Plenum Volume Confusion

[thomasair]

So just an FYI, this is a non linear problem. If you've taken a differential equations you can relate this to a tank mixing problem.

The other thing to remember is you are dealing with a compress able fluid. Not water. When you up the pressure of air, the amount of air does not scale linearly. Conversely a plenum is regulated. This you fix the pressure and increase the tank volume. But the gas volume does not increase proportionally to the tank volume. To maintain the same pressure of air across a larger volume you need a MUCH larger quantity of air.

Thus to tie it back to the original question. The key is the compression of the gas that yields higher shot count.

An easy anecdotal thing you can try out is get two air rifles with different tank sizes. A tank size of 150 CC does not take half as long to fill up as a tank size of 300 cc

Pressure and volume in a closed system are, in fact, (very nearly) proportional.

There is (very nearly) double the amount of air in a 300cc tank at 3000 psi compared to a 150cc tank at 3000 psi.

Mike

I have amended this post to reflect my misuse of wording. I originally used the word exact but have replaced it with very nearly.

 

[JimD]

Yes I think a larger mass and volume of air will come out of a larger plenum but it gets a little complicated because the higher pressure in the plenum should also close the valve quicker. The same mass of air at higher pressure will have lower volume. So several things are a little different and not all in the direction of increasing velocity. But velocity increases, that is the biggest effect. The bigger plenum will not fall in pressure as fast when the valve opens. So the pressure behind the pellet will also not decrease as quickly.

 

[purplepom]

Pressure and volume in a closed system are, in fact, proportional.

There is exactly double the amount of air in a 300cc tank at 3000 psi compared to a 150cc tank at 3000 psi.

Mike

Wrong!

Doubling the tank volume at the same pressure does not exactly double the amount of air if you take the compressibility of air into account. The relationship depends on how closely the air behaves like an ideal gas versus a real gas under the given conditions. Here's a detailed breakdown:

Ideal Gas Behavior

For ideal gases, the amount of air (in moles) is governed by the Ideal Gas Law:

PV = nRT

n being the moles of the gas we can obviously conclude for an ideal gas n scales proportionally to the volume by exactly P/(RT). But air is not an ideal gas!

Real Gas Behavior

For real gases, deviations from the ideal gas law occur due to factors like intermolecular forces and finite molecular volume. The compressibility factor Z is introduced to correct for these deviations:

PV = ZnRT

Where Z represents the deviation from ideal behavior:

Z = 1 for ideal gases.
Z ≠ 1 for real gases (especially at high pressures or low temperatures).

Z is also a function of volume

At higher pressures, is typically less than 1 because intermolecular attractions reduce the effective pressure. In this case, doubling the volume may result in more than double the amount of air.

At very low pressures, approaches 1, and the gas behaves more ideally, making the relationship closer to linear

You can compute the partial derivative of moles with respect to volume like so

Clearly not proportionally changing

Other complicating factors include temperature and Mach numbers but for the sake of comparibility we will just talk about tank volume Delta's.

The pressure differential between the plenum volume and the tank volume also change this behavior.

Tank pressure is at 250 bar, plenum is at 140 bar. You would actually have to treat these two tanks as having two different fluids and then you can model this system as a mixing problem. Then you change the volume of one of the tanks and run the analysis again. The discrepancy between those two systems would exactly explain away the extra shot counts.

I guarantee you those extra shots is due to the regulator system needing to mix less higher pressure air from the tank into the plenum to maintain the overall average pressure of the plenum

Finally we do not have perfect regulators, plenum pressure fluctuate over time and drop over time, again this further adds to the non linearity of the system.

 

[JungleShooter]

Well, I'm glad that after somebody was declaring the OP's question "had absolutely nothing to do with math" — we got someone else to prove the exact opposite:

He showed that there is so much math is involved — I almost un-watched this thread, as my math allergies kicked in with a vengeance that only a wood full of hazelnut bushes in February could compete with....

➠ How is that for the widest possible range of opinions at AGN?!?



Now from the philosophical to the practical:
Maybe someone could not just explain the advantages of larger plenums — but their disadvantages.

Because... — even though plenums are cheap to make — few airgun manufacturers are producing large plenums. They've GOT to have reasons (other than making us buy extra plenums...)!

I have a few more questions, but why don't we run with this one first.
Thanks.

Matthias

 

[Firewalker]

Well, I'm glad that after somebody was declaring the OP's question "had absolutely nothing to do with math" — we got someone else to prove the exact opposite:

He showed that there is so much math is involved — I almost un-watched this thread, as my math allergies kicked in with a vengeance that only a wood full of hazelnut bushes in February could compete with....

➠ How is that for the widest possible range of opinions at AGN?!?



Now from the philosophical to the practical:
Maybe someone could not just explain the advantages of larger plenums — but their disadvantages.

Because... — even though plenums are cheap to make — few airgun manufacturers are producing large plenums. They've GOT to have reasons (other than making us buy extra plenums...)!

