Navigational Risk Assessment in Offshore Wind Farms Using Spatial Ship Domain Models

Abstract

Navigation in offshore wind farm (OWF) areas is essential for construction, maintenance, safety, and traditional activities like fishing. However, the presence of OWFs extends to sea routes, negatively impacting maritime transport economics. This paper examines navigational risk indicators in the vertical and horizontal planes of the ship domain for three representative vessels navigating under different hydrometeorological conditions within the location of a proposed offshore wind farm in the Polish sector of the Baltic Sea. The study compares three types of domain parameters defined by the PIANC guidelines, Coldwell’s two-dimensional model, and Rutkowski’s three-dimensional model. The analysis includes navigational hazards located ahead of the ship’s bow and astern from the aft, as well as keeping under-keel and over-head clearance. Besides the main numerical indicators of navigational risk estimated for obstacles on the port and starboard sides, the study emphasizes the importance of such additional factors. The primary objective of this paper is to identify the ship types that can navigate and fish safely in proximity to and within the OWF area. The analysis employs hydrometeorological data, mathematical models, and operational data derived from maritime navigation and maneuvering simulators. This comprehensive approach aims to enhance maritime safety in OWF areas.

1. Introduction

In April 2021, under the Regulation of the Council of Ministers, the first spatial development plan for the Polish internal marine waters, territorial sea, and exclusive economic zone (EEZ) was adopted [1]. The plan addresses, inter alia, issues related to the location of offshore wind farms (OWFs) and cable corridors, the development of port approach infrastructure, hydrocarbon extraction, and the construction of coastal facilities [2,3]. As a result, the plan introduced spatial order at sea by designating zones with specific functions, including energy production, transport, tourism, fisheries, or military use. Since sea space is limited, trade-offs between different uses had to be made. Therefore, the concept of maritime space sharing is considered [4,5]. In this context, two main categories of issues must be taken into account: cost-related impacts resulting from the exclusion of specific sea areas (e.g., extension of shipping routes or the need to use fishing grounds located farther from the shore), and safety concerns (e.g., allision avoidance [6,7]), including those involving fixed offshore structures, such as OWF installations [8]. A particularly sensitive issue is the use of wind farm areas for the merchant ships transit (within designated transit corridors), as well as the implications for fishing and navigation by smaller surface vessels. Fixed installations pose a significant challenge by increasing the number of obstacles at sea that must be avoided. These installations directly affect navigational planning and vessel routing, particularly in areas previously used for transit, fishing, or pilotage. Therefore, navigational safety must be reassessed in the context of OWF layouts and operational zones, as ship movements are constrained by the physical presence of offshore structures and their associated safety zones.

According to the plan, approx. 3600 km² are allocated for OWFs, which is 12% of Poland’s EEZ. The location of Polish wind farms will therefore affect transport accessibility of Polish seaports, particularly those located on the open sea, including Darłowo, Kołobrzeg, Ustka, and Władysławowo. It is estimated that the first OWFs in the Polish EEZ will begin producing energy as early as 2026 [9], meaning that the construction phase is imminent.

The implementation of OWFs in the Polish EEZ is expected to bring significant ecological and economic benefits. For example, the Baltic Power OWF, located approximately 23 km north of Władysławowo, is projected to supply electricity to over 1.5 million households and reduce annual CO₂ emissions by around 2.8 million tonnes [10]. Beyond environmental advantages, offshore wind development is also expected to benefit both local and national economies. According to the Polish Wind Energy Association (PSEW), the offshore wind sector could create up to 77,000 jobs and generate up to PLN 60 billion in gross value added to Poland’s economy by 2040 [11]. Ports such as Łeba, Ustka, and Gdynia are already undergoing infrastructure upgrades to support OWF construction and maintenance, leading to increased employment in shipbuilding, logistics, and marine services [12]. These developments underscore the need for rigorous navigational risk assessment to ensure the safe integration of OWFs into heavily used maritime areas.

At this stage, the increase in vessel traffic associated with wind farm construction, along with the emergence of subsequent offshore installations, will impose certain restrictions on maritime navigation [8]. A key milestone will be the commissioning of the OWFs, as this will be crucial for ensuring the security of the existing infrastructure. Simultaneously, regulating access to those areas for other sea users will become necessary. European examples illustrate varying approaches to space sharing between OWF installations and maritime traffic. In countries such as Belgium and Germany, OWF zones have been designated as exclusion areas from vessel traffic. In contrast, in Denmark and the United Kingdom, navigation through wind farms is permitted under specific conditions.

In Poland, the issue of granting other users access to offshore wind farm (OWF) areas is currently the subject of intensive discussion among stakeholders. The Polish Maritime Administration is considering the introduction of so-called unconstrained passage and/or fishing within OWF zones for power-driven vessels with an overall length of up to 45 m. Currently, the Polish Maritime Administration [13], acting under Article 24 in conjunction with Article 47 of the Act of 21 March 1991 on Maritime Areas of the Republic of Poland, is contemplating the delineation of safety zones around the OWF facilities and installations located within Polish maritime areas. However, according to the Navigational Impact Analysis for the Baltic II OWF [14], navigation within OWF zones is to be permitted only at a minimum distance of 150 m from the OWF structures and installations, and only if visibility in the area at the time of passage as well as forecasted for the following 12 h, is not less than 2 nautical miles (3704 m), and the sea state does not exceed level 3 on the Douglas Sea Scale. Compliance with these conditions is to be determined based on a forecast issued by Poland’s National Meteorological Service.

Within the OWF safety zones, consideration is being given to permitting navigation for the following categories of vessels: (1) vessels operated by the Polish Maritime Administration, Polish Armed Forces, Border Guard, National Revenue Administration, and the Polish Marine Fisheries Administration; (2) vessels engaged in life- or property-saving operations or in exercises related to such activities; (3) vessels involved in marine hazard or pollution response operations or related exercises; (4) vessels compelled to enter safety zones due to adverse weather conditions or imminent danger; (5) vessels performing activities and services related to the OWF operation, including its infrastructure, or acting under legal regulations and decisions of state authorities, including maritime administration; (6) vessels conducting environmental surveys aimed at the analysis or assessment of marine resources associated with OWF operations; (7) other vessels for which written consent has been granted jointly by the director of the competent maritime office and the OWF owner or the entity responsible for the OWF operation, holding the relevant rights to the installation. The analyses presented herein constitute an important contribution to this ongoing discussion by introducing scientific perspectives. Moreover, providing a sound scientific basis for decisions regarding access to OWF areas may facilitate the establishment of a standardized approach to this issue at both the regional (Baltic Sea) and European levels.

The “ship domain” refers to the area surrounding a vessel that is essential for maintaining safe navigation. This concept has been extensively studied in the literature on maritime safety [15], particularly in the context of collision risk assessment [16]. Assessing the risk of allisions between vessels and offshore wind farm (OWF) structures is a key factor in determining appropriate separation distances and in establishing safe buffer zones between shipping routes and OWF installations. Numerous researches have investigated various methods for calculating allision risk and have comprehensively reviewed the related literature [17,18]. 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_N) and safety zones near OWFs. According to PIANC, the R_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_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 maneuvrability, 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 Coldwell’s recommendations [20], to assess minimum safety zones. Coldwell’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 Rutkowski’s three-dimensional (3D) domain model, as well as with the widely used PIANC guidelines, to evaluate safe navigation in OWF areas.

In 2023, Rutkowski and Kubacka [8] compared these three domain models and analyzed the numerical risk level indicators (R_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 astern 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 Rutkowski and Kubacka [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:

Evaluating how hazards ahead of the ship’s bow, astern of the ship’s aft and on the port and starboard sides, along with under-keel and over-head clearance requirements, influence the determination of safe navigation within Offshore Wind Farms (OWFs) areas by:

a.. Determining the navigational risk numeric indicators (R_NLF, R_NLA, R_NWP, and R_NWS) with respect to maintaining the required safe distance ahead of the ship’s bow, behind its stern, and on the ship’s port and starboard sides. This is carried out using the PIANC guidelines and the 2D ship domain model by Coldwell [20] and Rutkowski [23,24]. This includes consideration of the stopping maneuveres by reversing the engine from Full Ahead to Full Astern (FSAH-FAS), and from Half Ahead to Full Astern (HAH-FAS), as well as the turning circle maneuver at FSAH with a rudder angle of 35° starboard.

b.. Determining the numeric indicators of navigational risk (R_ND and R_NH) related to maintaining the required under-keel and over-head clearance to ensure the safety of vessel traffic lanes for representative ship types navigating within OWF areas. This is based on the 3D ship domain model by Rutkowski [8,23,25].

Identifying vessels that may pose specific risks to OWF operations, and determining vessel types that are considered safe and could be permitted to navigate or fish in or around OWF zones.

Comparing the domain parameters for the selected vessels based on the PIANC guidelines, Coldwell’s 2D model, and Rutkowski’s 3D model, across the OX, OY, and OZ planes.

To enhance clarity, Table 1 summarizes the abbreviations used throughout this manuscript to support the reader’s understanding of the technical terminology related to navigational risk assessment and offshore wind farm operations.

2. Materials and Methods

2.1. Defining the Method for Assessing the Navigational Risk Indicators R_N

The R_N evaluation is calculated using formulas based on Rutkowski’s research [23,24], focusing on maintaining safe distances around a ship (Appendix A). According to Rutkowski’s ship domain concept, a ship is considered safe if it is the only potential hazard within its domain. For the vertical component of navigational risk (R_ND), safety is ensured if the ship’s domain depth (SD_D) is less than the actual sea depth (h), which indicates the risk related to under-keel clearance (Formula (1)). When sea depth is less than or equal to the ship’s maximum draft (T_max), the navigational risk is high, possibly reaching 100% (indicating grounding). For sea depths between T_max and SD_D, the risk is between 0 and 1, showing varying degrees of potential danger. Similar principles apply for risks involving objects above the water, as described in Formula (2).

