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Choosing Capacitors for Railgun [was "Greetings..."]

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Quantum Singularity

Mon Feb 20 2006, 10:26PM

Registered Member #158 Joined: Sun Feb 12 2006, 09:53PM
Location: Central Ohio
Posts: 282

I'd like to add to the discussion that myself and maybe some others are of the thinking that I was when I set out to design a railgun in the 90's. Back then it was more unheard of to try to pulse thousands of amps out of electrolytics. When I was researching and designing mine, most designs were in the kilo-volt range and used some kind of spark gap switch. My design had a max of 12kJ, which would be dificult to switch solid state. We tend to push the limits of our components sometimes as experiemtners. I would have to beleive that any railgun design using lytics is probably pushing their limits severely. Will it work, probably. Will it work good, maybe. I have not attempted such things with lytics myself. Using the high esr of lytics to slow down the pulse sounds to me like plugging up your fuel injectors so your car cant go more than 65mph. And everyone is talking esr, what about esl? Most pulse caps which are actually designed for this kind of work have an esl rating. I dont happen to know what kind of esl ratings lytics have to compare though, and havent given it great thought to how it would effect performance ina railgun. Just thought I'd mention it to see if someone has.

Eric

Mon Feb 20 2006, 11:02PM

Registered Member #69 Joined: Thu Feb 09 2006, 07:42AM
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Posts: 116

I was just looking at this for some CDE computer grade filtering caps. Manufacturers usually don't come out and specify the DCL but by looking at an impedance/frequency graph it looks like it's about 40nH for a 7900uF 400V model (9KHz self resonance). Assuming other electrolytics have similar properties, this wouldn't be a significant issue in a rail gun. Transmission line and rail inductances would be much higher in comparison.

badastronaut

Tue Feb 21 2006, 12:24AM

Registered Member #222 Joined: Mon Feb 20 2006, 05:49PM
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When choosing capacitors for railguns, there are two things to consider: stored energy and ESR. It is always better to have higher energy for railguns.

If a railgun has a projectile with enough preloading force to prevent arcing, then the only reason that projectile might not move a millimeter is because of friction. If friction is overcoming the accelerating force, then that means there either isn't enough current or enough action integral or both. Friction force is usually greater than 200N for non-arcing railguns.

If a projectile moves through the rails but stops midway before exiting the barrel, then that means that the current pulse wasn't long enough.

Peak current has nothing to do with railgun performance because peak current is a measure of a single instantaneous value. Assuming negligible friction, which situation is better: constant 1,000,000 amps for 1 picosecond, or constant 100,000 amps for 10 milliseconds?

Yes, force is proportional to the square of the current, but that too is an instantaneous value. For accelerating an arbitrary object of fixed mass m to maximum velocity, which is better, a net accelerating force of 10,000 newtons for 1 millisecond, or a net accelerating force of .1 newtons for 1000 seconds?

All of this leads to the concept of impulse-momentum in railgun applications. It turns out that the amount of impulse due to electromagnetic force on a railgun projectile for solid non-arcing armatures is proportional to a constant times the action integral.

For those of you that don't know, the action integral is a scalar value equal to the integral of the square of the current with respect to time from time zero to t. Action is not a conserved property, and it represents the amount of electrical impulse in a circuit.

In order to maximize the momentum transfer to the projectile, it is necessary to maximize the action integral. It may also be necessary to take into account the amount of impulse that the friction force delivers to the projectile.

Sparing the pain of derivation, it turns out that the value of the action integral is equal to the energy stored in a capacitor divided by the TOTAL circuit resitance. (Action = E/R) This is assuming that the energy stored in the capacitor is discharged completely as time approaches infinity. For railguns, the total resistance of the circuit is equal to the sum of the parasitic resistances and the equivalent resistance due to energy transfer to the projectile from motional EMF.

The conclusion is that to maximize efficiency, it is necessary to reduce the total parasitic resistances as much as possible. It turns out that the majority of resistances in amateur railguns is in the capacitor banks, anywhere from 1 ohm to 1 milliohm. The resistance of the rest of the circuit is usually around less than 1-3 milliohms with the former being the typical for good railguns.

Therefore, when selecting capacitors, choose the ones with the lowest ESR. In order to reduce ESR, it is necessary to wire the capacitors in PARALLEL, and any other configuration will only hurt performance, assuming projectile velocity is less than 1km/s, instantaneous current is not much more than 200 kA, and initial cap voltage is >~200V.

One set of capacitors in series doubles the nominal ESR of the bank, one set of capacitors in parallel halves the nominal ESR of bank. The action integral is independent of voltage. The bank in parallel will have the higher action integral, which is why it will perform better, assuming the conditions in the above paragraph are true.

Increasing voltage has almost nothing to do with increasing performance, assuming you aren't using an electro-thermal gun. For example, which would you rather have, a railgun with a constant 100,000 amps flowing through it at 100 volts, or stick a resistor in the circuit and have 100,000 amps flowing through it at 10,000 volts?

