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gicos · Member

Hello all! First post here. What a treasure trove of information in this forum. You all are truly the cream of the crop and represent what all of humanity should be doing.

I found the forum by researching the physics for a rifle I'm preparing to start on after the holidays. It's definitely not the typical recreational/target/fun rifle, but a pack survival rifle. I've got a good deal of experience with this in powder burners, and the draw here is the elimination of brass, powder, and primers. Obviously, weight and bulk are of paramount concern for a rifle one hopes they never have to use for its intended purpose.

What I'm after is a .22 cal that fires 15 grain round ball, 30 grain .22 Short bullets, and 45 grain cast bullets (I know there's a .004 size difference to deal with here). The plan is for a Lothar barrel shortened to 16" and a two stage pump as the buttstock (think old, turn of the last century Benjamin rifles, only with the pump reversed). The reservoir is built into the receiver. To keep parts, weight, and failure points to the bare minimum, it'll be a full dump valve, single shot. Obviously, I want to keep the volume and pressure per shot to a minimum, leaning on the side of more volume than pressure, as moving from a two to a three stage pump increases the weight and complexity considerably.

Velocity goals are to take the 30 grainers to 1,025 fps, and the 15 and 45 grain can fall where they may. It would be fantastic if I could do this on 1,500 psi, as that can definitely be handled easily with a two stage pump, but doing a bunch of research here tells me that this velocity isn't doable at that pressure. I've seen Lloyd's video lanching 43 grainers to 1,218 fps in 25 cal with 3,000 psi and and a 280 cc reservoir. Very impressive, but that's a lot of pumping!

Anyway, I know that Bob and Lloyd and others have massive expereince predicting what it takes to achieve a given velocity with a given projectile, and have a bunch of work in the spreadsheet, so I'm hoping for a starting point here as far as reservoir size and pressure required. As you know, everything velocity starts with these two things, and the math is just something I've never dealt with. An upper and lower range for reservoir size and pressure would be great, along with a best guess on the sweet spot. I'm no stranger to testing things and don't expect this thing to fly together perfectly the first time. Thanks a bunch for any insight.

rsterne · Moderator

I'm currently working on a .25 cal pumper project that is a followup to my Carbine which reached 40 FPE for 1 shot and did 3 shots at 31 FPE.... It was running on 1500 psi, with a 27cc reservoir, and required 75-80 pumps to fill it from zero....

I personally think you are looking to push the limits for an MSP wayyyyyyyyy beyond what is practical.... Assuming you can achieve an efficiency of 1 FPE/CI, to develop the 70 FPE you want, you will need 70 CI of air per shot.... At 1500 psi (103 bar) that means you would have to dump 70/103 = 0.68 CI or 11.1 cc of 1500 psi air.... A 16" barrel in .22 cal has a volume of 0.61 CI or 10 cc.... Basically you can't cram 11.1 cc of air into a 10 cc space.... so 1500 psi simply won't work, even with a dump shot.... and dump shots will never reach 1.0 FPE/CI, you would be lucky to achieve half that....

My advice is to build something more realistic, learn as you go, and then decide what might be possible....
Bob

gicos · Member

It's good advise, Bob, and much appreciated. I knew from the start this wasn't going to be a very practical or enjoyable piece of equipment, though. It's better than sticks or rocks, so practical enough. I spend a lot of time deep in the Rockies where needing a survival rifle is a real possibility. You don't mind pumping so much when you're starving. 1,500 psi isn't carved in stone, it was just a ballpark. I'm sure I could generate 2,000 with a two stage pump if that's what it took. I really don't want to pump to 3,000, though, or add weight to the pump for the extra stage to get there.

