A MODEL OF VESSEL MOTION FOR DEAD RECKONING

Abstract

A 4-DOF vessel motion model for dead reckoning purposes is developed. The model is based on a system of nonlinear equations of vessel motion in calm water derived for the S175 container ship. The model additionally contains wind and wave influences. Wind is assumed to be constant for the velocity and direction. Waves are modelled as wind waves and irregular and assumed to be long-crested. Their direction equals wind direction. Only second-order wave disturbances (wave drift) are taken into account. They are determined on the basis of coefficients calculated by means of hydrodynamic software for ideal fluid. The model is programmed in the Scilab. Parameters of turning ability are determined and compared then with normative values governed by the IMO. A symmetric property test is proposed to validate the adequacy of the model. This algorithm supposes that sequences of rudder deflection, initial heading and true wind direction values are initially formed. The true wind direction and initial heading values may be of the same or reciprocal direction, or create an angle of 90 degrees. Inserted cycles for the elements of the above sequences are carried out, and matrices of end-of-time coordinates for each maneuver are calculated. Some of the matrices are transformed, and symmetric property conditions are formulated in a matrix form. The influence of time step value on a model output is studied. The maximum value of the distance between appropriate points of the trajectories during a maneuver is a criterion of their difference.