Wind Turbine Power Calculator

Wind Turbine Power Equation:

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

Air Density (ρ):

kg/m³

Rotor Swept Area (A):

m²

Wind Velocity (v):

m/s

Power Coefficient (Cp):

unitless

Wind Turbine Power (P):

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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 air density, rotor swept area, wind velocity, and the power coefficient. It provides an estimate of the maximum extractable power from wind energy.

2. How Does the Calculator Work?

The calculator uses the wind turbine power equation:

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

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)

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

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 of wind energy projects.

4. Using the Calculator

Tips: Enter air density in kg/m³ (typically 1.225 at sea level), rotor swept area in m², wind velocity in m/s, and power coefficient (typically between 0.35-0.45 for modern turbines, with a theoretical maximum of 0.59). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: Why is wind velocity cubed in the equation?
A: The kinetic energy in wind is proportional to the cube of wind speed, meaning doubling wind speed increases available power by eight times.

Q2: What is the Betz limit?
A: The Betz limit (approximately 0.59) is the theoretical maximum efficiency a wind turbine can achieve, representing the maximum fraction of wind energy that can be extracted.

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

Q4: What factors affect the power coefficient?
A: The power coefficient depends on turbine design, blade pitch angle, tip speed ratio, and aerodynamic efficiency.

Q5: Is this the actual power a turbine will produce?
A: This calculates theoretical power. Actual output is lower due to mechanical losses, generator efficiency, and other system losses.