Acceleration and velocity of a pellet inside a PCP - internal ballistics

[rsterne]

I think you will find that it's not the "air pressure drop" per se, but simple diminishing returns.... If you use Lloyd's spreadsheet and keep increasing the dwell, you will find that the efficiency drops off, and the muzzle velocity tends to plateau.... I don't know if you saw this in my other thread.... but I'll repost it here.... "Pellet Distance" is measured from the breech....



That graph was done using Lloyd's spreadsheet, only changing the valve dwell.... You can see that when the valve is open past the half way point, you gain very little velocity, but you sure use a LOT more air.... The graphs are VERY consistent with real-world results, which is why I am such a big fan of the spreadsheet.... I'm sure you have noticed that providing I can develop enough hammer strike to see it, the velocity plateaus in virtually every regulated PCP I make/test.... just as predicted by the spreadsheet.... Not only that, but the efficiency in FPE/CI tracks almost perfectly as well....

I have seen claims about Helium, but most of them have been when guys are trying to push air past Mach 1.... I have only seen a couple of shots with air over 1700 fps (1650 is the theoretical max), and they were done with a .177 Condor running full power on 3000 psi shooting a 1.7 gr. plastic sabot.... Just as air outperforms CO2 at the same pressure, it wouldn't surprise me that Helium is better again.... I'm guessing, as you are, that it flows better through the restrictions of the valve and ports.... probably even the barrel.... Lower "viscosity" ? ?

Bob

[Ribbonstone]

Past a certain point, won't get a hose to squirt more water.

[PakProtector]

hey Bob,
I believe the spreadsheet tracks the real world fairly well. I am also pretty darn sure that the claimed dwell is something like proportional to what is actually going on. It just looks like a more trustworthy method to run with a solution method that doesn't start out on drugs until you add enough other loses to get close. That massless, frictionless pellet should only come out at mean molecular velocity, and from there add in the losses.

I am quite comfortable believing that as speed increases the solution will depart from reality since that effect is becomming a larger and larger 'loss' that is getting ignored. How it departs is unclear, as I don't have enough information.
cheers,
Douglas

[lloyd-ss]

hey Bob,
I believe the spreadsheet tracks the real world fairly well. I am also pretty darn sure that the claimed dwell is something like proportional to what is actually going on. It just looks like a more trustworthy method to run with a solution method that doesn't start out on drugs until you add enough other loses to get close. That massless, frictionless pellet should only come out at mean molecular velocity, and from there add in the losses.

I am quite comfortable believing that as speed increases the solution will depart from reality since that effect is becomming a larger and larger 'loss' that is getting ignored. How it departs is unclear, as I don't have enough information.
cheers,
Douglas

Douglas,
All airgun velocities that i am familiar with stay below the average speed of the molecular mixture of air.  Ignoring the first three graphs, which were only included to demonstrate unbounded conditions, what is your concern with the application in the remainder of the graphs.  What do you think the maximum speed of 3000 psi air expanding into a barrel with no restriction would be? Also, what do you think the pressure of the advancing face of the column of air is?

If the air has advanced 20" down the barrel, what do you think the velocity and pressure of the air that is 10" down the barrel is. In other words, what do you think the velocity and pressure gradient in the unrestricted column is?

Now if you essentially plug the barrel with a pellet, how are the velocity and pressure gradients affected? Given that the speed of the pellet is quite a bit less that the avg speed of the mixture of molecules in air, does that speed really matter?  Are we back to just dealing with the force applied by the air pressure?
Thanks,
Lloyd-ss

[rsterne]

That massless, frictionless pellet should only come out at mean molecular velocity,

that assumes that you subscribe to that theory.... and build that limit into the spreadsheet.... Since I've seen (on video, and know the guy that made it) a couple of shots at over 1700 fps on air at room temp.... I'm not so sure it's 100% accurate.... I can't remember where, but I saw a paper on the Internet that said the maximum velocity of air molecules was Mach 5 (yes, five time the speed of sound!).... The argument presented was just as compelling as the RMS speed theory.... IMO....

