Wind Turbine Calculation Formula

Wind Turbine Power Formula:

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

Air Density (ρ):

kg/m³

Rotor Swept Area (A):

m²

Wind Velocity (V):

m/s

Power Coefficient (Cₚ):

dimensionless

Power Output (P):

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1. What is the Wind Turbine Power Formula?

The wind turbine power formula calculates the theoretical power output of a wind turbine based on air density, rotor swept area, wind velocity, and power coefficient. It represents the maximum extractable power from wind energy.

2. How Does the Calculator Work?

The calculator uses the wind turbine power formula:

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

Where:

\( P \) — Power output (watts)
\( \rho \) — Air density (kg/m³)
\( A \) — Rotor swept area (m²)
\( V \) — Wind velocity (m/s)
\( C_p \) — Power coefficient (dimensionless)

Explanation: The formula shows that power output is proportional to air density, rotor area, and the cube of wind velocity, multiplied by the turbine's efficiency coefficient.

3. Importance of Wind Power Calculation

Details: Accurate power calculation is essential for wind turbine design, site 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 0.35-0.45 for modern turbines). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the maximum theoretical power coefficient?
A: According to Betz's law, the maximum possible power coefficient is 16/27 ≈ 0.593. No wind turbine can exceed this limit.

Q2: Why is wind velocity cubed in the formula?
A: The kinetic energy of wind is proportional to the cube of wind velocity, meaning small increases in wind speed result in large increases in available power.

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.

Q4: How is rotor swept area calculated?
A: For horizontal axis turbines, swept area = π × (rotor radius)². For a turbine with blade length R, area = πR².

Q5: What are typical power coefficient values?
A: Modern utility-scale wind turbines typically achieve power coefficients between 0.35-0.45, while smaller turbines may have coefficients around 0.25-0.35.