# Navigational Risk Assessment in Offshore Wind Farms Using Spatial Ship Domain Models
## 4 Discussion  
The numerical values of the \(\mathrm{R_{N}}\) indicators calculated for the three representative vessels reveal significant disparities in navigational safety, depending on the ship type, prevailing environmental conditions, and the model applied. The VLCC vessel exhibited the highest risk values across all analyzed distances and scenarios, especially when evaluated using the PIANC and Coldwell models. These models do not account for ship-specific maneuvering limitations or vertical clearance requirements. In contrast, the Z-Tug demonstrated safe passage through the OWF area under both average and deteriorated sea conditions, especially when assessed using the 3D Rutkowski model. These findings underscore the importance of a multidimensional approach to accurately capture spatial constraints and ship dynamics. The results also confirm that relying solely on simplified 2D domain models may lead to the overestimation or underestimation of navigational risk, especially for vessels operating near maneuverability limits. The comparative performance of the models clearly highlights the limitations of conventional approaches. [PERSON]'s 2D domain model incorporates ship maneuverability in the horizontal plane, but does not address vertical risks such as under-keel clearance (UKC) or over-head clearance (OHC). Similarly, the PIANC guidelines provide a general framework for minimum distances, but they lack sensitivity to the vessel type and real navigational behavior. The [PERSON] 3D domain model addresses these limitations by incorporating vessel-specific dimensions, hydrometeorological conditions, and maneuvering characteristics across all three spatial planes. As a result, it offers a more realistic and adaptable tool for navigational risk assessment in complex environments such as offshore wind farms (OWFs). To support operational decision-making, the integration of 3D modeling in planning and regulatory processes should be further encouraged. As shown in Table 11 (Appendix C), the calculated \(\mathrm{R_{N}}\) indicators for the VLCC remain high across all evaluated turbine spacing distances, including 1000 m. This indicates that large vessels pose a significant navigational risk when attempting to operate within OWF areas, particularly under reduced visibility or increased sea state. In contrast, \(\mathrm{R_{N}}\) values for the Z-Tug consistently fall below critical thresholds at distances above 300 m, suggesting that such vessels can safely operate within OWFs under average and even deteriorated hydrometeorological conditions. These distinctions in \(\mathrm{R_{N}}\) values provide a quantitative basis for establishing vessel-type-specific access regulations to OWF zones. Based on the analysis of \(R_{N}\) factors in the vertical (OZ) and horizontal (OX and OY) planes in relation to the objects situated ahead (forward) of the ship's bow, astern from the ship's aff, as well as on the ship's port and starboard side, and with respect to keeping the required under-keel and over-head clearance estimated for the three representative vessel types, based on the 3D domain method by [PERSON], the navigating ship Z-Tug type proves to be completely safe. Using PIANC or 2D Coldwell analysis methods, none of these three vessels could safely navigate in the OWF area. Many researchers have examined the correlation between water passages and wind farms, thus contributing to the continuous enhancement of the secure separation distance between ships and wind farms by way of employing diverse methodologies [17; 18; 35] and scrutinizing a range of factors [21], e.g., ships, fans, wind, and flow. However, only a small number of peer-reviewed research papers have been found in the existing literature regarding the use of the ship domain to evaluate the allision risk for vessels operating near and within OWFs. This paper attempts to fill this research gap by way of comparing three types of domain parameters outlined by the PIANC guidelines, Coldwell (2D), and Rutkowski (3D).