In the horizontal plane, two components of R_N: R_NLF and R_NLA, represent the risk related to maintaining safe distances ahead and astern of the ship. If the distance to the nearest danger ahead (d_NF) is less than or equal to the forward ship domain (SD_LF), the risk will vary between 0 and 1, potentially reaching 100% if the danger is very close (Formula (3)). A similar method is used for analyzing the risk on the port and starboard sides (R_NWP and R_NWS) using formulas that account for safe distances to the nearest objects (Formulas (5) and (6)).

2.2. Types of Representative Ships

For our analyses, we selected three vessels: a Very Large Crude Carrier (VLCC), a fishing boat, and a Z-Drive Prevention Response Tug (Z-Tug). The three vessel types selected represent a spectrum of maritime operations in OWF areas, from small maneuverable service units to large transiting tankers. This selection enables the assessment of model sensitivity across vessel sizes and maneuvering capabilities.

The parameters of selected vessel types used in our analysis are presented in Table 2. Numerical models and operational (maneuvering) data were derived from various sources, including the specific details of the vessels, Wheel House Posters with the vessels’ maneuvering parameters, the author’s own sea experience when maneuvering on this type of vessel. Additionally, data from the maneuvering simulator provided by the Faculty of Navigation at Gdynia Maritime University was utilized. This included the NaviTrainer 5000 Professional (Wärtsilä Voyage Oy, Helsinki, Finland) (with ship models according to the Wärtsilä Navi-Trainer Professional 6, Technical Description and Installation Manual Version 6.0, issued in December 2022) in conjunction with the ECDIS NaviSailor 4000 electronic chart system from Transas, which is part of the Wärtsilä Group. Simulation data were generated using the NaviTrainer 5000 Professional system (Wärtsilä Voyage Oy, Helsinki, Finland) and ECDIS NaviSailor 4000. Key parameters extracted include initial and final speeds, stopping distances, turning radii, time to stop, and drift under no-thrust conditions. These values were input into the 3D domain model to define spatial safety margins for each vessel type. The simulator outputs were validated against standard maneuvering test data and literature values to ensure realism. It is noted that the R_N indicators calculated in this study are deterministic and scenario-specific; stochastic variability and probabilistic modeling approaches were not applied but are considered a direction for future research.

2.3. Hydrometeorological Data

Environmental scenarios, including moderate and deteriorated hydrometeorological conditions, were based on regional Baltic Sea data and reflect typical navigation challenges. Extreme weather such as ice-covered waters was excluded from this study but is recognized as a significant future consideration. The values of average and deteriorated conditions used for our analysis come from the publication entitled “Admiralty Sailing Directions: Baltic Pilot Vol. 2 (Np19), 18th Edition 2022” [26] and “Sailing Directions of the Baltic Sea—Polish Coast” [27] (Table 3). The spatial domain model parameters for the chosen vessel types were estimated based on the data presented in Table 2. This study specifically examines navigation under average and deteriorated hydrometeorological conditions relevant to the selected location.

This study does not explicitly account for potential local hydrometeorological changes caused by the presence of offshore wind turbine (OWT) structures, such as altered wind flow, current deflection, or localized wave disturbance. Although such effects may occur depending on the wind farm’s layout and density, as well as turbine dimensions and prevailing sea state, they are generally of limited spatial extent and were considered negligible in the context of the deterministic R_N model applied in this study. These secondary influences are therefore beyond the scope of the current analysis but are recognized as a potential limitation. Future research may incorporate high-resolution environmental modeling to investigate the impact of OWF-induced flow alterations on ship maneuverability and navigational risk levels.

2.4. Spatial Models of the Ship Domain

This paper focuses on three spatial models of the ship domain: the PIANC [28], the 2D domain by Coldwell [20], and the ship’s 3D domain model by Rutkowski [8,23]. The three domain models were selected based on their relevance and frequency of use in maritime risk assessments, each representing a different level of complexity. The PIANC model is widely recognized as a regulatory reference, the Coldwell 2D domain offers maneuverability-based insights, and the Rutkowski 3D model enables dynamic spatial risk analysis. In the following sections, these models are applied to three representative vessel types under defined environmental conditions to assess and compare navigational risk (R_N) values within offshore wind farm areas.

As outlined in the PIANC guidelines, the minimum distance necessary for safe navigation is linked to the COLREG regulations (1972) and is defined according to IMO resolutions, specifically MSC.137(76) [29] and MSC/Circ.1053 [30]. These resolutions address vessel maneuverability, particularly concerning the turning circle and emergency stopping distance. The PIANC guidelines stipulate that the minimum safe distance (d_{N min}) from a navigational obstacle should be calculated using the following formulas:

(1)${SD}_{LF}=d_{NF min}=5 \mathrm{N}\mathrm{m}=9260 \mathrm{m} \left[\mathrm{m}\right]$

(2)${SD}_{WP}=d_{NP min}=6·\mathrm{L}+500 \mathrm{m} \left[\mathrm{m}\right]$

(3)${{SD}_{WS}=d_{NS}=d}_{NP min}+0.3 \mathrm{M}\mathrm{m}\approx 6·\mathrm{L}+1056 \mathrm{m} \left[\mathrm{m}\right]$

According to Coldwell’s 2D domain model, the length of the ship’s domain is measured horizontally in both the forward and aft directions, as well as to the port and starboard sides from the center of the ship’s layout:

(4)${SD}_{LF}=6.1·\mathrm{L} \left[\mathrm{m}\right]$

(5)${SD}_{LA}=3.9·\mathrm{L} \left[\mathrm{m}\right]$

(6)${SD}_{WP}=1.75·\mathrm{L} \left[\mathrm{m}\right]$

(7)${SD}_{WS}=3.25·\mathrm{L} \left[\mathrm{m}\right]$

The 3D domain by Rutkowski was described with reference to the XYZ coordinate system by Rutkowski in 2000–2021 [23,24,25,31,32]. The Rutkowski 3D domain model integrates spatial safety margins in three planes: horizontal (OX and OY) and vertical (OZ). The model takes into account ship-specific dimensions, maneuvering characteristics (e.g., stopping distance, turning radius), and external conditions such as wave height, current speed, and wind force. Key assumptions include the requirement to maintain minimum under-keel clearance (UKC) and over-head clearance (OHC), as well as directional safety margins (forward, astern, port, starboard), computed dynamically from simulator data. The safe domain boundaries are derived from modeled maneuvers (e.g., crash-stop, turning circle) under various power and rudder settings. This dynamic structure allows the 3D model to adjust spatial safety zones based on the vessel type, operational profile, and surrounding environment. The Rutkowski 3D domain can be represented by the equations included in Appendix B.

A comparison of the three spatial ship domain models considered in this study is summarized in Table 4.

2.5. Seabed Characteristics in the Study Area

The FEW Baltic II offshore wind farm is located in the southern Baltic Sea, approximately 50 km north of Ustka, within the area defined by the “Ławica Słupska” sheet of the Geological Map of the Baltic Sea Floor (1:200,000). Geologically, the area lies on the eastern edge of the East European Craton and includes glacially shaped terrain formed during the final stages of the Pleistocene deglaciation [33].

The site covers approximately 41 km² at water depths between 30 and 50 m, with most of the area lying between 40 and 46 m. The seabed consists primarily of fine to medium sands, with interlayers of silty and clayey sediments, and occasional gravel and boulders. Morphological features include sand waves, low ridges, sand domes, and elongated depressions, resulting in under-keel clearance (UKC) variability important for navigational risk modeling.

Turbines at Baltica II will be mounted on large-diameter steel monopile foundations (~9 m diameter, embedded ~40 m), supporting Siemens SG 14-236 DD (14 MW) direct drive wind turbines. A total of 25 turbines are planned [34]. These foundations are adapted to local geotechnical conditions and may create localized scour zones that can modify bathymetry in their immediate vicinity. While such effects may influence UKC near turbine bases, they are spatially limited and have negligible impact on overall vessel maneuverability across the OWF. Bathymetric and sediment variability are explicitly included in the RN model to reflect realistic conditions affecting deep-draft navigation.

3. Results

In this part of the paper, SD_WP, SD_WS, SD_D, SD_H, SD_LF, and SD_LA (Appendix C, Table A1) parameters are presented for the three vessel types outlined in Table 1. These parameters were compiled according to the PIANC guidelines, Coldwell’s 2D domain model, and Rutkowski’s 3D domain model, utilizing maneuvering characteristics obtained from the maneuvering simulator at Gdynia Maritime University. The calculations were performed for both typical and adverse hydrometeorological conditions (Table 2).

What follows is the calculation of sample navigational risk indicators R_NWP (SD_WP), R_NWS (SD_WS), R_ND (SD_D), R_NH (SD_H), R_NLF (SD_LF), and R_NLA (SD_LA) in relation to maintaining the necessary distance from navigational hazards identified on both the port and starboard sides of the vessel, forward and astern side (Appendix C, Table A3), and the depth (under-keel clearance, UKC) and height (over-head clearance, OHC) reserve, respectively (Table A2). These metrics were calculated for the three representative ship types (Appendix C, Table 1) based on their domain dimensions, including width, length, depth, and height (Appendix C, Table A1), and were assessed under typical hydrometeorological conditions (Table 2).

