Combine atmospheric boundary-layer wind profiles (power law and log law) with IEC 61400 turbine classes to evaluate hub-height wind speed, vertical rotor shear, rotor-equivalent wind speed and electrical power output in real time. Change surface roughness and atmospheric stability to study turbine siting and design.
Parameters
IEC turbine class (terrain)
Sets reference wind speed V_ref and annual mean V_avg
Surface roughness z₀
Used in the log law. Characteristic length of surface elements
The curve on the right is V(z). The tower, rotor disk, hub marker and wind vectors at top/hub/bottom are drawn. Colour encodes the magnitude of vertical shear.
Available power P (kW). ρ: air density 1.225 kg/m³, A: rotor swept area, Cp: power coefficient (≈0.45 typical).
Wind Shear Profile — Power and Log Laws for IEC 61400 Wind Turbines
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I have heard that wind is faster higher up — how much faster, really?
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Surface friction slows the wind near the ground in what we call the atmospheric boundary layer, and the flow speeds up to the free-stream value above it. With the default settings (grassland z₀=0.03, 8 m/s at 10 m), extrapolating to a 100 m hub gives about 11.1 m/s by the power law and 11.2 m/s by the log law — 40% faster than at 10 m. And because turbine power scales with V³, that yields roughly 2.7× the energy.
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So that is why towers keep getting taller. Should we just push the GE Haliade-X all the way to 220 m then?
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You would gain more energy, but a new problem appears — vertical shear. With a 150 m rotor the blade tip swings between z=175 m and z=25 m, where the wind differs by about 2.93 m/s even at the default α=0.143. Every revolution the blade sees that delta, dumping cyclic loads into the root, main shaft and pitch system. Once ΔV/V_hub exceeds 0.20 the IEC fatigue check tightens. The tool's verdict watches that ratio for you.
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Then can I just estimate the power using the hub-height wind speed?
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That is exactly where the rotor-equivalent wind speed (REWS) comes in. The real power scales with the rotor-averaged V³, so with V_top≈12.0, V_hub≈11.1 and V_bot≈9.1 the cube average is V_eq≈10.86 m/s. Hub-height alone gives 6691 kW, REWS gives 6262 kW — a 6.4% overestimate if you ignore it. That is why modern resource assessments measure the full profile with LiDAR and report REWS by default.
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How much does atmospheric stability move α around?
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A lot. In stable conditions (night-time, the ground cools and mixing stops) α jumps to 0.3–0.5. In an unstable convective afternoon you can see α as low as 0.10. The same site has completely different profiles day and night, which is why proper annual energy predictions include a Monin–Obukhov-based stability correction. Switching the "Atmospheric stability" selector here shows the recommended α in the verdict.
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So the IEC I (coastal) vs II/III (inland) class system bakes that in?
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Right. IEC 61400-1 defines V_ref (the 10-min mean with a 50-year return period) as I=50, II=42.5, III=37.5, IV=30 m/s, with V_avg = 0.2·V_ref. Coastal, low-roughness sites take Class I; gentler inland hills take III or IV. Bringing a Class III machine into a coastal site will burn through its fatigue budget on strong winds. Pick the class first, then size hub height and rotor diameter against it.
Frequently Asked Questions
The power law V(z)=V_ref·(z/z_ref)^α is the workhorse for wind-energy practice. A single exponent α extrapolates to any hub height and IEC 61400 specifies values such as α=0.143 for neutral onshore and α=0.20 for simplified design. The log law V(z)=V_ref·ln(z/z0)/ln(z_ref/z0) is physically more rigorous when the roughness length z0 is well known, which is why airports and ports tend to use it for routine wind monitoring. This tool computes both at once so you can compare them at hub height.
If the wind speed differs from rotor top to bottom by ΔV, each blade sees a periodic aerodynamic load every revolution, fatiguing the blade root, main shaft and yaw drive. IEC 61400-1 uses α=0.20 in its Normal Wind Profile (NWP) for fatigue load cases. This tool flags ΔV/V_hub > 0.20 as NG (excessive fatigue) and > 0.15 as a warning. Even with α=0.143, a 150 m rotor at 100 m hub still develops about 3 m/s of top-to-bottom shear, one of the leading drivers of fatigue life.
REWS converts the actual wind speed distribution across the rotor disk into a single equivalent free-stream wind speed that produces the same kinetic-energy flux. It is computed as a cube-weighted average, V_eq = ((V_top³+V_hub³+V_bot³)/3)^(1/3). Because turbine power scales with V³, using the hub-height wind speed alone overestimates output by several percent in sheared flow. This tool reports the difference between hub-height power and REWS power as the "equivalent power loss (%)".
