Phase-Plane Analysis on Zig-Zag Test of a Ship with Asymmetrical Steady Turning Characteristic

Abstract

This paper treats of a phase-plane analysis on the zig-zag test of a ship with asymmetrical steady turning characteristics. Asymmetry in steady turning characteristics of a ship results in an asymmetrical phase-plane trajectory of zig-zag manouvre. Dividing this asymmetrical trajectory into two parts for positive and negative ψ region, the author has obtained a set of turning characteristic indices K and α. The indices thus obtained can interpret the assymetrical reverse spiral test results fairly well. The mathematical model employed is represented by the rudder-to-yaw response equation with a cubic-type non-linearity, i.e. T_1T_2/Kψ+T_1T_2/Kψ+1/Kψ+α/Kψ^3=δ+T_3δ