3.1. The Numeric Factors of R_ND and R_NH Estimated for Three Ship Types

The analysis of navigational risk factors R_ND for maintaining the required depth reserve was conducted using the ship domain depth (SD_D) and navigational risk definitions (Formulas (1) and (20)). The study considered three ship types, assessing their navigational safety in relation to underwater obstacles in a sea area with limited depth, such as an offshore wind farm (OWF) (Figure 3). According to the data from Table A2 (Appendix C), the sea depths (36.5 m ≤ h ≤ 54.5 m) are sufficient for safe navigation for all three ships (VLCC, fishing boat, Z-Tug) as long as the sea depth (h) exceeds the domain depth (SD_D). However, a corridor with a minimum sea depth of 14.5 m is non-navigable for the VLCC but safe for the smaller fishing boat and Z-Tug. In territorial waters with a minimum depth of 7.0 m, only the Z-Tug can navigate safely.

Regarding above-water obstacles, while the OWF area currently lacks any, future construction may introduce risks from wind turbine rotors for service vessels operating nearby. To ensure safe navigation under these rotors, which have a clearance from 22 m to 27 m, vessels must satisfy the condition SD_H < Ho (rotor clearance). Based on the analysis in Table A2 (Appendix C), only the Z-Tug can safely operate under these conditions, as its domain height ensures clearance from the wind turbine rotors.

3.2. The Numeric Factors R_NLF and R_NLA Estimated for Three Ship Types

In this paper, as in previous studies [8], it is assumed that the distances between offshore installations in the OWF area range from 700 m for substations and 1000–2000 m for wind turbines. However, this analysis expands to include seven different distances: 150 m, 300 m, 500 m, 600 m, 700 m, 800 m, and 1000 m. Table A3 (Appendix C) presents navigational risk indicators for different ship domain lengths ahead of and astern of representative ship types in the OWF area, considering average hydrometeorological conditions. Calculations were based on PIANC guidelines, Coldwell’s 2D domain model, and Rutkowski’s 3D domain model, which account for turning circles and emergency stop maneuvers.

For large vessels over 250 m (e.g., VLCC), navigational risk only significantly decreases when distances from hazards exceed 1000 m. The analysis shows that for a VLCC, risk indicators are acceptable only beyond this distance. The greatest distance between wind turbines in the OWF is 1976 m, meaning the minimum safe distance from hazards is approximately 988 m. Even then, VLCC navigation in the OWF area still entails some risk.

For smaller vessels like fishing boats or Z-Tugs, the risk of allision remains high at distances under 150 m, even at reduced speeds and favorable conditions. For Z-Tugs, the risk drops below 0.0 at distances beyond 250 m. Although lower risk values are noted for smaller vessels, the safety zone around wind turbines, according to PIANC guidelines, is 500 m. However, the PIANC method does not clearly define which vessels are considered small or large. The analysis concludes that navigating a VLCC in the OWF area is extremely risky and should be avoided, while smaller vessels could enter the area in emergencies.

3.3. The Numeric Factors of R_NWP and R_NWS Estimated for Three Ship Types

Table A3 (Appendix C) highlights the navigational risk indicators R_NWP (SD_WP) and R_NWS (SD_WS), which relate to maintaining safe distances from hazards on a ship’s port and starboard sides. The results reveal significant variation in risk levels depending on the method used. The PIANC method, the most restrained, shows higher risk values (indicated by red fields), but its results are minimally affected by vessel size and do not account for actual maneuvering capabilities. This makes it less practical for smaller vessels like fishing boats and Z-Tugs. For example, with a 350 m distance from the nearest hazard, the PIANC method gives a risk indicator of 0.61 for fishing boats and 0.55 for Z-Tugs on the port side, and 0.76 and 0.74, respectively, on the starboard side.

In contrast, the Coldwell 2D domain method and Rutkowski’s 3D domain model suggest safe navigation for both vessel types regarding side hazards. While Coldwell’s model is comparable to Rutkowski’s for emergency turns at full speed with a 35° rudder angle, it only considers the horizontal plane (XY) and ignores obstacles above or below the water. Rutkowski’s 3D model accounts for these factors and helps in selecting appropriate anti-collision maneuvers by adjusting the ship’s course or speed.

For instance, when evaluating the R_NWP (SD_WP) and R_NWS (SD_WS) for a VLCC at 500 m from the nearest hazard, a full-speed starboard turn shows a 42% risk on the starboard side (R_N = 0.42). An emergency stop reduces this risk to 18% (R_N = 0.18), and a half-speed stop lowers it to 5% (R_N = 0.05).

4. Discussion

The numerical values of the 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. Coldwell’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 Rutkowski 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 A3 (Appendix C), the calculated 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, 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 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 aft, 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 Rutkowski, 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). The PIANC method is a simplified method commonly used to determine the minimum distance of navigating vessels from offshore installations. This method gives the same values regardless of the ship’s size, speed, and planned anti-collision maneuvers. Coldwell’s 2D domain takes into account the ship’s stopping distance but does not take into account (similarly to the PIANC method) the navigational risk indicators assessed in the vertical plane, e.g., the possibility of the ship running aground or damage caused to the ship by obstacles suspended above the water (e.g., power lines, wind turbine blades, bridges). These two methods can be perceived as simplified ones, as they only depend on the spatial relationship between the ship’s location and the detected navigational hazard within a two-dimensional horizontal space. This hazard may include an offshore installation, but also another vessel or land. Although these domains are easy to describe, use, and model [16] which is their indisputable advantage, they are static domains with a fixed size, which does not correspond to the case under examination. This paper proves that a more accurate ship domain should be considered for conducting safe navigation analyses within an OWF. Similar conclusions were derived, e.g., by Nie et al. [36] according to whom the safe distance between wind farms and routes is related to the average speed of ships, load tons, and the length of wind farm boundaries. In this approach, Rutkowski’s 3D domain model seems to be more accurate because it takes into account UKC, OHC and, in addition, the safe distance ahead of the bow, astern, and on port and starboard sides, which is required for the ship, taking into consideration the ship’s size, type, and the stop maneuver by the reversing engine from FSAH to FAS and from HAH to FAS, and the turning circle maneuver at FSAH with a rudder angle of 35° starboard. Moreover, the method depends on many factors, in particular: (1) the current conditions prevailing in the examined navigable area (e.g., hydrometeorological disturbances from wind, current and wave, density of navigation obstacles, presence of other ships and offshore facilities, distance to the nearest navigation hazard, depth and width of navigable areas, traffic intensity); (2) the vessel’s parameters, its length, width, draft, height, maneuvering parameters, in particular, its initial speed and the distance and time needed for an emergency stop or turning circle at various engine and/or rudder settings, the type of cargo transported (safe or dangerous and its potential impact and threat to the natural environment and other ships and offshore installations).

This study has certain limitations. The safe distance model presented in this paper applies only to specific water areas, and the parameters influencing the output of the safe distance model are primarily associated with local wind and currents. Additionally, the data used are derived from simulators, and it is recognized that all models are not perfect, or at least not entirely accurate. Moreover, the human factor [37] and machinery can contribute to accidents involving ships navigating in OWF waters, such as misjudgment, miscommunication between officers aboard the ship, and malfunctions of navigation equipment. These factors will be taken into consideration in future research endeavors.

Although the R_N indicator-based modeling provides valuable spatial risk estimates, it does not fully capture the operational challenges faced by vessels navigating near offshore wind farms. For example, turbine towers and rotating blades may cause radar shadowing and blind zones, reducing the effectiveness of ARPA systems, ECDIS updates, and visual target tracking. These effects are particularly relevant in dense OWF layouts or under poor visibility.

Additionally, operating turbines generate aerodynamic wake effects that may alter near-surface wind patterns and produce wave–current interactions, which in turn can affect small vessel handling and station-keeping stability. Such phenomena have been observed and documented in the North Sea and UK sectors, particularly in connection with crew transfer vessels and service operations.

While this study focuses on fixed-bottom turbines (monopile foundations), it is worth noting that floating offshore wind structures, increasingly deployed in deeper waters, pose different navigational risks due to their motoring systems, anchor lines, and dynamic motion in response to the sea state. These differences require distinct safety buffers and vessel exclusion zones.

Incorporating such operational constraints and sensor-related limitations into future R_N models or navigational guidelines would improve the practical applicability of spatial risk assessments in OWF areas.

In practical terms, the Rutkowski 3D model offers valuable input for maritime authorities, pilot organizations, and port operators engaged in offshore spatial planning. Its output can support the identification of safe navigation corridors, service vessel access routes, and exclusion zones tailored to the vessel type, maneuvering capacity, and prevailing environmental conditions. These results are aligned with international safety standards and can serve as a tool for translating general PIANC and SOLAS guidelines into risk-based, location-specific navigation policies.

This study offers several key contributions to the current body of research on navigational safety in offshore wind farm areas. First, in contrast to most previous works that rely solely on two-dimensional ship domain models [16,17,21], this analysis applies a spatially explicit 3D ship domain model that accounts not only for vessel maneuvering characteristics but also for vertical risk factors such as under-keel clearance (UKC) and over-head clearance (OHC). Second, the study introduces a comparative framework by evaluating navigational risk indicators (R_N) using three distinct modeling approaches (PIANC, Coldwell 2D, Rutkowski 3D) across different vessel types and environmental scenarios, which has not been systematically carried out in the existing literature. Third, by integrating model-based simulation data with realistic traffic and environmental parameters, this paper provides an operationally useful tool for offshore spatial planners and maritime authorities. The enhanced R_N methodology and its application to three representative vessels offer a practical benchmark for developing vessel-specific access rules and corridor designs for OWF areas in the Baltic Sea and beyond.

