How to calculate wind energy and wind turbine energy

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 turbine animation

Image: Wind turbine animation

Go back

Wind energy formula

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

Ew = (1/2) · A · ρ · v3 · t
(1)

where:

  • Ew [J] – wind energy
  • A [m2] – air flow area
  • ρ [kg/m3] – air density, equal to 1.225 kg/m3 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:

A = π · r2
(2)

where:

  • r [m] – wind turbine blade length
Wind energy swept area

Image: Wind energy swept area

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

Ew = (1/2) · π · r2 · ρ · v3 · t
(3)

Go back

Wind turbine energy formula

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

Ewt = (ηwt / 100) · Ew
(4)

where:

  • Ewt [J] – wind turbine energy
  • ηwt [%] – wind turbine efficiency
  • Ew [J] – wind energy

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

Go back

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):

A = π · r2 = π · 102 = 314.16 m2

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

v = 15 / 3.6 = 4.1667 m/s

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

t = 3 · 3600 = 10800 s

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

Ew = (1 / 2) · 314.16 · 1.225 · 4.16673 · 10800 = 150334076.71 J

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

Ewt = (40 / 100) · 150334076.71 = 60133630.684 J

Go back

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.

Go back

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.

Leave a Reply

Ad Blocker Detected

Dear user, Our website provides free and high quality content by displaying ads to our visitors. Please support us by disabling your Ad blocker for our site. Thank you!

Refresh