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ETG gun theoretical efficiencies

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LAN_403

TheMerovingian

Thu Feb 26 2009, 12:11PM

Registered Member #14 Joined: Thu Feb 02 2006, 01:04PM
Location: Prato/italy
Posts: 383

With an oversimplified model i tried do calculate the theoretical efficiency for a plasma-discharge propelled gun.

Assumptions:

1) The plasma is considered an ideal gas (not far from reality)
2) The Cp and Cv of plasma are considered constant over the range of temp considered(very very far from reality)
3) The Gas (air) heating is considered irreversible, fast and adiabatic (so no barrel heating)
4) The expansion propelling the projectile is considered adiabatic as well (it takes some time, so some heat leaaks, quite far from reality)
5) The system is working against atm pressure = initial pressure
6) No frictions and the projectile is gas tight

I tried a calculation for a 0,6cm barrel 10 cm long with 4 gram projectile, 1ml initial gas volume and 1 Bar initial pressure, fired with a 1000uF 350V Cap bank (61J)

I got the following results

Mechanical Work = 8,75J
Efficiency = 14%

Projectile speed = 46m/s

Seems reasonable, but probably much less, maybe the half efficiency.

What do you think? Seems realistic?

DYI

Sat Feb 28 2009, 10:17PM

Registered Member #1917 Joined: Fri Jan 09 2009, 02:38AM
Location:
Posts: 62

I tried to simulate this situation on GGDT, but apparently it doesn't like 90k degree gas temperatures. Assuming that at such insane temperatures and low projectile speeds, an immensely hotter gas doesn't make much difference, I tried the same chamber pressure (2540 psi) and 20k degrees Fahrenheit, and ended up with a muzzle speed of 90m/s, giving 17J muzzle energy and 28% efficiency. (your 46m/s number actually gives 4.2J).

To get a good idea of how useful these simplified simulations are, I modeled my ETG using GGDT in the same manner that I modeled the last one. The result?
Input energy: 1442J (1130uF, 1600V)
Chamber volume: 1.93cm^3
Barrel Length: 20.32cm
Projectile mass: 0.12g
Muzzle speed: 2.48km/s
Muzzle energy: 368J
Efficiency: 25%

As you can see by looking at my thread, that plastic pellet did not carry 368J of kinetic energy. In fact, it is quite likely that it carried less than 20J.

There are a lot of factors to be considered that ruin these ideal models - chamber/barrel heating, discharge time, amount of energy dissipated in the switching and connectors, plus the factors you mentioned, and probably a whole host of others that I can't think of right now.

I've heard of pure thermoelectric gun designs that exceeded 50% efficiency, and the best amateur design I've seen so far reached a maximum of less than 6%. It makes me think that amateur designs are doing something fundamentally wrong. Pulse caps should help, but if my early tests are anything to go by, they aren't going to multiply efficiency by a factor of 8 by themselves.

Fnord

Sun Mar 01 2009, 12:48AM

Registered Member #2004 Joined: Sat Feb 28 2009, 11:43PM
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Posts: 39

I've heard of pure thermoelectric gun designs that exceeded 50% efficiency, and the best amateur design I've seen so far reached a maximum of less than 6%.

If you're referring to larda's gun, isn't it possible that most of the energy was wasted heating a large amount of aluminum up, instead of converting a small amount to plasma and heating the plasma up?

rp181

Sun Mar 01 2009, 01:00AM

Registered Member #1062 Joined: Tue Oct 16 2007, 02:01AM
Location:
Posts: 1529

Lol, 4hv is stealing people!
For those of you who are not familiar. GGDT is a gas gun simulator:

As fnord said, I think the main problem lies in two area's.
1)When people make ETG's, mostly they do because it looks cool. That means people are after more plasma, rather than more dense plasma.
2) People are used to normal guns, which use a more refined barrel chamber system. I think people keep trying to use too large chamber's and caliber's for a given power.

badastronaut

Sun Mar 01 2009, 03:32AM

Registered Member #222 Joined: Mon Feb 20 2006, 05:49PM
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Posts: 96

You could try using dry ice as the propellant...

rp181

Sun Mar 01 2009, 03:36AM

Registered Member #1062 Joined: Tue Oct 16 2007, 02:01AM
Location:
Posts: 1529

How would that help? Wouldn't co2 extinguish any arc that becomes present? I think dry ice is just a waste of energy (both in cooling it, and bringing it back to gas temperature). Might be worth a try.

DYI

Sun Mar 01 2009, 04:00AM

Registered Member #1917 Joined: Fri Jan 09 2009, 02:38AM
Location:
Posts: 62

Granted, Larda didn't get to do a whole lot of testing with his design because of its hazards (read: almost burning his house down with the first test shot and having to do the rest outside), but why would his design's efficiency be significantly different from mine? The superior construction would definitely allow higher efficiency after optimization, but 400% higher?

My ETG could be improved with a smaller chamber and less steel in the conduction path, a more efficient switch, and likely by propellant changes as well. Has anyone actually SEEN a well-documented amateur ETG that reached or exceeded 10% efficiency?

rp181

Sun Mar 01 2009, 04:18AM

Registered Member #1062 Joined: Tue Oct 16 2007, 02:01AM
Location:
Posts: 1529

I remember seeing one on here awhile ago, ile look for it.

badastronaut

Mon Mar 02 2009, 12:07AM

Registered Member #222 Joined: Mon Feb 20 2006, 05:49PM
Location:
Posts: 96

How would co2 extinguish an arc? If the capacitor bank energy isn't enough to vaporize and ionize the co2, then the bank is too small and there's too much co2. It's all about balance. CO2 doesn't even take that much energy to vaporize, unlike water.

You can't make the assumption that the system is adiabatic because you are using such high temperature gradients. The heat transfer rate from a 90000K plasma to a 300K wall is going to be very large. You'll need to do some transient analysis to estimate the actual average temperature of the gas. The more massive the projectile is, the worse this becomes since the time is longer. A smaller surface area will greatly help with the heat transfer problem.

Also note that not all of the energy of the capacitor bank will go to the place where you want it. For example, if the arc has zero resistance, then all the energy gets wasted in the capacitors and bus bars and cables. In terms of energy transfer, the cap bank and the arc act like a voltage divider, so it is best to have a high resistance arc relative to the resistance of the bank. This is true with any type of energy transfer problem.

DYI

Mon Mar 02 2009, 02:06AM

Registered Member #1917 Joined: Fri Jan 09 2009, 02:38AM
Location:
Posts: 62

Is it correct that, with two resistances in series, the larger one will dissipate more energy than the smaller one over a given time? If so, then the connector's total resistances should be as low as possible, and the arc's resistance should be as high as possible while still allowing a fast enough discharge for the intended muzzle speed (i.e., the caps shouldn't still be discharging after the projectile is clear of the barrel).

Of course, this raises a problem: as far as I know, most arcs have very low resistance, regardless of what substance they started off as. Does this mean that most of the energy in our ETGs is being lost in the connections and switching?

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