# What is the ideal shape for rail-gun?

I was trying to create a low voltage (30V) rail-gun. I have quite a hard source of power that doesn't drop voltage upon current drain, further more, this source is re-inforced by big Tesla capacitors.

Unfortunatelly, I've achieved nothing using my setup. I used materials at hand for the purpose.

The rails are pieces of a construction set for kid-engineers. They are made of iron. The projectile was a very thick piece of copper wire.

Obvious failure is, that the inital spark solders the set together. But even after further attempts to move it (poking it with my finger) it doesn't appear to be forced in either direction.

Is my rail-gun shape good? And is my low-power capable of moving anything this way?

• Is this more a question on arms/missile manufacture rather than EE? – Andy aka Aug 18 '14 at 17:47
• How do you know that you have a "hard source" of power? What've you done to measure it? What's the resistance of your railgun main path? A Tesla capacitor is meant to store high voltage, not sustained current. What you need is high sustained current. – horta Aug 18 '14 at 17:49
• horta I have no equipment to measure such informations. But I can create big sparks and still have power. @Andyaka Nope, that's not a question on missile manufacture. Rail-gun is a technical concept which is completely harmless with home equipment. – Tomáš Zato - Reinstate Monica Aug 18 '14 at 17:53
• Tomas, please use the @ symbol with people's name so that they get flagged with message. Your capacitors have no capability to sustain a current. I would agree that all rail-gun demos need capacitors, but they should be high capacitance moderate voltage caps. Not super high voltage caps with small capacitance. – horta Aug 18 '14 at 18:24
• @HariGanti My point was that you need a sustained current long enough to power it until the projectile has at least started moving. His setup is obviously nowhere near that. I'm sure that upon closing the switch, his power-supply internal resistance is preventing any decent amount of power from reaching the projectile. – horta Aug 18 '14 at 20:21

No, your rail shape is not good at all the gap between the rails should be small as possible, and the contact area between the rails and the armature as large as possible. You've maximized the former and minimized the latter. But it's also not the problem keeping it from working. Here are the issues, with number 3 being the most important, but the others are deal breakers as well.

Also, let's keep in mind that a railgun is simply a linear homopolar motor that ejects its armature.

1. Iron (well, more accurately, steel) cannot be used as the winding (rails). This is non-negotiable, you will need to use a nonferrous highly conductive material. Copper would be good but aluminum will work in a pinch.

This is because of the combination of the skin effect and terribly conductivity of iron. It's far too resistive to be practical, and while you might be thinking, "but the skin effect is only for AC!", that does not make it irrelevant here. From your reference frame, it is DC, but any change in current can be viewed as AC from the right reference frame, and the skin effect applies as much to DC that is rising (it doesn't rise instantaneously due to inductance), and the ferromagnetic properties of iron make this effect ~38 times more pronounced compared to copper.

The long and short of it is this which will force the current into a very small cross sectional area of the rails, causing much more resistance for the current path, which will happily heat the iron white hot and hotter. Iron is great for arc and spot welding rods, because the skin effect aids in striking the arc, and the crappy conductivity keeps things hot enough to maintain it. So you can expect fantastic performance from iron, as long as your performace criterium is how well you can spot weld something to the rails.

2. Your rail configuration is awful as well. You're using the corners, which forces all the current into a tiny contact point, which, of course, further improves the spot welder's performance. You want as much contact area between the armature and the rails, but what you've done here is picked the one configuration at minimizes this.

3. It doesn't matter how 'stiff' (having negative impedance) your power supply is. Who cares? 30V is much too low to produce the currents you need. 350V with additional augmentation of the field is the lowest I've ever seen a railgun 'shoot'. And that is discharged into milliohms. Unless your power supply is absurdly powerful, then it is only managing because your resistance is high enough to limit the current. The resistance from the wiring, the rails, the contact point between the rails and the armature, those are all resistive and those are determining your current. And your current is much too low (hint: if you aren't measuring it in kA, yes, kiloamps, it's too low) and all the energy is just heating everything up, the force on the armature is so small that it can't even overcome the whatever tiny forces are keeping the rod in equilibrium and sitting there, at rest. And that its continually getting spot welded probably isn't helpful either.

