## 4 Model Validation
### Ice Model Test  
The ice model tests for a shuttle passenger ferry were conducted in May 2017 for SSPA Sweden AB at Aker Arctic Technology Inc. [23]. The ferry model is shown in Figure 12. The vessel is designed to operate in the Stockholm archipelago and the main particulars are presented in Table 2. The model was built in scale 1:8.333 and its dimensions and the ice properties can be seen in Table 2. The level ice tests were performed at three speeds according to the specifications given in Table 3, where \(R_{bc}\) is ice breaking component and \(R_{ice}\) is ice resistance. The total resistance is calculated by dividing the resistance into breaking and submersion components. However, the breaking component in the test is independent of the ship velocity and is defined by the ITTC guidelines [24]. The breaking resistance is the total resistance in level ice minus the resistance in the pre-sawn ice which is assumed to represent the resistance without the breaking component.  
Photos of the ice breaking patterns are taken during the model tests and are shown in Figure 13. Each color strap on the ruler is 10 cm, which indicates that the broken ice floe field (less than 1 m) is created by the stem and shoulder of the ship model. In Figure 13a, the broken ice floe can be observed and their boundaries can be depicted. It is be assumed that the out layer ice floe fail only once. The stem and shoulder collision can be roughly indicated by the black dot in Figure 13. Figure 13b shows small ice pieces and they may fail more than once. After they first break off due to ice bending  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{2}{c}{**Full-Scale Ship**} & \multicolumn{2}{c}{**Model**} \\ \hline \(L\) (m) & 26.155 & Scale factor & 8.333 \\ \(B\) (m) & 7.5 & \(L\) (m) & 3.18 \\ \(T\) (m) & 2.3 & \(B\) (m) & 0.9 \\ \(\varphi_{1}\) (deg) & 25 & \(T\) (m) & 0.276 \\ \(\alpha\) (deg) & 30 & \(\mu\) (1) & 0.05 \\ \(C_{b}\) (1) & 0.549 & E (kPa) & 77,979 \\ \(C_{m}\) (1) & 0.896 & \(\sigma_{\ell}\) (kPa) & 53.6 \\ Displacement (kg) & 247,091 & E/\(\sigma_{\ell}\) & 1456 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Principal particulars of the ferry NB550 and model ship.  
Figure 12: Side view and bottom view of the ferry model NB550 (In Appendix C of AARC Report A-555): (**a**) Side view; (**b**) Bottom view [23]. “Reproduced with permission from [Aker Arctic Technology Inc, SSPA Sweden AB and SLLI] published by [Aker Arctic Technology Inc.], 2017”.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**No.** & \(V\) **[m/s]** & \(h_{i}\) **[mm]** & \(\sigma_{f}\) **[kPa]** & \(R_{bc}\) **(F\({}_{x}\)) [N]** & \(R_{ice}\) **[N]** & \(F_{x}\) **[N]** \\ \hline
1 & 0.41 & 26 & 58.7 & 16.6 & 67.2 & 31.4 \\
2 & 0.92 & 26.8 & 51 & 44.8 & 157.6 & 84.75 \\
3 & 1.38 & 30.8 & 55.1 & 77.6 & 240.7 & 146.8 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Model test conditions.  
failure, they break into more pieces when sliding along the ship hull. The ice breaking length is around 10-30 cm. Multi-contact seems to be happening around the shoulder area. By considering the ship symmetry, the ship geometry, and ice breaking pattern, it is assumed that the stem contact is a single event while the shoulder impact has multiple collision locations ranging from one to four on each side. The simulation is conducted according to such assumption.