CUP & PSI in Reloading Manuals

[Buckshot Bear]

Just wondering in reloading manuals why some pistol cartridge pressures are given in CUP and some in PSI?

 

 

[Sedalia Dave]

Depends on who and when the data was created. Older data was always in CUP. Newer data, it depends on the equipment used.

 

Copper Unit of Pressure (CUP) Defined by Hodgdon

 

CUP vs. PSI — What’s The Difference in Pressure Measurements

 

 

CUP vs. PSI — Do You Understand the Difference?

 

Know Your Terminology — CUP vs. PSI

 

[Garrison Joe, SASS #60708]

Analog measurement system (CUP) where a crusher pellet was hit by the chamber pressure (through a hole cut in the chamber), and amount of deformation was measured.  Somewhat the same as the PSI, but not really close.  Expensive and slow to take measurements.

 

Digital measurement system (PSI) uses an electronic strain gauge or pressure transducer that measures the expansion of the chamber wall.  Gives pretty precise measures of pressure.  Rapid testing, and almost no cost to do more testing.   All testing is done this way now.

 

good luck, GJ

[Pat Riot]

I have read that it is not a good idea to try and correlate the two together or try to calculate either using creative math. In other words don’t try to guess PSI using CUP. They aren’t the same thing. 

[Larsen E. Pettifogger, SASS #32933]

You have to be careful as CUP and PSI are not the same and there is no conversion table or direct method to convert.  Same with shotgun loads.  Some current manuals and manufacturers websites still have some pressures in LUP (lead units of pressure) and some in PSI.

[Buckshot Bear]

Thanks pards.....whilst I have the Wire's Brains Trust's attention....in the 1800's how did they work out velocity?

[Larsen E. Pettifogger, SASS #32933]

Ballistic pendulum.

[Buckshot Bear]

3 minutes ago, Larsen E. Pettifogger, SASS #32933 said:

Ballistic pendulum.

 

Copied the above and Googled.....interesting read....the math's equations were way out of my league but shows how clever humans can be when they need to find out something.

[Sagebrush Burns, SASS # 14226]

Here is a formula I copied some years ago - sorry, don't remember the source.

 

CONVERT CUP TO PSI

 

(1.516 X CUP) - 17,902 = PSI.
Example: 45,000 CUP X 1.516 = 68,220
68,220 - 17,902 = 50,318 PSI

 

or 

 

1.5CUP-18000 (only useful at higher pressures)

[Equanimous Phil]

2 hours ago, Sagebrush Burns, SASS # 14226 said:

Here is a formula I copied some years ago - sorry, don't remember the source.

 

CONVERT CUP TO PSI

 

(1.516 X CUP) - 17,902 = PSI.
Example: 45,000 CUP X 1.516 = 68,220
68,220 - 17,902 = 50,318 PSI

 

or 

 

1.5CUP-18000 (only useful at higher pressures)

Have you read the articles linked by Sedalia Dave?

 

To quote Philip Mahin (Sierra Bullets Ballistic Technician):

"Q: Is there a standardized correlation or mathematical conversion ratio between CUP and PSI values?
Mahin: As far as I can tell (and anyone else can tell me) … there is no [standard conversion ratio or] correlation between them. An example of this is the .223 Remington cartridge that lists a MAP of 52,000 CUP / 55,000 PSI but a .308 Winchester lists a 52,000 CUP / 62,000 PSI and a 30-30 lists a 38,000 CUP / 42,000 PSI. It leaves me scratching my head also but it is what it is. The two different methods will show up in listed powder data[.]"

 

And here you come and post on a public forum safety relevant formulas you've copied somewhere somewhen from somebody on the internet.... 

[Pat Riot]

Here is an interesting excerpt from the Lyman 47th manual by a guy that says that the two can be correlated. 
 

https://www.shootingsoftware.com/ftp/psicuparticle2.pdf

 

He can keep his opinion, math and justifications. I don’t fool with things of this nature and I keep my loads recipes within the margins outlined in reliable reloading sources. The gentleman that wrote the article is definitely a lot more knowledgeable than I am, but I have a little man that rides along with me wherever I go. His name is Murphy and he has this Law…

[Equanimous Phil]

1 hour ago, Pat Riot, SASS #13748 said:

Here is an interesting excerpt from the Lyman 47th manual by a guy that says that the two can be correlated. 
 

https://www.shootingsoftware.com/ftp/psicuparticle2.pdf

 

Thanks for this interesting document.

 

Of course, the guy is right saying CUP and PSI correlate in a certain degree. But so does - just the first example that came to mind - BMI and expectancy of life. While I think the diagram below is adequate, I cannot determine someone's death by his/her BMI, despite the correlation.

