Holding Position in the Ocean
Floating offshore structures — FPSOs, semi-submersibles, tension-leg platforms, and floating wind turbines — must maintain position against wind, waves, and current. Mooring systems provide this stationkeeping using multiple lines arranged in symmetric patterns. The catenary mooring is the most common configuration: heavy chain or wire rope hangs in a curve from vessel to seabed, with its weight providing the restoring force that resists environmental loads.
The Catenary Equation
The shape of a hanging chain under its own weight is a catenary curve, described by the hyperbolic cosine function. The horizontal tension T₀ is constant along the entire line (in the static case), while vertical tension increases linearly with height above the seabed. The line length, geometry, and tension at any point are determined by just two parameters: horizontal tension and line weight per unit length.
Restoring Force & Stiffness
When the vessel moves horizontally, the catenary profile changes — on the loaded side, more line lifts off the seabed, increasing tension; on the slack side, more line settles to the seabed. This asymmetric response creates a nonlinear restoring force that increases with offset. The mooring stiffness (force per unit displacement) determines how much the vessel moves under environmental loading.
Deepwater Challenges
In water depths beyond 1000m, the weight of steel chain catenaries becomes prohibitive — the vessel must support enormous top tensions even in calm conditions. The industry solution is hybrid mooring: chain at the seabed and fairlead for abrasion resistance, with lightweight polyester or HMPE rope for the long suspended span. This reduces top tension dramatically while maintaining catenary restoring characteristics.