# Maximum Safe Parameters of Ships in Complex Systems of Port Waterways
## 2 Methods  
The problem of maximum safe parameters of ships arises in the case of the construction, conversion or modernization of a port waterways system. This particularly applies to complex port waterways systems, composed of several port basins (cargo handling terminals), fairways (straight sections and bends) and turning basins. Individual sections of waterways (system components) differ in technical and operational parameters:  
* Cargo-handling terminals (port basins): type and maximum parameters of ships handled (\(t_{yp}\), \(L_{C}\), \(B\), \(T\));
* Fairways (bends and straight sections): depth (\(h\)), width at bottom (\(D\)) and slope angle;
* Turning basins: depth (h), length and width (\(l_{obr}\), \(b_{obr}\)) or diameter. In addition, mooring ships are taken into account in port basins and quays or piers located along the fairways of the system, anchorages and lay-by berths. A complex port waterway system is usually composed of the following sections:
* Approach channel (from an anchorage);\(\bullet\) Port entrance; \(\bullet\) A number of inner fairway sections leading to various terminals; \(\bullet\) Port basins of the terminals; \(\bullet\) Turning basins for ships handled at a given terminal. In order to take into account all constraints on individual sections of the fairway, the following procedure is proposed. It allows us to determine the maximum safe parameters of ships that may use the system between specific turning basins:  
1. Preliminary determination of ships' maximum drafts in specific fairway sections: \[T_{zvi}=h_{i}-\Delta_{zvi}\] (9) The underkeel clearance \(\Delta_{zvi}\) was determined for the pre-defined ship speed \(V_{zvi}\). 2. Determination of maximum overall lengths \(L_{co}\) of ships in turning basins, taking into account the possibility of turning in port basins of the terminals; location of turning basins in the fairway accounting for the length overall of ships safely turned: \[L_{co}max,\ldots,\ L_{co}min\] (10) It was assumed that maximum lengths of turning ships decrease along with the increase in turning basin distance from the fairway entrance. 3. The division of the fairway into sections between the turning basins (_j_ turning basins): \(\bullet\) First section: from port entrance (into fairway) to the turning basin where the maximum length ship can be turned (\(L_{co}max\)); \(\bullet\) Next sections were determined between subsequent turning basins in the fairway. Further calculations were made separately for each section between the turning basins. 4. Determination of length overall \(L_{cz}\) and breadth of \(B_{z}\) of ships safely maneuvering in fairway bends (_z_). Making calculations by starting from the turning basin where a vessel of greater length can turn, we should assume the safe overall length and breadth of the ship on the fairway section running from the considered turning basin as: \[L_{c}^{zak}=\underset{z}{\text{min}}L_{cz}\] (11) \[B^{zak}=\underset{z}{\text{min}}B_{z}\] (12)
5. Determination of maximum safe breadths of ships in straight one-way fairway sections (\(B_{p}\)); here, we should assume the safe ship breadth for all straight fairway sections (_p_) from the considered turning basin as: \[B^{pr}=\underset{p}{\text{min}}B_{p}\] (13)
6. Determination of maximum safe lengths and breadths of ships in particular sections between the considered _j_-th turning basin: \[L_{cj}=L_{c}^{zak}\text{ for }L_{cj}<L_{coj}\] (14) \[B_{j}=\min\left(B^{zak},B^{pr}\right)\] (15)
7. Determination of ship's safe draft and allowable speeds in specific fairway sections of the considered waterway, taking into account ship and fairway section parameters.