In neutral conditions (windy, well-mixed) α is around 0.14; in stable conditions (night-time, ground cooling) α can rise to 0.30–0.50; in unstable conditions (sunny daytime, convective mixing) α drops to about 0.10. Annual energy yield assessments typically use α≈0.14–0.20, while fatigue analyses for night-time peak loads pick the higher stable-air value. The "Atmospheric stability" selector displays the recommended α so you have a sensible default when site measurements are not yet available.
Real-World Applications
Offshore and coastal wind farms: Offshore sites like the North Sea or Taiwan Strait have roughness z₀≈0.0002 (sea surface) and α≈0.10, which delivers 10–12 m/s hub-height winds at 100–150 m. Large machines such as Vestas V236 or Siemens Gamesa SG 14-222 reach annual capacity factors of 45–55%, nearly double typical onshore numbers. Wave loading, corrosion and scour bring their own challenges, and design follows IEC 61400-3 alongside the basic 61400-1 framework.
Onshore low-wind optimisation: At low-wind inland sites (annual mean 5–6 m/s, IEC III/IV) the recipe is longer blades (D=160–170 m) and taller towers (140–160 m) to capture both swept area and higher-altitude wind. The GE 6.1-158 and Vestas V162 were built for exactly this segment. Try Class III, hub 140 m, D=160 m here for a feel of low-wind design.
WRF / OpenFOAM micrositing: In complex mountain or hill terrain a single-α extrapolation is too crude, so mesoscale models (WRF) and microscale CFD (OpenFOAM ABL, WindSim, Meteodyn WT) compute the 3-D wind field. Use this tool as a quick 1-D reference, then anchor the final estimate to CFD and LiDAR-calibrated measurements.
LiDAR remote sensing: Doppler lidars such as ZephIR and WindCube measure the full wind profile from the ground up to about 300 m, far higher than a conventional 80–100 m met mast. Fitting the measured profile against the power law and log law in this tool back-calculates the local α and z₀, improving annual energy estimates by 5–10%.
Common Misconceptions and Pitfalls
The first trap is "α=0.143 (the 1/7th-power law) is a universal value". The 1/7th rule is an empirical fit for neutral conditions over smooth grass; offshore it falls to 0.10, over forests it rises to 0.20–0.30, and over cities it can exceed 0.30. Applying 0.143 blindly will under-predict offshore yield and over-predict forest yield. Plan for at least one year of met-mast observations to fit α site by site.
The second trap is estimating energy yield from hub-height wind alone, which becomes dangerous on large rotors. Even at the default settings (D=150 m, α=0.143) the REWS correction is 6.4%. For next-generation 200 m+ rotors the bias can reach 10%, equivalent to many millions in revenue forecast error. Always apply REWS (defined in IEC 61400-12-1 Annex E) or a coupled 3-D CFD analysis when assessing resource.
The third trap is fixing the log-law z₀ from a single aerial photo. Roughness varies with vegetation height, density, season (before and after leaf-fall) and crop growth stage. A bare spring field (z₀≈0.01) and a summer wheat field (z₀≈0.05) produce more than 5% spread at 100 m hub height. For annual averages use a seasonally-weighted z₀; for monthly forecasting use month-specific z₀.
How to Use
Enter reference height (10 m standard) and measured wind speed at that height (e.g., 9.5 m/s from anemometer data).
Input hub height (typical range 80–120 m for utility-scale turbines) and rotor diameter (90–220 m).
Simulator calculates power-law and log-law wind profiles, computes shear across rotor disk, and estimates hub-height power output normalized to IEC 61400-1 turbine class.
Worked Example
Reference: 10 m height, 10 m/s measured wind speed. Hub height 100 m, rotor diameter 120 m. Power-law exponent 0.2 (neutral stability) yields hub speed ~12.6 m/s. Log-law (z₀=0.05 m roughness) gives 12.3 m/s. Shear from blade tip to bottom: ΔV=1.8 m/s. Equivalent wind speed 12.8 m/s produces 4200 kW at hub, with 3.2% power loss from rotational averaging.
Practical Notes
Use power law (α=0.2–0.3) for flat terrain; switch to log law (z₀=0.01–0.1 m) near forests or urban areas where roughness dominates.
IEC 61400-1 Class II turbines rated 10 m/s at 10 m; verify input wind speed against anemometer calibration to avoid power performance underestimation.
Rotor shear ΔV exceeding 2.5 m/s indicates high fatigue load on blade root; inspect extreme wind direction changes.