If I understand the math, taking it to 2,000 psi (about 138 bar) would be 70/138 = .507 CI or 8.3 cc at 1 FPE/CI, or 140/138 = 1.01 CI or 16.5 cc at .5 FPE/CI. The barrel is 14.9 cc at 24" length, so even leaving it full length won't equal 16.5 cc. Do I need to higher pressure, a bigger reservoir, or what magic would you sprinkle on this scenerio? Going to .25 caliber isn't out of the question if this is too much to expect from a .22 caliber.

rsterne · Moderator

To achieve reasonable efficiency of ~1.0 FPE/CI you need to have the valve close at about the point where the pellet has only moved half the barrel length.... This saves nearly half the air compared to a "dump shot" (more than half if you are blowing a lot of wasted air out).... Saving half the air means half the pumping to reload.... The cool thing is that the velocity difference is very tiny, you get virtually no extra performance by dumping the last half of the air in the valve....

In order to close the valve that early, you need to pack that 70 CI of air into a very small volume of about 8 cc (half of a 24" barrel).... That requires about 145 bar, or 2100 psi.... It may be possible to do what you want on 2000 psi, but I don't know of any existing .22 cal PCPs that can do that.... The only readily available PCP with that kind of performance is the AirForce Condor, which runs at 3000 psi, dropping to maybe 2200 before refilling it.... Basically you need to build one of those with a pump....

One other thing to consider is the reservoir volume.... To avoid excessive pressure drop you should strive for a reservoir of 1 cc per FPE, so that means 70 cc.... To fill that to 145 bar means you have to move 10,150 cc.... A Benji 392 pump in a Disco tube moves 54 cc per stroke.... which sounds like 188 strokes, but then you lose the pump efficiency.... I'm guessing 300 pumps, and believe me, it's not easy to pump 54 cc to 1500 psi with a single stage pump.... To reach 2000 psi you would need a 2-stage pump or reduce the pump tube to 5/8" instead of 3/4" ID.... and then there goes your volume, meaning more strokes....

LIke I said, you need to tackle something do-able first.... Why not just get a Condor and a stirrup pump?....

Bob

gicos · Member

Much thanks again, Bob. You answered a number of questions without me having to ask. You truly are a gold mine.

The reason I'm not interested in the Condor and a pump is weight and bulk. If this were a plinker and enjoyment rifle, sure. But the Condor weighs 6 pounds and the pump 8. A .22 LR can be had at 15 ounces. For the same weight, 13 pounds of .22 rimfire is an awful lot of ammo. More than I would carry. There's no weight savings on the brass, powder, and prime mixture at this point. Not even close. One would have to get into tens of thousands of rounds before they realized any weight savings and God help anyone who's stuck in a survival situation that long. If I can't get this thing into the rimfire class and keep it under 4 pounds (preferably 3--there's a lot of potential weight savings in the retail pump by getting away from brass pistons and valves), it's just not a viable option to me for a survival rifle. With all of the improvements in the PCP world and high performance in recent years, I thought I'd see if I could pull it off.

I'm going to tackle the pump first, since this has everything to do with whether or not I can do it. I've seen a two stager put together with heavy wall sweated copper pipe, so that'll be an inexpensive experiment in different diameters. If I haven't lost my marbles, my understanding is that, for a dump shot (I know, your skin is crawling), any reservoir volume above the barrel volume is a no-go, as the excess does nothing but blow out the barrel. For a reservoir the same volume as the barrel, the pressure should be half at the muzzle as it was at the breech. At 10 cc barrel volume (16" barrel 'cause the math is easier) a 70cc tank valved to half the barrel length would belch only 5cc of fill, or 7%. If we we're talking 2,200 psi to achieve my goal, the pressure would be 2,046 when the valve closed half way down the barrel. But at 70cc, we're talking multiple shots. To do this with a 10cc reservoir, pressure at half the barrel would be 75% of it's starting pressure, requiring 2,730 psi in the resrvoir to achieve the same pressure at the midpoint. A 5cc reservoir, dropping to half pressure at the barrel midpoint, would require 4,092 psi. But then, there are small gains made in the last half of the barrel with a dump shot, and the initial pressure would be higher, so it wouldn't be quite that high. It's becoming clear that, for this to work, I'll need a teeny reservoir at really high pressure and a large multistage pump. Thankfully, the design from inception is such that the pistol grip can be stood on for pumping and/or the pump is operated with bent legs directly over the shaft, utilizing one's full body weight.

