Enrichment · STEM Explorations · Energy

Twice the wind,
eight times
the power.

Type the rotor size and how many hours the wind blows at each speed. The estimator works out the power at every speed, the energy over the year and the capacity factor, and shows why a windy site matters more than a bigger turbine.

Estimate the powerWhat you get

The wind turbine power estimator

The worked example is made up: a 2.5 m, 1 kW turbine on a school farm with a year of wind sorted into five speeds. Nothing you type leaves this browser.

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What you get

Enrichment · STEM ExplorationsFree

What you finish with
The power in the wind and the turbine’s power at each speed, the energy over the hours listed, the average power and the capacity factor, with steps. It prints as a summary and downloads as a spreadsheet.
Who it is for
Students studying energy, engineering and environmental science classes, science teachers and families comparing small turbines.
Format
Browser calculator for a phone, tablet or computer, by touch or keyboard. m/s or mph. Up to 30 wind speeds. Prints a summary; downloads a spreadsheet (.csv); export and import a file.
Access
Free. No account, no sign-in and nothing to install. Everything you type stays in this browser; nothing is sent to Caveat.
Where it lives
The STEM Explorations space in Caveat Enrichment.
Support
Questions, a correction or a request: team@caveatacademic.com.

How to use it

  1. Name the turbine and type its rotor diameter.
  2. Keep or change the power coefficient and air density, and add the rated power if you know it.
  3. Add each wind speed with its hours.
  4. Read the energy and capacity factor, then try a windier site.
  5. Print the summary or download the spreadsheet.

Estimate the power

How the power is worked out

Area, density, the cube of the speed, and the share caught.

The worked example at 7 m/sSwept area4.91 m²π × 1.25²Power in 7 m/s wind1,031 W½ × 1.225 × area × 7³Turbine takes361 W× 0.35Over 1,800 hours650 kWhpower × hours ÷ 1,000The worked example at 7 m/sSwept area4.91 m²π × 1.25²Power in 7 m/s wind1,031 W½ × 1.225 × area × 7³Turbine takes361 W× 0.35Over 1,800 hours650 kWhpower × hours ÷ 1,000
At 7 m/s the wind through a 2.5 m rotor carries about 1,031 W; the turbine converts 35% of it.

The power equation

The wind’s kinetic energy flowing through the rotor each second is half the air density times the swept area times the wind speed cubed. A turbine can catch only part of it, the power coefficient; Albert Betz showed in 1919 that no turbine can catch more than 16/27, about 59.3 percent. Real small turbines reach roughly 25 to 40 percent, and stop rising at their rated power.

Why the site matters

Because power goes with the cube of speed, a site with winds a quarter faster yields nearly twice the energy, and average wind speed alone hides the strong hours that do most of the work. Wind near the ground is slowed by buildings and trees, which is why turbines go on tall towers. Real turbines also need a minimum cut-in speed to start turning.

Sources

  1. U.S. Department of Energy, Wind Energy Technologies Office. How a wind turbine works, and the small wind guidebook (energy.gov).
  2. Betz, A. (1920). Das Maximum der theoretisch möglichen Ausnützung des Windes durch Windmotoren. Zeitschrift für das gesamte Turbinenwesen, 26, 307–309.
  3. National Renewable Energy Laboratory. Wind resource data and capacity factor (nrel.gov).
  4. U.S. Energy Information Administration. Wind explained: electricity generation from wind (eia.gov).

The worked example is made up. The figures are estimates from the power equation. Your figures stay in this browser. Support: team@caveatacademic.com.