# Statistical Analysis of the Weight and Center-of-Gravity Position of an Empty Container Ship
## 1 Introduction
### Weight Light Ship  
The ship displacement \(D\) is equal to [14; 15]:  
\[D=WLS+DWT \tag{1}\]  
where  
* \(WLS\)--weight light ship, [t],
* \(DWT\)--deadweight tonnage, [t]. * As a rule of thumb, the weight light ship \(WLS\) is equal [15; 16; 17]:  
\[WLS=M_{1}+M_{2}+M_{3}+M_{4}+M_{5}+M_{6}+M_{7}+M_{8} \tag{2}\]  
where \(M_{1},\ldots,M_{8}\) are the weights in various classes shown in Table 1. Each of the listed classes from \(M_{1}\) to \(M_{8}\) can still be subdivided into subclasses from 1 to 8. The weight light ship \(WLS\) has thus a tabular form with rows from 1 to 8 and columns from 1 to 8. The individual weights in Table 1 are most often shown in the form of corresponding indices defined as follows:  
\[\text{e.g., }\ C_{k}=\frac{M_{k}}{P_{k}} \tag{3}\]  
where\(C_{k}\)--index for class \(k\),  
\(M_{k}\)--class \(k\) weight, [t],  
\(P_{k}\)--ship parameter appropriate for class k (the number of containers, volume, propulsion power, number of crew, power of electrical loads, etc. ; commonly used in many shipbuilding yards; parameters for individual weight classes are given in Table 1). where  
\(M_{1}\)-\(M_{8}\)--weights in classes 1 through 8, [t],  
\(C_{1}\)-\(C_{8}\)--weight indexes for classes 1 through 8,  
\(L\)--length, [m],  
\(B\)--breadth, [m],  
\(H\)--depth, [m],  
\(LB\)--product \(L\cdot B\), [m\({}^{2}\)],  
\(LBH\)--product \(L\cdot B\cdot H\), (volumetric module), [m\({}^{3}\)],  
\(J\)--number of crew, [-],  
\(N_{C}\)--maximum power of the main engine, [kW],  
\(Ne\)--power of generating sets, [kW]. The chart in Figure 2 shows the average statistical share of each weight class for the container ships under study. The weight of a container ship mostly depends on the hull (class \(M_{1}\)) and to a lesser extent on deck equipment (class \(M_{2}\)) and the engine room (class \(M_{4}\)). The other weight classes have less or minimal impact on the weight light a container ship, but in the case of unmanned container ship design, they too will have a significant impact on the final weight of an unmanned empty container ship. In addition to the weight indices (Table 1), sometimes the total weight light ship \(WLS\) or its index in the form given below is sufficient at the preliminary design stage:  
\[C_{PS}=\frac{WLS}{DWT}\] (4a) or \[C_{PS}=\frac{WLS}{TEU} \tag{4b}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Class No.** & **Weight Classes** & **Weight Indices** \\ \hline
1 & \(M_{1}\) Hull, superstructure, funnel & \(C_{1}=M_{1}\)/\(LBH\) \\ \hline
2 & \(M_{2}\) Deck equipment with hatch & \(C_{2}=M_{2}\)/\(LB\) \\  & cover and crane & \(C_{3}=M_{3}\)/\(J\) \\ \hline
3 & \(M_{3}\) Accommodation and painting & \(C_{3}=M_{3}\)/\(J\) \\ \hline
4 & \(M_{4}\) Machinery & \(C_{4}=M_{4}\)/\(N_{C}\) \\ \hline
5 & \(M_{5}\) Piping systems & \(C_{5}=M_{5}\)/\(LBH\) \\ \hline
6 & \(M_{6}\) Electric equipment & \(C_{6}=M_{6}\)/\(N_{e}\) \\ \hline
7 & \(M_{7}\) Special equipment & \(C_{7}=M_{7}\)/\(LBH\) \\ \hline
8 & \(M_{8}\) Inventories & \(C_{8}=M_{8}\)/\(LBH\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Weight classes and weight indexes for a light ship. For each class and subclass, the position of the center of gravity \(CG\) is specified (Figure 3). Since the ship has a longitudinal plane of symmetry and cannot list to one side while sailing, the longitudinal coordinate \(x_{CG}\) and vertical coordinate \(z_{CG}\) are generally given (in cases where some machinery is mounted asymmetrically the transverse coordinate \(y_{CG}\) is given). The coordinates of the center of gravity for class 1 through 8 are first calculated from the coordinates of the individual component weights, then the resultant position of the center of gravity for the entire light ship is determined.