# Analysis of a Collision-Energy-Based Method for the Prediction of Ice Loading on Ships
## 4 Results
### Analysis of Data Set B  
Based on the description of the prevailing operating conditions of data set B, we calculate corresponding line ice loads for each collision scenario defined in Table 2. An excerpt of the results is presented in Figure 7, comparing measured and calculated line ice loads for four different contact geometry assumptions, namely round and angular, right-apex oblique and symmetric v-wedge. In Figure 8, we compare loads calculated for each collision scenario with the corresponding measurements in terms of 10-min mean, standard deviation (SD) and maximum. Table 4 presents the percentage-deviations between the measured and the calculated 10-min mean \(\Delta_{mean}\) and extreme \(\Delta_{max}\) values. As per Table 4, we find that a relatively good agreement is obtained by assuming either angular or symmetric v-wedge contact geometry in combination with ship-ice floe impact with a load length of 0.4 m. All other combinations of assumptions result in \(\Delta_{max}\) and or \(\Delta_{mean}\) exceeding \(\pm\) 40%, indicating that their descriptions of the ship-ice interaction significantly deviate from the actual ship-ice interactions behind data set B. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline
**Contact** & \multicolumn{3}{c}{**Ship–Ice Floe Impact**} & \multicolumn{3}{c}{**Ship–Ice Field Impact**} \\ \hline
**Geometry** & **Load Length of 0.4 m** & **Load Length of 0.8 m** & **Load Length of 0.4 m** & **Load Length of 0.8 m** \\ \hline  & \(\Delta_{mean}\) & \(\Delta_{max}\) & \(\Delta_{mean}\) & \(\Delta_{max}\) & \(\Delta_{mean}\) & \(\Delta_{mean}\) & \(\Delta_{max}\) \\ Angular & \(\mathbf{-0.80\%}\) & \(\mathbf{-36.00\%}\) & \(\mathbf{24.20\%}\) & \(-46.60\%\) & \(\mathbf{-14.00\%}\) & \(-84.90\%\) & \(\mathbf{11.00\%}\) & \(-93.60\%\) \\ Right-apex & 70.30\% & \(\mathbf{37.30\%}\) & \(91.30\%\) & \(\mathbf{26.60\%}\) & \(56.30\%\) & \(\mathbf{-18.90\%}\) & \(78.50\%\) & \(\mathbf{-29.70\%}\) \\  Round & 54.00\% & \(\mathbf{13.70\%}\) & \(76.50\%\) & \(\mathbf{2.80\%}\) & \(\mathbf{-25.90\%}\) & \(-86.80\%\) & \(\mathbf{-0.90\%}\) & \(-95.50\%\) \\  Symmetric V Wedge & \(\mathbf{23.40\%}\) & \(\mathbf{-12.10\%}\) & \(\mathbf{47.70\%}\) & \(\mathbf{-23.00\%}\) & \(49.70\%\) & \(\mathbf{-19.00\%}\) & \(72.50\%\) & \(\mathbf{-29.80\%}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Percentage-deviations between loads calculated for various collision scenario assumptions and the measured values of data set B. (Bold font indicates that the deviation is below \(\pm\)40%.) \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Contact** \\ **Geometry** \\ \end{tabular} } & \multicolumn{3}{c}{**Ship–Ice Floe Impact**} & \multicolumn{3}{c}{**Ship–Ice Field Impact**} \\ \cline{2-9}  & **Load Length of 0.4 m** & **Load Length of 0.8 m** & **Load Length of 0.4 m** & **Load Length of 0.4 m** & **Load Length of 0.8 m** \\ \cline{2-9}  & \(\Delta_{mean}\) & \(\Delta_{max}\) & \(\Delta_{mean}\) & \(\Delta_{max}\) & \(\Delta_{mean}\) & \(\Delta_{max}\) & \(\Delta_{mean}\) & \(\Delta_{max}\) \\ \hline Angular & \(\mathbf{33.10\%}\) & \(\mathbf{32.20\%}\) & \(54.40\%\) & \(64.60\%\) & \(\mathbf{9.50\%}\) & \(\mathbf{-34.70\%}\) & \(\mathbf{31.80\%}\) & \(\mathbf{-0.50\%}\) \\ Right-apex & 98.30\% & \(97.60\%\) & \(114.40\%\) & \(121.70\%\) & \(78.00\%\) & \(\mathbf{37.30\%}\) & \(96.30\%\) & \(69.30\%\) \\ \
\begin{tabular}{c} Round \\ \end{tabular} & \(55.50\%\%\) & \(75.30\%\) & \(75.60\%\) & \(102.80\%\) & \(-58.00\%\) & \(\mathbf{-36.80\%}\) & \(\mathbf{-36.80\%}\) & \(\mathbf{-2.70\%}\) \\
\begin{tabular}{c} Symmetric V \\ \end{tabular} & \(56.20\%\) & \(76.20\%\) & \(55.30\%\) & \(85.40\%\) & \(52.70\%\) & \(\mathbf{27.00\%}\) & \(73\%\) & \(59.70\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Percentage-deviations between loads calculated for various collision scenario assumptions and the measured values of data set A. (Bold font indicates that the deviation is below \(\pm\)40%.