There is no accurate and reliable "translation" available between CUP as defined by SAAMI procedures and psi. At the present, SAAMI still allows use of the old CUP pressure limits and procedures, but new cartridges are specified in terms of psi using the conformal piezo transducer.
If you caliber has a maximum average pressure of 64,000 psi, it is probably a modern caliber for which there is no CUP specification.
Would it be correct to say that once you set a pressure limit in CUP, to get the pressure limit for that cartridge in psi, you have to take reference ammo for the specified pressure limit in CUP and then test with the piezo transducer to get the psi limit?
Jim, Ken is of course right about there not being a straightforward conversion between the two pressure measurement systems. However, I'm remembering somebody on this site with a statistics background (denton?) has done an approximation of a translation based on cup and psi limit data for several cartridges and found a line or curve, within "reasonable" bounds of error (i.e., close enough for general informational/entertainment purposes rather than safety purposes). I believe the information was posted (or at least a link to the info was posted) within the last two years, so you may be able to find that data through the search function.
Edited to add link to previous discussion, which references a previous discussion with the data from denton.
First let me express a little bias. Having fired many rounds in barrels with dual instrumentation (CUP and psi), I do have slightly higher regard for CUP than for reading primers, case head expansion, bolt lift, and shiny spots. All are indicators of pressure, but I would not consider them to be reliable measurements of pressure.
The primary function of reference ammo is to establish the mythical "standard" or average barrel. Reference ammo is not an absolute standard of pressure, and lots typically are assessed at lower pressures that the specified max average pressures. If you do both CUP and psi measurement, the observed difference is applicable only to that lot of reference ammo. There are just too many other variables.
As I recall, Denton's work was based on comparing the two published tables of maximum average pressure, the old table expressed in CUP and the newer table in terms of psi. I don't consider that to be an accurate or reliable method of translation. SAAMI looked for a translation from CUP to psi for many years before they decided to generate a new psi table. If such a translation existed, I expect that they would have found it and would not have bothered with a new table just for psi.
We should respect the CUP system, play taps, salute it, and move on.
The Much Sharper Ken is (as usual) absolutely right.
What appears to be sloppiness on SAAMI's part is actually the inevitable limitation of an insurmountable problem � there's no known way to measure a sporting firearm's chamber pressure directly and precisely. The best that we can do is to measure certain related phenomena indirectly and conclude from those results what the actual pressure probably is.
The strain-gauge method in the Oehler "Personal Ballistics Laboratory," for example, dynamically measures the changes in resistance to an electric current through the strain gauge as the expansion of the barrel (under internal pressure) stretches the gauge. This system, then, measures one thing (the changes in an electric current] to indicate a second thing (the expansion of the barrel) to get an approximation of a third thing (the internal pressure that expands the barrel).
The gap in our knowledge is that we can only guess within a certain limited degree of accuracy how much pressure expands the barrel by a known, measurable amount.
The piezo crystal that SAAMI uses does essentially the same thing. It measures the changes in resistance to an electric current though the piezo crystal as a piston driven by chamber pressure compresses it. The same knowledge gap still limits us � we still don't know, and can only guess with limited precision, how much pressure causes the piston to compress the crystal by a measurable amount.
This situation is more beneficial to us than it may seem. Since we also have only a relatively vague idea of how much pressure to consider safe, we can not know where to scratch a narrow line in the sand or know how to march right up to it without risk. We have to observe a wider "warning track" that warns us that the edge of the cliff is near and try not to cross that "warning track" lest we run right off the edge of the cliff in the fog.
In the immortal words of Inspector "Dirty Harry" Callahan, "a man's gotta know his limitations" � and live within 'em.
edited to add:
The "copper units of pressure" (CUP) system was even less precise and far more limited and variable than either of the two systems that measure electrical resistance. In the old days, SAAMI called the "measurements" that they obtained by compressing a copper cylinder "pounds per square inch" (PSI or lb/sq in.) but in time came to realize that there was no way to know how much pressure actually compressed those copper slugs by a known, measurable amount.
Changing the terminology from "pounds per square inch" to "copper units of pressure" was a small step forward. Moving on to the electrical approximations was a larger step forward � and still short of perfect precision.
Last edited by Ken Howell; 12/23/06.
"Good enough" isn't.
Always take your responsibilities seriously but never yourself.
