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:

$$A=\pi r^2=\pi \times {50}^2\approx 7,854m^2$$

Now, apply the wind power formula:

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

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%.