Wind Speed at Height Calculator Formula
Understand the math behind the wind speed at height calculator. Each variable explained with a worked example.
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) * 100Power Ratio (V³ scaling)
power_ratio = pow(pow(target_height / measured_height, wind_shear_exp), 3)Variables
| Variable | Description | Default |
|---|---|---|
measured_speed | Measured Wind Speed(m/s) | 6 |
measured_height | Measurement Height(m) | 10 |
target_height | Target Hub Height(m) | 80 |
wind_shear_exp | Wind Shear Exponent | 0.143 |
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.
- 01Height ratio = 80 / 10 = 8
- 02Speed factor = 8 ^ 0.143 = 1.353
- 03Speed at 80 m = 6 x 1.353 = 8.12 m/s
- 04Power ratio = 1.353³ = 2.477 (nearly 2.5x more wind power)
Frequently Asked Questions
What is the wind shear exponent?
The wind shear exponent (alpha) describes how quickly wind speed increases with height. Smooth terrain like open water uses ~0.1, open land ~0.14, suburbs ~0.2, and cities ~0.3.
Why do taller turbines produce more power?
Higher hub heights access faster, more consistent winds. Since power scales with wind speed cubed, even modest speed gains translate to large power increases.
Is the power law always accurate?
It works well for neutral atmospheric conditions. During temperature inversions or strong convection, the logarithmic wind profile may be more appropriate.
Ready to run the numbers?
Open Wind Speed at Height Calculator