Enhancing Collision Prevention Between Ships in a Close-Quarters Situation Using Simulated Avoiding Strategies

Abstract

“Close-quarters situation” is the term that appears in the International Regulations for Preventing Collisions at Sea, but it lacks a precise definition. For this reason, the authors explore various interpretations and definitions provided by different scholars and court rulings, relying on legal precedents and judicial decisions. Ultimately, they propose their own definition of the term. Each navigator aims to establish the minimum safe distance from another vessel and the time until the closest point of approach within which a collision can still be avoided through appropriate action. Based on the proposed definition of a close-quarters situation, simulations were conducted using a navigational simulator to establish the minimum safe distances and the time frame in which a vessel can still maneuver to prevent a collision. A total of 168 simulations were performed, utilizing three different sizes of fine-form vessels and three sizes of full-form vessels. Due to the extensive data set, this paper presents results for only two vessels. To facilitate a better comparison of the maneuvering characteristics of different hull forms, one fine-form vessel and one full-form vessel of approximately the same dimensions were selected for analysis.

1. Introduction

The process of taking action to avoid a collision at sea involves the Officer of the Watch or the Master making timely and appropriate decisions in line with the International Regulations for Preventing Collisions at Sea (COLREGs), ensuring that ships pass at a safe distance from one another. These rules, established by the IMO (International Maritime Organization) in 1972, serve as guidelines for navigating such situations. Over the years, several terms and provisions have been criticized for lacking precision, resulting in inconsistent interpretations by individuals and organizations alike. These differing interpretations may lead to uncertainty in the practical application of the rules, where personal judgment, shaped by the experience of officers or Masters, frequently takes precedence over strict compliance with regulatory guidelines. Consequently, formalizing the rules for practical use would be highly beneficial and would likely enhance navigational safety. One specific term in the COLREGs that needs further clarification is the “close-quarters situation.” Many navigators rely primarily on their own experience and professional judgment when determining whether a close-quarters situation exists. However, seafarers, maritime experts, and even court officials often disagree on the definition of a close-quarters situation, leading to potential misunderstandings. Therefore, one objective of this research is to define and clarify this concept by reviewing existing considerations and interpretations. A second objective focuses on conducting simulations with various ship models in a navigational simulator to identify the minimum distance at which a “stand-on vessel” can independently take effective avoiding action to prevent a collision, even in scenarios where the “give-way vessel” does not comply with the rules. This distance will help define the minimum safe distance between vessels and the time before the closest point of approach at which immediate action must be taken to prevent a collision. The findings from this research, based on navigational simulations, will provide valuable insights for navigators, enabling them to better understand the limit distances and times within which they must take immediate action to avoid collisions. These results will also be useful for Vessel Traffic Service (VTS) operators and, in the future, for operators of unmanned vessels and artificial intelligence systems responsible for avoiding collisions at sea.

For now, the research results have certain limitations. The ships chosen in the research are real ships, and the scenarios can also happen in reality. The results obtained from the research are only suitable for the selected ships and for the selected scenarios. The limitation is the fact that the simulations were conducted under controlled conditions, without the inclusion of meteorological and oceanographic factors such as wind, waves, or shallow waters. By introducing different combinations of external influences into the simulations, the values of time and distance required for a safe maneuver would certainly be affected. For example, crosswinds and currents can increase drift and necessitate earlier course changes; in shallow waters, squat effects and reduced maneuverability can increase the turning radius, especially for fuller-form vessels, and so on. The inclusion of external influences on vessel movement during simulations is planned for future research. Given that a vessel’s maneuvering characteristics, hull form (fine or full), and speed have a significantly greater impact on the outcome than external environmental factors, we considered it more important to present these core results as a starting point.

