R-WEST

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.

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.

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http://stevespages.com/page8.htm

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

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.

quote:

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Originally posted by denton:
Peak pressure is what breaks guns.

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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

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

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

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.

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).]

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.

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