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Converting PSI to CUP ?
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Picture of Leo M
posted
Does any body know the factor used to convert PSI tp CUP? Thanks.
 
Posts: 188 | Location: New Brunswick, Canada | Registered: 25 May 2001Reply With Quote
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Picture of Dutch
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There isn't one. Sorry. Different measurement methods, and different for each cartridge. HTH, Dutch.
 
Posts: 4564 | Location: Idaho Falls, ID, USA | Registered: 21 September 2000Reply With Quote
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Picture of R-WEST
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Dutch and Leo -
In response to a post by me earlier regarding PSI/CUP, I received an e-mail with an ANSI PSI/CUP conversion chart. I can't figure out how to post it in here, but, if you're interested, shoot me an e-mail and I'll send it to you.

R-WEST

 
Posts: 1483 | Location: Windber, PA | Registered: 24 January 2001Reply With Quote
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I previously posted the formula for converting CUP to PSI. Here is the reverse formula, for PSI to CUP--

CUP = 14395 + .612 x PSI

Both measurement systems attempt to measure the same thing: peak chamber pressure. Both have substantial random measurement error. For that reason, the conversion cannot be completely precise, since the errors in both measurement systems show up in the formula.

Someone who should have known better published a statement a long time ago that you cannot convert from one to the other. This notion is wrong, a situation for which I assume no responsibility whatsoever. For the math minded, the alpha risk on the regression is .000 and the R^2 is .927. Arguing against them being correlated, and connected by a formula is like arguing against 2 + 2 = 4.

All that said, you do have to be careful with the formula. Random errors in both measurement systems are at work, and they are substantial. The standard deviation of the total error is around 2,000 CUP, or 3,000 PSI, so the formula will get you within 6,000 PSI (2 standard deviations) about 95% of the time.

Don't feel TOO bad about the error--neither measurement system is very precise. The fact that most of us still have both eyes and all our fingers is more a tribute to conservative gun design that to either system.

 
Posts: 2281 | Location: Layton, UT USA | Registered: 09 February 2001Reply With Quote
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Picture of Dutch
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Denton, I disagree on a couple of points. First, a copper crusher measuring CUP is a measure of total pressure, and an approximation of peak pressure. The shape of the pressure curve impacts the CUP measurement, not just the peak. When done by Piezo or even strain gauge, the PSI measurement still has both accuracy and precision problems, but it is much, much closer measurement of Peak pressure. Indeed, both meassurement methods can not only closely estimate true peak pressure, they can closely estimate the pressure curve.

For that reason, simply running a least squares regression on the two columns shows some correlation. The model shows there is considerable unexplained variation. If we would include some other things in the model, specifically burning rate of the powder, or perhaps bullet sectional density, the model would have a much higher R value. JMO, Dutch.

 
Posts: 4564 | Location: Idaho Falls, ID, USA | Registered: 21 September 2000Reply With Quote
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Picture of ricciardelli
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http://stevespages.com/crusher.html

------------------
http://stevespages.com/page8.htm

[This message has been edited by ricciardelli (edited 02-27-2002).]

 
Posts: 3282 | Location: Saint Marie, Montana | Registered: 22 May 2002Reply With Quote
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Peak pressure is what breaks guns.

Both the piezo system and the crusher system are used to estimate the maximum safe load, which is determined by peak pressure. The purpose of both systems is to estimate peak pressure.

The crusher system is, indeed, influenced by non-peak pressure. That is part of its measurement error.

The piezo system works. The crusher system works. Any two measurement systems that work and that measure the same thing are always convertible from one to the other. The correlation can be found because fundamental mathematics requires it to exist in this case. It is not accidental, or a by-product.

The regression study finds the conversion formula, and, through analysis of residuals, lets you estimate the precision of the conversion. The conversion between PSI and CUP is not extremely precise, partly because both systems have a large amount of random variation. The combined random error of both measurement systems is present in the regression.

In a couple of months, I will have the data to compare the relative precision of the strain gauge, piezoelectric, crusher, and head case expansion methods of testing peak pressure, and I'll post the results here.

 
Posts: 2281 | Location: Layton, UT USA | Registered: 09 February 2001Reply With Quote
<Mats>
posted
quote:
Originally posted by denton:
Peak pressure is what breaks guns.

I disagree, to a point. Though a high peak pressure can be found in detonation occurences that indeed destroys guns, it is normally a sign of high average pressure. It is not the nine millionth straw that breaks the donkey's back, it is the whole load...

Coupled to the fact that metal fatigue accumulates over time - I'd say you're wrong.

-- Mats

 
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Mats...

So you're saying that if a firearm survives the peak pressure, the lower pressure that follows is likely to destroy it?

