CUP to PSI

[Euler]

A little while ago I was interested in comparing SAAMI specifications of different rounds, but I ran into a small problem: SAAMI lists the maximum chamber pressure for some rounds only in CUP (copper units of pressure) and many others only in PSI (pounds per square inch). Based on a PDF from 2002, the Internet seems to have decided that converting CUP to PSI goes as follows:

 

c = CUP/100
p = PSI/100
p = (1.516) c - (179.02)

 

I have more data from SAAMI that is also more recent (2015). I get a different result, which I present here in case anyone might find it useful.

 

Data (? = no corresponding psi value)

Standard	Cartridge	Max Ave Pressure (cup/100)	Max Ave Pressure (psi/100)
SAAMI Centerfire Pistol and Revolver 2015	32 S&W Long	120	150
	32 S&W	120	170
	38 S&W	130	145
	32 Short Colt	130	175
	45 Colt	140	140
	44 S&W Special	140	155
	32 ACP	150	205
	45 Auto Rim	150	?
	38 Special	170	170
	38 Special Match	170	170
	380 Auto	170	215
	45 ACP	180	210
	45 ACP Match	180	210
	25 ACP	180	250
	38 Special +P	200	200
	32 H&R Mag	210	?
	38 ACP	230	265
	30 Luger	280	280
	9mm Luger	330	350
	38 Super +P	330	365
	41 Rem Mag	400	360
	44 Mag	400	360
	45 Win Mag	400	415
	357 Mag	450	350
	221 Fireball	520	600
SAAMI Centerfire Rifle 2015	6mm Rem	520	650
	6.5x55 Swedish	460	510
	7mm Mauser	460	510
	7mm Rem Mag	520	610
	7mm STW	530	650
	7mm-08 Rem	520	610
	7x64 Brenneke	505	?
	7-30 Waters	400	450
	7.62x39	500	450
	8mm Mauser	370	350
	8mm Rem Mag	540	650
	17 Rem	520	630
	17 Fireball	460	550
	218 Bee	400	?
	22 Hornet	430	490
	22-250 Rem	530	650
	220 Swift	540	620
	222 Rem	460	500
	222 Rem Mag	500	550
	223 Rem	520	550
	225 Win	460	?
	243 Win	520	600
	25-06 Rem	530	630
	25-20 Win	280	?
	25-35 Win	370	?
	250 Savage	450	?
	257 Roberts	450	540
	257 Roberts +P	500	580
	257 Weatherby Mag	535	625
	264 Win Mag	540	640
	270 Weatherby Mag	535	625
	270 Win	520	650
	280 Rem	500	600
	284 Win	540	560
	30 Carbine	400	400
	30-06 Springfield	500	600
	30-30 Win	380	420
	30-40 Krag	400	?
	30 H&H Mag	540	580
	300 Savage	460	470
	300 Win Mag	540	640
	303 British	450	490
	307 Win	520	?
	308 Win	520	620
	32 Win Special	380	420
	32-20 Win	160	?
	338 Win Mag	540	640
	340 Weatherby Mag	535	625
	348 Win	400	?
	35 Rem	350	335
	35 Whelen	520	620
	350 Rem Mag	530	?
	356 Win	520	?
	358 Win	520	?
	375 H&H Mag	530	620
	375 Win	520	?
	38-40 Win	140	?
	38-55 Win	300	?
	416 Rem Mag	540	650
	416 Weatherby Mag	535	?
	44-40 Win	130	110
	444 Marlin	440	420
	45-70 Gov	280	280
	458 Win Mag	530	600
470 Nitro	350	410

Plotting and fitting only the data pairs:

 

 

p₁ = (1.16) c - (16.8)

p₃ = (4.83x10^-6) c³ - (3.64x10^-3) c² + (1.79) c - (27.7)

 

[EdDinIL]

It's been awhile since I've tried to wrap my brain around a statistical problem like that.  Did you calculate the R2 value for your linear plot?  The spread in values seems larger, but it's still linearish. 

 

I didn't take a close look at the charts.  Are the data points from the 2002 PDF the same as the 2015 chart you presented?  If so, then it's only the additional that are messing with the linear plot. 

[gunuser17]

The key is that CUP and PSI are measured to different scales and measure two different things and are not interchangeable.  One explanation that I have seen is that CUP uses a copper crusher that is effected by the duration of the pressure as well as the pressure itself, whereas PSI is done by an electronic transducer that takes a virtually instantaneous measurement of the highest pressure.  Put another way, since a longer duration, lower pressure pulse can crush the cylinder as much as a shorter duration, higher pressure pulse, CUP pressures frequently register lower than actual peak pressures (as measured by a transducer) by up to 20%. For example, the SAAMI maximum pressure for the 7.62×51mm is given as 52,000 psi (CUP), or 62,000 psi (430 MPa); the .45-70, on the other extreme, is listed as 28,000 in both CUP and psi (190 MPa). 

[Euler]

On 4/4/2022 at 10:55 AM, EdDinIL said:

It's been awhile since I've tried to wrap my brain around a statistical problem like that.  Did you calculate the R2 value for your linear plot?  The spread in values seems larger, but it's still linearish. 

 

I didn't take a close look at the charts.  Are the data points from the 2002 PDF the same as the 2015 chart you presented?  If so, then it's only the additional that are messing with the linear plot. 

 

I didn't calculate r² (or just r). A fit has to be pretty crappy before r gets close to 0. I also didn't compare the 2015 values to the 2002 values.

 

On 4/4/2022 at 4:49 PM, gunuser17 said:

The key is that CUP and PSI ... measure two different things and are not interchangeable.  ...

 

They're measured different ways, because the technology to measure instantaneous pressure wasn't very good not that long ago, particularly on millisecond time scales. The people trying to do it did their best, but piezoelectric transducers are definitely better instrumentation than copper rods.

[MrTriple]

On 4/4/2022 at 3:49 PM, gunuser17 said:

The key is that CUP and PSI are measured to different scales and measure two different things and are not interchangeable.  One explanation that I have seen is that CUP uses a copper crusher that is effected by the duration of the pressure as well as the pressure itself, whereas PSI is done by an electronic transducer that takes a virtually instantaneous measurement of the highest pressure.  Put another way, since a longer duration, lower pressure pulse can crush the cylinder as much as a shorter duration, higher pressure pulse, CUP pressures frequently register lower than actual peak pressures (as measured by a transducer) by up to 20%. For example, the SAAMI maximum pressure for the 7.62×51mm is given as 52,000 psi (CUP), or 62,000 psi (430 MPa); the .45-70, on the other extreme, is listed as 28,000 in both CUP and psi (190 MPa). 

I would second the fact that CUP and PSI aren't directly comparable to each other, at least according to my research on the subject. That being said, as Euler has shown here, it may be possible to examine the numbers and develop a basic means of converting them from one unit of measurement to the other. Now are they good for determining, say, the maximum pressure that a particular action can handle for a given cartridge? Maybe, maybe not, but it's interesting to see someone make an attempt at a conversion.

 

I would also add that SAAMI specs are supposedly lower for certain cartridges compared to what the CIP shows for the same cartridge, so that may be something to bear in mind; the CIP specs may be surprisingly hotter than what their American counterparts consider safe.

[RandyP]

I too have been lead to believe there is no direct correlation between CUP and PSI. When I began reloading some 14 years ago I was promised there would be no Math - lol - so I've always simply chosen to load to the MID range of powder for each caliber. I enjoy the slight benefit of the safety margin that can offer.