Railguns, at the end of the day, are really just the world's worst impedance matching problem. Impedance matching is about being able to deliver power to something. If you have a row boat, and row with a black smith's hammer, you'll probably produce the same amount of power as using an oar. But it will do you little good, because it's poorly impedance-matched to the water. The water gives little impedance to the hammer, so your boat doesn't really go anywhere. An oar, on the other hand, is well-matched in impedance. The water offers it a LOT of impedance, and so you can effectively push against the liquid and go on your merry way.

In a railgun, the armature is needs something to push against too. This is a very loose analogy, but we can pretend the magnetic field strength is like the surface area of our oar. The stronger it is, the more there is to push against, and the more of the energy goes towards pushing the armature (moving the boat) and less to just stirring up the water chaotically (heat). Unfortunately for us, the currents needed for an oar just barely wide enough to overcome even the tiny forces of rolling resistance and produce any movement at all are....not trivial. There is no such thing as 'low-voltage railgun.' The lowest voltage I've seen that was able to impart any velocity to a projectile was 350V. And a capacitive discharge. The high voltage is to force huge currents through the load. Capacitors are the least-stiff power supply you can have, they lose voltage very quickly, but that's not what matters. What matters is having high enough voltage for just long enough to generate the huge currents necessary. To make your oar wide enough to matter.

The resistance of your railgun is certainly quite high, and will still be high even if using proper rail material and proper contact area. 'high' in this context is milliohms. Let's say there was 30mΩ of resistance in your setup. This comes from the wires, the contact points of the armature to the rails, the rails and armature themselves, so on. 30mΩ is being exceedingly generous, you likely have much higher resistance in your setup, because I doubt your 'stiff' power supply is rated for 1kA. Is it rated for 1000 amps? That's what 30V would push through 30mΩ. So I think your resistance is much higher.

Oh, and again, being exceedingly generous in the L' (inductance per meter of your rails, which is worse the larger the gap between them is - and yours is quite large - note the per meter. Total inductance is larger with more widely spaced rails, and thus loop area, but inductance per unit distance will drop substantially), IF the rails were copper (ferromagnetic windings are going to work against this to some degree), and we say it is 100nH/m, then the Lorentz force is $$F=\frac{1}{2}L'I^2$$

If we plugin 1000A, we get.... 50mN. I am not sure 50mN is enough to roll that thing. It might be, but probably not. So you'll need currents far in excess of 1000A, and I'd note that even 5000A is considered impractically low generally, and reaching those currents can only be done reasonably with high voltage capacitive discharges. And with that squared term, if your current is, say, 100A, which it possibly could be, the force is vanishingly small.

Of course it doesn't move.

## Let's make it move

Don't worry, I tore your railgun apart with the intent of ending this with a easy road to success. In conclusion, here is how to make it work (and you probably already have what you need)!

There is a variation on railguns called the permanent magnet railgun. They are configured and operate more or less identically, but the key difference is you have a strong magnetic field at right angles to the rails. So if your rails are parallel to the ground, the field's north (or south, depending) should point towards the ceiling. If you place a series of high grade (>1 Tesla) rare-earth permanent magnets in a grid where all their poles are in the same direction and pointing vertically, and put this directly beneath the rails and armature (basically, as close as you can but still prevent them from shorting the rails. A sheet of construction paper may work and simply rest the rails on the magnets), this will dramatically increase the force that is generated at low currents. Ironically, this benefit rapidly vanishes to negligible as you increase currents to levels that are practical for something that could really be called a 'gun', but if you switch to copper rails and augment yours with magnets, you will certainly get the armature to move. It will probably be more in a motor like way, and firing will be akin to a marble rolling off a table, but it will move.

Let's come back to what I said to keep in mind: a railgun is a linear homopolar motor. Adding these magnets are no different than than how we add permanent magnets to all sorts of DC motors, homopolar or not. Here is a video demonstrating how simple it is to make a demo using two speaker magnets. I don't think you'll shoot anything, but if you use a 350V discharge with magnets, you can probably shoot something into an apple (the fruit, not the computer heh).

• Well, that was an answer worth waiting for! Thanks a lot, I enjoyed the reading as much as I enjoyed the knowledge. – Tomáš Zato - Reinstate Monica Dec 12 '15 at 14:01
• +1. Big railguns vaporise the armature and push against the plasma. – tomnexus Dec 12 '15 at 15:15