Effect of Plenum Size on FPE in Regulated PCPs

[rsterne]

There are always many questions about the effect of Plenum size on the performance of PCPs, so I thought I would try and explain what happens internally, using Lloyd Sikes Internal Ballistics Spreadsheet.... It models what happens to the pressure, velocity, and energy inside the barrel, with a huge number of variables you can change to see what happens.... For this set of graphs, I used a .22 cal, 24" barrel, and a fixed dwell of 2 mSec for the 1800 psi graph and 1.8 mSec for the 2000 psi graphs.... I used a pellet breakaway force of 2 lbs. and a bore drag of 1 lb., a transfer port volume of 0.02 CI, an overall mechanical efficiency of 55% (typical for a gun like a Disco), and included the air mass in the calculations.... The pellet was 14.3 gr., and I varied the plenum volume ONLY on the first two graphs to show it's effect.... On the third graph, I increased the pressure for the smaller setpoints to keep the FPE output constant.... Here are the results, based on a 30 FPE design point....



A stock Disco plenum is 135 cc, which at 30 FPE is 4.5 cc per FPE.... The other two volumes are 1 cc per FPE and 1/2 cc per FPE, based on the 30 FPE design point.... You can see immediately what happens during the time the valve is open.... it closes when the pellet is about 10-11" down the barrel, and the pressure is dropping as the air in the plenum expands into the barrel.... The smaller the plenum, the less air available to expand, so the greater the drop in pressure by the time the 2 mSec has passed and the valve has closed.... While the gun shot ~30 FPE with the full 135 cc reservoir available, that dropped to ~28 FPE with a 30cc plenum, and down to ~ 26 FPE with a 15 cc plenum....



Since we are interested in what happens in a Regulated PCP, and it is not possible to use the entire 135 cc reservoir for the plenum, the second graph looks at plenums that are 1 cc per FPE and smaller (1/2 cc and 1/4 cc per FPE, based on the 30 FPE design point).... I increased the setpoint pressure to 2000 psi, and adjusted the dwell using the 30 cc plenum to get 30 FPE, and the graphs show what happens as you cut the plenum volume in half, and then in half again.... The power drops to ~ 28 FPE and 25 FPE respectively.... The next graph shows what happens if you increase the pressure to get back to 30 FPE using the smaller plenums....



The title of this graph gives the plenum size @ the pressure required to get back to 30 FPE.... Dropping from 30 cc down to 15 cc requires increasing the pressure from 2000 psi to 2190 psi to get back to 30 FPE.... If you cut the plenum in half again, to 7.5 cc, you have to boost the pressure to 2560 psi to get back to 30 FPE.... These figures are all calculated using a constant dwell of 1.8 mSec, which means the valve is closing when the pellet is about 10" down the barrel.... However, similar curves can be drawn using different parameters....

I hope that this series of three graphs helps you understand the importance of having a decent size plenum in an Regulated PCP.... There is no "one" correct answer, many variations can be made to work.... However, the fact remains that for a given designed FPE level, reducing the plenum volume reduces the pressure during the shot, and therefore the potential FPE at a given setpoint pressure.... To get that power back, you must either increase the dwell (lowering the efficiency), or increase the setpoint pressure.... A small decrease in plenum volume below the 1 cc per FPE level won't require much pressure increase.... but using too small a plenum for the desired FPE will mean you have to make a much larger increase in pressure....

Bob

[Motorhead]

Good stuff tho a bit overwhelming for us to digest the data with many of the same color graphing lines per chart

[nielsenammo]

That is great info. Had to read it a few times but wow super indepth. Thanks for the info.

[rsterne]

I didn't think about the colours being confusing, I guess because I work with Lloyd's Spreadsheet so much.... The lines starting upper left, with the inflection in them when the valve closes, are pressure (psi), and the values are read on the right scale.... The upper set of curved lines that start at zero are energy (FPE) and the values are read on the left scale.... The lower set of curved lines that start at zero are velocity(fps) and the values are read on the right scale.... On the bottom chart, where all three versions are producing the same fps and FPE, the three lines are nearly superimposed, and end at exactly the same value at the 24" point (muzzle)....

The thing that for me is the most interesting is the pressure drop while the valve is open.... You can see the drastic effect that reducing the plenum has on that.... If you look at the middle graph, using 2000 psi, at the moment the valve closes (when the pellet has moved 9-9.5") the pressure is about 1660 psi for a 30cc plenum, about 1430 psi for a 15cc plenum, and only about 1120 psi for a 7.5cc plenum.... Just understanding that gives you a good understanding of why plenum volume is so important....