In summary, this study confirms that multidimensional navigational risk assessment models are essential for evaluating the feasibility of vessel movement within OWF areas. The 3D spatial model, which includes horizontal and vertical safety margins and accounts for vessel-specific dynamics, provides a reliable and operationally meaningful framework. Its implementation can enhance the coexistence of offshore renewable infrastructure with existing maritime traffic and support more adaptive and evidence-based regulatory practices. Furthermore, these results offer a practical foundation for formulating vessel-specific transit guidelines and safety buffer zones within OWF layouts, thereby improving navigational safety and strengthening offshore spatial planning frameworks.

5. Conclusions

This study demonstrates that a multidimensional approach to navigational risk assessment is essential for the safe integration of offshore wind farms into busy maritime areas. The comparative framework presented herein shows that the 3D ship domain model developed by Rutkowski, which accounts for both horizontal and vertical clearances as well as vessel maneuverability, provides a realistic and flexible tool for regulators, port authorities, and other stakeholders involved in offshore spatial planning and management. Importantly, this approach supports the design of safely navigable corridors, service routes, and operational safety zones within offshore wind farm areas. Furthermore, by applying these methodologies to representative ship types under realistic environmental conditions, the study offers a fundamental tool for developing tailored, risk-informed navigational guidelines. This, in turn, enhances operational safety and promotes the sustainable coexistence of offshore energy infrastructure with other maritime activities.

Author Contributions

Conceptualization, G.R. and M.K.; methodology, G.R. and M.K.; software, G.R.; validation, G.R.; formal analysis, G.R.; investigation, G.R.; resources, G.R.; data curation, G.R.; writing—original draft preparation, G.R. and M.K.; writing—review and editing, G.R. and M.K.; visualization, M.K.; supervision, G.R.; project administration, G.R. and M.K.; funding acquisition, G.R. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data that support the findings of this study are available from the first author, Grzegorz Rutkowski ([email protected]), upon justified request.

Acknowledgments

We sincerely thank Karolina Rogóż-Badzińska for her precise translation of this manuscript, and Teresa Moroz-Kunicka and Mateusz Kunicki for their valuable edits, all of which greatly improved the clarity and quality of the final text.

Conflicts of Interest

The authors declare no conflicts of interest.

Footnotes

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Figures and Tables

Figure 1 Illustrative drawing of the simplified and composite three-dimensional (3D) ship domain model by G. Rutkowski, based on [8]. The model dimensions include SD_L—the domain’s length; SD_W—its width; SD_D—its depth; and SD_H—its height.

Figure 2 A graphical representation of navigational risk indicators (R_N) based on ship domain parameters (SD_LF, SD_LA, SD_WP, SD_WS) and the proximity to the closest navigational obstruction (d_N).

Figure 3 The wind turbine generator parameters with air clearance under the rotor F = 22 m to 26 m.

Table 1

List of abbreviations used in the manuscript.

Abbreviation	Full Term
ADT	Ship’s Air Draft (HN), the vertical height of the ship’s highest point above the waterline
COLREG	International Regulations for Preventing Collisions at Sea
dN	Distance to the nearest navigational danger (hazard)
ECDIS	Electronic Chart Display and Information System
EEZ	Exclusive Economic Zone
FAS	Full Astern
FSAH	Full Speed Ahead
HAH	Half Ahead
IMO	International Maritime Organization
OHC	Over-Head Clearance
OWF	Offshore Wind Farm
OWT	Offshore Wind Turbine
PIANC	World Association for Waterborne Transport Infrastructure
RL	Risk Level
RND	Vertical component of the navigational risk indicator (RN) that concerns keeping an adequate required under-keel clearance (UKC)
RNH	Vertical component of the navigational risk indicator (RN) that concerns keeping an adequate required over-head clearance (OHC) or air draft clearance
RNLF	Horizontal component of the navigational risk indicator (RN) that concerns keeping an adequate required safe distance from the nearest danger ahead of the ship
RNLA	Horizontal component of the navigational risk indicator (RN) that concerns keeping an adequate required safe distance from the nearest danger astern of the ship
RNWP	Horizontal component of the navigational risk indicator (RN) that concerns keeping an adequate required safe distance from the nearest danger on the ship’s port side
RNWS	Horizontal component of the navigational risk indicator (RN) that concerns keeping an adequate required safe distance from the nearest danger on the ship’s starboard side
SDD	Ship Domain Depth calculated below the waterline
SDH	Ship Domain Height calculated above the waterline
SDLF	Ship Domain Length Forward calculated horizontally ahead from the center of the ship’s layout
SDLA	Ship Domain Length calculated horizontally astern in the aft direction from the center of the ship’s layout
SDWP	Ship Domain Width (beam) calculated to the Port side from the ship’s heading line
SDWS	Ship Domain Width (beam) calculated to the Starboard side from the ship’s heading line
TSS	Traffic Separation Scheme
UKC	Under-Keel Clearance
VLCC	Very Large Crude Carrier
Z-Tug	Z-Drive Prevention Response Tug

Table 2

The representative vessel types and their parameters. Data derived from the Wheel House Posters.

Type of Ship and Its Parameters
	VLCC (Very Large Crude Carrier)	Fishing Boat (Fisher)	Z-Drive Prevention Response Tug
DWT [t]	159,584 DWT	1676 DWT	300 DWT
Engine power [kW]	15,500 kW	840 kW	2 × 3800 kW
Length overall (L = LOA), from stern to bridge (LRF) and from bridge to bow (LRF) [m]	L = LOA = 261.3 mLAR = 51.8 mLRF = 209.5 m	L = LOA = 65.6 mLAR = 25.3 mLRF = 40.3 m	L = LOA = 45.0 mLAR = 30.5 mLRF = 14.5 m
Width B [m]	48.3 m	10.3 m	12.5 m
Draft T = Tmax [m]	15.0 m	5.4 m	4.9 m
Overall height Hc [m]	77.3 m	32.3 m	21.0 m
Air draft HN = ADT [m]	62.3 m	27.0 m	16.1 m
Hull Block coefficient CB	0.85	0.64 m	0.614
Ships Speed [kn]	Full Ahead (FSAH) = 15.0 kn ≈ 7.7 m/sHalf Ahead (HAH) = 10.1 kn ≈ 5.2 m/s	Full Ahead (FSAH) = 12.6 kn ≈ 6.5 m/sHalf Ahead (HAH) = 8.9 kn ≈ 4.6 m/s	Full Ahead (FSAH) = 15.0 kn ≈ 7.7 m/sHalf Ahead (HAH) = 5.7 kn ≈ 2.9 m/s
Parameters for ship turning (circulation) and emergencyADmax; TRmax [m]	Advance = ADmax = 926 m ≈ 3.5∙LTransfer = TRmax = 889 m ≈ 3.4∙L	Advance = 213 m ≈ 3.2∙LTransfer = 241 m ≈ 3.7∙L	Deep Water: Advance = 86 m ≈ 1.9∙LTransfer = 78 m ≈ 1.7∙LShallow Water: Advance = 89 m ≈ 1.9∙LTransfer = 108 m ≈ 2.4∙L
Stopping DistanceADmax [m]	FSAH-FAS = 3704 m ≈ 14.2∙LHAH-FAS = 1482 m ≈ 5.7∙L	FSAH-FAS = 667 m ≈ 10.2∙LHAH-FAS = 333 m ≈ 5.1∙L	FSAH-FAS = 77 m ≈ 1.9∙LHAH-FAS = 22 m ≈ 0.5∙L

Table 3

The average and deteriorated conditions, table from [8], source: Sailing Directions. Polish Coast, 2016 [27] and “Admiralty Sailing Directions: Baltic Pilot Vol. 2 (Np19), 18th Edition 2022” [26].

Parameter	Average Conditions	Deteriorated Conditions
Visibility	At least 5 NM	Reduced to 2 NM
Wave height	hf ≈ 1.0 m	hf ≈ 3.0 m
Wind	3–4 °B	5–6 °B
Permanent surface current velocity	Vp ≤ 0.2 kn	Vp ≤ 0.4 kn
Current direction (Kp)	In line with the direction of the vessel traffic flow within the TSS	Perpendicular to the direction of the vessel traffic flow within the TSS
Water level vertical oscillations referred to chart datum (Chart Datum = MSL)	±0.3 m	Not more than ±0.60 m
Water density (ρ)	1.0066 g cm−3	1.0066 g cm−3
Ship drift angle (a)	Not more than ±1°	Not more than ±2°
Maximum yawing (Δ)	Up to ±2°	Up to ±4°
Roll angle (a)	Up to ±4°	Up to ±8°

Table 4

Comparison of spatial ship domain models used in the analysis.

