# Simulation Tests of the Passing Distance of Ships on a Two-Way Fairway
## 5 Conclusions  
In this paper, the distance of passing ships on waterways was determined using the simulation method of ship traffic. The simulation experiment was carried out on the FMBS simulator for passing loaded ships of equal size with overall lengths LOA = 103.6 m, 220 m, 228 m, and block coefficients CB = 0.76, 0.8 and 0.67 (tanker, bulk carrier, sea ferry), respectively. The research was conducted for four straight sections of the Swinoujscie-Szczecin waterway with different parameters and different navigation marking systems. The results show that the minimum safe passing distances of ships on fairways at speeds up to 8 knots do not practically depend on ship-to-ship interaction, but on the breadth of the ships and the accuracy of position determination, i.e., directional error perpendicular to the axis of the fairway. Based on the analysis of the results of simulation tests, it was found that the passing distances of ships are:  
* For the vessel breadth \(B\geq 30\) m \(d_{r(0.95)}^{s}=B+\frac{1}{4}p_{y(0.95)}\)
* For the vessel breadth \(B<30\) m \(d_{r(0.95)}^{s}=B+\frac{1}{2}p_{y(0.95)}\)  
The passing distance, determined by the simulation method at the confidence level (1-\(\alpha\)) = 0.95, takes into account the navigational components of the width of the safe maneuvering area (accuracy of position determination) on the side of passing ships. This allows for the modification of the deterministic-probabilistic MTE method. A simulation method for determining the passing distance can be used to design two-way fairways and determine the conditions for their safe operation using the deterministic-probabilistic MTE method. The modified deterministic-probabilistic MTE method presented in the article considers the accuracy of position determination at a certain confidence level. It makes it possible to reduce the width of the required safe maneuvering area or to allow larger vessels to pass each other while ensuring the required level of safety and efficiency and, as a result, improves the traffic flow and fairway capacity (and thus harbor turnovers and revenues). The next step in follow-up research to the present study, which is being planned by the authors in the near future, will be a quantitative investigation on the influence of the two factors found (the ship breadths and the directional/lateral positioning accuracy). This will involve a different simulation experimental design and regression analysis towards an analytical model that describes the input/output relationships. Conceptualization, S.G., J.A., R.G. and M.P. ; methodology, S.G., J.A., R.G. and M.P. ; software, J.A. and R.G. ; validation, S.G. and J.A. ; formal analysis, S.G., J.A., R.G. and M.P. ; investigation, R.G. and M.P. ; resources, J.A., R.G. and M.P. ; data curation, J.A., R.G. and M.P. ; writing--original draft preparation, S.G.; writing--review and editing, J.A., R.G. and M.P. ; visualization, R.G. and M.P. ; supervision, S.G.; project administration, S.G. and J.A. ; funding acquisition, R.G. and M.P. All authors have read and agreed to the published version of the manuscript. This research received no external funding. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{2}{c}{**Passing Distance \(d_{r(0.95)}^{s}\)**} \\ \cline{3-4}  & **Fairway Section/** & **Results of Simulation** & **Results According to a Proposed Relationship** \\ \hline  & \multicolumn{2}{c}{Kanal Piastowski} & \multicolumn{2}{c}{26.4 m} & \multicolumn{2}{c}{\(B+\frac{1}{2}p_{y(0.95)}=26.6\ m\)} \\
1 & LOA = 103.6 m, B = 16.6 m & & \\
2 & Zalew Szczecinski I-II BT & 20.8 m & \(B+\frac{1}{2}p_{y(0.95)}=21.6\ m\) \\
3 & Zalew Szczecinski II-III BT & & \\  & LOA = 220.0 m, B = 32.5 m & & \\
4 & Port of Swinoujscie & & \\  & LOA = 228.0 m, B = 32.0 m & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The passing distance determined by simulation and empirical methods. **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** Not applicable.