Bob

[SpiralGroove]

Thanks Bob -> I'll re-read in the AM after a double shot of espresso
Reminds me of pushing my palms against my eyes when they're closed -> A Light Show
Kirk

[Motorhead]

Thank you Bob ... my mind now is one with the charts 

[Bill G]

Hey Guys,
Thanks Bob -> I'll re-read in the AM after a double shot of espresso
Reminds me of pushing my palms against my eyes when they're closed -> A Light Show
Kirk

ROFL!!!! that hurt me.  I had to try it to remind myself what it was like. my gut hurts.  LOL

Bob, you sure you don't want to open up an air gun academy of some sort.  Your nack for explanation and attention to detail is seconded by none that I've seen.  Great work!

Bill

[FuzzyGrub]

Bob, you always makes my head hurt... in a good way!    and its been too long since I've dug into one of your threads.

So, looking at the last graph, I can have a range of plenum/pressures to get the desired 30FPE.   Given the fixed airtube (135cc) volume, and value for the space used for the reg, how would you find the optimum res to plenum ratio?    The optimum being the most number of shots before falling off reg with an assumed 3K psi fill. 
 

[shorty]

Bob, sorry about my post about plenum size didn't go so well with you. I will learn "one day" on how to ask correctly.

The data you supplied was exactly what I was looking for. There is absolutely no where what you have done is referenced (anywhere). It is much appreciated.

It looks like from your data, (please correct me if I am wrong) that 2 times the barrel volume will give you the correct plenum volume and adjusting the pressure of the regulator will determine the fpe at the most efficient setting or what I would call the most shots before falling off regulation.

Thanks again Bob.

[HYspd]

i had to increase the magnification setting of my browser to 200% so my eyes wouls stop crossing, the sense of the graphs became clear to me...

excellent visual explaination of the plenum volume to pressure relationship that I only had limited understanding of from reading alot of your previous work...

Thank You Sir for your continued efforts to understand and explain the physical operating charactoristics of these deceptively simple arms

[rsterne]

Sorry, barrel volume has really nothing to do with it except indirectly.... The amount of air used for the shot is the key.... Most PCPs, once running efficiently, have an efficiency of 1 FPE/CI, and it is that volume of air used that determines the pressure loss for a given size plenum.... Yes, a .177 uses less air than a .357, but it also produces less FPE.... That is why by using the FPE to determine the plenum size needed is an easier calculation than bringing barrel length, caliber, pressure, and all the other variables into it.... For example, one guy might want a 12 FPE setup for FT, while another a 36 FPE setup for hunting, but both are using a .22 cal 24" barrel, and a tank (reservoir) pressure of 3000 psi.... The barrel volumes are the same, but the hunter needs a plenum 3 times as big....

There is only a limited range of setpoint pressures that make sense.... they have to be low enough below the fill pressure to give a reasonable shot count, and yet high enough to produce the power you want.... For the FT shooter above, you might pick 1200 psi for a setpoint, while the hunter might need 1800 to get the power he needs.... Determining the starting setpoint is the first thing to do when considering a regulator, and it is based on how the gun shoots unregulated.... Generally, you use a pressure just slightly higher than what is required for the fps/FPE you want in the gun you start with.... If an MRod shoots 850-900-850 from 3000 psi down to 1600, and you want to shoot 850, you would use about 1800 psi and a plenum of 1cc per FPE.... If you must use a smaller plenum, then you will move the setpoint up even more....

FuzzyGrub, your question is the exact problem faced by anyone installing an "in-tube" regulator.... The regulator and the plenum both take up volume inside the reservoir, reducing the air available.... The more power you want, the higher the setpoint, and the larger the plenum, and pretty soon you have such a small reservoir left, and so little pressure difference between "full" and "setpoint" pressures your shot count is dismal.... That is EXACTLY why in-tube regulators are more suitable to low-medium power applications, you have to trade off power and shot count.... It is possible to build a high-powered, regulated PCP, but you need to design it from the ground up, with a large plenum, and an even larger tank (bottle) feeding that to get any kind of a useful shot count.... An example is my "Grizzly" .30 cal repeater, which has a 90 cc plenum, fed by a 22CI (360cc), 3000 psi tank regulated to 2200 psi output, and gets 14 shots @ 100 FPE.... for an efficiency of 1.15 FPE/CI....