Model	Dimensionality	Accounts for Vessel Size/Speed?	Considers Vertical Risks (UKC/OHC)?	Reflects Maneuvering Capability?
PIANC guidelines	2D (horizontal)	No	No	Partially (via generic maneuvering standards)
Coldwell (1983) [20]	2D (horizontal)	Partially (via stopping distance)	No	Yes (limited to turning/stopping distance)
Rutkowski (2000) [23]	3D (horizontal + vertical)	Yes	Yes	Yes (detailed maneuvering behavior under different conditions)

Appendix A

The navigational risk assessment R_N formulas based on Rutkowski’s research (2000) [23]:(A1)$$R_{ND}=\left\{\begin{array}{ccc}0& \mathrm{when}& h>{SD}_D\\ {\displaystyle \frac{{SD}_D-h}{{SD}_D-T_{max}}}& \mathrm{when}& T_{max}<h\le {SD}_D\\ 1& \mathrm{when}& h\le T_{max}\end{array}\right.$$(A2)$$R_{NH}=\left\{\begin{array}{ccc}0& \mathrm{when}& H_o>{SD}_H\\ {\displaystyle \frac{{SD}_H-H_o}{{SD}_H-H_N}}& \mathrm{when}& H_N<H_o\le {SD}_H\\ 1& \mathrm{when}& H_o\le H_N\end{array}\right.$$(A3)$$R_{NLF}=\left\{\begin{array}{ccc}0& \mathrm{when}& d_{NF}>{SD}_{LF}\\ {\displaystyle \frac{{SD}_{LF}-d_{NF}}{{SD}_{LF}-L_{RF}}}& \mathrm{when}& L_{RF}<d_{NF}\le {SD}_{LF}\\ 1& \mathrm{when}& d_{NF}\le L_{RF}\end{array}\right.$$(A4)$$R_{NLA}=\left\{\begin{array}{ccc}0& \mathrm{when}& d_{NA}>{SD}_{LA}\\ {\displaystyle \frac{{SD}_{LA}-d_{NA}}{{SD}_{LA}-\left(L-L_{RF}\right)}}& \mathrm{when}& \left(L-L_{RF}\right)<d_{NA}\le {SD}_{LA}\\ 1& \mathrm{when}& d_{NA}\le \left(L-L_{RF}\right)\end{array}\right.$$(A5)$$R_{NWP}=\left\{\begin{array}{ccc}0& \mathrm{when}& d_{NP}>{SD}_{WP}\\ {\displaystyle \frac{{SD}_{WP}-d_{NP}}{{SD}_{WP}-0.5·B}}& \mathrm{when}& {\displaystyle \frac{B}{2}}<d_{NP}\le {SD}_{WP}\\ 1& \mathrm{when}& d_{NP}\le {\displaystyle \frac{B}{2}}\end{array}\right.$$(A6)$$R_{NWS}=\left\{\begin{array}{ccc}0& \mathit{when}& d_{NS}>{SD}_{WS}\\ {\displaystyle \frac{{SD}_{WS}-d_{NS}}{{SD}_{WS}-0.5·B}}& \mathit{when}& {\displaystyle \frac{B}{2}}<d_{NS}\le {SD}_{WS}\\ 1& \mathit{when}& d_{NS}\le {\displaystyle \frac{B}{2}}\end{array}\right.$$ where:

RND=	numeric factor defining the vertical component of the navigational risk RN that concerns keeping an adequate required under-keel clearance;
RNH=	numeric factor defining the vertical component of the navigational risk RN that concerns keeping an adequate required over-head clearance (OHCR) or air draft clearance;
RNLF=	numeric factor defining the horizontal component of the navigational risk RN that concerns keeping an adequate required safe distance from the nearest danger ahead of the ship;
RNLA=	numeric factor defining the horizontal component of the navigational risk RN that concerns keeping an adequate required safe distance from the nearest danger astern of the ship;
RNWP=	numeric factor defining the horizontal component of the navigational risk RN that concerns keeping an adequate required safe distance from the nearest danger on the ship’s port side;
RNWS=	numeric factor defining the horizontal component of the navigational risk RN that concerns keeping an adequate required safe distance from the nearest danger on the ship’s starboard side;
SDD=	ship domain dept expressed in meters, [m];
SDH=	ship domain height expressed in meters, [m];
SDLF=	the length of the ship domain calculated horizontally in the forward direction ahead from the center of the ship’s layout; the starting point is in the vertical projection of the radar’s aerial (antenna) on the water plane, [m];
SDLA=	the length of the ship domain calculated in meters horizontally astern in the direction aft from the center of the ship’s layout, [m];
SDWP=	the width (beam) of the ship domain calculated in meters to the port side from the ship’s heading line (the center line of the ship = true course (TC) line, [m];
SDWS=	the width (beam) of the ship domain calculated in meters to the starboard side from the ship’s heading line (the ship’s TC line), [m];
h=	the actual water depth expressed in meters, [m];
Tmax=	the maximum draft of the vessel expressed in meters, [m];
Ho=	the distance between the water level and the height of the nearest objects hanging above the water (for the bridge, the vertical clearance is usually obtained above high-water level), [m];

(A7) $$H_o=CVC\pm \Delta Tide \left[m\right]$$

CVC=	the charted vertical clearance under the bridge or power cable referred to the high water (HW) or mean sea level (MSL), [m];
ΔTide=	the tide correction for vertical distance between the charted datum used for the vertical clearance referred usually to HW (HAT, MHWS) or MSL and the current sea water level: ΔTide = Charted Vertical Clearance datum referred to Chart Datum—Height of Tide referred to Chart Datum, [m];
HN=	the ship’s air draft, HN = Air Draft, the distance between the waterline to the highest point on the ship’s hull expressed in meters, [m];
dNF=	the distance to the dangerous zone (e.g., target domain guard zone, obstructions, safety depth contour or other navigational hazard) measured in the direction ahead along the ship’s course line (heading line) expressed in meters, [m];
dNA=	the distance to the dangerous zone (e.g., target domain guard zone, obstructions, safety depth contour or other navigational hazard) measured in the direction astern along the ship’s course line to the aft expressed in meters, [m];
dNP=	the distance to the dangerous zone (e.g., target domain guard zone, obstructions, safety depth contour or other navigational hazard) measured in meters on directions perpendicular to the ship’s course line on the port side, [m];
dNS=	the distance to the dangerous zone (e.g., target domain guard zone, obstructions, safety depth contour or other navigational hazard) measured in meters on directions perpendicular to the ship’s course line on the starboard side, [m];
L=	the ship’s length overall (LOA) in meters obtained from the ship’s particulars, expressed in meters, [m];
LRF=	the distance in meters between the vertical projection of radar aerial on the water plane and the ship’s bow obtained from the ship’s particulars, expressed in meters, [m];
CVC=	the charted vertical clearance under the bridge or power cable referred to the high water (HW) or mean sea level (MSL), [m];

Appendix B

The 3D domain by Rutkowski described with reference to the XYZ coordinate system by Rutkowski in 2000–2021 (Rutkowski 2000, 2006, 2017, 2020, 2021) represented by the following equations:(A8)$$\begin{gathered} {SD}_{LF}=p·\left(L_{RF}+\Delta \mathrm{L}\right)+30.87·t_r·SOG·\mathit{cos}\left(\mathit{COG}\text{-}\mathit{TC}\right)+r_L \\ ·\left[s_L·{AD}_{\mathit{max}}+30.87·t_m·Drift·\mathit{cos}\left(Set-\mathit{TC}\right)\right] \end{gathered}$$(A9)$${SD}_{LA}=p·\left({L-L}_{RF}+\Delta \mathrm{L}\right)+30.87·t_r·SOG·\mathit{cos}\left(\mathit{COG}\text{-}\mathit{TC}\right)$$(A10)$$\begin{gathered} {SD}_{\mathrm{WP}}=p·\left({\displaystyle \frac{B_C}{2}}+\Delta \mathrm{B}\right)+30.87·t_r·SOG·\mathit{sin}\left(\mathit{COG}-TC\right)+r_W \\ ·\left[s_W·{TR}_{neg}+30.87·t_m· \mathrm{Drift}·\sin (Set-TC)\right] \end{gathered}$$(A11)$$\begin{gathered} {SD}_{\mathrm{WS}}=p·\left({\displaystyle \frac{B_C}{2}}+\Delta \mathrm{B}\right)+30.87·t_r·SOG·\mathit{sin}\left(\mathit{COG}-TC\right)+r_W \\ ·\left[s_W·{TR}_{\mathit{max}}+30.87·t_m· \mathrm{Drift}·\sin (Set-TC)\right] \end{gathered}$$ where:

SOG=	the ship’s speed over ground values in knots obtained from a Doppler log or the fixed ship’s positioning system such as GNSS/GPS, (SOG = Vd) where $\overrightarrow{V_d}=[COG,SOG]$, the value expressed in knots, [kn];
COG=	the ship’s course over ground ($\overrightarrow{V_d}=[COG,SOG]$) expressed in degrees of angle, [°];
TC=	the ship’s true course expressed in degrees of angle, [°];
ΔB=	a factor showing an increase in the width (beam) of the ship domain. The increase amounts to error MOY of the total ellipse errors δy(Bi) of all factors Bi that affect SDW, estimated with probability level P = 95% (C = 2.44). In this paper, we will assume ΔB = 10 m;
ΔL=	a factor showing an increase in the length of the ship domain. The increase amounts to error MOX of the total ellipse errors δx(Bi) of all factors Bi that affect SDL, estimated with probability level P = 95% (C = 2.44). In this paper, we will assume ΔL = 20 m;
BC=	the seeming width of the ship’s trace calculated horizontally in meters [m], with wind leeway angle α [ °], current deviation (drift angle) β [°], and the ship’s yawing Δ[°]:

(A12) $$B_C=L·\sin \left(\alpha +\beta +\Delta \right)+B·\cos \left(\alpha +\beta +\Delta \right)$$

