## 4 Model Validation
### Simulation Results  
The computation of the impact force on the shuttle ferry is performed by using the ship model data at different speeds. The results are plotted in Figures 14-16 and also given in Table 4. In Figures 14-16, the blue vertical lines indicate the ice force at each time step. The red horizontal lines are the model test data while the black dashed lines are the mean values and the green lines indicate the standard deviation of computed results. It can be seen that the predicted ice force converges to the model test data with the increasing speed. However, the discrepancy is large at the lowest speed, case 1. For the two cases, Cases 2 and 3, a good agreement is observed with an error less than 10%. Figure 14: Result comparison for \(V=0.41\) m/s: (**a**) Case 1: Initial setup; (**b**) Case 1.1: Modified setup. Figure 13: Two examples of Ice breaking pattern captured from ice model test (In Appendix B of AARC Report A-555): (**a**) an estimation of the breaking points indicated by back dots and ice floes marked with numbering for an average ice thickness of 26 mm, (**b**) ice breaking pattern with an average ice thickness of 31 mm [23]. “Reproduced with permission from [Aker Arctic Technology Inc, SSPA Sweden AB and SLL], published by [Aker Arctic Technology Inc], 2017”. The ice breaking lengths are calculated and compared with the reference one from empirical Equations (2) and (3), as shown in Table 5. The computed breaking length \(l_{b1}\) is larger than the \(l_{b2}\), and both increase with increasing ship speed. Compared to the ice breaking patterns in Figure 13, the computed values of \(l_{b1}\) seem reasonable when studying the size of ice pieces in the outside layers from Figure 13. The small ice pieces in the middle are created by the ship body movement when the ice floes slide down along the hull surface, those ice floes deform several times thus cannot represent the ice breaking length. As the different collision locations are evaluated along the ship shoulder, it is interesting to investigate its influence on the discrepancy of the ice forces. Crushing forces in relation to collision locations at different speeds are presented in Figure 18. It clearly seen that the higher speed triggers higher contact forces and the closer to the ship stem, the bigger the force is. Usually, a shoulder collision is only evaluated at location (\(x_{3}\), B/4), but Figure 18 can be a good example to illustrate the effect of location on the deciding ice-shoulder impact force. In order to understand the discrepancy in the predicted force and the model test results at the lower speeds, computed crushing and bending forces are plotted together with measured model test data in Figure 19. The maximum ice bending force and crushing force at (\(x_{3}\), B/4) for both the stem and shoulder are selected to make a comparison. The red triangle represents the ice breaking force for the model test data. It can be seen from Figure 19, that the model test data, at the lowest speed, is approximately equivalent to the crushing force, while the second one is in between of crushing and bending force, while the third one, at the highest speed, matches the ice bending force. It can be observed that for low speeds, the ship model test data only indicates crushing not bending. The ice breaking force should be larger with a combination of two components from a statistical point of view. Ship speed also plays an important role in deciding the main failure mode. It can be concluded that the prediction model may be accurate when both crushing and bending occurs and the ice bending force is assumed to be the dominant component in the ice breaking modes. Figure 18: Crushing force in relation to collision location at different speeds.