Tension-Leg Platform Tendon Dynamics

Wave Conditions

Wave height H 3.0 m

Wave period T 9.0 s

Mooring System

Water depth / tendon length L 500 m

Total tendon pretension T₀ 40 MN

Live Response

Heave z

0.00 m

Surge x

0.00 m

Min tendon tension

10.0 MN

Max tendon tension

10.0 MN

T_heave ≈ 0.0 s · T_surge ≈ 0.0 s (natural periods, real time)
Structural time runs 6× accelerated so surge is visible

How it works

A Tension-Leg Platform (TLP) is a buoyant floating hull held down by pre-tensioned vertical steel tendons anchored to the seabed. Because the tendons are nearly inextensible, heave, roll and pitch are stiffly restrained (tendon axial stiffness), while surge, sway and yaw stay compliant (restored only by the small horizontal component of tendon tension, like an inverted pendulum) — the defining trait of this mooring type.

Heave:  m z̈ + c_z ż + k_z z = F_heave(t),   k_z = n·E·A / L
Surge:  m ẍ + c_x ẋ + k_x x = F_surge(t),   k_x = n·T₀ / L
Tendon tension:  Tᵢ = T₀/n + (k_z/n)·z ± (T₀/n·L)·x

Wave kinematics use linear (Airy) deep-water theory. Surface elevation η(t) = (H/2)cos(ωt); a water parcel at rest depth z₀ ≤ 0 traces a circular orbit that decays exponentially with depth:

ξ(t) = -(H/2) e^(k z₀) sin(ωt),  ζ(t) = (H/2) e^(k z₀) cos(ωt)
dispersion (deep water):  ω² = g k,  ω = 2π/T

Wave height / period — set the forcing. Longer periods sit well below the stiff heave natural frequency, so heave stays small (the whole point of a TLP); surge, forced far above its own very soft natural frequency, is mass-dominated and also stays modest under a single regular wave.
Water depth L — longer tendons soften both k_z and k_x (both scale as 1/L), lengthening natural periods and increasing motion.
Pretension T₀ — the main tunable safety margin: raising it stiffens surge restraint and raises the tension floor, cutting slack-tendon ("snap load") risk in large waves.
Min tendon tension — turns red at ≤ 0: the tendon has gone slack and would suddenly re-tension with an impulsive snap load, a real design-limiting failure mode for TLPs.

The pitch tilt shown is a small-angle visual proxy driven by the fore–aft tension imbalance, not an independently integrated degree of freedom; heave and surge are the two DOFs actually solved here.

Tendons (mooring legs) Water particle orbits

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