ADmax=	the ship’s advance maximum values measured in meters as the maximum movement of the ship forward along the ship’s course line, observed after changing the course ΔTC ≥ 090° or after the ship’s stopping maneuver is completed, [m];
TRmax=	the ship’s transfer maximum values measured in meters as the maximum movement of the ship to the port or starboard side (transverse horizontally to the ship’s initial course line), observed after changing the course ΔTC ≥ 180° or after the ship’s stopping maneuver is completed, [m];
TRneg=	the ship’s “negative” transfer (maximum value) measured in meters, observed after on the side opposite to the general direction during the ship’s turning and/or stopping maneuver, known also in maritime terminology as “Kick” distance on turning circle diagrams. TRneg is specified for merchant ships as a value from 1.0 to 1.5 ship breadth B (for turning circulation) or about 1.5 ship length L (for a Crash Stop (Full Ahead-Full Astern) emergency maneuver), [m];
tm=	the time needed to stop the ship or change its direction of movements by ΔTC ≥ 090° obtained in minutes from the Pilot Card, Wheel House Poster or Turning Circle Diagrams, [min];
tr=	the time needed for the appropriate reaction, that is the right assessment of the navigational situation and giving maneuver order. In practice, tr ≈ 0.5 min up to 3.0 min depending on the competence of the seafarer and his professional experience, [min];
Drift=	the total current speed values in knots (Drift = Vz) where $\overrightarrow{V_z}=[Set,Drift]$, and total current = water flow = sea current + tide stream, [kn];
Set=	the total current ($\overrightarrow{V_z}=[Set,Drift]$) direction in degrees, [°];
p=	the factor (numeral coefficient) depending on the harmfulness of the cargo carried on board the ship. This factor (1 ≤ p ≤ 2) increases the safety margin of navigational reserve in the case of abnormal situations, which can result either in a catastrophe (disaster) or the contamination of the environment. In this paper, we recommend using the following values for factor p: For ships in the ballast condition without dangerous cargo or harmless charge, neutral for people and the environment: p = 1. For ships carrying a load of high harm for people and the environment, e.g., flammable substances, oil, natural gas: p = 1.5. For ships with a very harmful load for people and the environment, e.g., radioactive substances, corrosive chemicals, explosive substances: p = 2.0;
rL=	the numeral coefficient (factor) correcting length (rL) of the ship domain (0 ≤ rL ≤ 2), depending on the situation (privilege) according to COLREG (Collision Regulations at Sea Convention 1972). In this paper, we recommend using the following values for factor rL: For the ship aground or at anchor: rL = 0. For privileged ships such as vessels with restricted ability to maneuver (except vessels engaged with mine clearance and vessels engaged in fishing): rL = 1.5. For sailing ships, ships restricted by draft and/or ships that are not under command: rL = 2;
rW=	the numeral coefficient (factor) correcting width (rW) of the ship domain (0 ≤ rW ≤ 2), depending on the situation (privilege) according to COLREG regulations. In this paper, we recommend the following values for factor rW: For the ship aground or at anchor: rW = 0. For ships restricted by the draught: rW = 1. For privileged ships such as vessels with restricted ability to maneuver (except vessels engaged with mine clearance and vessels engaged in fishing): rW = 1.5. For sailing ships and ships that are not under command: rW = 2;
sL=	the numeral coefficient (factor) correcting the ship’s advance (AD) parameter on the turning circle in the case of the appearance of unexpected meteorological conditions than previously observed during sea trials and recorded on Pilot Card and Wheel House Posters (with the currents excluded);
sW=	the numeral coefficient (factor) correcting the ship’s transfer (TR) parameter on the turning circle in the case of the appearance of unexpected meteorological conditions than previously observed during sea trials and recorded on Pilot Card and Wheel House Posters (with the currents excluded).

Appendix C

Table A1

The domain parameters for the three vessel types.

The Ships Domain SD Parameters as a Function of Ship Type and Water Depth h1 and h2	VLCC (Very Large Crude Carrier)						Fishing Boat (Fisher)						Z-Drive Prevention Response Tug
	SDD[m]	SDH[m]	SDLF[m]	SDLA[m]	SDWP[m]	SDWS[m]	SDD[m]	SDH[m]	SDLF[m]	SDLA[m]	SDWP[m]	SDWS[m]	SDD[m]	SDH[m]	SDLF[m]	SDLA[m]	SDWP[m]	SDWS[m]
$\mathrm{PIANC} \mathrm{Guidelines}: {SD}_{LF}=5 \mathrm{N}\mathrm{m} for VLCC, 1 \mathrm{N}\mathrm{m} for Fisher Ship\&500 \mathrm{m} for Z-drive Tug; {SD}_{WP}=6·LOA+500 \mathrm{m};$ ${SD}_{WS}=6·LOA+1056 \mathrm{m}$
N/A	N/A	N/A	9260 m	N/A	2068 m	2624 m	N/A	N/A	1852 m	N/A	894 m	1450 m	N/A	N/A	500 m	N/A	770 m	1326 m
2D ship domain according to T.G. Coldwell guidelines: SDLF = 6.1 L; SDLA = 3.9 L; SDWP = 1.75 L; SDWS = 3.25 L
N/A	N/A	N/A	1594 m	1019 m	457 m	849 m	N/A	N/A	400 m	256 m	115 m	213 m	N/A	N/A	275 m	176 m	79 m	146 m
3D ship domain according to G. Rutkowski for circulation with FSAH at a rudder deflection of 35° to the starboard in average sea conditions
h1 = 2∙T ± 0.3 m	19.9 m	65.0 m	1543 m	319 m	153 m	970 m	8.2 m	29.5 m	507 m	98 m	47 m	272 m	7.1 m	18.9 m	375 m	68 m	51 m	110 m
h2 = 1.4∙T± 0.3 m	20.2 m	64.8 m					8.3 m	29.5 m					7.2 m	18.8 m
3D ship domain according to G. Rutkowski for the FSAH-FAS maneuver (data from the Wheel House Poster) in average sea conditions
h1 = 2∙T ± 0.3 m	19.9 m	65.0 m	4321 m	243 m	472 m	603 m	8.2 m	29.5 m	961 m	98 m	130 m	162 m	7.1 m	18.9 m	363 m	68 m	57 m	77 m
h2 = 1.4∙T ± 0.3 m	20.2 m	64.8 m					8.3 m	29.5 m					7.2 m	18.8 m
3D ship domain according to G. Rutkowski for the HAH-FAS maneuver (data from the Wheel House Poster) in average sea conditions
h1 = 2∙T ± 0.3 m	19.7 m	65.1 m	2024 m	243 m	392 m	523 m	8.1 m	29.6 m	570 m	98 m	98 m	131 m	6.7 m	19.1 m	214 m	68 m	57 m	77 m
h2 = 1.4∙T ± 0.3 m	19.9 m	65.0 m					8.1 m	29.6 m					6.8 m	19.1 m
3D ship domain according to G. Rutkowski for circulation with FSAH at a rudder deflection of 35° to the starboard in deteriorated sea conditions
h1 = 2∙T ± 0.6 m	22.2 m	65.0 m	1515 m	353 m	221 m	1038 m	9.8 m	29.5 m	479 m	98 m	110 m	335 m	8.7 m	18.9 m	366 m	68 m	76 m	135 m
h2 = 1.4∙T ± 0.6 m	22.5 m	64.8 m					9.9 m	29.5 m					8.8 m	18.8 m
3D ship domain according to G. Rutkowski for the FSAH-FAS maneuver (data from the Wheel House Poster) in deteriorated sea conditions
h1 = 2∙T ± 0.6 m	22.2 m	65.0 m	4293 m	243 m	541 m	672 m	9.8 m	29.5 m	933 m	98 m	193 m	225 m	8.7 m	18.9 m	354 m	68 m	58 m	78 m
h2 = 1.4∙T ± 0.6 m	22.5 m	64.8 m					9.9 m	29.5 m					8.8 m	18.8 m

Table A2

R_ND numeric indicators as a function of the ship’s initial speed according to the risk assessment model based on the ship’s domain spatial model [23].

Ship (Tmax)	SDD for Speed FSAH or HAH	${\mathit{R}}_{\mathit{N}\mathit{D}}=\left\{\begin{array}{ccc}0& \mathbf{when} & \mathit{h}>{\mathit{S}\mathit{D}}_{\mathit{D}}\\ \frac{{\mathit{S}\mathit{D}}_{\mathit{D}}-\mathit{h}}{{\mathit{S}\mathit{D}}_{\mathit{D}}-{\mathit{T}}_{\mathit{m}\mathit{a}\mathit{x}}}& \mathbf{w}\mathbf{h}\mathbf{e}\mathbf{n}& {\mathit{T}}_{\mathit{m}\mathit{a}\mathit{x}}<\mathit{h}\le {\mathit{S}\mathit{D}}_{\mathit{D}}\\ 1& \mathbf{when}& \mathit{h}\le {\mathit{T}}_{\mathit{m}\mathit{a}\mathit{x}}\end{array}\right.$
		FEW-Area			CI Corridor			Territorial Waters
		hmin	hav	hmax	hmin	hav	hmax	hmin	hav	hmax
		36.5 m	43.02 m	54.5 m	14.5 m	27.26 m	39.0 m	7.00 m	24.35 m	33.5 m
VLCC15.00[m]	FSAH	0	0	0	1	0	0	1	0	0
	HAH	0	0	0	1	0	0	1	0	0
	FSAH *	0	0	0	1	0	0	1	0	0
Fisher5.40[m]	FSAH	0	0	0	0	0	0	0.45	0	0
	HAH	0	0	0	0	0	0	0.41	0	0
	FSAH *	0	0	0	0	0	0	0.64	0	0
Z-Tug4.9[m]	FSAH	0	0	0	0	0	0	0.09	0	0
	HAH	0	0	0	0	0	0	0	0	0
	FSAH *	0	0	0	0	0	0	0.50	0	0
Ship (HN)	SDH for speed FSAH or HAH	$R_{NH}=\left\{\begin{array}{ccc}0& \mathrm{when}& H_o>{SD}_H\\ {\displaystyle \frac{{SD}_H-H_o}{{SD}_H-H_N}}& \mathrm{when}& H_N<H_o\le {SD}_H\\ 1& \mathrm{when}& H_o\le H_N\end{array}\right.$
		H 0			H 0			H 0
		22 m	26 m	∞	∞	∞	∞	∞	∞	∞
VLCC62.3[m]	FSAH	1	1	0	0	0	0	0	0	0
	HAH	1	1	0	0	0	0	0	0	0
	FSAH *	1	1	0	0	0	0	0	0	0
Fisher27.0[m]	FSAH	1	1	0	0	0	0	0	0	0
	HAH	1	1	0	0	0	0	0	0	0
	FSAH *	1	1	0	0	0	0	0	0	0
Z-Tug16.1[m]	FSAH	0	0	0	0	0	0	0	0	0
	HAH	0	0	0	0	0	0	0	0	0
	FSAH *	0	0	0	0	0	0	0	0	0

Note: * denotes the indicators of navigational risk R_ND and R_NH for the parameters of the ship domain SD_D and SD_H estimated for deteriorated conditions observed in the autumn and winter seasons. No * denotes the indicators of navigational risk R_ND and R_NH estimated for average conditions. Red color denotes dangerous circumstances, green color denotes safe circumstances, and yellow color denotes doubtful circumstances, which require additional intervention from the user (undertaking actions to correct and/or mitigate a given risk indicator). OHC_R = 3 m.

