Hydrodynamic Forces Acting on a Longitudinally Non-symmetric Ship Under Manoeuvring at Low Speed

Abstract

This paper presents results of circular motion tests with large drift angles for a stern trawler under manoeuvring at low speed. The hull form used is longitudinally non-symmetric and differs from hull forms ever investigated in previous works. Since the non-symmetry emphasizes defects of previous mathematical models, a mathematical model is developed for both longitudinally non-symmetric and symmetric ships. Hydrodynamic lateral force and yaw moment are assumed to consist of two components, that is, forces caused by cross flow effect and lift forces affected by stall effect. Local drag coefficients in conventional models are regarded as a polynomial of longitudinal ordinate x. They cannot explain experimental values under towing abeam, or are beyond rational values as steady-state drag coefficients. To bypass this difficulty, we regard local drag coefficients as a quadric form of longitudinal ordinate x and yaw rate r. These coefficients explain the cross flow effect for the trawler and a car carrier, and are within rational values as steady-state drag coefficients. Derivatives of the lift forces are determined from three experimental conditions where drift angles are 0,90 and 180 degrees. The derivatives coincide with theoretical values derived from a slender body theory. Stall effect is simply approximated by change in the derivatives of the lift forces. As a whole, values approximated for the lateral force and yaw moment agree with experimental values. In addition, experimental values of longitudinal force and heeling lever due to the lateral force from water surface for the trawler are presented.