Bob

[shorty]

Bob, I am not trying to make you crazy but is it 1fpe/cu in or 1 fpe/cc ?

[shorty]

Ok, I am now really confused.

let's take my .357 marauder with a 215 cc "stock" reservoir. Shooting at 100 fpe for and average of 100 fpe for 6 shots and with a 3000psi charge (16" barrel). If I where to regulate it according to 1cc per fpe, I would need 100cc of plenum.

The confusing part to me would be that it is almost half the reservoir size and give only 2 shots at 100fpe according to the pressure drop across the valve. That don't make sense to me.

How does that work ?

[SpiralGroove]

Hey Shorty  - 1CC per 1 FPE

All 3 of my regulated (.177 cal.) PCP's can shoot CPUM (10.5 gr.) pellets about 890/915 fps.  This is between 18/20 FPE.
I have made all my plenums between 18/20 cc's.  I probably could gotten away with 15cc's, but I have chosen to stay near 20cc, because in the future I may want to shoot JSB Monster or Beasts 13/16 gr. with the same regulator set-point and just a more hammer strike. 

I could raise the regulator's set-point to give a higher velocity (which would help a smaller plenum), but have decided to sacrifice a few cc's on the high pressure side to ensure I have enough plenum for maxing power (FPE's).  If you have to drill a vent hole in the air cylinder for reg. venting and this was done using a 10cc plenum, your stuck and don't have the plenum capacity for great FPE flexibility.

The only downside to the 1FPE/1CC plenum rule of thumb is you loose some air on the high pressure side of the regulator and shot count.  The plenum volume discussion is more concerned with Power than Efficiency.  So IMHO, it's best to give yourself some flexibility in power at the expense of shot count.  You can then otherwise tune the gun for efficiency to bring up the shot count. 

The "Otherwise Tuning" would entail Air Flow management (valve, transfer, barrel ports and valve throat adjustments), Valve Poppet adjustments, Hammer Strike management (Spring Pre-load, Hammer weight and Hammer travel adjustments).  All these tweaks can get your efficiency up to 1.25/1.50 (FPE/CI), thus increasing shot count near 30 to 50%.     

[rsterne]

shorty.... The EFFICIENCY is calculated in FPE/CI, and can vary from about 0.3 to 1.5, with most PCPs running around 1.0 - 1.2.... That is the amount of air (at 1 bar) used from the tank to create a shot, divided into the FPE for that shot.... or the total volume in CI used for a shot string, divided into the total FPE of the string....

The PLENUM SIZE should be about 1 cc (of HPA at the setpoint pressure) per FPE.... and yes, for a gun shooting 100 FPE, you want about a 100cc plenum.... Note above, I used a 90cc plenum for my Grizzly.... I would have used 100cc if I could have, but didn't have the room.... The result of the slightly undersized plenum was I had to increase the setpoint from 2000 psi to 2200 to get the 100 FPE I wanted at decent efficiency.... High powered PCP are VERY difficult to regulate, just because of the large plenum required to maintain the pressure to produce the big FPE numbers.... Trying to regulate an MRod (for example), with 215 cc of reservoir, and produce 100 FPE, will leave you with exactly the problem you face.... just a few shots, because half the reservoir ends up being plenum or regulator.... As I said above, in-tube regulators are great for low-medium power, pretty much useless for high power....

Using an MRod as an example, let's say it's a .30 cal, designed to produce 100 FPE (like my Grizzly).... The reservoir is 215 cc, the regulator will take up about 15cc (assuming an inch of length), and you have a 100 cc plenum, so your remaining reservoir is only 100 cc (6.1 CI).... Let's say you can achieve your 100 FPE at a pressure of 2000 psi (in the unregulated gun), so you choose a setpoint of 2200 psi to make up for the pressure loss with a 100cc plenum, compared to the 215cc reservoir.... That means you have 800 psi of pressure drop available from the 3000 psi fill to the 2200 psi setpoint, which is (800/14.5) = 55 bar.... Multiply that by the reservoir volume of 6.1 CI, and you have a total of 336 CI of air (at 1 bar) available before the reservoir pressure drops below 2200 psi.... If the gun shoots at an efficiency of 1.00 FPE/CI, each 100 FPE shot will use 100 CI of air (at 1 bar), so you will get 3 shots.... If you can get the efficiency up to 1.20 FPE/CI, then you could get 4 shots....