 

I'd like to point out a few things in this paper:

1. He uses his belt size vs. his weight as example for correlation. He should have used belt size of different people vs. their weight as an adequate analogy. This would still correlate very well, but would also illustrate the impossibility to assign a weight based on someone's belt size.
2. I doubt somewhat the guy's conclusion on measurement uncertainty. He references the Lyman manual, p91. I don't have that manual and don't know Lyman's statement or what collection of data is printed there, so it's just my guess.
3. As I see, only data for SAAMI maximum pressures is available. Values for lower (or even higher) loads don't have to necessarily follow the same distribution and may lead to different formulas.

 

Just my thoughts...

[Equanimous Phil]

1 hour ago, Pat Riot, SASS #13748 said:

I don’t fool with things of this nature and I keep my loads recipes within the margins outlined in reliable reloading sources.

+ 10^1000000 !!!!

[Savvy Jack]

There certainly is no magic formula to convert cup to psi, nor psi to cup. Like has been said, they are two totally different measurement techniques.

If folks would care to go look at SAAMI, some loads have been tested for both cup and psi. Some, like the 44-40, have different results and some like the 45-70 and 38 Special are equal. The 38 Special shows 17,000cup and 17,000psi. This, however, does not mean they will be the same with different loads, low recoil loads to hot loads, up and down the scale. SAAMI 38 Special Data

This is what I did with the 44-40 to see if there was a way to get close for this particular cartridge only. Like the 38 Special, SAAMI lists both cup and psi results for the 44-40. As I said earlier, they are different, being 11,000psi/13,000cup. We can do basic math to get the difference which is .846. Because these are low pressure cartridges, we can do basic math to get close. The way we check for accuracy up and down the scale is to cross reference with existing load data such as from manufacture data or listed in manuals, which I did. It works out that we can safely "convert" cup to psi for 44-40 loads with reasonable confidence. Feb 1917 WRA Cartridge Engineering data published 18,000cup service pressures for their 44 Winchester High Velocity loads, not 22,000cup. With this published data we were able get a high end cross reference check for the 44-40.

Also note that my pressuretraceII results are in psi and then converted to cup and then cross referenced with existing data....green, yellow and first light shade red colored results. The blue and dark red conversion results may not be accurate.

This is NOT for load development, but only to cross reference existing loads.

I have published such results here for the 44-40, as well as here..... and even here to include pressure curve charts and animated gifs

 

but for those that dislike links.......

 

 

For an exhaustive 96 Test list, check here

[Marauder SASS #13056]

One of the problems with CUP (and LUP) is that they are essentially averages.  The pressure is measure by how much a sample of copper (or lead) is deformed at the end of the test. So you don't know of any short pressure peaks.

 

PSI can give a much more complete picture of the pressures though out the test - not instantaneous, but much closer to that.

So after the industry started using PSI gauges, they noted that some loads had much higher pressure spikes than they would have thought.  A pressure spike for a short duration will deform the copper but doesn't really measure the full shock to the chamber, barrel and gun.

So one this was discovered, many loads were reduced to reduce wear and risk.

 

When you are shooting, you can sometimes feel the difference in recoil - it is sometimes very "snappy" with higher but shorter peaks - other times it is more of a push and slightly longer duration.

[Savvy Jack]

On 6/30/2022 at 12:02 PM, Marauder SASS #13056 said:

One of the problems with CUP (and LUP) is that they are essentially averages.  The pressure is measure by how much a sample of copper (or lead) is deformed at the end of the test. So you don't know of any short pressure peaks.

 

PSI can give a much more complete picture of the pressures though out the test - not instantaneous, but much closer to that.

So after the industry started using PSI gauges, they noted that some loads had much higher pressure spikes than they would have thought.  A pressure spike for a short duration will deform the copper but doesn't really measure the full shock to the chamber, barrel and gun.

So one this was discovered, many loads were reduced to reduce wear and risk.

 

When you are shooting, you can sometimes feel the difference in recoil - it is sometimes very "snappy" with higher but shorter peaks - other times it is more of a push and slightly longer duration.

 

Very interesting information Marauder!

I never did have any "pressure spikes", per say, with any group of shots but I did notice that many were not as "even" as we would like or think they would be. Even some factory loads were a bit interesting. 

However, to add to your information, this is why SAAMI has "variations" set into the equations. It gets complicated

 

Quote

SAAMI barrels have minimum chambers and nominal bore dimensions. To mimic one, you have to get a barrel blank made to their bore cross-sectional area dimensions and then chamber it with a special reamer ground to produce the SAAMI minimum chamber diameters and not run it in past half a thousandth beyond what produces SAAMI minimum headspace. That's ±¼ of a thousandth, which can take some skill to do. Standard reamers are commonly made a little wider so they can be resharpened without losing dimensional precision. Denton Bramwell points out in the article most chambers made with standard reamers can expect to produce lower numbers.

