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Old August 8, 1999, 12:00 AM   #1
Grayfox
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Anybody got a math formula for converting C.U.P. to Psi and vice versa? Some of my manuals use one and some the other. I'd like to be able to get a direct comparison on some loads.
Does such a formula even exist?
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Old August 8, 1999, 12:53 AM   #2
Mal H
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Grayfox - I don't think there is an equation that will work for CUP to psi or vice versa. CUP is a useful method of determining chamber pressure effects but not actual pressure. In other words, it is an inexact science based on what happens to a variable object (the cupper pellet, which may have an ever so slightly different hardness or size from pellet to pellet) vs. a measurement of a more exacting type. Even though psi measurements are taken with a strain guage on the barrel, it's the same barrel each time and therefore is more repeatable and can be equated to a known pressure in that barrel. There is no repeatability with copper crushers, it's sort of like testing a box of matches to be sure they will all light. Once you know they're all ok, you can't use them.

A fairly good treatise on it can be found in Lyman's 47th. One table where they measured both CUP and psi for the same load effectively shows that they cannot be equated with any formula. For example, one test got 42,000 CUP and 51,000 psi. But another test, same gun, same load, again yielded 42,000 CUP and 55,300 psi.

Another table shows that the CUP to psi values change dramatically from caliber to caliber. For example, the 223 Rem. has a max CUP of 52,000 and a max psi of 55,000. And the 7mm Rem Mag also has a max CUP of 52,000, but max psi of 61,000. Yet the 45-70 has identical values of 28,000 CUP and psi.
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Old August 8, 1999, 01:51 AM   #3
Rod WMG
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MalH, the info I have is essentially the same. There is apparently no conversion possible from CUP to PSI or vice versa.
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Old August 8, 1999, 10:04 AM   #4
Grayfox
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That's exactly what I was afraid of. Thanks for the info
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Old August 8, 1999, 04:37 PM   #5
Contender
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If I'm not mistaken, CUP was actually referred to as PSI up until the late 60's when the term CUP came into wide use so, be careful if you come across any old literature on this subject as it can make for some serious false assumptions.

[This message has been edited by Contender (edited August 08, 1999).]
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Old August 8, 1999, 05:23 PM   #6
Rod WMG
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And though this mayh be needless repetition, never trust just one source. I have an older powder company manual that lists a load with IMR4227 which is grossly overpressure (by any measure) and has to be a misprint.
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Old August 8, 1999, 10:06 PM   #7
James K
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The common way of measuring pressure for years was the copper crusher. The results were published as "pounds per square inch", or PSI. This was, as others have pointed out, not an exact science, but it was the best anyone had and probably as accurate as it needed to be, since guns are overdesigned anyway.

When strain gages, supposedly more accurate, were invented, they showed different figures.

Rather than try to explain the differences, the ammo companies decided to keep using the copper crusher method and the older figures and call the result "copper units of pressure" or CUP, which supposedly would be the same as the old PSI, even if it was not really the true PSI any more.

Everyone understand? If so, please explain it to me.

Jim

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Old August 9, 1999, 09:01 AM   #8
bfoster
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Such a formula apparently does exist. Ken Oehler's M82 system is able to predict CUP "values" from Piezo gauge readings. As far as I know, the math is proprietary. But if you have a need for it, you might call Oehler Research and talk to them. The 'phone # is 800 531 5125.
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Old August 12, 1999, 03:32 PM   #9
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Take a look at the Sierra 50th anniversary rifle reloading guide. Although its been a year or so since I read it (I tend to do my reloading in the fall), it had a pretty good discussion on this subject.

I seem to recall that the CUP method was completely replaced by the strain guage since it was more accurate and repeatable. Not to mention that you and I can now buy the hardware to read out own pressure on our rifles and pistols.

Regards,

Albin
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Old August 17, 1999, 01:28 PM   #10
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CUP *was* called PSI in the old days, and was converted from precise measurements of the deformation of the copper pellet in a special pressure test barrel which had a cut-out in the chamber area. A steel "anvil" would fill the hole and the pellet would be affixed in some sort of fixture.

The pellets were precisely machined from either pure copper or a known alloy (I don't know which), and the poundage was calculated from a "Tare Table" which listed the average deformation dimensions taken from real-life testing of known poundage pressures on those copper pellets.

Think calibrated ordinance gelatin for a modern analogy. For really low-pressure stuff like shotgun and some originally blackpowder cartridges, they used LEAD pellets.

Two problems arose:
1. Between 3,000 and 5,000 PSI difference, IIRC, between pressure readings taken with regular cartridge casings (the case wall would just blow into the hole and drive the anvil into the pellet) and readings taken with drilled cases. They typically used "Scotch" tape to hold the powder in during handling. Drilled cases read higher and were the standard.

2. The readings were always known by engineers to be only an approximation. A rapid pressure impulse, combined with the inertia of the anvil and the "object at rest" nature of the pellet's atoms, could result in some very rapid pressure spikes being undetected by the pellet. Think of the difference between dial/needle sound level meters, and an LED display on your tape recorder. The first is great for averaging, but the second is best for indicating rapid peaks.

Thus, Piezoelectric strain gage readings (themselves an approximation!) often but do not always read higher pressures than CUP readings. But there is no easy conversion factor...unless maybe you're using the same powder and bullet (diameter, weight, bearing surface AND manufacturer!) in the same caliber.
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