2. About the Term Close-Quarters Situation

According to Tsai et al. [1], the process of avoiding collisions at sea involves taking appropriate and timely measures in line with the International Regulations for Preventing Collisions at Sea (COLREGs), allowing vessels at risk of collision to pass each other at a safe distance. In this context, it is necessary to define threshold parameters that determine when a collision avoidance maneuver should be executed. These thresholds may differ depending on the vessel type or may vary for the same ship under different operational conditions. Prompt decision-making is essential to ensure sufficient spacing between ships and to retain enough time and sea room to prevent a collision, even under exceptional circumstances. However, in situations of high traffic density or non-compliance with the rules, vessels may occasionally approach one another too closely, falling below safe standards and significantly increasing the risk of collision. The term “close-quarters situation” is commonly used to refer to such cases where the separation distance between ships is no longer deemed safe. This concept is explicitly addressed in COLREGs, specifically in Rule 8 (Action to Avoid Collision) and Rule 19 (Conduct of Vessels in Restricted Visibility). Despite its frequent use in maritime practice, the term remains ambiguously defined, with various authors offering different interpretations. Numerous attempts have been made during conferences focused on the COLREGs to establish a clearer and more precise definition of the term; however, these efforts have largely been unsuccessful. Cockcroft and Lameijer [2] state when two ships are in sight of one another and a risk of collision exists, action to avoid a collision can be divided into four sequential phases. In order of sequence, these are the following phases: free maneuver, action required by the give-way vessel, action permitted by the stand-on vessel, and action required by the stand-on vessel. The aforementioned four phases are shown in Figure 1.

A close-quarters situation, as described by the authors, arises when the give-way vessel is no longer able to prevent a collision through its own maneuvers intended to stay clear of another vessel. In these circumstances, it becomes necessary for the stand-on vessel to also take appropriate action to help avoid a collision. Although efforts were made during the 1972 conference to establish a precise minimum distance for defining close-quarters situation, no fixed value in nautical miles was formally adopted. Furthermore, the authors cite various court rulings and expert witness interpretations regarding close-quarters situations, such as in the Grepa-Verena case, in which the term was not explicitly defined and continues to be a subject of ongoing debate. In a same way as Cockcroft and Lameijer, He at al. [3] presented a situation-identifying model and defined four distinct stages in the entire encounter process for autonomous collision avoidance (ACA), where appropriate collision avoiding (CA) actions must be taken according to different situations and stages. The authors created quantitative models to calculate the first time-in-point of close-quarters situation (FTCS) and first time-in-point of immediate danger (FTID) for ship encounters in open sea under good weather conditions. They included “close-quarter” and “immediate danger” stages in the third stage of their defined scenario. Craig [4] examines different ways in which the term “close-quarters situation” has been interpreted and defined in legal decisions by courts in both the United States and the United Kingdom. He emphasizes that this term does not have a precise or formal definition within the text of the COLREGs themselves. After extensive deliberation, the delegation responsible for adopting the 1972 Rules for Preventing Collisions at Sea concluded that it was not feasible to establish a specific distance for defining a close-quarters situation. With a few exceptions, courts have also generally refrained from offering more than broad guidelines for determining such situations. One commonly acknowledged definition in case law describes a close-quarters situation as one in which two vessels, based on their courses and speeds, will not pass each other at a safe distance. However, this definition presents challenges as it relies on the concept of a “safe distance,” which is itself not clearly defined within the rules, limiting its practical applicability. In their book, Cockroft and Lameijer [2] address the concept of a “close-quarters situation”, which is first mentioned in Rule 8(c) of the COLREGs. They explain that the distance at which such a situation arises depends on various factors, including visibility conditions. According to their analysis, in open waters and restricted visibility, close-quarters situations typically begin at distances of 2 to 3 nautical miles. However, for vessels that are in sight of one another, this distance is usually reduced to approximately 1 nautical mile. Cahill [5] suggests a definition for a close-quarters situation where collision avoidance is no longer controlled by a single ship but involves vessels that 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.” The report [6] highlights that a close-quarters situation does not inherently imply a risk of collision. It also stresses that there is no clear distinction between the concepts of a close-quarters situation and a risk of collision. The English Admiralty Court, in the case of the vessel Maloja II, firmly stated the importance of taking timely action to prevent a close-quarters situation. This ensures that ships, whenever possible, avoid situations where a collision risk arises, requiring critical decisions to be made under time pressure, often without sufficient time to choose the correct course of action. In his book, Mankabady [7] acknowledges the difficulty of precisely defining a close-quarters situation. He elaborates that its characteristics depend on various factors and describes it as a scenario where a collision can no longer be avoided through a significant alteration of course by a single vessel. In 1970, the British Merchant Navy Association published an article in its journal discussing 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 a 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 [8] describe a close-quarters situation as the one occurring when vessels come into such close proximity that there is very limited time and maneuvering space left to take effective action to avoid a collision. Although they refrain from assigning fixed numerical values, they emphasize the difficulty in defining a standard distance, as each situation is highly dependent on its specific circumstances. According to the authors, factors such as the vessels’ relative speeds, headings, and distances all contribute to the development of such scenarios. In practical maritime contexts, the term typically refers to a high likelihood of collision due to the relative positioning and closeness of ships. A notable study conducted by the Faculty of Law and Political Science in Nantes [9], commissioned by the French Government, focused on close-quarters encounters in the Ushant traffic area. The research aimed to enhance navigation safety in the Ushant area and improve monitoring and control by the Ushant Vessel Traffic Service (VTS) center. In their definition, the authors link the term “close-quarters situation” to the concept of a near miss, describing it as a sequence of events or interactions between ships with the potential to lead to a collision. Over a 68-month period, from 2008 to September 2013, 120 cases of close-quarters situations were reported by vessels, and the analysis was based on the data obtained. The criteria for identification included the closest point of approach (CPA) of 0.5 nautical miles or less and a time to CPA (TCPA) of 10 min or less. Furthermore, Bakdi et al. [10] introduced a Risk Identification Methodology aimed at determining the minimum safe distance required to prevent accidents in navigation scenarios. They introduce the concept of blocking areas, dividing the vessel safety domain into four distinct zones. Similar to some other authors, they emphasize that in a close-quarters situation, actions taken by a single vessel alone are insufficient to effectively mitigate the risk of collision.

