CUP to PSI Calculation???
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PSI and CUP do not share a mathematical relationship that we know of so it cant be converted from one to the other. Both numbers are usually close but they represent 2 very different way of reading pressure. The CUP use a perforated chamber and a plunger that crush a copper pellet (hence the name Copper Unit Pressure) and the amount the pellet is crushed will be proportional to a number on a scale. The PSI on the other hand is a direct reading of chamber pressure. Interestingly, there was another scale used for shotguns and some other lower pressure application called the Lead unit pressure that, obviously, used a lead pellet instead of a copper one. One may wonder why it is that we cannot convert from one scale to the other. To this question I sadly cannot offer a definitive answer. However, it has something to do with the way material deform under stress being non-linear.
Hope that help
Hope that help
Download the SAAMI "Voluntary industry performance standards for pressure and velocity of centerfire commercial ammunition".
It contains the pressures of all SAAMI cartridges in CUP and PSI.
Milspec standards for M193 ammunition
MIL-C-9963F
15 October 1976
SUPERSEDING
MIL-C-9963E
12 May 1970
MILITARY SPECIFICATION
CARTRIDGE, 5.56MM, BALL, M193
3.7 Chamber pressure.
3.7.1 Measurement by copper-crush cylinder.-The average chamber pressure of the sample cartridges, conditioned at 70° ± 2°F, shall not exceed 52,000 pounds per square inch (PSI). The average chamber pressure plus three standard deviations of chamber pressure shall not exceed 58,000 PSI.
3.7.2 Measurement by piezoelectric transducer.-The average chamber
pressure of the sample cartridges, conditioned at 70° ± 2°F, shall not
exceed 55,000 PSI. The average chamber pressure plus three standard
deviations of chamber pressure shall not exceed 61,000 PSI.
It contains the pressures of all SAAMI cartridges in CUP and PSI.
Milspec standards for M193 ammunition
MIL-C-9963F
15 October 1976
SUPERSEDING
MIL-C-9963E
12 May 1970
MILITARY SPECIFICATION
CARTRIDGE, 5.56MM, BALL, M193
3.7 Chamber pressure.
3.7.1 Measurement by copper-crush cylinder.-The average chamber pressure of the sample cartridges, conditioned at 70° ± 2°F, shall not exceed 52,000 pounds per square inch (PSI). The average chamber pressure plus three standard deviations of chamber pressure shall not exceed 58,000 PSI.
3.7.2 Measurement by piezoelectric transducer.-The average chamber
pressure of the sample cartridges, conditioned at 70° ± 2°F, shall not
exceed 55,000 PSI. The average chamber pressure plus three standard
deviations of chamber pressure shall not exceed 61,000 PSI.
The Denton Bramwell equation for SAAMI pressure is:
PSI = (1.51586 x CUP) - 17902.0
Which can be rearranged to solve for CUP using PSI as:
CUP = (PSI + 17902.0) / 1.51586
The R^2 value is .927 based on his calculations.
R^2 (R-squared) values are between 0 and 1 and the closer it is to 1 the more statistically true the equation can be considered to be.
It isn't a perfect correlation but at 92.7% it's hard to say the equation isn't roughly true.
I only use this equation for my own curiosity, not for anything that could actually cause safety concerns. It also uses the SAAMI method of pressure measuring which gives different results than the CIP method or NATO method.
The equation he calculated for CIP pressure measurements is:
PSI = (1.20911 x CUP) - 2806.88
or
CUP = (PSI + 2806.88) / 1.20911
This equation had an R^2 value of .997 so could be said to be more statistically true than the one for SAAMI pressures.
PSI = (1.51586 x CUP) - 17902.0
Which can be rearranged to solve for CUP using PSI as:
CUP = (PSI + 17902.0) / 1.51586
The R^2 value is .927 based on his calculations.
R^2 (R-squared) values are between 0 and 1 and the closer it is to 1 the more statistically true the equation can be considered to be.
It isn't a perfect correlation but at 92.7% it's hard to say the equation isn't roughly true.
I only use this equation for my own curiosity, not for anything that could actually cause safety concerns. It also uses the SAAMI method of pressure measuring which gives different results than the CIP method or NATO method.
The equation he calculated for CIP pressure measurements is:
PSI = (1.20911 x CUP) - 2806.88
or
CUP = (PSI + 2806.88) / 1.20911
This equation had an R^2 value of .997 so could be said to be more statistically true than the one for SAAMI pressures.
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I used to work in the CIL ammunition R & D lab. Did a bazzillion pressure tests. The pressure readings are taken at different places in some calibers. That is, for one reading the pressure might be at the shoulder of the case and for the other system it might be in front of the case mouth.
For some calibers the place of reading is the same and the specs are the same.
It might be possible to have a conversion formula for a given caliber, the formula would tend to be different for other calibers.
Before transducer readings (in psi) became common, it was not unusual for CUP values to be referred to as "PSI". This really tends to screw up the universe. Military specs for 7.62 referred to "PSI", when in fact they measured in CUP. Since 308Win limits are in PSI, this created then impression that 308 and 7.62 had different pressure limits, when in fact they are about the same.
Ganderite, pressure is measured in PSI here in the U.S. when we switched from copper units pressure (psi) we went to the transducer method (psi) ALL pressures are pounds per square inch but we have two methods for measuring pressure. We call the old method "cup" and the new method "psi" BUT both are still "pounds per square inch"
Now read what I posted before from a military specification. (52,000 cup = 55,000 psi and both are the same pressure)
MIL-C-9963F
15 October 1976
SUPERSEDING
MIL-C-9963E
12 May 1970
MILITARY SPECIFICATION
CARTRIDGE, 5.56MM, BALL, M193
3.7 Chamber pressure.
3.7.1 Measurement by copper-crush cylinder.-The average chamber
pressure of the sample cartridges, conditioned at 70° ± 2°F, shall not
exceed 52,000 pounds per square inch (PSI).
