# How to calculate wave energy

### Definition

Wave energy is the energy produced by wind waves in the oceans and sea due to the motion of water. A machine that can harvest wave energy is called a WEC (Wave Energy Converter).

Waves are formed due to the interaction between the wind passing over the surface of the sea water. As long as the waves propagate slower than the wind speed just above the waves, there is an energy transfer from the wind to the sea waves.

Image: Wave energy

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### Formula

There are two types of waves for which we can calculate energy [5]:

• periodic waves (defined as waves which are generated in a specific periodic pattern, e.g. 1 wave each 10 seconds)
• random waves (waves that generated randomly)

Wave energy is a specific energy and it’s calculated pe unit of horizontal area [J/m2].

The formula (equation) to calculate wave power is [5]:

Epw = (1/8) · ρ · g · H2m0
(1)
Erw = (1/16) · ρ · g · H2m0
(2)

where:

• Epw [J/m2] – periodic wave energy density
• Erw [J/m2] – random wave energy density
• ρ [kg/m3] – water density, equal to 1000 kg/m3
• g [m/s2] – gravitational acceleration, equal to 9.81 m/s2
• Hm0 [m] – significant wave height

The significant wave height is defined as the mean wave height (trough to crest) of the highest third or fourth of the waves. The unit of measurement of wave energy is joule per square meter [J].

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### Periodic wave example

Calculate the theoretical energy density of periodic waves with a significant wave height of 5 feet.

Step 1. Convert the wave height from [ft] to [m], by dividing the [ft] value to 3.281:

Hm0 = 5/3.281 = 1.524 m

Step 2. Calculate the wave energy density using equation (1):

Epw = (1/8) · 1000 · 9.81 · 1.5242 = 2848.06 J/m2

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### Random wave example

Calculate the theoretical energy density of random waves with a significant wave height of 7 feet.

Step 1. Convert the wave height from [ft] to [m], by dividing the [ft] value to 3.281:

Hm0 = 7/3.281 = 2.1335 m

Step 2. Calculate the wave energy density using equation (2):

Erw = (1/16) · 1000 · 9.81 · 2.13352 = 2790.836 J/m2

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### Calculator

The wave energy calculator allows you to calculate the specific wave energy using the equations defined above. You need to enter the type of wave, significant wave height and choose the desired unit of measurement. The gravitational acceleration is assumed to be 9.81 [m/s2] and water density 1000 [kg/m3].

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

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### 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.