## Gearing up to 'c'

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The_Alchemist
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### Gearing up to 'c'

So, I was debating whether to toss this in blind or just be upfront as to what I was thinking, and I figure the folks here are sharp enough, I'll just cut to the quick.

I've been working with gear ratios lately on a DIY project, and my thoughts went eventually to setting up a series of 10 interconnected 10:1 gears. Given a very nominal motor speed of 1600 rpm and a final gear diameter of a meter, 'simple' calculations show that last gear would be well over the speed of light. Bogus and not possible I know. The question I have is what would happen if you built it? Any hands on people have an answer? Could you get to a good fraction of c? Would the motor just fail? Would the gears shatter? etc.

Thoughts?

jaap
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### Re: Gearing up to 'c'

It would be like trying to drive off in a car with manual gears set in top gear. The force required to turn the mechanism would be immense, not just from the friction that needs to be overcome but also from the inertia. There is a lot of kinetic energy in fast spinning wheels, which is the reason flywheels work.
Either the engine would not be able to turn, or the materials of your gearing would not be able to withstand the engine's forces working against its friction/inertia and break apart.
The less friction you have and the less mass the gears have, the further you could get, but you'd never be able to get anywhere near relativistic speeds.

scarecrovv
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### Re: Gearing up to 'c'

And even assuming you could turn the mechanism really fast, the gears would indeed explode. And if you assume they didn't, then the torque required to accelerate the mechanism would increase asymptotically as the last gear approached the speed of light.

Technical Ben
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### Re: Gearing up to 'c'

Would it not require infinite energy? Even with gearing, you need the energy to go it. So you could attempt to make the gears, but never have the power to turn them fast/hard enough.
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Cobramaster
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### Re: Gearing up to 'c'

Yep even with the gearing 10^-10 * infinity is still infinity.
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bigglesworth
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### Re: Gearing up to 'c'

It's perhaps more interesting to think of what happens when you gear up to close fractions of c.
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Technical Ben
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### Re: Gearing up to 'c'

You would have to account for time dilation on the gears!
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The_Alchemist
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### Re: Gearing up to 'c'

bigglesworth wrote:It's perhaps more interesting to think of what happens when you gear up to close fractions of c.

That was in many ways part of my point and curiosity. I'm well enough versed in relativity to know the system isn't going to reach c. But as bigglesworth says, I find it interesting to know what happens real world that keeps it from happening, and should you overcome a lot of the hurdles (reduce friction, gear up gear gear slowly, a few thousand hp on the motor, etc) what do you end up seeing? Noting considerable potential interference from vibration, might you see and measure a relativistic increase in mass?

bigglesworth
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### Re: Gearing up to 'c'

I think that the most important effect would be the friction; that affects even low-speed setups. Next would be the source of power, but there are enormous ship engines that could be used that pump out incredible amounts.

The next problem, I believe, would not be relativity, but the strength of the gears. I think that they would break.
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Technical Ben
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### Re: Gearing up to 'c'

The_Alchemist wrote:
bigglesworth wrote:It's perhaps more interesting to think of what happens when you gear up to close fractions of c.

That was in many ways part of my point and curiosity. I'm well enough versed in relativity to know the system isn't going to reach c. But as bigglesworth says, I find it interesting to know what happens real world that keeps it from happening, and should you overcome a lot of the hurdles (reduce friction, gear up gear gear slowly, a few thousand hp on the motor, etc) what do you end up seeing? Noting considerable potential interference from vibration, might you see and measure a relativistic increase in mass?

You do know we could try and find a natural geared system right?!
How about a set of binary stars or planetoids. Any chance some of them are moving or rotating fast enough to have a relativistic increase in mass?
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charonme
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### Re: Gearing up to 'c'

my guess is you'd need a tremendous force to even move the wheels and after applying that force, something would probably break off first?

firechicago
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### Re: Gearing up to 'c'

Remember that the centripetal force necessary to keep the gears from exploding is mv^2/r, so if your largest gear has a radius of one meter, and the outer edge is approaching .1c then the centripetal force is approaching 9 x 10^14 newtons per kg of mass around the rim. Any theoretically plausible material is going to have exploded long before that.

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### Re: Gearing up to 'c'

So, in practice, what would happen is either a gear would bend/break, or the entire system would be too hard to move to start it moving.

If you made even a handful of gears you could experience the same effect.

Practical problems (like gear strength and friction) become theoretical as what they are fighting against goes to infinity.
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Technical Ben
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### Re: Gearing up to 'c'

Perhaps a more interesting things to actually do, would be to gear down to zero.
As in, have a set of gears, where, no matter how fast you turn them, you will never turn the last gear around. I remember seeing a video of a set of cogs made up. Turn the first, and it turns the second once a minuet. Then the next once an hour, then once a day, etc. The last was something like once a millennium.
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gmalivuk
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### Re: Gearing up to 'c'

The MIT museum has a setup that's like 10 iterations of gears that each slow it down by a factor of 50 or something absurd. Needless to say none of us will be around to see the last gear move perceptibly.
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Technical Ben
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### Re: Gearing up to 'c'

It's all physics and stamp collecting.
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Cobramaster
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### Re: Gearing up to 'c'

Now imagine turning the final gear at 1 revolution per year and you will see the exploding gears principal, because I know that the first gear cannot handle a few trillion RPM.
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zmatt
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### Re: Gearing up to 'c'

If we are talking about a setup similar to a car with an internal combustion engine and a manual transmission then you would see what we already do all the time in economy cars with tall gears. You would just never pass a certain speed. Whatever the maximum speed that the power you have allows is where you would end up. Most of the time this is realized when you hit the redline in the next to top gear, go into top gear and get stuck at a low rpm never accelerating. The solution is more power but when trying to break C with brute force never is enough.
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### Re: Gearing up to 'c'

Cobramaster wrote:Now imagine turning the final gear at 1 revolution per year and you will see the exploding gears principal, because I know that the first gear cannot handle a few trillion RPM.

