-7.10\) \\ \hline \multirow{4}{*}{Roll} & Mean (\({}^{\circ}\)) & \(0.00\) & \(-0.05\) & \(-0.32\) & \(-0.62\) & \(-0.73\) & \(-0.08\) & \(-0.16\) & \(-0.54\) & \(-0.87\) & \(-0.96\) \\  & Std. Dev. & \(0.00\) & \(0.11\) & \(0.27\) & \(0.58\) & \(0.96\) & \(0.01\) & \(0.12\) & \(0.29\) & \(0.61\) & \(0.95\) \\  & Max (\({}^{\circ}\)) & \(0.02\) & \(0.42\) & \(0.81\) & \(1.65\) & \(2.63\) & \(-0.03\) & \(0.31\) &The minimum amplitude of surge motion is observed at the condition LC5, as the loads at a heading angle of 90\({}^{\circ}\) have little impact on surge motion. However, the maximum amplitude of surge motion is observed at the condition LC4, rather than LC1. This is likely due to the asymmetry in the longitudinal direction. Similar results for the amplitude of surge motion can be found for damaged survival conditions. The amplitude of sway motion increases gradually with the incident angle gradually varying from 180\({}^{\circ}\) (LC1) to 90\({}^{\circ}\) (LC5), for both intact and damaged survival conditions. The sway motion is minimally impacted by the condition of the mooring lines. Under the conditions LC1, LC2, and LC3, the amplitude of heave motion is almost the same, measuring 0.88 m for LC1, 0.87 m for LC2, and 0.85 m for LC3. Under the condition LC4, the amplitude of heave motion increases to 1.34 m, a 58% increase compared with the condition LC3. The maximum amplitude of heave motion, reaching 2.22 m, is observed at the condition LC5. This indicates that the loads of 90\({}^{\circ}\) heading angle have the largest effects on the motion of heave, which is consistent with the variation of the mooring line tension of Line 1. The differences in heave motion between intact and damaged survival conditions are not significant.