# Determination of the Waterway Parameters as a Component of Safety Management System
## 4 Materials and Methods  
The Polish method of water channel design was developed at the Maritime University of Szczecin [3; 24]. It is based on the minimising of the objective function related to the parameters of a fairway composed of one-way and two-way sections with respect to the fairway reconstruction and operational costs, taking into account the costs of delays of ships belonging to specific size groups for projected traffic intensities [25]. In this study, due to the maximum parameters of the tested vessel, two-way traffic was not taken into account. However, the specific fairway types were taken into consideration, divided into straight sections and bends [26]. Taking into consideration the one-way traffic, the safety passage is performed under the following conditions:  
\[d_{j}(1-\alpha)+d_{r}^{p}+d_{r}^{l}\leq D_{j} \tag{1}\]  
Figure 3: Areas of the tested sections at the Swinoujscie–Szczecin fairway, southern part. where: \(D_{j}\): width at the bottom of the \(j\)th point of the fairway (axis) for a safe depth [m]; \(d_{j}(1-\alpha)\): width of the safe manoeuvring area at the given confidence level \((1-\alpha)\) for the \(j\)th point of the fairway (axis) (m); \(d_{r}^{p}\): fairway width reserve for the bank-channel effect on the right side of the fairway (m); \(d_{r}^{1}\): fairway width reserve for the bank-channel effect on the left side of the fairway (m). The width of the safe manoeuvring area is calculated according to the formula  
\[d_{j}(1-\alpha)=\overline{X_{jp}}-\overline{X_{jl}}+c\sigma_{jp}+c\sigma_{ jl}[\text{m}] \tag{2}\]  
where: \(c\): confidence factor; \(\overline{X_{jp}};\overline{X_{jl}}\): arithmetic mean of the vessel maximum port and starboard distances from the \(j\)th point of the fairway (m); \(\sigma_{jp};\sigma_{jl}\): standard deviations of the vessel maximum port and starboard distances from the \(j\)th point of the fairway (m). On a straight fairway, we can assume that  
\[\overline{X_{jp}}=\left|\overline{X_{jl}}\right|=\overline{X_{j}} \tag{3}\]  
and  
\[\sigma_{jp}+\sigma_{jl}=\sigma_{j} \tag{4}\]  
Taking the above into account, we have  
\[d_{j}(1-\alpha)=2(\overline{X_{j}}+c\sigma_{j})[\text{m}] \tag{5}\]  
and, finally,  
\[D_{j}\geq 2\overline{X_{j}}+2c\sigma_{j}+d_{r}^{p}+d_{r}^{l} \tag{6}\]  
In the Polish method [3], the manoeuvring component of the manoeuvring area (fairway lane) width is defined deterministically, while the navigational component of the manoeuvring area's width is probabilistic and is determined at a certain confidence level. Taking this into account, the width of the safe manoeuvring area for a straight waterway section is determined as follows:  
\[d(1-\alpha)=d_{m}+2d_{n}(1-\alpha)[\text{m}] \tag{7}\]  
The results of the research carried out have shown that, to determine the mean width of the manoeuvring area, some modifications of the deterministic PIANC method can be used. In this method, the width of the safe manoeuvring area for straight fairways is determined according to the following equation [13]:  
\[d=d_{mp}+\sum_{i=1}^{9}d_{i}+d_{r}^{p}+d_{r}^{l}[\text{m}] \tag{8}\]  
where: \(d_{mp}\): basic manoeuvring width of the traffic lane (m_; \(d_{i}\): additional corrections of the traffic lane width: \(i=1\), vessel speed; \(i=2\), prevailing transverse wind; \(i=3\), prevailing transverse current; \(i=4\), prevailing longitudinal current; \(i=5\), height and length of the significant wave; \(i=6\), navigational markings and traffic regulation system; \(i=7\), type of bottom; \(i=8\), the ratio of the depth to the draft of the vessel; \(i=9\), the risk caused by the cargo carried.\(d_{r}^{l}\): lane width reserve on the left (m); \(d_{r}^{p}\): lane width reserve on the right (m). The basic width of the traffic lane is determined depending on the vessel's steerability: \(d_{mp}=1.3\)\(B\)--very good steerability; \(d_{mp}=1.5\)\(B\)--good steerability; \(d_{mp}=1.8\)\(B\)--poor steerability.