Analysis of navigational risk indicators as a function of the ship's domain width for the selected offshore wind farm in the Baltic Sea

This study concerns the analysis of navigational risk indicators as a function of the ship's domain width estimated for nine selected representative ships sailing under various hydrometeorological conditions (average and deteriorated ones) observed within the Offshore Wind Farm to be constructed within the Polish offshore zone on the Baltic Sea. For this purpose, the authors compare three types of domain parameters according to the guidelines by the PIANC, Coldwell and Rutkowski (3D). The study enabled selection of a group of ships which can be considered safe and can optionally be allowed to navigate and/or fish in the immediate vicinity and within the offshore wind farm. The analyses required the use of hydrometeorological data, mathematical models and operating data obtained with the use of maritime navigation and manoeuvring simulators.

1. If the distance between the turbine boundary and the shipping route is less than < 0.5 nm (< 926 m), it is deemed intolerable; 2. If the distance is between 0.5 and 3.5 nm (926-6482 m), it is deemed tolerable provided that the risk being reduced to as low as reasonably practicable (ALARP)-additional risk assessment and proposed mitigation measures required; 3. If the distance is more than > 3.5 nm (> 6482 m), it is deemed broadly acceptable.
Currently, the Polish maritime administration bodies, acting under Art. 24 in connection with Art. 47 of the Act of 21 March 1991 on maritime areas of the Republic of Poland, are considering the introduction of safety zones around structures and devices constituting elements of OWFs situated within the maritime areas of the Republic of Poland. At the moment of writing this paper, the above-mentioned legal regulations have not been developed and/or published on the official websites of the Polish maritime administration bodies.
General guidelines regarding the risks of navigation and safety zones in the vicinity of OWFs were presented by the World Association for Waterborne Transport Infrastructure PIANC 18 , according to which the level of navigational risk from the OWF impacts depends on the distance between a Traffic Separation System (TSS) shipping route and the first row of wind turbines. According to the PIANC guidelines, the level of unacceptable risk will be estimated for ships to which the SOLAS Convention 19 applies, and which are manoeuvred at a distance of less than 0.25 NM (463 m) and/or 500 m from the designated high-density shipping routes.
According to the PIANC, ships navigating within the TSS area situated at a distance of more than 5 NM (≈ 9260 m) from the OWF can be considered to be safe in restricted sea areas. As per the PIANC guidelines 18 , the minimum distance that guarantees the safety of navigation refers to the COLREG regulations 20 and is determined based on the resolutions of IMO [21][22][23]MSC.137 (76) 22 and MSC/Circ.1053 21 , which address ship manoeuvrability and, in particular, the parameters of the turning circle manoeuvre and the emergency stopping (decelerating) distance. According to the PIANC guidelines, the minimum safe distance from a navigational obstacle that defines the ship's domain should be determined using the following formulae: where d NP = the minimum distance from a navigational obstacle situated on the ship's port side identified with the ship's domain on the port side (SD WP ); expressed in meters, [m]; d NS = The minimum distance from a navigational obstacle situated on the ship's starboard side identified with the ship's domain on the starboard side (SD WP ); expressed in meters, [m]; LOA = ship's length overall expressed in meters, [m].
The term 'ship's domain' 24 has been widely analyzed in the existing literature concerning the safety of shipping [25][26][27][28] and assessment of the navigational collision risk 26,29,30 , and is defined as the area around a vessel which is indispensable for maintaining the safety of navigation. Therefore, the navigational risk increases when any navigational obstruction appears within the ship's domain. Most of the proposed ship's domain models are two-dimensional (2D) 28,31 rather than spatial (3D) 27,32 . This paper compares three domain models according to the guidelines by the PIANC, Coldwell, and Rutkowski (3D). The ship's domain by Rutkowski (3D), which was developed based on the author's own research, is presented in Fig. 1. Figure 2 illustrates the simplified and composite approaches for the 3D model of the ship's domain in the XY horizontal plane with its length forward (SD LF ), length aft (SD LA ), width to port (SD WP ), and width to starboard (SD WS ). However, due to the limited nature of our work, this paper focuses only on the analysis of two of the six parameters of the 3D model of the ship's domain by Rutkowski 12 , and, in particular, the ship's domain width in the horizontal plane on the port side (SD WP ) and the starboard side (SD WS ) of the ship.

