Windmill 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 Velocity (V):

m/s

Power Coefficient (Cp):

dimensionless

Power Output (P):

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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, wind velocity, and power coefficient. It represents the maximum extractable power from wind energy.

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 velocity (m/s)
\( C_p \) — Power coefficient (dimensionless)

Explanation: The equation shows that power output is proportional to the cube of wind velocity, making wind speed the most critical factor in wind energy generation.

3. Importance of Wind Power Calculation

Details: Accurate wind power calculation is essential 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 (typically 1.225 kg/m³ at sea level), swept area (π × radius² for circular blades), wind velocity, 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: How does air density affect power output?
A: Power output is directly proportional to air density. Colder air is denser, so turbines generate more power in colder conditions at the same wind speed.

Q3: Why is wind velocity cubed in the equation?
A: The kinetic energy in wind is proportional to the cube of velocity, meaning doubling wind speed increases available power by eight times.

Q4: What factors affect the power coefficient?
A: Blade design, angle of attack, number of blades, and turbine efficiency all influence the power coefficient value.

Q5: How accurate is this calculation for real-world applications?
A: This provides theoretical maximum power. Actual output is lower due to mechanical losses, generator efficiency, and other practical constraints.