I have a few more questions, but why don't we run with this one first.
Thanks.

Matthias

How about a nice Notos plenum?

 

[Firewalker]

...He showed that there is so much math is involved — I almost un-watched this thread, as my math allergies kicked in with a vengeance that only a wood full of hazelnut bushes in February could compete with.... ...

 

[Camaro454]

Well, I'm glad that after somebody was declaring the OP's question "had absolutely nothing to do with math" — we got someone else to prove the exact opposite:

He showed that there is so much math is involved — I almost un-watched this thread, as my math allergies kicked in with a vengeance that only a wood full of hazelnut bushes in February could compete with....

➠ How is that for the widest possible range of opinions at AGN?!?



Now from the philosophical to the practical:
Maybe someone could not just explain the advantages of larger plenums — but their disadvantages.

Because... — even though plenums are cheap to make — few airgun manufacturers are producing large plenums. They've GOT to have reasons (other than making us buy extra plenums...)!

I have a few more questions, but why don't we run with this one first.
Thanks.

Matthias

The reason is the law of diminishing returns.

 

[JimD]

I think the lack of good sized plenum is much more common on less expensive airguns. My P35s have really small plenum, like 15ccs. The bigger one I put on is 35ccs, I think. That is much less than the 60ccs the P35X has. I think it's a combination of making guns to a price point and thus not putting in more than necessary to get the sale versus the seemingly growing realization that 15cc plenum are pretty limiting. As we start buying the guns with bigger plenum suddenly there will be more guns with bigger plenum. But I also see plenum volume a bit like the race to ever increasing fpe. If 15cc is "bad", is 100cc really really good? In reality it would depend on the gun. I don't think the little plenum on my P35-177 limits it much but I am sure it limited my P35-25. To some degree bigger plenum seem to be being a new marketing gimmick. The plenum of my Caiman X is not really big but it will push 18 grain pellets about 940 fps at 100 bar due to the large valve and internal passageway. I mention this to illustrate that the gun is a system and the plenum should fit the guns other design decisions.

 

[thomasair]

Wrong!

Doubling the tank volume at the same pressure does not exactly double the amount of air if you take the compressibility of air into account. The relationship depends on how closely the air behaves like an ideal gas versus a real gas under the given conditions. Here's a detailed breakdown:

Ideal Gas Behavior

For ideal gases, the amount of air (in moles) is governed by the Ideal Gas Law:

PV = nRT

n being the moles of the gas we can obviously conclude for an ideal gas n scales proportionally to the volume by exactly P/(RT). But air is not an ideal gas!

Real Gas Behavior

For real gases, deviations from the ideal gas law occur due to factors like intermolecular forces and finite molecular volume. The compressibility factor Z is introduced to correct for these deviations:

PV = ZnRT

Where Z represents the deviation from ideal behavior:

Z = 1 for ideal gases.
Z ≠ 1 for real gases (especially at high pressures or low temperatures).

Z is also a function of volume

At higher pressures, is typically less than 1 because intermolecular attractions reduce the effective pressure. In this case, doubling the volume may result in more than double the amount of air.

At very low pressures, approaches 1, and the gas behaves more ideally, making the relationship closer to linear

View attachment 517809
You can compute the partial derivative of moles with respect to volume like so



View attachment 517811

Clearly not proportionally changing

Other complicating factors include temperature and Mach numbers but for the sake of comparibility we will just talk about tank volume Delta's.

The pressure differential between the plenum volume and the tank volume also change this behavior.

Tank pressure is at 250 bar, plenum is at 140 bar. You would actually have to treat these two tanks as having two different fluids and then you can model this system as a mixing problem. Then you change the volume of one of the tanks and run the analysis again. The discrepancy between those two systems would exactly explain away the extra shot counts.

I guarantee you those extra shots is due to the regulator system needing to mix less higher pressure air from the tank into the plenum to maintain the overall average pressure of the plenum

Finally we do not have perfect regulators, plenum pressure fluctuate over time and drop over time, again this further adds to the non linearity of the system.

Could you please calculate the moles of air in a 150cc tank at 3000 psi and a 300cc tank at 3000psi?

From your chart it certainly looks like it's pretty proportional... at least for the purpose we were talking about.

Mike

 

[purplepom]

Could you please calculate the moles of air in a 150cc tank at 3000 psi and a 300cc tank at 3000psi?

From your chart it certainly looks like it's pretty proportional... at least for the purpose we were talking about.

Mike

Unfortunately screenshots and scale are bad, but ran the numbers, making some assumptions like the air is at room temp.

It comes out to

3000psi
150cc - 1.09mols
300cc - 2.20mols

Just to outline here is 4000psi
150cc - 1.39mols
300cc - 2.8 mols

These are obviously under certain assumptions. And I picked out Z by eye ball used published compressibility charts that were computed by people much smarter than me

It's almost double but not quite, there is almost a 1% difference from exactly double so not negligible

 

[thomasair]

I have edited my prior post for accuracy.

