doublegunshop.com - home Forums General Discussion DoubleGun BBS @ doublegunshop.com Pressure Question for Engineers....

Why are we talking about squaring bore diameter to calculate bore volume? The formula for volume of a cylinder is pi (3.14159) times radius squared times height. Of course, our volume is constantly increasing as the wad/shot charge moves down the bore. Pressure is variable dependant upon the ever increasing bore volume AND the burning rate of the powder used. Boyles Law or Pascals Principle might be more applicable if we were dealing with say 9000 psi of compressed air or CO2 as our pressure source. We are assuming perfect obturation of the wad with zero blow-by as we transition from smaller to larger bore section. So without actual extensive and expensive testing, a lot of our assumptions are based upon conjecture and educated guessing. As such, I am not ready to admit that any of my assumptions are incorrect, nor would I wish to put my foot in my mouth and claim anyone else is wrong. It's all very interesting and I hope it inspires someone to do the actual testing to give us definitive answers.

Radius (R) = Diameter (D)/2, thus D:R::d:r.
Double the "Radius" of a pipe & you get 4 Times the volume, but GUESS WHAT Double the Diameter of a Pipe & you Get "Four (4) times the volume.
As to a circle A (area) = PiR². = PiD²/4
Choice is strictly yours whether you prefer to work with radius or diameter.
You best go back to Math 101 if you think you can change the radius without correspondingly changing the Dia.
As the size of a shotgun bore is virtually always stated by Diameter I just work with that.

We have a lot of data that shows chamber reducers "work." That is they launch shot loads at near enough to expected/required and with good enough patterns to be relatively widely used. We can check our assumptions to some extent against that fact. If there were no blow-by and no pressure reduction due to bore volume increase, there would be a velocity increase. A large pressure loss due to either blow-by or bore volume increase would lead to a lower velocity. We may have a small increase or decrease in velocity, so we have to believe that pressure changes are relatively small.

That's exactly what I get out of the available data. More testing may uncover new findings, but absent that anything more is speculation (and sometimes speculation is later proved to be right, but we're not there yet).

I used the following formula to calculate the volume of a cylinder [Dia; squared x 3.142 x L] divided by 4. The.752 diameter used in my pressure calculation was derived from [.775-.729]divided by 2 + .729] =.752 which was an arbitary diameter that I thought would likely approximate the diameter/volume change as the charge transitioned from 12G to 10G whilst traversing the 10G forcing cone.The resultant 6% estimated, drop in pressure is modest.Assuming an intial muzzle velocity of 1200 ft/sec at 6000 psi breech pressure, the resultant drop in muzzle velocity would be 72 ft/secapprox.This minimal reduction in velocity would appear to support user reports that gaugemates function in a satisfactory manner.

RH, you lost me on the 72 fps change in MV. How did you get that? I see that 6% of 1200 fps is 72 fps. However, you can't equate a change in a point pressure to MV (you must integrate the pressure-displacement curve). Remember, loads of slower burning powder can generate equal MV with lower chamber pressure (but higher barrel pressure such that the faster and slower powder have equal area under the pressure-displacement curve).

I wish that I had access to a chronograph. Perhaps after hunting season, I can work something out locally to chronograph my reduced power loads. I'd like to shoot the same load in a 12 gauge and my 10 gauge to measure the velocity decrease; which I think is sizeable.

Maybe someone can bring a chronograph to Flatwater next April.

I can see and feel reduced velocity when shooting the same 12 gauge load, in the 10 ga. Baker using the Gauge-Mate adapters. For the moment, I am increasing the SR7625 powder charge somewhat to try to reasonably increase the pressure/velocity up to a satisfactory level - without stressing the gun.

I had hoped for a more scientific solution, rather than this "trial & error" approach....

JERRY

So are we to believe that just because the wad skirt of a 28 ga. wad can be flared out to .729" or so, it will still contain perhaps 9000 p.s.i. without that skirt blowing forward and losing its' perfect seal? That would be some tough skirt. Whew! I will still contend that even if that wad could contain the pressure, as the area almost instantly increased, the pressure would have to drop and force would remain equal (assuming zero blow by). Anything else would absolutely be claiming a physical free lunch. Are you saying that if we have, for example, 9000 p.s.i. gas pressure contained in a one cubic inch cylinder and we increase the volume of the cylinder to two cubic inches, that we would still have 9000 p.s.i.? Certainly not... not without adding more gas or superheating the same gas in the doubled volume. Now, I wish I knew how to put your following statement in red letters: "If the wad base expands to fill the larger bore, then, yes, the force increases. This is how a small hydraulic piston raises a large load on a bigger bore cylinder." Whiskey Tango Foxtrot. No, no, no. Huh uh. Nope. In a hydraulic pump, be it a simple hand Porta Power type pump, or a multi stage variable displacement rotary piston pump, the small diameter pump piston(s) driven by hand or motorized force displace a volume of relatively incompressable oil equal to the bore radius squared times pi times the stroke (length). This volume of incompressable fluid under pressure acts upon the base of the larger cylinder piston and moves it a porportionately shorter stroke. The larger the cylinder piston, the less one stroke of the pump piston will move it. Again, there are no free lunches here. We are talking about x grains of powder acting upon y dia. wad base containing z ounces of shot. Ain't no quantum mechanics where light speeds up, quarks and muons become charmed, and time goes backwards.

This is a debate that could carry on adinfinitum.I would refer interested parties to the book," The Modern Shotgun", by Major Sir Gerald Burrard, Vol;2 "The Cartridge". The 306 pages of this book are largely dedicated to the analysis of,powder,pressure velocity and recoil[ie: not an easy read!]. Appendix 6,is relevant because it details; "The analysis of the internal ballistics of a 12 G shotgun."
I shall be interested to see the results of the tests planned for Gaugemates and to compare same with the various points of view expressed on this forum.