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gicos · Member

Thanks so much again, Bob. I won't pester you any more for graphing. That told me an awful lot. Not quite as rosy a picture as I'd hoped for, but such is engineering. The reason I was curious as to using 5,000 psi is because I ran across an employee of a stirrup pump manufacturer (they declined to identify which one, only that they manufactured one of the mainstream pumps) who claimed that their pump could easily do 350 bar. He said that the only reason they put 250 bar guages on the pump is because that's what is common in the PCP market. "Easily" is a pretty subjective term here. I believe he was referring to the physical capabilities of the pump, not the amount of effort required to get to that pressure. And that's saying nothing of the difficulty of containing and dealing with that level of pressure, but it may not be totally out of the question.

I did some work with the Powley computer today. Most powder burner reloaders are familiar with this. The reason I took a look is because it's darn near impossible to find actual chamber pressure measurements for the .22 rimfires. I guess they've been out so long that manufacturers just know what those numbers are. Testing is expensive.

I got some surprising results. The following are a best and worst case scenerio for a standard velocity .22 Short firing a 29 grain bullet at 1,045 fps through a 22" barrel and a 16" barrel:

The pressures look low to me. Powley does warn that the smaller the case the bigger any errors in the algorithm will be, and the Short is about the smallest case around. The highest pressure Powley predicted with the hottest load out there, matching the velocity with a 16" barrel (which we know is shorter than the manufacturers test with), was 9,000 psi.

Things look a bit more realistic with the 22 LR. This is the old standard velocity load of a 40 grain bullet traveling 1,138 fps:

I then plugged in the hottest load out there for 22 LR, out of a 22" barrel, and got 20,000 psi. Dropping the barrel length to 16" put the round over SAAMI max pressure (24,000 psi), so Powley appears to be pretty close with the LR.

Plotting out the pressures, which seems to have become my new hobby, is pretty interesting. First, we need to establish pressure percentages at various points in the barrel. The .22 Short, as already mentioned above, has a case capacity of .2cc. The 22 LR has a capacity of .31cc. For comparison, a 1cc and 2cc airgun reservoir are plotted. All of this through a 16" barrel, with the pressure points at the breech, 4" travel, 8" travel, 12" travel, and the muzzle:

22 Short: Breech -> 8% -> 4% -> 2.6% -> 2%

22 LR: Breech -> 12.4% -> 6.2% -> 4.1% -> 3.1%

1cc: Breech -> 40% -> 20% -> 13% -> 10%

2cc: Breech -> 80% -> 40% -> 26% -> 20%

Now plugging in the best and worst case scenario pressures from the attachments above and the curves of the airgun charges (sorry, I don't have the fancy graphing capabilities Bob has):

22 Short: 2,000 160 80 52 40
22 Short: 8,000 640 320 208 160

22 LR: 11,000 1,364 682 451 341
22 LR: 14,000 1,736 868 574 434

1cc: 5,000 2,000 1,000 650 500
1cc: 4,000 1,600 800 520 400
1cc: 3,000 1,200 600 390 300
1cc: 2,000 800 400 260 200

2cc: 5,000 4,000 2,000 1,300 1,000
2cc: 4,000 3,200 1,600 1,040 800
2cc: 3,000 2,400 1,200 780 600
2cc: 2,000 1,600 800 520 400

Of course, none of this matters until I put up some real world numbers, but interesting food for thought.

rsterne · Moderator

I think you can use the graph I did with the three valve closures at 3000 psi as a guide.... It's within the values the spreadsheet works with on a regular basis.... The only value in question is the efficiency factor of 70%, which is pretty optimistic, especially when you start pushing for high power levels....

Reducing the reservoir volume will require raising the pressure, as the loss during the shot becomes greater.... You already found that out....

Bob

gicos · Member

OK, here is the grand plan of attack. I've gleaned enough information to start laying out the money and time in testing. These are design goals, and they are lofty, so reality may not bear these things out. But, two things I'm really good at are falling on my face and pushing the envelope. Plus, I have to give Bob the opportunity to say, "I told ya so". Wink

Hopefully all of the testing will provide useful numbers not previously explored, or not shared by those PCP manufacturers who have.

Goals are to achieve 1,025 fps with a 30 grain bullet in a 16" barrel with a 1cc - 2cc reservoir at 5,000 psi shooting MOA at 50 yards. Keeping the reservoir as small as possible reduces the needed pump volume capacity, which reduces the size of piston, which is required to reach this level of pressure. If the 1cc reservoir achieves this velocity goal, which doesn't look likely, the total air volume to be compressed to this high level of pressure, allotting 1cc for volume at the check valve, air behind a balanced piston, and air in the quick release valve passage, is 2cc. 2cc at 5,000 psi is 690 cc's of air at atmospheric pressure.