Research objectives
This study focused on the following research objectives:

Materials and methods
The navigational risk with respect to keeping the required ship's domain width. According to the definition of navigational risk (R N ) 12 , a risk coming from factors A i (objects) and equal to 0 denotes full safety of navigation with respect to these factors (objects). Analogously, the higher the risk (parameter R N approximating 1), the lower the level of the safety of navigation (S N ) → (R N + S N = 1; S N = 1 − R N ). Therefore, the navigational risk indicator reaching R N = 1 denotes the occurrence of such conditions and/or circumstances which are going to prevent safe navigation and may entail a 100% probability of a collision. R N will be analysed in this paper based on the definition of the ship's domain (SD) 12 and the definition of R N 12,13 , the values of which can be determined with reference to the vertical plane OX and the horizontal plane OY 33 . The analysis will further focus, in particular, on the components of R N defined with reference to the OY plane and in relation to objects situated on the ship's port side (R NWP ), and the ship's starboard side (R NWS ), which can be presented with the use of the following formulae: where R NWP is a dimensionless value defining a component of R N with respect to keeping the required safe width of the ship's passage route (distance d NP from the nearest navigational danger situated on the OY axis) on the ship's port side related to the possibility of the ship colliding with a navigational obstacle situated on the ship's port side; SD WP (Ship's Domain Width Port Side) is the ship's domain width as measured on the ship's port side. It is expressed in meters measured along the OY axis perpendicular to the ship's heading (true course line TC) on the ship's port side; d NP is the distance from the nearest hazard (navigational danger) measured in meters perpendicular to the ship's heading (true course line TC) on the ship's port side; B is the ship's width in meters as per the ship's particulars, the pilot card or the AIS.
where R NWS is a dimensionless value defining a component of R N with respect to keeping the required safe width (distance d NS from the nearest navigational hazard situated on the OY axis) on the ship's starboard side (index WS = Width Starboard Side). This parameter describes the navigational risk (estimated as ranging from 0 to 1) related to the possibility of the ship colliding with a navigational obstacle on the ship's starboard side (Adequate Required Safe Distance from the Nearest Danger on Ship's Starboard Side); SD WS (Ship's Domain Width Starboard Side) is the ship's domain width as measured on the ship's starboard side. It is expressed in meters measured   12 , every ship will be safe (in navigational meaning) as long as she is the exclusive object capable of generating hazards within her domain.
With reference to the horizontal plane OY distinction between R NWP and R NWS of the navigational risk R N , which can be referred to as the horizontal components of the navigational risk related to keeping a safe distance from the nearest danger adequately on the port and starboard sides of the ship, or, in short, the risk of keeping a safe distance from the port and starboard sides, can be depicted by means of formulas (3) and (4). According to the patterns presented above, (R NWP formula 3) with the (d NP > SD WP ) condition and (R NWS formula 4) with the (d NS > SD WS ) condition guarantee safe navigation of the ship in relation to the objects detected on the ship's starboard side and port side respectively. When analysing formulas 3 and 4, one can also notice that the value of navigational risk R NW will be limited to a range between zero and one (R NW ϵ 7 ) only if the distance from the nearest danger on the port side (d NP ) or starboard side (d NS ) is either less or equal to the ship's domain width calculated respectively for the ship's port side (SD WP ) and/or starboard side (SD WS ). In all probability, assumption d N ≤ B 2 indicates a navigational accident or collision with some objects (obstructions) detected respectively on the ship's port side (formula 3 : d NP ≤ B 2 ) and/or starboard side (formula 4: d NS ≤ B 2 ) and/or an unquestionable (100%) risk of collision with those objects.
A graphical display of R N as a function of the ship's domain parameters (SD WP , SD WS ) and distance from the nearest navigational hazard (d N ) is presented in Fig. 3. The analysed R N factors in the horizontal plane OY in relation to the objects situated on the ship's port and starboard sides obtained for different ship types navigating within the OWF sea area are presented below.

