A design tool for floating offshore wind turbines (FOWTs) deployed at water depths of 50-1500 m. Choose Spar, Semi-Submersible, TLP or Barge, adjust rotor diameter, water depth, significant wave height and wind speed, and instantly see rotor thrust, overturning moment, static pitch angle and pitch natural period — together with a wave-period resonance check.
Reference wind at 10 m above sea. Hub value uses the power law alpha = 0.11
Results
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Hub wind speed (m/s)
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Thrust T (kN)
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Overturning moment (kNm)
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Static pitch angle (deg)
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Pitch natural period (s)
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Stability verdict
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Floater + turbine section — pitch animation
Sea surface, waves, floater, turbine and mooring lines. The turbine tilts according to the pitch angle; colour shows the stability margin (green / orange / red).
Thrust T uses air density rho = 1.225 kg/m³, thrust coefficient C_T = 0.8, rotor area A_R = pi(D/2)². V_hub is the hub-height wind from the marine power law alpha = 0.11.
Floating Offshore Wind — Spar/Semi-Sub Stability and Dynamic Response
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So a "floating" wind turbine literally sits on the ocean and isn't bolted to the seabed — why doesn't the wind just topple it?
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It's the same idea as a ship that rolls and then rights itself. When the rotor pushes sideways, the floater pitches forward a little. As soon as it tilts, the centre of buoyancy shifts downwind and a restoring moment appears between the centre of gravity and the new centre of buoyancy. We call that the restoring coefficient C_55, and it grows with the tilt angle, so the floater settles at an angle where wind and restoring balance out. Hywind Scotland actually runs at only 5-7 degrees of pitch at rated power.
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Then why are there so many different floater shapes — Spar, Semi-Sub, TLP, Barge?
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Good question — they're different strategies for generating that restoring moment. A Spar is a slender column with a draft above 100 m and a heavy ballast at the bottom, so the low centre of gravity acts like a pendulum. A Semi-Sub spreads 3-4 columns over the waterplane to gain a large metacentric height BM — basically a raft-style approach. A TLP is held down by vertical tendons under permanent tension, and a Barge is a wide, shallow pontoon that uses sheer waterplane area. Switch the floater type on the left and you'll see the static pitch angle and the natural period change dramatically for the same wind.
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Why is the pitch natural period a big deal?
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This is the single most important number in FOWT design. Real sea waves carry most of their energy at periods of 6-15 s, so if the floater's pitch natural period falls in that band you get first-order resonance and the pitch amplitude blows up. The golden rule is to "straddle the wave spectrum": Spars and Semi-Subs sit around 25-30 s, TLPs land around 2-4 s. In this tool, when the gap between the natural period and the dominant wave period drops below 2 s, you'll see a resonance warning fire.
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Are there real commercial FOWT farms running today?
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Yes — quite a few. Equinor's Hywind Scotland (2017, 5 × 6 MW Spars) was the world's first. Then came Kincardine (2021, 5 × 9.5 MW Semi-Sub) and Hywind Tampen (2023, 11 × 8.6 MW Spar, the world's largest so far). Japan ran a Fukushima demo and still operates a 2 MW Spar off Goto Island, and after auction rules came in in 2024 the country is aiming for GW-scale projects in the 2030s. The game-changing point of floating wind is that you can deploy turbines almost anywhere in the world's deep oceans.
Frequently Asked Questions
Compute rotor thrust T = ½·rho_air·C_T·A·V² at the hub, multiply by the lever arm from the waterline to the hub (hub-height + 10 m) to get the overturning moment M, then compute the pitch restoring coefficient C_55 = Mass·g·(BM + h_ballast). The static pitch is theta = M / C_55 [rad]. For a Spar, the small waterplane BM is offset by a deep ballast pendulum effect (about draft/3), which gives most of C_55.
Both can keep the static pitch within a few degrees, but they suit different conditions. A Spar uses a deep ballast (draft 100 m+) to lower the centre of gravity, fits deep sites (>200 m water depth such as decommissioned gas fields), and naturally separates its pitch natural period from the wave spectrum, but it cannot be assembled in shallow harbours. A Semi-Submersible uses 3-4 columns spread on the waterplane to gain a large metacentric height BM ~ 10 m, allowing a shallow draft of ~20 m and quayside assembly, but the larger waterplane area collects more wave loads and the hull is heavier.
Ocean wave spectra concentrate energy around peak periods of 6-15 s. If the floater's pitch natural period T_theta falls in that band, first-order resonance amplifies pitch motion, causing structural fatigue, capacity-factor loss, and unsafe crew transfer. The FOWT design rule is T_theta > 20 s or T_theta < 5 s — Spars typically aim for ~30 s, Semi-Subs ~25 s, and TLPs 2-4 s, all "straddling" the wave spectrum. This tool warns when the period gap drops below 2 s.
A TLP (Tension Leg Platform) restores with vertical tendons under permanent pretension, giving very small heave/pitch/roll. It has a strong commercial track record in oil platforms but is still at demonstration scale for FOWT (e.g. PelaStar) because tendon and seabed-anchor costs are high. A Barge is a shallow-draft (~7 m) flat pontoon: cheap and easy to assemble at quay but very wave-sensitive, so it suits sheltered seas such as inner bays or aquaculture sites.