Interestingly this is actually a physical reason why, in the original "gearing up" setup, you will never reach speeds greater than c, even with infinite energy. Because the speed of sound in a perfectly rigid material is c, the gear must break if any peice of it tries to move faster than c. Of course such a perfectly rigid material isn't possible, but an interesting thought experiment nonetheless.

Here's another fun thought experiment; Consider the last gear. For the sake of simplicity let's say it is 10m in circumference, with a tooth every metre. Now, as we spin up the gears, we know that relativiy suggests we should see a contraction in the direction of motion. So we see that there is less than 1m between each tooth. But the circumference is still 10m right? I mean, it still has to form a circle of 3.14 metres. Work that one out (note: This is a simple problem if you know the requisite theory, but rather complex if you're considering it knowing only the basics of SR. It is however a rather good way of showing how GR can mess with your head).

Bonus points will be awarded for working out the value of pi for the observer in the lab, and for an observer on the wheel rim.
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Technical Ben
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### Re: Gearing up to 'c'

Sounds like something that needs to be added to Discworld.
"They made a gear that when turned, would turn a second at the speed of light. However, as it caused the second to contract due to relativity it would then also stop it turning. This device created a paradox..."
Bearing in mind that the speed of light is very slow in the Discworld series.
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### Re: Gearing up to 'c'

Technical Ben wrote:Sounds like something that needs to be added to Discworld.
"They made a gear that when turned, would turn a second at the speed of light. However, as it caused the second to contract due to relativity it would then also stop it turning. This device created a paradox..."
Bearing in mind that the speed of light is very slow in the Discworld series.

haha yeah 600 MPH if I recall? I always wondered if the magical field emitted by the central structure that allowed for magic and caused light to travel at 600 MPG cast an enormous rainbow in space behind the turtle away from the Sun
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firechicago
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### Re: Gearing up to 'c'

I suspect I'm thinking about this a little too hard, but I'm pretty sure that, while the speed of light on the Discworld is somewhat slower than the speed of sound through the atmosphere, c is still the good old ~3x10^8 m/s that we know and love. After all, Pratchett does explicitly say that light is slowed by its interaction with the magic field surrounding Discworld, which I imagine being more like the way light slows down when it travels through a medium, rather than altering the fundamental constants of the universe. Besides, if c were only 600mph you would start to see significant relativistic effects on your average broomstick ride.

Or maybe Discworld just works on good old Newtonian principles. All in all, the excess of narrativium makes precisely calculating these things rather difficult. Roundworld physical equations lack the critical terms for things like destiny, divine intervention and poetic irony.

gmalivuk
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### Re: Gearing up to 'c'

firechicago wrote:Besides, if c were only 600mph you would start to see significant relativistic effects on your average broomstick ride.
How fast do you think a broom goes, exactly?
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Aelfyre
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### Re: Gearing up to 'c'

gmalivuk wrote:
firechicago wrote:Besides, if c were only 600mph you would start to see significant relativistic effects on your average broomstick ride.
How fast do you think a broom goes, exactly?

well I'd say at least 300-400 since one witch was able to encircle an entire kingdom in a single night.. allowing for periodic recharging of course.. but come to think of it she did so with the intent of slowing time down inside the kingdom while time marched forward outside effectively moving it into the future so maybe there is something to this after all. Of course you'd think he would have mentioned the pronounced blueshift as she made the trip
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gmalivuk
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### Re: Gearing up to 'c'

Aelfyre wrote:well I'd say at least 300-400 since one witch was able to encircle an entire kingdom in a single night.
Yeah, but it was Lancre. Which measures about 40x10 miles and thus has a perimeter of only 100 miles or so.

Of course you'd think he would have mentioned the pronounced blueshift as she made the trip
He does, for people who are *actually* traveling fast, such as while flying on Binky.
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firechicago
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### Re: Gearing up to 'c'

gmalivuk wrote:
firechicago wrote:Besides, if c were only 600mph you would start to see significant relativistic effects on your average broomstick ride.
How fast do you think a broom goes, exactly?

As fast as the plot needs it to, which tends to vary between barely above jogging pace to a couple hundred miles per hour, depending on the influence of the narrativium.

gmalivuk
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### Re: Gearing up to 'c'

When is it a couple hundred miles per hour?
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Aelfyre
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### Re: Gearing up to 'c'

gmalivuk wrote:
Aelfyre wrote:well I'd say at least 300-400 since one witch was able to encircle an entire kingdom in a single night.
Yeah, but it was Lancre. Which measures about 40x10 miles and thus has a perimeter of only 100 miles or so.

Of course you'd think he would have mentioned the pronounced blueshift as she made the trip
He does, for people who are *actually* traveling fast, such as while flying on Binky.

you know now that I think about it I think he mentioned something similar for the Time Slicing in Thief of Time
Xanthir wrote:To be fair, even perfectly friendly antimatter wildebeests are pretty deadly.