Cups vs PSI

[wistlepig1]

Can someone tell me how to convert from one to the other. Thanks:veryconfu

[swheeler]

There is no conversion.

[KCSO]

The older books gave a rough formula but it was not exact. I think HANDLOADING in the 70's had something on this. There is no hard fast direct conversion from LUP to CUP to PSI.

[madsenshooter]

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

[wistlepig1]

Madsenshooter,

Thanks for the article, that sure clears that up for me. With data in both sure makes things tuff when trying see what a bullit of a given Brindell can take.

[Gelandangan]

strangely, on 45-70, both CUP and PSI are the same!!
so how do you convert it?

[405]

Well, the conversion formula really can't convert exactly enough, expecially when working near the maximum pressure margins. The formula will show divergence between CUP and PSI at pressures above or below about 35,000. Or put another way the only pressure range where there is convergence (CUP and PSI mean about the same thing) is near 35,000. I use caution and always re-read data... to make sure I know how it was measured.

[35remington]

You can't.

Example? Sure.

Look up the CUP rating for 308 and 270 Winchester.

Now look it up for the 307, 356, and 375 Winchester. They're very, very close or identical, depending upon which cartridge we're talking about. As in about 50-52,000 CUP for all five.

Yet the actual working pressure of the 307, 356 and 375 Winchester is nowhere close to the 308's or 270's in psi. The first three are actually closer to the 45-48Kpsi range. The 270 and 308 are 60Kpsi plus.

Try converting that! Better yet, don't bother! You'll draw entirely erroneous conclusions trying to relate them, and it's better to not go there. The "conversion formulae" are makework detail for a bored mind with nothing to do, and no purpose is served in trying to do it, as no information is gained.

It's a useless dead end.

As is that linked internet source above. He's misapplying regression analysis completely. A better research of the matter would have proven this and made writing that piece the unnecessary waste of time that it is.

I realize that was blunt, but it's bad reasoning.

[462]

I once used that formula to convert a .44 Special load from C.U.P. to P.S.I. and ended up with a negative number.

If there was a proven formula, it would be published in every reloading manual, in addition to every gun-related Internet sites.

[KYCaster]

Madsenshooter,

Thanks for the article, that sure clears that up for me. With data in both sure makes things tuff when trying see what a bullit of a given Brindell can take.



I'm far from being an authority on the subject, but even with my limited experience, I've found enough successful loads that fall well outside the rules-of-thumb and XX.X by BHN formula to believe that there's any way to accurately predict results.

If you limit your experimenting to the formula's predictions you'll miss out on some great shooting loads.

Jerry

[badgeredd]

I'm far from being an authority on the subject, but even with my limited experience, I've found enough successful loads that fall well outside the rules-of-thumb and XX.X by BHN formula to believe that there's any way to accurately predict results.

If you limit your experimenting to the formula's predictions you'll miss out on some great shooting loads.

Jerry

Jerry is totally correct. Before I knew enough about this casting thing I loaded some air cooled 22 boolits at a bit over 2500 fps...without any problem. And decent accuracy for a starting load.

Edd

[405]

Madsenshooter,

Thanks for the article, that sure clears that up for me. With data in both sure makes things tuff when trying see what a bullit of a given Brindell can take.

I'd use great caution if trying to use the formula for extrapolating data for load development. However, if you're trying to put together a minimum BHN vs Pressure table as is seen in the Lee Manual 2nd Edition pg 134 then no problem using the formula. What's the worse that could happen... inaccurate loads or a leaded bore :)

I looked at the same thing and put together a little cross reference chart.... not as a guide for load development extrapolation ... just another thing to look at as a starting point for a potential alloy (hardness) for a particular range of pressures.

CUP ------ PSI ------ BHN
31600 --- 30000 --- 23
28300 --- 25000 --- 20
25000 --- 20000 --- 16
21700 --- 15000 --- 12
18400 --- 10000 --- 8

[wistlepig1]

405,

thanks, that is just what I was going to do and you saved me the trouble.