Edit:
It is also interesting to note that the action integral does not depend on the circuit inductance. This is because the property of inductance dissipate no energy i.e. it gives the energy back to the circuit. Assuming no friction, a railgun with or without an added ideal inductor will perform the same, also assuming no rail resistance and rails long enough to allow the capacitor to discharge completely. However, this is a different story when friction or parasitic resistances are included. Can you guess which one?

The only reason I can think of to add an inductor is to lower peak current without seriously degrading performance.

Edit:
Also note, that if you're having problems with the projectile welding to the rails, then that means that there isn't enough preloading contact force to prevent arcing. Either way, if welding is a problem, then that projectile isn't going to move no matter how much preloading force you have.

The reason welding happens is that the capacitor ran out of energy way before the projectile had a chance to move; therefore, the molten metal had a chance to cool and fuse together.

If the capacitor had enough energy, and there was enough current to produce a significant net accerlating force, then the projectile would just slide along a layer of molten metal and plasma.

Using injection for the sole purpose of preventing welding indicates that there was no significant projectile energy due to EM energy transfer since it could not overcome welding. However, that does not mean that injection isn't beneficial to a legitimate railgun system, and there is a electro-kinetic reason for that............

Eric

Tue Feb 21 2006, 01:14AM

Registered Member #69 Joined: Thu Feb 09 2006, 07:42AM
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The only thing I'd add to what you are saying about the importance of system resistance is that you want to choose the capacitors that give you the *bank* with the lowest ESR for a given capacitance/energy, not necessarily the *cap* with the lowest ESR.

For example, if you have the option to get 4700uF caps, 28.1 mOhm ESR or 15000uF caps, 13.1 mOhm ESR at a certain voltage you would want the former since ESR*C is substantially less than the latter. If you build a bank of a certain capacitance out of those smaller caps with the higher ESR you'll have a lower overall ESR.

Re: injection, it's funny but I was just running some simulations of my prospective system, fairly well optimized without injection and found that injection *decreased* energy transfer out of the system. For reasonably small injection speeds up to several 100s of m/s it actually decreased muzzle velocity... I'm not planning on using injection, just thought it was interesting/counter intuitive.

Quantum Singularity

Tue Feb 21 2006, 06:00AM

Registered Member #158 Joined: Sun Feb 12 2006, 09:53PM
Location: Central Ohio
Posts: 282

As I dont understand all the details on every aspect of engineering a railgun, I have made a simpler model in my head and am trying to figure a few things out. I am sure if there is a much more complicated answer someone will chime in. Adressing series/parallel caps, esr, and action integral.

Take 4 matched caps and a certain load. Assume the circuit resistence is greater than the cap bank ESR. In series config you will get 4X the peak current for 1/4 the time approximately, as compared to parallel config.

Yes, force is proportional to the square of the current, but that too is an instantaneous value. For accelerating an arbitrary object of fixed mass m to maximum velocity, which is better, a net accelerating force of 10,000 newtons for 1 millisecond, or a net accelerating force of .1 newtons for 1000 seconds?

Isnt this like apples and oranges? The integrated force over time is 10x different between the two. Can we not view the current as an average value over the pulse length not just an instantaneous peak? If so the 4x higher AVG current in the series config would then give 16X the AVG force. This is all in 1/4 the time, but still your integrated force would then be 4x greater wouldnt it? And if the force is close to the friction, a lower amount of force over longer duration might not even get it to move?

If a projectile moves through the rails but stops midway before exiting the barrel, then that means that the current pulse wasn't long enough.

Doesnt that mean that the friction was greater than what the integrated force is? If a 4x longer pulse might have fixed this problem, wouldnt a 4x higher current also have?

Friction force is usually greater than 200N for non-arcing railguns.

What is it for arcing railguns? And what really defines the difference here in terms of how they function?

badastronaut

Tue Feb 21 2006, 06:51AM

Registered Member #222 Joined: Mon Feb 20 2006, 05:49PM
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Oh dear...

I hope that your cap ESR isn't lower than your circuit resistance....

When you say you have 4 matched capacitors, do you mean they are all in series?

Regardless, when you add capacitors in parallel or series, you must obey conservation of charge when analyzing them .

Ok, lets consider this problem as averages.

First we must assume that our capacitors have no ESR.
You have 4 capacitors. In parallel, they output 1X current for a time of 1t. In series, the output current (this is average current remember) will be 4X. Now the trick here is that in order for conservation of charge to be observed, the time must be equal to 1/16 t and not 1/4 t.

This is because of conservation of charge. When you wire the capacitors in series, you are reducing the capacitance, and that reduction of capacitance cannot be overcome by the increased working voltage.

In short, two caps wired in parallel charged to 1V will store more charge then the same caps wired in series charged to 2V. This is the origin of the 1/16 time factor in your example.

The only thing that remains constant , assuming the caps have no ESR, is the action integral delivered by the capacitors. In other words, it doesn't matter if they are in series or parallel, the action is the same.