Representative ship types.
For the purposes of the paper, our analysis covered nine representative ship types (Table 1)       ) direction in degrees, p = a factor (numeric 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 case of an abnormal situation, which can result either in a catastrophe (disaster) or contamination of the environment. In this paper, we recommend using the following values for factor p: for ships in ballast condition without dangerous cargo or harmless charge, neutral for people and the environment: p = 1; for ships carrying a load of high harm to 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,r W = a numeric coefficient (factor) correcting the width (r W ) of the ship's domain (0 ≤ r W ≤ 2), depending on her situation (privilege) according to the COLREG Rules. In this paper, we recommend the following values for factor r W : for a ship aground or at anchor: r W = 0; for ships restricted by their draught: r W = 1; for privileged ships such as vessels with restricted ability to manoeuvre (except the vessels engaged in mine clearance and vessels engaged in fishing: r W = 1.5; for sailing ships and ships that are not under command: r W = 2, s W = a numeric coefficient (factor) correcting the ship's transfer (TR) parameter on turning circle in case of unexpected meteorological conditions other than those previously observed during sea trials and recorded in the Pilot Card and Wheel House Posters (currently excluded).
The parameters were estimated for the turning cycle manoeuvre with the ship at full sea speed ahead (FSAH) with the rudder angle of 35° starboard and emergency stop manoeuvres by reversing the engine to full astern (FSAH-FAS and HAH-FAS). The results are presented in the further part of this paper.