[joeb33050]

The Lyman 47th Handbook has a table of CUP and psi values for a series of cartridges (pg. 93) and says (pg. 92) "It (the table) clearly points out that it would be an error to assume any correlation between the two test methods."
However, I found this on the Internet:

http://www.steyrscout.org/intballi.htm
"New statistical data analysis suggests that for most cartridges ANSI/SAAMI Maximum Average Piezo (PSI) and Maximum Average copper crusher (CUP) taken in a "standard" barrel can be related by the following formula which has an R^2 value (a statistical measurement of certainty) of .927.
(1.51586 * CUP) - 17902.0 = PSI
While the relationship is generally within Kpsi (it assumes that the CUP was determined using ANSI/ SAAMI standards) one should not rely on this conversion for absolute maximum loads."

The Lyman 47th Handbook table, pg. 93, shows both CUP and psi pressures for a set of cartridges. This table was developed by the Hercules Powder Co.
I applied the formula to the CUP pressures in the Lyman table and the formula worked pretty well.
The left three columns in this table duplicate the Lyman table.
"ESTIMATED PSI" shows the pressure estimated using the formula above, from the CUP values in the Lyman table.
"ESTIMATED PSI/MEASURED PSI" shows percentage values indicating how close the estimated pressure is to the measured pressure.
The largest percentage is 110.77% (estimated pressure was 110.77% of measured pressure), the smallest percentage was 87.65%, and average was 100.5%.
Given the fuzziness of chamber pressure measurements this appears to be a reasonably accurate method of converting CUP to PSI and the reverse.
Heed the warning on the Internet cite-"one should not rely on this conversion for absolute maximum loads."




MEASURED
MEASURED
ESTIMATED
ESTIMATED PSI/

CUP
PSI
PSI
MEASURED PSI
22-250 Rem
53000
62000
62439
100.71%
222 Rem
46000
50000
51828
103.66%
223 Rem
52000
55000
60923
110.77%
6MM Rem
52000
65000
60923
93.73%
243 Win
52000
60000
60923
101.54%
25-06 Rem
53000
63000
62439
99.11%
257 Roberts
45000
54000
50312
93.17%
257 Roberts +P
50000
58000
57891
99.81%
270 Win
52000
65000
60923
93.73%
7MM-08 Rem
52000
57500
60923
105.95%
7X57 Mauser
46000
51000
51828
101.62%
7MM Rem Mag
52000
61000
60923
99.87%
280 Rem
50000
60000
57891
96.49%
30 Carbine
40000
40000
42732
106.83%
30-06 Spr.
50000
60000
57891
96.49%
30-30 Win
38000
42000
39701
94.53%
300 Savage
46000
47000
51828
110.27%
300 Win Mag
54000
64000
63954
99.93%
303 British
45000
49000
50312
102.68%
308 Win
52000
60000
60923
101.54%
8X57 Mauser
37000
35000
38185
109.10%
8MM Rem Mag
54000
65000
63954
98.39%
338 Win Mag
54000
64000
63954
99.93%
35 Rem
35000
33500
35153
104.93%
45-70 Gov't.
28000
28000
24542
87.65%

From
CAST BULLETS FOR BEGINNER AND EXPERT


http://sports.groups.yahoo.com/group/CB-BOOK (http://sports.groups.yahoo.com/group/CB-BOOK)
joe b.

[Glen]

There IS a direct correlation between CUP and PSI pressure measurements, but it is not a simple linear relationship. It was studied in great detail and reported in Handloader magazine back in the 1960s. Basically, CUP and PSI are pretty much identical for pressures up to about 30,000, and then they start to deviate from one another, and the higher you go the greater the deviation is. I strongly recommend that you get a copy of "Firearms Pressure Factors" by Wolfe Press and read the original research.

[405]

405,

thanks, that is just what I was going to do and you saved me the trouble.

Glad I finally figured out what the thread was supposed to get into.
While no system is perfect I think there is merit in what Lee put together as far as minimum hardness or maximum pressure limits that affect cast bullet performance. Other variables can affect the system... like powder burn rate and acceleration of the bullet, twist rate, land/groove design, what kind of wad/filler is used, if a gas check is used or not, etc. I've found that by using a gas check on a softer bullet that should not be able to stand the pressure, I can increase the pressure/velocity a little beyond what the table would indicate.

[MtGun44]

I believe the problem is that the copper crusher system, which was the basis for
CUP measurements is affected at the upper end by the work hardening of the copper
crusher as it is compressed. If this isn't compensated for, the system would have less
deformation per 1,000 ACTUAL psi of pressure, so at a given "CUP" level the actual
true pressure would be higher, with the effect increasing as pressures increase. Copper
dramatically hardens as it is deformed, so the amount of deformation to be expected
with (true) 25,000 psi is NOT half of what you would get with (true) 50,000 psi because
the last bit of the deformation is happening when the copper is harder and stronger.

