# Simulation Tests of the Passing Distance of Ships on a Two-Way Fairway
## 1 Introduction  
There are several empirical methods for determining the width of safe maneuvering areas for ships on fairways [1; 2; 3; 4]. In the case of two-way traffic, which improves the traffic flow and fairway capacity (and, thus, harbor turnovers and revenues by cost and energy savings), the basic problem is to determine the passing distance considering:  
* Parameters of passing ships;
* Reservoir parameters (e.g., depth, cross-section);
* Ship-to-ship interactions;
* Parameters (e.g., accuracy) of the navigation positioning systems on site;
* Individual navigator characteristics (e.g., qualifications).  
The most frequently used method for determining the parameters of safe maneuvering areas is the deterministic method, developed and recommended by PIANC [2; 5] (World Association for Waterborne Transport Infrastructure). In this method, the passing distance (\(d_{r}^{s}\)) was determined using model studies of ship-to-ship interaction, and its value is expressed in the breadth (\(B\)) of the larger ship [2]:  
* For speeds V \(\leq\) 8 knots: \[d_{r}^{s}=1.0B\text{ for }B\geq 30m\] (1) \[d_{r}^{s}=30m\text{ for }B<30m\] (2)
* For speeds V = 8-12 knots: \[d_{r}^{s}=1.5B\] (3)
* For speeds V > 12 knots: \[d_{r}^{s}=2.0B\] (4)  
The solution proposed by PIANC was adopted in the authors' deterministic-probabilistic MTE (Marine Traffic Engineering) method [6], for which the differences relate to the methods of calculating the remaining components of the width of the safe maneuvering area.  
Another method for determining the width of a two-way fairway is the method recommended by the Spanish company Puertos del Estado, responsible for the management of state-owned ports [3]. According to this method, the passing distance is calculated as a sum of two factors determined on the assumption that the operation is undertaken with pilots or captains experienced in the site under consideration. The values of the factors are presented in Table 1.  
* A further method used to determine the width of a two-way waterway is the method developed by the Japan Institute of Navigation [4]. In this solution, it is recommended to assume the value of the passing distance based on the type of the ship. The values range from 0.67\(B\) for fully loaded tankers to 1.95\(B\) for container ships.
* In view of the above, it can be concluded that the solutions proposed by the PIANC (and MTE) method as well as Spanish and Japanese methods do not take into account neither the results of contemporary model studies of ship-to-ship interactions regarding the particularly limited speeds at which the ships travel on fairways when passing, nor the accuracy of their positioning and the qualifications of navigators.
* The article attempts to determine, on the basis of the results of simulation studies, a safe and efficient distance between passing vessels considering the shortcomings of the above methods. The main assumptions of the proposed solution are:
* The simulation (mathematical) models of the movement of the studied ships consider the results of contemporary model studies on ship-to-ship interaction;
* The simulation experiment is carried out on a specific sections of the Swinoujscic-Szczecin (Poland) waterway with existing visual navigation markings (aids-to-navigation) implemented on a FMBS-type simulator;
* The simulation experiment involves navigators experienced in maneuvering ships on investigated fairway (captains and pilots).