This paper outlines the concept of a domain and an evasion area, called an arena, around a ship which are then applied to produce a computer model of ship behaviour. The arena determines when a ship takes avoiding action, as does the land arena which reacts with a discrete series of coastal points to prevent the ship running aground.The increase in the number and size of ships has resulted in the introduction of traffic routing schemes and the need to understand ship behaviour more thoroughly. The concept of ‘the effective area around a ship which a navigator would like to keep clear with respect to other ships and stationary objects’ has been used by various authors including Goodwin, Fujii and Lewison with varying names such as domain, collision diameters and encounter area. There has been no fixed shape for these areas. Some are circular, others elliptical, while Goodwin's has three segments each with its own portion of a circle. By developing the theory of the domain, it was hoped to be able to produce a model of traffic behaviour which could be used to simulate traffic flows, or specific incidents, in order to study them more fully.

In a previous paper a model was outlined for an encounter between two vessels. This paper shows how the model has been developed to include the simulation of the behaviour of more than two ships, the entrance to harbours, and narrow channels.In a previous paper by the authors the concept of a domain was examined. Goodwin's definition of a domain was used, namely, ‘the effective area around a ship which a navigator would like to keep clear with respect to other ships and stationary objects’. The concept of distinct sectors for sidelights and sternlight was modified mathematically so that an area equal to the total of the segments was contained within a circle. By off-centering the position of the ship within this circle, the weighting of the differing areas for the various sectors was retained (Fig. I). A second circle with the ship off-centre was introduced called an arena or ‘sphere of influence’. When a ship is inside the arena a navigator becomes aware of the other ship and decides what action, if any, is needed to keep his own domain unviolated. This resulted in a model which obeyed the Collision Regulations.

In a previous paper a model was outlined for an encounter between two vessels using the ‘range to domain over range rate’ (RDRR) criterion. This paper shows how the model has been developed to simulate traffic flow and collision avoidance through the main south-west bound lane of the Dover Strait traffic separation scheme. B. A. Colley and C. T. Stockel are at Plymouth Polytechnic, R. G. Curtis with the Department of Trade and Industry. The paper was presented at an ordinary meeting held in London on 16 November 1983.

Two main concepts in mathematical modelling of ship encounters have been proposed by Davis. The first, the ‘domain’, was an adaptation of a concept originally introduced by Goodwin, who defined the domain as the ‘area about own-ship that a navigator wished to keep free with respect to ships and other stationary objects’. The second, the ‘arena’, conceived by Davis, is the area around the domain which when infringed causes the mariner to consider whether to make a collision-avoidance manoeuvre. Thus, in a computer model, when a vessel enters the arena the computer analyses the situation and, depending on the severity of the threat, makes a collision-avoidance manoeuvre.Goodwin's domain was divided into three sectors corresponding to the ‘giveway’, the ‘stand-on’ and the ‘overtaking’ regions as defined by the relative velocity of approach. The domain was derived from radar films of ship tracks and records of radar simulator experiments. Davis smoothed the sectored domain to a circle with own-ship off-centred astern and to port, and the weighting of each of the sectors retained. Davis's domain had a solid theoretical grounding; the arena, however, was simply a larger version of the smoothed domain. Its size and position were obtained by means of a well-distributed questionnaire. It served its purpose in the model, but lacked any real validation.One problem with the Davis arena was its inability automatically to take into account different velocities, both of own-ship and of targets.

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