Please take time to read and understand my article before reaching conclusions.
The basic mathematical argument is that any two measurement systems that are successful at measuring the same thing must be correlated and convertible. It is a mathematical impossibility for it to be otherwise. The posting format here at 24HC does not allow mathematical notation, but I would be happy to write out the very simple proof and email it to anyone who is curious. One result of my investigation is that practically all the deformation of the copper slug happens at peak pressure. So, both the piezoelectric method and the copper crusher method measure the same thing: Peak pressure.
Finding the conversion formula is not only possible, it is trivial. IIRC, from the moment the question entered my head (wondering how many PSI would be a reasonable maximum limit for my Swedish M96), until I had my answer, about 20 minutes elapsed.
After I published my findings, I was delighted to find that Dr. Lloyd Brownell of University of Michigan had preceded me by a few decades. In his landmark work on pressure factors, he includes not one, but two graphs for converting between CUP and PSI.
CIP, Europe's equivalent of SAAMI, has obviously been taking one set of measurements, and using a formula such as the one that I published, to convert from PSI to CUP. As nearly as I can determine, after analyzing their data, only two possibilities exist: 1) European instrumentation is a full order of magnitude better than US instrumentation, or 2) they are taking data in one system, and using a formula conversion for the other untis of measure. The second alternative is vastly more likely.
I can do it. Dr. Lloyd Brownell could do it CIP can do it. Anything that happens must be possible. Since the conversion routinely happens, it must be possible. Furthermore, statistical analysis of the errors in the conversion indicate that the conversion is about as precise as our ability to measure pressure with the piezo method. It may not be perfect, but it is as good as the measurement system we are presently relying on.
All that said, there is one thing in the article that I wish I had done differently. In discussing the precision of the conversion, I developed the error distribution for converting single measurements from CUP to PSI. The question that usually comes up is different. The usual question is how to convert a specification. In that case, you get the benefit of multiple measurements, and the conversion is good to about plus or minus 1,000 PSI in the center of the curve, around 45 KPSI, and plus or minus 2,000 PSI near the ends, around 30 and 60 KPSI. If the question is how to convert between PSI and CUP specifications, what would you use for input except a table of equivalent specifications?
Note that the linear relationship is valid only for rifles, and only from about 28 KPSI to about 60 KPSI. We know that the actual relationship is curved, but within those bounds, a straight line is a good fit.
As noted by two contributors above, only The Almighty knows exactly how much pressure happens in the chamber of a firearm. The rest of us have to rely on methods of approximation. All approximations are lies. However, some of those lies are close enough to truth to be useful. So the key question is, how close to truth is the measurement likely to be? In the case of chamber pressure, CUP, piezo, and strain gauge measurements all provide some measure of useful information. Piezo and strain gauge measurements have the great advantage of producing output directly in useable engineering units. Both are capable of higher precision that the CUP method, but SAAMI has failed to exploit the full available precision of the piezo method.
The whole issue will soon be moot, anyway. CUP is clearly on its way out, and, eventually, PSI will be as well. Eventually, we will all shed our archaic measurement systems, and join the rest of the world in using more modern units of measure. Both PSI and CUP will be regarded as quaint historical footnotes.
Please take time to read and understand my article before reaching conclusions.
I have read your article.
To the best of my knowledge, "CUP" is unique to SAAMI. CUP implies adherence to SAAMI procedures, not simply the use of a copper crusher element. From the appearance of Dr. Brownell's "conversion graph", it is apparent that he was probably referring to pressure measurements made in accordance with US military procedures. Did Dr. Brownell really refer to his copper measurements as CUP? Don't you wonder why your conversion algorithm is significantly different than Dr. Brownell's? The US military and SAAMI used different procedures and got different answers. The CIP procedures are different still. CIP's use of their formula to convert their copper procedure readings to piezo equivalent readings is appropriate. Incidentally, their formula is not quite linear, but close. All the "copper" procedures seem to give different answers.
I do not deny that CUP and psi measurements are correlated, but I regard correlation coefficients in the order of 0.9 to indicate only a correlation. It does not indicate that a measurement procedure should be be trusted or used. For comparison, I have been able to demonstrate correlations of 0.99 or even 0.999 between the SAAMI conformal piezo transducers, strain gages, and case-mouth piezo transducers used per NATO. I've been able to demonstrate correlation in the order of 0.98 between CIP copper and piezo transducer on a shot-by-shot basis.
