Statics of a three component mooring line

Catenary equations are solved for a three component mooring made up of two lines, connected at a point buoy or sinker where water depth and fairlead tension are given. This configuration is typical of deep water moorings and solutions are required for preliminary design of mooring systems and measurement of stability in service of moored floating platforms. The problem is transformed to a single polynomial equation of degree eight and is solved by Laguerre's iteration. Where there is no buoy or sinker the equation reduces to a quartic and can be solved in closed form. Elongation of the lines is shown to be equivalent to small uncertainties in the weights per unit length. The method is computationally efficient.