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Is there some sort of formula or chart to correlate CUP and PSI??
CUP and PSI
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There was a long thread about this some time ago, with differing opinions. Search for threads by Denton Bramwell. He believes they do correlate, while others point out indiscrepancies that suggest any apparent correlation to be more coincidence.
Since the two methods are very different in how they calculate pressure, and in their relative accuracy, I personally feel that it is better to just work with whatever numbers are published for each and not try to correlate them. YMMV.
Since the two methods are very different in how they calculate pressure, and in their relative accuracy, I personally feel that it is better to just work with whatever numbers are published for each and not try to correlate them. YMMV.
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They definitely correlate. The correlation just isn't tight, free of scatter, nor entirely monotonic, so you can't rely on it to define data for one measuring system from the other. Sometimes if you try to calculate PSI from CUP the result is too high and sometimes it's too low even though you use the correct correlation. Denton's article is here.
The heart of the problem is that the old copper crusher technique just never was very precise. Some years ago Precision Shooting had an article in which, IIRC, sets of very carefully made identical loads were sent to several labs to measure both CUP and PSI. The CUP results were different enough from one place to the next that they concluded it just isn't a reliable system of obtaining absolute measurements. PSI did much better on consistency.
If you have the same technician and the same test equipment and conditions every time, you can match one load to another in the same chambering, but copper crushers just aren't a whole heck of a lot better than that. I don't know if you ever noticed how some lots of older surplus ammo seemed to be a good bit hotter than others. That's from the military sticking to copper crushers for their "PSI" (they never adopted the CUP terminology) long after the expiration date.
The heart of the problem is that the old copper crusher technique just never was very precise. Some years ago Precision Shooting had an article in which, IIRC, sets of very carefully made identical loads were sent to several labs to measure both CUP and PSI. The CUP results were different enough from one place to the next that they concluded it just isn't a reliable system of obtaining absolute measurements. PSI did much better on consistency.
If you have the same technician and the same test equipment and conditions every time, you can match one load to another in the same chambering, but copper crushers just aren't a whole heck of a lot better than that. I don't know if you ever noticed how some lots of older surplus ammo seemed to be a good bit hotter than others. That's from the military sticking to copper crushers for their "PSI" (they never adopted the CUP terminology) long after the expiration date.
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Without diving into that can of worms, I've noticed many loads previously listed in CUP, are now published from the same in PSI, and charges are often reduced.
I've wondered if the effect was a matter of legal considerations, or the product of hot loads and real potential problems.
?
I've wondered if the effect was a matter of legal considerations, or the product of hot loads and real potential problems.
?
I'm not the most scientific mind, but if 1 gallon is always 2.2 liters, that is a correlation. If 3 feet is a yard, that is a correlation. If "X" Copper Units of Pressure equal "Y" PSI, that would correlate, but that is not consistently true, so I don't see how CUP and PSI correlate.
Maybe I just don't know enough about mathematics to understand how it works.
Maybe I just don't know enough about mathematics to understand how it works.
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These days, if you see psi in a manual, that means they used a transducer or similar modern system. If they used a crusher, it is listed in CUP.
The two can't be correlated because CUP was never very accurate to begin with.
The two can't be correlated because CUP was never very accurate to begin with.
I agree with your view Rocky. CUP sure got us through alot of years though! How can that be? Something wrong "worked" right?
Sure would be interesting to presure test some vintage ammunition.
http://www.shootersforum.com/showthread.htm?t=63912
Cheezywan
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I always appreciated Denton writing up that summary. Nevertheless, the article merely demonstrates that SAAMI's (and CIP's) max avg pressure numbers correlate. It goes on to point out that CIP's numbers are so closely correlated that they were probably using only one system the whole time, and simply calculated the other number for publication. I've always wished that Denton had had the opportunity to run a pressure barrel with a crusher on one side and a transducer on the other, so to speak. Now, SAAMI may have done exactly that, and I don't claim they didn't. Still, the unreliability shown in the copper crusher system argues against quite so tight a correlation as what Denton's evaluation of SAAMI's numbers reflect.
