# Comparative Studies of Major Sea Routes
## 3 Theoretical Basis of the Evaluation Sea Routes
### Mathematical Model
The following components can be used to calculate the transportation time: the average (commercial) speed of the ship, the waiting time before entering the canals if the Suez or Panama Canals are used, possible interruptions due to weather conditions, technical and organizational problems, and other problems; i.e., the following formula can be adopted for calculating the sailing time of the ship:  
\[T_{T}=\frac{\eta_{k}(T_{K}+T_{w})}{\left(1-\frac{Q_{1}}{T_{K}}\right)\left(1- \frac{Q_{2}}{T_{K}}\right)\left(1-\frac{Q_{3}}{T_{K}}\right)}, \tag{3}\]  
where \(\eta_{k}\)--correlation coefficient depends on similar factors or processes and can be taken from 0.95 to 1.0 (if there are no similar factors or processes or only one factor or process is evaluated); \(Q_{1}\), \(Q_{2}\), \(Q_{3}\)...--adverse time factors, such as hydro-meteorological conditions, ship maintenance or breakdown problems, and organizational problems while waiting for entry into ports, canals, etc., expressed in days (can be taken from statistical data); \(T_{w}\)--average waiting time when entering ports or channels, waiting for icebreaker escort, etc., expressed in days (can be taken from statistical data); \(T_{K}\)--the vessel's commercial sailing time, which can be calculated using the following formula:  
\[T_{K}=\frac{S_{S}}{v_{K}}, \tag{4}\]  
where \(S_{S}\)--sailing distance of the ship, in nautical miles; \(v_{K}\)--commercial vessel speed, in knots. The possible maximum ship draft of the analyzed sea routes is especially important for certain parts of the sea routes. The limitations of the main parameters of ships, especially the draft of ships, do not allow for the efficient use of cargo transportation by sea. The required amount of energy (fuel) when transporting goods from Southeast Asia to Europe is important not only from an economic point of view but also from the point of view of environmental impact since fuel consumption and engine working time are directly related to the generated amount of emissions ([PERSON], 2013; 2014). Ship engine power (\(N\)) and the amount of fuel consumed (\(q_{f}\)) over a given period of a ship's active working time, during which the ship is sailing between ports; time (\(t\)), e.g., an hour; and the relative fuel consumption (\(q_{f}^{\prime}\)) correlate to the following formula, as seen in Refs. ([PERSON], 2013; 2014):  
\[N=q_{f}/\left(q_{f}^{\prime}t\right) \tag{5}\]  
The fuel consumption of a ship can be calculated using the following formula ([PERSON], 2013):  
\[q_{f}=\int q_{f}^{\prime}N_{av}dt, \tag{6}\]  
here, \(N_{av}\) is the average engine power of the ship during the sailing between ports. Emissions from ships while sailing between ports directly depend on the quantity and quality of fuel used, engine power, and engine running time [33; 34; 35]. The main emissions from ships constitute carbon dioxide (\(CO_{2}\)), nitrogen oxide (\(NO_{x}\)), carbon monoxide (\(CO\)), sulfur oxide (\(SO_{x}\)), and particulate matter (\(PM\)) [33; 35]. Thus, the carbon dioxide emissions, for example, are calculated according to the following formula [33]:  
\[CO_{2}=k_{CO_{2}}q_{f}, \tag{7}\]  
here, \(k_{CO_{2}}\) is carbon dioxide coefficient for petroleum products (diesel, fuel oil) is between 3.0 and 3.5, and for LNG, between 2.5 and 2.9. Other emissions generated by the ship can be calculated using the methodology presented in Ref. [33] or other similar methodologies. Other possible factors of the analyzed sea routes are mostly associated with political factors, such as sanctions; particularly difficult hydro-meteorological conditions when the navigation of ships becomes too difficult or inappropriate, such as, for example, particularly dangerous waves in the area of the island of Madagascar or the southern Horn of Africa; and by other similar factors. Weight coefficients of the factors could be defined by calculation methods (in cases where large amounts of data are available), by experts' methods in cases of limited data, or by other methods.