Energy Content

The energy content in ocean waves can be calculated, the official formula is:

Power in ocean waves: P = 0.57*(Hs)^2*Tp

P: Power in kW per meter of wave front.
Hs: Significant wave height, see below.
Tp: Time periode between each wave crest. Can only be estimated accurately with regular waves, which only occur under controlled environments. In practical terms this mean the Tp is estimated from the wave height, and the water depth.
Practical values for wave Tp is 5 sec. for 1-2 m wave height, up to 10 sec. for 5 m wave height. Swells have about twice the value for Tp. The wave height and Tp distribution over a year can be read in a scatter diagramme, (for example at www.waveclimate.com) from which the wave generator can be optimized.

Example:
A wave height Hs of 3 m, and period time Tp of 6 sec, contains the power:

0.57 * 3^2 * 6 = 30.78 kW/m.

If a particular area has an significant of 3 m Hs waves (over a year), and average Tp 6 sec, it is referred to as having a waveclimate of 30 kW/m.

The Capture width is the width perpendicular to the wave direction, in which the wave energy machine takes up power from the waves. It is a matter of debate how this capture width should be defined in detail, but the most prevailing model is to draw a circle around the wave machine, and define the diameter of the circle as the capture width.

Definition and calculation of Significant Waveheight Hs.
There are two ways of defining Significant wave height (Hs). One is The average of the highest third of the incident waves. This method is useful for manual observations (on a measureing stick), but very difficult for a computer to process.

Therefore NOAA (National Oceanic and Atmospheric Adminstration USA) have presented an alternative formula, which is easier for a computer to deal with:

Significant wave height: Hs = 4 * sqrt(M0) 
Hs: Significant wave height from crest to trough sqrt: Square root 
M0: Variance of water level   
 
The variance is easy for the computer to handle, since you only need a series of water level measurements. From these you can determine the mean value, and then add up the squared differences. Divide by the number (n) of samples, and you have the variance. If you take the square root of the variance, you have the root mean squared (RMS) value of the variance of the wave height. In other words the wave height Hs can also defined as: H(RMS) * 4.   
This definition is debatable, since regular waves will show too high an amplitude with this formula. For regular waves Hs = 2.82 * H(RMS). However, the formula is regarded as the closest match to Hs, and is the official standard.   
 
Froude's Model Scaling Law 
Froude's model scaling law gives a fairly accurate estimate of the output power for a wave system, based on measured power from an exact scale model, and a scaling factor.   
 
Froude's theory: Pf = Pm^3.5   
Pf = Power Full Scale 
Pm = Power Model   
 
This means that every time the model is scaled up by 2 (twice the size), 11 times as much power is generated. Similarly, when a wave energy converter is scaled down by 2 (half the size), only 1/11^th of the power is generated. This explains why the scale models of wave energy converters are so big, and deliver so little power.