The geometry of collision at sea has been dealt with in a series of papers published in the Journal, notably by Sadler (10, 306), Calvert (13, 127), Garcia-Frias (13, 316) and Morell (14, 163); and a further contribution from Calvert (to which reference is made in this paper) will be published in the next number.The object of the present paper is to examine whether anti-collision manœuvres, here considered for the case of two craft moving in a plane, can be formulated on a rigorous logical basis. If they can, then clearly a proper appreciation of the geometry of collision is a prerequisite to the formulation of any rules and regulations. In this important paper the author gives a precise and complete answer to the basic problem, and he proves mathematically that it is the only answer. As Dr. Hollingdale freely acknowledges, however, this can only be a contribution to the study of the collision problem, which involves innumerable operational factors in addition to the geometry of the situation.The convention adopted in the present paper is that each craft shall manœuvre so that if the other craft stands on, the sight line always rotates in the anti-clockwise direction. The analysis shows that a simple set of manœuvres can in fact be developed on this basis and that such manœuvres are the only ones that, geometrically, meet all the specified requirements. In all cases the combined manœuvre converts a collision situation into a ‘miss’ of at least a specified magnitude.

At a meeting of the Technical Committee of the Institute held on 9 January 1963 it was suggested that recent theoretical treatments of the collision problem could usefully be extended to include a discussion of the near-miss situation and the effect of observational errors. The basic mathematical relations for near-miss encounters have been set out in this Journal on several occasions, notably by Sadler and Morrell, and in graphical form by Wylie. The recent paper by Parker deals with the effects of both systematic and random errors of radar observations of relative range and bearing.My previous discussion of the collision problem was presented in terms of the idealized situation where two ships are on an actual collision course, in which case the sight line is in the same direction as the relative velocity vector (the relative track). To extend the results to a near-miss situation, one has only to redefine the angle α (see p. 24s of ref. 3) as the angle through which the relative velocity vector rotates when one or both ships manœuvre. I have pointed this out on a previous occasion: ‘The two craft need not be on a collision course; this definition of α applies equally well to a “miss” situation provided that no reference is made to the sight line.

The last occasion on which a lecture was given to the Society on the subject of digital computing was in 1954, when Dr. Goodwin, of the Mathematics Division, N.P.L., spoke on “ The uses of the ACE Pilot Model Computer.” At that time there were very few electronic digital computers in regular operation in this country and only one was primarily engaged on aeronautical work.

This paper is primarily concerned with principles, not with practical implementation. It is therefore reasonable to start by constructing a simplified model of the physical situation in the hope that its analysis will provide guide lines for practical action.Consider two vessels on a collision course in the open sea. An acceptable system of manoeuvres to ensure a safe passing should satisfy the following requirements;(i) Each vessel must make a positive contribution to the safety of the encounter.(ii) A mariner must be able to decide on his course of action on the basis of information readily available to him, i.e. on the compass bearing of the threat, not on its true motion or aspect.(iii) All vessels must be able to operate in accordance with the same set of rules, i.e. use a standard diagram showing the prescribed manoeuvres as a function of compass bearing only.(iv) The same set of rules must apply whether the two vessels are in visual or in radar contact.

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