## 6 Results
### Optimal Hull  
Table 9 compares the hydrostatics of the optimal hull form with that of original hull form. Firstly, the displacement and the block coefficient \(C_{B}\) are essentially unchanged. This is because the displacement of the modified hull forms was allowed to vary within 0.015% of the original hull displacement, which is equivalent to \(|\Delta C_{B}|\leq 0.0001\). The wetted surface area has been changed only slightly by 0.021%. The longitudinal center of buoyancy \(LCB\), however, is increased noticeably, which implies that more volume is displaced to the frontal part. This is consistent with the trend of hull form variation described earlier, i.e., the volume increase at the bulbous bow in the entrance part ahead of 17 ST and the volume decrease in the shoulder part. Figure 9 presents the SAC, the body plan, the waterplane, and the profile of optimal hull form in comparison with those of original hull form. The forward movement of volume for the optimal hull is also discernible from the SACs as well as the body plans. On the other hand, the waterplane and the profile shapes scarcely exhibit the difference between original hull and optimal hull. This indicates that the hull form modification was not significant in terms of volume distribution at the design draft \(Z_{D}\) and the bulb height. Figure 8: Development of hull form variation during the optimization process. (**a**) Initial optimization period; (**b**) Latter optimization period. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Displacement** & \(C_{B}\) & **Wetted Surface** \\  & **(m\({}^{3}\))** & **\(C_{B}\)** & **Area (m\({}^{3}\))** & **\(LCB\)(\%)** \\ \hline Original & 52,030 & 0.6505 & 9495 & \(-1.47\) \\ Optimal & 52,036 & 0.6506 & 9497 & \(-1.34\) \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Comparison of hydrostatics between original and optimal hull forms. It is worth mentioning that the hydrodynamic performance of the optimal hull described in the previous section is not the final one. This is because the running attitude of the optimal hull was assumed to be the same as that of the original hull. Therefore, it needs to be recalculated under the free condition with the correct force and moment balance being accounted for. Table 10 contains such results for the optimal hull and further compares with the original hull. Although the \(C_{TM}\) value in Table 10 is slightly different from the value in Table 8, the amount of \(C_{TM}\) reduction of 1.8% remains unchanged. Figure 10 compares the wave profiles on the hull between the original hull form and the optimal hull form. It is noteworthy that the optimal hull form yielded generally milder wave profile except for the slightly higher 1 st peak. This suggests the reduction in the wavernaking resistance for the optimal hull form, which is also consistent with the 6.5% reduction in the pressure resistance coefficient \(C_{P}\). In order to facilitate the comparison between the wave generation in a wider space, Figure 11a plots the contours of wave elevation for two hull forms. It is observed that the area of wave trough region, colored blue, near the shoulder is diminished for the optimal hull form. This is also consistent with the milder wave profile for the optimal hull form observed in Figure 10. Figure 11b provides a comparison in different perspectives--hull pressure distribution. Except at the confined region near the bulbous bow, the optimal hull form exhibits relatively wider spacing between pressure contours in the entire forebody than the original hull form. This also leads to the contraction of pressure minima near the midship. These are closely associated with the diminished shoulder wave observed in Figures 10 and 11a. In summary, the free surface RANS simulation results indicate that the wavernaking performance of the optimal hull has been notably improved over the original hull form.