2. About the term close-quarters situation

According to Tsai et al. (Reference Tsai, Chang and Chen2017), avoiding collision at sea is a process in which the navigator takes proper and timely action in accordance with the International Regulations for Preventing Collisions at Sea and after which ships under the risk of collision pass at a safe distance. However, when avoiding collision at sea, it is necessary to determine some limit values within which a collision avoidance manoeuvre must be taken. Of course, these values may not be the same for all ships, or even for the same ship under different conditions. Action to avoid a collision at sea should always be taken in a timely manner so that ships can pass at a safe distance and that in the event of some extraordinary circumstances, there is still sufficient time and space to avoid a collision. However, sometimes due to heavy maritime traffic or non-compliance with the Rules, ships pass at dangerous distances, thereby increasing the risk of collision. For ships passing at distances that cannot be considered safe, the term close-quarters situation is most commonly used. In the Rules, the term close-quarters situation is specified in Rule 8 (Action to avoid a collision) and in Rule 19 (Conduct of vessels in restricted visibility). Although very commonly used, when it comes to avoiding collisions at sea, the term is still not precisely defined and many authors have different interpretations and explanations. At conferences dedicated to the International Regulations for Preventing Collisions at Sea, efforts were made to define the term more precisely, but without success. Cockcroft and Lameijer (Reference Cockcroft and Lameijer2011) state that action to avoid a collision when two ships are in sight of each other and there is risk of collision can be divided into four stages. In order of sequence, these are the following stages: free manoeuvre, action required by the give-way vessel, action permitted by the stand-on vessel and action required (Figure 1).

