### Table of Contents

### Definition

**Wind energy** is the kinetic energy possessed by air in motion (also called wind). The higher the wind speed, the higher its kinetic energy.

Wind energy is the use of wind to provide mechanical energy through wind turbines to turn electric generators for electrical energy. Wind energy is a popular sustainable, renewable source of energy that has a much smaller impact on the environment compared to burning fossil fuels.

**Wind turbine energy** is the energy output of a wind turbine, which is using the wind energy and converts it into mechanical and further electrical energy.

### Wind energy formula

The formula (equation) to calculate **wind energy** is [6]:

_{w}= (1/2) · A · ρ · v

^{3}· t

where:

- E
_{w}[J] – wind energy - A [m
^{2}] – air flow area - ρ [kg/m
^{3}] – air density, equal to 1.225 kg/m^{3}at pressure of 1013.25 hPa and temperature of 15°C - v [m/s] – wind (air) speed
- t [s] – time

The unit of measurement of **wind energy** is joule [J].

The air flow area, also called swept area, is the area through the air (wind) is flowing. The swept area of the turbine can be calculated from the length of the turbine blades using the equation for the area of a circle:

^{2}

where:

- r [m] – wind turbine blade length

Combining equations (1) and (2) gives the formula (equation) for **wind energy** as:

_{w}= (1/2) · π · r

^{2}· ρ · v

^{3}· t

### Wind turbine energy formula

The formula (equation) to calculate **wind turbine energy** is:

_{wt}= (η

_{wt}/ 100) · E

_{w}

where:

- E
_{wt}[J] – wind turbine energy - η
_{wt}[%] – wind turbine efficiency - E
_{w}[J] – wind energy

The unit of measurement of **wind turbine energy** is joule [J].

### Example

Calculate the energy output of a wind turbine during 3 h of continuous operation, with a blade length of 10 m and efficiency of 40 %, when the wind speed is 15 kph and the air pressure and temperature are 1013.25 hPa and 15 °C.

**Step 1**. Calculate the wind turbine swept area using equation (2):

^{2}= π · 10

^{2}= 314.16 m

^{2}

**Step 2**. Convert wind speed from [kph] to [m/s] by dividing the [kph] value to 3.6:

**Step 3**. Convert the wind turbine operation time from [h] to [s] by multiplying the [h] value with 3600:

**Step 4**. Calculate the wind energy using equation (1):

_{w}= (1 / 2) · 314.16 · 1.225 · 4.1667

^{3}· 10800 = 150334076.71 J

**Step 5**. Calculate the wind turbine energy using equation (4):

_{wt}= (40 / 100) · 150334076.71 = 60133630.684 J

### Calculator

The wind energy calculator allows you to calculate the wind energy and wind turbine energy using the equations defined above. You need to enter the wind (air) speed, wind turbine blade length, wind turbine efficiency, wind turbine operation time and choose the desired unit of measurement. You can also enter the air density in order to see the influence of altitude (pressure) and temperature on the wind turbine energy output.

The default unit of measurement for energy is **Joule**. If you want the result displayed in another unit, use the drop down list to choose and click the CALCULATE button again.

### References

[1] David Halliday, Robert Resnick, Jearl Walker, Fundamentals of Physics, 7th edition, John Wiley & Sons, 2004.

[2] Benjamin Crowell, Light and Matter – Physics, 2007.

[3] Raymond A. Serway and John W. Jr. Jewett, Physics for Scientists and Engineers, 6th edition, Brooks/Cole Publishing Co.,2004

[4] Jiansong Li, Jiyun Zhao, and Xiaochun Zhang, A Novel Energy Recovery System Integrating Flywheel and Flow Regeneration for a Hydraulic Excavator Boom System, Energies 2020.

[5] Leo H. Holthuijsen, Waves in oceanic and coastal waters, Cambridge University Press, 2007.

[6] Kira Grogg, Harvesting the Wind: The Physics of Wind Turbines, Carleton College, 2005.