Just for an idea, the 10cc reservoir at 2,730 psi (188 bar) is 1,880 cc's (114 CI, .61 FPE/CI or 1.6 CI/FPE) of air, 18.5% of the 10,150 cc's you mentioned above. With the estimated 300 strokes to fill 10,150 cc's with a 54cc pump stroke, that would equal 55.5 strokes on the 10cc reservoir. The pump design I've got in mind compresses on both the up and down stroke, so that would be 28'ish pumps with a 54 cc stroke volume. While not efficient, 28 is doable, if I can get there with a two stage pump.

I'm going to do up a mock 15cc reservoir, adjustable down to 5cc in 1 cc increments with HDPE discs, and start testing. First the pump testing, then I've got in the works an electronic high pressure valve, 13 CI 3,000 psi HPA tank, and the barrel. That'll allow me to get on the range and lock in the specifics of how much pressure is required at various volumes. I'll be sure to update here for everyone else's benefit. Valving the piston after I've nailed down what it takes for a dump shot isn't totally out of the question, though I'd like to avoid the complexity. It's viable to get slightly over my velocity goal, then valve the thing down for half-barrel-volume blasts. Such a tiny reservoir wouldn't be enough for a follow up shot without pumping, but it certainly would reduce the amount of pumping. I may have to slightly (very slightly) lower my velocity goals as well, but I won't know until I give it my all. For those who haven't picked up on it yet (Bob, of course, never misses a beat and caught it right away), 70 PFE with a 30 grain .22 bullet (3.2 cents a piece from North American Arms) is exactly the power of a .22 Short standard velocity round. That's what we're talking about here--a .22 Short air rifle. I can't thank you enough for getting me in the ballpark, Bob.

rsterne · Moderator

All I can say is good luck, especially with a 3 lbs. target weight....

Bob

robert w · Senior Member

well your first post ! there is a vast coverage on guns here and you look like your in it deep like the rest of us here

gicos · Member

I could use some critiquing on my math here. Before I start testing, I need to make sure I've got my head completely wrapped around the numbers for multi stage pumps. I realize the scenerio below may have technical limitations that may not jive in real life, but it'll suffice for a check on learning.

Assume the target pressure is 3,500 psi. The highest pressure stage of the pump has a volume below the fully extended piston of 4.75 cc (really small piston). Assume the plunger seal is affixed to the front of the plunger and that it bottoms out completely in the cylinder. The only headspace is on the piston side of the check valve. We'll assume this dead space on the piston side is .2 cc. This gives a compression ratio of 23.75, capable of 349 psi if it were used as a single stage pump.

In order to reach the target of 3,500 psi, the air in the high pressure stage in this example must be pre-pressurized to 147 psi on the up stroke, given the limitation created by the headspace of the check valve. 147 psi is very close to 10 atmospheres or 10 bar, meaning the compression ratio of the first stage, if a two stage pump, would need to be 10:1. That would mean that the 4.75 cc volume in the high pressure stage would need to be filled 10 times to reach 147 psi, for a swept volume in the first stage of 47.5 cc.

Subtracting the volume occupied by the OD of the high pressure stage tube, say 10 cc, from the capacity of a hollow outer tube gives the size of first stage tube needed. A 57.5 cc or 3.5 cubic inch outer tube, given 10.5 inches of piston travel, must have an ID of .65 inches. This is about a 3/4" OD tube, so 47.5 cc swept volume sounds about right.

I'm aware that 147 psi on the upstroke isn't likely to happen, this is just an exercise in theory. .2 cc dead space may be a bit large as well. Lowering that to .1 cc would give the high pressure stage a compression ratio of 47.5. This would generate 698 psi as a single stage pump, or require 73 psi from another stage to achieve the 3,500 psi final pressure.

On a side note, I've seen it mentioned that pumping losses are estimated at 15%. Does this match anyone else's experience?

rsterne · Moderator

Your math seems reasonable, give the assumptions.... I find you have to move about 50% more air than you end up using once it has cooled and during the shot.... ie if the gun uses 1 CI of air to produce 1 FPE, you have to move about 1.5 CI through the pump.... some of that loss is pumping loss, and some firing loss, but that seems to be about the total loss....