Table A3

R_NLF, R_NLA, R_NWP, R_NWS based on the ship’s initial speed according to the risk assessment model based on the ship domain spatial model [23].

Ship Type and Length L [m]	Domain parameters	${\mathit{R}}_{\mathit{N}\mathit{L}\mathit{F}}=\left\{\begin{array}{ccc}0& \mathbf{when}& {\mathit{d}}_{\mathit{N}\mathit{F}}>{\mathit{S}\mathit{D}}_{\mathit{L}\mathit{F}}\\ \frac{{\mathit{S}\mathit{D}}_{\mathit{L}\mathit{F}}-{\mathit{d}}_{\mathit{N}\mathit{F}}}{{\mathit{S}\mathit{D}}_{\mathit{L}\mathit{F}}-{\mathit{L}}_{\mathit{R}\mathit{F}}}& \mathbf{when}& {\mathit{L}}_{\mathit{R}\mathit{F}}<{\mathit{d}}_{\mathit{N}\mathit{F}}\le {\mathit{S}\mathit{D}}_{\mathit{L}\mathit{F}}\\ 1& \mathbf{when}& {\mathit{d}}_{\mathit{N}\mathit{F}}\le {\mathit{L}}_{\mathit{R}\mathit{F}}\end{array}\right.;{\mathit{R}}_{\mathit{N}\mathit{L}\mathit{A}}=\left\{\begin{array}{ccc}0& \mathbf{when}& {\mathit{d}}_{\mathit{N}\mathit{A}}>{\mathit{S}\mathit{D}}_{\mathit{L}\mathit{A}}\\ \frac{{\mathit{S}\mathit{D}}_{\mathit{L}\mathit{A}}-{\mathit{d}}_{\mathit{N}\mathit{A}}}{{\mathit{S}\mathit{D}}_{\mathit{L}\mathit{A}}-\left(\mathit{L}-{\mathit{L}}_{\mathit{R}\mathit{F}}\right)}& \mathbf{when}& \left(\mathit{L}-{\mathit{L}}_{\mathit{R}\mathit{F}}\right)<{\mathit{d}}_{\mathit{N}\mathit{A}}\le {\mathit{S}\mathit{D}}_{\mathit{L}\mathit{A}}\\ 1& \mathbf{when}& {\mathit{d}}_{\mathit{N}\mathit{A}}\le \left(\mathit{L}-{\mathit{L}}_{\mathit{R}\mathit{F}}\right)\end{array}\right.$
		PIANC Guidelines							2D Domain Model by Coldwell							Domain Model by G. Rutkowski for Turning Circle Maneuver at FSAH with the Rudder 35° Starboard							Domain Model by G. Rutkowski for FSAH-FAS Maneuver							Domain Model by G. Rutkowski for HAH-FAS Maneuver
		dN 1	dN 2	dN 3	dN 4	dN 5	dN 6	dN 7	dN 1	dN 2	dN 3	dN 4	dN 5	dN 6	dN 7	dN 1	dN 2	dN 3	dN 4	dN 5	dN 6	dN 7	dN 1	dN 2	dN 3	dN 4	dN 5	dN 6	dN 7	dN 1	dN 2	dN 3	dN 4	dN 5	dN 6	dN 7
		150m	250m	300m	350m	400m	500m	1000m	150m	250m	300m	350m	400m	500m	1000m	150m	250m	300m	350m	400m	500m	1000M	150m	250m	300m	350m	400m	500m	1000m	150m	250m	300m	350m	400m	500 m	1000m
VLCC261.3	SDLF	1.00	1.00	0.99	0.98	0.98	0.97	0.91	1.00	0.97	0.93	0.90	0.86	0.79	0.43	1.00	0.97	0.93	0.89	0.86	0.78	0.41	1.00	0.99	0.98	0.97	0.95	0.93	0.81	1.00	0.98	0.95	0.92	0.90	0.84	0.56
	SDLA	N/A							0.90	0.80	0.74	0.69	0.64	0.54	0.02	0.63	0.26	0.07	0.00	0.00	0.00	0.00	0.49	0.00	0.00	0.00	0.00	0.00	0.00	0.49	0.00	0.00	0.00	0.00	0.00	0.00
Fisher65.6	SDLF	0.94	0.88	0.86	0.83	0.80	0.75	0.47	0.70	0.42	0.28	0.14	0.00	0.00	0.00	0.76	0.55	0.44	0.34	0.23	0.01	0.00	0.88	0.77	0.72	0.66	0.61	0.50	0.00	0.79	0.60	0.51	0.42	0.32	0.13	0.00
	SDLA	N/A							0.46	0.03	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
Z-Tug45	SDLF	0.72	0.51	0.41	0.31	0.21	0.00	0.00	0.48	0.10	0.00	0.00	0.00	0.00	0.00	0.62	0.35	0.21	0.07	0.00	0.00	0.00	0.61	0.32	0.18	0.04	0.00	0.00	0.00	0.32	0.00	0.00	0.00	0.00	0.00	0.00
	SDLA	N/A							0.18	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
Ship type and width B [m]	Domain parameters	$R_{NWP}=\left\{\begin{array}{ccc}0& \mathrm{when}& d_{NP}>{SD}_{WP}\\ {\displaystyle \frac{{SD}_{WP}-d_{NP}}{{SD}_{WP}-0,5·B}}& \mathrm{when}& {\displaystyle \frac{B}{2}}<d_{NP}\le {SD}_{WP}\\ 1& \mathrm{when}& d_{NP}\le {\displaystyle \frac{B}{2}}\end{array}\right.$ $;R_{NWS}=\left\{\begin{array}{ccc}0& \mathrm{when}& d_{NS}>{SD}_{WS}\\ {\displaystyle \frac{{SD}_{WS}-d_{NS}}{{SD}_{WS}-0,5·B}}& \mathrm{when}& {\displaystyle \frac{B}{2}}<d_{NS}\le {SD}_{WS}\\ 1& \mathrm{when}& d_{NS}\le {\displaystyle \frac{B}{2}}\end{array}\right.$
		dN 1	dN 2	dN 3	dN 4	dN 5	dN 6	dN 7	dN 1	dN 2	dN 3	dN 4	dN 5	dN 6	dN 7	dN 1	dN 2	dN 3	dN 4	dN 5	dN 6	dN 7	dN 1	dN 2	dN 3	dN 4	dN 5	dN 6	dN 7	dN 1	dN 2	dN 3	dN 4	dN 5	dN 6	dN 7
		150m	250m	300m	350m	400m	500m	1000m	150m	250m	300m	350m	400m	500m	1000m	150m	250m	300m	350m	400m	500m	1000M	150m	250m	300m	350m	400m	500m	1000m	150m	250m	300m	350m	400m	500 m	1000m
VLCC48.3	SDWP	0.94	0.89	0.87	0.84	0.82	0.77	0.52	0.71	0.48	0.36	0.25	0.13	0.00	0.00	0.02	0.00	0.00	0.00	0.00	0.00	0.00	0.72	0.50	0.38	0.27	0.16	0.00	0.00	0.66	0.39	0.25	0.11	0.00	0.00	0.00
	SDWS	0.95	0.91	0.89	0.87	0.86	0.82	0.62	0.85	0.73	0.67	0.60	0.54	0.42	0.00	0.87	0.76	0.71	0.66	0.60	0.50	0.00	0.78	0.61	0.52	0.44	0.36	0.18	0.00	0.75	0.55	0.45	0.35	0.25	0.05	0.00
Fisher10.3	SDWP	0.84	0.72	0.67	0.61	0.56	0.44	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
	SDWS	0.90	0.83	0.80	0.76	0.73	0.66	0.31	0.30	0.00	0.00	0.00	0.00	0.00	0.00	0.46	0.08	0.00	0.00	0.00	0.00	0.00	0.08	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
Z-Tug12.5	SDWP	0.81	0.68	0.62	0.55	0.48	0.35	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
	SDWS	0.89	0.82	0.78	0.74	0.70	0.63	0.25	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00

Red indicates a hazardous situation, green signifies a safe situation, and yellow denotes a questionable situation that necessitates further user intervention (such as corrective and/or mitigating actions) regarding the emerging risk indicator.

