1. What is the Wind Power Equation?

The wind power equation calculates the theoretical power available in the wind that can be captured by a wind turbine. It's based on fundamental physics principles of kinetic energy in moving air.

2. How Does the Calculator Work?

The calculator uses the wind power equation:

Where:

• \( P \) — Power (Watts)
• \( \rho \) — Air density (kg/m³, typically 1.225 at sea level)
• \( A \) — Rotor swept area (m²)
• \( v \) — Wind speed (m/s)
• \( C_p \) — Power coefficient (dimensionless, max 0.59 according to Betz's law)

Explanation: The equation shows that power increases with the cube of wind speed, making site selection critical for wind energy projects.

3. Importance of Wind Power Calculation

Details: Accurate wind power estimation is crucial for designing wind turbines, selecting appropriate sites, and predicting energy production for wind farms.

4. Using the Calculator

Tips: Enter air density (default is 1.225 kg/m³ for sea level), rotor area in square meters, wind speed in meters per second, and power coefficient (typically 0.35-0.45 for modern turbines).

5. Frequently Asked Questions (FAQ)

Q1: Why does wind speed have a cubic relationship with power?
A: The kinetic energy in wind increases with the cube of velocity because both the mass flow rate and the kinetic energy per unit mass increase with velocity.

Q2: What is Betz's law?
A: Betz's law states that no turbine can capture more than 59.3% of the kinetic energy in wind (maximum C_p = 0.593).

Q3: How does air density affect power output?
A: Power is directly proportional to air density. Colder air is denser, so turbines produce more power in winter than summer at the same wind speed.

Q4: What's a typical power coefficient for real turbines?
A: Modern turbines typically achieve C_p values between 0.35 and 0.45, with some reaching up to 0.5.

Q5: How do I calculate rotor area?
A: Rotor area A = π × (blade length)². For a turbine with 50m blades: A = π × 50² ≈ 7854 m².