Review on Explanation of the Term Close-Quarters Situation

An analysis of the existing literature and various perspectives on the concept of a close-quarters situation reveals a wide range of viewpoints. Some authors focus primarily on discussing the term itself and the factors that may influence its interpretation, without proposing a concrete, measurable distance. Ideally, however, a close-quarters situation should be defined in terms of distance between vessels, expressed in meters, cables, or nautical miles. Therefore, any meaningful analysis aiming to define such a situation should ultimately result in a measurable distance. Yet, many studies fail to provide this crucial piece of information. Conversely, some authors offer more specific definitions. Although their wording may vary slightly, the underlying principle remains consistent: a close-quarters situation exists when a collision cannot be avoided by the actions of a single vessel alone, and both vessels must take avoiding actions to prevent the collision. While this definition may be legally valid, it is entirely unsatisfactory for the person navigating the ship. This raises a critical question: why was the ship allowed to reach such a state in the first place. The most plausible explanation is that one of the vessels failed to take all necessary actions to prevent a collision. This responsibility primarily falls on the give-way vessel, which, for various reasons, failed to take action in ample time. In accordance with Rule 17, the vessel required to keep her course and speed shall take appropriate action to best aid in avoiding a collision as soon as it becomes apparent to her that the other vessel is either not taking sufficient action or is failing to act at all. Therefore, before a close-quarters situation develops, the stand-on vessel may take action to avoid a collision, thereby preventing the situation from arising in the first place, thus avoiding the risk of collision altogether. It is widely recognized that navigators must maintain a proper lookout in accordance with the ordinary practices of seamen. This raises the question of whether it can truly be considered ordinary practice of seamen if the navigator allows the vessel to enter a close-quarters situation. As previously mentioned, while there may be several reasons why ships end up in close-quarters situations, the most common cause is the failure of the give-way vessel to take appropriate action to avoid collision. Such failures often constitute a breach of conduct that is not in accordance with the ordinary practice of seamen. According to Rule 17(b), the stand-on vessel, when in a close-quarters situation, is required to take such action as will best aid in avoiding a collision. This raises an important question of whether a seafarer acting in accordance with the ordinary practices of seamen would wait until reaching such a critical point, where avoiding a collision would require appropriate actions from both vessels involved. If the navigator of the give-way vessel had acted in line with the ordinary practices of seamen, they would have already taken action in ample time, ensuring a safe passing distance between the vessels. Consequently, the definition offered by some authors that a close-quarters situation represents the distance at which a collision cannot be avoided by the actions of one vessel alone but requires both to act is inconsistent with the principles of ordinary practice of seamen. A more acceptable definition for a seafarer adhering to standard practice of ordinary seamen would describe a close-quarters situation as the minimum distance between vessels at which a collision can still be avoided by the action of only one ship [11]. However, in such scenarios, it is important to note that this action may not ensure passing at a safe distance, but it would still allow for the prevention of a collision. In maritime practice, such situations are often referred to as “near miss”. Adopting this definition would make it easier to identify and quantify the position and distance between vessels that constitute a close-quarters situation. Key factors in determining this distance would include the turning characteristics of the vessels, their relative positions and movements, and external influences such as wind, currents, waves, water depth, etc., all of which can affect a ship’s maneuverability.

