Analysis of the Tension Leg Platform
Authors: Paulling J.R. , Horton E.E. 
Published: December 2007

Abstract
The tension leg platform is a type of moored stable platform whose buoyancy exceeds the weight. The supplementary equilibriating downward force is supplied by tensioned vertical anchor cables. For such a platform, heave, roll and pitch motions will be suppressed. In order to design a reliable anchoring system, it is necessary to predict accurately the forces in the mooring legs predict accurately the forces in the mooring legs induced by wave action and the platform motions. A method of predicting the platform motions and these forces in regular or random waves is developed using a linearized hydrodynamic synthesis technique. Model experiments have been conducted whose results display good agreement with predictions.

Introduction
The term "tension leg platform" is used here to describe a moored floating stable platform whose buoyancy exceeds the weight. The supplementary downward force required to maintain equilibrium of vertical forces is supplied by vertical mooring cables which are under tension at all times. It is seen that such a platform, moored by three or more anchors, is free to surge, yaw, and sway in the horizontal plane, but the motions of roll, pitch, and heave are suppressed. In many cases, by proper choice of parameters, the former three motions in the horizontal plane may be "de-tuned" from any significant wave frequencies, and the resultant forced motions in a seaway will be small. The absence of heave, roll and pitch, together with minimal lateral motions, make the concept especially attractive for many deep-water operations such as oil drilling undersea mining and recovery or emplacement of heavy objects. (See Fig. 1).
An important design consideration is the total static plus time-dependent load in the mooring legs of the structure. At any instant of time, the total force in the mooring legs will consist of the aforementioned weight/buoyancy discrepancy, plus a time varying component induced by a combination of the incident waves and the lateral motion of the platform. In order for the mooring system to be platform. In order for the mooring system to be reliable, it is necessary that
(1) the total tension equal to the sum of the time-dependent plus steady-state terms should not become zero at any time and
(2) the maximum tension in any line at any time should not exceed the tensile capacity of the anchor or cable.
It is seen that fulfillment of these conditions insures that an anchor cable will not be subjected to a sudden slackening, followed by an abrupt jerk, nor is there danger of failure of an anchor leg. The designer may choose appropriate geometric parameters for the platform in order to satisfy these conditions provided that he has a reliable method of predicting and analyzing the structure's behavior.
Two general methods are available for analysis of the performance of such marine structures. In the first, we proceed on the basis of classical hydrodynamic theory to seek a solution to Laplace's equation in the fluid region subject to certain boundary conditions. These include kinematic conditions on the free surface and surface of the structure itself, a constant-pressure dynamic condition on the free surface, a dynamic condition derived from the rigid-body equations of motion on the wetted surface of the structure, and other conditions far from the body that are necessary for uniqueness. Such an approach, while yielding great insight into the fundamental fluid phenomena present, is confronted with almost insurmountable present, is confronted with almost insurmountable computational difficulties in dealing with all but the most geometrically simple bodies.
The second method is less exact in principle but more tractable in dealing with geometrically complex configurations. This procedure, which is the one selected for the present analysis, is termed hydrodynamic synthesis. Here we consider a complex structure to be assembled from a group of simpler bodies whose individual hydrodynamic properties are known. The fundamental assumption is then made that the hydrodynamic force on the assembled structure is equal to the sum of the forces on the component bodies.