Wind Power Calculator: Understanding Wind Energy Generation

What is Wind Power?

Wind power is the conversion of wind energy into electricity using wind turbines. It's a clean, renewable energy source that has become increasingly important in the global shift towards sustainable energy production.

The Wind Power Formula

The power generated by a wind turbine is given by the equation:

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

Where:

• \(P\) is the power output in watts (W)
• \(\rho\) (rho) is the air density in kilograms per cubic meter (kg/m³)
• \(A\) is the swept area of the turbine blades in square meters (m²)
• \(v\) is the wind speed in meters per second (m/s)
• \(\eta\) (eta) is the efficiency of the turbine as a decimal

Calculation Steps

1. Determine the wind speed (\(v\)) in m/s.
2. Calculate the swept area (\(A\)) using the blade length: \(A = \pi r^2\)
3. Use the air density (\(\rho\)) at the turbine's location (typically about 1.225 kg/m³ at sea level).
4. Input the turbine's efficiency (\(\eta\)) as a decimal.
5. Apply these values to the wind power formula.

Example and Visual Representation

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

• Wind speed (\(v\)) = 10 m/s
• Blade length (\(r\)) = 50 m
• Air density (\(\rho\)) = 1.225 kg/m³
• Efficiency (\(\eta\)) = 40% = 0.4

First, calculate the swept area:

\[A = \pi r^2 = \pi \times 50^2 \approx 7,854\ m^2\]

Now, apply the wind power formula:

\[P = \frac{1}{2} \times 1.225 \times 7,854 \times 10^3 \times 0.4 \approx 1,924,350\ W \approx 1.92\ MW\]

This diagram illustrates a wind turbine with a blade length of 50 meters. The power output of 1.92 MW is based on a wind speed of 10 m/s and a turbine efficiency of 40%.