3. Preparation for Research

As per the definition of a close-quarters situation proposed earlier in this paper by the authors as the minimum distance between ships at which a collision can still be avoided by the action of only one vessel, the following sections define scenarios simulated on a navigational simulator. These simulations aim to determine the minimum distance at which the stand-on vessel can take effective action to prevent a collision in cases where the give-way vessel, for any reason, fails to take appropriate action in compliance with COLREGs. Krata and Montewka [12] conducted similar research in which they sought to define the concept of critical distance between two ships on a collision course. They described critical distance as the shortest distance at which effective, last-minute evasive actions can still be carried out successfully by the stand-on vessel alone, assuming the give-way vessel fails to take action. The authors compared the dimensions of this critical distance or area with the sizes of various ship domains found in the literature. Building on previous research, Szlapczynski at al. [13] explored scenarios where the ship acts as the stand-on vessel, and the give-way vessel fails to respond in a timely manner. In these cases, the authors examined, in accordance with COLREGs, the point at which the stand-on vessel should initiate a maneuver, taking into account the desired separation. They represented this separation using a decentralized elliptic domain. Baldauf et al. [14] conducted a comparative analysis of collision avoidance processes between ships and aircraft, emphasizing key differences and proposing enhancements for maritime navigation systems. The authors argue that the existing CPA (Closest Point of Approach) and TCPA (Time to Closest Point of Approach) alarms are inadequate, as they merely alert navigators to the risk of a potential collision without issuing subsequent warnings if the initial alarms are ignored, a feature already implemented in aviation systems. To address this limitation, they propose the introduction of an additional collision alarm for ships, referred to as the “Last Line of Defence” (LLoD), modeled after the airborne collision avoidance system (ACAS). This LLoD alarm, also termed the “Ultimate Action Alarm” (UAA), is designed to activate at the critical point where the remaining options for maneuvering to avoid a collision are reduced to a minimum. The concept of the LLoD aligns closely with the aim of this research: to determine the minimal distance at which a collision can still be avoided through the actions of a single vessel. In their simulations, Baldauf et al. [15] calculated the time needed to initiate a maneuver that would achieve a passing distance of 3 cables between ship hulls in one scenario and 2.5 cables in another, assuming a rudder angle of 30°. While the authors do not provide a detailed explanation for selecting these specific passing distances, they emphasize 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 the distance between the two ships on collision courses and the time to the collision when the avoidance action should be taken so that the ships would pass at a minimum distance. Collision-avoidance maneuvers at sea can lead to one of three possible outcomes. The first scenario involves the ships passing each other at a safe distance. The second scenario occurs when the ships pass at a distance smaller than what is generally considered safe, an extremely narrow margin, yet still avoiding physical contact. The third scenario, however, results in contact between the ships, indicating a collision. Without specifying an exact value for what constitutes a safe distance, a close-quarters situation can be reasonably defined as a distance between passing ships that falls below the safe distance threshold but still avoids a collision. In this research, the simulations were designed to execute collision-avoidance actions at a distance that ensured a passing distance of 100 m between the ships [11]. While this distance is not one a navigator would typically consider desirable during routine operations, it was deliberately chosen for the purpose of identifying the shortest distance at which one ship could initiate avoidance maneuvers. This distance is frequently observed in constrained environments such as narrow channels, two-way waterways, port entrances, or anchorages; however, such contexts fall outside the scope of this research. This study aimed to determine the minimum distance at which collision avoidance actions could begin, with the passing distance fixed at 100 m. This value was selected as the minimum passing distance at which hydrodynamic interactions between two overtaking vessels would not result in contact between their hulls. Although such interactions may exert a force, it would remain insufficient to cause physical contact. As overtaking scenarios produce the strongest hydrodynamic effects between vessels, this study assumes that this minimum passing distance is also valid for head-on and crossing situations. The minimum passing distance identified in the simulations corresponds to the closest point of approach at the moment of passing. Under controlled conditions of the simulations, excluding the effects of shallow water, wind, waves, or currents, the closest point of approach would theoretically remain approximately 100 m in reality. However, if external factors affecting ship maneuverability were introduced, the closest point of approach would likely deviate from this baseline, either increasing or decreasing. To determine the closest point of approach during passing that can be deemed safe under varying conditions, it is essential to account for the influence of external factors and the potential inaccuracies of distance-measuring equipment, particularly the radar. However, given the extensive range of possible scenarios and combinations of these factors, such cases were beyond the scope of this research and are reserved for future studies. In the context of this study, the closest point of approach of 100 m during passing is considered a worst-case scenario under idealized conditions. Similarly, Szlapczynski et al. [13] reference the work of Krata et al. [12,16], noting that the authors assumed “a near-zero ship separation”, which aligns with the worst-case scenario described in this paper. The simulations for this study were conducted using the state-of-the-art TRANSAS NTPRO 5000 navigational simulator, located at the Faculty of Maritime Studies in Rijeka. The adoption of advanced simulators and computational tools has become increasingly prevalent in maritime research, providing precise and sophisticated models for predicting ship maneuvering behaviors [14].