 
Posts: 2281 | Location: Layton, UT USA | Registered: 09 February 2001Reply With Quote
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Denton, I'm new to this forum. I found this thread interesting. It has been a while since I've used algebra but I wondered if something is amiss with this math:
CUP=14395+.612xPSI
subtract14395 from both sides
CUP-14395=.612xPSI
divide both sides by .612
CUP-14395=PSI
_________
.612


On 2-24-02 you posted PSI=-17902+1.51xCUP
using the same process for this equation gives CUP=PSI+17902
_________
1.51
What is the mistake? One of your equations or with my conversions. Thanks! This is a great site

 
Posts: 267 | Location: Tampa | Registered: 01 March 2002Reply With Quote
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lonniemike--

Dang good question! I had to scratch my head for a minute. You would expect that the formulas could be converted from one to the other. They do convert to a close approximation, but not exactly.

The lengthy explanation has to do with how regression works. It tries to minimize sum of the squared distances from the regression line (the graph of the formula) to each of the data points. The horizontal distance from each point to the line is not the same as the vertical distance, so when you turn the graph 90 degrees (swap PSI and CUP), it is trying to minimize a different set of distances, and will come up with a slightly different estimate of where the line is.

I ran a set of numbers through the PSI to CUP conversion, then converted them back, using the CUP to PSI conversion. The answers were within 1,000 PSI, which is within the accuracy I indicated. So it's not your math, it's the way the regression thing works. The conversions are approximate, not exact.

Mats, Dutch, sorry if I sound a little cranky. Actual fact is that I am a little cranky these days, but I will try to do better.

 
Posts: 2281 | Location: Layton, UT USA | Registered: 09 February 2001Reply With Quote
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Peak pressure for one pica second does not matter to me and my gun.

What does matter to my gun?
1) The primer piercing
2) the bolt sticking
3) the case blowing
4) the gun blowing up

In measured powder work ups for 22 calibers, most of the guns I tested do not blow up*.

When I read a load book, I want a starting point. They can use psi, cup, cip, or just plain old try it and see, and give me a place to start. I want that place to start to be somewhere between where the bullet sticks in the barrel on the lower end, and results 1), 2), 3), and 4) on the higher end.

I will then find the load I like.

This forum is on reloading. Presumably for one's own gun.
If were loading for someone else's gun, my system would not work.

As an example of what does matter to me, in 357 mag, the primer will give out with H110 powder in a work up [lower peak pressure integrated over a longer time]. With Bullseye, the cases will stick [higher pressure integrated over a shorter time. I don't care if the is 10 cup or 1,000,000,000 psi. I don't care if that is r.m.s averaged over 10 milliseconds. It does not matter to me. There is no way some one else with test equipment one can measure when my primer will top hat as accurately as it can be measured with my primer.

The load book fundamentalism one reads in handloading forums reminds me of my Sunday school days. We were told that dancing was sinful because it might lead to fornication. Later in confirmation, we were told that married couples making love standing up is sinful, because it looks too much like dancing. So we have a pressure measurement system to prevent primer piercing. But we can't test for primer piercing because that might lead to pressure.

* Some guns did blow up in my testing: CZ52 spilt barrels and slides, antique breaktop revolvers stretch the eye of the latch, an Aluminum frame 38 special stretched its frame.

[This message has been edited by Clark (edited 03-01-2002).]

 
Posts: 2249 | Registered: 27 February 2001Reply With Quote
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Steel has a fairly well defined yield point, above which it definitely permanently deforms, i.e. stays bent.

There is a region below this point where repeated stress will cause it to slowly deform over many cycles.

There is a safe operating region below that, where you can stress the steel for many, many cycles with very little change. This is the region you need to operate in if you want your gun to last.

The first sign of pressure being too high is almost never catastrophic failure of the gun, so not having a gun blow up is not evidence that a load is safe. Pressure out of the safe region usually simply wears out firearms much, much faster than pressure in the safe region. The damage inflicted is pretty much determined by peak pressure. Almost any modern firearm will tolerate a few really hot rounds. The question is, how many, and how hot?

Knowing the type of steel, and the critical dimensions, it is fairly easy to determine how much pressure the firearm will tolerate in the long term. We're all free to ignore that, and we're all free to go buy a new gun if we overstress the one we have.

 
Posts: 2281 | Location: Layton, UT USA | Registered: 09 February 2001Reply With Quote
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I hear about metal fatigue.
I can calculate the threshold of yeild.
I have not been able to idinify any modes in the gun stress that aproach yeild, and the 5 million cyles are not there either.
Never the less, I have had MANY persons in the reloading on line discussions bring up metal fatigue. So far NONE of them has been able to lead me through a calcultaton of the effects of metal fatigue in say a 38 special firing 357 mag +P+ ammo. I have tried firing 357 mag +P+ in 38 specials, but I am wearing out my hand collecting data.

I need the metal fatigue calculttion. If it s 5 million cycles, I give up.

 
Posts: 2249 | Registered: 27 February 2001Reply With Quote
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