Wind speed at height: power-law and log-law extrapolation

How this calculator works

Wind slows down near the ground because of friction with grass, crops, trees and buildings. The rougher the surface, the slower the bottom layer and the steeper the increase with height. This is the wind shear. Weather stations measure at 10 m, but turbines spin at 20 m (small) to 150 m (utility), so converting a measured speed to hub height is the first step of any wind assessment.

This calculator applies the two standard models side by side over the whole 0–200 m profile:

• the power law (Hellmann), controlled by a single shear exponent α;
• the logarithmic law, controlled by the surface roughness length z₀ and, over tall vegetation, a zero-plane displacement d.

Choose a terrain class to load matching α and z₀ values, or enter your own. The stability option scales α for unstable (sunny afternoon) or stable (clear night) conditions, so you can see the range a real site experiences.

The formulas

The equivalent α of a log profile between two heights is ln(v₂/v₁) / ln(h₂/h₁); it shows that α is not a constant of the terrain alone: it depends on the heights involved.

Worked example: weather-station data to a 100 m hub

The default case takes a 10 m anemometer reading of 5.0 m/s over open, flat terrain (z₀ = 0.03 m, α = 0.14) and extrapolates it to 100 m.

• Power law: 5.0 × (100/10)^0.14 = 6.90 m/s
• Log law: 5.0 × ln(100/0.03) / ln(10/0.03) = 6.98 m/s

Both agree within about 1%. The wind is 38% faster at hub height, and because power scales with the cube of speed, a rotor at 100 m sees about 2.6 times the power density of one at 10 m. Change the terrain to suburbs/forest and the same 5 m/s at 10 m becomes over 9 m/s at 100 m with the power law. Measurements taken in rough terrain near the ground are very hard to extrapolate reliably.

How to read the results

• Speed at target height shows the two model estimates. A large disagreement means the input height is too low relative to the roughness, or the terrain is too complex for either formula.
• Wind power gain is how much more power the wind carries at the target height. This is the number that justifies a taller tower.
• Friction velocity u* is the turbulence scale of the surface layer, used in boundary-layer meteorology and dispersion models.
• The profile chart shows both laws from the ground to 200 m, plus the power gain on the right axis.

Typical values

IEC 61400-1 uses α = 0.2 as the “normal wind profile” for turbine design loads; offshore design uses 0.14.

Tips for better extrapolation

• Measure at two heights. α derived from two anemometers on the same mast (e.g. 40 m and 60 m) is far more reliable than a terrain-class guess.
• Stay close. Extrapolating 2–3× the measurement height is reasonable; 10× is a guess. A 60 m mast or a LiDAR campaign beats any formula for a large project.
• Use the Global Wind Atlas at 50 or 100 m instead of 10 m data where possible, then shift by small height differences only.
• Respect obstacles. Within about 20 obstacle heights downwind of a building or tree line, the flow is disturbed and neither law applies.
• Feed the result into the wind power density calculator or the wind turbine calculator in manual mode.

Limitations

Both laws describe a horizontally uniform, neutrally stratified surface layer. They do not capture speed-up over hills and ridges (often 10–40% on crests), channelling in valleys, sea-breeze circulations, low-level jets or the strong night-time shear of stable atmospheres beyond the simple scaling offered here. Above about 150–200 m the surface layer gives way to the Ekman layer, where wind direction also turns with height. For complex terrain, use flow models (WAsP, CFD) calibrated with on-site measurements.

Method & assumptions

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