3.1. Ship Models Used in Simulations

Given the wide variety of ship types and characteristics, it was necessary to rationalize the number of models to reduce the complexity of possible combinations while ensuring the representativeness of ship types. In defining the scenarios, variations in ship type, size, loading condition, and speed were considered. Rationalization was primarily achieved by categorizing ships based on their block coefficient (Cb). According to this criterion, ships were divided into two categories: those with a block coefficient less than 0.7 (Cb < 0.7), classified as fine-form ships, and those with a block coefficient greater than 0.7 (Cb > 0.7), classified as full-form ships. In this article, due to the extensive volume of results obtained, the focus will be on presenting the results for one fine-form ship and one full-form ship. Pilot cards detailing the characteristics of the selected ships used in the simulations are shown in Figure 2 and Figure 3 and type and size of selected ships are shown in

Table 1. The type and size of selected ships [17].

Ship Type	LOA (m)	B (m)	Loading Condition	Displacement (t)	T (m)
Bulk Carrier (Cape Size)	290.00	46.00	loaded	202,000	18.10
			ballast	76,800	7.48
Container Vessel (9300 TEU)	299.95	48.20	loaded	142,213	14.85
			ballast	23,991	6.50

below.

A ship that takes action to avoid a collision is described as an Own Ship, while the ship she encounters or the ship she wants to avoid is the Target Ship. Figure 2 shows the turning circle of a full-form bulk carrier, and Figure 3 shows the turning circle of a fine-form container vessel used in the simulations while executing “hard to port” and “hard to starboard” rudder.

The Target Ships selected for the simulations included a Panamax bulk carrier and a container vessel, chosen to represent distinct vessel types and operational characteristics. The Panamax bulk carrier had dimensions of 230 m in length, 32 m in beam, and a draft of 12 m, while the container vessel measured 365.5 m in length and 51.65 m in beam and had a draft of 16 m. These vessels were selected based on their operational speeds to analyze collision avoidance dynamics under varying conditions. The Panamax bulk carrier was assigned a speed of 14.8 knots, reflecting the average operational speed range of most merchant vessels, typically between 13 and 15 knots. Conversely, the container vessel was assigned a speed of 25.4 knots to represent the increasing prevalence of high-speed ships in modern maritime operations. This higher speed aligns with the performance profiles of contemporary vessel types, including container ships, passenger ships, liquefied gas carriers, refrigerated cargo ships, ro-ro passenger ships, and high-speed craft. By simulating interactions between vessels of differing speeds and maneuverability, this study aims to provide comprehensive insights into collision avoidance strategies for diverse maritime scenarios.

3.2. Scenario Development

To determine the distance and timing for initiating collision avoidance actions that would ensure ships passed at a minimum distance of 100 m, external factors such as environmental influences (wind, current, and wave) were excluded from consideration. The only force factored into the simulations was the hydrodynamic interaction between the ships. The key parameters for a navigator in these scenarios were the current distance to the other vessel (measured by radar) and the time to the closest point of approach (TCPA), calculated using radar tracking functionalities. At the outset of each simulation, the closest point of approach (CPA) was set to 0 m, indicating that the ships were on a collision course, and a collision would inevitably occur if neither vessel took evasive action. The initial TCPA, determined by radar, represented the time remaining until the moment of collision. However, as the Own Ship altered her course to avoid a collision, causing an indirect change in speed due to the turning maneuver, the TCPA at the initial moment of collision risk naturally differed from the TCPA when the vessels ultimately passed at a closest point of approach of 100 m. This did not compromise the validity of the simulations at all, as the crucial information for the navigator was the minimum time to collision, in order to take action to avoid a collision in a timely manner. The measured distance at the commencement of the collision avoidance maneuver was the actual distance between the vessels, not the distance to the collision point. To eliminate the influence of water depth on ship maneuverability, the simulation area was set with a depth of 500 m. The Own Ship was simulated in fully loaded and ballast conditions for both categories, while the Target Ship was tested at two different speeds: 14.8 knots (representing a slower vessel) and 25.4 knots (representing a faster vessel). In each scenario, the ships began in positions where CPA equaled 0 m, and the objective was to avoid collision while achieving the fixed passing distance of 100 m. The simulations were designed to determine the minimum distance at which the Own Ship must initiate its maneuver to avoid a collision, relying solely on its own actions. A “hard-to-starboard” rudder maneuver was selected for the Own Ship, as course alterations on large displacement vessels are significantly more effective than speed adjustments (either acceleration or deceleration). Also, the maximum rudder deflection was used during the simulations, which has some limitations for certain types of ships, but such cases may be considered as exceptional circumstances when any action is justified to prevent a more serious incident. Figure 4 shows an excerpt from the navigational simulator at the moment when the Own Ship passes the Target Ship with a closest point of approach (CPA) of 100 m.

