Wind Speed at Height Calculator Formula

Understand the math behind the wind speed at height calculator. Each variable explained with a worked example.

Use the Wind Speed at Height Calculator

Formulas Used

Wind Speed at Target Height

speed_at_height = measured_speed * pow(target_height / measured_height, wind_shear_exp)

Speed Increase

speed_increase_pct = (pow(target_height / measured_height, wind_shear_exp) - 1) * 100

Power Ratio (V³ scaling)

power_ratio = pow(pow(target_height / measured_height, wind_shear_exp), 3)

Variables

VariableDescriptionDefault
measured_speedMeasured Wind Speed(m/s)6
measured_heightMeasurement Height(m)10
target_heightTarget Hub Height(m)80
wind_shear_expWind Shear Exponent0.143

How It Works

Wind Speed Profile with Height

Wind speed generally increases with height above ground due to reduced surface friction. The power law provides a practical approximation.

Formula

V2 = V1 x (H2 / H1) ^ alpha

Where V1 is measured speed at height H1, H2 is the target height, and alpha is the wind shear exponent. The standard value of alpha is 1/7 (0.143) for open terrain. Forested or urban areas use higher values (0.2-0.3).

Worked Example

Wind measured at 6 m/s at 10 m height. Estimate speed at 80 m hub height with alpha = 0.143.

measured_speed = 6measured_height = 10target_height = 80wind_shear_exp = 0.143
  1. 01Height ratio = 80 / 10 = 8
  2. 02Speed factor = 8 ^ 0.143 = 1.353
  3. 03Speed at 80 m = 6 x 1.353 = 8.12 m/s
  4. 04Power ratio = 1.353³ = 2.477 (nearly 2.5x more wind power)

Ready to run the numbers?

Open Wind Speed at Height Calculator