Wind Energy

Overview

Engineering reference data for Wind Energy in dynamics.

Key Formulas

Newton's Second Law

$F = ma$

Force = mass × acceleration.

Kinetic Energy

$E_k = \frac{1}{2}mv^2$

Energy of motion.

Momentum

$p = mv$

Mass × velocity.

Work

$W = Fd\cos\theta$

Force × displacement × cos(angle).

Variables

Wind Resource by Terrain

Example: Energy Output Calculation

The annual energy output $E$ (in $\text{kWh/m}^2$) from a wind turbine can be calculated from the wind power density $P$ (in $\text{W/m}^2$), the turbine's efficiency $\eta$ (%), and the annual operational hours $t$ (in $\text{h/year}$):

$$E = P \cdot \frac{\eta}{100} \cdot t$$

For a sheltered location with average wind speed 5 m/s ($P \approx 140\ \text{W/m}^2$), a turbine efficiency of 25%, and 8000 operational hours per year:

$$E = (140\ \text{W/m}^2) \cdot \left(\frac{25}{100}\right) \cdot (8000\ \text{h/year}) = 280{,}000\ \text{Wh/m}^2\text{/year} = 280\ \text{kWh/m}^2\text{/year}$$

Key Concepts

• Wind Power Density ($P$): The power available in the wind per unit swept area, typically measured at a reference height of 50 m. It is proportional to the cube of the wind speed ($P \propto v^3$).
• Turbine Efficiency ($\eta$): The fraction of the available wind power that a turbine can convert into electrical power. Typical values are between 20% and 30%.

Interactive Charts

References

• Original Source