Figure 1. Four stages of collision risk

Cockcroft and Lameijer (Reference Cockcroft and Lameijer2011) defined a close-quarters situation as the position when a collision can no longer be avoided solely by an action by the give-way vessel which is directed to keep out of the way of the other vessel, but also the stand-on vessel is required to take such action as will best aid to avoid collision. They state that a close-quarters situation is not defined by a value in nautical miles, although at the 1972 conference there were some efforts to define that value. Furthermore, they provide statements and explanations of court judgments and the interpretation of expert witnesses referring to close-quarters situations, e.g. the Grepa-Verena litigation, where the phrase ‘close-quarters situation’ is not clearly defined and requires further discussion. Similarly to Cockcroft and Lameijer, He et al. (Reference He, Jin, Huang, Xiong, Chen and Mou2017) presented a situation-identifying model and defined four distinct stages in the entire encounter process for autonomous collision avoidance, where appropriate collision avoiding actions must be taken according to different situations and stages. He et al. developed quantitative computing models for the first time-in-point of a close-quarters situation (FTCS) and the first time-in-point of immediate danger (FTID) for ship encounters in open sea under good weather. They includes ‘close-quarter’ and ‘immediate danger’ stages in the third stage of the defined scenario. Craig (Reference Craig2005) presented several interpretations and definitions of a close-quarters situation that have emerged from judgments of U.S. and British courts. He emphasises that the term ‘close-quarters situation’ is not defined by the Rules and points out that a delegates of the committee that adopted the Rules in 1972 concluded, after several discussions, that it was not possible to define the distance at which a close-quarters situation would be considered. With a few exceptions, the courts were generally reluctant in their judgments to provide anything other than general guidance regarding the determination of a close-quarters situation. One of the definitions of a close-quarters situation well known in case law is that the phrase refers to any situation where two ships will not pass at safe distance based on their courses and speeds. However, the above definition relies on another undefined phrase in the Rules, which is safe distance, and as such is not very helpful. Cockcroft and Lameijer (Reference Cockcroft and Lameijer2011) in their book discuss the term ‘close-quarters situation’, where it first appears in the Rules, at Rule 8 (c). They state that the distance at which a close-quarters situation first applies will depend upon a number of factors, including visibility. They further state that in the open sea, distances of the order of 2 to 3 nm are usually considered as the outer limits in restricted visibility but smaller distances, probably of the order of 1 nm, would probably be accepted for vessels in sight of one another. Considering a close-quarters situation in which collision avoidance is no longer controlled by a single ship, Cahill (Reference Cahill1983) proposed the definition of a close-quarters situation when ships are in sight of one another: ‘We offer here a provisional definition of “close-quarters” as that area around a ship where a collision with an approaching vessel could not be avoided by the action of the approached vessel alone if the approaching vessel made a major, sudden and unexpected course change.’ Lloyd's Da Ye ship collision report (1993) states that not every close-quarters situation necessarily means collision risk and emphasises that there is no boundary in distinguishing between the notions of a close-quarters situation and collision risk. The English Admiralty Court made it very clear in the case of the ship Maloja II that timely action is necessary to avoid a close-quarters situation: to ensure that, whenever possible, ships do not come into a close-quarters situation where there is a risk of collision and in which a decision must be made in a very short time, without enough time to make the right decision. Mankabady (Reference Mankabady1987) also confirmed that it is very difficult to define a close-quarters situation. He further explained that its value depends on several factors and defines a close-quarters situation as a collision that can no longer be avoided by manoeuvring a single ship with significant alteration of course. In 1970, the British Merchant Navy Association published an article in its journal concerning a close-quarters situation, which referred to a court judgment stating: ‘ … in the case of the size of the ships we have here, the close-quarters situation means a fairly long distance and I would dare to think that distance is measurable in miles rather than in yards’. In 1981, the German government sent letter 26/4/2 to the International Maritime Organization (IMO) stating that the ‘close-quarters situation can only be avoided if the navigator is aware of the shape and size of the waters in which he navigates and in which intends to carry out an avoidance action …’. Sjekavica and Kacic (Reference Sjekavica and Kacic1982) state that a close-quarters situation occurs when ships come so close to each other, to some boundary proximity, that they are left with very little time and manoeuvring space to undertake a successful action to avoid a collision. These authors do not present any numerical values, they merely emphasise that the distance between ships in a close-quarters situation is not easy to define because its meaning is conditioned by the circumstances in which it is applied. They consider that the inter-position of ships is defined by relative speed, relative direction and distance between them. They also state that, according to maritime practice, the term indicates an imminent risk of collision due to the position and proximity of ships. A very interesting study of a close-quarters situation was made by the Faculty of Law and Political Science in Nantes (Cornillou, Reference Cornillou2014), when, at the request of the French government, research was undertaken to increase the safety of navigation in Ushant and to facilitate monitoring and safety of navigation controlled by the VTS Centre Ushant. In defining a close-quarters situation, the report associates the phrase with near miss, as a series of events or occasions between ships that may cause a collision. In the period from January 2008 to September 2013 (68 months), 120 cases of close-quarters situation were reported by ships and an analysis of a close-quarters situation was made on the basis of the data obtained. Reference data were taken for cases where the closest point of approach (CPA) was up to 0⋅5 nm, while the time to the closest point of approach (TCPA) was up to 10 min. Bakdi et al. (Reference Bakdi, Glad, Vanem and Engelhardtsen2019) introduced a risk identification methodology to define the minimum distance to avoid accidents in a navigation scenario, using the concept of blocking areas (four areas) to define a vessel safety domain. Similar to some other authors, they stated that in a close-quarters situation, actions taken by only one vessel will not be enough to avoid the risk of collision.

