Windmill Output Calculator

Wind Power Equation:

\[ P = 0.5 \times \rho \times A \times V^3 \times C_p \]

Air Density (ρ):

kg/m³

Swept Area (A):

m²

Wind Speed (V):

m/s

Power Coefficient (Cp):

dimensionless

Power Output (P):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Wind Power Equation?

The wind power equation calculates the theoretical power output of a wind turbine based on air density, swept area of the turbine blades, wind speed, and the power coefficient that represents the turbine's efficiency.

2. How Does the Calculator Work?

The calculator uses the wind power equation:

\[ P = 0.5 \times \rho \times A \times V^3 \times C_p \]

Where:

\( P \) — Power output (watts)
\( \rho \) — Air density (kg/m³)
\( A \) — Swept area of turbine blades (m²)
\( V \) — Wind speed (m/s)
\( C_p \) — Power coefficient (dimensionless, 0-0.59)

Explanation: The equation calculates the kinetic energy available in the wind that can be converted to mechanical power by the wind turbine.

3. Importance of Wind Power Calculation

Details: Accurate wind power calculation is crucial for wind farm planning, turbine selection, energy production forecasting, and evaluating the economic viability of wind energy projects.

4. Using the Calculator

Tips: Enter air density in kg/m³ (typically 1.225 at sea level), swept area in m², wind speed in m/s, and power coefficient (typically 0.35-0.45 for modern turbines). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the maximum theoretical power coefficient?
A: The Betz limit states that no wind turbine can capture more than 59.3% of the kinetic energy in wind, making 0.593 the maximum possible Cp value.

Q2: Why is wind speed cubed in the equation?
A: Wind power is proportional to the cube of wind speed because kinetic energy increases with the square of velocity, and the mass flow rate is proportional to velocity.

Q3: How does air density affect power output?
A: Higher air density (colder temperatures, lower altitudes) increases power output, while lower density (warmer temperatures, higher altitudes) decreases it.

Q4: What is typical swept area for commercial turbines?
A: Modern utility-scale turbines have rotor diameters of 100-150 meters, resulting in swept areas of 7,850-17,700 m².

Q5: How accurate are these calculations for real-world applications?
A: This provides theoretical maximum power. Actual output depends on many factors including turbine efficiency, wind consistency, and transmission losses.