Anti-collision Radar Sectors

Extract

Both the argument and the geometry in this paper require careful study before they can be appreciated; it is hoped that the following notes, which are restricted to purely geometrical considerations, will assist readers to understand them.

The author's fundamental argument is that it is geometrically impossible for ships A and B, at distance r apart and moving with constant speeds v and u, to approach each other more closely than distance d (less than r) if the courses of ships A and B are each restricted to a semi-circular anti-collision sector, depending only on the angle δ sin δ = d/r, and on an agreed universal convention. This is illustrated in Fig. 1 in which the two sectors are indicated by vv' for ship A and uu' for ship B. Adopting the convention that the ships pass ‘port to port’, the permissive anti-collision sector for each ship is, relative to the bearing of the other ship, from δ to starboard, increasing to 180° and to port from 180° to 180° −δ . This is equivalent to restricting the course so that the other ship bears more than δ to port or more than 180°−δ to starboard.