Wind Power Calculator

The Formula

The formula for calculating wind power output is:

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

Where:

• P: Power output (in watts)
• ρ (rho): Air density (in kg/m³)
• A: Rotor swept area (in m²)
• v: Wind speed (in m/s)
• C_p: Power coefficient (turbine efficiency)

Calculation Steps

1. Calculate the rotor swept area: A = π × (Diameter ÷ 2)²
2. Apply the wind power formula: P = 0.5 × ρ × A × v³ × C_p
3. Convert the result to kilowatts (kW) if necessary

Example Calculation

Let's calculate the wind power output for a turbine with the following parameters:

• Wind speed: 10 m/s
• Rotor diameter: 80 m
• Turbine efficiency: 40%
• Air density: 1.225 kg/m³

1. Rotor swept area: A = π × (80 ÷ 2)² = 5026.55 m²
2. Power output: P = 0.5 × 1.225 × 5026.55 × 10³ × 0.40 = 1228.5 kW

Visual Representation

This visual shows the wind power output for a turbine based on our example calculation.