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Chamber to barrel ratio question.

Post questions and info about pneumatic (compressed gas) powered cannons here. This includes discussion about valves, pipe types, compressors, alternate gas setups, and anything else relevant.
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Chamber to barrel ratio question.

Unread postAuthor: nortonn » Wed Nov 20, 2013 7:32 am

Hey guys!

Long time lurker, first time poster...

Thanks for all the valuable info guys! Im building my second launcher. its a european QEV piloted by a 3 way spool valve.

Im going for a multishot with simple breech loading system.

my question is barrel to chamber volume ratio, i cant run GGDT (i have a mac)

so what should i be aiming for? il be using CDS piping for a makeshift .22 barrel around 60cm length.

what would be the optimum firing chamber volume? il be using standard diablo shaped .22 pellets.

any help appreciated!!!

jay
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Re: Chamber to barrel ratio question.

Unread postAuthor: Ragnarok » Fri Nov 22, 2013 11:29 pm

Hello Jay.

The answer to your question depends on two things: How you define optimum, and the pressure in question.

If optimum is defined as the highest kinetic energy, there's no upper limit. Any increase in chamber size will increase energy, although at ever diminishing returns!

If optimum is defined as using the air as efficiently as possible, then that's far more dependent on pressure - this depends on having the air decompressed down to nearly atmospheric pressure at the muzzle, using all the push the air volume can offer. This, however, will result in quite a low overall kinetic energy, as the projectile will barely accelerate in the last section of the barrel - effectively giving a performance little different from a barrel a fraction of the length.

A happy medium is usually a similar volume for both chamber and barrel - a smaller chamber for greater air efficiency, a larger one for a bit more punch. (However, going larger than twice the volume of the barrel is unlikely to confer any meaningful boost, except at very low pressures).
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Re: Chamber to barrel ratio question.

Unread postAuthor: jackssmirkingrevenge » Sun Nov 24, 2013 5:54 am

Remember that for the same quantity of air, its better to have a small high pressure chamber than a large low pressure one.

Here's the data from a virtual GGDT model I had done to "prove" the point:

in each case, we're talking about the same quantity of air, but in a reduced volume and therefore at higher pressure.

(chamber is of constant diameter but different length, projectile size, weight and valve flow/barrel length are constant)

20 inch chamber at 50 psi - 406 feet per second

10 inch chamber at 100 psi - 537 feet per second

5 inch chamber at 200 psi - 684 feet per second

2.5 inch chamber at 400 psi - 830 feet per second

1.25 inch chamber at 800 psi - 958 feet per second

0.625 inch chamber at 1600 psi - 1006 feet per second
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Re: Chamber to barrel ratio question.

Unread postAuthor: Ragnarok » Sun Nov 24, 2013 7:21 am

Not too great a surprise...

<science>

....as the stored energy (even if not the amount of stored gas) is greater in the later cases. In a pneumatic system, the stored energy is Pa*v*LN(Pa/Pb), so as the ratio between stored pressure (Pa) and atmospheric pressure (Pb) goes up, so does the stored energy, even if Pa*v is functionally the same (although in those cases, it's not quite so, as the pressures here are absolute, not gauge pressures).

However, it's not invariably true that increasing pressure improves performance. Remembering that thermodynamic effects come into play...

In an adiabatic system (one where heat does not enter or escape - relatively true on our timescales), P*V^k is constant. As, k, the ratio of specific heats of most gasses is about 1.4, the equation is usually P*V^1.4.

So, every time you double the (absolute) pressure and halve the volume the gas will only expand to about 76% of the final volume.
There is a peak to the graph, as the gas will eventually not expand to the full volume of the barrel, which will create a vacuum that will detract from performance faster than the diminishing returns of slightly more compressed gasses.

And remembering that PV = nRT, where R is a constant and n is a constant in a closed system (and the compressibility factor is insignificant enough to not actually be included in the ideal gas law), this results in a change in temperature in the gas... lowering the speed of sound in the gas (limiting its expansion velocity) and potentially even leading the gas to liquefy in the launcher.

Certainly, it's true under the vast majority of real world circumstances, but it's not a point that can be proved to be exhaustively true.

</science>

But, basically, yeah. More pressure can be assumed to be better than more volume.
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Re: Chamber to barrel ratio question.

Unread postAuthor: DYI » Mon Dec 02, 2013 12:57 am

The stored energy given by Ragnarok assumes an isothermal process, where the system is by definition receiving energy input during the process through heat transfer. A form more appropriate to our purposes (and more in line with what I would call the "stored energy") is E[sub]stored[/sub]=(k[sup](γ+1)/γ[/sup]/(1-γ))*{P[sup](γ-1)/γ[/sup]-P[sub]0[/sub][sup](γ-1)/γ[/sup]}.
Where k=P[sub]0[/sub]V[sub]0[/sub][sup]γ[/sup].

Assuming PV=1, this reduces to E[sub]stored[/sub]=(1/1-γ)*(P[sub]0[/sub]/P)[sup]1/γ[/sup]. A constant other than one produces a result of the same form but with a different constant. Thus we see in a more direct way that in the scenario JSR proposes (PV=const.), available energy for work increases with increasing pressure.

Also, the code for subscripts/superscripts has apparently changed, but I don't know to what. Rag seems to have fudged it by using smaller text. I've PMed PCGUY about it and will fix this post when I get a response.
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Re: Chamber to barrel ratio question.

Unread postAuthor: Ragnarok » Mon Dec 02, 2013 6:23 am

DYI wrote:The stored energy given by Ragnarok assumes an isothermal process

You're quite right, but it's the only equation I could remember at the time. I've not really done this for a few years, and I couldn't find where it was in my old thermofluids lecture notes.

But yeah - going and actually doing the maths (assuming an ideal, massless gas, anyway*), it does ultimately look like my intuition was wrong. Although eventually a vacuum will form behind the projectile, the increases in initial force on the projectile will offset the relatively low "negative" forces the vacuum produces later in the barrel.

*But not a spherical horse in a vacuum.

Basically, disregard my previous post.

That said, a repetitive doubling/halving of pressure and volume will still produce a point at which the barrel is over-long and detracts from performance.
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