Equation: Gauging the Awesome Power of Waves

Friday, 17 September 2010 13:00

Equation: Gauging the Awesome Power of Waves

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A surfer on a 30-foot wave is basically riding pure, unbridled energy—a single such monster swell can release 10,000 kilowatts of power as it crashes to the shore. How do we know that? Because of the equation below, which gauges a wave’s power in the open sea from variables like height, length, and period (time from the top of one wave to the top of the next). Swells off the Pacific Coast of the US average about 6 feet and come about 10 seconds apart;

they’re weaker in the Atlantic, but even so, if we could harness all the wave energy in US waters, it would meet half the nation’s electricity demand. This equation shows that bigger, less frequent waves contain more power. Now all we need is a formula for building machines to transform all that endless up-and-down to electrical current.
Illustration: Sakke Soini

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Power of a wave in deep water, measured in watts

Density of seawater (1,025 kg/m³)

Acceleration due to gravity (9.81 m/s²)

Wave period—the time between successive peaks, in seconds

Wave height—distance from trough to peak, in meters

Length of wave front (perpendicular to direction of travel), in meters

Mathematical constant (3.1416 …)

Illustration: Sakke Soini

Authors: Julie Rehmeyer

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