Have you read and understand the SAAMI, CIP, US, and NATO procedures for pressure measurements using both copper and transducers?
Specifically, what procedure for measuring chamber pressure are your referring to when you say we will "join the rest of the world in using more modern units of measure"?
You have also read Brownell, as I have. I would expect that from you.
Dr. Brownell learned his use of strain gauges from the same poeple I did, the Physical Measurements Group at Tektronix, and at about the same time. My job at that time was to be the regional Tektronix resource for physical measurements methods.
Most of my early published articles were in electronics, with more recent work in the statistics of measurement systems, designed experiments, and industrial processes.
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Don't you wonder why your conversion algorithm is significantly different than Dr. Brownell's?
Actually, no.
As nearly as I can read Brownell's Figure 14, page 35, I get the following, comparied with my model:
I would say that they track pretty closely, especially since Brownell identifies his graph as the "approximate relation".
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it is apparent that he was probably referring to pressure measurements made in accordance with US military procedures
Perhaps you are correct, but I am unable to find any such evidence within the article. His numbers appear to me to correspond directly to those you would get with the SAAMI CUP method.
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It does not indicate that a measurement procedure should be be trusted or used
You cannot make that evaluation on R^2 alone. But, FWIW, my R^2 of .937 corresponds to a correlation coefficient of .967.
This goes directly to the point I made about wishing I had written something a little different in my article. When the question is predicting one measurement from another, you have a valid point. When the question is converting one specification to another, the aggregation of the data reduces random error by the square root of N, giving a much better estimate than you can get for an individual point. The precision of the conversion formula is as I have stated: Good to plus or minus 1,000 PSI near the middle of the curve, and to plus or minus 2,000 PSI near the ends. Per the analysis I have done of the limited data I have available, this isn't much different from the magnitude of the random error in the piezo system, as applied by SAAMI.
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Have you read and understand the SAAMI... procedures for pressure measurements using both copper and transducers?
Yes, very carefully. Wouldn't you expect that?
The CIP and NATO documents are not readily available to me in English. My familiarity with CIP methods is through what has been published in English on European reloading sites. If you have them in English, I would be grateful for a copy.
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I have been able to demonstrate correlations of 0.99 or even 0.999 between the SAAMI conformal piezo transducers, strain gages, and case-mouth piezo transducers used per NATO
That speaks very well for careful technique, and a knowledge of what you are doing. Good work.
Now, turnabout is fair play: Have you read and understood any of the authors on formal measurement systems analysis? Wheeler? My own humble and obscure publications on the topic? If not, wouldn't it be appropriate for us to pool the knowledge we both have?
Almost forgot: The more modern system of measures I mentioned is the metric (SI) system of measures.
Dr. Lloyd Brownell of University of Michigan had preceded me by a few decades. In his landmark work on pressure factors, �
Again and again, I wish that Dr Brownell and my friend Homer Powley were alive (and still lucid!) to clarify something that Homer told me years ago.
Shortly before Dr Brownell died, Homer apprised him of basic errors in his approach to studying pressure factors. According to Homer, Dr Brownell then reexamined his work and conceded � graciously and gratefully � that Homer was right.
I've wished many times that I'd pursued that point with Homer. I have no idea what Dr Brownell's error[s] was [were], so his work has always been under an undefined cloud for me. Ignorance is Hell. Irresoluble curiosity makes it worse.
"Good enough" isn't.
Always take your responsibilities seriously but never yourself.
The copper-crusher system was like a fisherman's rubber ruler � not accurate when stretched to its limit.
The piezo and strain-gauge systems are like surveyors' ropes � more nearly accurate but not when they sag noticeably in the middle.
We simply don't yet have a pressure-measurement system that approaches an accuracy level like that of a precision-etched machinists' stainless scale � which itself is more accurate at one temperature than others.
The rubber ruler's units of measurement correlate with the surveyors' ropes' units in different ways under different conditions.
"Good enough" isn't.
Always take your responsibilities seriously but never yourself.
We simply don't yet have a pressure-measurement system that approaches an accuracy level like that of a precision-etched machinists' stainless scale
Aye, there's the rub.
As nearly as I can determine, a single technician, working with the same piezo equipment, on the same day, and measuring ammunition from the same lot, can repeat a 10-shot pressure average within plus or minus about 1,000 PSI. Move it from lab to lab, and it gets nothing but worse.
