# Navigation Safety on Shipping Routes during Construction
## 3 Materials and Methods
### Mathematical Model
It should be noted that distances between platform location and ship passage bands, calculated using the developed theoretical method (lines in Figure 10) and achieved from real ships (experimental data received using AIS--designations in Figure 10), have almost  
\[\Delta Y^{\prime}=\Delta Y+P^{\prime}.\sigma_{Y}, \tag{2}\]6 Distances between platform and ships passage bands (\(\Delta B_{P}\)) depending on ships sizes and hydro-meteorological conditions [own elaboration], where lines are data achieved from conducted calculations, and designations are data from real ships passages received via AIS and simulator [62,64]. \[\Delta Y^{\prime}=\Delta Y+P^{\prime}.\sigma_{Y}, \tag{2}\]7 The widths of the passages depending on the sizes of the ships (lengths) and hydro-meteorological conditions [own elaboration], where lines are data achieved from conducted calculations, and designations are data from real ships’ passages received via AIS [own elaboration based [62,64]]. similar values with differences between theoretical and experimental data less than 10%. Negative \(\Delta B_{P}\) values may mean that the risk of ships sailing in the passage band is too high, so it is necessary to provide restrictions on ships' sailing conditions in the analyzed area. According to the decision of the hardormaster, a minimum distance of at least 25 m must be maintained between the platform and the shipping band (horizontal line in Figure 10). However, some vessels sailed on a distance that was less than 25 m to the platform (the smallest distance was 20 m). Similar results were obtained during experiments conducted by experienced operators (captain and harbor pilots) using a calibrated \"SimFlex Navigator\" simulator [62]. Applying the dispersion and maximum distribution methods, the widths of the ship's bands occupied by ships were calculated, which were up to 10% of the distance between the center line of the channel and the platform. The accuracy of the calculation results is confirmed using the analysis of the data obtained from real ships sailing in the studied area, which allowed us to state that the developed calculation method may be applied in other similar places. The illustration of the containership MSC \"Lisbon\" [65] (length = 337 m, width = 45.6 m, draft = 12.1 m, container capacity 9200 TEU) sailing trajectory analysis while crossing the approach to Klaipeda port is shown in \[\Delta Y^{\prime}=\Delta Y+P^{\prime}.\sigma_{Y}, \tag{2}\]8  
In case of difficulties of sailing in such complicated conditions due to the high probability of an accident, it is necessary to take external assistance (tugs), which can increase the maneuverability of the ship. For example, in Klaipeda port, LNG standard tankers (with a capacity of about 150,000 m\({}^{3}\)) need to use four tugs with a bolland pool not less than 500 kN to avoid sailing too close to the working platform (Figure 12). Two tugs are used for increasing the ship's maneuverability on tugging ropes, and two tugs are involved as assistance tugs. Difficult sailing conditions may be also observed in other navigation areas. A similar study may be conducted, for example, in the Fehrmam Belt strait [66] during the construction work of underwater tunnels (Figure 13). Using the presented methodology, it would be possible to plan safe ship trajectories in this restricted area during the performance of construction work. Fehrmam Belt Strait services different kinds of ships, including G-class container vessels, which have capacities of up to 24,000 TEU. The length of such vessels is about 400 m, width about 61 m, and draft up to 15 m [67]. Moreover, tankers and bulk ships with lengths up to 320 m (LNG Q-Flex tankers), widths up to 60 m (VLCC tankers and bulk ships), and a permitted draft up to 15 m (according to Denmark Maritime Authority regulations [68]) may pass this strait. In such complicated sailing areas, it is very important to provide preliminary investigations to determine the needed passage width.