CUP to peak PSI conversion...

[JohnKSa]

Can NOT be done writes Ken Oehler in an Article in Sept 2006 Shooting Times.

Dr. Oehler determined this from his successful efforts to derive a model which converted electronic pressure (PSI) measurements to CUP. While he managed to make the conversion, it was only possible if the entire electronically measured pressure curve was analyzed. A peak PSI measurement (which is the normal PSI number quoted by SAAMI) did NOT contain sufficient information to make the conversion accurately.

A direct quote from the article:

"...there is no way to predict CUP from a peak PSI reading, and there is no way to predict a peak PSI reading from a CUP reading."​

Interesting article--worth the read. Apparently Dr. Oehler is going to be a regularly contributing Shooting Times author.

 

[esheato]

I was under the impression that we already knew that.



Ed

 

[unloaded]

I've been meaning to ask, what exactly is CUP pressure?

peace.
unloaded

 

[rbernie]

Copper Units of Pressure.

Essentially, a copper cylinder of known composition is placed against the cartridge in a pressure chamber; when the cartridge is fired, it expamds and crushes the copper cylinder a bit. Due to trial and error experiments over the decades, the pressure needed to cause a set amount of deformation of the cylinder is known.

This allowed ballisticians to test loads and approximate the internal working pressure of the cartridge.

 

[brickeyee]

“Due to trial and error experiments over the decades, the pressure needed to cause a set amount of deformation of the cylinder is known.”

Not exactly. Every batch of copper crushers has a table that converts the final dimension to the force required to compress the crusher a like dimension. A sample of the set was actually tested to get the table.
The pressure has been used for years but it is not nearly as accurate as a modern piezo unit. The mass of the moving components and the requirement for a significant dimensional change in the copper system causes it to read lower than the true peak.
A piezo system has a much smaller deformation and far less moving mass.

There are approximations for converting between the two (CUP and PSI) but they are just that, approximations. You can do a search and find them.

 

[JohnKSa]

There are approximations for converting between the two (CUP and PSI) but they are just that, approximations. You can do a search and find them.

It may be possible to come up with a decent approximation/conversion for a SINGLE caliber, but Dr. Oehler's research indicated in no uncertain terms that there is no way to come up with an accurate generic conversion algorithm that converts from PSI to CUP unless you take the entire pressure curve into account. That information (entire pressure curve) is not quoted by SAAMI.

Converting from CUP to PSI based only on the two numbers is similarly impossible in the generic case.

If someone says that they have a conversion that works for a SINGLE caliber, they may or may not know what they're talking about. If they tell you they have one that works in general, you can be sure that they do NOT know what they're talking about.

Dr. Oehler made a point of noting that it's not even possible to say accurately that PSI will be higher than CUP. His measurements under carefully controlled conditions showed that it is definitely possible for accurate PSI readings to be lower than accurate CUP numbers.

There is no accurate general rule of thumb--there can be no accurate approximation. Peak PSI can NOT be accurately converted to CUP nor can CUP be accurately converted to peak PSI.

 

[Clark]

It seems to me impossible that there can be no conversion between two repeatable methods of measuring the same thing.

If the transducers are tracking peak pressure and the time it takes to crush Copper becomes a big part of the difference, time effects too can be defined.

Pressure and time are both traceable to he US National Institute of Standards and Technology.

 

[JohnKSa]

It seems to me impossible that there can be no conversion between two repeatable methods of measuring the same thing.

Exactly correct.

The reality is that CUP is not, strictly speaking, a measure of pressure. It is a measure of the RESULTS of pressure acting on a rather complex system. A system which includes the rupture strength of the case and the entire area under the pressure vs time curve.

time effects too can be defined.

The conversion CAN be made if the entire pressure vs time curve is considered. However, SAAMI specs are not quoted in terms of pressure vs time curves which makes such a conversion of only limited value.

If you're interested in the topic, the article is definitely worth the read.

 

[brickeyee]

Look here.
You will notice a pretty decent spread on the data away from the regression
line.
Interesting but not very useful as more than an estimate.

http://www.shootingsoftware.com/ftp/psicuparticle2.pdf#search='cup%20to%20psi%20conversion'

 

[JohnKSa]

brickeyee,

Dr. Oehler addressed this in the article.

There is correlation between CUP and PSI, but that was expected--it's not even necessary to resort to a correlation algorithm to note that there is relatively good correlation (though not as high as quoted in the linked article). Dr. Oehler's research indicated that the correlation was not as close as it needs to be to come up with an accurate general conversion.

This is borne out by the comments in the linked article.