The issue of correlation is of off-topic professional interest to me because we use multiple assessment tools on certain organisms at work, and there is interest in testing for and defining a correlation between them. The tools don't measure quite the same thing, though, which introduces the concern that, while there appears to be a correlation, in fact there is not. There is also the possibility that the 'correlation' is very strong under certain circumstances/conditions, but non-existent under others. That latter is undeniably the case with CUP vs. PSI. There is simply no correlation near 30 psi, nor near 300,000,000 psi, in part because the CUP measurement tools cannot respond adequately to those extremes. This case is of little importance to us in the rifle world, as we're dealing with a fairly narrow pressure range. Still, the fact argues against a flat 'there is a strong correlation' statement. One might more accurately say that there is a correlation within a certain, fairly narrow, pressure range. But I realize now I'm too tired and must go to sleep...
The issue of correlation is of off-topic professional interest to me because we use multiple assessment tools on certain organisms at work, and there is interest in testing for and defining a correlation between them. The tools don't measure quite the same thing, though, which introduces the concern that, while there appears to be a correlation, in fact there is not. There is also the possibility that the 'correlation' is very strong under certain circumstances/conditions, but non-existent under others. That latter is undeniably the case with CUP vs. PSI. There is simply no correlation near 30 psi, nor near 300,000,000 psi, in part because the CUP measurement tools cannot respond adequately to those extremes. This case is of little importance to us in the rifle world, as we're dealing with a fairly narrow pressure range. Still, the fact argues against a flat 'there is a strong correlation' statement. One might more accurately say that there is a correlation within a certain, fairly narrow, pressure range. But I realize now I'm too tired and must go to sleep...
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If the Precision Shooting article from long ago was correct, Denton's crusher results would simply not match the results used to set the SAAMI standard all that well. The way SAAMI maintains standards is one manufacturer is responsible for each cartridge, providing its reference and proof loads to the whole industry. That way just one crusher or non-conformal piezo tester is being used as the standard. Other makers buy the reference loads from the responsible manufacturer and calibrate their equipment to the pressures those reference loads provide, even if that gives them a different numerical result.
Jason and Rocky,
CUP and PSI do have a correlation within the range of pressure Denton's article examines for SAAMI maximums. A correlation is, in effect, a statistical tendency, so it can vary in degree of perfection from one case to the next. For example, if you are driving north on a perfectly straight road on a perfectly spherical part of the earth's surface, you have a perfect correlation between how many miles and how many degrees north latitude you travel. A perfect correlation is the same thing as a conversion relationship, as Mike described. But if you take a road that goes up and down over uneven terrain, meanders back and forth and goes sideways some of the time, and even turns backward for short stretches to go around geological features, then you can no longer exactly convert miles traveled to degrees north latitude traveled. Nonetheless, you have a correlation in that, on average, it is still true that the more miles you go the further north you are. It may not be true between any two particular mile markers, but it is true on average for the whole trip. At the end of the trip you can divide the number of degrees north latitude you traveled by the number of miles it took to get there, and you will have the average number of degrees traveled per mile. That's the correlation between degrees and miles for that trip route. Again, it may not work at all between any two particular mile markers, but it works overall, so the correlation will be something less than R=1 (100%), but it will have some lesser positive value.
In statistics, having no correlation requires that the relationship between two things being compared be completely and truly random. If they are not completely, 100% random, then a correlation exists. It may be very weak and hard to identify in some instances but it is still real.
Jason and Rocky,
CUP and PSI do have a correlation within the range of pressure Denton's article examines for SAAMI maximums. A correlation is, in effect, a statistical tendency, so it can vary in degree of perfection from one case to the next. For example, if you are driving north on a perfectly straight road on a perfectly spherical part of the earth's surface, you have a perfect correlation between how many miles and how many degrees north latitude you travel. A perfect correlation is the same thing as a conversion relationship, as Mike described. But if you take a road that goes up and down over uneven terrain, meanders back and forth and goes sideways some of the time, and even turns backward for short stretches to go around geological features, then you can no longer exactly convert miles traveled to degrees north latitude traveled. Nonetheless, you have a correlation in that, on average, it is still true that the more miles you go the further north you are. It may not be true between any two particular mile markers, but it is true on average for the whole trip. At the end of the trip you can divide the number of degrees north latitude you traveled by the number of miles it took to get there, and you will have the average number of degrees traveled per mile. That's the correlation between degrees and miles for that trip route. Again, it may not work at all between any two particular mile markers, but it works overall, so the correlation will be something less than R=1 (100%), but it will have some lesser positive value.