The average chamber pressure plus three standard deviations of
chamber pressure shall not exceed 58,000 PSI.
3.7.2 Measurement by piezoelectric transducer.-The average chamber
pressure of the sample cartridges, conditioned at 70° ± 2°F, shall not
exceed 55,000 PSI. The average chamber pressure plus three standard
deviations of chamber pressure shall not exceed 61,000 PSI.
The above pressures are "NOT" the NATO EPVAT testing method which is the European CIP method where the pressure is mesured at the case mouth. NATO EPVAT pressure for the same cartridges above would be 62,000 psi and again it would be the same pressure just measured another way.
I made the tire pressure joke below and said the following about 7.62 and .308 chamber pressures.
As you can see below it is safe to put 32 psi in your tires but if you put 220 kPa in your tires they will blow up and kill everyone in a 300 radius.
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And why the reason for measuring different chamberings at different placements, intentionally to screw with data comparisons ?
And that's an interesting mention of .308 and 7.62. Does the same go for .556 and .223, are the actual pressures the same if measured at the same location?
And that's an interesting mention of .308 and 7.62. Does the same go for .556 and .223, are the actual pressures the same if measured at the same location?
Ah, so when a pressure is listed as "50,000 CUP" it should be read as "50,000 psi by the CUP method".
Yet when it is listed as "50,000 psi" it should be read as "50,000 psi by piezoelectric method".
bigedp51, for a second there I thought you where saying 52,000 psi = 55,000 psi regardless of method which sounded crazy.
I always assumed CUP was some old, wonky, unit of measurement.
Yet when it is listed as "50,000 psi" it should be read as "50,000 psi by piezoelectric method".
bigedp51, for a second there I thought you where saying 52,000 psi = 55,000 psi regardless of method which sounded crazy.
I always assumed CUP was some old, wonky, unit of measurement.
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The .223 and 5.56 are loaded to the exact same chamber pressures, the only difference is the military throat is longer than the recommended SAAMI throat.
When the ammunition is shot in their corresponding chambers the pressures are equal, if military ammunition is fired in a commercial SAAMI chamber the pressure will be approximately 4,000 psi higher.
Now welcome the the real world, my Savage bolt action .223 has a longer throat than my two AR15 rifles do.
HOLLIGER ON .223/5.56 CHAMBERS
http://www.radomski.us/njhp/cart_tech.htm
More chamber and throat variations.
I was pressuring Savage to switch from 1:12 to 1:7, so they would have a market advantage with heavy bullets that had been introduced. They turned down 1:7, but went with 1:8. I suggested the Wylde chamber, since that is what I used. They decided to keep it simple, and went with a 223 chamber and a throat more like NATO.
I have not looked at the market, but I doubt that any commercial maker today would use a SAAMI throat, just for liability reasons. I assume they all use some kind of longer throat to accommodate heavier bullets.
As I recall, when we did CUP testing, the piston was located on the side of chamber/case. When we did transducer, it was located wherever the spec called for, but there was not a physical issue about where it had to be, like with the crusher piston. For a given caliber, the actual number for one system vs the other was usually different, even though the pressure was obviously the same.
A pressure barrel is expensive, but does not last forever. In the early 60's we would be buying a transducer barrel for a new caliber (like 264Win Mag) but kept on using crusher barrels for existing calibers until the barrel needed to be replaced. I don't recall pressure testing shotgun ammo with anything but lead crusher barrels.
By today's standards, our equipment in 1964 was antique. The chronograph was the size of two cases of ammo. It was triggered by two magnetic coils the size of basketballs. The chronograph coil also trigger an electronic flash (very fast flash) that we used to take a photo of the bullet/wad column near the muzzle. The camera was a Polaroid B&W on Bulb (open shutter, with me pushing the bulb). I would load the gun, turn off the range lights, open the shutter, pull the trigger, release the shutter, turn the lights on and record the velocity and pressure and number the Polaroid picture. Today we doe the same thing with all the data, including pressure, pressure trace, picture getting downloaded to laptop.
P51's analogy of tire pressure is a good one, or mph vs kph. Numbers are different but limits are the same.
I have not looked at the market, but I doubt that any commercial maker today would use a SAAMI throat, just for liability reasons. I assume they all use some kind of longer throat to accommodate heavier bullets.
As I recall, when we did CUP testing, the piston was located on the side of chamber/case. When we did transducer, it was located wherever the spec called for, but there was not a physical issue about where it had to be, like with the crusher piston. For a given caliber, the actual number for one system vs the other was usually different, even though the pressure was obviously the same.
A pressure barrel is expensive, but does not last forever. In the early 60's we would be buying a transducer barrel for a new caliber (like 264Win Mag) but kept on using crusher barrels for existing calibers until the barrel needed to be replaced. I don't recall pressure testing shotgun ammo with anything but lead crusher barrels.
By today's standards, our equipment in 1964 was antique. The chronograph was the size of two cases of ammo. It was triggered by two magnetic coils the size of basketballs. The chronograph coil also trigger an electronic flash (very fast flash) that we used to take a photo of the bullet/wad column near the muzzle. The camera was a Polaroid B&W on Bulb (open shutter, with me pushing the bulb). I would load the gun, turn off the range lights, open the shutter, pull the trigger, release the shutter, turn the lights on and record the velocity and pressure and number the Polaroid picture. Today we doe the same thing with all the data, including pressure, pressure trace, picture getting downloaded to laptop.
P51's analogy of tire pressure is a good one, or mph vs kph. Numbers are different but limits are the same.
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