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Am trying to see how a heavier spring yields lower operating pressure. I get the lower sweet spot with a higher flowing system, and get the closing force issues, and would agree that a heavy valve spring is better for closing because it's both quicker and also isn't susceptible to pressure fluctuations. But I don't see how, by itself, a heavier spring would allow for lower operating pressure. As I see it, a heavier valve spring, all things equal, only means a heavier hammer spring to knock it open for the same effect.
To get back to this (sorry - jumping in an out of a few things here) - the sweet spot is independent of the velocity - it really is just a curve. Say the sweet spot is 200psi on one gun. Your velocity is going to be higher at 200psi with the same hammer spring tension than if your gun was sweet spotted to 180psi. You are just finding a point of balance between valve flow and back pressure effects. If you want to run lower pressure, then run a heavier valve spring. A heavier valve spring will also increase your efficiency. BUT - if you were not adjusting the hammer spring, this velocity will go down. So you tick up the hammer a bit (nominally a small bit, the hammer tension is a couple ounces to a lb difference and we are talking pounds of back pressure.)
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Post volume, pre-ball capacitance effects?
Paging PBSteve re: Chasing the Dragon (Inside Paragon dev joke)
Yea, it modulates the effective flow through the valve because is changes the dP across the orifice. Consider that if you had a valve with infinite flow and infinitely fast closing speed (e.g. an idealized Paragon valve) and a ball with a perfect seal, you'd be able to change the ball acceleration profile only by the P*V energy of the slug of pneumatic energy you placed behind the ball. That slug would then fully expand in almost a batchwise process, and you'd theoretically have yourself something very efficient...
YEARS ago, late 90's? Early 2000's? I CADed up a large number of guns, and found an interesting figure - if I build a solid mass of the entire internals; valve chamber, bolt, body sections, and 6 or 8" of barrel - I could take the energy they nominally used per cycle and average it across the entire volume mass and get 50psi. This wasn't so easy to get from most poppet units, but was consistent on the spoolers. Even chased it in some of my initial prototypes because they ran 50psi off of my first calculations. The last 50psi was wasted (then) in most guns.