# Navigation Safety on Shipping Routes during Construction
## 3 Materials and Methods
### Mathematical Model
For the minimum ship's passage width calculation, Equation (4) could be applied as follows [2]:  
\[B_{p}^{\prime}=L\cdot\sin\beta+B\cdot\cos\beta+L\cdot\sin\Delta K+P^{\prime} \cdot\sigma_{Y}+b_{n}, \tag{4}\]  
where \(L\) is length of the biggest ship; \(B\) is width of the biggest ship; \(\beta\) is possible maximum drift angle for the big ships (length of more than 200 m), drift angle in ports and other navigational channels on straight sections cannot be more than 5\({}^{\circ}\) (not in circulation); \(\Delta K\) is ship's course fluctuation, for the big ships (length of more than 200 m), and ship's course fluctuation cannot be more than 2\({}^{\circ}\)-3\({}^{\circ}\) (wheelman's ability to keep the ship on course in various conditions); \(P^{\prime}\) is probability factor for the line, which is equal to the passage central line the following factors could be taken into account: in case the probability factor is 1, probability is 62-68%; in case the probability factor is 2, probability is 95.3%; in case the probability factor is 3, probability is 99.7%. For the ship's position (observation) in case  
Figure 5: Ship’s (length = 350 m) sailing trajectory band at the entrance to the Klaipeda port during renovation works close to the quay wall No. 1 (blue square depicts lifting platform, shown in Figure 2; red color depicts the ship; green color depicts ship’s sailing trajectory) [own elaboration based on [62]]. of using at least three directions or three distances, it could use \(3\sigma\) regular and in case of probability factor 3, probability is about \(97\%\). \(\sigma_{Y}\) is accuracy of the ship's observation position in passage, depending on ships observation methods and systems; for example, if lead line is used, ships observation position accuracy is between 3 and 10 m; \(b_{n}\) is addition to the passage width, depending on the passage bottom conditions, navigation situation, ship's maneuverability, and so on (could be between 0.25 and 1.5\(B\)). According to PIANC recommendations, the width of the passages could be calculated using Equation (5) as follows [11]:  
\[B_{P}=B_{BM}+\sum B_{i}+B_{BR}+B_{BG}, \tag{5}\]  
where \(B_{BM}\) is ship's basic maneuvering line, could range from 1.3\(B\) to 1.8\(B\); \(B_{i}\) is additional corrections to the width of the passage on straight sections, could range from 0 to 1\(B\) depending on the permitted ship's speed, privileged wind, current velocity and direction, wave characteristics, the aids of navigation characteristics, the depth and types of cargo; \(B_{BR}\) and \(B_{BG}\) are distances to shallow water on the right and left sides of the passage depending on the channel's slopes e and ship's speed (vary from 0.3\(B\) to 1.0\(B\)). Today, simulators are frequently used for testing the passages and approaches to channels and waterways [62]. The accuracy of the received results is influenced by the reliability of ship models and external conditions simulation. The human factor is considered in real-time simulations, and, therefore, it matters who is handling the ship in the given terms and conditions because the obtained results strongly depend on the experience of a simulator operator. Moreover, simulations must be repeated (considering wind characteristics, current speed and direction, wave characteristics, etc.) a certain number of times under the same external conditions to collect appropriate data.