Serious challenges are to safely contain this level of pressure with good part longevity and to create this pressure with a practical amount of hand pumping. All parts must be rated to a minimum safety factor of 4, meaning some must be custom made as they don't exist on the open market. Building the receiver to handle the pressure is no problem, but the beating the piston and QRV will take at 5,000 psi is a different matter. The pump will be under extreme strain as well and sealing will be difficult.

Testing will begin with a CNC machined stainless reservoir. I have a relative with a CNC machine, so thankfully I'll have his help. The reservoir will be built with a 15cc inner volume. HDPE rods will be inserted to modify the volume to various points for testing. The barrel will be threaded to the front of the reservoir. The rear of the reservoir will contain a 5,000 psi gauge, fill port, and check valve. The gauge and fill port will be attached to a gauge tee and enter the reservoir through the same hole. The QRV will be a high pressure ball valve. Initially, the reservoir will be filled by a FX 4 stage pump. This mock reservoir will be central to pump testing as well.

An attempt will be made at using 3/16 (.1875") Grade 5 titanium rod as the high pressure stage pump plunger. This is some tough stuff, with a 180,000 psi tensile strength, and it's also incredibly hard to machine. I'm going to attempt a precision fit with no seals. This is done routinely on disc brake calipers on vehicles under many thousands of pounds pressure, but the accuracy required is difficult to attain. The smallest plunger I've seen on the commercial PCP pumps is about 3/8", so 3/16" would bring pumping effort into the realm of comfortable. Hence the need for a tiny reservoir. Concern exists over wear between the piston and chamber wall if they were of dissimilar materials, so titanium tubing of the same hardness will be used.

I've not ignored Bob's advise on valving the rifle. I have a different approach as to how to accomplish this, however. Because of the intended usage of this rifle, with weight, bulk, and failure points being of paramount concern, I'm going to attempt this with a gas port. I'll pull a chunk of pressurized air from some point in the barrel and redirect it back to the rear of the piston, using this to close the piston before all of the air is released. Since we can't have a situation of the air pressure "chasing its tail" at the piston, the rear will have a greater surface area than the front. It'll be a stepped design, rather than a straight cylinder. Dimensions will have to be determined based on testing measurements. On its way back to the reservoir, the ported gas will force the QRV closed (I seem to remember shooting a CO2 pistol that did this, but it's been too many decades to be positive). The trigger will snap back forward almost the instant it's pulled, and I'll trip the safety with air pressure as well if I can.

Timing, sizing, and location of the gas port will be the most challenging aspects of the design. The test barrel will be drilled in 1" increments with .125 holes, tapped, and plugs inserted into each one. At each 1" increment, the plug will be removed and vented to atmosphere during the shot and the effect on velocity noted. Then, a gauge with max pressure memory will be screwed into the hole and the pressure recorded, adjusting for the volume inside the gauge. Once velocity and pressure measurements are made, piston dimensions can be determined. It will then be implemented on the test device and worked from there. I could attempt to do the math ahead of time, but I'd likely loose what's left of my mind. Attempting to calculate the lag through ports, forcing the QRV closed, the pressure drop, etc. is beyond the realm of sane. This is a case better left to testing.

There you have it. This won't be a short term or cheap project, but I'm in it for the long haul. All testing and data will be posted here as I progress.

gicos · Member

Bob,

I'm a bit cornfused with the graph you did at 5,000 psi. I see one line starting at about 3,400 psi and the other starting at 4,000. All the other graphs I've seen you do start on the left with the reservoir pressure and end on the right at the muzzle. Am I being a dufus or is there a boo-boo in there?

rsterne · Moderator

They actually start at 5000 psi, but they drop vertically at zero time because of the transfer port volume (between the valve seat and the pellet base).... I used the volume from my .22 cal Disco, which works out to 0.46 cc.... It has a huge affect because of your small valve volumes.... If you look at the 70cc reservoir, 3000 psi graph, the pressure drop is there, but it's only about 20 psi....

Bob

gicos · Member

Thanks for that, Bob.

Since I'm at a lull until after the holidays, I started studying the Second Law and trying to calculate the rate of acceleration of a projectile, and, in particular, the pressure or point in the barrel where the bullet (pellet) no longer accelerates (or accelerates at a rate so slow to be of no real use). That would be a handy piece of information to be able to calculate. It's a given that in a high powered powder burner this point would rarely if ever be reached inside the barrel, but in an airgun that's not necessarily the case. Once the pressure gets low enough, there's just not enough steam to increase the speed of an already fast moving bullet, given its natural resistance to a higher velocity, air resistance, and friction in the barrel.

