Analysis of Spread Moorings by Dimensionless Functions
Authors: Adams Roy B. 
Published: October 2008

ABSTRACT
Design or evaluation of spread moorings requires analysis of system response to environmental force of wind, current, and waves. Laborious hand calculation of critical variables (vessel translation, line tension, etc.) has been replaced by computer analysis. Since computers are not always accessible to operating personnel, these computer methods have been used to develop mathematical functions which simultaneously describe the response of many distinct mooring systems. These functions permit rapid, reasonably accurate analysis by graphic techniques.

INTRODUCTION
In offshore oil operations spread mooring systems are used to moor floating vessels on location. These mooring systems are characterized both by their mechanical components and by the angular pattern in which the anchors are distributed. The spread mooring patterns most frequently used are illustrated in Fig. 1, where an abbreviation in the form Nz is used to identify the mooring pattern. N denotes the number of mooring lines, and z is a suffix indicating a particular angular distribution of the lines. In particular, z = s is used to indicate maximum angular symmetry--a pattern with equal angles between all adjacent lines.
Design of such spread moorings or their evaluation for use in particular environmental conditions has in the past required lengthy hand calculation in which some inaccuracies resulted. Much more rapid and accurate analysis of spread moorings is now possible by use of a computer program developed to treat a wide variety of such moorings. This computer technique permits more accurate inclusion of multiline effects and of mooring line elasticity.
The computer program relates the critical mooring variables to forces exerted on the vessel by wind and sea conditions. Maximum line tension, maximum anchor load, maximum suspended line length between the chock on the vessel and the point where it touches the sea floor, and horizontal translation of the vessel are determined as functions of the total steady force.
Since such a computer program is not readily accessible to operating personnel, a study was initiated to seek an alternative method - a reasonably accurate yet rapid technique for analyzing spread moorings without a computer. For mooring systems with identical lines of uniform weight per unit length and sufficient line length so that considering the submerged weight of the line the catenary formed becomes tangent to the sea floor, this study resulted in the development of generalized mathematical functions which simultaneously relate the critical variables of many distinct moorings to the environmental forces. Graphic display of these functions provides a rapid method for analysis of such spread moorings.

THE MOORING ANALYSIS PROBLEM

Initial Mooring Configuration
When a floating drilling rig is moved to an offshore location, the first major operational procedure is mooring the vessel. This initial mooring configuration is characterized not only by the mechanical components (anchors, wire rope, chain, etc.) but also by the pattern of mooring lines and the tension initially set in each line. This initial configuration must be designed to minimize rig movement away from the hole during drilling operations without permitting excessive loads on individual mooring lines or anchors.