SAAMI test barrels are fired with the cartridge manipulated to ensure the powder has fallen back over the flash hole. They are not tapped against anything to do this, as that packs the powder which can lower its burn rate a little. They want worst case highest pressure, so they just turn the case around to let the powder fall back to the rear, then load it carefully so as to avoid shifting the powder position. If you don't do that, you will get lower numbers than they do.

For rifle cartridges, SAAMI expects no more than 4% standard deviation in pressure. If your readings produce a higher SD than that, you are probably using a sample too small to be relied on to produce a good SD number. SAAMI uses ten rounds. Our own board member, Statshooter, who is a professor of statistics, says 30 rounds are needed. Denton Bramwell feels 15 rounds give him what he needs to know. So, why does SAAMI just use 10? They accept the SD results produced by 10 can be off on the high side by two standard errors (about another 2.5%), so they have a second number in addition to the MAP called the Maximum Probable Lot Mean, or MPLM, that allows the next sample of 10 from the same lot could produce a standard deviation that was different by that much. So, while the MAP is 11,000 psi, they allow they might get an average as high as 11,300 psi from another random sample of 10 from the same lot, and that is acceptable. They have a still higher number, called the Maximum Probable Sample Mean (MPSM) that allows that bullet bonding with the case and other factors can produce an increase in pressure as a lot of ammunition ages, and for the 44-40 that number is 11,700 psi. So, in effect, they are saying 11,700 psi is the safe limit, but, wait, there's more: All those numbers, the MAP, the MPLM, and the MPSM are averages produced by 10 round samples. The individual rounds making up that average will go above and below that average. SAAMI controls that by allowing what they call the Maximum Extreme Variation (MEV) which is the maximum spread between pressure readings for any of the 10 rounds in any sample taken at any time in the life of the lot. For the 44-40, the MEV is 2300 psi (this has to be calculated per the standard's instructions; it is not in a table). Theoretically, you could have aged loads centered on 11,700 psi whose 10 shots had one round as high as 13770 psi that would still be acceptable to SAAMI (though it is extremely improbable as it requires all 9 other shots to be exactly 11,470 psi). Mostly, though, you don't see individual rounds more than about ten percent above the MAP.

Even with all of that care, the fact is the absolute pressures are not exactly knowable. SAAMI reference cartridges are made in lots that are sent around to member's test facilities every two years to watch for reading changes. The members use SAAMI standard calibration methods (see the SAAMI standard) and report their results for both pressure and velocity from SAAMI standard test barrels. Interestingly, these vary more than the SAAMI standard deviation limit. The old 1992 standard gave an example for each method firing the same lots of reference loads, and the copper crushers, using targe tables for calibration, produced over 23% difference in average pressure for 10 shots among 9 labs. The transducers, using hydraulic pressure for calibration, produced over 11% difference in 10-shot averages among 7 labs. The reported results for each set of tests from each lab were, in turn, averaged and the final average was declared to be the pressure value that reference lot produced. This way, in effect, the reference lot pressure in the example was evaluated by looking at 90 and 70 total sample shots for the crusher and transducer, respectively. It compensates for average measurement calibration and operation errors, combined, to give a practical expected correct reading.

 

That approach may seem a bit tenuous, but understand the objective is to get everyone producing ammunition to the same standard, even if its absolute accuracy is not perfect. When a manufacturer wants to load a million rounds in a particular chambering, he buys a sample of a current lot of reference ammunition for that chambering and fires it in his own test equipment and compares his results to its agreed-upon rated pressure. This gives him a calibration factor for correcting his equipment's output to match the average output produced by the rest of the test labs that measured the lot. In the end, he doesn't load to the raw pressure readings his equipment provides, but to pressure readings corrected by what the reference load told him was his equipment's error factor.

So, if you wanted to compare strain gauge results to commercial equipment, one would ideally get some SAAMI reference ammunition to calibrate to. Unfortunately, reference ammunition is only sold to ammunition makers or others who can show a real need to have it. Otherwise, I think, they fear a run on it would occur that could interfere with the industry.

I notice all Hodgdon's psi-rated loads for the 44-40 exceed the SAAMI MAP, while their CUP-rated loads (in their pistol section) do not. Makes me wonder if someone confused the digits? It's still below the CIP's pressures, but those are measured on a different style of transducer (a channel transducer).

 

[Savvy Jack]

I failed to mention that it is obvious that  most loads I tested would fail the above SAAMI specs although they averaged at or below SAAMI MAP pressures.