# Analysis of Trends in Mega-Sized Container Ships Using the K-Means Clustering Algorithm
## 2 Materials and Methods
### Prediction of Rrends for Mega-Sized Container Ship  
In this study, the size of future mega-sized container ships was predicted by analyzing the main dimensions of container ships. Table 8 presents the results for a 75% coverage rate calculated through regression analysis. The results indicate that a larger ship size corresponds to a larger change in B than in LOA and Lpp. Table 9 shows the average and standard deviation values of changes in LOA and B of the ship according to the change in the ship's main dimensions whenever 10,000-DWT is increased for each cluster. As a result, the average change in LOA according to the 10,000-DWT increase in Cluster 1 was 29.29 m, and the average change in B was 2.91 m. It was analyzed that the change according to the 10,000-DWT increase was the largest among all clusters. For Cluster 2, LOA was analyzed as 9.13 m and B as 1.71 m. In the case of Cluster 3, LOA was 4.73 m and B was 1.10 m, showing the smallest change when increasing 10,000-DWT. The coefficient of variation is a measure of the ratio of the standard deviation to the mean value, and since it is a relative value, it can be used to compare variations between distributions. That is, the higher the coefficient of variation, the greater the deviation of the length change. In the case of Cluster 3, the coefficient of variation was analyzed to be high, and this section is a section in which the main dimensions increase step by step as the size of the ship increases. Draft does not increase further and remains constant at approximately 16.0-16.7 m. This is because major container piers worldwide cannot accommodate ships with a maximum d that exceeds 17.0 m. Table 10 presents the maximum depth at major container ports such as Rotterdam Port, Hong Kong Port, Shanghai Port, Singapore Port, and Busan New Port. According to [PERSON] and [PERSON] [4], if a 25,000-TEU container ship has a maximum d of 16.9 m, the only port that would satisfy the water depth requirements even at high tide is Singapore Port. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Classification** & **DWT (ton)** & **TEU** & **LOA (m)** & **Lpp (m)** & **B (m)** & **d (m)** \\ \hline \multirow{4}{*}{Small Feeder} & 3000 & 302 & 86 & 80 & 15.9 & 5.4 \\ \cline{2-7}  & 5000 & 503 & 105 & 98 & 18.4 & 6.4 \\ \cline{2-7}  & 10,000 & 1006 & 138 & 129 & 22.4 & 8.0 \\ \hline Large Feeder & 20,000 & 2012 & 180 & 169 & 27.3 & 10.0 \\ \hline \multirow{4}{*}{Panamax} & 30,000 & 3018 & 211 & 198 & 30.6 & 11.3 \\ \cline{2-7}  & 40,000 & 4024 & 235 & 222 & 33.1 & 12.4 \\ \cline{2-7}  & 50,000 & 5030 & 257 & 243 & 33.1 & 13.3 \\ \cline{2-7}  & 55,000 & 5533 & 266 & 252 & 34.2 & 13.8 \\ \cline{2-7}  & 60,000 & 6036 & 275 & 261 & 36.9 & 14.0 \\ \hline Post & 70,000 & 7042 & 297 & 283 & 40.7 & 14.0 \\ \cline{2-7} Panamax & 85,000 & 8551 & 313 & 299 & 40.7 & 14.4 \\ \hline Super Post & 100,000 & 10,060 & 328 & 313 & 45.1 & 14.8 \\ \cline{2-7} Panamax & 120,000 & 12,072 & 336 & 329 & 47.8 & 15.2 \\ \hline \multirow{4}{*}{Very Large Container Ship} & 130,000 & 13,078 & 348 & 333 & 48.9 & 16.0 \\ \cline{2-7}  & 140,000 & 14,084 & 368 & 352 & 48.9 & 16.0 \\ \cline{1-1} \cline{2-7}  & 165,000 & 16,599 & 378 & 361 & 51.2 & 16.0 \\ \cline{1-1} \cline{2-7}  & 180,000 & 18,108 & 378 & 361 & 56.1 & 16.3 \\ \hline Ultra Large Container & 200,000 & 20,120 & 400 & 385 & 59.5 & 16.3 \\ \cline{1-1} \cline{2-7} Ship & 240,000 & 24,144 & 400 & 385 & 61.0 & 16.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Standard design of container ship according to a 75% coverage rate. In this study, the maximum d was fixed at 17 m for the trend analysis of mega-sized container ships. The increases in LOA, Lpp, and B were set based on the size of a 40-ft container. This is because 40-ft containers are the most common and constitute \(\sim\)90% of all shipping containers. Because container shipping transports 90% of the world's freight, over 80% of the world's freight moves via 40-ft containers.