1. What is the Wind Turbine Power Equation?

The wind turbine power equation calculates the theoretical power available in the wind that can be converted to mechanical energy by a wind turbine. It's fundamental for wind energy system design and performance evaluation.

2. How Does the Calculator Work?

The calculator uses the wind turbine power equation:

Where:

• \( P \) — Power output (watts)
• \( \rho \) — Air density (kg/m³, typically 1.225 at sea level)
• \( A \) — Swept area of turbine blades (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 output is proportional to the cube of wind speed, making site selection critical for wind energy projects.

3. Importance of Wind Power Calculation

Details: Accurate power calculation helps in sizing wind turbines, estimating energy production, and evaluating project feasibility. It's essential for both small-scale and utility-scale wind energy projects.

4. Using the Calculator

Tips:

• For swept area, use \( A = \pi r^2 \) where r is blade length
• Typical Cp values range from 0.35-0.45 for modern turbines
• Standard air density at sea level is 1.225 kg/m³
• Wind speed measurements should be taken at hub height

5. Frequently Asked Questions (FAQ)

Q1: Why is wind speed cubed in the equation?
A: The kinetic energy in wind increases with the cube of velocity, meaning small increases in wind speed produce large increases in available power.

Q2: What is Betz's law?
A: Betz's law states that no wind turbine can capture more than 59.3% of the kinetic energy in wind (maximum Cp = 0.59).

Q3: How does air density affect power output?
A: Power is directly proportional to air density. Colder, denser air produces more power than warm air at the same wind speed.

Q4: What's a typical power coefficient for real turbines?
A: Most modern turbines achieve Cp values between 0.35-0.45 when accounting for various inefficiencies.

Q5: How do I calculate swept area?
A: Swept area is the area covered by rotating blades: \( A = \pi \times \text{(blade length)}^2 \).