I have been asked on occasion what is the optimum volume for the valve in a pumper.... There has been a guideline around for a while, from James Perotti, to use a valve that is half the barrel volume, regardless of pressure.... I've never seen the math behind it, so I thought I'd explore it, using Lloyd's Internal Ballistics Spreadsheet.... I set the variables to roughly what you might expect for a 24" barrel in .22 cal which has a barrel volume of 15.0 cc.... I used a 16 gr. pellet, and tried it with 1500 psi (typical for a pumper) and 3000 (just from curiosity).... and the plotted the energy and efficiency versus the valve volume as a percentage of the barrel volume.... Here are the results.... The blue lines are at 1500 psi....
The first thing you will notice is that the overall efficiency is very low.... That is because with a dump valve a lot of the air is leaving the barrel after the pellet is long gone, and the larger the valve, the worse that is.... In the case of a valve that equals the barrel volume, think of it this way.... If we start with 1500 psi in the 15 cc (100%) valve, when the pellet reaches the muzzle, that air has expanded to fill the 15 cc barrel as well.... The total volume is 30 cc, and the pressure is down to 750 psi.... Once the pellet leaves the barrel, the energy in that 750 psi of air only produces noise and no longer accelerates the pellet.... If we were to close the valve at the instant the pellet left the barrel, we would retain HALF the air in the valve, and only have to pump half the air back into it for the next 1500 psi shot.... This is how a retained air pumper (also known as an ACP or air conserving pumper) works.... PCPs work in the same manner, and the valve typically shuts when the pellet has only moved 25-33% of the way down the barrel.... Compared to a dump valve, closing the valve when the pellet has travelled only 50% of the barrel length will use only 500 psi of air instead of the whole 1500, and yet the velocity will be nearly as great.... At 25%, the pressure will only have dropped to 1200 psi instead of zero, using only 20% of the air in the valve.... However, the velocity will have only decreased about 10% and the efficiency will be about 4 times as great....
Now, back to the size of a dump valve.... As you can see, there is still a small increase in FPE when you go larger than the recommended 50% valve size, but the drop in efficiency is great.... I can see why James Perotti recommends 50% because going larger uses a lot more air for the additional gains.... It might help if we look at what valve sizes are used in some of todays pumpers.... A 1377, with a 10" long .177 barrel has a barrel volume of only 4.0 cc.... a 1322, same gun with a .22 cal barrel, is 6.2 cc.... The older 2289, with a 14.5" barrel in .22 cal has a volume of 9.0 cc, and the newer one with a 12" barrel is 7.5 cc.... A stock 13XX/XX89 valve is about 1.5 cc, so that works out to 38% for a 1377, 24% for a 1322, and 17-20% for a 2289.... If we look at a Benjamin 397, with a 19" long .177 barrel, the volume is 7.7 cc, and for the 392 in .22 cal the volume is 11.8 cc....The valve in a 39X is 4.2 cc, which works out to 55% in .177 cal and 36% in .22 cal.... During the development of my Millenium Pumper, I made a .25 cal Carbine version with a 20" barrel that had a volume of 16.1 cc.... The first valve I used was 5.5 cc (34%) and the second one I used was 6.7 cc (42%).... From my experience I think a valve of about 1/3rd of the barrel volume is a good balance between power and efficiency.... and I would agree with Perotti that 1/2 is about the maximum, beyond that you will be wasting a lot of air.... The trade off in going to a 50% valve instead of a 33% valve is about 13.5% more FPE at the expense of 50% more air used (and therefore 50% more pumping).... assuming the same pressure in both cases.... Going to a 100% valve increases the FPE only an additional 19%, but needs a 100% increase in air (and double the pumps) over a 50% valve....
Bob
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