Results and discussion
It has been assumed in this paper that the actual distances between individual offshore installations within the OWF area range from d min1 = 700 m (in the case of substations) and from d min2 = 1000 m to d min3 = 2000 m in the case of measuring distances between individual offshore wind turbines, however our analysis has been extended to address seven different distances: 300 m, 500 m, 600 m, 700 m, 800 m, 1000 m and 2000 m. When analysing emergencies, when ships are allowed to enter the OWF area, it was assumed that they sail at an optimal (maximum) distance from any navigational hazards detected nearby and situated respectively ahead of their bows and on their port and starboard sides. Here, an assumption can be made that, in the vicinity of substations, the minimum distance from the nearest hazard will be a value defined as half of the distance between individual offshore installations, i.e. d N1 = 0.5•d min1 = 350 m, and for the location of wind turbines within the OWF area, this will be the distance ranging from d N2 = 0.5•d min2 = 500 m to d N3 = 0.5•d min3 = 1000 m. Table 3 presents the domain parameters for the nine ship types (Table 1) compiled as per the PIANC guidelines 18 , 2D domain by Coldwell and the method by Rutkowski 13 using the manoeuvring characteristics obtained by the manoeuvring simulator of the Gdynia Maritime University calculated for average and deteriorated hydrometeorological conditions. www.nature.com/scientificreports/ Table 4 presents sample navigational risk indicators R NWP (SD WP ) and R NWS (SD WS ) with respect to keeping the required distance from navigational hazards detected on the ship's port side and starboard side respectively. These indicators were estimated for nine representative ship types (Table 1) as a function of the width of their domains calculated for average hydrometeorological conditions ( Table 2). The navigational risk numeric factors R NWP and R NWS were estimated using the domain parameters SD WP and SD WS compiled in the tables (Table 3). In Table 4, the numeric indicators of R N ranging from 0 to 33% ( 0 ≤ R N ≤ 0.33 ) are assumed to be acceptable and are marked in shades of green colour. They denote a navigational situation for which the values of the estimated R N factors are considered to be safe, making it possible to execute a voyage. The R N numeric indicators ranging from 66 to 100% ( 0.66 ≤ R N ≤ 1 ) are considered to be dangerous or highly risky, and are marked in shades of
According to the analysis of the indicators R NWP (SD WP ) and R NWS (SD WS ) (Table 4), depending on the method applied (in this case, the PIANC guidelines, the 2D domain by Coldwell and the 3D domain by Rutkowski estimated for the turning circle manoeuvres at FSAH with the rudder angle of 35º starboard, and emergency stop manoeuvres by reversing the engine to full astern FSAH-FAS and HAH-FAS), the R N indicators sometimes assume radically different values. In addition, the PIANC method seems to be the most restrictive one (red fields in Table 4). However, according to the PIANC method, the values of the estimated R NW (SD W ) depend on the overall dimensions of the analysed representative vessels to a small extent only, and, moreover, this method fails to take account of their actual manoeuvring parameters. Hence, it is doubtful whether this method should be used for practical estimation of the navigational risk factors for small surface vessels type D, E, F and I, for which, according to the PIANC method, for the distance from the nearest danger d N1 = 350m on the ship's port and starboard sides, the estimated navigational risk indicators range from 39% for ship E to 61% for ship D, 46% for ship F and 55% for ship I, taking into account the risk factors estimated for the port side: R NWP (SD WP ) ∈ (0.39; 0.46; 0.55; 0.61), and from 69% for ship E to 76% for ship D, 71% for ship F and 74% for ship I, taking into account the risk factors estimated for the starboard side: R NWS (SD WS ) ∈ (0.69; 0.71; 0.74; 0.76).
As regards the 2D domain method by Coldwell and the 3D domain method by Rutkowski, navigating ship types D, E, F and I proves to be completely safe, taking into account the presence of navigational hazards situated on the ship's port side and starboard side respectively. Moreover, the parameters of the 2D domain by Coldwell are very similar to those of the 3D domain by Rutkowski as estimated for the emergency turning circle manoeuvre performed at full speed ahead FSAH with the rudder angle of 35º starboard. Additionally, the 2D domain by Coldwell is an empirical domain estimated in the XY horizontal plane only and it does not take account of the navigational risk generated by above-water and underwater navigational obstacles. In addition, the 3D domain by Rutkowski allows for choosing the right anti-collision manoeuvre, which is performed by way of changing the course (turning circle manoeuvre) and/or changing the ship's speed ahead (FSAH or HAH). For example, an analysis of R NWP (SD WP ) and R NWS (SD WS ) conducted for ship A (a VLCC), assuming that the distance from the nearest danger on the ship's port and starboard sides is d N2 = 500m , proves that performing a turning circle manoeuvre to starboard at full speed ahead FSAH will generate a navigational risk on the ship's starboard side of 42% = R NWS (SD WS ) = 0.42. In case of performing an emergency stop manoeuvre by reversing the engine to full astern FSAH-FAS, the navigational risk factor generated on the ship's starboard side will be reduced to 18% = R NWS (SD WS ) = 0.18. On the other hand, performing the same manoeuvre at the ship's speed reduced to half ahead (HAH-FAS) will result in generating the navigational risk factor of only 5% = R NWS (SD WS ) = 0.05 (see Table 4).

Conclusions
This paper presents the numeric indicators of navigational risk R N as estimated for nine representative ship types with reference to navigational obstacles situated on the ship's port side and starboard side respectively. However, a comprehensive analysis of the navigational risk in the navigable sea area analysed requires that the distribution of all navigational hazards situated within the three XYZ axes as a function of relevant parameters of the ship's 3D domain model is studied.
The paper compares three types of domain parameters according to the guidelines by the PIANC, Coldwell and Rutkowski (3D). The results obtained for R N indicators at times assume radically different values, whereby the domain model by Rutkowski seems to be the most accurate one. To sum up, according to the 2D domain method by Coldwell and the 3D domain method by Rutkowski, navigating the following ship types: fisher ship (D), high speed water jet rescue ship (E), fishing boat (F) and z-drive prevention response tug (I), proves to be completely safe. The analyses that were conducted required the use of appropriate hydrometeorological data for the area under consideration.
The presented method can be perceived as a universal one, as it depends only on the interrelation between the ship position and the position of the detected navigational obstacle, which obstacle may be land, another ship or object (e.g. an offshore installation), or a hydrometeorological factor generating a risk to the safety of navigation within a given navigable sea area (an open and/or restricted one). www.nature.com/scientificreports/ Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/.