Benjamin 392 power limit

[Tom Tucker]

Have you thought about making a flat-top piston?  In my 1322, I made an adjustable rubber cup piston at one point, but I found that a flat-top piston with an o-ring was much easier on the linkage because it didn't need as much interference to make full pressure at higher pump counts.

Of course the 392 is different in that there seems to be less material in the nose of the valve ahead of the check.  When I had mine open, I intended to stick a pin in the check valve like I do on my 13XX guns to eat dead space, but it didn't seem necessary because the check valve was so close to the air inlet hole.  I don't recall if there was enough material there to completely flat top it without additional modifications.

[Psipumper]

Have you thought about making a flat-top piston?  In my 1322, I made an adjustable rubber cup piston at one point, but I found that a flat-top piston with an o-ring was much easier on the linkage because it didn't need as much interference to make full pressure at higher pump counts.

Of course the 392 is different in that there seems to be less material in the nose of the valve ahead of the check.  When I had mine open, I intended to stick a pin in the check valve like I do on my 13XX guns to eat dead space, but it didn't seem necessary because the check valve was so close to the air inlet hole.  I don't recall if there was enough material there to completely flat top it without additional modifications.

A flat top piston is possible but I can’t imagine much improvement over current. You are not going to trim 2 pumps and make the same power. If the oring used in the conversion were not square you could end up losing power instead. The square ones usually aren’t available in 90 duro hardness. Wear and extrusion could become an issue over time.
I did sleeve the air inlet hole to about 1 mm. I turned a wire welder tip down. Saved me from drilling the hole.

[Psipumper]

Fantastic work!

I tend to favor the bigger valves.  To me the power limit of a pumper is the amount of power it can make at the safest pressure that it can take over and over again without significant wear.  "Significant wear" is subjective but to me if I can go through a few tins of pellets without my piston and valve moving away from each other detectably, I'm pumping to a safe pressure.  So I prefer to increase the valve volume quite a bit and then fill it to whatever I consider max pressure.  Number of pumps doesn't really matter because they become easier to do, as long as I don't run out of fingers and toes to count on.

Of course, it's hard to talk about valve volume without considering barrel volume.  I think that if someone were to de-solder the stock barrel and replace it with a 26-inch maximus barrel, or something .25 cal, they could really see some high muzzle energy.

.25 caliber would be interesting. Crosman should do that. I have never seen a 397 modified.
The safe pressure for a 392 depends. My gun is 1900 to 2300. Other people have said 1800 for a stock 392. I sized my valve volume to develop this maximum pressure at the desired 14 pumps.
Since I have the pressure gauge added to the gun, I was able to do this.
If I could improve headspace more  the valve cc would be larger @ 14.
One thing for sure headspace is extremely important. My 392  only made 1600 psi at 25 pumps before work. Probably close to its maximum.
About par with the rest. Seems the 392 is a good time proven design of proper proportions in need of a lot of fine tuning and blueprinting without throwing it out of balance.

[rsterne]

What is the barrel length on a 392?.... Maximum practical valve volume is 50% of the barrel volume when going for power.... but it takes a LOT of pumping and the efficiency is poor.... The smaller the valve the higher the efficiency, but the lower the potential FPE.... when the number of pumps is not an issue and you are pumping to a constant fill pressure....

Bob

[Psipumper]

What is the barrel length on a 392?.... Maximum practical valve volume is 50% of the barrel volume when going for power.... but it takes a LOT of pumping and the efficiency is poor.... The smaller the valve the higher the efficiency, but the lower the potential FPE.... when the number of pumps is not an issue and you are pumping to a constant fill pressure....

Bob

Barrel is 11.8cc
Factory valve cc is 4.2 cc =36%
4.2 cc would overpressure my gun before 14 pumps. Right now I get 2100 psi @14 with a 4.9 cc valve.=41%
At 50% it would take 20 pumps to get 2100 psi.
Since I had a desired number of pumps of 14 at maximum operating pressure. I sized the valve cc @ 4.9cc to get this. This should be the optimal valve size for maximum power at 14 pumps.

[Rob M]

What is the barrel length on a 392?.... Maximum practical valve volume is 50% of the barrel volume when going for power.... but it takes a LOT of pumping and the efficiency is poor.... The smaller the valve the higher the efficiency, but the lower the potential FPE.... when the number of pumps is not an issue and you are pumping to a constant fill pressure....

Bob

Barrel is 11.8cc
Factory valve cc is 4.2 cc =36%
4.2 cc would overpressure my gun before 14 pumps. Right now I get 2100 psi @14 with a 4.9 cc valve.=41%
At 50% it would take 20 pumps to get 2100 psi.

Charles you must have strong shoulders pumping that thing to 2100 (-'

[rsterne]

Thanks for that info.... so about 19".... Around 40% sounds like a good place to be.... but don't forget you could get the same FPE with a larger valve and a bit less pressure, so maybe 18 pumps and 1900 psi but with a 5.9 cc valve.... and still have the option of going to 20 pumps without overstressing the gun and get even more FPE.... All I'm saying is that 14 pumps is just a number, it has to be combined with the valve volume to tell you the stress you are putting on the parts....

