The Calvert Methods of Manœuvring to Avoid Collision at Sea and of Radar Display

Abstract

These methods were briefly described in the Journal (Vol. 13, No. 2). They were prefaced by some comments designed to draw a comparison between the air and sea problems and collision rates. Statistics are liable to be misleading if not perfectly understood and definitive, and marine collision statistics as much as any. It should be realized that Lloyd's List figures include almost every collision incident to ships of joo tons and over and that a comparable air figure would probably need to include damage to aircraft by aircraft on airfields and in hangars and whether under their own power or in tow.

The Mathematics of Collision Avoidance in Two Dimensions

“…These matters have been discussed at some length in recent issues of this Journal by Calvert 2 and the contributors to the Forum, 3 and little more can usefully be said by a non-mariner at this stage. A decision on whether or not some further mathematical analysis would be worthwhile can best await the outcome of the current discussions.…”

“…ic shows how f varies with 0 in the two relevant quadrants. (Here/denotes eitherf A orf 3 It should be noted that the minimum value of J is tana, this value occurring when 0 = 90° or 270 0 . It is apparent from Fig.…”

“…It is sometimes, but not always, the same as the 'C.P.A.' of Captain Wylie,3 and it must not be confused with the 'instantaneous miss distance' of Calvert. 2 If, however, |«| > 90 0 , as in Fig.…”

“…To simplify the problem, let us suppose that both craft make instantaneous changes of course at the same instant when they are at a distance R apart, and that they continue thereafter on their new courses. Then, to achieve a 'miss distance' of R m , where R m a$ R, the combined manoeuvre must cause the relative velocity vector to rotate through an angle a, given by equation (3). Let us therefore consider the situation when the two craft, initially on collision courses, turn at the same instant through angles y A and y B (positive to starboard), and also change speed to V A ' and V B ' respectively ( Fig.…”

Dynamic optimal UAV trajectory planning in the National Airspace System via mixed integer linear programming

“…Following the tragic incident of mid-air collision of two commercial airlines in 1956 over Grand Canyon, a lot of effort was dedicated to streamline the traffic management and onboard collision avoidance mechanisms. 13,14 This included the maneuvers to avoid collision 13 and as discussed by Wylie, 15 it was proved not to be efficient enough. After a while researchers intended to focus collision avoidance by installing the traffic alert and collision avoidance system (TCAS) in some aircraft but the inadequacy of that has been discussed in various publications.…”