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What determins the top speed of the railgun? is it when watts = friction?

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Steve Conner

Fri Oct 04 2013, 10:25AM

Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706

The discussion we've had so far hasn't included friction between the projectile and rails, and this is in fact the main source of inefficiency in a railgun.

A huge part of railgun design is the tradeoff between friction, contact resistance and current density. The more current you want to ram through it, the higher contact pressure and larger contact surface you need, so the more friction you get. If you try to push a high current through a projectile with small, low-pressure contacts, it may well just vaporise instead of moving.

It follows that railguns of all sizes are only as efficient as their contact systems. The best way of addressing this on a hobbyist budget that I've seen is Rapp Instruments' projectile made of a plexiglass oblong with a hole through it stuffed full of stranded copper wire.

PS: A motor with no back EMF is impossible according to conservation of energy. In order for mechanical power to come out, something must consume the power out of the electrical domain.

PlayNice

Fri Oct 04 2013, 09:36PM

Registered Member #8032 Joined: Tue Nov 13 2012, 01:22AM
Location: Chicagoland USA
Posts: 33

Steve Conner wrote ...

The best way of addressing this on a hobbyist budget that I've seen is Rapp Instruments' projectile made of a plexiglass oblong with a hole through it stuffed full of stranded copper wire.

Do you have more info on this, link maybe? I'd love to read more about it, but can't seem to find the project you are talking about.

PS I found more info actually, thanks

BigBad

Fri Oct 04 2013, 10:57PM

Registered Member #2529 Joined: Thu Dec 10 2009, 02:43AM
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Steve Conner wrote ...

The motion of the projectile generates a counter EMF that opposes the voltage of the power supply. So the faster it goes, the less voltage is available to drive current through it, hence the less Lorentz force pushing it along.

At a certain speed, the counter EMF will equal the power supply voltage and the projectile won't accelerate any more, it will just keep on going at that speed. In a good railgun design, this should happen just about the time that it reaches the end of the rails.

Doesn't sound right off hand. Wouldn't that imply that the current is zero?

Isn't it more like a universal motor, no particular limit, just thrust goes down with speed? Isn't it a type of series 'wound' electric motor? So it will keep accelerating until the friction equals thrust, but if there's low friction, it will keep getting faster?

BigBad

Fri Oct 04 2013, 11:13PM

Registered Member #2529 Joined: Thu Dec 10 2009, 02:43AM
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Basically, the back-emf causes field weakening, so it never stops accelerating when driven with a constant voltage (at least until friction stops it.)

Also, rail guns run on both AC/DC, never knew that!

...

Fri Oct 04 2013, 11:29PM

Registered Member #56 Joined: Thu Feb 09 2006, 05:02AM
Location: Southern Califorina, USA
Posts: 2445

I think your comments are consistent with Steve's, you are just looking at it differently.

You said 'just thrust goes down with speed', which is what Steve means when he says 'at a certain speed the counter EMF will equal the power supply voltage, and the projectile won't accelerate anymore'--in the absence of friction these statements are identical at the limiting case of the motors top speed, where thrust=0 and speed=maximum (determined by the supply voltage and Kv of the motor)

And like has been mentioned, there are 2 sources of inefficiency in a railgun:
1. Resistance -- this leads to energy being dissipated as heat in the wire/contacts
2. Friction -- this leads to energy being dissipated as heat at the contacts (and possibly some air compression if you start getting to high enough efficiencies that this becomes significant)

If you could create a frictionless, superconducting railgun you could accelerate a particle at 100% efficiency (ignoring practical things like a power supply that can output the necessary ramping voltage to match the back emf, with 100% efficiency, etc)

BigBad

Fri Oct 04 2013, 11:52PM

Registered Member #2529 Joined: Thu Dec 10 2009, 02:43AM
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No, no. With a constant voltage, in the absence of friction there's no upper speed limit; on an infinite rail (neglecting rail resistance) it won't tend to a speed, it will continue to accelerate with an acceleration inversely proportional to speed.

The trick is that the back EMF reduces the current in the rail, which in turn reduces the back EMF, so it reaches a compromise; it's called field weakening, it's a fairly common thing in electric motors done to increase top speed, sometimes it's done deliberately, but series wound motors do it automatically.

So there's no top speed (unless friction says otherwise)

PlayNice

Sat Oct 05 2013, 12:44AM

Registered Member #8032 Joined: Tue Nov 13 2012, 01:22AM
Location: Chicagoland USA
Posts: 33

So you're saying as the back emf increases as the projectile speed increases, if you could increase the supply voltage at the same rate then the projectile would just keep accelerating? (infinite rail, no friction)

PS. so building something like a custom built ballast specifically for a railgun that keep the current constant but can very the voltage would be the best solution?

Steve Conner

Sat Oct 05 2013, 01:05PM

Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706

You are right, the counter EMF is proportional to current, so it behaves like a series wound motor, not a permanent magnet one.

The motor textbooks will tell you that the speed of a series wound motor is only limited by friction, and a big one can race to destruction if it loses its load.

BigBad

Sat Oct 05 2013, 05:05PM

Registered Member #2529 Joined: Thu Dec 10 2009, 02:43AM
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Posts: 600

-QQ- wrote ...

So you're saying as the back emf increases as the projectile speed increases, if you could increase the supply voltage at the same rate then the projectile would just keep accelerating? (infinite rail, no friction)

No, you keep the voltage the same, and it keeps accelerating indefinitely, albeit ever slower, but it doesn't tend to a limit.

The trick is that the back EMF is proportional to the field strength due to the rail at the projectile mulitplied by the current multiplied by the length of the sabot.

F = B i L

but the field is proportional to the current also:

B = i k

where k is some geometric constant

so:

F = i ^2 k L

The back EMF is:

E = i L v

And the current is just determined by the voltage across and resistance through the sabot, R:

(V - E) = i R

i = (V - E)/R

i = (V -iLv)/R

i = V/(R (1+Lv)

so as you can see, as v increases the current comes down, but never goes to zero. As v->infinity the current tends to V/RLv. But the force/acceleration is a square law. So it takes four times as long to double the speed each time, but it WILL double the speed.

This is because it's 'series wound' if the magnetic field was provided by an external permanent magnet, the magnetic field through the sabot would be constant and the back-emf would eventually reduce the current to zero. But here, as the current goes down, the field weakens, and that never happens.

PlayNice

Tue Oct 08 2013, 03:15AM

Registered Member #8032 Joined: Tue Nov 13 2012, 01:22AM
Location: Chicagoland USA
Posts: 33

Thanks for the explanation, I think I get it now. So then basically only thing that limits the speed of a railgun is my budget lol

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