This 2D side-view model is an independent, more detailed rigid-body twin of the 3D TLP simulation: instead of one lumped heave/surge pair, it solves three coupled degrees of freedom — heave z, surge x and pitch θ — for a hull held down by a bow tendon group and a stern tendon group spaced ±b from the centre of gravity.
Heave: m z̈ + c_z ż + k_z z = F_z(t) - (k_each/L)·x²
Surge: m ẍ + c_x ẋ + k_x x = F_x(t)
Pitch: I θ̈ + c_θ θ̇ + k_θ θ = M(t)
Tendon i (bow/stern): T_i = T₀/2 + k_each·(z + i·b·θ) + k_each·x²/(2L)
Each tendon's length change is computed from its exact geometry (Pythagoras: horizontal offset x, vertical offset z±bθ, against a fixed-length leg to its seabed anchor), not just added linearly. That geometric nonlinearity produces the real, well-documented TLP "set-down" effect: any surge sideways stretches both tendon groups a little regardless of direction, so the platform's mean heave position drifts measurably downward whenever surge motion is large — watch "Mean set-down" turn increasingly negative as wave height grows.
Wave forcing uses linear (Airy) deep-water theory, sampled independently at the bow and stern stations (±b) rather than at one point:
η(x,t) = (H/2)cos(ωt - kx), ω² = gk (deep water)
F_z(t) = ρgA·(H/2)·cos(kb)·cos(ωt) — heave excitation
M(t) = ρgAb·(H/2)·sin(kb)·sin(ωt) — pitch excitation (new: absent from the single-point 3D model)
Sampling two stations instead of one is what actually creates a pitch-exciting moment — a single-point force can never twist a rigid body about its own centre. Surge is still driven by Morison-type wave-particle inertia, as in the 3D model.
- Wave height / period — set the forcing amplitude and frequency; larger H drives more surge, which (via set-down) also pulls mean heave down.
- Water depth L — longer tendons soften every stiffness (k_z, k_x, k_θ all scale as 1/L), lengthening natural periods and increasing all three motions.
- Pretension T₀ — raising it stiffens surge and raises the tension floor on both tendon groups, the main design lever against slack-line "snap load" risk.
- Bow / stern tension — turns red at ≤ 0: that tendon has gone slack, a real TLP design-limiting failure mode.