I'm growing more gray hairs trying to pick apart the methods I'm able to find from physicists who calculate these things. The biggest problem is that most of them assume a straight line acceleration through the barrel, which we know isn't the case. The pressure changes continuously for every molecule of air moved, so the force on the back of the bullet is never the same at any two points in the barrel. An example is, yet again, the .22 Short where I've calculated and ballistics software has calculated the muzzle pressure to be somewhere between 40 and 400 psi. That's very little force to apply to the back of a bullet that's already moving just shy of supersonic speed.

In the .22 Short graph Bob did above (thanks again, Bob), it shows that almost all of the acceleration of the bullet occurs in the first 4" of travel, and almost all of that comes from just the initial jolt at zero travel. I understand that the math to solve this can be difficult, but the concept is simple. One line on a chart indicates acceleration, taking into account mass, friction, air resistance, and supplied pressure, while the other indicates a bullet's resistance to further acceleration, based upon speed already traveling, friction, and air resistance. The chart is graduated into inches traveled. The point on the chart where the two intersect is the point where the bullet no longer accelerates. The curve leading up to that point would show where the acceleration reached a rate too slow to be of much use.

Any mathematicians care to chime in?

rsterne · Moderator

Virtually all airguns are still acclerating the pellet at the muzzle, it's just that the rate of acceleration (the "G" force) drops as the pellet proceeds down the bore and the air behind it expands.... If the valve closes early, the air will expand more, the pressure at the muzzle will be less, and most of the work (but not all) will occur early in the barrel.... If the valve closes late, the air in the bore behind the pellet has less time to expand, and more (proportionately) of the work is done in the second half of the barrel....

Study that triple graph I showed you on the Disco.... there is a wealth of information in there about PCPs and how they work....

Bob

gicos · Member

I'm studying away and it is definitely a wealth of information you gave me there. I'm just trying to understand how the numbers work behind the graph. Like you, I have an insatiable appetite to know how things work. It's the old mechanic diagnostician in me.

Spending a number more hours on this, I came to the conclusion that most folks trained in physics can't figure this one out, and that's why bullet acceleration is a question in almost all physics curriculum. They're let off the hook, though, as they only have to figure straight line acceleration through the barrel, which is much simpler than what actually happens. Since I've never had a physics class, I decided that it would be better to let this one go. Math was never my strong suit anyway.

This did lead me to another aspect I need to test, though, so it wasn't for nothing. What I know about PCP piston/QRV type setups is that the piston is "considered" fully open when it has traveled 1/4 the diameter of the bore. "Considered" doesn't cover the how, the why, or the changes that occur with different calibers, reservoir sizes, and starting pressures. There has to be a sweet spot where the pressure drop versus shrouding is optimized for each different setup. More piston travel means less shrouding and more pressure drop, and less travel means less pressure drop and more shrouding. So, I decided that the test apparatus would have adjustable piston stops that will allow adjustment from 1/8 (~.050) up to 1/2 (~.125) bore size. I expect that with a small reservoir and caliber minute adjustments to piston travel will make large changes in performance.

rsterne · Moderator

The physics aren't all that difficult in a PCP.... The air expands according to P1 x V2 = P2 x V1 which rearranged is P2 = P1 x V1 / V2.... if you are using Isothermal expansion (ie no temperature change).... You start with the volume in the valve V1 at the valve pressure P1.... At any given point while the valve is open, there is a new volume V2 which is the total of the valve, barrel, and dead space (transfer port) at a lower pressure P2.... Whatever the pressure is at that instant pushes on the area B of the base of the pellet and P2 x B creates a force F.... That force acts on the mass of the pellet, producing acceleration by Newton's Second Law, F=MA....

Once the valve closes, P2 and V2 become fixed as new air is no longer being added.... As the pellet moves down the bore, the volume increases and at any instant is V3 with an associated pressure P3.... You can throw in an added complication here if you want, by using adiabatic expansion (where the air cools, and the pressure drops more rapidly).... In this case P3 = P2 x (V2 / V3) ^1.4.... (ie the volume change is raised to the power of 1.4).... The true answer may in fact be in between....