Don't forget, the first "real" graph Lloyd did, with a 0.5 gr. pellet but INCLUDING the mass of the expanding air.... peaked at "only" about 2900 fps (about Mach 2.5).... All the graphs with air plus pellet had velocities well under 1650 fps, so even the RMS "speed limit" isn't exceeded....

Bob

[ericw]

Interesting topic.  It seems there is some difference of opinion out there on just what the maximum velocity limit really is.    Check this out from the Physics Forum and see what you think.   http://www.physicsforums.com/archive/index.php/t-200607.html.  Bob, maybe this is the same information you  were referring to? 
The equations come up with a limit of 5 times the speed of sound (for the gas at NTP).  I suspect the real answer is somewhere between the RMS free space molecular speed and the ideal conditions for the speed inside a barrel as determined by the (Seigel, 1965) equations.   Anyway... FYI.

I would sure like to get a copy of Lloyd's spreadsheet to see the equations used.  I was working on the same kind of thing but using MathCad instead of Excel.  I  was digging into details of poppet valve flow  based on this work:
http://www.mathworks.com/help/physmod/hydro/ref/poppetvalve.html
and that is as far as I have taken it.  The laminar /turbulent air flow dynamics will have an effect but with as close as Lloyd has come with his spread sheet, all that may be overkill.   Ideal on/off valve design  with some assumed flow rate during the open/close and dwell periods might be all that is ever needed.   It is amazing how close the data matches reality from what Lloyd has done.  Engineering kudos Lloyd!

Eric

[lloyd-ss]

ericw,
Thank you!  I just rushed thru  the first link, and it is sooo helpful.  I will study it more carefully tonight.  But I think the jist of it is, that at the velocities we are talking about with airguns, we don't even get near the max velocity of an expanding gas mixture.
This is good stuff.  I will also explain the methodology I use in my spreadsheet. 
Thanks,
Lloyd-ss

[PakProtector]

The short suggestion is to build into the model one more loss that accounts for molecular speed. Bob, you mention that little plastic pellet and compare it to Lloyds 2900 fps...and I'll make an additional wager that Lloyd would not be using a model the way he is( and we for that matter ) that was off by 29/17.

cheers,
Douglas

[lloyd-ss]

The short suggestion is to build into the model one more loss that accounts for molecular speed. Bob, you mention that little plastic pellet and compare it to Lloyds 2900 fps...and I'll make an additional wager that Lloyd would not be using a model the way he is( and we for that matter ) that was off by 29/17.

cheers,
Douglas

Douglas, Thank you, and I agree.  I want the model to be as accurate as possible while working withing the velocity range of PCPs.  But I don't want to bother with modeling in anything that only has an affect above, shall we say 1500 fps??  But the dilemma is that there is so much conflicting information about what that max air velocity is and how that limit should be applied.  The model is very close to being correct now, so how do I model this additional loss(es)?  The burning question that I have is, given the significant, and verifiably real, losses that are already modeled into the spreadsheet, if the pellet does not even get close to that velocity ceiling, does it have any effect on the pellet at all? So far, I have not seen any compelling arguments that would demonstrate that it applies below 1500fps.
If there are any, I would love to hear about them.
Thanks,
Lloyd-ss

[rsterne]

Exactly what I saw trying to say.... If (unproven) limits don't kick in until the velocity is above 1500 fps, is it really worth worrying about them.... Additionally, that 2900 fps was at 100% efficiency with a 0.5 gr. pellet in .25 cal.... The test was done in .177 with a 1.7 gr. "pellet" (two big changes right there, the SD is nearly 7 times as high).... and the efficiency was (ready for this?).... 3%.... Don't forget, that 1650 fps number is the RMS velocity, which means that some air molecules are at rest, and others moving twice that fast, or more.... My "guess" is that IF the 1650 number really means anything, there are "enough" molecules travelling over 1700 fps to still provide "some" acceleration.... maybe 3%?.... Either that, or maybe the few cc's of air in the Condor transfer port (it is unusually large) was hammered by the sudden compression to 3000 psi that it was "burning" the back of the plastic pellet, and that combustion was adding to the velocity.... In any case, velocities in that region remain a curiousity, and an anomaly, in airguns that aren't using Helium....

