## 4 Determining the Consequences of an Accidents
### The Effects of a Collision with Another Ship on a Crossing Course  
It is assumed that the vessel does not move and is hit by the bow perpendicularly, which can cause the most severe effects. If the ship moves, the absorbed energy is lower given the losses of speed and slipping of the vessel after the accident. As stated in the introduction, the first scenario assumes a simulated collision of a cruise ship with a length of 220 m approaching the Szczecin Port and a LPG tanker moored at its pier. The second is a real accident that occurred in the Port of Koper when a 265 m container ship collided with a cruise ship of 214 m length. Two collision scenarios were analysed in the study but only the consequences of the Slovenian case are presented below. The expected parameters of striking and struck vessels are presented in Table 2. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Symbol** & **Value** & **Unit** & **Description** \\ \hline \(d_{b}\) & 1.6 & [m] & distance between tank and hull \\ \(d_{d}\) & 2.5 & [m] & distance between tank and bottom \\ \(d_{dz}\) & 27.5 & [m] & distance between tank and bow \\ \(t\) & 35 & [mm] & plating thickness \\ \(d\) & 2 & [m] & the average size of plates (stiffeners) \\ \(t\)/\(d\) & 0.018 & [32] & ratio of /\(d\) \\ \(\sigma\) & 270 & [N/mm\({}^{2}\)] & steel ductility limit \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The parameters of studied tanker in terms of collision analysis needed for consequences estimation. Figure 7: The critical distances for the tanks of chemical carrier. The shape of the bow part is assumed in simplified form as presented in Figure 8. The volume of the penetrating part could be expressed as a surface integral or calculated numerically as presented here according to a simplified bulbous bow expression as follows [29]:  
\[R_{t}=\sum R_{t}(h_{di})=\pi\sum\Delta h_{di}\Delta R_{vi}\Delta R_{hi} \tag{13}\]  
where: \(R_{t}\) is the volume of damaged material, \(R_{v}\) is ellipse major axis and \(R_{hi}\) is ellipse minor axis. Applying the parameters of the stuck cruise ship in Equation (13) over different depth of penetration results in the penetration volume presented in Figure 9. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Poland Case**} & \multicolumn{2}{c}{**Slovenia Case**} \\ \hline
**Vessel** & **Striking** & **Struck** & **Striking** & **Struck** \\ \hline Type & Cruise vessel & Ammonia tanker & Container vessel & Cruise vessel & \\ \hline \(L\) [_m_] & 220 & 145 & 265 & 214 & Length \\ \(B\) [_m_] & 31 & 23 & 32 & 27 & Breadth \\ \(T\) [_m_] & 7.5 & 9 & 10.2 & 7.8 & Depth \\ \(m\) [_t_] & 33,000 & 21,000 & 60,000 & 34,000 & Weight \\ \(H\) [_m_] & 24 & 13 & 19.3 & 24 & Height to upper deck \\ \(R_{h}\) [_m_] & 1.12 & - & 1.5 & 1.12 & \\ \(R_{v}\) [_m_] & 3 & - & 3.5 & 3 & ref. to Figure 8 \\ \(R_{t}\) [_m_] & 1.5 & - & 2 & 1.5 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of vessels in study. Figure 8: Side view of collision scenario and a simplified form of striking bulbous bow. Figure 9: Numerical solution of depth of penetration by bulbous bow as function of destroyed material. In the literature, one can find information [29] as to how much energy is absorbed by the part of the bow of the colliding ship (due to the stiffness and construction of the bow part the values are given from 0 to 20%). In the presented calculations, it was set as 0% as a conservative value, which means the bow of the colliding vessel is not damaged at all. The results of calculations are presented in Table 3. The energy, damaged material, and depth of penetration \(h_{d}\) are shown. The colours indicating the exceeding of critical limit and the possibility of damage to the tank are marked according to the following ranges of \(h_{d}\):  
1. Red--exceeded the value of \(h_{d}\), certain damage to the tank i.e., \(h_{d}>=1.5\) m,
2. Orange--likely damage to the tank, dangerous values: i.e., 1 m \(<h_{d}<1.5\) m,
3.