What determins the top speed of the railgun? is it when watts = friction?
PlayNice, Thu Oct 03 2013, 08:31AMSome basic railgun questions, thanks for reading
1) Imagine you build a very long railgun track (say 1 miles long). What will determine the projectiles final top speed?
Or would the projectile keep accelerating all the way to the end of the 1 mile track regardless of V&Amps (assuming they stay constant)?
2) Also say you have a: 1 mile track and @ 100v at 100amp AND you have 10 mile track but 10v at 100amp, will the speed in the end be about the same on both setups?
3) Now say you make a 100 mile long track and just use constant 10v 100amp, will the projectile keep on accelerating all the way to the end of the 100 mile track or will it at some point stop accelerating and just stay at constant speed?
Hope someone can clarify these questions for me. Thanks
Re: What determins the top speed of the railgun? is it when watts = friction?
Steve Conner, Thu Oct 03 2013, 10:10AM
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.
Steve Conner, Thu Oct 03 2013, 10:10AM
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.
Re: What determins the top speed of the railgun? is it when watts = friction?
Yandersen, Thu Oct 03 2013, 10:49AM
And in addition, the inductance of the tracks depend on the projectile' position - the further the bullet, the bigger the loop of the current, square higher the inductance of that loop. So current starts to decay, even if cap is not depleted yet. With the addition of increasing counter-EMF, current may even reverse, I think (I may be wrong) and suckback with recuperation will start.
Yandersen, Thu Oct 03 2013, 10:49AM
And in addition, the inductance of the tracks depend on the projectile' position - the further the bullet, the bigger the loop of the current, square higher the inductance of that loop. So current starts to decay, even if cap is not depleted yet. With the addition of increasing counter-EMF, current may even reverse, I think (I may be wrong) and suckback with recuperation will start.
Re: What determins the top speed of the railgun? is it when watts = friction?
Steve Conner, Thu Oct 03 2013, 11:10AM
Yes, but it's not a separate effect. The change in inductance with time is the very same thing that causes the counter EMF.
Faraday's law: V=L*di/dt
But if inductance changes with time you have to write it as
V=d/dt(LI)
which to a first order approximation is
V= (L*di/dt) + (I*dL/dt)
The second term is the counter EMF. The electrical power represented by (counter EMF * current) is the mechanical power delivered to the projectile.
Steve Conner, Thu Oct 03 2013, 11:10AM
Yes, but it's not a separate effect. The change in inductance with time is the very same thing that causes the counter EMF.
Faraday's law: V=L*di/dt
But if inductance changes with time you have to write it as
V=d/dt(LI)
which to a first order approximation is
V= (L*di/dt) + (I*dL/dt)
The second term is the counter EMF. The electrical power represented by (counter EMF * current) is the mechanical power delivered to the projectile.
Re: What determins the top speed of the railgun? is it when watts = friction?
PlayNice, Thu Oct 03 2013, 11:51PM
So to make sure I understand this correctly, if the length of the rail is the cause of the back EMF & more inductance, and that's what eventually hampers the top speed:
Highest speed railgun would be: one with short rails so very low EMF & inductance, and very high voltage? (balance rail length depending on voltage) right?
Sooo then the voltage is the biggest player in the top speed of the rail-gun, and amperage just determines acceleration, does that sound about right?
PlayNice, Thu Oct 03 2013, 11:51PM
So to make sure I understand this correctly, if the length of the rail is the cause of the back EMF & more inductance, and that's what eventually hampers the top speed:
Highest speed railgun would be: one with short rails so very low EMF & inductance, and very high voltage? (balance rail length depending on voltage) right?
Sooo then the voltage is the biggest player in the top speed of the rail-gun, and amperage just determines acceleration, does that sound about right?
Re: What determins the top speed of the railgun? is it when watts = friction?
klugesmith, Fri Oct 04 2013, 12:19AM
Do you understand that you can't specify the voltage AND the current, as if they were independent inputs?
Doesn't matter what your power supply nameplate says.
The railgun's voltage and current are absolutely connected to each other by the (time-varying) impedance and back EMF of the gun.
Given a gun and projectile system, closely analogous to a motor with an inertial load, you could...
klugesmith, Fri Oct 04 2013, 12:19AM
Do you understand that you can't specify the voltage AND the current, as if they were independent inputs?
Doesn't matter what your power supply nameplate says.
The railgun's voltage and current are absolutely connected to each other by the (time-varying) impedance and back EMF of the gun.
Given a gun and projectile system, closely analogous to a motor with an inertial load, you could...
- force a particular current at the terminals, and see what happens
- force a particular voltage between the terminals, and see what happens
- Connect railgun to a voltage or current source with finite impedance (the previous 2 cases are special cases of this one)
- Connect railgun to an energy storage device with finite impedance (capacitor bank is a popular special case).
Re: What determins the top speed of the railgun? is it when watts = friction?
PlayNice, Fri Oct 04 2013, 02:34AM
I get V and I are related through R and BEMF. I just wish I understood the relationship between projectiles top speed and V better. So supplying higher V is the only way of increasing the speed then?
PlayNice, Fri Oct 04 2013, 02:34AM
I get V and I are related through R and BEMF. I just wish I understood the relationship between projectiles top speed and V better. So supplying higher V is the only way of increasing the speed then?
