## Dr. Ahmed G. Abo-Khalil

Electrical Engineering Department

## Wave power formula

In deep water where the water depth is larger than half the wavelength, the wave energy flux is

$P = frac{ ho g^2}{64pi} H_{m0}^2 T approx left(0.5 frac{ ext{kW}}{ ext{m}^3 cdot ext{s}} ight) H_{m0}^2; T,$

with P the wave energy flux per unit of wave-crest length, Hm0 the significant wave height, T the wave period, ρ the water density and g the acceleration by gravity. The above formula states that wave power is proportional to the wave period and to the square of the wave height. When the significant wave height is given in meters, and the wave period in seconds, the result is the wave power in kilowatts (kW) per meter of wavefront length.

Example: Consider moderate ocean swells, in deep water, a few kilometers off a coastline, with a wave height of 3 meters and a wave period of 8 seconds. Using the formula to solve for power, we get

$P approx 0.5 frac{ ext{kW}}{ ext{m}^3 cdot ext{s}} (3 cdot ext{m})^2 (8 cdot ext{s}) approx 36 frac{ ext{kW}}{ ext{m}},$

meaning there are 36 kilowatts of power potential per meter of wave crest.

In major storms, the largest waves offshore are about 15 meters high and have a period of about 15 seconds. According to the above formula, such waves carry about 1.7 MW of power across each meter of wavefront.

An effective wave power device captures as much as possible of the wave energy flux. As a result the waves will be of lower height in the region behind the wave power device.

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