"About 2/3 of the time the formula will land you within 3,000PSI..."
"Also do not attempt to use this conversion for handguns or shotguns, or to use it outside the range shown."

Dr. Oehler mentions that it is possible to come up with an accurate conversion between CUP and PSI for a SINGLE caliber. The linked article's author merely extended this observation to a range of rifle calibers but at the cost of degradation in the accuracy of his "conversion formula". Further attempts to extend his limited case "formula" to a more generic range of calibers and firearms will, no doubt, confirm Dr. Oehler's rather exhaustive research on the topic.

Again, the Shooting Times article is definitely worth the read...

 

[jeepmor]

No curves, no dice.

This is due to due the bell curve of the pressure impulse. A wide bell curve of the same peak pressure will exceed a narrow curves energy by a considerable margin. It is the impulse, or total energy required. The copper slug has some slop in it so it fits into a test plug hole. There can be energy losses here also which impede accurate modeling. Pressure losses are a function the the escaping gasses velocity squared. Which quickly skews modelling again. Especially since the slug is crushing and creating a seal in the process also.

The piezo sensor doesn't move much, if at all regarding volume during combustion. This fouls up modelling yet again. I'm sure he covered this. I prefer PSI units. It's a number I can wrap my head around more easily as a mechanical engineering type.

jeepmor

 

[Sergeant Sabre]

It seems to me impossible that there can be no conversion between two repeatable methods of measuring the same thing

They aren't the same thing, though. Peak PSI is exactly that, the pressure at the peak of the pressure curve. Peak PSI does not take into account the shape of the pressure curve. Is it short and sharp, almost like a spike? Or is it long and blunt, with several milliseconds of near-peak pressure?

the CUP system, as an above poster told us, was derived from how much a particular cartridge/load combination would deform a copper chamber. This deformation is a function of the entire pressure curve. A load that develops a peak PSI of 40,000, but whose pressure curve lasts only X number of milliseconds, would deform the pressure tube differently than a load with equal peak PSI with a curve that lasts for three times X milliseconds.

 

[Clark]

As I said, if it is pressure they measure, the can be correlated.
As I said, if it is pressure and time they measure, it can be correlated.
Further I will say that if it is time and pressure convoluted through the non linear and hysteresis of the deformation of Copper that changes the chamber volume, that all can be correlated as well.

Someone just has to do the work.
My wife designs calibrators, you should see the compensation formulas on thermocouples.

I am so busy building a math model of one non linear system driving another, that I will not eat lunch today.
Dr. Oehler needs to spend less time out to lunch.

 

[RecoilRob]

Mr. Clark,
The CUP method shows the results of the entire pressure curve.....effectively showing an average. If two loads were compared....one with a long, gentle bell curve and the other with a brief but violent spike, they could easily show the same amount of copper compression as time is NOT measurable with CUP.

I think it is the inability to measure the time of the curve that can throw off the making of a valid comparison formula. If proper burning rate powders are being used, you COULD probably get real close to a valid comparison....but there would always be the chance of the odd pressure phenomenon mucking up the works sometimes.

 

[Clark]

There in no information stored in the Copper compression that is not available to the pressure curve. The problem is someone is too lazy to get it out of there.

http://mathworld.wolfram.com/Convolution.html

 

[AFhack]

Clark - I disagree and I think recoilrob did a fairly good explanation of why.


CUP is a pressure vs time expression whereas peak psi is a momentary measurement.

When you measure pressure then conversions are pretty simple; x PSI = y bar etc. It's a very linear relationship.

When time is introduced as a variable you have a curve. X PSI in Y milliseconds = Z Bar in T seconds. While the actual numbers are easily converted you've also introduced a variable: time.

I can produce a load that produces a peak pressure of 10,000 psi. That's peak psi and it's simple.

I can produce a load that creates the exact same effects of a peak pressure of 10,000 psi, but it's actual pressure is an average of 8,000 psi for 15 milliseconds.

Similarly I can produce a load that creates the exact same effect of a peak pressure of 10,000 psi, but it's actual pressure is an average of 9,000 psi for 8 milliseconds.

Obviously the most common difference is that in one choice I'm using a powder that burns faster than in the other choice.

 

[JohnKSa]

There in no information stored in the Copper compression that is not available to the pressure curve.

This statement is exactly correct.

However, that does NOT mean that there is a generic conversion between peak PSI (SINGLE number) and CUP (SINGLE number.)

If you have the entire pressure curve available, you can work out a model to do the conversion (if you have the entire pressure curve available for each measurement you wish to convert) and Dr. Oehler did so (and partially described the difficulty of the process in the article.)

The problem is someone is too lazy to get it out of there.

From my first post on this thread.

"While he managed to make the conversion, it was only possible if the entire electronically measured pressure curve was analyzed."

YES, it is possible develop a generic conversion algorithm to convert between a PSI vs Time curve and CUP. It is NOT possible to develop a generic conversion algorithm to convert between a peak PSI measurement (SINGLE NUMBER) and CUP.

 

[Clark]

I am not saying there is a generic linear conversion.
I don't know, It might be a high order equation with many variables to get 1% accuracy, if someone did the work.
But someone selling an expensive pressure tracing set up with electronics could certainly do the signal processing, and should feel compelled to do the job.

I don't care about c.u.p. myself, my strain gauge amplifier design simply displays a peak value on digital multi meter.

 

[JesseL]

I don't know, It might be a high order equation with many variables to get 1% accuracy, if someone did the work.

That's exactly the problem. We only get one variable. The other variables that would be useful for conversion aren't available. CUP alone is only representative of the area under the pressure curve, it could be a long low curve or a short high curve - we don't know for sure. We calibrate CUP to an approximation of what kind of peak pressure we think it represents based on some assumtions based on what we know of internal ballistics. No amount of math is going to give us any information we didn't have before.

This is akin to trying to find the peak temperature outside during the day by leaving a crayon in a parking lot and seeing how much it melts. You can't tell if it was a moderate temperature all day or if it was cold most of the day with a short peak when the sun came out.

 

[JohnKSa]

But someone selling an expensive pressure tracing set up with electronics could certainly do the signal processing, and should feel compelled to do the job.

Clark,

It has been done. I said so in my first post. Dr. Oehler said so in his article. What you are ignoring is that the signal processing and pressure tracing setup is providing pressure versus time curves and that (a curve--a series of numbers) is what's required to make the conversion.

A peak PSI measurement is a single number (not a series of numbers nor a curve) and does not contain enough information to make the conversion.

No amount of modeling, analysis or application of high order equation can derive more information from a peak psi measurement than it contains and since it does not contain enough information to make an accurate conversion possible, no amount of modeling, analysis or application of high order equations will make it possible to come up with an accurate general algorithm that allows one to convert from peak PSI to CUP.

 

[Clark]

You mean science can calculate plastic deformation to Copper from a pressure and time curve?

Others seem to think that plastic deformation can be done with finite element analysis.

 

[BluesBear]

Several years ago, when loading guides started listing load data in P.S.I. instead of C.U.P. I went looking to see if there was a chart somewhere that listed a comparision of both measurements for the same loads.

If's frustrating trying to compare load dats from one manual to another when they use different standard.

I found an article online where a person had devised a simple formula to convert PSI into CUP and vice versa.

Great I thought, so I copied the formula into my load data spreadsheet.
I put thm into two columns so that whenever I entered the reading into one column it would auto calculate in the remaning column.

That when I discovered that certain loads in .44 Special developed only 400PSI and certain .45 acp loads developed 95,000CUP!
That's when I started to suspect that something was wrong.

With the easy access to strain gauge technology today hopefully all manuals will abandon CUP and use only PSI. It would make load performance comparison so much easier.

 

[JohnKSa]

You mean science can calculate plastic deformation to Copper from a pressure and time curve?

Dr. Oehler claims to have done so.

Others seem to think that plastic deformation can be done with finite element analysis.

He did not describe the specific mathematical modeling method required to effect the conversion model. He did state that it took "the better part of a year" to refine the model.

With the easy access to strain gauge technology today hopefully all manuals will abandon CUP and use only PSI. It would make load performance comparison so much easier.

That was Dr. Oehler's conclusion as well. That is why the conversion model he developed was never put to commercial use.

 

[Jim Watson]

Granting morbid curiosity, I don't see the usefulness of a CUP-psi conversion.

Compare data? The manuals give maximum loads for whichever pressure gun they use, doesn't matter if it is 52,000 CUP or 63,000 psi, SAAMI has come up with that as a maximum and the component makers are going to stop there.

People might use a conversion to shop for data. Hmm, they only go to 50,000 CUP which is 60,479 psi here but over there they load to 61,500 psi so I will go with the high side.
Or worse they can extrapolate, a top load of NR4995 gives 49,500 CUP which converts to only 58,943 psi, but the maximum of Alpha boom9 is shown in psi at 60,500 so it must be ok for me to load more 4995 than the wimpy NR people say.

If you are going to load beyond the books, use the traditional criteria and go ahead, but don't think that a conversion equation would make it any less experimental.