Once they got REAL pressure sensors, they now have actual pressures and this accurate
system reports different numbers than the indirect CUP system would report for the same shot.

Hope this adds to understanding rather than obfuscating the situation.

Bill

[rhead]

The CUP system is also effected by the amount of time that the pressure is above some threshold. The copper pellet can be deformed the same amount by 4 milli seconds at 14000 PSI or 1 milli second at 28000 psi. for each CUP result there will be an infinite number of PSI results that will give the same conversion, also for each PSI an infinite number of CUPs can be calculated. Both numbers are useful but are incomplete by themselves.

There is no formula for converting one to another because they measure two different things.

[felix]

Absolutely correct, Rhead. ... felix

[dakotashooter2]

The CUP system is also effected by the amount of time that the pressure is above some threshold. The copper pellet can be deformed the same amount by 4 milli seconds at 14000 PSI or 1 milli second at 28000 psi. for each CUP result there will be an infinite number of PSI results that will give the same conversion, also for each PSI an infinite number of CUPs can be calculated. Both numbers are useful but are incomplete by themselves.

There is no formula for converting one to another because they measure two different things.

That is the understanding I had. One always has to consider the duration of pressure. In effect CUP will often allow for higher pressures provided they are short term but if one doesn't account for the duration of pressure when using PSI the interpretation could result in excess pressure even though the max pressure measured is the same.

Kind of like whether a 250 lb guy sits on your chest for 30 seconds or 5 minutes. it's only 250# but the results may be vastly different.

[felix]

Exactly!!! The piezo is more transient and also more linear in response, no doubt, but all these transducers have to be calibrated to some sort of standard to eliminate any bias. For example: in the piezo situation, the barrel thickness in itself is a shield and will slow (skew) the response. That means each gun has unique characteristics whereas the crusher method picks up its energy directly through an open port eliminating barrel distortion. The copper in itself will slow the response, however. ... felix

[jmf85718]

This is NOT a perfict conversion but is the closest I have found. Convert CUP to PSI:: -17,902 + (1.516 X CUP) = PSI
( if CUP is 46,000 X 1.516 - 17,902 = PSI or 51,834)

To convert PSI to CUP:: PSI + 17,902 ./. 1.516
(if PSI is 51,834 + 17,902 = 69736 ./. 1.516 = 46,000 CUP

Hope this helps - it helped me - JMF Tucson, AZ.

[sundog]

Methinks one plays with fire (pun intended) when trying to find a link between these measurements...

[Larry Gibson]

There IS a direct correlation between CUP and PSI pressure measurements, but it is not a simple linear relationship. It was studied in great detail and reported in Handloader magazine back in the 1960s. Basically, CUP and PSI are pretty much identical for pressures up to about 30,000, and then they start to deviate from one another, and the higher you go the greater the deviation is. I strongly recommend that you get a copy of "Firearms Pressure Factors" by Wolfe Press and read the original research.

This basically correct as it applies to CUP measurement of the maximum peak pressure (that is all that CUP measures) vs peizo-elctric measurements. Bear in mind that there are also various methods of peizo-electiric measurements. A lot of older "PSI" figures were actually based on CUP measurements but reported as PSI.

rhead is correct; "The CUP system is also effected by the amount of time that the pressure is above some threshold. The copper pellet can be deformed the same amount by 4 milli seconds at 14000 PSI or 1 milli second at 28000 psi. for each CUP result there will be an infinite number of PSI results that will give the same conversion, also for each PSI an infinite number of CUPs can be calculated. Both numbers are useful but are incomplete by themselves.

There is no formula for converting one to another because they measure two different things."

The formaul jmf85718 mentions works fairly well but only in the middle 1/3 of cartridge pressure ranges. The lower pressured cartridges can give negative PSIs as mentioned and the higher pressure cartridges get too close together with the results because the constant (17,902 ) does not change.

Based on my experience measuring pressures of a multitude of different loads in 17 different cartridges in 23 different firearms with a peizo-electirc system leads me to add that sundogs statement; "Methinks one plays with fire (pun intended) when trying to find a link between these measurements..." is a very wise one.

Larry Gibson