# Statistical Analysis of the Weight and Center-of-Gravity Position of an Empty Container Ship
## 1 Introduction
### The Aim and Scope of the Study  
Few scientific publications deal with the estimation of ship weight or ship weight classes. The known methods can be divided into two groups:  
* methods for calculating ship weight from basic geometric or operational-technical parameters--these methods can be used at the stage of preliminary ship design,
* methods for estimating ship weight from the design of hull or its elements--these methods are not used at the preliminary design stage, because at this point the ship's structure (thickness of plating, type of stiffeners, etc.) is not yet known. The simplest formulas for estimating the weight of a ship's hull have been developed in the form of coefficients depending on the ship's displacement \(D\) or deadweight tonnage _DWT_: [18; 19; 20; 21]. These formulas, in the form of a single coefficient, linearly dependent on \(D\) or _DWT_ are not very accurate. Besides, they were developed for old types of ships. Most often, formulas are given for calculating only certain weight groups, e.g., hull, machinery and engine room weights. The remaining weights, shown in Table 1, are taken into account as weight reserve (the sum of these three groups and the reserve weight makes up the weight light ship). Approximate formulas for calculating hull weight and engine room weight are contained in [14; 15; 18; 19; 22; 23]. Publications [14; 15; 24; 25; 26; 27; 28; 29; 30] provide relationships to determine the hull weight for various types of ships. The study [6] contains formulas for hull weight of container ships. Some authors present methods for calculating the weight of a ship based on its structure, which is not yet known at the preliminary design stage. Also shipbuilding computer programs (AVEVA [31], NAPA [32]) for the design of ship structures contain modules for direct calculation of the weight and position of the center of gravity of the designed hull section. However, these methods and computer tools are not useful in the preliminary design of a container ship. There are very few scientific papers on methods of determining the position of the ship's center of gravity based on the basic geometric parameters of the ship. The only approximate formulas that have been found are in scripts or unpublished auxiliary materials prepared for shipbuilding students [23]. The results of calculating the coordinates of the center of gravity for individual classes and for an entire light container ship (2700 _TEU_) are also contained in [16], and approximate formulas for calculating the position of the center of gravity for the hull (class \(M_{1}\)) are contained in [17]. Based on the analysis of available articles and research works, it was found that there are no approximation formulas for the weight light ship (_WLS_) and the center of gravity for modern container ships in the range of 270-3100 _TEU_. There is also a complete lack of approximation formulas for all classes (Table 1), which are also useful for designing container ships. The main objective of our research was therefore to develop a set of regression formulas for calculating the weight and center of gravity coordinates of container ships in the range of 270 to 3100 _TEU_. This range was established for two reasons:  
* 270 to 3000 _TEU_ capacity range covers container ships classified as Small Feeder, Regional Feeder and Feedermax, which together make up the largest group of container ships under construction [33], (graph in Figure 4 is based on the database of ships--Sea-web Ships built in 2000-2024, a total of 50.9% of all container ships),
* design and research work is continued on unmanned, remotely or autonomously controlled container ships; the first unmanned container ships will belong to the Small or Regional Feeder group. The knowledge of accurate regression formulas for determining the weight and position of the center of gravity of a light container ship will be very useful for designing both manned and unmanned vessels, especially at the preliminary design stage.