Interesting, though understanding little of the theory and science, but some light shed into dense mind.
Any chance since measurements can be linear within perimeters, you guys are simply debating + and/or - of magnitudes at opposing ends of measurement - the rubber ruler, or variables? Did I understand that right?
The variables are what always got my attention, don't like to go there, unless VERY calculated.
Has anybody used Ken Howells' method of meausuring barrel pressure?
The Mayans had it right. If you�re going to predict the future, it�s best to aim far beyond your life expectancy, lest you wind up red-faced in a bunker overstocked with Spam and ammo.
In a very gracious PM, our friend Denton tells me that this is incorrect:
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The piezo crystal that SAAMI uses � measures the changes in resistance to an electric current though the piezo crystal as a piston driven by chamber pressure compresses it.
He then explains:
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The pressure in the chamber is converted to force by the area of the face of the piston. The piston presses against a piezoelectric crystal, which, by its mechanical properties, converts the force to strain. The strain on the crystal causes an electrical charge to appear on opposing faces of the crystal. The electrical properties of the crystal and holder (capacitance) converts the charge to a voltage. Voltage is then amplified and displayed as a function of time, and is proportional to chamber pressure.
In a strain gauge system, the pressure in the chamber is converted to stress in the steel, which, by the mechanical properties of the steel is converted to strain. Strain is converted to voltage by the strain gauge, which has a small electrical current running through it. The voltage is then amplified, and displayed as a function of time, and is proportional to chamber pressure.
I'm not about to quarrel with any of that! As I told him in my PM response, I just call 'em as I understand 'em as a layman, and what I posted was my admittedly correctable understanding. So now I'll let Den 'n' Ken hash it out. (But I still doubt that there's a useful way to relate CUP to lb/sq in., no matter how you "measure" the latter. Seems to me � outsider looking in � like comparing apples to algebra.)
"Good enough" isn't.
Always take your responsibilities seriously but never yourself.
Has anybody used Ken Howells' method of meausuring barrel pressure?
I haven't. Don't even know what "Ken Howell's method" is. <img src="/ubbthreads/images/graemlins/confused.gif" alt="" /> <img src="/ubbthreads/images/graemlins/help.gif" alt="" />
"Good enough" isn't.
Always take your responsibilities seriously but never yourself.
In the attachment, there is a scatterplot of SAAMI CUP measurements vs. SAAMI PSI measurements.
You can put aside all the math, and interpret the plot this way: If it resembles a straight line, there is a conversion between the two. If it more resembles a shotgun splat, then there is not.
I'll go so far as to speculate why SAAMI has not succeeded in finding the relationship: I suppose they may have taken both CUP and PSI measurements off the same lot of ammunition. If you think about that for a minute, that is taking an infinitesmal slice out of the line, spanning perhaps a few hundred PSI on the horizontal axis. In that case, all you can see is measurement system noise, and you won't find a correlation. In order for the math to work, you have to span a range of pressures that is much larger than your measurement system random noise.
In the graphic, the red lines are the 95% Confidence Interval. We're 95% sure that the real regression line falls between them. The blue lines are projections of error. For each vertical blue line, the true value on the vertical axis lies between the two horizontal lines.
The CIP procedures are different still. CIP's use of their formula to convert their copper procedure readings to piezo equivalent readings is appropriate. Incidentally, their formula is not quite linear, but close... I've been able to demonstrate correlation in the order of 0.98 between CIP copper and piezo transducer on a shot-by-shot basis.
KenOehler, could you briefly describe for us how the CIP uses copper crushers and perhaps shed some light on why their crusher method better allows a simple conversion formula to piezo? I've wondered this ever since I first saw denton's plot of CIP copper and piezo numbers.
From denton's plot of SAAMI CUP and piezo, it was obvious something was quite different between the two copper systems. What is it about SAAMI's approach that creates greater variability than CIP's?
One result of my investigation is that practically all the deformation of the copper slug happens at peak pressure.
denton, I for one would be very happy to hear more about your investigation. I've read of two theories as to why crushers increasingly underestimate pressure as the true peak pressure rises. One is inertia effects. The other is a peculiar strain-rate property of materials, where very high rates of strain can alter the final deformation as compared to static (low rates) tests, a phenomenon I do not understand.