Where you are talking about the "piston travel", I think you are talking about the limiting factor on flow through a poppet valve.... Once a poppet opens to 1/4 of the throat diameter, no additional flow can occur, as the "curtain area" equals the throat area.... The curtain area is the circumference of the valve throat times the lift (PI x D x L) while the throat area is (PI x D x D / 4).... set them equal and you will find (PI x D x L = PI x D x D /4).... therefore (L = D / 4)....

Bob

gicos · Member

Wow, that is some juicy stuff, Bob. Again, thank you sir. I'm going to have to chew on these equations for a while and improve my math skills.

The design I'm working with isn't a poppet valve. It's a balanced coaxial piston that seals directly against the bore. When the QRV (exhaust valve) drops the pressure behind the piston, the pressure on the front of the piston (the reservoir) pushes the piston back and the reservoir air rushes into the breech. Like so:

The word "Chamber" in the drawing should actually say "Reservoir" and it should be both above and below the projectile, but it's what I've got to work with for the moment. You have to open the attachment to see the valves behind the pilot area--the server crops them out. Of course, this isn't to scale or specific design, it only represents the concept.

rsterne · Moderator

So the air makes a 108* turn when the valve opens?.... got it!.... The limiting lift in that case would be 1/4 of the caliber.... Adding lift would IN THEORY add no more flow, although with that 180* turn I would think a bit more might be in order....

Bob

gicos · Member

This is just a session of thinking out loud here. I know a lot of folks enjoy discussing design on this forum, so here goes. If anyone sees any flaws in my logic, feel free to shoot holes in it. Better now than after I've got a receiver machined.

A few definitions before I lose everyone. For lack of a better term, I'll refer to the air behind the piston as the pilot air, the air in the reservoir as reservoir air, and the air in the gas tube, which is pulled off the barrel during the shot, as gas tube air.

A couple of performance concepts as well. This piston setup works by having the same pressure at the front and rear of the piston when ready to fire. If you look at the drawing above, you'll see that the surface area exposed to the air pressure is much lower on the front of the piston than the back--most of the front of the piston is covered up by the breech. When the air pressure is dropped behind the piston by opening the QRV (exhaust valve), the force at the front of the piston pushes it back and the gun fires. Once the piston moves just a tiny bit, the area of the front of the piston formerly covered up by the breech is now exposed and the force pushing it back increases drastically. Key to good performance with this setup is exhausting the air behind the piston almost instantaneously. If the pressure is lowered slowly, or if too much residual pressure remains in the pilot area, the piston will release slowly and performance will suffer. It's the sudden extreme blast on the back of the projectile that does the most work, so it's critical to make sure this blast is in fact sudden and jolting.

Two challenging areas at this point in the design phase are what to do with the pilot air and a few concerns with the gas tube air. First, the pilot air.

A large number of PCP rifles with this piston setup simply exhaust the pilot air to atmosphere each time the gun is fired. While this works, it isn't the most efficient. We had to pump or pay in one form or another for that air to be compressed, so it makes sense to use it for all it's worth. Pilot air is a necessary evil with this type of piston setup, though there are other benefits that make this small amount of wasted air worth it. In my setup, the pilot air will be about .18 cc's. Not a lot, but very close to one pump or a bit more each time the gun is fired, so it is significant.

In order to improve the efficiency of the design, I'd like to put this air to work rather than just blowing it out an exhaust port. I considered porting the air into the main reservoir charge, but by the time it got there it would be at such a low pressure it would be useless. I also considered porting it into the pump and pre-charging the next pump sequence a bit, but same story. Not enough to be of any use. There are two bits of work that need to be done, however, that I believe this air can take care of. One is forcing the QRV back to the closed position and the other is tripping the safety back to the "safe" position.

The QRV has to be closed when the air starts coming in from the gas tube in the barrel, otherwise the gas tube air will just blow out of the exhaust valve. I also consider it important with this design for safety reasons, because of where the pump is located, that the rifle be on "safe" when pumping. The plan for using the pilot air to accomplish these two acts is to loop it back around to the QRV, force it closed, then trip the safety. By closing the QRV before flipping the safety, the design of the safety is simplified, as it need only be designed to be capable of flipping to "safe" when the trigger is in the forward position. The timing of these two acts can be controlled by the length of the air loop and diameter of the orifice. These are the advantages I see to doing this:

1. The air isn't wasted, improving the efficiency of the design.

2. The main charge coming down the gas tube doesn't have to be diverted through the QRV to close it before pressurizing the reservoir. This allows a straight B line for the gas tube air to the reservoir without obstructions or delays, which are important for reasons I'll cover below.

3. The pressure of the pilot air is reduced greatly by the time it exits, leaving no risk of being stung by high pressure exhaust. Pilot air blown straight out of the rifle unhindered could be high enough pressure to sting if a finger were too close to the exhaust port and would, for this reason, have to be dealt with in the design regardless.

