# Maximum Safe Parameters of Ships in Complex Systems of Port Waterways
## 1 Introduction
### Conditions of Safe Operation of Ships in Port Waterways Systems  
From the perspective of marine traffic engineering, a system of port waterways is composed of a set of waterways (port areas), such as approach channels, port entrance, inner fairways (port channels, rivers, lakes), turning basins and port basins of various terminals.  
In a port regarded as a system of sea waterways, different areas make up separate waterway sections that can be grouped into several criteria [3]:  
* Technical parameters of the port area;
* Technical parameters of navigation systems used;
* Prevailing hydrometeorological conditions;
* Conditions of safe operation.  
The conditions for the safe operation of ships in the \(i\)-th section of the waterway can be written as a set:  
\[W_{i}=\left[t_{yp},L_{ci},B_{i},T_{i},H_{sti},V_{i},\mathcal{C}_{i},H_{i}\right] \tag{1}\]  
where:  
\begin{tabular}{l l l} \(t_{up}\) & -- & Type of'maximum ship'; \\ \(l_{ci}\) & -- & Overall length of'maximum ship'; \\ \(B_{i}\) & -- & Breadth of'maximum ship'; \\ \(T_{i}\) & -- & Draft of'maximum ship' in i-th section of waterway; \\ \(H_{sti}\) & -- & Airdraft in i-th section of waterway (useful while passing under a bridge or overhead power line); \\ \(V_{i}\) & -- & Allowable speed of'maximum ship' in i-th fairway section; \\ \(C_{i}\) & -- & Tug assistance in i-th section of fairway, if it is required (required number and bollard pull of tugs); \\ \(\mathbf{H}_{i}\) & -- & Set of hydmeteorological conditions acceptable for'maximum ship' in i-th fairway section. \\  &  
The state vector of safe ship operation conditions in waterway systems is a function of the parameters of this system [10; 11]:  
\[\textbf{W}=F\begin{bmatrix}\textbf{A}_{i}\\ \textbf{N}_{i}\\ \textbf{Z}_{i}\end{bmatrix} \tag{6}\]  
where:  
\begin{tabular}{r c l} \(W\) & -- & Conditions of safe ship operation (state vector); \\ \(A_{i}\) & -- & Subsystem of \(i\)-th section of the waterway, determining the area parameters and the type of maneuver performed in that area (area subsystem); \\ \(N_{i}\) & -- & Subsystem of ship position determination, characterizing parameters of navigational systems in use (navigational system); \\ \(Z_{i}\) & -- & Subsystem of traffic control, characterizing its parameters and waterway capacity. \\ \end{tabular}  
In cases where port waterways are covered by the identical system of regulations, each of the waterway sections consist of two basic components [12; 13]:  
1. Waterway subsystem;
2. Navigational subsystem (ship position determination subsystem). These elements affect each other and have a vital impact on the system characteristics. The parameters of subsystems of individual port waterway sections determine the conditions for the safe operation of ships in the waterway system: \[\textbf{W}=F\begin{bmatrix}\textbf{A}_{i}\\ \textbf{N}_{i}\end{bmatrix}\] (7) Conditions for the safe operation of ships in seaports are subject to two restrictions [11; 12]:  
1. The basic maximum parameters of ships that can safely pass through the waterway system cannot be greater than maximum parameters of ships safely passing through all of the sections of the system. Therefore: \[\begin{array}{l}L_{c}=\min_{i}L_{ci}\\ B=\min_{i}B_{i}\\ T=\min_{i}T_{i}\end{array}\] (8)
2. The hydrometeorological conditions that allow for maneuvering in the given waterway system of ships with maximum parameters are identical. This applies to the time of day (\(d\)/\(n\)), visibility (s) and wind speed (\(v_{w}\)).