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c:b ratio

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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c:b ratio

Unread postAuthor: randompkguy » Sun Dec 06, 2009 1:42 am

I know that this might have been answered before, but what is the optimum c:b ratio for an air cannon? I know from others' testing that 1:1 seems to work well, but what about higher pressures such as 1000 or even 3000 psi? I'd assume that as pressure increases, you could benefit from a smaller ratio?
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Unread postAuthor: Major Collins » Sun Dec 06, 2009 2:41 am

yes good question i would also like to find this out :D
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Unread postAuthor: SpudBlaster15 » Sun Dec 06, 2009 2:44 am

"Optimum" depends on what you're trying to achieve.

For power, the larger the better, though you do reach a point of diminishing returns.

For maximum efficiency, the ideal ratio will depend on the pressure used. The ratio at which the internal pressure equalizes with the dynamic friction of the projectile at the end of the round's travel down the barrel is the most efficient. This can be mathematically modeled quite easily using the P1V1 = P2V2 equation.

My guess is that you want a reasonable ratio; not overly wasteful, but not perfectly efficient either. You are correct in your assumption that smaller ratios can be used with higher pressures. For 1-3KPSI, somewhere around 0.02 - 0.05:1 would be a good start.
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Unread postAuthor: jackssmirkingrevenge » Sun Dec 06, 2009 2:48 am

It depends completely on the individual launcher, valve type etc., the best thing to do is model it in GGDT. In general, moar chamber volume = moar powah! but it comes to a point where you increase the chamber volume by 200% and only get a 1% increase in power, the trick is in finding that sweet spot and again, GGDT is very useful here.

For a given quantity of air, if you make the chamber smaller but use a correspondingly higher pressure, power should increase. Herewith a virtual example.
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Unread postAuthor: SpudBlaster15 » Sun Dec 06, 2009 3:00 am

jackssmirkingrevenge wrote:For a given quantity of air, if you make the chamber smaller but use a correspondingly higher pressure, power should increase. Herewith a virtual example.


This is the case only with launchers that have oversized chambers/undersized barrels. An efficiency optimized launcher should not see a performance change when you vary the pressure and volume, but maintain the PV value.
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Unread postAuthor: Ragnarok » Sun Dec 06, 2009 3:45 am

SpudBlaster15 wrote:An efficiency optimized launcher should not see a performance change when you vary the pressure and volume, but maintain the PV value.

I can't agree. If you consider efficiency to be zero acceleration at the muzzle, a higher pressure (but smaller) chamber still results in higher acceleration at the breech end.

Of course, adiabatic decompression and the fact that we are not dealing with an isobaric system complicates things. (Way beyond being able to use Boyle's law accurately)
I talk about the issues of adiabatic cooling and non-isobaric conditions on choosing a C:B ratio here: There are diagrams!

If you read my own and Jack's links, then fire up a copy of GGDT, you can likely answer your own question.
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Unread postAuthor: SpudBlaster15 » Sun Dec 06, 2009 5:30 am

Ragnarok wrote:I can't agree. If you consider efficiency to be zero acceleration at the muzzle, a higher pressure (but smaller) chamber still results in higher acceleration at the breech end.


Higher initial acceleration yes, but the pressure in the large P small V system is going to drop more quickly, and the end result will be the same average barrel pressure, and thus the same total acceleration. IF the launchers are completely efficiency optimized, the integral of Force*Distance should be the same for both systems.

However, GGDT seems to disagree somewhat, so as you mentioned, there are obviously more factors at work in a less abstract view of the problem.
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Unread postAuthor: john bunsenburner » Sun Dec 06, 2009 5:38 am

So what would you guys recomend as pressure once the projectile has reached the end of the barrel?

I am thinking that 0psi in the end would give a quiet shot with acceleration until the projectile left the barrel, or am I wrong?
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Unread postAuthor: jackssmirkingrevenge » Sun Dec 06, 2009 5:53 am

john bunsenburner wrote:I am thinking that 0psi in the end would give a quiet shot with acceleration until the projectile left the barrel, or am I wrong?


With a relatively heavy projectile, pretty much, though I would still recommend a suppressor to cut out the inevitable "uncorking" noise.
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Unread postAuthor: john bunsenburner » Sun Dec 06, 2009 6:34 am

No, its not about a quiet shot, its about a cartridge with the smallest possible volume for a large barrel...
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Unread postAuthor: jackssmirkingrevenge » Sun Dec 06, 2009 6:49 am

In that case, if it's maximum power you're after, the idea pressure at the muzzle isn't zero. Have a play with GGDT ;)
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Unread postAuthor: john bunsenburner » Sun Dec 06, 2009 7:06 am

Haha, i hoped for a specific answer from our cartidge guru, well i'll have a look.
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Unread postAuthor: Ragnarok » Sun Dec 06, 2009 8:09 pm

SpudBlaster15 wrote:Higher initial acceleration yes, but the pressure in the large P small V system is going to drop more quickly

Drop more quickly yes - but it had more pressure to begin with.

For a simplified explanation, consider this. If we have two optimised launchers (where optimised relates to zero acceleration at the muzzle) with identical barrels - only one runs at 100 psi and the other at 200 psi.

The 100 psi one has 100 psi at the breech, and 0 psi at the muzzle - which, assuming it to be linear (which of course, it isn't), that's a 50 psi average.
The 200 psi one has 200 at the breech and 0 psi at the muzzle, so that's a 100 psi average.

Of course, if you actually model it properly, the pressure is not close to linear, but the average pressure is still higher in the 200 psi one.

john bunsenburner wrote:So what would you guys recommend as pressure once the projectile has reached the end of the barrel?

Insufficient data.

Personally, I'd recommend reading my post that I link above. I define C:B ratios not by the pressure they generate at the muzzle, but as a fraction of the muzzle energy that an infinite ratio provides (An infinite ratio can be closely predicted in GGDT by just an arbitrarily large chamber).

More than 90% is almost certainly a waste.
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Unread postAuthor: Technician1002 » Sun Dec 06, 2009 10:32 pm

Due to the fact the projectile at the muzzle is plowing it's way through air, it is undesirable to have a muzzle pressure of zero. It will be decelerating at the muzzle as the pressure in front of the projectile is higher then the pressure behind it.

I prefer to cut the barrel to where the acceleration is dropping off towards zero but still accelerating as it exits.
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Unread postAuthor: Ragnarok » Mon Dec 07, 2009 3:31 am

Technician1002 wrote:Due to the fact the projectile at the muzzle is plowing its way through air, it is undesirable to have a muzzle pressure of zero.

Zero pressure at the muzzle shouldn't be written off. From one perspective, it results in a lack of muzzle blast and thus a more stable projectile.

Either way, I wouldn't suggest anyone attempted to optimise a launcher to that extent. In most cases, similar performance could be had from a tiny increase in chamber size but a halving of barrel length.
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