Bob

gicos · Member

While on the subject of theory, I thought I'd post the thought process leading to the idea that I could pull this project off, in the hopes that it may help someone. Sorry for the long post, but theory gets wordy...

I've spent the last 20 years making my living as a trumpet player. It's been measured in a laboratory that the pressure on a trumpeter's face while playing a high C is 110 psi. That's diaphram pnuematics for ya, something I have to think about every single day. The tiniest changes in the instrument, in 1/10,000th inch increments, makes a big difference when your talking about human pnuematics. Before that, I made my living as a mechanic. Both of these careers forced me to spend an awful lot of time pondering pressure, air speed, and volume.

In an internal combustion engine it's pressure that drives the pistons, not the actual act of combusting vaporized liquid fuel. The heat of combustion creates rapidly expanding air, and, since that air is in a confined space, the pressure rises. It's the pressure that does all of the work, not the heat. The same concept applies to powder burner firearms. The gunpowder creates massive heat in a very small space, but it's the air pressure generated that does all the work. In airguns, we don't have heat to do work, we have muscles, pumps, and air storage reservoirs. The volume of air delivered affects the rate of pressure drop once the valve is opened, but the volume itself does no work. Only the pressure.

SAAMI maximum pressure for a .22 Short is 21,000 psi. We'll assume that for liability reasons, manufacturers stay slightly below this at 20,000 psi. The military has done massive testing on the .22 caliber rifle and determined that nothing beyond 14.5 inches of barrel provided any real benefit on the M855 round with a 62 grain bullet traveling 3,150 fps. They may have overdone this, as the 20" barrel of the M16 generates a noticable velocity increase over the 14.5" barrel of the M4. Anyway, a 16" barrel is very close to the optimal length for a powder burner in .22 caliber.

Taking that .22 Short and firing it in a 16" barrel produces pressure results that may be surprising to those who haven't pondered it. The internal volume of a loaded .22 Short round (the area inside the case) is .2 cc. I've torn them apart and measured. The internal volume of a .22 caliber barrel 16" in length is 10 cc. That means that for every cubic centimeter of barrel volume, the pressure of a .22 Short is dropping five times, or 50 times in a 10cc barrel. At 4" of travel, the pressure is 1/12.5 of what it was in the casing, 1/25th at 8" travel, 1/37.5 at 12" travel, and 1/50th at the muzzle. This shakes out to:

20,000 psi -> 1,600 psi -> 800 psi -> 533 psi -> 400 psi

It's an eye opener to think that a round that starts at 20,000 psi at the breech can drop all the way to 400 psi over the course of a 16" barrel, but that's exactly what happens. This illustrates that almost all the work being done on the bullet is in the initial high pressure blast, with almost no velocity increase in the latter half of the barrel. From half barrel to the muzzle, these pressures can easily be exceeded by an airgun.

Obviously, for an airgun to "catch up" to the velocity of a .22 Short, given that no where near 20,000 psi chamber pressure can be produced, it must do more work further down the barrel. How much work and how far down the barrel are two questions I intend to answer. But it's obvious that the higher the starting pressure the better, as this is where the most work is done. Here are some pressure curves in psi in a 16" barrel for different size air blasts for a comparison. They're not all in nice cozy 4" increments, but they'll suffice. I've used 3,500 psi as a starting pressure, since most of the stirrup pumps out there can do this. The high and low are always the breech and muzzle pressures:

