Power From Wind Turbine Calculator

Wind Turbine Power Equation:

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

Efficiency Cp (%):

Air Density ρ (kg/m³):

kg/m³

Swept Area A (m²):

m²

Wind Speed V (m/s):

m/s

Power Output:

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1. What is the Wind Turbine Power Equation?

The wind turbine power equation calculates the theoretical power output of a wind turbine based on wind speed, turbine efficiency, air density, and swept area. It represents the maximum extractable power from wind energy.

2. How Does the Calculator Work?

The calculator uses the wind turbine power equation:

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

Where:

\( P \) — Power output (Watts)
\( C_p \) — Power coefficient (efficiency as decimal)
\( \rho \) — Air density (kg/m³)
\( A \) — Swept area of turbine blades (m²)
\( V \) — Wind speed (m/s)

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

3. Importance of Wind Power Calculation

Details: Accurate power calculation is essential for wind farm planning, turbine sizing, energy production forecasting, and economic feasibility studies of wind energy projects.

4. Using the Calculator

Tips: Enter efficiency as percentage (typically 35-45% for modern turbines), standard air density is 1.225 kg/m³ at sea level, swept area is π × (blade length)², and wind speed in meters per second. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the Betz limit?
A: The Betz limit (59.3%) is the theoretical maximum efficiency for wind turbines. No turbine can extract more than 59.3% of the wind's kinetic energy.

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 also increases linearly with velocity.

Q3: What factors affect air density?
A: Air density decreases with altitude and increases with lower temperatures. Standard sea level density is approximately 1.225 kg/m³ at 15°C.

Q4: How does swept area affect power output?
A: Power output is directly proportional to swept area. Doubling the rotor diameter quadruples the swept area and thus quadruples the power output.

Q5: What are typical Cp values for modern turbines?
A: Modern wind turbines typically achieve Cp values between 0.35-0.45 (35-45%), approaching but not exceeding the Betz limit.