A Consideration on the Effective Domain

Abstract

Since the size of the effective domain is an important quantity for the estimation of traffic capacity, it has been studied by measuring two-dimensional separation between ships. A theoretical estimation for the effetive domain is tried by defining it as the totality of (R_1^^^→-V_2^^^→t) expanded with a radius equal to that of the geometrical collision radious over a time range from t=t_0 to t=t_0+T, where R_1^^^→ is the position of a keeping-way vessel, V_2^^^→ is the velooity of a giving-way vessel, and T is the sum of time length necessary for the detection of the change in the velocity of the keeping-way vessel and that for the evasive motion of the giving-way vessel. When R_1^^^→ is equal to R_1^^^→_(t=t_0)+V_1^^^→(t=t_0)t, the effective domain is equal to the manoeuvable limit. However, the velocity of the keeping-way vessel is not guaranteed to be constant, and consequently, it is given as a representation of a group of equi-probability curves. These equi-probability curves may be obtained by the statistical investigation of behaviors of vessels. The time length, T, is obtained from the distribution of motional characteristics of vessels and the minimum value should be about 5τ_1, +3τ_2, where τ is the characteristic time and is equal to (ship length)/(speed) and suffixes, 1 and 2, correspond to the keeping-way vessel and giving-way vessel respectively. Above consideration allows derivation of formulea for the effective domains for different encounter condition, e.g., crossing, taking over, by adopting equi-probability curve corresponding to a probability of 99.99%, which is obtaned from the study of collision probability.