A New Procedure of Analysing Zig-zag Test

There are a number of procedures of analysing the zig-zag test to obtain the steering quality parameters of a relevant ship, ranging from the simple method with the first-order (K and T) equation to the phase-plane analysis taking the higher-order time constants and non-linearity into account.Growing importance of closed-loop studies of steering control and increasing number of less course-stable ships (e. g. very large tankers) call for the latter type of comprehensive mathematical model of steering response. However, it is not an easy task, unlike the simple K-T analysis, to define all the parameters involved in such mathematical model from a zig-zag test record. The more numbers of parameters to be defined, the harder to keep the numerical accuracy and to assure the feasibility of such analysis.The present paper relates to a new approach to this task which proved promising. That is, (1) to adopt numerical filtering to minimize the noise involved in the yaw-rate record and at the same time to obtain a reasonably noise-free yaw-acceleration ; the result gives us a measured yaw-acceleration to yaw-rate phase-plane trajectory of a relevant zig-zag test.(2) to adjust the parameters of the mathematical model built in an analogue computer by turning a number of knobs, keeping one eye to the phase-plane trajectory displayed on a cathode-ray oscilloscope, so that the displayed trajectory coincide with the measured one.The mathematical model employed is the rudder-to-yaw response equation with a cubic-type non-linear term, i. e.T1T2ψ+ (T1+T2) ψ+ψ+αψ3=Kδ+KT3δ