The decision to focus exclusively on rudder deflection for collision avoidance was based on the superior effectiveness and quicker response time of course alterations compared to speed changes for full displacement vessels. Based on the defined conditions, four (4) head-on situation simulations and twenty-four (24) crossing situation simulations were conducted for each individual vessel type. In the head-on scenarios, the course difference or angle of intersection (ΔCRS) between the vessels was 180°, shown in Figure 5. The phrase “angle of intersection” typically refers to the angle formed when two paths, trajectories, or courses cross each other. In maritime contexts, it is often used to describe the angle between the course or heading of two vessels when they are approaching one another. For crossing situations, the course differences analyzed included 67.5°, 90°, 115°, 135°, 150°, and 165°, shown in Figure 6. In these crossing scenarios, the Own Ship acted as the stand-on vessel, while the Target Ship represented the give-way vessel. However, as it was explained earlier, the Target Ship did not perform any avoidance maneuvers [11].

In the end, a total of 168 simulations were performed. The figure of 168 simulations is not arbitrary, but it results from the combination of different ship types (fine- and full-form), two simulated speeds of the target vessel, various crossing angles (six variations), and loading conditions (fully loaded and in ballast). We believe that this number of scenarios demonstrates that the topic has been explored in depth.

A simplified flowchart of the simulation process (scenario setup, ship model selection, parameter input, simulation execution, data collection, and results analysis) is shown in Figure 7.

4. Research Results

Due to the amount of survey data, only the results obtained for one fine-form vessel and one full-form vessel (which were described earlier) will be shown below. The results for both vessels will be presented only in the fully loaded condition. Schematic representations of the starting positions of the ships for which simulations were performed are shown in Figure 5 and Figure 6.

Figure 8 and Figure 9 show the distances at which the selected Own Ship began to alter course when approaching a faster (25.4 knots) or slower (14.8 knots) Target Ship.

The conducted analysis indicates that, in crossing scenarios, the Own Ship (bulk carrier) commenced maneuvering at an approximate distance of 0.5 nautical miles when encountering a slower vessel and at approximately 0.8 nautical miles when facing a faster vessel, with an intersection angle of 67.5°. When the angle of intersection increased to a range between 115° and 150°, the minimum distances at which evasive actions were initiated more than doubled. In such circumstances, the Own Ship (bulk carrier) began to alter course at around 1.2 nautical miles in encounters with slower vessels, and approximately 2.1 nautical miles when meeting faster vessels.

In head-on situations, the Own Ship (bulk carrier) initiated maneuvering at a minimum distance of approximately 1.0 nautical mile when the opposing vessel was slower, and about 1.4 nautical miles when the opposing vessel was faster.

A comparable trend was observed for the Own Ship (container vessel). In crossing encounters at an intersection angle of 67.5°, maneuvering began at approximately 0.4 nautical miles when facing slower vessels, and around 0.5 nautical miles when encountering faster ones. When the angle of intersection ranged between 115° and 150°, these distances increased substantially, with the Own Ship (container vessel) initiating action at roughly 0.9 nautical miles in response to slower ships and around 1.3 nautical miles when confronted with faster vessels.

In head-on approaches, the Own Ship (container vessel) commenced maneuvering at about 0.8 nautical miles when meeting a slower ship and at approximately 1.1 nautical miles in encounters with faster ships.

Figure 10 and Figure 11 illustrate the respective time to collision values at which each Own Ship initiated course alterations in response to either faster (25.4 knots) or slower (14.8 knots) Target Ship.

