A Phase Plane Analysis on Steering Motion of Directionally Unstable Tankers

Abstract

Full ships, such as supertankers, are generally poor in stability on course. Consequently the first-order linear equation of steering motion is no more accurate to describe steering performance of such ships, though it has so far been used successfully for other variety of ships. There have been a few ideas of improving this by introducing a simple nonlinear term to be added to linear equation proposed by Norrbin, Nomoto and Bech, e. g. Eq. (6) or Eq. (7). Making use of these approximate nonlinear equations of steering motion, the authors propose a procedure of defining the characteristic coefficients of a given ship by analysing the zigzag steering test records by means of the phase plane analysis. According to the results of applying this analysis on the zigzag test of directionally unstable supertankers and models, it is concluded that: (1) The second-order nonlinear equation works well to describe steering motion of unstable ships. (2) Phase plane analysis is proved to be a useful procedure to define the manoeuvrability of a given ship from steering trial, especially in case of unstable ships. (3) The first-order equations of motions do not work well in spite of introducing the nonlinear term, especially at frequent rudder movement.