You can also calculate the pressure drop in that 100 cc plenum during a shot.... You are starting with 100 cc of air at 2200 psi in the plenum.... At an efficiency of 1.00 FPE/CI, and a 100 FPE shot, you use 100 CI of air at 1 bar.... However, the air in the plenum is at 2200 psi, which is (2200/14.5) = 152 bar, so the volume of air you will draw out of the plenum for a shot is (100 x 16.4 / 152) = 10.8 cc of air at 2200 psi.... You will then be left with (100-10.8 ) = 89.8 cc of air at 2200 psi, expanding into that 100 cc space, so the pressure after the shot will be (2200 x 89.8 / 100) = 1976 psi.... and the average pressure during the shot will be 2088 psi.... If you decrease the plenum size to 50 cc, but still need that same 10.8 cc of air to make the shot.... the air remaining after the shot will be (50-10.8 )  = 39.8 cc, expanded into that 50 cc space, so the pressure will only be (2200 x 39.8 / 50) = 1751 psi.... and the average pressure during the shot will only be 1976 psi, instead of 2088 psi.... You would have to increase the setpoint from 2200 psi to 2310 psi to compensate for the smaller plenum.... Going smaller than 1/2cc per FPE for the plenum will require even greater increases in the setpoint....
 
Using the 50 cc plenum, and a 2310 psi setpoint, we can calculate the possible number of shots for the MRod example above.... The reservoir will now be 150 cc (9.1 CI), but the pressure drop will only be 690 psi (48 bar).... making the total volume of air available (9.1 x 48) = 437 CI at 1 bar.... At an efficiency of 1.00 FPE/CI you will now get 4 shots of 100 FPE.... and if you can get the efficiency up to 1.20 FPE/CI you should get 5 shots.... So, in this case, using the smaller plenum, of 1/2 cc per FPE instead of 1 cc per FPE, and increasing the setpoint to compensate, should give you one extra shot.... As Spiralgroove pointed out, however, should you ever wish to push the FPE higher by using a heavier bullet, you won't have the same flexibility as with the larger plenum.... Your actual results will depend on what setpoint you require to get 100 FPE while maintaining usable efficiency, of course.... I used numbers which worked for my Grizzly, which should be similar, providing you can get the airflow you need....

Bob

[FuzzyGrub]

FuzzyGrub, your question is the exact problem faced by anyone installing an "in-tube" regulator.... The regulator and the plenum both take up volume inside the reservoir, reducing the air available.... The more power you want, the higher the setpoint, and the larger the plenum, and pretty soon you have such a small reservoir left, and so little pressure difference between "full" and "setpoint" pressures your shot count is dismal.... That is EXACTLY why in-tube regulators are more suitable to low-medium power applications, you have to trade off power and shot count.... It is possible to build a high-powered, regulated PCP, but you need to design it from the ground up, with a large plenum, and an even larger tank (bottle) feeding that to get any kind of a useful shot count.... An example is my "Grizzly" .30 cal repeater, which has a 90 cc plenum, fed by a 22CI (360cc), 3000 psi tank regulated to 2200 psi output, and gets 14 shots @ 100 FPE.... for an efficiency of 1.15 FPE/CI....

Bob

So, for the medium power of the 30fpe, why is the 30cc (1cc per fpe) better than 1/2 cc per fpe?  Yes, it takes 190psi more, but it is unclear to me why that is significantly worse.  Now, going to 2cc per fpe (60cc), looks like the pressure would only drop to close to 1900psi.   That is easy to see that you ate up the majority of your volume with little psi gain, and would be a poor choice.   I suspect the optimum may be somewhere between 1/2 and 1 cc per fpe, but don't know how to graph or prove or dis-prove it.

FWIW: I only have one reg gun, and it is a 177 mrod, where I basically just followed Scott's recipe.  I am getting 80 18.5fpe shots at 1600psi set point.   The only plenum is a hogged out gauge port and valve.  I measured the volume and will have to find the numbers but don't believe it was 1cc per fpe.   I know, significantly different than this disco model, but I'm just trying to relate the math to practical application. 

[MicErs]

Good stuff, you never fail to make me learn a bit more about how these things work.  By the way, I get as much content from your writings, probably more, as I do from your graphs.  Well expressed.