In a crossing situation, with an angle of intersection of 67.5°, the time to collision at which Own Ship (bulk carrier) commenced maneuvering action was approximately 1.7 min when meeting a slower vessel and around 2.0 min when meeting a faster vessel. The longest time to collision at which the Own Ship (bulk carrier) commenced maneuvering action occurred with an angle of intersection ranging from 120° to 140° and was approximately 2.7 min when meeting a slower vessel and around 3.4 min when meeting a faster vessel. When vessels met in a head-on situation, the time to collision at which Own Ship (bulk carrier) commenced maneuvering action was around 2.0 min for both slower and faster vessels. On the other hand, in a crossing situation, the time to collision at which Own Ship (container vessel) commenced maneuvering action was approximately 1.3 min when meeting both slower and faster vessels with an angle of intersection of 67.5°. The longest time to collision at which Own Ship (container vessel) commenced maneuvering action occurred with an angle of intersection ranging from 120° to 140° and was approximately 1.7 min when meeting a slower vessel and around 2.1 min when a meeting faster vessel. When vessels met in a head-on situation, the time to collision at which Own Ship (container vessel) commenced maneuvering action was around 1.3 min for both slower and faster vessels.

5. Discussion

Based on the conducted simulations, it can be determined that some results are consistent with standard procedures typically followed by bridge officers, while other results may lead the officer to question whether the decision they make, based on these results, aligns with the rules or not. It is evident that the rules cannot account for every possible situation involving the risk of collision at sea. Rule 2 acknowledges this limitation by allowing for exceptions in cases involving special circumstances and immediate danger. Both conditions must be present to justify and departure from the rules. Even so, compliance with the rules should remain standard, and the reference to special circumstances or immediate danger should be reserved for rare cases. When evaluating the minimum distances at which the Own Ship must begin maneuvering to avoid a collision with the Target Ship in order to pass at a distance of 100 m, it is concluded that this distance is influenced by the turning circle characteristics of the Own Ship, the course difference between the two vessels, and the relative approach speed. Ships with the same shape but shorter length, and therefore a smaller turning circle diameter, can start collision avoidance at shorter distances, while still ensuring a 100 m clearance. The figure illustrating the results is omitted due to the large amount of material. The most unfavorable cases, which imply the largest distances at which avoidance should be initiated, occur when the course difference between the ships ranges from 90° to 180°. The largest distances are observed when the course difference is between 115° and 150°. In addition to these course differences, an extra challenge arises when selecting an avoidance maneuver. More specifically, if the intention is to avoid crossing ahead of the Target Ship, the Own Ship must perform a complete turn over the starboard side in order to avoid the collision. In this research, when comparing two similar ships of equal length but different forms in a crossing situation, it is observed that when encountering a faster Target Ship traveling at 25.4 knots, the required distance to initiate an avoiding action is approximately 2.1 nautical miles for a bulk carrier and around 1.3 nautical miles for a container vessel. In such scenarios, the question arises as to whether collision avoidance initiated at these relatively long distances of 2.1 nautical miles by the stand-on vessel constitutes a breach of the rules. The appropriate answer depends on the specific circumstances. For smaller vessels capable of safely executing collision avoidance maneuvers at shorter distances, taking such actions over longer distances by the stand-on vessel could be interpreted as a violation of the rules. Conversely, for larger vessels, whose maneuvering characteristics require initiating collision avoidance actions at greater distances, such actions may be considered in accordance with the rules. For simulations where the course difference ranged from 115° to 165°, the Own Ship executed maneuvers by turning to starboard, crossing the Target Ship’s trajectory, and maintaining a minimum passing distance of 100 m. It is important to highlight that 100 m represented the closest point of approach, while the bow crossing distance was slightly greater. This method of avoidance reduced the initial separation between the ships required to commence the third stage of avoidance, where the stand-on ship may take action to prevent a collision. As previously mentioned, such a scenario involving intersection along the bow of the Target Ship can be regarded as the worst case. By simulating scenarios where the relative approach speed between the ships was higher, it was anticipated that the collision avoidance maneuver would need to begin at a greater distance from the other ship. Analyzing the time to the closest point of approach revealed that the point at which a ship must start maneuvering to avoid a collision and pass the other ship at a minimum distance of 100 m depends on several factors. These include the turning circle characteristics of the Own Ship (e.g., ROT with hard over rudder for the bulk carrier was around 40°/min while ROT for the container vessel was around 60°/min), the difference in courses between the two ships, and the speed of the Own Ship. The shape of the curve representing the time to the closest point of approach, the moment at which collision avoidance must commence, and the minimum distance curve required for initiating collision avoidance are similar, which aligns with expectations. When analyzing the time to the closest point of approach at which a ship must initiate collision avoidance with another vessel, it is important to note that this time significantly varies with the difference between Own Ship and Target Ship speeds, as illustrated in Figure 10 and Figure 11. A bulk carrier moving at a significantly lower speed than the faster Target Ship requires a much larger TCPA compared to a container vessel, whose speed is only slightly lower than that of the faster Target Ship. The bulk carrier needs significantly more time (about 60%) than the container vessel to clear the Target Ship by 100 m. Additionally, a much greater decrease in the ship’s speed occurs during the turn, due to the larger drift angle that is characteristic of vessels with fuller forms compared to those with finer forms. Furthermore, positions between 115° and 150° represent the most unfavorable relationship between the Own Ship and the Target Ship. In such a relation, the Own Ship must deviate the most from its initial position, and this is why the highest values are observed in this part of the curve. Finally, one might question why no avoidance maneuver was performed by the Own Ship turning to port when the course differences in the crossing situation ranged from 115° to 165°. While turning to port could indeed have allowed the avoidance maneuver to be executed at even shorter distances from the Target ship, the Own Ship acts in accordance with Rule 17(c), which states: “A power-driven vessel which takes action in a crossing situation in accordance with subparagraph (a) (ii) of this rule to avoid collision with another power-driven vessel shall, if the circumstances of the case admit, not alter course to port for a vessel on her own port side” [18]. It is well understood that Rule 17, paragraph (c), does not strictly prohibit a turn to port, as indicated by the clause “if the circumstances of the case admit”. However, the authors emphasize that actions should be as closely aligned as possible with the rules and conducted in accordance with the ordinary practice of seamen. The authors believe that turning the ship to port to avoid a collision should be regarded as a measure of last resort, to be considered only when circumstances make all other appropriate collision avoidance actions impossible. The survey determined the limit values for avoiding collisions and maintaining a passing distance of 100 m from the other ship. As previously mentioned, avoiding a collision by passing the other ship at a minimum distance of 100 m can be regarded as the worst-case scenario. We believe that providing the officer on watch with information about the angle of intersection between vessels would greatly assist in decision-making. If the ARPA radar system could display such data, the officer on the stand-on vessel would be able to accurately assess the TCPA and the minimum distance up to which they can wait for the officer on the give-way vessel to take action to avoid a collision [11]. It is evident that TCPA and distance values vary significantly depending on the angle of intersection, which highlights the importance of incorporating this type of information into ARPA systems in the near future. In their future research, the authors plan to consider potential errors in radar measurements of distance, inaccuracies in the Target tracking facility when calculating CPA and TCPA (as per Res. MSC.192 (79)), as well as factors such as ship length and breadth, the position of the radar antenna, the common reference point, and external influences that may impact the ship’s maneuverability. These external factors include sea currents, wind, waves, and under keel clearance (UKC) [19].