If I had a 5.9 cc valve I would probably end up tuning it to retain air and get two equal shots.... That's the cool thing about pumpers, so many ways to tune them....

I agree, 2100 psi would be quite hard to pump, and very hard on a stock 392 linkage.... I used 1800 psi for a maximum and usually only 1500 with my .25 cal Disco based Carbine with the stock 392 linkage.... and 2000 psi for the maximum and 1800 for most shooting with a Steroid linkage.... I was worried about the stock linkage failing so never even tried 2000 psi.... That was hard enough for me to pump, and the Disco tube is only 0.74" ID, slightly smaller than a 392 tube....

Bob

[Tom Tucker]

I've found that with pumpers, I can predict the effect of small changes in pressure and volume with a couple of formulas.  Increasing pressure at the same volume gives an increase in velocity of roughly sqrt(pressureA/pressureB) and increasing volume at the same pressure gives an increase of roughly sqrt(sqrt(VolumeA/VolumeB) [4th root of the VolA/VolB)].  Likewise, increasing volume with a proportionate decrease in pressure results in a loss of velocity equal to sqrt(sqrt(VolA/VolB).  The reverse is true for decreasing volume.  The catch is that this only works when you can actually measure (or at least accurately estimate) the pressure.  In a multi-pump, you can't just assume that when you double valve volume you need twice as many pumps to reach the same pressure - it will actually be less than that because % of head space is lower if the valve volume is increased.  The reverse is true if you make the valve smaller - the cumulative effect of head space losses will become unmanageable at a lesser number of pumps.  I believe that this is why stock guns can actually gain FPS in some cases with a larger valve and no other changes - they have so much head space and they have so much built-in flex (head space that increases with pressure) that they will perform better pump for pump with a larger valve after a certain number of pumps.

[rsterne]

Yes, with constant volume (and everything else), the velocity should increase with the square root of the pressure, because the FPE is (at least in theory) proportional to the pressure.... and of course FPE uses the square of the velocity in its calculation....

Bob

[Psipumper]

With the math then we could calculate to some degree what 50 fpe would require?
I got 839 fps with 25.3 grain with 5.75 cc valve @ 2300 psi. What would be your prediction of pressure needed for a 6.5 cc valve to make 50fpe.
Assuming the hammer strike could open the valve. Maybe a retractable bolt probe and other refinements  added could assist.
32 grain pellet?

[Tom Tucker]

So that's 39.7 FPE with 5.75cc and 2300 PSI.  That same pressure with 6.5cc should get you 42.2 FPE (39.7*sqrt(6.5/5.75)).  To get to 50... 50/42.2 * 2300 = 2725 PSI

[rsterne]

Well, I made a couple of .25 cal pumpers, and my Millennium Pumper would do one shot at 50 FPE with a JSB 25.4 gr. pellet, 2 equal shots at 45 FPE, or 3 shots within a narrow ES at 40 FPE.... These were achieved at 1800 psi with a valve volume of 28.5 cc.... The barrel length was 23.8".... The gun required 80 pumps to fill to 1800 psi from empty, which is why I added a Foster fitting for initial fill.... When tuned for 3 shots of 40 FPE, it took 11 pumps to refill after 1 shot, 24 after 2, and 40 to refill to 1800 after 3 shots.... After my experience with that gun, I would never even consider trying to build a .22 cal pumper that could achieve 50 FPE....

Having said that, if I put your results into Lloyd's Internal Ballistics spreadsheet, and assume a dump shot (no retained air)…. and then change one thing at a time, going to 6.5 cc increases the velocity with the 25.3 gr. pellet to 855 fps at 2300 psi (41.1 FPE).... Increasing the pressure to 3000 psi should allow a 25.3 gr. pellet to hit about 949 fps (50.6 FPE)…. At 2300 psi with a 32 gr. pellet (6.5 cc valve) you should get 779 fps (43.2 FPE)…. Increase that to 2800 psi with the 32 gr. you should hit about 845 fps (50.8 FPE)…. It is possible that with full bore-area porting and a retractable bolt you may be able to achieve 50 FPE at an even lower pressure.... The above calculations were done with a 19" barrel length....

To achieve those pressures would, IMO, require a much smaller diameter pump tube, and a lot of pumps, however.... Dropping down from a 7/8" OD Disco tube to a 3/4" OD 1322 diameter tube would require the same pumping effort at 3000 psi as the Disco tube at 2100.... I wouldn't want any more effort than that, as filling my Millennium Pumper to 1800 was hard enough, and 2000 was more effort than I wanted to expend, except for a couple of tests.... With the same stroke length, you would need more than twice as many strokes to reach 3000 psi with the small tube as 2100 with the larger one.... Bear in mind that the 392 tube is even larger ID than the Disco tube....

Could it be done, I have no doubt.... providing you properly engineered all the components to stand the strain....

Bob

[Tom Tucker]

Bob, do you have a link to Lloyd's spreadsheet?  When I was contemplating my last build, I searched high and low for it, but I neglected to ask...

