Wind Shear Hub Height Correction Calculator
Correct measured wind speed to turbine hub height using the wind shear power law.
Pick terrain class and measurement height for an accurate hub speed.
Wind speed at the ground is not wind speed at the turbine. Friction with the surface slows the lowest wind layer; above it, wind accelerates with height. The turbine rotor at 80 to 120 meters experiences a significantly different wind speed than your 10-meter anemometer. Without correcting for this, every estimate of annual energy production is wrong — usually low.
The wind shear power law.
V_h = V_ref × (h / h_ref)^α
Where:
- V_h = wind speed at hub height
- V_ref = wind speed measured at reference height
- h = hub height (meters)
- h_ref = reference height (meters)
- α = wind shear exponent (terrain-dependent)
The shear exponent α is the key — it captures how aggressively wind speed grows with height. It depends entirely on what’s underneath the wind:
| Terrain | Shear exponent α |
|---|---|
| Open water, smooth ice | 0.10 |
| Open grass, low crops | 0.14 (standard reference) |
| Sparse rural, scattered farms | 0.17 |
| Suburbs, tree shelterbelts | 0.22 |
| Dense suburbs, forest | 0.28 |
| Urban, broken terrain | 0.35-0.40 |
For wind resource assessment, α = 0.14 is the standard reference value (smooth open terrain). It’s also called the “1/7 law” because 1/7 ≈ 0.143.
Why the exponent matters so much.
The power law is non-linear. A higher exponent makes hub-height wind significantly faster than ground wind:
For a 6 m/s wind at 10 m, corrected to 80 m hub height:
- α = 0.10 (smooth water): V_h = 6 × (80/10)^0.10 = 6 × 1.231 = 7.4 m/s
- α = 0.14 (open grass): V_h = 6 × (80/10)^0.14 = 6 × 1.345 = 8.1 m/s
- α = 0.22 (suburbs): V_h = 6 × (80/10)^0.22 = 6 × 1.604 = 9.6 m/s
- α = 0.35 (urban): V_h = 6 × (80/10)^0.35 = 6 × 2.082 = 12.5 m/s
The same 6 m/s ground reading translates to anywhere from 7.4 to 12.5 m/s at the rotor depending on terrain. Since turbine power scales with wind speed cubed, that’s a factor of 4 to 5 difference in available power.
Picking the right shear exponent.
For real wind farm siting, you measure at multiple heights and calculate α directly from the data:
α = ln(V₂ / V₁) / ln(h₂ / h₁)
A typical meteorological tower for resource assessment has anemometers at 10 m, 40 m, 60 m, and 80 m. You compute α between adjacent heights and use the value that best matches the height range you’re predicting into.
For early-stage scoping when you only have one ground measurement, use the terrain class lookup. Refine as soon as you have multi-height data.
Limits of the power law.
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It breaks down close to the ground. Below about 5 meters, wind is dominated by individual obstacles (buildings, trees), not by smooth shear.
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Stable vs unstable atmospheres. The power law assumes a neutral atmosphere. Stable boundary layers (cold nights over warm ground) have stronger shear than the table values suggest; unstable layers (sunny afternoons) have weaker shear. Daytime estimates may be 10-20% off from neutral predictions.
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It doesn’t capture turbulence. Two sites with identical mean shear can have wildly different turbulence intensity, which affects turbine fatigue more than mean power output.
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It’s a smooth approximation. Real wind profiles bend, especially around inversion layers and over heterogeneous terrain.
For most siting decisions, the power law gets you within 5-10% of the truth. Beyond that, you need on-site multi-height measurement.
Hub height as an engineering decision.
Larger turbines benefit twice from hub height: they sit higher (more wind) and have larger rotors (more swept area). Hub heights have climbed from 60 m in the 1990s to 120-180 m for modern offshore turbines. Each 20 m of additional hub height typically yields 4-7% more energy in moderate-roughness terrain.
The economic tradeoff: taller towers cost more (steel + foundation + cranes). For a 3 MW turbine, every additional 20 m of tower adds roughly 8-12% to the installed cost, which has to be offset by the extra energy generated. In low-shear sites (offshore, plains), the height premium pays back slower than in high-shear sites (forested, mountainous).
Single-site vs distributed measurement.
If you have one anemometer at 10 m, the power law is your only correction. If you have a met tower with anemometers at multiple heights, you can fit α to your actual data instead of looking it up. The latter is what real wind farm developers do — siting decisions on a multi-million-dollar installation aren’t made on a single number from a table.