Real-World Applications
Commercial FOWT farms: Hywind Scotland (2017, 5 × 6 MW Spar, UK) was the world's first commercial floating-wind project. Kincardine (2021, 5 × 9.5 MW Semi-Sub, UK), Hywind Tampen (2023, 11 × 8.6 MW Spar, Norway, currently the largest), and WindFloat Atlantic (2020, 3 × 8.4 MW Semi-Sub, Portugal) are all in operation. Japan ran the 2013-2020 Fukushima Forward demo (now decommissioned) and still operates a 2 MW Spar off Goto Island, and is targeting GW-class deployment in the 2030s after the 2024 auction rounds.
Re-using deep-water gas fields: Decommissioned oil and gas fields in the North Sea and offshore Norway (water depths 100-300 m) have ready-made subsea pipelines, power cables and offshore helipads. Hywind Tampen actually supplies electricity to the Snorre and Gullfaks fields to electrify ageing oil operations and cut CO₂ emissions — a high-profile case of FOWT reusing existing offshore infrastructure.
Hydrogen and green-fuel production: Far-offshore FOWTs with no cable route to shore can host an electrolyser to convert wind power into hydrogen, ammonia or methanol on the platform itself. Pilot "Power-to-X" projects are underway in the North Sea, Mediterranean and around Japan, and Europe has published several proposals for GW-scale offshore hydrogen hubs in the 2030s.
CAE workflow and condition monitoring: Commercial FOWTs are designed with coupled aero-hydro-mooring-control simulators such as OpenFAST (NREL), OrcaFlex, SIMA and Bladed, running long time-domain analyses under JONSWAP wave spectra. A linear tool like this one is used for early screening — pitch angle and natural period sanity checks — before non-linear time-domain runs evaluate fatigue (DEM) and extreme response (DEL). Operators are also starting to use SCADA-based natural-period tracking to detect mooring corrosion or ballast change remotely.
Common Misconceptions and Pitfalls
The biggest trap is "trusting the static pitch angle alone." This tool reports the mean pitch under a steady wind load, but in real seas the combined effect of waves, gusts and pitch control pushes the dynamic pitch amplitude to 1.5-3× the static value. Design assessment requires time-domain simulation under NTM (Normal Turbulence Model) plus a JONSWAP wave spectrum to evaluate maximum pitch (DEL — design equivalent load) and fatigue accumulation (DEM — damage equivalent moment) separately. Treat this tool as an early-stage screen, not a final verdict.
Second misconception: "A Spar is just a deep cylinder, nothing tricky." With a draft above 100 m, a Spar cannot be erected in port — it has to be towed on its side, up-ended in deep water, fitted with the turbine, and then towed to the installation site. Only a handful of yards and heavy-lift vessels worldwide can do this. Hywind Tampen, for example, built all eleven concrete Spars at Stord yard in Norway. A Semi-Sub is easier to assemble at quay, but pays for it in heavier wave loading and harder dynamic-stability work. Pick the platform with full awareness of this trade-off.
Third pitfall: "Mooring lines just hold position." FOWT moorings — catenary for Spar/Semi-Sub or tendons for TLP — also provide significant horizontal stiffness in surge/sway and rotational stiffness in yaw. A mis-sized mooring can leave the pitch stable while letting the platform resonate horizontally or losing yaw alignment with the wind. Line-tension cycling is also the leading cause of anchor pull-out and fatigue failure of chain/rope segments; some European projects have had to swap mooring lines after only 3-5 years. Floater, mooring and turbine control must be designed as a coupled system from the start.
How to Use
Input turbine rated power (MW), hub height (m), and rotor diameter (m) based on your FOWT specification.
Enter water depth (m) to establish mooring system stiffness and added mass coefficients for your spar or semi-submersible platform.
Run the simulator to compute hub wind speed at rated conditions, thrust force (kN), overturning moment (kNm), static pitch angle, pitch natural period, and stability verdict against DNV-GL or ABS criteria.
Worked Example
For a 12 MW turbine with hub height 112 m, rotor diameter 178 m, deployed in 200 m water depth: hub wind speed yields ~11.5 m/s at rated power, rotor thrust reaches 2850 kN. The overturning moment (thrust × hub height) calculates to approximately 319,000 kNm. Static pitch angle stabilizes at 18 degrees. Pitch natural period of 8.2 seconds confirms separation from wave excitation (typical peak periods 10–14 s). Stability verdict: PASS if metacentric height exceeds 4 m and restoring stiffness remains positive across the operating envelope.
Practical Notes
Spar platforms suit deepwater (300–3000 m) with narrow draft; semi-submersibles fit transitional depths (50–300 m) with larger spread footprints and mooring stiffness tuning.
Overturning moment directly couples to wind shear exponent and surface roughness; adjust hub height conservatively to avoid resonance near dominant sea-state periods (typically 8–12 s).
Stability verdict flags pitching instability if natural period drops below 6 s or metacentric height falls below 3 m; increase platform buoyancy or stiffer mooring chains accordingly.