## 2 Analysis and Literature Review of Clearance in Port Channels and Basins
### Mathematical Model
Some of the results of the experiments carried out on real ships are presented in Table 1. Comparing the results of real ship experiments regarding the relative power of the ships' main engine(s) and the ships' relative speed using the maximum distribution method, the maximum changes, expressed as a percentage, were obtained (presented in Table 1). Experiments were carried out for many years on various ships, in which at least one of the authors of the article participated. The navigation equipment available on the ship was used for the experiments (ship speed was measured with an accuracy of at least 0.1 knots) as were the power measurement indicators of the main engine(s) on board the ships, the measurement accuracy of which was at least 2% of the instantaneous power. The power of the engine and the speed of the ship are related by a quadratic relationship [3,10,38]. In most cases, the relative power of the ship's engine(s) and the ship's speed can be used. For this purpose, a graph based on the experimental results from more than 1000 ship passages can be used [3,10,11] (Figure 5). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Ship Type** & **Displacement, t** & \(N_{0}\)**, MW** & \(v_{0}\) & \(N^{\prime}\) & \(v^{\prime}\) & **Max Difference between Calculation and Experiments Results, \%** \\ \hline Container & 220,000 & 75 & 25 & 0.15 & 0.28 & 5.2 \\ Container & 130,000 & 50 & 24 & 0.17 & 0.32 & 4.8 \\ LNG tanker & 91,500 & 24 & 21 & 0.44 & 0.69 & 7.6 \\ Bulk & 80,000 & 10 & 14.6 & 0.33 & 0.54 & 8.5 \\ Oil tanker & 72,900 & 10 & 14 & 0.34 & 0.58 & 6.5 \\ Container & 70,230 & 25 & 23 & 0.33 & 0.52 & 4.6 \\ Oil tanker & 34,300 & 11 & 15.5 & 0.31 & 0.51 & 5.4 \\ General & 15,200 & 7 & 14.3 & 0.24 & 0.41 & 3.5 \\ Ro-Pax & 10,200 & 12 & 18.2 & 0.41 & 0.65 & 4.4 \\ Coaster & 5200 & 3.5 & 12.5 & 0.45 & 0.70 & 8.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Experiments results of relative main engine power and relative speed of the real ships. A limitation of the graph (Figure 5) with a very high overall hull fullness factor (8) is that with the overall fullness factor of the ship's hull greater than 0.9, the form resistance parameters of the ship's hull shape change significantly and the accuracy of the graph is not good enough (error size can reach more than 10 percent). Engine power can be calculated by taking into account the amount of fuel consumed over a given period of time, e.g., an hour, and the relative fuel consumption, i.e., [9; 11; 12]:  
\[N=\frac{q_{k}}{q_{k}^{\prime}\cdot t}, \tag{8}\]  
where \(N\)--engine power, kW; \(q_{k}\)--fuel consumption, kg; \(q_{k}^{\prime}\)--relative fuel consumption, kg/kWh; \(t\)--engine running time, h.  
Due to their powerful engines, ships consume a lot of fuel while sailing, especially when performing additional, not always justified, maneuvers in ports. A ship's fuel consumption is often calculated over a voyage or other period. In a general case, the fuel consumption of a ship on a voyage (\(q_{LP}\)) or other sailing places and times can be calculated according to the following formula [9; 11; 38; 42]:  
\[q_{LP}=\int\limits_{0}^{t}q_{k}^{\prime}\cdot N_{av}\cdot dt, \tag{9}\]  
where \(N_{av}\)--ship main engine average power during time \(t\). The relative fuel consumption of the main and auxiliary engines of most ships ranges from 0.13 to 0.25 kg/kWh (for more precise data, please refer to the engine specification of the individual ship) [11]. Depending on the type of fuel, the amount of fuel used can be different, so when using LNG, its calorific value is on average about 15 percent higher than other petroleum products, which means that about 15 percent less fuel mass is consumed [15; 46]. Emissions from ships and other transport vehicles directly depend on the quantity and quality of fuel used, engine power and engine running time [11; 17; 42]. The main emissions from ships constitute carbon dioxide (\(CO_{2}\)), nitrogen oxides (\(NO_{x}\)), carbon monoxide (\(CO\)), sulfur oxides (\(SO_{x}\)) and particulate matter (\(PM\)) [11].