1. ## Centrifuge Forces Equation

I recently heard of something really cool that they are using on the International Space Station. They're called... control moment gyroscopes (CMG), they're big spinning masses that spin so fast they help the station hold it's position and orientation in space. I heard that further advances in this technology could allow us to build spaceships which can turn without expelling any fuel. You just have a series of powerful gyros that pivot and the ship would turn in response. More slowly than the gyros of course, but still enough.

But even more fascinating! I found out that these gyros might one day be used as power storage devices (http://en.wikipedia.org/wiki/Flywheel_energy_storage). Supposedly these things will one day replace common batteries and such. I find that very interesting, but I'd like to know how much energy a given gyro can hold.

Does anyone know the equation that can give us for instance... Z energy for a mass of X kilograms, spinning at Y RPMs? I'd really like to find out how fast a small mass has to spin before it can power a weapon's grade laser...
Last edited by Philippe Lemay; 2009-Sep-23 at 02:24 PM.

2. Originally Posted by Philippe Lemay
Does anyone know the equation that can give us for instance... Z energy for a mass of X kilograms, spinning at Y RPMs? I'd really like to find out how fast a small mass has to spin before it can power a weapon's grade laser...
Here is the rotational kinetic energy equation. [Power is simply the rate of energy that is added to or taken away from the rotating object with respect to time.]

The equation requires knowing the moment of inertia, which may be found here (for simple forms).
Last edited by George; 2009-Sep-23 at 04:20 PM. Reason: corrected power def.

3. Thanks, I'll digest that as I can, but I think it will help me in my goal.

There was another thing I wanted to ask... I heard somewhere that an object's kinetic energy becomes equivilent to it's mass-energy density when it reaches 86.6% the speed of light. I wonder... does this mean that if I take a 10 kg mass and get it to spin close to 90% the speed of light, it would hold more energy than a 10kg block of pure antimatter? Or more precisely, 5 kg of matter + 5 kg of antimatter.

Could flywheel batteries one day (hypothetically) outstrip antimatter technology!?

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There are limits to how fast you can spin something before it breaks itself apart. You also need an input of energy in order to spin the thing up, so you're not getting something for nothing.

5. Yes and no. Yes, IF you could get a mass spinning that fast then it would have a better energy density than antimatter (I'm assuming the mass is concentrated around the edge).

But no, you couldn't do it with flywheel batteries. Molecular bonds are nowhere near strong enough to keep the flywheel in one piece. Other forces may be strong enough...like the gravitational force near a black hole...but not the electromagnetic bonds which hold solid materials together.

Basically, flywheel energy storage systems are physics limited in energy density to levels on par with chemical fuel energy density. This isn't coincidental--they're both fundamentally limited by the strengths of chemical bonds.

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...and the amount of deformation of a spinning object will be related to it's Young's modulus. This is the change of length due to forces applied. At high enough forces, as the others have said, all objects will eventually fail. SEE:http://en.wikipedia.org/wiki/Young's_modulus

7. Ok, so in practice it could never be built.

Still... it's fun to think that Star Trek's famous antimatter reactors are not in fact the most energetic form of power that we can conceive (aside for those pesky black holes in a bottle of course, but that's REALLY pushing the whole... realistic sci-fi angle).

Oh and I did the numbers, according to the very helpful wiki page the moment of inertia of a 60 centimeter wide disc, weighing about 23 kilograms is precisely 1.0 (or close to 1 anyway).

I've heard that the best speed we've gotten a flywheel so far is 60,000 RPM, but that future ones could reach as high as 100,000 RPM. I assume the equation uses radians per second though, and not RPM, because radians are the SI unit. 100,000 RPM is about 10500 Rad-per-sec.

½ × 1.0 × 10500² = 55 125 000 joules
Thus our little spinning top can hold... 55 megajoules. Not bad.

EDIT:
Oh wait... I used the moment of inertia along the Z-axis. Is that... bad?

If that's our spinning disc, and we want to establish the kinetic energy of it's spin, which axis do we use for our calculations?

8. Originally Posted by Philippe Lemay
Still... it's fun to think that Star Trek's famous antimatter reactors are not in fact the most energetic form of power that we can conceive (aside for those pesky black holes in a bottle of course, but that's REALLY pushing the whole... realistic sci-fi angle).
That's true, they aren't.

See, the "problem" with your near-c flywheel is that it's impossible for it to stay in one piece if it is spinning. But you can get around that problem if you don't bother with the spinning!

A stream of near-c pellets accelerated from the Solar System to a starship is more energetic per kilogram than antimatter, and there are known ways to accelerate things up to near-c velocities which aren't insanely inefficient (antimatter generation is insanely inefficient). The starship can utilize this stream of pellets by letting them collide with puffs of sacrificial propellant. The resulting "relativistic kinetic impact powered rocket" is more powerful, more effective, and more efficient than an antimatter rocket. And it's a lot cheaper. And it's a lot more doable with known technology. (And yes, it can produce thrust in any direction, including back toward the Solar System for purposes of braking and returning.)

So, your basic notion of using near-c kinetic energy for energy storage superior to antimatter isn't wrong. It's just that you can't do it in a convenient "spinning" package.

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Originally Posted by Philippe Lemay
Still... it's fun to think that Star Trek's famous antimatter reactors are not in fact the most energetic form of power that we can conceive (aside for those pesky black holes in a bottle of course, but that's REALLY pushing the whole... realistic sci-fi angle).
Totally off topic and I'm enjoying reading the thread... but.. Must point out that Star Trek does employ the pesky black hole in a bottle.

The Romulans used them to power their Warbirds.

10. @Neverfly
Fair enough, but like I said I just find that too far-fetched for my taste. Using bits of antiparticles stored somehow, or just bits of matter moving really really fast feel much more... plausible. It's the kind of sci-fi technology you imagine might really be developed and used in 50, 80, or 100 years, you know?

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Originally Posted by Philippe Lemay
@Neverfly
Fair enough, but like I said I just find that too far-fetched for my taste. Using bits of antiparticles stored somehow, or just bits of matter moving really really fast feel much more... plausible. It's the kind of sci-fi technology you imagine might really be developed and used in 50, 80, or 100 years, you know?
Oh, I agree.

IsaacKuo's post just above yours touches on an interesting alternative.

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