Wind Speed At Height Log Power Law Calculator
Our meteorology & atmospheric science calculator computes wind speed at height log power law accurately. Get results you can export or share.
Reviewed by Daniel Agrici, Founder & Lead Developer
Formula
Log: V(z) = Vref*ln(z/z0)/ln(Zref/z0); Power: V(z) = Vref*(z/Zref)^alpha
Where V(z) is speed at target height z, Vref is reference speed at Zref, z0 is roughness length, and alpha is the power law exponent.
Worked Examples
Example 1: Wind Turbine Hub Height Extrapolation
Problem:Weather station measures 10 m/s at 10 m. Extrapolate to 80 m hub height over agricultural terrain (z0=0.03 m, alpha=0.143).
Solution:Log: V(80) = 10*ln(80/0.03)/ln(10/0.03) = 10*7.888/5.809 = 13.58 m/s\nPower: V(80) = 10*(80/10)^0.143 = 10*1.349 = 13.49 m/s\nu* = 10*0.4/ln(10/0.03) = 0.689 m/s\nPower density = 0.5*1.225*13.58^3 = 1534 W/m2
Result:Log: 13.58 m/s | Power: 13.49 m/s | Density: 1534 W/m2
Example 2: Urban Wind Assessment
Problem:Estimate wind at 50 m over urban area (z0=1.0 m, alpha=0.30) given 5 m/s at 20 m.
Solution:Log: V(50) = 5*ln(50/1.0)/ln(20/1.0) = 5*3.912/2.996 = 6.53 m/s\nPower: V(50) = 5*(50/20)^0.30 = 5*1.316 = 6.58 m/s\nu* = 5*0.4/ln(20/1.0) = 0.668 m/s\nPower density = 0.5*1.225*6.53^3 = 171 W/m2
Result:Log: 6.53 m/s | Power: 6.58 m/s | Density: 171 W/m2
Frequently Asked Questions
What is the logarithmic wind profile?
The logarithmic wind profile describes how wind speed increases with height above ground in the atmospheric surface layer the lowest 50 to 200 meters. Derived from Monin-Obukhov similarity theory under neutral stability conditions it states that speed at height z equals friction velocity divided by the von Karman constant times the natural log of z over roughness length. This profile is most accurate in the constant-flux layer where wind direction is approximately constant and mechanical turbulence dominates. It is preferred for wind energy resource assessment air pollution dispersion modeling and meteorological analysis when roughness information is available.
What is the power law wind profile?
The power law is an empirical approximation relating wind speed at a target height to a reference using V(z) = Vref times (z/Zref) to the power alpha. It is simpler than the log profile requiring only reference speed two heights and an exponent without roughness length. The standard exponent of one-seventh or 0.143 was derived for flat terrain with moderate roughness. The two methods agree well for height extrapolation ratios up to about 3:1 but can diverge significantly for larger ratios or non-neutral stability. The power law is used when detailed surface characterization is unavailable while the log law is preferred for rigorous engineering.
How does atmospheric stability affect wind profiles?
Atmospheric stability significantly modifies the vertical wind profile from its neutral logarithmic form by changing turbulent mixing intensity. In unstable conditions like sunny afternoons enhanced mixing brings momentum downward reducing shear and creating more uniform profiles. In stable conditions like clear nights suppressed mixing leads to stronger shear and potentially very light surface winds even with strong winds aloft. Monin-Obukhov theory accounts for stability through correction functions based on height to Obukhov length ratio. Ignoring stability can introduce 20 to 40 percent errors in wind speed extrapolation especially for large height differences.
Why is wind speed extrapolation important for wind energy?
Modern wind turbine hub heights have increased from about 30 m in the 1990s to 80 to 120 m or more but most weather stations measure wind at 10 m height. Extrapolating speed to hub height is essential for wind resource assessment and project feasibility analysis. Since wind power is proportional to the cube of speed even small errors in extrapolation produce large energy estimate errors. A 10 percent speed overestimate translates to roughly 33 percent power overestimate affecting project financial viability. Modern campaigns deploy met towers or lidar at hub height to reduce uncertainty in speed extrapolation.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy