Converting CUP to PSI

Correlation (which exists -- big time) does not equal, say, or mean. . . . "Conversion"
The gymnastic semantics going on here, in an attempt to obscure the obvious, are worthy of the Cirque du Soleil.

Can't we just go back and all have a Kumbaya moment on something less controversial . . . say, like . . . headspace ?
Maybe the right engine oil for vintage British twin motorcycle engines .. . ?

(You'll have to forgive me while I channel a Charlie Brown moment on the pitcher's mound)

MEHavey said:

Correlation (which exists -- big time) does not equal, say, or mean. . . . "Conversion"

Click to expand...

........you are correct sir.

There is also the existence of relevancy.........

denton said:

LOL... well, it's time to quit beating this horse, don't you think?

There is the theory that the words you use mean exactly what you think they do. I'm more than willing to grant you that.

I simply reject your claim that my definition of conversion is odd. You might want to take a stab at answering my question: If the chain of events in a piezoelectric pressure measurement system isn't a conversion, or even a direct conversion, what word do you use to describe it? Conversion is what transducers do. Piezoelectric transducers convert pressure to voltage. Copper slugs convert pressure to dimensional change. Neither is perfect. Only The Almighty gets perfect information.

Click to expand...

I started a long rambling post about the nuances of how the copper crusher method is not a direct measure of peak pressure and how the transducer is but I will skip that for now.

ETA: I skipped that line of reason since Denton earlier has said that, "If you're trying to fit a model, the simplest model that gives adequate correlation is the one to be preferred." But it must be a sufficient model and in this case its not. Setting the mechanics and physics aside for the moment and just look at the math. By definition a mathematical function is, "a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output." So a function can multiple different inputs that may result in the same output but a function can never take a single input and create multiple different outputs from it.

It is well document that you can have two different loads (either two different loads in one particular cartridge or two completely different cartridges) that will measure to the same CUP value and yet will result in different transducer peak pressure measurement. That fact alone means there is no mathematical way to create an equation that can model that without more data. This would violate the basic definition of a mathematical function.

Look at the proof pressures for more examples of this impossibilities.

41 Rem Mag 40 36
44 Rem Mag 40 36
45 Win Mag 40 41
7-30 Waters 40 45
218 Bee 40 35
30 Carbine 40 40

The first number is proof pressure in KCUP and second number is proof pressure in KPSI. With this subset of data where they all have the same KCUP value and different PSI values there is no mathematical function using only KCUP as in input that will give you the correct KPSI output. NONE! Mathematically impossible.

There are multiple areas in the proof pressure chart that make this one dimension "conversion" mathematically impossible.

357 Mag 45 35
257 Roberts 45 54
303 British 45 49

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6.5x55 Swedish 46 51
7mm Mauser (7x57) 46 51
222 Rem 46 50
300 Savage 46 47

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7.62x39 50 45
222 Rem Mag 50 55
257 Roberts +p 50 58
280 Rem 50 60
30-06 50 60

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221 Rem Fireball 52 60
6mm Remington 52 65
7mm Rem Mag 52 61
7mm-08 Rem 52 61
17 Rem 52 63
221 Rem Fireball 52 60
223 Rem 52 55
243 Win 52 60
270 Win 52 65
308 Win 52 62
35 Whelen 52 62

---------

8mm Rem Mag 54 65
220 Switf 54 62
264 Win Mag 54 64
284 Win 54 56
300 H&H Mag 54 58
300 Win Mag 54 64
338 Win Mag 54 64
416 Rem Mag 54 65

Without more data there is no conversion from CUP to PSI. There is a strong correlation but no one input conversion without more data.

ETA: Pick any one of these subsets of data an plug it into Excel and let it try to fit a function to the subset of data. It can't...

here is the link for the center-fire rifle data. the cup/piezo measurement explanation is on page ten: https://saami.org/wp-content/uploads/2019/01/SAAMI-Z299.4-Centerfire-Rifle-Approved-12-14-2015.pdf

finding out how the cup tarage table is derived (linear, log, polynomial) and the piezo scale are derived, may help solve this mystery. the good fit at one end of the pressure scale and the poor fit at the other may be due to differing scaling methods.

luck,

murf

I am sorry I do not buy it at all. The error in my mercury thermometer is not because I don't understand or bother to model the underlying physics. For a give mass of mercury I know it volume is linearly dependent on its temperature, again not due to empirical data fits but due to physics. The conversion from the length up the tube to temperature is exact I can write the equation down that exactly captures the relationship and any error in my temperature sensor is due to manufacturing tolerance not a missing understanding of the physics involved.

The conversion from one unit of temperature to another (ie Celsius to Rankin) is by definition exact no error whatsoever. This is true of all US Customary units to/from SI units. All US Customary units are defined by exact conversions from the SI units. ie 1-inch is exactly .00254 m. The metre is the length of the path traveled by light in vacuum during a time interval of 1/299792458 second.

357 Mag MAP is 45 KCUP or 35 KPSI
257 Roberts MAP is 45KCUP or 54 KPSI

Even if we assume there is a fair amount of error in all of those numbers there is no way to create an equation that take the input of 45 CUP and gives us a remotely accurate number for both cartridges in PSI. A PSI number that splits the different between those two cartridges requires us to accept 22% error, or more, in the results for one of those two cartridges. Those SAAMI numbers are not nearly that inaccurate by the way.

The idea of a CUP to PSI conversion is intellectually interesting, I have thoroughly enjoy the discussion and playing with the numbers. I have now have a three dimensional input second order function that takes CUP, case-volume and bore-diameter and fits it to the data with 7 parameters resulting in an R^2 = .968 and I got the worst case error on 357 Mag and 44-40 down to ~25% and a lot better on all the rest. Even with that much more sophisticated fit I wouldn't trust it with my worst enemy's face behind the gun.

In practice the equations claiming a simple CUP input to PSI output are dangerous and misleading. 357 Magnum. 7.62x29 and 44-40 are prime examples of how dangerously over pressure those equation can result in. If you have a cartridge that only has CUP data (no traducer standards created) and put the CUP data into one of these simple equation you have the potential (with no way to knowing) to calculate a number that could be more than 50% over or under what the number would have been if had been measured with a transducer correctly. Other than intellectual curiosity I can think of no good reason to use these equation as it is simply too inaccurate and dangerous for practical safe use.

. . . equations claiming a simple CUP input to PSI output are dangerous and misleading.

Click to expand...

No such statement was made, implied, or left as an exercise for the student.
The fact that someone could somehow find that in the discussion is evidence of failure to RTP.

Denton, it's time to walk away from the Philistines.
The rest of us know what you mean, how & when to use it, when not to use it,
and the error bars clearly pointed out when it is used.

Many thanks for your patience.


.

MEHavey said:

No such statement was made, implied, or left as an exercise for the student.
The fact that someone could somehow find that in the discussion is evidence of failure to RTP.

Denton, it's time to walk away from the Philistines.
The rest of us know what you mean, how & when to use it, when not to use it,
and the error bars clearly pointed out when it is used.

Many thanks for your patience.


.

Click to expand...

From denton's original post near the end of it, "The raw data have significant random noise. Since the input data is imperfect, the output is not exact, but it is close enough for most practical purposes. Also, the exact results will vary a bit if you choose cartridges different from my selection. "

denton does claim is it close enough for most practical purposes, that is, in my not so inexpert opinion, a dangerous claim give the error we have all seen those equations can produce in the course of this thread.

If the exact results may vary if I choose a different cartridges then denton's then what is the point of this exercise? If I have both CUP and PSI MAP for a cartridge then I don't need the conversion. If I only have one of those two measurements and want to use the conversion to to find the other measurement then that cartridge cannot have been in denton's original data set. How then does one tell if the conversion will be an accurate conversion or another 357 Magnum level error?

I would also like to see support for the claim that the data he starts with has errors in it. Assuming he is referring to SAAMI MAP pressures that definitely does not have significant error. A claim to that effect had better come with stronger evidence than hearsay or not be made at all given the liability nature of what SAAMI does. As I said previously that data is establish through hundreds of rounds of testing over many test barrels, test systems, and operators using both methods to establish the MAP specification (assuming both are being set). Even at the QC production level of validation testing using the spec (not establishing it) manufactures are held to a 4% coefficient of variation over a 10 shot sample (minimum sample size for SAAMI approved testing to the spec) when doing lot acceptance testing. Many many more rounds are fired before a new cartridge is accepted as a SAAMI cartridge and the MAP and proof specs are created. And finally one must ask why would you use bad data to create an even worst conversion?

I hope this is not taken personally, technically contentious, but not personally. As I said previously I have enjoy the discussion and the motivation to play with the numbers. But as an engineer and one that has processed a fair amount of experimental data I also see the dangers of blindly fitting curves if not well grounded in the first principles underlying what generated the data. An over dependence on statistics at the expense of first principles can become a hammer and every data set a nail, but sometimes the data really needs a wrench or two.

ArchAngelCD said:

I was always told there is no way to convert the data from the two different testing methods. The equipment is just too different.

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A few years ago I read an interesting piece regarding 7.62x 51mm vs. .308 Winchester by a ballistics engineer who had worked for, I think it was CIL in Canada. Anyhow in the piece, he stated flatly that CUP could not be converted to PSI or vice versa because the testing equipment for CUP and PSI worked differently. Who knows?

But if indeed CUP can be mathematically converted to PSI, why would Lyman have converted all their CUP figures to PSI?

35W

Remember that before the piezo based sensors came along the CUP measurement was thought to be an accurate measure of actual peak pressured and was calculated as actual PSI because it was though to actually be that. Hence many manuals publish before the acceptance of the transducer method report crusher data in PSI even though it was done using a CUP or LUP system. Copper and lead crusher was the height of pressure measurement technology for many many years. There was nothing equal or more accurate to compare crusher data to, and prove or disprove it. It was not until the advent of data acquisition systems that could record data fast enough (first analog and now digital) to actually get a meaningful representation of a firing's pressure event did it become clear that in some situation crusher was not capturing the data they though it was. Once we had digital data acquisition system fast enough it became easy to acquire the data and process the data fast and easy on a computer. Once these better systems came along they realized the short coming of the crusher measurement system and had to make the unit distinction of CUP vs PSI. But clearly we had been using CUP for a long time safely so there was no need to abandon it. It may not capture peak pressure correctly in all cases but the measurement was sufficient and repeatable enough to maintain safe loading practices.

Also remember the reason SAAMI has move from crusher to transducer has less to do with accuracy (though transducers do bring that) and far more about saving money. If you are doing 10 pressure tests ever shift, potential even more often, that is a lot of copper crushers to consume and a lot of man-hours consumed doing the pre and post processing work to arrive at the a final value. With the transducer system your do periodical calibration checks and have to occasional remeasure your offsets as brass batches change but for the most part it's load, fire, and the computer spits out the data. The cost savings are measurable.

From a previous thread on the subject at TFL, I posted:
I have (had) a little book The .30-'06, A Source Book for the Advanced Handloader by W.L. Godfrey. In 1975 he set up with some strain gauges and an oscilloscope to read chamber pressures. His confidence limits on pressure readings are wide, but if you want to know what you could expect from full charges of Bullseye in a .30-06, this may be the only place to look. (24 gr B.E. + 150 gr JSP = 50,500 psi, 2353 fps. With a very steep slope on the pressure versus powder charge weight graph. Y'all be careful, now, you hear?)

The book includes bullet weights from 50 to 300 grains and all powders then available whether normally suitable or not, Bullseye to H870. (His 300 grain .30 bullet had the length of a 250 but the rear half of the core was tungsten, the front half lead to give expansion.)

I understand he did a similar project on .243 but the book is much less common.