If anyone sees anything else I could use this air for, or sees any holes in my thinking, please throw them out there. I'll move on to the gas port now, in a new post since this is getting pretty long.

gicos · Member

OK, on to the gas port. I see two different approaches in the execution of this. In both approaches, the air is pulled off the barrel and directed behind the piston, forcing it closed. This is one of the advantages of the piston/QRV setup. The fill port/gas tube is behind the piston, so any pressurization behind the piston first forces it closed before bleeding air into the reservoir. No springs or other hardware required.

The first approach to the gas tube is to pull air out of the barrel soon enough to force the piston closed when the projectile is about half way down the barrel. These are the challenges of doing this:

1. In order for the air to make it back to the rear of the piston in time to close it, the gas tube must be located very near the breech. This is undesirable, as the most work by far is done in the first 4" of barrel, and there will be a pressure drop wherever the gas port is located. Locating it in the first 4" of barrel travel creates a pressure drop right where the most gravy work is being done. Of course this can be minimized by restricting the size of the the orifice, but then this slows the air from getting to the back of the piston where it's needed. It's a catch 22.

2. The pressure has to be high enough to slam the piston shut. It can't coax it shut, otherwise the projectile will be out the muzzle by the time it closes. Even though the piston can be designed in a stepped manner where the back is significantly larger in surface area than the front, a good deal of pressure will still be required to accomplish this.

3. Regardless of where the gas port is located, there will be a significant pressure drop in the tube by the time the air reaches the back of the piston. Naturally, the further down the barrel the port is located, the greater the pressure drop. This is not good, either, since high pressure is what's needed at the back of the piston.

This first approach lends itself to a bigger reservoir. More air volume will minimize the pressure drop when the projectile crosses the gas port and will result in the gas port having less negative effect on velocity. The drawbacks to a larger reservoir are that the receiver ends up bulkier and heavier and the amount of pumping to initially fill it increases a lot.

The second approach involves locating the gas port about mid barrel and giving up on the idea of closing the piston while there's still air in the reservoir. This lends itself to a smaller reservoir, as we want the pressure drop to be such that little air is wasted out the muzzle. The gas port can capture and recycle a good amount of this air, but it only has half a barrel length to pressurize before the projectile is out the muzzle and the barrel pressure drops to zero. This would have a similar effect as closing the piston at half barrel, except that a good amount of air would be in the tube instead of in the reservoir where we want it. Then there's the pesky pressure drop in the tube, where if the air were retained in the reservoir to start with, there would be no pressure drop. This can be alleviated, however, by check valving the tube right at the barrel, so that all of the pressure scavenged remains in the tube instead of blasting out the muzzle and accomplishing nothing. The air in the tube would be too far behind the projectile in timing, were the gas port not check valved, to contribute anything to velocity.

The question is what to do with this air once it's captured in the tube behind the check valve. It will fill the reservoir until the pressure in the reservoir equals that in the tube, then the check valve will close. We end up, prior to pumping for the next shot, with the same pressure in the tube as that in the reservoir. If this pressure is left in the tube, it will blow straight out the exhaust port when the QRV is opened on the next shot. It could be used to assist the pilot air in closing the QRV and tripping the safety, but this is a significant amount of air (about 1/4 barrel's worth in volume), so most of it would blow out the exhaust port.

My solution is to port the gas tube air into the bottom of the pump cavity. Remember that the pump on this setup is actually the buttstock itself. There are no levers or pivot mechanisms. The pump shaft extends straight into its housing, just like a stirrup pump. The high pressure pump check valve is located directly behind the piston in the receiver. By pushing the gas tube air into the pump cavity, we're utilizing a pump check valve that has to be there anyway, saving an additional check valve for the gas tube. As the pressure increases in the pump cavity from the gas tube air, the check valve is opened between the pump and receiver and the reservoir is pressurized. Once the pressure is equalized between the pump cavity and the reservoir, the check valve closes. Now we have the same pressure in the gas tube, the pump cavity, and the reservoir. Here's the trick. Once the pumping starts for the next shot, the pressurized air in the gas tube pushes/is sucked into the pump, providing pre-pressurized air for the first pump. The check valve at the barrel for the gas port now becomes the intake check valve for the pump, saving another check valve that had to be there anyway. The gas tube now becomes completely depressurized, the scavenged air remaining in the tube after the shot is not wasted, and the pump intake valve is located inside the barrel away from mud and most of the dust that's floating around.

Fire away!