Hub Height Wind Speed Calculator

Calculator inputs

Hub Height Wind Speed Inputs

Reference wind speed Measured wind speed at the known reference height, in m/s.

Reference height Height where the reference speed was recorded, in meters.

Hub height Target turbine hub height, in meters.

Hellmann exponent (α) Typical values often range from about 0.10 to 0.40.

Roughness length (z₀) Terrain roughness parameter for the logarithmic law, in meters.

Displacement height (d) Use zero for open terrain without tall canopy effects.

Air density Used for wind power density estimation, in kg/m³.

Graph points Controls the number of points plotted on the wind profile graph.

Primary displayed result Both methods are always shown. This controls the main headline result.

Reset

Tip: Use the power law when a reliable shear exponent is available. Use the log law when roughness and displacement are better known.

Example data

Example Data Table

Scenario	Reference Speed (m/s)	Reference Height (m)	Hub Height (m)	α	z₀ (m)	d (m)	Power Law Result (m/s)	Log Law Result (m/s)
Open farmland turbine	6.80	40	100	0.16	0.08	0.00	7.87	7.80
Coastal low roughness site	7.30	30	120	0.11	0.02	0.00	8.52	8.60
Suburban mixed terrain	5.90	50	110	0.24	0.35	4.00	7.02	6.80

Formulas

Formula Used

1) Power Law

V_hub = V_ref × (H_hub / H_ref)^α

This method estimates wind speed change with height using the Hellmann exponent. It is widely used when the vertical shear behavior is known or approximated from site data.

2) Logarithmic Law

V_hub = V_ref × ln((H_hub − d) / z₀) / ln((H_ref − d) / z₀)

This method uses terrain roughness length and displacement height. It is useful when surface characteristics are known and boundary-layer assumptions are reasonable.

3) Wind Power Density

P_d = 0.5 × ρ × V³

Power density rises with the cube of wind speed. Even modest increases in hub-height speed can materially improve theoretical energy capture.

Instructions

How to Use This Calculator

Enter the measured wind speed at the known reference height.
Provide the target turbine hub height.
Enter the Hellmann exponent for the power-law estimate.
Enter roughness length and displacement height for the log-law estimate.
Set air density if you want wind power density results.
Select which method should appear as the main displayed result.
Click the calculate button to view the result, comparison table, and graph.
Use the CSV or PDF buttons to export the calculation summary.

FAQs

Frequently Asked Questions

1) What does this calculator estimate?

It projects wind speed from a measured reference height to a turbine hub height. It also compares power-law and logarithmic-law results, then estimates wind power density.

2) When should I use the power law?

Use the power law when you have a reasonable Hellmann exponent from local studies, mast data, or accepted terrain assumptions. It is simple and commonly used for preliminary assessments.

3) When is the log law more useful?

The logarithmic law is more useful when roughness length and displacement height are known. It better reflects terrain-driven boundary-layer effects near the surface.

4) Why do the two methods give different results?

They model vertical wind shear differently. The power law relies on an exponent, while the log law depends on roughness and displacement. Different site assumptions change the projected speed.

5) What is a typical Hellmann exponent?

Typical values can range from around 0.10 over smooth open terrain to about 0.40 in rougher or built environments. Site measurements remain the best source.

6) What is roughness length?

Roughness length is a terrain parameter that represents how strongly the surface slows near-ground wind. Water, grassland, forests, and cities each have very different values.

7) Why does the calculator show energy gain?

Wind power scales with the cube of wind speed. A modest speed increase at hub height can create a much larger change in theoretical energy potential.

8) Is this suitable for final turbine design?

It is best for screening, comparison, and early planning. Final design should use long-term measured data, turbulence analysis, wake studies, and standards-based assessment.