3. Preparation for research

In accordance with the definition previously proposed by the authors of this paper of the term close-quarters situation as the smallest distance between ships when a collision is still avoidable if only one ship takes appropriate action to avoid it, the following sections define scenarios that are subsequently simulated on the navigational simulator to obtain the shortest distance between ships when the stand-on vessel can take an action to avoid a collision because the other ship obliged to do so for some reason does not. Similar research was conducted by Krata and Montewka (Reference Krata and Montewka2015) who attempted to define a critical distance between two encountering ships. They defined critical distance as the shortest distance between two ships on collision courses at which effective evasive last minute actions can be successfully taken by one vessel alone (stand-on vessel), in the situation where the give-way vessel does not take an action. The dimension of critical distance/area they compared with dimensions of various ship domains found in the literature. Work of Krata and Montewka inspired research conducted by Szlapczynski et al. (Reference Szlapczynski, Krata and Szlapczynska2018) who investigated situations when one ship is the stand-on vessel and the give-way vessel does not react in due time. In such cases, according to the Rules, Szlapczynski et al. investigated when the stand-on vessel will start a manoeuvre, depending on the desired separation, which they represent by a decentralised elliptic domain. Baldauf et al. (Reference Baldauf, Mehdi, Fischer and Gluch2017) compared the collision avoidance process between two ships and the collision avoidance process between two aircraft. They clearly explained that the CPA and TCPA alarms are not sufficient because they warn of a possible collision, while nothing else warns the officer if they ignore the CPA and TCPA alarms, which is the case in aviation. Therefore, Baldauf et al. proposed one more collision alarm on a ship, which they call the ‘last line of defence’ (LLoD) as it is used in airborne collision avoidance systems (ACAS) and which may be applied as the ‘ultimate action alarm’. The LLoD alarm corresponds to the moment when the amount of remaining options for manoeuvres to successfully avoid a collision is getting close to a critical minimum. The LLoD alarm suggested by Baldauf et al. (2017) has the same meaning as the goal of this study, which is to show the smallest distance between two ships when a collision can still be avoided by only one ship taking the avoiding action. In the simulations conducted in that study, the time for initiating a manoeuvre to realise the passing distance was determined to be 3 cables from ship's hull to ship's hull in one scenario and 2⋅5 cables in another. Simulations were performed assuming a rudder angle of 30°. The authors did not provide an explanation of how they selected the aforementioned passing distance, but emphasise that, ‘The minimum passing distance needs to be defined and shall always be greater than the hydrodynamic safe passing distance.’ The purpose of the simulations in our research was to show at what distance between the two ships on collision courses, and the time to the collision, the avoidance action should be taken so that the ships would pass at a minimum distance.

Ships passing each other while taking action to avoid collision at sea can result in three cases. The first is that the ships pass at a safe distance; the second is when ships pass at a distance less than safe distance, a distance that is very small, but nevertheless no contact between the ships occurs; and the third case is when there is contact between the ships, which means that there is a collision. Without debating about the value of safe distance, a close-quarters situation can certainly be considered to be a distance between passing ships that is less than safe distance, but again such that no collision occurs. Thus, during the simulation, actions taken to avoid a collision were taken at a distance that would allow passing the other vessel at a distance of 100 m. This distance is certainly not the distance one would like to experience when navigating a ship as a result of collision avoidance action. Such a passing distance is common when passing in narrow channels, two-way waterways, entrances to ports, anchorages, etc., but this is not the topic of the research. However, as the aim of this study was to obtain the shortest distance at which one of the ships could take (start) the action to avoid a collision, the passing distance between ships was intentionally fixed at 100 m. Certainly, determining the minimum passing distance between ships requires further research, which is also emphasised in Baldauf et al. (2017). For the purposes of this research, the passing distance between ships of 100 m was determined as the minimum passing distance value at which hydrodynamic interaction between two overtaking vessels will not lead to contact between the ship's hulls. Although a certain force of interaction may occur, it will not cause the hulls of ships to touch. As it is known that the force of interaction between ships has the greatest effect on overtaking ships, it can be concluded that the minimum passing distance defined for overtaking is considered acceptable for head-on and crossing situations as well. The resulting minimum passing distance between ships actually represents CPA at the moment of passing. Theoretically, if the conditions as set out in the simulations (no shallow water, no wind, waves, or sea currents) prevail, then CPA at the moment of passing would be approximately 100 m in reality. In the event of external influences that change the ship's manoeuvrability, CPA at the moment of passing would normally no longer be 100 m (could be more or less). To define CPA at the moment of passing, which could be considered safe in such circumstances, the impact of the above external factors and the errors of the devices determining the distance from other ships (primarily the radar) should be considered in such cases. Due to the scope of possible combinations, such scenarios are not predicted in this research, but will be the subject of future research. A CPA of 100 m at the moment of passing can also be considered as the worst-case scenario. Similarly, Szlapczynski et al. (Reference Szlapczynski, Krata and Szlapczynska2018), referring to the works of Krata and Montewka (Reference Krata and Montewka2015) and Krata et al. (Reference Krata, Montewka and Hinz2016), state that the authors in their works assumed ‘a near-zero ship separation’ which can be understood as the worst-case scenario listed in this paper. The simulations were performed on the latest generation TRANSAS NTRPO 5000 navigational simulator installed at the Faculty of Maritime Studies in Rijeka. Today, the use of sophisticated simulators/computers has become quite common. Many researchers use simulators that offer advanced models for the prediction of ship manoeuvres (Baldauf et al., Reference Baldauf, Mehdi, Deeb, UweSchröder-Hinrichs, Benedict, Krüger, Fischer and Gluch2015).

