# Statistical Analysis of the Weight and Center-of-Gravity Position of an Empty Container Ship
## 4 Analysis of the Test Results
The qualitative verification was carried out by comparing the accuracy of the weight calculations for class \(M_{1}\) (weight of the ship's hull with superstructure without equipment) and for class \(M_{4}\) (weight of the engine room) of a light ship from the developed formulas with the corresponding formulas published in the scientific literature [14; 15; 29]. The results of these analyses are shown in Table 8, (measured data for container ship A [39] and B [16] were used for these analyses). The predicted weight of class \(M_{1}\) from the formulas in the publications varies from 2% to 43% compared to the measurement (ships A and B). The \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Container Ship A [39].**} & \multicolumn{3}{c}{**Container Ship B [16].**} \\ \cline{2-7}  & **Measured** & **Calculations as per Reg.** & **Error** & **Measured** & **Calculations as per Reg. Formulas (34)–(41)** & **Error** **of Calculation [\%]** \\ \hline \(M_{1}\) & 4153.8 & 4462.7 & \(-7.4\%\) & 9331.0 t & 8778.71 t & 5.9\% \\ \hline \(M_{2}\) & 1137.2 & 1092.1 & 4.0\% & 1367.0 t & 1202.8 t & 12.0\% \\ \hline \(M_{3}\) & 236.6 & 275.6 & \(-16.5\%\) & 416.0 t & 430.3 t & \(-3.4\%\) \\ \hline \(M_{4}\) & 738.7 & 695.9 & 5.8\% & 1073.0 t & 1022.4 t & 4.7\% \\ \hline \(M_{5}\) & 385.6 & 348.9 & 9.5\% & 505.0 t & 462.8 t & 8.4\% \\ \hline \(M_{6}\) & 112.0 & 105.3 & 6.0\% & 170.0 t & - & - \\ \hline \(M_{7}\) & 21.9 & 25.8 & \(-17.8\%\) & 41.0 t & 45 t & \(-10.9\%\) \\ \hline \(M_{8}\) & 15.4 & 16.28 & \(-5.7\%\) & 31.5 t & 23.3 t & 26.1\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of values measured for each class of container ship weights with calculations according to regression formulas. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Container Ship A [39]**} & \multicolumn{3}{c}{**Container Ship B [16]**} \\ \cline{2-7}
**Parameter** & **Measurement** & \multicolumn{3}{c}{**Formulas (42)–(44)**} & \multicolumn{3}{c}{**Formulas (42)–(44)**} \\ \cline{2-7}  & **Value** & **Error** & **Value** & **Error** \\ \hline _WLS_ & 6824 t & 6752 t & 0.9\% & 12,935 t & 12,871 t & 0.5\% \\ \hline \(x_{CG}\) & 62.4 m & 63.8 m & \(-2.1\%\) & 80.6 m & 84.4 m & \(-4.7\%\) \\ \hline \(z_{CG}\) & 10.74 m & 10.3 m & 4.1\% & 12.7 m & 12.4 m & 2\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison of measured values of weight light ship and position of center of gravity of container ships with calculations according to regression formulas. results of these analyses are also shown graphically (Figure 41) where the \(M_{1}\) class weight was estimated for the second set of container ships (Table 3). Table 9 shows the results of calculating the weight of a container ship's engine room (class \(M_{4}\)) obtained from formulas in the publications [14; 15; 22; 25; 29] for ship A and B and from the regression Formula (35). The values for estimating the weight of class \(M_{4}\) from the formulas given in scientific publications are much less accurate than from the developed Formula (35). Figure 41: Scatter of predicted versus observed values for weight light ship without equipment \(M_{1}\)—comparison of calculations with measurements for different methods [14; 15; 29].