EricW, thanks for that Seigel link, I had forgotten where I saw it.... I'll have to study it, as it may very well be that the 1650 RMS limit is not applicable at all.... we are looking at more like 5650 fps with air.... which really means WHO CARES ! ? !

Regarding the modelling of specific valve shapes, and trying to model the "shape" of the valve dwell, I would suggest that it is extremely difficult, and compared to the "square pulse" dwell used in Lloyd's spreadsheet are probably relatively unimportant.... Don't forget, the way you use the spreadsheet is to put in the "knowns" and then jiggle the dwell and efficiency numbers until the output equates with the real world.... So, you might end up using a "square" dwell of 0.002 sec, but in reality the "actual" dwell is 0.003 sec with less flow on both ends.... My opinion is that the differences are small, hard to measure, even harder to predict, and therefore beyond what is reasonable to look for in a model.... especially when you consider how well Lloyd's works already....

Bob

[rsterne]

Just out of curiouslity, I used Lloyd's spreadsheet to model the .177 Condor shot with 1.7 gr. pellet at 3000 psi.... I used infinite reservoir, air mass included, but no other degrading factors.... I can't be bothered publishing the graphs, but the MV worked out to 2157 fps.... Adding 1 lb. pellet drag and 2 lbs. breakaway did little, but adding in a 1cc transfer port dropped the velocity just below 1700 fps.... For such an unrealistic set of conditions, I think that is excellent agreement with the empirical results....

Bob

[PakProtector]

Now y'all have me considering a Hydrogen powered, Mach 3+ 'pneumatic'. Somethig capable of slinging a 30 cal, 50-60 gr pellet out at powder-burner velocity. The only safety issue I see worth paying attention to would be the muffler volume filled up with a combustible mix...and so it would be loud, which defeats a significant portion of the sub-sonic airgun alure( and that completely neglects the pellet's sonic boom ). An interesting experiment for a hunter...but since I am having trouble with something simple like a tank adapter it isn't really worth spending any more energy on.
cheers,
Douglas

[Motorhead]

Just tossing this out for the entertainment value ....

As tests above read, velocity was based off a 1.7Gr pellet and with this said ...
Would not a tuner with a chronograph and some featherweight FELT cleaning pellets get a clue of the expanding air columns speed shooting felts point blank across chrony ?

There in bore drags lower than a pellet, there minimal mass should accelerate fairly close to the speed of the escaping pressure pulse ... No ?

I know when I launch the occasional felt in the PCP the Supersonic CRACK is Really pronounced.

Just a silly question really 

[rsterne]

I just weighed some Beeman .177 cleaning pellets, and they run 0.45 gr.... I'm not 100% sure, but I think the guy who tested the plastic 1.7 gr sabot tried felts and they were slower.... He suspected blowby.... so he used the plastic base from (IIRC) an RWS Hypermax....

BTW, I just realized I had the weight wrong.... the sabot was 1.4 gr.... Here is the video....



Bob

[lloyd-ss]

Great video! Thanks for posting that Bob.  I certainly have never been able to get those sorts of speed. I believe that part of the success of the Condor comes from the fact the air comes straight in line with the pellet, no corners to turn.
Thanks for sharing that with us.

[rsterne]

I've never seen anthing over about 1250 fps.... but on the other hand I've never shot anything lighter than 6.9 gr. in .177 or 11.9 gr. in 22 either....

Bob

[Cal]

Perhaps only the recording,  but where was the sonic crack on those two shots?

I listened for them,  but no....

[rsterne]

The sound on videos seldom record gunshots well.... I've heard lots of sonic cracks, but none on a video.... I have also tried measuring sound levels with an $80 dB meter and it was useless.... totally inconsistent, shot to shot.... I assume the sampling rate is way to slow....

Bob

[Cal]

Like taking a photograph at an arena event with flashes seen everywhere.  Just not in the photo  you have taken.  unless by some freak chance of timing, on other "click" is recorded.   

Data point.  The Evanix AR-6 .22 spits out "lightened *'CPHPs at 1232 fps without anything more than putting the pell in the bore and firing from a 200 bar fill.

* the head cut off , and shot the skirt ;-)

cheers

Cal

[lloyd-ss]

I did shoot a 21 gn .25 cal at 1354fps once. I will try post the video tonight. It is on my youtube channel.