## 4 Results  
### Bow Hull form Variation  
The objective function is to minimize the wavemaking resistance in calm water (\(R_{\text{W}}\)) at the design speed. The equality constraints are the principal dimensions of \(L_{WL}\), \(B\), \(T\) (\(T_{F}\), \(T_{A}\), \(T_{M}\)), and \(\
abla\). Two design variables of chine breadth increment ratio (\(\Delta Y\)) and deadrise angle (\(\beta\)) are taken into account. The chine breadth increment ratio is the independent variable and defined as the nondimensional increment ratio between \(B_{C}\) of the varied hull form and that of the initial hull form, i.e., \(\Delta Y=2(B_{C,paried}-B_{C,initial})/B\). \(\Delta Y\) can vary along the longitudinal position of the ship, attaining a maximum value of \(\Delta Y_{M}\) at the midship. The deadrise angle is a dependent variable and defined as the angle between the horizontal plane and the hull bottom. In order to satisfy the displacement constraint, \(\beta\) has been adjusted for each \(\Delta Y_{M}\) value. The design variable \(\Delta Y_{M}\) and \(\beta\) are displayed in Figure 5.  
Among other design variables, \(\Delta Y\) has a significant influence on the resistance performance of fishing vessels with chine lines [14; 15]. Since the chine breadth mainly affects the wavemaking resistance, it is varied only in the forebody in this study. In other words, \(\Delta Y\) increases linearly from zero to \(\Delta Y_{M}\) in the forebody, maintaining \(\Delta Y_{M}\) throughout in the afterbody. Figure 6 illustrates five different hull forms with varying \(\Delta Y_{M}\). Note that \(\Delta Y_{M}=0.0\) corresponds to the initial hull form. Further, the case \(\Delta Y_{M}=0.042\) becomes the maximum allowable increment for which the chine breadth \(B_{C}\) becomes equal to the mold breadth \(B\). \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \(R_{TM}\) [N] & Trim [\({}^{\circ}\)] & **Sinkage [m]** \\ \hline Model Test & 106.45 & 3.55 & \(-0.014\) \\ CFD (coarse, 1.39M cells) & 109.13 & 3.69 & \(-0.001\) \\ CFD (medium, 1.89M cells) & 108.18 & 3.46 & \(-0.008\) \\ CFD (fine, 2.66M cells) & 108.03 & 3.48 & \(-0.005\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Model test and CFD results of the initial hull form at design speed. Figure 5: Design variables for hull form variation. Figure 7a presents the ratio of total resistance (\(R_{TM}/R_{TM0}\)) in model scale predicted at the design speed with varying \(\Delta Y_{M}\). Here, \(R_{TM0}\) corresponds to the total resistance of the initial hull form (\(\Delta Y_{M}=0\)). Note that the values of \(R_{TM}\) are compared instead of resistance coefficient \(C_{TM}\). This is because the wetted surface area varies for each hull form variation. It is observed that \(R_{TM}\) decreases for negative values of \(\Delta Y_{M}\), i.e., for narrower chine breadths. In particular, maximum resistance reduction by 2.36% occurs at \(\Delta Y_{M}=-0.084\), which is considered to be the optimal value. Variation of trim and sinkage are plotted against \(\Delta Y_{M}\) in Figure 7b,c, respectively. For a relatively small change in the chine breadth \(B_{C}\) (\(-0.05\leq\Delta Y_{M}\leq 0.05\)), the trim and the sinkage do not change appreciably. On the contrary, both change significantly for a larger change in the chine breadth \(B_{C}\) corresponding to \(\Delta Y_{M}\leq\,-0.05\). In this region, the hull sinks less, and the trims more to the stern. The trim angle for the optimal \(\Delta Y_{M}=-0.084\) becomes approximately \(4^{\circ}\). This large trim angle may cause a serious safety issue due to the limited forward visibility. Therefore, a second measure to decrease the excessive trim angle without deteriorating the resistance performance, which will be discussed in the next section. Wave patterns and pressure distributions of the initial and optimal hull form at design speed are compared in Figure 8. The optimal hull form shows a significant decrease in the bow wave, and the stern shoulder wave is also found to decrease slightly.