In statistics, having no correlation requires that the relationship between two things being compared be completely and truly random. If they are not completely, 100% random, then a correlation exists. It may be very weak and hard to identify in some instances but it is still real.
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I have absolutely no technical ability to discuss much less debate with Denton (who is a good friend of mine). However, I do know that the problem with his carefully reasoned argument is that the crusher numbers are probably faulty. It's like trying to correlate your steps per mile with another guy's - except he can't count very well.
Another friend of mine (and Denton's) is Dr Ken Oehler. Ken has fitted a receiver with not only a copper crusher and a transducer but with a strain gauge system as well. He's able to get three readings with each shot, and what those readings tell him is that the crusher suffers from physical lag due to momentum as well as a directly related undershoot. In other words, the crusher can't respond as fast as the pressure rises, and therefore the true peak passes before the crusher can respond. Varying rise rates means that the gap between the true peak and what the crusher responds to can seldom if ever repeat. The faster the burn rate, the more the crusher lags. (I hope I'm explaining that well enough.)
A transducer suffers much less from inertial lag because there's less mass moving. It can also respond about as fast as the pressure rise, and doesn't over- or under-shoot the peak. Its major drawback is the need for calibration, but that isn't a major one.
The best of the three? The strain gauge. Near-zero instrument mass means zero inertial lag. It can respond as fast as the barrel metal, which is very fast, and it also has no over- or undershoot issues. Once fitted to a barrel and the electrical property of that gauge entered into the computer, no further manipulation of the test gear is required.
Another friend of mine (and Denton's) is Dr Ken Oehler. Ken has fitted a receiver with not only a copper crusher and a transducer but with a strain gauge system as well. He's able to get three readings with each shot, and what those readings tell him is that the crusher suffers from physical lag due to momentum as well as a directly related undershoot. In other words, the crusher can't respond as fast as the pressure rises, and therefore the true peak passes before the crusher can respond. Varying rise rates means that the gap between the true peak and what the crusher responds to can seldom if ever repeat. The faster the burn rate, the more the crusher lags. (I hope I'm explaining that well enough.)
A transducer suffers much less from inertial lag because there's less mass moving. It can also respond about as fast as the pressure rise, and doesn't over- or under-shoot the peak. Its major drawback is the need for calibration, but that isn't a major one.
The best of the three? The strain gauge. Near-zero instrument mass means zero inertial lag. It can respond as fast as the barrel metal, which is very fast, and it also has no over- or undershoot issues. Once fitted to a barrel and the electrical property of that gauge entered into the computer, no further manipulation of the test gear is required.
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What I was saying is that Denton made no actual measurements for the linked article, or if he did he neither included nor referenced them, as far as I can tell from reading and re-reading it. He took SAAMI's maximum average pressure standards (and separately CIP's), assumed they were "careful" in setting the two number pairs as standards, and ran a regression analysis on them. The article explicitly said that it didn't look like CIP actually ran 2 sets of tests, but rather simply took the numerical values from one test and ran them through a calculator to set the corresponding pair value in most cases. It is interesting to consider the cartridges that were excluded from the CIP data analysis consequent of their number pairs not falling in line with the expected outcome, though.
A great set of posts, though the actual "answer" remains as fuzzy as it was before - and that may be all we can ever expect.
Nick - that analogy to driving north was very helpful to me in my on going effort to make useful sense out of pressure data - especially with shotshell loads.
Pete
And how about LUP data? Where does that fit in to a discussion like this one?
Nick - that analogy to driving north was very helpful to me in my on going effort to make useful sense out of pressure data - especially with shotshell loads.
About CUP - my take is that it is not so much that it is wrong as that it is not very precise. Kinda the way some people give directions "It's right down the street" as opposed to "that brown house there with the glass door, third one on the left."
Pete
And how about LUP data? Where does that fit in to a discussion like this one?
