# Navigational Risk Assessment in Offshore Wind Farms Using Spatial Ship Domain Models
###### Abstract
However, only a limited number of peer-reviewed studies have specifically addressed the use of the ship domain concept in assessing the allision risks for vessels operating in the vicinity of, or within, OWF areas. Currently, there is no universally accepted standard for establishing safe distances between vessels and offshore wind farms (OWFs). As previously indicated [8], European countries adopt varying approaches to spatial coexistence between OWF installations and maritime activities. These approaches predominantly relay on the overarching recommendations provided by the World Association for Waterborne Transport Infrastructure (PIANC) concerning the risk level indicator (R\({}_{\text{N}}\)) and safety zones near OWFs. According to PIANC, the R\({}_{\text{N}}\) risk level indicator associated with offshore wind farm (OWF) impacts depends on the distance between the Traffic Separation Scheme (TSS) shipping route and the nearest row of wind turbines. The PIANC guidelines indicate that the risk level (R\({}_{\text{N}}\)) from offshore wind farm (OWF) impacts depends on the distance between the Traffic Separation Scheme (TSS) shipping route and the nearest row of wind turbines. For vessels covered by the SOLAS Convention [19], significant navigational risk arises when operating within 0.25 nautical miles (463 m) or within 500 m of high-density shipping routes. Conversely, vessels operating within TSS areas located more than 5 nautical miles (9260 m) from an OWF are generally considered to be navigating safely. The PIANC guidelines also emphasize that the minimum safe distance should be consistent with the International Regulations for Preventing Collisions at Sea (COLREGs) and relevant IMO resolutions, particularly those addressing vessel maneuverability, such as turning circle and stopping distances. The PIANC ship domain formulas, which define minimum safe distances from navigational hazards, are presented in the methods section. Most European countries follow the PIANC guidelines when designing OWFs. However, some national or local maritime administrations adopt slightly modified criteria [14]. For instance, in the British offshore sector, certain wind farms have employed a two-dimensional (2D) ship domain model, based on [PERSON]'s recommendations [20], to assess minimum safety zones. [PERSON]'s 2D ship domain model has been extensively analyzed in the literature, especially in the context of collision avoidance and ship path planning [21; 22]. Because the Coldwell 2D domain is static and does not account for factors such as the vessel's speed and maneuverability, we have chosen to compare it with [PERSON]'s three-dimensional (3D) domain model, as well as with the widely used PIANC guidelines, to evaluate safe navigation in OWF areas. In 2023, [PERSON] and [PERSON] [8] compared these three domain models and analyzed the numerical risk level indicators (R\({}_{\text{N}}\)), calculated for nine representative ship types. These calculations were based on navigational obstacles positioned on the port and starboard sides of the vessel along the OY axis (Figure 1) and were analyzed in relation to the parameters of the ship's 3D domain model. The present study extends this earlier work by incorporating an analysis of navigational hazards located ahead of the ship's bow and aster of the aft section (OX plane, Figure 2), as well as by considering the required under-keel and over-head clearance (OZ plane, Figure 1). This paper builds upon the methodological approach proposed by [PERSON] and [PERSON] [8], but focuses on a narrower group of three representative vessel types. It contributes to the growing body of research on maritime risk assessment by providing a comparative evaluation of both established and emerging ship domain models, including a 3D spatial approach, to quantify navigational safety in the context of offshore wind farm development--an increasingly critical aspect of marine spatial planning and integrated maritime operations. The research objectives are as follows:  
1.