# Navigation Safety on Shipping Routes during Construction
## 3 Materials and Methods
### Mathematical Model
\[\Delta Y^{\prime}=\Delta Y+P^{\prime}.\sigma_{Y}, \tag{2}\]4 The part of trajectory of ship’s passage in the presence of current and wind to the starboard side (considering the kinematic parameters of the ship, motion, and current presented in Figure 6) (as an example) [own elaboration based on [62]]. A case study of the ship's movement within the navigational channel during reconstruction work of the port infrastructure close to the approach to Klaipeda port was considered. The big working platform was located near the navigational channel (Figure 8). That fact impacted ships' movement in this area. Vessels entering the port and departing from the port had to make turns about 25\({}^{\circ}\) with very high accuracy very close to the port gate. The main task of this case study analysis was to define the limit conditions for vessels, considering their displacement, maneuverability, and external forces influence (e.g., wind, current, etc. ), needed to plan the route allowing to pass mentioned area safely. The analysis of the sailing trajectories for ships with different displacements was carried out considering set hydro-meteorological and hydrological conditions observed in explored navigational areas. The theoretical calculations were conducted using a developed mathematical model. Then, the calculation results were compared to the data collected from the following:  
* Simulator \"SimFlex Navigator\" [62];
* AIS for real ships crossing the analyzed area [64]. For the considered case study, the sailing trajectories, passage bands, and minimal distances between the platform and ship sailing bands for the different types, dimensions, and displacements of ships both entering and departing from the port were calculated. The evaluated ship lengths were from 145 m to 300 m. Analyzed ship displacement constituted from 10,000 t to 150,000 t (considering the density of the water is 1000 kg/m\({}^{3}\)). Moreover, different wind directions were considered. The southwest was the worst wind direction due to the drift occurrence and the rotation of the ship, in turn, when the ship's superstructure was at the stern, the northwest wind direction was considered. In case the wind was blowing in the southwest and west directions, the waves broke through the port gate. The currents in many analyzed cases were directed from the port to the sea, and the velocity of the current was up to 2 knots. The widths of the passages depending on the size of the ships (lengths) and hydro-meteorological conditions received applying developed calculation methods are presented in Figure 9, where the orange line shows the maximum possible safe widths of the passages depending on the sizes of the ships. \[\Delta Y^{\prime}=\Delta Y+P^{\prime}.\sigma_{Y}, \tag{2}\]5 Ship sailing near working platform located close to navigational channel within approach to Klaipeda port (blue square depicts lifting platform, shown in Figure 2; arrow depicts the distance from platform to the passing ship) [own elaboration based [62]]. By analyzing ships' passage bands calculated using the theoretical method presented in Section 3 (lines in Figure 9), and comparing it to experimental data received from real ships, it can be stated that differences between theoretical and experimental data were less than 10%. Moreover, experiments conducted on the \"SimFlex Navigator\" simulator by experienced operators (captain and port pilots) allowed us to achieve the values with the same accuracy (up to 10% difference compared to calculated values). The calculated distance from the platform to ship passage bands depending on the ship's size and hydro-meteorological conditions is presented in Figure 10, where the orange line shows the minimum distance between the platform and ship passage bands needed to be assured for safe navigation.