Just curious, but is there a formula for converting CUP to PSI and vise-versa
-Mike

Yes and no, depending on who you want to believe. There was a thread on this in the Ask The Gruwriters section of the Campfire a while back.

Converting CUP to PSI?

There is no direct conversion between the two.

There is a highly correlated conversion between the two. The problem is the error introduced by each measurement system and anomalous outliers in the data which produces results limited by those discrepancies.

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

The European CIP has been using a similar conversion for years.

Our statistical/mathematic whiz denton almost has me convinced that he's cracked the conversion. But I ain't smart enough with cipherin' to argue it, so I have to take his word. Fortunately, denton's word is golden.

I have read that Shooting Times for September has an article on this subject by Dr. Ken Oehler, the same fellow who joined the gunwriters forum last week.

Sounds like a good question to me, why not ask him on the gunwriters forum? I might pick up a copy of this months magazine just to read it myself.

Will

No formula that I know of. I checked several of my reloading
books and they all said the same thing. DO NOT mix the 2
references and assume pressure loadings for reloading from
that. Very dangerous to do. Stick to what the manuals say.
Do not exceed mfg specs.

By happenstance I was re-reading some older reloader
magazines and ran across another warning about that too.

HandLoader Magazine
April 2004
Issue #228
pg 74
"Pressure Calculations"

"Over the last few years reloading pressure data for rifle,
handgun and shotshells has slowly switched from copper units
of pressure (cup) to pounds per square inch (psi). That has
led to confusion. There is NO correlation between the two and
no way to convert one to the other. Psi is a standard unit of
measurement, while cup is only used as a ballistic
measurement" - Allan Jones of Speer Bullets

Read what denton had to say HERE

It's a PDF file, so you could save/print it if you desired.

Good article. Lots of math involved but I understand the basis
he was putting forth. Would I still follow it? Absolutely not!
While I am not doubting his calculations per se, I will cede to
the mfgs of the guns, powder manuals, etc on this point. They
are after all the experts who built and rigorously tested their
own products.

Have never understood the desire for people who cannot be
bothered to ever read the mfg maint manuals about anything
but are more than willing to do a little "backyard" tinkering
of their own, in direct contradiction of it.

Be Safe. Play it by the established numbers. If you need to
shoot that much faster, get a more powerful rifle caliber to
do so, not try to make a volkswagon into a corvette.

HWGA <img src="/ubbthreads/images/graemlins/grin.gif" alt="" /> (Here We Go Again)

If SAAMI was right, and CUP and PSI are not convertible back and forth, then it is the first time in the history of the universe that two measurement systems that successfully measure the same thing cannot be converted to each other.

After I completed the article that has been referenced, I found that I was a few decades late. Dr. Lloyd Brownell, the U of M physics professor who published an extensive series of articles on pressure factors in Handloader in the late '60s and early 70's shows a curve for converting back and forth between PSI and CUP. So he was there first. And I believe it caused controversy then, too. But he was right. By an odd quirk of fate, he learned about strain gages at the same place, and from the same people I did: The Physical Measurements group at Tektronix.

The European equivalent of SAAMI has been converting back and forth for years.

If you'll take time to read the article, I think your questions will be answered. BTW, I made the most conservative math assumptions for the article. They work if you are converting a single pressure measurement from one system to the other. If you are converting a specification from one system to the other, the result is quite a bit more precise than what I indicated. I should probably have presented that instead, since that is the usual question.

In a few decades, the whole discussion will go away anyway. Both CUP and PSI will be regarded as quaint historical relics as we get on board with the rest of the world, and start doing our measurements in modern units.

Bottom line: If you're in the 38 CUP area, the spec conversion is good to within 1 KPSI or so. If you're out at the end of the curve, 28 CUP or 50 CUP, it's good to within about 2 KPSI. To a good approximation, for rifles, operating between 28 KPSI and 60 KPSI,

ANSI/SAAMI PSI = 1.51*ANSI/SAAMI CUP - 17,902.

Oh.. one more thing... in the article, I listed the cartridges I used, along with both their PSI and CUP ratings. I believe some of the cartridge names are wrong, but the PSI and CUP numbers match each other, which is all that matters.

Denton, I believe you would find Dr. Oehler's work in this area interesting. He references it in the current issue of "RIFLE SHOOTER", I believe. HTH, Dutch.

Denton wrote:
<The European equivalent of SAAMI has been converting back and forth for years.>

There are often wrong statements about differences between SAAMI and CIP standards.

CIP has never calculated back and forth between CUP and bars.
Within the last decade the CIP measurement method has changed from copper crusher
to piezo transducer. The gas port position has almost remained at 25 mm from breech
for rifle cartridges (for smaller cartridges and pistol calibers the distance from
breech is smaller).
Some report CIP is locating the transducer at case mouth, which was never true.
NATO and MIL standard use case mouth transducers.
The change from CUP to tranducer pressure standard has led to much confusion
by European shooters. Now the MAP for the 9 mm Luger was lowered from 2700 (CUP)bars
to 2350 bars when using a transducer. But it is the same pressure. When you put in
a tranducer barrel a reference cartridge and you get 2350 bars, the same cartridge will
read 2700 CUP using a copper crusher. This will not be an absolut value , because the
standard MAP's are rounded to the next 50 bars.

After using the new standard all pistol cartridges had "lower than CUP" figures and
almost all rifle received "higher than CUP" MAP numbers.
That's because the pistol copper cylinders have been smaller giving high readings,
and the rifle types have been bigger while giving lower readings.

There is no formula or function to convert from CUP to psi, or from CUP to bars, but
Dentons approximations might be useful then and when.

I've seldom been involved in this senseless debate, but from a great explanation eons ago on another board, I'm certain it was Ken Howell who clearly explained the reason for the conversion not being possible. My recollection is that the progression of pressure in the transducer and strain gages is linear and that of the others is the antonym of that (don't recall my college math.) In any case, the crusher method is progressive in a different sense. The proof of that is that no one has yet ever posted a published a formula that worked; they say it's there but there is no proof. That's a good reason for this debate to be very boring and useless to me. I'd sure like to see Ken weigh in!

Thank you. I'll bet I will.



Give the article a whirl. See what you think.