Wind Generator Calculator

Wind Power Equation:

\[ P = \frac{1}{2} \rho A v^3 C_p \eta \]

Air Density (ρ):

kg/m³

Rotor Swept Area (A):

m²

Wind Velocity (v):

m/s

Power Coefficient (Cp):

unitless

System Efficiency (η):

unitless

Generated Power (P):

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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 conversion.

2. How Does the Calculator Work?

The calculator uses the wind power equation:

\[ P = \frac{1}{2} \rho A v^3 C_p \eta \]

Where:

\( P \) — Power output (Watts)
\( \rho \) — Air density (kg/m³)
\( A \) — Rotor swept area (m²)
\( v \) — Wind velocity (m/s)
\( C_p \) — Power coefficient (unitless, max 0.59)
\( \eta \) — System efficiency (unitless, 0-1)

Explanation: The equation calculates the kinetic energy available in moving air, accounting for turbine efficiency and the Betz limit (maximum theoretical efficiency of 59.3%).

3. Importance of Wind Power Calculation

Details: Accurate wind power estimation is crucial for wind farm planning, turbine selection, energy production forecasting, and economic feasibility studies for renewable energy projects.

4. Using the Calculator

Tips: Enter air density (typically 1.225 kg/m³ at sea level), rotor swept area, wind velocity, power coefficient (typically 0.35-0.45 for modern turbines), and system efficiency. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: Why is wind velocity 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.

Q2: What is the Betz limit?
A: The Betz limit (59.3%) is the maximum possible efficiency for a wind turbine, derived from conservation of mass and momentum. No turbine can extract more than this percentage of power from the wind.

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

Q4: What is a typical power coefficient for modern turbines?
A: Modern wind turbines typically achieve power coefficients between 0.35 and 0.45, which is about 70-80% of the theoretical Betz limit.

Q5: Why is rotor swept area important?
A: Power output is directly proportional to the swept area. Doubling the rotor diameter quadruples the swept area and thus quadruples the potential power output.