MATHEMATICAL MODELLING OF SHIP'S RUDDERS OPERATION UNDER VARIOUS MANEUVERING MODES

Abstract

The availability of adequate mathematical models of the ship propulsion system is essential for developing effective ship control systems, building high-quality simulators, and studying the ship’s maneuvering behavior. With the advancement of new computing and information technologies, the mathematical models of the ship propulsion system need to meet higher requirements and cover wider applications. This leads to the need for continuous improvement of mathematical models, especially those of non-inertial forces acting on the ship. This work investigates the influence of the ship’s curvilinear movement on the rudder performance. Mathematical models of the forces and moments acting on the rudder at different values of the local drift angle and the rudder angle are derived. The resultant force on the rudder is decomposed into components due to the rudder lift, drag, normal force, and tangential force. Expressions for the coefficients of rudder hydrodynamic quality, reverse quality, and normal force are obtained. The existing mathematical models of the rudder hydrodynamic coefficients are analyzed and their limitations and applicability are discussed. New mathematical models of the rudder lift and drag coefficients are proposed, which take into account the aspect ratio, relative thickness, and angle of attack of the rudder. The proposed models are validated by comparing them with experimental data for NACA series rudders. t is shown how the lift and drag of the rudder, as well as the components of the resulting force, change for the maximum possible range of changes in the local drift angle and the rudder angle, for different values of the rudder aspect ratio and relative thickness. Keywords: mathematical models, ship rudders, curvilinear movement, longitudinal and transverse components of forces, dimensionless hydrodynamic coefficients.