How to use it
- Choose metres and m/s or feet and mph.
- Enter the rotor diameter (tip to tip) and the wind speed at hub height.
- Set the power coefficient Cp from the turbine’s data, or keep the example value.
- Change the air density for high or hot sites.
The formula
- Swept area A = π × (D ÷ 2)²
- Power in the wind = ½ × ρ × A × v³
- Turbine power = power in the wind × Cp, with Cp ≤ 16/27 ≈ 0.593
- Energy in 24 h = power × 24 h (at a constant wind, which real wind never is)
Worked example
A 10 ft rotor in an 18 mph wind:
- 10 ft = 3.048 m, so A = π × 1.524² = 7.3 m²;
- 18 mph = 8.047 m/s; v³ = 521.0;
- power in the wind = 0.5 × 1.225 × 7.3 × 521.0 = 2,329 W;
- with Cp 0.35: 815 W; the Betz limit would be 1,380 W.
Tips
- Wind at rooftop height is usually lower and more turbulent than at an open site or on a tall mast; that matters more than any other input.
- Use the average of v³, not the cube of the average wind, to estimate yearly energy; the power curve and a wind speed distribution do this properly.
- Compare turbines by swept area: a larger rotor captures more energy at the same wind than a higher generator rating suggests.