References

1. Council of Ministers. Regulation on the Adoption of the Spatial Development Plan for Internal Marine Waters, Territorial Sea and Exclusive Economic Zone of Poland, Scale 1:200,000. Journal of Laws of the Republic of Poland, Item 935. 2021; Available online: https://isap.sejm.gov.pl/isap.nsf/DocDetails.xsp?id=WDU20210000935 (accessed on 9 June 2025).

2. Tafon, R.; Saunders, F.; Zaucha, J.; Matczak, M.; Stalmokaitė, I.; Gilek, M.; Turski, J. Blue justice through and beyond equity and participation: A critical reading of capability-based recognitional justice in Poland’s marine spatial planning. J. Environ. Plann. Manag.; 2023; 67, pp. 2206-2228. [DOI: https://dx.doi.org/10.1080/09640568.2023.2183823]

3. Zaucha, J. Methodology of maritime spatial planning in Poland. J. Environ. Prot. Ecol.; 2018; 19, pp. 713-720.

4. Gilek, M.; Armoskaite, A.; Gee, K.; Saunders, F.; Tafon, R.; Zaucha, J. In search of social sustainability in marine spatial planning: A review of scientific literature published 2005–2020. Ocean Coast. Manag.; 2021; 208, 105618. [DOI: https://dx.doi.org/10.1016/j.ocecoaman.2021.105618]

5. Przedrzymirska, J.; Zaucha, J.; Calado, H.; Lukic, I.; Bocci, M.; Ramieri, E.; Varona, M.C.; Barbanti, A.; Depellegrin, D.; de Sousa Vergílio, M. . Multi-Use of the Sea as a Sustainable Development Instrument in Five EU Sea Basins. Sustainability; 2021; 13, 8159. [DOI: https://dx.doi.org/10.3390/su13158159]

6. Wróbel, K.; Gil, M.; Huang, Y.; Wawruch, R. The Vagueness of COLREG versus Collision Avoidance Techniques—A Discussion on the Current State and Future Challenges Concerning the Operation of Autonomous Ships. Sustainability; 2022; 14, 16516. [DOI: https://dx.doi.org/10.3390/su142416516]

7. Kulkarni, K.; Goerlandt, F.; Li, J.; Banda, O.V.; Kujala, P. Preventing shipping accidents: Past, present, and future of waterway risk management with Baltic Sea focus. Saf. Sci.; 2020; 129, 104798. [DOI: https://dx.doi.org/10.1016/j.ssci.2020.104798]

8. Rutkowski, G.; Kubacka, M. Analysis of navigational risk indicators as a function of the ship’s domain width for the selected offshore wind farm in the Baltic Sea. Sci. Rep.; 2023; 13, 9269. [DOI: https://dx.doi.org/10.1038/s41598-023-36114-3]

9. Serwis Rzeczypospolitej Polskiej. Available online: https://www.gov.pl (accessed on 25 May 2025).

10. Baltic Power Sp. z o.o. Baltic Power Offshore Wind Farm—Environmental Impact Assessment Report. 2023; Available online: https://www.balticpower.pl (accessed on 9 June 2025).

11. Polish Wind Energy Association (PSEW). Offshore Wind Energy Development in Poland—Economic Potential Report. 2021; Available online: https://psew.pl/wp-content/uploads/2021/06/PSEW_Report_Offshore_2021.pdf (accessed on 9 June 2025).

12. Ministry of Infrastructure, Poland. National Offshore Wind Energy Development Program Until 2040 (NOP-OZE). 2022; Available online: https://www.gov.pl/web/infrastruktura (accessed on 9 June 2025).

13. Urząd Morski w Gdyni. Available online: https://www.umgdy.gov.pl/en/ (accessed on 3 November 2023).

14. Polish Maritime Administration: Navigation Expertise for OWF Dated 2023-02-14 (Doc. No.: PMO-MAAC-PMP-CO-01).

15. Wielgosz, M.; Pietrzykowski, Z. The ship domain in navigational safety assessment. PLoS ONE; 2022; 17, e0265681.Available online: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0265681 (accessed on 9 June 2025). [DOI: https://dx.doi.org/10.1371/journal.pone.0265681]

16. Li, W.; Zhong, L.; Xu, Y.; Shi, G. Collision Risk Index Calculation Based on an Improved Ship Domain Model. J. Mar. Sci. Eng.; 2022; 10, 2016. [DOI: https://dx.doi.org/10.3390/jmse10122016]

17. Gao, H.; Xie, C.; Liu, K.; Chen, S.; Zhou, L.; Liu, Z.; Wang, R. Modeling of Safe Distance Between Ship Routes and Offshore Wind Farm Based on Tolerable Collision Probability. IEEE Access; 2022; 10, pp. 71777-71790. [DOI: https://dx.doi.org/10.1109/ACCESS.2022.3187117]

18. Lv, P.; Zhen, R.; Shao, Z. A Novel Method for Navigational Risk Assessment in Wind Farm Waters Based on the Fuzzy Inference System. Math. Probl. Eng.; 2021; 2021, 4588333. [DOI: https://dx.doi.org/10.1155/2021/4588333]

19. International Maritime Organization (IMO). International Convention for the Safety of Life at Sea, 1974, SOLAS; International Maritime Organization (IMO): London, UK, 1974; Consolidated text Retrieved 5 June 2022; 2015

20. Coldwell, T.G. Marine Traffic Behaviour in Restricted Waters. J. Navig.; 1983; 36, pp. 430-444. [DOI: https://dx.doi.org/10.1017/S0373463300039783]

21. Wang, N.; Meng, X.; Xu, Q.; Wang, Z. A Unified Analytical Framework for Ship Domains. J. Navig.; 2009; 62, pp. 643-655. [DOI: https://dx.doi.org/10.1017/S0373463309990178]

22. Zhou, J.; Wang, C.; Zhang, A. A COLREGs-Based Dynamic Navigation Safety Domain for Unmanned Surface Vehicles: A Case Study of Dolphin-I. J. Mar. Sci. Eng.; 2020; 8, 264. [DOI: https://dx.doi.org/10.3390/jmse8040264]

23. Rutkowski, G. Modelling the Ship’s Domain in the Process of Manoeuvring in Restricted Sea Areas. Doctoral Dissertation; Warsaw University of Technology, Faculty of Transport: Warszawa, Poland, 2000; (In Polish)

24. Rutkowski, G. Risk analysis when navigating in restricted sea areas. Ann. Navig.; 2006; 11, pp. 103-122.

25. Rutkowski, G. Analysis of a practical method for estimating the ship’s best possible speed when passing under bridges or other suspended obstacles. Ocean Eng.; 2021; 225, 108790. [DOI: https://dx.doi.org/10.1016/j.oceaneng.2021.108790]

26. United Kingdom Hydrographic Office (UKHO). Admiralty Sailing Directions: Baltic Pilot Vol. 2 (Np19); 18th ed. United Kingdom Hydrographic Office: Taunton, UK, 2022.

27. Nowakowski, Z.; Magierek, R.; Deorocki, M. Locja Bałtyku. Wybrzeże Polskie; 10th ed. Biuro Hydrografczne Marynarki Wojennej: Gdynia, Poland, 2016; (In Polish)

28. PIANC—The World Association for Waterborne Transport Infrastructure. Interaction Between Offshore Wind Farms and Maritime Navigation, MarCom Working Group WG 161; The World Association for Waterborne Transport Infrastructure: Brussels, Belgium, 2018.

29.Resolution MSC.137(76) International Maritime Organization (IMO). (Adopted on 4 December 2002). Standards for Ship Manoeuvrability; International Maritime Organization: London, UK, 2002.

30. International Maritime Organization (IMO). MSC/Circ.1053. Explanatory Notes to the Standards for Ship Manoeuvrability. 2002; Available online: https://www.register-iri.com/wp-content/uploads/MSC.1-Circ.1053.pdf (accessed on 5 June 2022).

31. Rutkowski, G. Determining Ship’s Safe Speed and Best Possible Speed for Sea Voyage Legs. TransNav; 2017; 10, pp. 425-430. [DOI: https://dx.doi.org/10.12716/1001.10.03.07]

32. Rutkowski, G. Determining the Best Possible Speed of the Ship in Shallow Waters Estimated Based on the Adopted Model for Calculation of the Ship’s Domain Depth. Pol. Marit. Res.; 2020; 27, pp. 140-148. [DOI: https://dx.doi.org/10.2478/pomr-2020-0055]

33. Kramarska, R. Geological Map of the Baltic Sea bottom, 1:200,000, Sheet Ławica Słupska N.; Państwowy Instytut Geologiczny: Warsaw, Poland, 1991.

34. Power-Technology. F.E.W. Baltic II Offshore Wind Farm (Poland). Available online: https://www.power-technology.com/projects/f-e-w-baltic-ii-offshore-wind-farm-poland/ (accessed on 9 June 2025).

35. Zhen, R.; Lv, P.; Shi, Z.; Chen, G. A novel fuzzy multi-factor navigational risk assessment method for ship route optimization in costal offshore wind farm waters. Ocean Coast. Manag.; 2023; 232, 106428. [DOI: https://dx.doi.org/10.1016/j.ocecoaman.2022.106428]

36. Nie, Y.Y.; Liu, K.Z.; Yang, X.; Chen, S.Z.; Ma, J. The safe distance between the offshore wind farm and the airway. Navig. China; 2019; 42, pp. 12-17.

37. Wróbel, K. Searching for the origins of the myth: 80% human error impact on maritime safety. Reliab. Eng. Syst. Saf.; 2021; 216, 107942. [DOI: https://dx.doi.org/10.1016/j.ress.2021.107942]