The rotor extracts aerodynamic power and thrust from the wind. With air density ρ, rotor area A and wind speed v:
P_wind = ½ρ·Cp·A·v³ (capped at rated power, 8 MW)
F_thrust = ½ρ·Ct·A·v²
Cp(β) = Cp_max·cos²(β), Ct(β) = Ct_base·cos²(β)
β is the blade pitch (feathering) angle. Feathering the blades — rotating them toward "flat to the wind" — sheds both power and thrust, which is exactly how real turbines survive high winds above their rated speed.
The floating platform is treated as a damped spring-mass system in two degrees of freedom: surge (horizontal offset x) restrained by the catenary mooring lines, and pitch (tilt θ) restrained mainly by hydrostatic buoyancy stiffness (the metacentric righting moment):
m·x″ = F_thrust + F_wave(t) − k_surge·x − c_surge·x′
I·θ″ = F_thrust·h_hub + M_wave(t) − k_pitch·θ − c_pitch·θ′
The three catenary mooring lines sit 120° apart. Catenary stiffness grows with pretension, so k_surge ∝ pretension. Each line's tension is its pretension plus stiffness times how far the platform has moved toward or away from that line's anchor:
T_i = max(0, T0 + k_line · (−x·cos φ_i))
- Wind speed — drives thrust (and hence surge/pitch) and, through the Cp curve, power output.
- Wave height — sets the amplitude of an oscillating wave-frequency forcing on top of the steady wind loads (real wave period ≈ 3.5·√Hs s).
- Mooring pretension — a stiffer mooring system (higher pretension) cuts surge offset and evens out line loads, but raises the baseline tension every line already carries.
- Blade pitch — the operator's main lever for keeping thrust, platform tilt and mooring loads inside safe limits once wind exceeds the ~12 m/s rated speed.
This mirrors real floating wind design: turbines like Hywind and WindFloat use exactly this pitch-to-feather strategy, and mooring engineers size line pretension against the same surge/tension trade-off shown here.