Thursday, December 22, 2011

update re: Tidal energy

Part of why physics is fun is that it lets you put numbers to off-the-wall concepts.

For instance, I mentioned a couple of posts ago that if you use the tides to make electricity, you are actually taking energy out of the Earth's rotation, making the day longer.  But by how much?

You can start by calculating the energy stored in the rotation of the Earth.  As a freshman in college (if you take physics) you learn that there's a quantity called Rotational Inertia (I) for solid bodies that behaves like normal inertia (mass).  So, where energy for linear motion is E = (1/2)*(mass)*(velocity)^2,  energy for rotational motion is E = (1/2)*(I)*(rotational speed)^2.  And you can calculate I for any geometry of solid.

For a rigid, uniform sphere, I = (2/5)*(mass)*(radius)^2.  Earth is neither rigid nor uniform, but we'll assume this is close for now.

Then with the magic of Google Calculator, you can just plug all these in for the earth and get it's rotational energy.  Seriously, copy-paste this into Google:

" (1/2)*(2/5)*mass of earth * radius of earth^2 * (2*pi / day)^2 in gigawatt*hours".

It will tell you that the Earth stores about 7*10^16 gigawatt-hours of energy.  Google calculator is so magic.

Well, the US uses 30,000 gigawatt-hours of energy a year.  So the annual energy usage of the US is about 0.4 billionths of the energy stored in the rotation of the Earth.  If you take that amount out of the Earth's rotational energy, you can use the energy formula in reverse to figure out how much the Earth slowed down.  The answer: 18 microseconds (that's 18 millionths of a second).

So there you go.  If you run the entire US on tidal energy, you slow the Earth's rotation down by 18 microseconds each year.  Amazingly, this is almost exactly the amount of slowing that is measured to occur naturally due to torque from the Moon (17 +/- 0.5 microseconds/year).

Obviously the aliens living inside the hollow sphere of the Earth are powering their invasion bases with tidal power.  It's the only explanation.  Don your tinfoil hats!

"Someday, after mastering the winds, the waves, the tides and gravity, we shall harness for God the energies of love, and then, for a second time in the history of the world, man will have discovered fire."
- Pierre Teilhard de Chardin

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