Now this will imply that the performance of either series or parallel is the same. The conclusion is true if and only if the capacitors have no ESR.

When we include ESR in the analysis, it turns out that parallel capacitors always wins because it can deliver the higher action integral since the total resistance is lower in the parallel case.

Apples and oranges???? Yes you're right, the whole point of that is that force and impulse are different. The significance is that impulse is a better measure of performance than peak force in this particular application.

Doesnt that mean that the friction was greater than what the integrated force is? If a 4x longer pulse might have fixed this problem, wouldnt a 4x higher current also have?

It means that the impulse due to friction was equal to the impulse due to EM forces. A 4x higher current might fix the problem if the duration of the current isn't changed. This means you will need to have a bigger capacitor bank. Another way to fix this problem is to shorten the rail length.

I define a non-arcing railgun as a railgun such that the armature never losses contact with the rails in a way as to create electrical arcing. In more technical terms, it means that transition doesn't occur. Arcing and non arcing function the similarly. The difference is the amount of relative friction force between the two, all else constant. Usually the magnitude of the EM force is much greater than the magnitude of the friction force for most of the duration of the pulse. Friction is much more of a serious problem for amateur experimenters than the multi megajoule facilities.

Arcing railguns can be classified as ones that have transition as well as ones that use plasma armatures. With plasma armatures, the physics becomes extremely complex, and there is an addition thermal consideration when trying to analyze them.

Quantum Singularity

Tue Feb 21 2006, 09:35AM

Registered Member #158 Joined: Sun Feb 12 2006, 09:53PM
Location: Central Ohio
Posts: 282

badastronaut wrote ...

Oh dear...

I hope that your cap ESR isn't lower than your circuit resistance....

When you say you have 4 matched capacitors, do you mean they are all in series?

I was under the impression by the little bit of documented info out that in a railgun (atleast an arcing one) that the circuit resistance will always be higher than your caps ESR... unless your using some crappy lytics with really poor ESR.

ABout the 4 caps... I was just using that as my example, meaning 4 of the same caps compared in a series versus parallel config.

I see my mistake on the 1/16 duration vs 1/4. I flubbered up my calculations.

Are there really non-arcing railguns out there?

And finally, when picking out cap values, is there a fairly easy way to get a ball park figure on the pulse length? It probably isnt quite as simple as a RC time constant because there is some L in there too. Would the whole system resonate for a few cycles dampened by the resistance in the circuit? Or is the L so small that it has no effect?

Eric

Tue Feb 21 2006, 07:07PM

Registered Member #69 Joined: Thu Feb 09 2006, 07:42AM
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Posts: 116

Quantum Singularity wrote ...

And finally, when picking out cap values, is there a fairly easy way to get a ball park figure on the pulse length? It probably isnt quite as simple as a RC time constant because there is some L in there too. Would the whole system resonate for a few cycles dampened by the resistance in the circuit? Or is the L so small that it has no effect?

I've found the only way to understand the circuit is to simulate it. It's not hard to do, just write a differential eqn integrator for an RLC circuit and then include the term for the back emf from the armature. That'll give you a pretty good idea of what to expect, minus friction and some rather nasty-to-calculate AC effects.

You can sort of model the circuit as a simple RLC circuit but it falls pretty short becuase R and especially L are changing during the shot. Still it might give you some ballpark values for pulse length. L is very important to the calculations, moreso than R (in decent systems where R is small).

pulslaser

Tue Feb 21 2006, 08:56PM

Registered Member #156 Joined: Sun Feb 12 2006, 07:04PM
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Posts: 23

It's very interesting to read all this theoretical discussions but I think "ERQ" want's to build a real railgun and not to simulate one. So I think it would be more helpfull for him to read about practical experiences and not plans about somebody want's to do or somebody should do. Once again, arcing and big bang may impress spectators, but are harmful for the effiency and the speed of a gun. High currents, short time are not the same than lower currents longer time. At high currents you can't apply Ohm's law because of nonlienarities of arcing.
Forget about injectors, if you once the seen, the magnetic pressure of high currents ( even whith relatively small banks, 12kJ 350V, eletolytic)distroying well solded connections and even open bolted ones, you don't care about static friction. Use a switch to start the shot and uses some serial augmentation if you don't get enough farad in your bank to lengthen the puls.
By the way, I should like to get information about the speed of railguns of other builders, not estimated ones, but measured, to compare if my way of low voltage, high capacity is right

Quantum Singularity

Thu Feb 23 2006, 02:27AM

Registered Member #158 Joined: Sun Feb 12 2006, 09:53PM
Location: Central Ohio
Posts: 282

pulslaser wrote ...

It's very interesting to read all this theoretical discussions but I think "ERQ" want's to build a real railgun and not to simulate one. So I think it would be more helpfull for him to read about practical experiences and not plans about somebody want's to do or somebody should do.

As I will probably like to finish my railgun project someday, I thought it would be better to understand how it really works not just try to copy someones elses project. BTW, anyone with real world results is more than welcome to post... I dont beleive anyone banned such info from this thread

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