Computer Simulation of Single Point Moorings
Authors: Muga Bruce J. , Freeman M.A 
Published: October 2008

ABSTRACT
The behavior of a vessel moored to a single point has been studied analytically using the impulse response functions and constant inertia coefficients in a time domain formulation of the governing equations of motion. The excitations are considered to be due to wind and/or current from any direction. The output consists of time histories of vessel displacement (surge, sway and yaw) and hawser line loads. The results have been compared with reduced scale model studies.
The work differs from previous works on the subject in several important aspects. First, the results are presented in terms of the actual time histories rather than frequency graphs. Second, the solutions of the equations of motion are obtained using both a moving coordinate system (i.e., fixed in the vessel) and an inertial system (fixed in space). Thus, no assumptions regarding small displacements and/or motions are required. Third, the influences of the previous histories of motion of the vessel are taken into account via the impulse response functions.
The results of this work have direct application to the analysis and design of single point mooring systems. Mooring system requirements for differing environmental conditions and specific vessels (whose characteristics are known) can be evaluated over a wide range of circumstances given the predicted time histories of line loads and vessel motions. The results of reduced scale model tests (which are very expensive) can be greatly extended by use of the technique reported herein.
A method is presented for evaluation of the performance of single point ship-mooring systems under the influence of wind and current. For one specific ship-mooring system, facsimiles of the time histories of line loads and vessel displacements are presented. Summary results of line loads, current speeds and direction, wind speeds and direction and mooring line stiffnesses are presented.
It is concluded that the method presented herein is vastly superior to present practice of utilizing empirical data (obtained largely from reduced scale model studies) in order to evaluate the performance of proposed single point mooring systems.

INTRODUCTION
The behavior of single point mooring systems has received intense interest within recent years. TI1is interest has been heightened by the increasing awareness of environmental risks arising from the failure of such systems and/or excessive vessel motions.
Although design criteria have been in use for a number of years, these criteria were largely obtained from reduced sea expensive model tests. The latter are expensive, time consuming and require unique facilities to ensure accurate prediction of prototype behavior. moreover, model tests alone, by their very nature, are limited in the scope of phenomena which can be studied. Therefore, an alternative method for studying single point moorings not burdened by these inherent disadvantages would appear to be an attractive development.
The study reported on herein is intended to contribute to this development. This study is a report on the numerical 'results obtained from a solution of the time-domain equations of motion.