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

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PlayNice

Thu Oct 03 2013, 08:31AM

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

Some 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

Steve Conner

Thu Oct 03 2013, 10:10AM

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

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.

Yandersen

Thu Oct 03 2013, 10:49AM

Registered Member #6944 Joined: Fri Sept 28 2012, 04:54PM
Location: Canada
Posts: 340

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.

Steve Conner

Thu Oct 03 2013, 11:10AM

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

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.

PlayNice

Thu Oct 03 2013, 11:51PM

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

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?

klugesmith

Fri Oct 04 2013, 12:19AM

Registered Member #2099 Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1714

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).

PlayNice

Fri Oct 04 2013, 02:34AM

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

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?

klugesmith

Fri Oct 04 2013, 06:46AM

Registered Member #2099 Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1714

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:

PlayNice

Fri Oct 04 2013, 10:10AM

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

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, 10:21AM

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

This guy explains a DC motor that cancels out nearly all back EMF, hows that even possible?

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