[rsterne]

You would have to work out the specifics for your individual gun, and you can really only do that if you know the efficiency.... Let me give you another example, this time with a QB.... I did a regulated setup at 1500 psi, 13CI 3000 psi tank, same valve, barrel, breech and bolt, but in one case used a QB79 tube and in the other a QB78 tube.... The QB78 shot 40 shots at 31.1 FPE, which was 0.90 FPE/CI.... and the QB79 did 39 shots at 26.4 FPE, which was 0.74 FPE/CI.... I then cut the QB78 tube to make it half way between, and it did 40 shots at 30.5 FPE, which was 0.85 FPE/CI.... The QB79 had a plenum plus valve volume (yes, the valve volume counts) of about 10 cc, the QB78 was about 50 cc, and the half tube '78 was about 30 cc.... It is pretty obvious that it was the best compromise.... In this case, increasing the setpoint pressure to compensate for the small plenum of the QB79 was not possible, because of safety considerations, where the regulator had to be fitted with a 1.8K burst disc, and going higher than 1500 psi would have popped the disc.... If you had the ability to increase the setpoint safely, such as you do in an in-tube installation, then it may have been possible to get as high a total FPE (ie same number of shots at the same FPE) with a plenum that is 1/2 cc per FPE.... It will all depend on the efficiency you can get with the two different configurations....

There is another thing which influences how big the plenum should be, and that is the setpoint pressure itself.... Let's compare a setpoint of 100 bar (1450 psi) to 200 bar (2900 psi).... Let's assume that the shot consumes 400 cc (24.4 CI) of air at 1 bar.... That is 4 cc at 100 bar, but only 2 cc at 200 bar.... Now let's assume the plenum is 20 cc.... In the 100 bar system, the air left after the shot will be (20-4) = 16 cc, and the pressure after the shot will be (100 x 16/20) = 80 bar, a 20% loss.... However, in the 200 bar system, the air left after the shot will be (20-2) = 18 cc, and the pressure after the shot will be (200 x 18/20) = 180 bar, a loss of only 10%.... Therefore, as the setpoint pressure increases, the size of the plenum you need to minimize the pressure loss decreases.... If you are running a 4500 psi tank, regulated down to 3000 psi, you can use a smaller plenum.... However, most regulated systems have a setpoint pressure of 1000-2000 psi, with the majority between 1400-1800.... so that is the pressure range I based my 1 cc per FPE recommendation on.... Remember, there is no downside to having a bigger plenum from a performance point of view.... but there are definitely situations where running a plenum that is only 1/2 cc per FPE, at a higher pressure, may give you more shot count.... particularly in low-medium power applications.... but IF AND ONLY IF doing that gives you a larger reservoir to draw from (eg an in-tube regulator).... If you are after high power (relative to the caliber) you are generally better off using 1 cc per FPE.... There may be some situations, however, such as very low power setups (eg. a 500 fps target rifle), where a plenum even smaller than 1/2 cc per FPE, running at several hundred psi higher pressure, may be the best choice.... One additional advantage in this use is that tiny sips of higher pressure are quieter....

I guess the best way to sum this up is as follows....

If you can achieve a plenum size of 1 cc per FPE, there is little point in going larger, the gains in power are too small.... If you are using an in-tube regulator, however, going that large may reduce the reservoir and shot count, so you MAY be better off using a plenum as small as 1/2 cc per FPE, running at a slightly higher pressure.... Only rarely, in very low power applications, would it be worthwhile going less than 1/2 cc per FPE.... If in doubt, use the largest plenum that will give you a decent shot count, up to 1 cc per FPE.... with a minimum of 1/2 cc per FPE....

Bob

[FuzzyGrub]

Bob, it will take me some more time to walk thru and understand  the example, but the summary was clear! 


The model only is calculating based on chamber size, and does not model the true effect of a reg that will refill the plenum, if I'm understanding correctly.   Is the reg dwell time to refill the plenum significant longer than the valve dwell?, that it doesn't impact the calculation?   I think I've seen people talk about reg cycles that are in seconds, vs millisecond timing on valve dwell, so that would seem to make sense. 

[rsterne]

Correct, the refill time on the regulator is MUCH slower than the shot cycle, which is 1-2 mSec.... I have had gauges in the plenum, and you can see the pressure drop and refill on the gauge, it often doesn't stop moving for over 1 second.... For all practical purposes, the only air available for the shot is what is inside the valve and plenum.... To make it worse, if the feed hole between the plenum and valve is smaller than the exhaust port of the valve, you may not even keep the pressure in the valve you should have in the calculations.... I strive for an entrance hole in the valve AT LEAST as large as the hole in the throat of the valve, not counting the area of the stem of the poppet, to make sure....

Bob