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I think that's what I was saying about CUP: it just wasn't very accurate - or precise, either.
LUP (Lead Units of Pressure, used for low-pressure guns like shotguns) suffered exactly the same drawbacks as CUP. It may be even less accurate due to the low impulse given to the slug. It would take exceedingly good measuring technique to gauge the length of a lead slug without deforming it and thus artificially boosting the pressure reading.
LUP (Lead Units of Pressure, used for low-pressure guns like shotguns) suffered exactly the same drawbacks as CUP. It may be even less accurate due to the low impulse given to the slug. It would take exceedingly good measuring technique to gauge the length of a lead slug without deforming it and thus artificially boosting the pressure reading.
Different batches of copper/and or lead will not have the same properties. Steel is the same way buy the same grade of steel and ask for the mill certs and you will find that different batches have different strengths, this is as close as the manufacturers can make them
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Very interesting! That would partly explain why, supposedly, "safe" loads under the CUP system were found to be too hot under the PSI system... in layman's terms that is.
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Sorry I haven't responded very quickly.
It would seem to me, that no matter how precise or imprecise the CUP pressure method is, that SAAMI would have had some idea as to approximately how much/many units of pressure it would take to squeeze a piece of copper so far. Otherwise, they never would have used it in the first place. The numbers meant something to someone. And if they actually meant something, then it could be correlated to a different system of numbers. Like inches to millimeters. I seriously doubt it was a total random thing.
I'm just wondering what the "theorectical" matching numbers would be.
Oh well, thanks anyway. Maybe I'll try a SAAMI contact. If I can find one........
It would seem to me, that no matter how precise or imprecise the CUP pressure method is, that SAAMI would have had some idea as to approximately how much/many units of pressure it would take to squeeze a piece of copper so far. Otherwise, they never would have used it in the first place. The numbers meant something to someone. And if they actually meant something, then it could be correlated to a different system of numbers. Like inches to millimeters. I seriously doubt it was a total random thing.
I'm just wondering what the "theorectical" matching numbers would be.
Oh well, thanks anyway. Maybe I'll try a SAAMI contact. If I can find one........
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My problem with the modern PSI system is that it also is imprecise. Let's face it, CUP actually measured the crushing of metal. What does PSI mean? I know what it actually is, pounds per square inch. But what is it really in a gun? So what if a round is 68000PSI? If it doesn't "have time" to crush a piece of copper it will not have time to crush (or explode) a piece of steel either. And I also remember reading of a manufacturer (I want to say weatherby, but not sure of it) testing his guns to some 130,000 plus PSI without failure.
But, that's beside the point of my original post......
There has to be a correlation somewhere....
But, that's beside the point of my original post......
There has to be a correlation somewhere....
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The problem is that it isn't just squeezing a piece of copper and measuring how much a given force deforms it (which is the theory). Because you can't do that "calibration squeezing" in two milliseconds. When you apply a force that fast, you have to take in the mass and inertia of the material - and the CUP system doesn't and can't do that.
That's also why a gun barrel can take 65,000 real psi without bursting. It happens too fast to respond. If you pumped a barrel up with continuous pressure, it would burst long before that. In fact, barrels swell a measurable amount during firing - that's how a strain gauge works. It is only the fact that the pressure is released in a tiny fraction of a second that it doesn't just keep swelling until it bursts.
That's also why a gun barrel can take 65,000 real psi without bursting. It happens too fast to respond. If you pumped a barrel up with continuous pressure, it would burst long before that. In fact, barrels swell a measurable amount during firing - that's how a strain gauge works. It is only the fact that the pressure is released in a tiny fraction of a second that it doesn't just keep swelling until it bursts.
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CUP was useful in it's day and surely an improvement over whatever came before - which was probably closer to guessing than actual science.
The transducers and such are yet a further improvement. To say CUP never had any use because PSI is better is akin to saying that the sextant never had any use, because GPS is now available.
The newer system(s) are simply more precise - which is not to say they are perfect. But they are an improvement.
The transducers and such are yet a further improvement. To say CUP never had any use because PSI is better is akin to saying that the sextant never had any use, because GPS is now available.
The newer system(s) are simply more precise - which is not to say they are perfect. But they are an improvement.
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