# Statistical Analysis of the Weight and Center-of-Gravity Position of an Empty Container Ship
## 1 Introduction  
### Preliminary Ship Design  
Along with inexpensiveness, modernly designed transport ships must be characterized by a limited impact on the natural environment. One such parameter is a ship's energy efficiency design index (EEDI) [1], which determines exhaust emissions (including CO\({}_{2}\)) per unit of transport work. The value of this index is influenced, among other things, by the weight of the empty ship. Research is also being carried out on unmanned ships that will be characterized by even lower CO\({}_{2}\) emissions [2]. The ship design process, carried out iteratively (Figure 1, [3]), begins with an analysis of the shipowner's assumptions. For a transport vessel, the basic assumed parameters are  
* Ship speed \(V\);
* Deadweight tonnage _DWT_ or _TEU_ container capacity (for container ships);
* Cruising range \(R\). Additional assumed factors include the shipping line, sailing restrictions (bridges, canals), type of engine, type of fuel, additional equipment, etc. For these assumptions, the design should  
* Comply with all regulations and conventions regarding the construction and strength of a ship's hull and equipment and its navigational safety and meet environmental protection requirements;
* Have the best economic parameters regarding \(\bigcirc\) The lowest cost of building the ship; \(\bigcirc\) The lowest cost of ship operation, i.e., the lowest propulsion power and fuel consumption for the predicted speed \(V\) and deadweight tonnage (or \(TEU\) capacity). * Be accepted by the shipowner as the ship expected to make profits. The design process begins with a preliminary design stage (Figure 1), which will include the basic geometric dimensions and technical and operational parameters, as well as the relevant drawings: theoretical lines of the hull and a general plan including a functional-spatial division. From the assumptions (_DWT_, _TEU_) presented earlier, only the size of a ship's holds can be determined. The geometric dimensions thus determined are insufficient because of the following:  
* In order for a ship to have the assumed deadweight tonnage or cargo capacity, its displacement (volume of the submerged part of the hull) must be greater because the hull \(\bigcirc\) Has its own weight; \(\bigcirc\) Contains the power plant and various auxiliary systems; \(\bigcirc\) Supports the superstructure, deck equipment, etc. * The engine room must accommodate the propulsion engine with all its equipment, with power sufficient for the newly built ship to develop an assumed speed \(V\); the ship's hull must also contain fuel tanks for the ship to travel in the assumed range \(R\)  
Figure 1: Design spiral of ships. * The power output of the engine room plant depends on the resistance and speed \(V\) of the ship, and the resistance depends on the dimensions and form of the hull containing the engine room--the dimensions and weight of the engine room at this stage are not known, since the propulsion power is not yet known. * At this stage, under these assumptions, the design cannot be optimized. To create a preliminary design, the designer should use approximate relationships between the basic dimensions of the ship and its technical and operational parameters and the design assumptions made. Using such relationships, we can create an iterative design of the ship, (Figure 1), while at the same time optimizing its parameters. Examples of approximate relationships useful in preliminary ship design, used in the specific steps shown in Figure 1, are as follows:  
* Relationships between main particulars: vessel length \(L\), breadth \(B\), draft \(T\), and depth \(H\) as a function of \(DWT\) tonnage or \(TEU\) container capacity, \(L,B,T,H=f(DWT/TEU)\);
* Relationship between the lightship weight \(WLS\) and the center of gravity coordinates \(CG\) as a function of \(DWT\) or \(TEU\): \(WLS,CG=f(DWT/TEU)\);
* Relationship between propulsion power \(N_{C}\) as a function of ship speed \(V\): \(N_{C}=f(V)\).