3.1 Ship models used in simulations

Due to the large number of different types and characteristics of ships, in order to reduce the number of possible combinations (scenarios), a certain rationalisation of the number of models was made, while keeping them representative of the type of ship. In determining the scenario, it was necessary to vary the type, size, loading condition and speed of the ship. The rationalisation was primarily made by the choice of ships according to the ship's block coefficient Cb. According to the selected criterion, the ships were divided into two categories where ships with block coefficient lower than 0⋅7 (Cb < 0⋅7) were considered as fine-form ships while ships with block coefficient larger than 0⋅7 (Cb > 0⋅7) were considered to be full-form ships. Due to the amount of the results obtained, only results obtained for fine-form ships will be shown below. The group of ships with a Cb < 0⋅7 includes container ships and the characteristics of the ships used in the simulations are shown in Table 1.

Table 1. Type and size of the selected fine-form ships, C_b < 0⋅7

The ship that takes action to avoid a collision is defined as Own Ship, while the ship it encounters or the ship it wants to avoid is the Target Ship. Own Ship was a container ship 365⋅5 m in length, 51⋅65 m in breadth, 16⋅00 m draft and a speed of 25⋅4 knots. Figure 2 shows the turning circle for Own Ship using ‘Hard to starboard’ rudder.

Figure 2. Turning circle for Own Ship using ‘Hard to starboard’ rudder. cbls = cables

One Target Ship was a Panamax bulk carrier 230 m in length, 32 m in breadth and 12 m draft, and the second Target Ship was container vessel 365⋅5 m in length, 51⋅65 m in breadth and 16 m draft. Target Ships were chosen according to speed. In order to obtain concrete collision avoidance data, the slower Target Ship (Panamax) sailed at 14⋅8 knots, while the faster Target Ship (container) sailed at 25⋅4 knots. These speeds were chosen because the average speed of most merchant ships ranges from 13 to 15 knots, but today there is an increasing number of high-speed ships on the maritime market such as container ships, passenger ships, liquefied gas vessels, refrigerated cargo ships, ro-ro passenger ships, high-speed craft etc.

3.2 Scenario development

In determining the distance and the time when an action to avoid a collision was required and allow ships to pass at a distance of 100 m, external influences are not taken into account and the only force that occurred is the interaction force between the ships. The most relevant information to the person navigating the ship in the scenarios described is the current distance from the other ship (measured by radar) and TCPA, determined using radar target tracking facilities. The simulations were started by setting the value of the CPA to 0 m, which means that the ships were sailing so that the risk of collision existed and a collision would surely occur if none of the ships took the avoidance action. TCPA was determined by radar, which in the initial part of the simulation represented the time until the moment of collision. Due to the change of direction of the Own Ship to avoid a collision and indirectly the change of speed due to turning of the ship, it is normal that the initial TCPA by the moment of collision differs from the TCPA at a distance of 100 m. The above did not affect the quality of the simulations at all, since the information required by the person navigating the ship was, in fact, the minimum time to collision in order to take action to avoid a collision in a timely manner. The distance between ships at the time of commencement of the action to avoid collision is the actual distance between the ships and not the distance to the point of collision. A sea area with depth of 500 m was selected for the simulation area, so that there would be no influence of the depth of the sea on the ships’ manoeuvrability. Own Ship was simulated in fully-loaded and ballast condition, resulting in a smaller speed change, while for the Target Ship two speeds were simulated: 14⋅8 knots (slower ship) and 25⋅4 knots (faster ship). The simulations were performed in such a way that the ships were placed in an initial position with CPA = 0 m. As we wanted to avoid a collision at the shortest passing distance (in simulations fixed at 100 m), the simulations were required to give the mutual distance (minimum) between the ships when the avoidance action should be started by manoeuvring only by Own Ship, in order to avoid the collision. The manoeuvre of setting the rudder on the Own Ship ‘Hard to starboard’ was chosen because it is known that changing direction on large displacement ships is far more efficient than changing speed (increasing or decreasing). Also, the largest rudder deflection was chosen, which has some limitations for a particular type of ships, but such cases may be considered as extraordinary circumstances when any action is allowed to avoid an even greater accident. Figure 3 shows an excerpt from the navigational simulator at the moment when Own Ship is passing at the CPA of 100 m to the Target Ship.

