How this instrument works
Wind carries kinetic energy in proportion to the mass of air moving through a given area and the cube of its speed — that cubic relationship is the single most important fact about wind power: doubling wind speed doesn't double available power, it multiplies it by eight, which is why turbine siting focuses so heavily on finding consistently windier locations rather than just any breezy spot.
A turbine's rotor swept area — the circular area its blades trace as they spin — determines how much of that moving air it can intercept, and a power coefficient (Cp) captures what fraction of the wind's kinetic energy the turbine mechanically extracts. That fraction is capped by physics itself: German physicist Albert Betz proved in 1919 that no wind turbine design can ever extract more than 16/27, about 59.3%, of the kinetic energy in wind passing through its rotor — a hard ceiling known as the Betz limit, since capturing 100% would mean stopping the wind completely, which would prevent more air from flowing through at all.
Real turbines run well below even that theoretical Betz ceiling once mechanical and electrical losses are included, with well-designed modern turbines commonly reaching power coefficients around 0.35-0.45 in practice — still a substantial share of the wind's available energy, just short of the absolute physical maximum.
- Enter Air density (kg/m³) — 1.225 is standard sea-level air density and is the default; use a lower figure at high altitude.
- Enter Rotor swept area (m²) — the circular area the blades trace, roughly π times (blade length)².
- Enter Wind speed (m/s) — the wind speed hitting the rotor at this moment.
- Enter Power coefficient (Cp) — the turbine's extraction efficiency, capped at the Betz limit of 0.593; 0.35-0.45 is realistic for a well-designed turbine.
- Read Power output (W) — the turbine's electrical power output at this wind speed.
Worked example — a 100 m² rotor at 10 m/s wind speed
A turbine has a 100 m² swept area, standard air density of 1.225 kg/m³, faces a 10 m/s wind, and runs at a power coefficient of 0.4. Power = 0.5 × 1.225 × 100 × 10³ × 0.4 = 0.5 × 1.225 × 100 × 1000 × 0.4 = 24,500 W.
That 24,500 W (24.5 kW) output would roughly double to about 49,000 W if the power coefficient alone rose toward the Betz limit of 0.593, but it would rise far more dramatically — by a factor of eight — if wind speed simply doubled to 20 m/s with Cp unchanged, since power depends on the cube of wind speed but only linearly on Cp.
Questions
Why does doubling wind speed increase power eightfold?
Because the power formula includes wind speed cubed (v³), not just v — doubling any number that's cubed multiplies the result by 2³ = 8. This cubic relationship is why even a small increase in a site's average wind speed can dramatically improve a turbine's output, and why wind developers invest heavily in finding locations with consistently higher wind speeds rather than settling for a marginally breezy site.
What exactly is the Betz limit, and why does it exist?
The Betz limit, proven by physicist Albert Betz in 1919, is the theoretical maximum fraction of wind's kinetic energy any turbine design can extract — 16/27, about 59.3%. It exists because a turbine slows the wind passing through it to extract energy, but it can never stop that wind completely (a 100%-efficient turbine would need to be a solid wall, blocking any further air from flowing through and being captured at all), so there's a physical trade-off between slowing wind enough to extract energy and letting enough wind keep flowing through.
What power coefficient should I use for a realistic estimate?
Well-designed modern utility-scale turbines commonly achieve power coefficients around 0.35-0.45 in real operating conditions, comfortably below the 0.593 Betz ceiling once mechanical, electrical, and aerodynamic losses are accounted for. Smaller or older turbine designs, and rougher approximations of turbine performance, sometimes run lower; checking a specific turbine's published performance curve gives the most accurate figure for that model.
How is rotor swept area calculated from blade length?
Swept area is the area of the circle the blade tips trace as the rotor spins, calculated as π times the blade length (radius) squared — a turbine with 10 m blades has a swept area of π × 10² ≈ 314 m². Manufacturers typically publish rotor diameter directly, so halve that figure to get blade length (radius) before squaring it.
Does air density change meaningfully with altitude or temperature?
Yes — air density falls at higher altitude and with rising temperature, both of which reduce available wind power for the same wind speed, since power scales directly with density. A turbine site at high elevation or in a hot climate needs either faster wind or a larger rotor to match the output of an otherwise identical turbine at sea level in cooler air; wind resource assessments typically use site-specific air density rather than the sea-level default.