## 3 Results and Discussion
### Hydrographic Surveys of the Water Body of the Same Area and Different Depths  
In the next scenario, it was assumed that the measurements are made in water bodies of different depths but the size of the water area is constant. Simulations were carried out for five different depths of 10 m, 30 m, 50 m, 75 m, and 100 m. In order to perform calculations, specific parameters presented in Table 3 were adopted. The simulation results of the duration of the survey area with dimensions of 6 \(\times\) 3 Nm for five different water depths are shown in Figure 4.  
The variables of the depth of survey area determined the use of MBES swath angles in the calculations. For the depth of 10 m, \(\theta_{u}=140^{\circ}\) was assumed; for the depth of 50 m, the angle \(\theta_{u}=100^{\circ}\) was used; and for the deepest body of water, the angle \(\theta_{u}=70^{\circ}\) was substituted. Decreasing MBES swat angles directly affect the change in survey speed. The results of the calculations clearly show that the survey of the shallowest basin, despite setting the widest MBES transmitting sector, will take the most time, i.e., 7.4 days. As the depth increases, the total survey time of the water body of the same area decreases. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \multicolumn{11}{c}{\(\beta\)} \\ \hline a [m] & 0\({}^{\circ}\) & 5\({}^{\circ}\) & 10\({}^{\circ}\) & 20\({}^{\circ}\) & 30\({}^{\circ}\) & 40\({}^{\circ}\) & 50\({}^{\circ}\) & 60\({}^{\circ}\) & 70\({}^{\circ}\) & 80\({}^{\circ}\) \\ \hline \(a_{x}\) & 0.52 & 0.53 The simulation results (Figure 4) can be used to determine an additional parameter, namely, the so-called hydrographic survey effectiveness \(E_{son}\). The hydrographic survey effectiveness can be expressed by the ratio of the surveyed water body size to the time unit, i.e., the survey speed of the vessel following survey lines. The speed can be neither arbitrary nor the maximum one. The effectiveness of the hydrographic survey work \(E_{son}\) can be determined as the product of the swath width of the multi-beam echosounder and the maximum speed adopted for the survey:  
\[E_{son}=SW\cdot V_{son}, \tag{24}\]  
where: \(E_{son}\)--effectiveness of the hydrographic survey [m\({}^{2}\)/s]; \(V_{son}\)--maximum vessel's speed adopted for the survey [m/s]; \(SW\)--swath width of the multi-beam echosounder [m]. The swath width of the multi-beam echosounder is calculated using formula no. 5. The results are presented in Table 4.  
Assuming the useful MBES swath angles values \(\theta_{u}\), calculated survey speed \(V_{son}\), and the swath widths of the multi-beam echosounder \(SW\), the hydrographic survey effectiveness was determined and presented in Figure 5.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Size of the survey area & 11,112 \(\times\) 5556 m \\ Average water depth \(D\) & 10 m \\ Useful MBES swath angle \(\theta_{u}\) & 60–150\({}^{\circ}\) \\ Overlap \(p\) & 10\({}^{\circ}\) \\ Length of the main survey line \(L_{pp}\) & 11,112 m \\ Survey vessel speed \(V_{pp}\) & 4–10 kt \\ Time to perform vessel turns \(T_{21}\) & 300 s \\ Number of SVP measurements \(n_{sep}\) & 8 \\ Time of a single SVP measurement \(T_{sep1}\) & 600 s \\ Number of survey cross lines \(N_{PK}\) & 6 \\ vessel speed at turns to the next cross line \(V_{2 PK}\) & 10 kt \\ Time to conduct Patch test calibration \(T_{kal}\) & 2400 s \\ Number of cross-check maneuvers \(n_{cc}\) & 4 \\ Time of a single cross-check maneuver \(T_{c1}\) & 900 s \\ Distance to survey area \(S_{r\!{\!{\!{\!{\!{\!{\!{\!{\!{\!{\!{\!{\!\!{\!\! The effectiveness increases with the water depth of the survey area. Very shallow waters, ports, canals, and port basins belong to areas where bathymetric measurements are characterized by low efficiency, which undoubtedly affects the costs that the contractor must incur. The number of survey lines can, of course, be reduced by using wider or maximum MBES swath angles.