Figure 3. Ships passing at CPA of 100 m

The reason for selecting only rudder deflection for collision avoidance is because collision avoidance by changing direction has a greater and faster effect than speed change for all full displacement vessels. Based on the selected simulated conditions, four head-on situation simulations and 24 crossing situation simulations for each individual ship were conducted. In the head-on situation, the course difference (ΔCRS) between the ships was 180°, while the selected scenarios in the crossing situation included a course difference of 45°, 90°, 115°, 135°, 150° and 165°. In the crossing situation scenario, Own Ship represented the stand-on ship, while Target Ship represented the give-way ship but, as explained earlier, the latter did not take any action to avoid a collision.

4. Research results

Due to the amount of survey data, only the results obtained for a single 365⋅50 m long container vessel will be shown below. Schematic representation of the starting positions of the ships for which simulations were performed is shown in Figures 4 and 5.

Figure 4. Schematic representation of conducted simulation for head-on situation

Figure 5. Schematic representations of conducted simulations for crossing situations

Figures 6 and 7 show the distances at which a 365⋅50 m long fully-loaded container ship began to alter course when approaching a faster (25⋅4 knots) or slower (14⋅8 knots) Target Ship. The results obtained showed that in a crossing situation, the minimum distance between ships at which Own Ship initiated manoeuvring action was approximately 0⋅4 M (M is used in the paper as an abbreviation for nautical mile) when meeting a slower ship and approximately 0⋅5 M when meeting a faster ship, with the difference in courses of 45°. In the event of a crossing situation, the minimum distances between ships at which Own Ship commenced manoeuvring action increased more than twice or three times when the course differences ranged from 115° to 150°. In these cases, the minimum distance between ships at which Own Ship commenced manoeuvring action was approximately 1⋅3 M when meeting a slower ship and approximately 1⋅7 M when meeting a faster ship. When ships met in a head-on situation, the minimum distance between ships at which Own Ship commenced manoeuvring action when meeting a slower ship was approximately 1⋅0 M and when meeting a faster ship approximately 1⋅3 M.

Figure 6. Distances at which the container ship began to alter course for different scenarios expressed as a function of the difference in headings between ships (ΔCRS)

Figure 7. Distances at which the container ship began to alter course for different scenarios expressed as a function of the relative bearings

Figures 8 and 9 show the time to collision at which a 365⋅50 m long fully-loaded container ship began to alter course with the faster (25⋅4 knots) or the slower (14⋅8 knots) Target Ship.

Figure 8. Time at which container ship began to alter course for different scenarios expressed as a function of the difference in headings between ships (ΔCRS)

Figure 9. Time at which container ship began to alter course for different scenarios expressed as a function of the relative bearings

The time to collision at which Own Ship commenced the manoeuvring action is very little affected by the speed of the Target Ship and the time differences, measured in seconds, can be considered negligible. In a crossing situation, when the course difference is 45°, the time to the moment of the collision at which Own Ship commenced manoeuvring action was approximately 1′18″. The longest time to collision at which Own Ship commenced manoeuvring action occurred when the course differences ranged from 115° to 135° and was approximately 2′. When ships met in a head-on situation, the shortest period to the moment of the collision when Own Ship commenced manoeuvring action was approximately 1′30″.