ARTICLE: Equation: Gauging the Awesome Power of Waves

[Ryan Goble]

Equation: Gauging the Awesome Power of Waves

• By Julie Rehmeyer  
• August 30, 2010  |  
• 12:00 pm  |  
• Wired September 2010

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.

URL: http://www.wired.com/magazine/2010/08/st_equation_seapower/

[Joshua Zucker]

It's clear enough why it should be proportional to density, amplitude squared, period, and length. The proportionality to g^2 is a bit surprising to me -- why is it that way? And where does the 32 come from?

Let's see, with the g^2, what are the units like?

kg/m^3 * m^2/s^4 * s * m^2 * m ... um, that's kg m^2 / s^3, ok, so that is power units right? let's see, watts = joules/sec = newton*m / sec = kg m^2 / s^3, yup. So that 32 in the bottom is dimensionless. Whoa. What does it mean, anyway? Does it have anything to do with shapes of waves?

I think this would be a lot more interesting if it came with explanations of all those proportionalities.

[Ryan Goble]

Joshua - it is true that I won't be able to add any clarity there but you do pose some interesting ?s. Perhaps you need to copy and paste this into an e-mail to Wired?