# Simulation Tests of the Passing Distance of Ships on a Two-Way Fairway
## Materials and Methods
### Ship-to-Ship Interaction in Model and Simulation Studies  
The magnitude of the mutual hydrodynamic interaction between two vessels directly depends on their absolute speeds as well as their relative speeds, and on the lateral distance between the vessels. Ship-to-ship interactions are also very much affected by the \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Fairway in Exposed** & **Fairway in Sheltered** \\  & **Areas** & **Areas** \\ \hline First factor: Vessel’s absolute speed & & \\ Greater than 6 m/s & 2.0\(B\) & - \\ Between 4 and 6 m/s & 1.6\(B\) & 1.4\(B\) \\ Less than 4 m/s & 1.2\(B\) & 1.0\(B\) \\ Second factor: Traffic density & & \\
0–1 vessels/hour & 0.0\(B\) & 0.0\(B\) \\
1–3 vessels/hour & 0.2\(B\) & 0.2\(B\) \\ \textgreater{}3 vessels/hour & 0.5\(B\) & 0.4\(B\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Factors for passing distance calculation (Spanish method) [3]. simultaneous restriction of the body of water by depth. Other important factors in the phenomenon are the mutual relationship of dimensions and shape of the vessels, and the type of encounter:  
* Passing, i.e., parallel movement on opposite courses (the subject of this article);
* Overtaking, i.e., similar movement, but on the equal courses and with different speeds;
* Passing a stopped or moored vessel--for methodological and application reasons, this case is treated independently, especially from the point of view of the danger to the moored vessel. Ship-to-ship reactions are a fast-varying phenomenon. The instantaneous values of the individual components of the ship-to-ship effect interactions, the most important of which are the transverse force and moment, depend directly on the actual longitudinal position (stagger) of the vessels. Other factors are treated as parameters of these relationships. Due to the number of arguments and the vast variety of possible conditions, especially related to the arbitrariness of the target vessel, it is difficult, at the current stage of scientific development, to describe mathematically the occurring process in a universal way. This poses a major scientific challenge despite the significant progress in ongoing and published research in recent years, both theoretical and, above all, experimental (model) methods on ship-ship interaction (see, among others, the series of six MASHCON conferences from 2009 to the present on ship maneuvering in shallow and restricted waters especially [7]). Most data are on the interaction forces themselves, either measured on captive models or computed numerically via CFD (Computational Fluid Dynamics) methods. Especially, there is an insufficient amount of research on ship-to-ship interaction, either through model tests of free-running (self-propelled) models or through motion simulation. In the latter method, the acquired data on interaction forces must be combined with the hydrodynamic characteristics of the hull, propeller, and rudder, which also need to be identified. Passing in a restricted area is widely regarded as safer than overtaking. This is due to the high relative speed of the target vessel and the short time the vessels are in each other's vicinity. It can be concluded that the order of magnitude of the lateral force and moment of the ship-to-ship effect at similar speeds and lateral distances of the vessels is similar for passing and overtaking. However, during passing, this will translate into comparatively small changes in lateral distance (due to lateral suction/push forces) and heading angle of both vessels (due to moments), since the magnitude of vessel displacement (linear and angular) according to [PERSON]'s law, depends on the square of the interaction time. Qualitative changes in the lateral force and moment of the ship-to-ship effect, and, thus, the tendencies of movement in the absence of control, are shown in the case of passing ships in Figure 1. These are based on the consideration of identical vessels with longitudinal symmetry.