Re: What determins the top speed of the railgun? is it when watts = friction?
klugesmith, Fri Oct 04 2013, 06:46AM
When I say impedance, I mean the combination of the rails' R, L, and C.
All of them affect the current draw for a given voltage, and increase as the armature moves.
I think you could reduce the ratio of back EMF to armature velocity,
by reducing the inductance per unit of length.
That means make the rails wider and/or closer together, thus changing the aspect ratio of the barrel.
It would be the analog of choosing an electric motor with a higher K_v.
If the two motors are otherwise identical, there's no difference in efficiency.
But for same acceleration of same load, the higher K_v motor would use lower V and higher I.
A classic example in electromagnetism classes is a rectangular conducting loop
formed by two parallel fixed wires and two parallel cross wires, one of which is free to slide.
With a uniform B field perpendicular to the loop, you figure how the mechanical
force, velocity, and power relate to the loop current, voltage, and power.
An Internet search just turned up many examples, including figure 10.2.2 here:
klugesmith, Fri Oct 04 2013, 06:46AM
When I say impedance, I mean the combination of the rails' R, L, and C.
All of them affect the current draw for a given voltage, and increase as the armature moves.
I think you could reduce the ratio of back EMF to armature velocity,
by reducing the inductance per unit of length.
That means make the rails wider and/or closer together, thus changing the aspect ratio of the barrel.
It would be the analog of choosing an electric motor with a higher K_v.
If the two motors are otherwise identical, there's no difference in efficiency.
But for same acceleration of same load, the higher K_v motor would use lower V and higher I.
A classic example in electromagnetism classes is a rectangular conducting loop
formed by two parallel fixed wires and two parallel cross wires, one of which is free to slide.
With a uniform B field perpendicular to the loop, you figure how the mechanical
force, velocity, and power relate to the loop current, voltage, and power.
An Internet search just turned up many examples, including figure 10.2.2 here:
Re: What determins the top speed of the railgun? is it when watts = friction?
PlayNice, Fri Oct 04 2013, 10:10AM
Thanks for the link. Well the design I have in mind will have the rails very very close together, 1 or 2 mm apart and the rails are pretty fat so that should help lower the inductance and R. And yea comparing it to a motor helps a lot. Higher K_v motors have higher rpms, and they usually achieve that by higher V and having lower inductance (turns). Motors tend to be very efficient because of the CEMF, so why isn't same true for real-gun?
PlayNice, Fri Oct 04 2013, 10:10AM
Thanks for the link. Well the design I have in mind will have the rails very very close together, 1 or 2 mm apart and the rails are pretty fat so that should help lower the inductance and R. And yea comparing it to a motor helps a lot. Higher K_v motors have higher rpms, and they usually achieve that by higher V and having lower inductance (turns). Motors tend to be very efficient because of the CEMF, so why isn't same true for real-gun?
Re: What determins the top speed of the railgun? is it when watts = friction?
PlayNice, Fri Oct 04 2013, 10:21AM
This guy explains a DC motor that cancels out nearly all back EMF, hows that even possible?
PlayNice, Fri Oct 04 2013, 10:21AM
This guy explains a DC motor that cancels out nearly all back EMF, hows that even possible?
Re: What determins the top speed of the railgun? is it when watts = friction?
Steve Conner, Fri Oct 04 2013, 10:25AM
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.
Steve Conner, Fri Oct 04 2013, 10:25AM
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.
Re: What determins the top speed of the railgun? is it when watts = friction?
PlayNice, Fri Oct 04 2013, 09:36PM
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
PlayNice, Fri Oct 04 2013, 09:36PM
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.
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
Re: What determins the top speed of the railgun? is it when watts = friction?
BigBad, Fri Oct 04 2013, 10:57PM
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, 10:57PM
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?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.
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?
Re: What determins the top speed of the railgun? is it when watts = friction?
BigBad, Fri Oct 04 2013, 11:13PM
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!
BigBad, Fri Oct 04 2013, 11:13PM
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!
Re: What determins the top speed of the railgun? is it when watts = friction?
..., Fri Oct 04 2013, 11:29PM
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)
..., Fri Oct 04 2013, 11:29PM
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)
Re: What determins the top speed of the railgun? is it when watts = friction?
BigBad, Fri Oct 04 2013, 11:52PM
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)
BigBad, Fri Oct 04 2013, 11:52PM
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)
Re: What determins the top speed of the railgun? is it when watts = friction?
PlayNice, Sat Oct 05 2013, 12:44AM
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?
PlayNice, Sat Oct 05 2013, 12:44AM
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?
Re: What determins the top speed of the railgun? is it when watts = friction?
Steve Conner, Sat Oct 05 2013, 01:05PM
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.
Steve Conner, Sat Oct 05 2013, 01:05PM
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.
Re: What determins the top speed of the railgun? is it when watts = friction?
BigBad, Sat Oct 05 2013, 05:05PM
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.
BigBad, Sat Oct 05 2013, 05:05PM
-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.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)
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.
Re: What determins the top speed of the railgun? is it when watts = friction?
PlayNice, Tue Oct 08 2013, 03:15AM
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
PlayNice, Tue Oct 08 2013, 03:15AM
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
Re: What determins the top speed of the railgun? is it when watts = friction?
BigBad, Tue Oct 08 2013, 02:19PM
always
BigBad, Tue Oct 08 2013, 02:19PM
always
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