Subsea Cable Lay Catenary

What is modelled

A heavy cable hanging between the ship and the seabed forms a catenary. At the touchdown point the cable is horizontal and carries only the horizontal tension H that the ship keeps on it. Higher up the tension grows by the cable weight per metre of height, so the ship carries the most. The seabed tension sets how far behind the ship the cable touches down.

Equations

• Catenary z = a (cosh(x/a) − 1) with a = H / w, weight per metre w in water.
• Suspended length s = a sinh(x/a) = √(D² + 2 a D); layback x = a acosh(1 + D/a).
• Tension T = H + w z, angle at the ship atan(s/a), vertical force w s.
• Cable laid per distance sailed: 1 + slack.

Checks run in the page

• Direct Runge-Kutta integration of the cable equations against the catenary.
• Tension profile against H + w z.
• Taut-cable limit against the parabola.
• Force balance at the ship.

Honest simplifications

The cable is perfectly flexible and inextensible, the sea is still, with no current, no ship motion or waves, no drag on the cable and a perfectly flat seabed. Real lays include current drag, ship heave, bending stiffness, burial plough loads and a changing bottom depth, and fixed numbers here are not a lay plan.

• Press Trench crossing and watch the top tension climb toward the breaking load.
• Press Light cable, low tension and see the cable hang almost straight down with a short layback.
• Raise the seabed tension and see the cable lie flatter and the layback grow.