In my actual testing experience.... a double volume tank actually produced twice the number of shots. Of course, I have no means of attaining the level of accuracy needed to observe the small difference with any of the common equipment available to me.

The ideal gas law seems to fit my intellectual budget.

I apologize for my use of the word exact. It seems it wasn't exactly correct.

Mike

 

[purplepom]

I have edited my prior post for accuracy.

In my actual testing experience.... a double volume tank actually produced twice the number of shots. Of course, I have no means of attaining the level of accuracy needed to observe the small difference with any of the common equipment available to me.

The ideal gas law seems to fit my intellectual budget.

I apologize for my use of the word exact. It seems it wasn't exactly correct.

Mike

Nah man don't apologize, I love this conversation. I'm new here only reason I know this is cause my wife is a chemical engineer and I had the same exact conversation with her.

But anyway big tldr here is 1% more air translates to 1% more shots. Just from that property. Obviously people on this thread are talking about seeing more than 1% more shots... So there is more to this conversation than just compressibility. Just saying if you are normally shooting 50 shots and you doubled the plenum volume and now you can shoot 56 shots, 0.06 of those shots come from that property

So yes ideal gas law is a great approximation... For air... At room temperature...

 

[thomasair]

I'm gonna go out on a limb and suggest that in regard to the use of a plenum....a double sized plenums additional increase in actual volume of 1 % translates to a much smaller figure (than .06) in the actual shot count percentage since you are not depleting the plenum each shot. The larger the plenum, the less that will be used each shot. Does that make sense?

Mike

 

[thomasair]

In the example of 150cc plenum vs 300cc plenum at 3000psi ....how much would an additional 3cc added to the 300 affect things.

If we used a 15cc barrel volume which is typical of a 22 cal barrel....we can see the pressure difference that we can expect.

(300/315)3000=2857.14 psi
(303/318)3000=2858.49 psi

The 300cc plenum produces 99.95% of the 303cc plenums pressure. So .0005% more pressure.

I think that is right...but please verify.

Mike

 

[ctshooter]

You're only using a portion of the plenum for each shot.

A bigger plenum will have a smaller amount of pressure drop as the pellet travels down the barrel. The amount of pressure drop is proportional to the plenum volume versus the barrel volume.

You can make the same power at a lower reg pressure with a larger plenum...So you can achieve more shots on a fill.

Having a higher average pressure will also accelerate the projectile faster in the initial portions of the barrel which can produce added efficiency if you tune to take advantage of this by closing the valve a little earlier.

Mike

This is a really good explanation, but it does leave one thing out which I think is important.

You can also make the plenum too big for the amount of air used each shot. This will cause the plenum pressure to drop a very small amount which will result in the regulator not being opened wide enough to give a good refill and some variance in pressure in the plenum and the regulator cannot go through a full refresh cycle each shot.

I believe this will be more impactful on smaller calibers like .177 and some lighter .22 which don't use much air for a low power shot.

This same scenario can also exist if you run your regulator at too high a pressure and set the gun for a very low power.

 

[purplepom]

In the example of 150cc plenum vs 300cc plenum at 3000psi ....how much would an additional 3cc added to the 300 affect things.

If we used a 15cc barrel volume which is typical of a 22 cal barrel....we can see the pressure difference that we can expect.

(300/315)3000=2857.14 psi
(303/318)3000=2858.49 psi

The 300cc plenum produces 99.95% of the 303cc plenums pressure. So .0005% more pressure.

I think that is right...but please verify.

Mike

I think for the ideal gas approximation it's,

Pfinal = pinitial * (vplenum / (vplenum + vbarrel))

So those are correct

But deltaP between the two examples is 1.35 PSI

So percentage difference is (deltaP / Pinitial) * 100 = 0.045%. so two orders of magnitude off, but remember that's per shot. What matters is the cumulative gains that add up to give you that extra shot or two

One additional thing is, regulators function more effectively when the pressure delta in the plenum after a shot is within a set range. When the plenum is larger you won't have such a high pressure swing that the regulator needs to compensate for. Think impulse response of a PID control loop


You also have effect of temperature on air density, when air rapidly decompresses it gets colder. This causes an even more dramatic (albeit temporary) reduction in plenum pressure after a shot. Larger plenum volume makes this temp change less pronounced

 

[Franklink]

 

[thomasair]

Yes, I'm not suggesting anyone use a 300cc plenum...unless maybe they are using an extremely powerful gun.

I understand the refresh requirement of regulators.

 

[thomasair]

I'm personally going to ignore things that I cannot measure with my tools.

Mike

 

[purplepom]

View attachment 517888

That's pretty funny .

I think where I'm going with this is, those extra shots people are observing is coming from compounding small gains that the ideal gas law and other linear approximations count as "negligible"