6. Conclusions

The purpose of this research was to systematically analyze the concept of a close-quarters situation, which plays a critical role in collision avoidance at sea. Since the likelihood of a collision increases considerably in close-quarters situation and the outcomes of such incidents are often severe, it is vital to identify the parameters under which collision avoidance can still be achieved by initiating maneuvers by at least one of the vessels involved. This research highlights that the concept of a “close-quarters situation” is still not clearly defined and is subject to varying interpretations within the maritime literature and operational practice. To address this gap, this paper introduces a practical and applicable definition of close-quarters situations that aligns with maritime practices and can be reliably used by ship officers in real-world conditions. This study provided data on the distances between vessels and the times to the closest point of approach at which an action to avoid a collision can still be initiated under defined scenarios, ensuring that ships pass at a distance of 100 m. For an Officer of the Watch on the bridge, knowing such critical values for their vessel and the specific circumstances, including the angle of intersection, can significantly assist in understanding the limits within which a collision can still be prevented. The research further established that the stand-on vessel should initiate an avoidance maneuver to determine the ultimate point at which the stand-on vessel can wait for the give-way vessel to comply with the rules. To achieve this, various ship models were used in the simulations, selected based on their form and dimensions, providing valuable insights depending on the vessel’s size. The findings are also relevant for Vessel Traffic Service (VTS) operators, whose role in collision avoidance is expected to grow in the future. Additionally, the research has implications for those managing unmanned ships from land and for artificial intelligence systems that will autonomously manage collision avoidance actions between vessels. As this paper presents only a limited number of results, readers interested in further data not included in the publication are encouraged to contact the authors directly for additional information.