1cc blast in fifths of a barrel: 3,500 -> 1,155 -> 700 -> 490 -> 385 -> 315

2cc blast in fifths of a barrel: 3,500 -> 1,750 -> 1,155 -> 875 -> 700 -> 560

5cc blast in quarters of a barrel: 3,500 -> 2,625 -> 1,750 -> 1,166 -> 875

10cc blast in quarters of a barrel: 3,500 -> 3,062 -> 2,625 -> 2,187 -> 1,750

The 1cc blast never catches up at this starting pressure. Since chamber pressure higher than 3,500 psi is impractical, at least at this point, 1cc simply won't get there. The 2cc blast, however, has caught up with the 22 Short by half barrel, the 5cc by 1/8 barrel, and the 10cc blast only about an inch out of the chute. The muzzle pressure in these examples, excluding the 1cc blast, exceeds the .22 Short by 160, 475, and 1,350 psi respectively. Obviously, in the case of the 10cc blast, blowing 1,750 psi out the muzzle is extremely wasteful, so the smaller the air volume the more efficiently we're using air. As Bob has illustrated many times, a higher pressure smaller volume blast is always more efficient. The .22 Short illustrates this concept perfectly. The limitation, of course, comes in the mechanical limits of a pump being powered by human muscle versus applications where gasoline or gunpowder is creating the pressure for us. Any advances improving the practicality of higher pressures in airguns will allow the use of smaller blasts to achieve the same results. I intend to give this a thorough testing as well. Much more to follow.

rsterne · Moderator

This can also be modelled using a spreadsheet based on the basic Physics involved (F=MA).... Lloyd Sikes, who designed the Crosman Rogue was kind enough to share his internal ballistics spreadsheet with me.... Here is the data for a stock Discovery at the beginning, middle, and end of the shot string....

Note the discontinuity in the pressure curves at the point where the valve closes.... When you get more deeply into this, you will find that very little useful acceleration occurs in the second half of the barrel, compared to the massive additional amount of air required....

Bob

rsterne · Moderator

I ran your numbers for a .22 Short.... here are the results....

Note that the acceleration curve follows your pressure curve, this was just a clearer graph because the fps was easier to read....

Bob

rsterne · Moderator

Here is a trial run for what you are trying to accomplish, as I understand it.... Inputs are .22 cal, 30 gr. bullet, 3000 psi, 24" barrel, 70 cc reservoir/valve (because your aim was 70 FPE), and 70% efficiency (which is high, but possible with the right choices).... I adjusted the dwell time to produce a "dump shot" (barely, the valve closes exactly as the bullet exits the muzzle), plus two others where the valve closes at the point the bullet has travelled at 50% and 33% (ie 12" and 8") down the barrel....

Here are the predicted results:

"Dump": 1048 fps (73.2 FPE) at an efficiency of 0.46 FPE/CI (541 psi drop) - 2613 barcc of air used
"50%": 1023 fps (69.8 FPE) at 0.78 FPE/CI (302 psi drop) - 1457 barcc used
"33%": 985 fps (64.6 FPE) at 1.02 FPE/CI (214 psi drop) - 1033 barcc used

Consider the HUGE difference in air used for the very small decrease in velocity, particularly when the valve closes at half way.... Note that if your actual efficiency is lower than 70% (most are) you will need a longer dwell to achieve the same muzzle velocity, and hence use more air....

Bob

gicos · Member

Bob,

That is just flippin' awesome! It's the coolest thing since sliced bread. Thank you so much. This will come in very useful and I won't forget you for it.

I wonder if I could impose upon you to run a few more numbers in the chart for me? I've got a couple of ideas to pursue and it would be very useful to see how they pan out. They're dump shots, but that doesn't mean I've tossed the idea of valving or recouping the air by other means.

They're in quarter barrel increments, just like the .22 Short you plotted. I know, they're out there, but they're of interest. Same 30 grain bullet and 16" barrel. Same way with the first being breech pressure and the last muzzle pressure.

1cc blast: 5000 -> 2000 -> 1000 -> 650 -> 500

2cc blast: 5000 -> 4000 -> 2000 -> 1300 -> 1000

Thanks again.

rsterne · Moderator

Here you go.... red line is 1cc, green is 2cc dump, purple is 2cc with valve closing at mid-barrel (8")....

Huge difference in power with the 2cc valve.... By closing it at mid-barrel the barcc used drops from 579 to 501 (15% savings) yet the power is almost identical.... Closing the 2cc valve at the 4" point drops the FPE to 38, and the barcc to 406....

Bob