[Tom Tucker]

The way I calculate the effect of a change in pellet weight on FPE is to compare the mass of each pellet to the combined mass of the respective pellet and the air charge.  Mass of a compressed gas = (pressure * volume) / temperature.

5.75cc air at 14.7 PSI and 300 Kelvin = 0.1 grain
5.75cc air at 2300 PSI and let's say 350 Kelvin = 13.4 grain

So with a 25.3 grain pellet, the mass of the pellet is 65% of the total mass of compressed air + lead, which is 38.7
With a 32 grain pellet, the mass of the pellet rises to 32 and the total mass rises to 45.4.  Now the pellet is 70.5% of the total load compared to 65% before.  This is an 8% [70.5/65] increase in the proportion of the energy that goes towards accelerating the lead rather than the air.

So with the heavier pellet, you have the potential for 8% more FPE at your current pressure and volume.

Taking this calculation to an extreme... you SHOULD be able to hit 50 FPE as your guns stands with a 64.1 grain slug at about 592fps, but this is all theoretical of course.  The bigger the change, the greater the effect of factors that my simple calculations don't account for 

64.1/(64.1+13.4) = 82.7%

82.7/65 is a 27.2% increase.  39.3 FPE actual * 1.272 = 50.0 FPE predicted

The easiest way to test this would be to glue two 32 grainers together and see what actually happens.

[Psipumper]

Thanks Tom and Bob for crunching the numbers and thoughts on that.
I am getting closer to my optimal version of the 392. I will be sure to create a more detailed thread of it here when it’s done.

[rsterne]

Tom, Lloyd's spreadsheet is proprietary, and I am one of the fortunate few to have a copy.... partly because I assisted him with suggestions to improve it....

Not all of the air in the valve is accelerated out the barrel with the pellet.... If the valve is 40% of the bore area, over 31% of it is still in the valve at the instant of pellet exit (the residual pressure at pellet exit is 725 psi), and some of that has barely left the valve, so it's velocity is not the same as the pellet.... If I take the original setup with a 5.75 cc valve at 2300 psi, and substitute a 64.1 gr. slug for the 25.3 gr. pellet I only get 564 fps (45.3 FPE), not 50.... According to Lloyd's spreadsheet, even a 200 gr. bullet would only get to 48.5 FPE at 2300 psi with the 5.75 cc valve....

In practical tests, the FPE does not increase forever with bullet weight, it peaks at some weight, different of course for every gun....

Bob

[Tom Tucker]

Ah, understood.  It sounds like his spreadsheet has evolved into a very effective model.  It's great to have guys like you as a resource.

As I look back at my own crude model, I will take note of the fact that using the full air mass contained in the valve of 13.4 grains is much too high for the reasons you outlined.  Interestingly, if I account for your figure of air remaining in the valve and reduce my estimated air charge mass by 31% to 9.2 grains, the numbers DO get a lot closer to the numbers you got from the spreadsheet.  [64.1/(64.1+9.2)]/[25.3/(25.3+9.2)] * 39.3 = 46.8 FPE.  Plugging in 9.2 grains of air with a 200 grain slug would give a figure of 51.2 FPE.  So it's still too high, but almost close enough for a satisfactory back-of-the-napkin type calculation.  Like you said, some of the air that has left the valve has "barely left the valve."  Air is a fluid, and fluids do funny things.

I think that if the model developed in the Internal Ballistics spreadsheet were ever made commercially available in a user-friendly format, there would be a lot of us lining to buy it!

[rsterne]

Try using half the mass of air that has exited the valve and see what you get.... IIRC, Lloyd's spreadsheet adds 1/2 the air mass "previously" released by the valve to the mass of the pellet at each interval.... but I'm too lazy to go into the code to confirm that.... 

I'm pretty sure the reason for using half the mass is that the air is expanding behind the pellet, so the air immediately following the pellet is travelling at pellet velocity, but the air just coming out of the valve is not requiring any real work done on it (at that moment).... 

Bob

[Tom Tucker]

1/2 the air mass gets me 45.0 for 64.1 grain and 48.1 for 200 grain - you're right, that's very close!  I also guessed at an internal temperature of 350K (170F) in my calcs so there is some wiggle room there as well.

Speaking of temperature... Let's imagine what would happen if someone equipped the valve with custom high temperature Viton seals, a non-flammable silicone-based lubricant, a thermistor and digital pressure sensor both sending data to a micro controller programmed to keep the valve below, say, 3000 PSI and 600K, while regulating the output of a heating element on the valve powered by a couple of high-drain safe chemisty Li-MN 18650 batteries... FPE could be nearly doubled with digitally-controlled electronic heating of the valve.  Just put 10 pumps in and wait for the oven timer to go off

[rsterne]

The air charge in a pumper cools on sitting, of course.... My Uber-Carbine, which was set up for two shots at 600 fps using 18 pumps needed topping up to 20 (ie 2 more pumps) if you let it sit to cool, as it would in hunting....

I dunno about the idea of heating the air to raise the pressure after pumping.... It would certainly slow down the rate of fire, no?.... I'm thinking no follow-up shots....

Bob