Anyone have a conversion factor to convert cup to psi?

I dont believe there is...

...well, let's see... it's four cups to a quart... or is it 8 cups to a gallon? Wait... 8 oz to a cup... Heck, I don't know...

There is no way.

ditto...

There is no conversion .... many have tried and all have been proven wrong and flawed at some point.

To a good approximation, ANSI PSI = -17902 + 1.51 x ANSI CUP.



(sigh)



This almost always starts a flame war, because SAAMI put out some incorrect information several years ago, stating that PSI and CUP are not correlated, and cannot be converted from one to the other. This is manifestly incorrect, because regression of a few dozen points where both numbers are known produces an R^2 of .927. Once that result is obtained, it is impossible to successfully argue that they are not correlated or convertible.



CIP, the European equivalent of SAAMI, does this all the time. They take their data in one system, and use a formula similar to the one shown, to create the second set of data. They do not perform both measurements.



Dr. Lloyd Brownell, U of Michigan, who did a landmark set of articles on pressure, published a graph that does the same thing as the formula. It's on page 35 of his work. I stumbled across that a couple of months ago, and it was nice to find that someone else had gotten there before me, and had reached the same conclusion.



Now, it is true that the formula does not provide an exact conversion. That is because when you touch off a cartridge, you will never know how much pressure actually happened in the chamber. Both the piezoelectric and the copper crusher method have considerable random error in them. Even if the conversion formula were perfect, which it is not, individual data points would fall up to a few thousand PSI above or below the expected value, just because of random error in the measurement system.

Thanks for the info.

denton,

Could you point to that piece of work, I really would like to read it and find out what underlying tests and methods were used..

I still have my douts and am hoping to educate myself here.

Pick...

You have a private mail.

denton, could you please share with us the name of that report by Brownell? I've read reference to his works on other sites. Via google, I see he was a prof. at U. MI's chemistry dept. at least back to the 1960s. I didn't look too much further. Thanks,

Karl

these are just restatements to make this a little more rational

to express in a more common layout
PSI=1.51Cup - 17092

so, to solve for CUP
cup = (17902+psi)/1.51

right?

I'm pretty distrustful of the validity of the formula. I've seen published tables of CUP vs. PSI for standard loads in various calibers and noted wide differences in the relationship from one cartridge to another. I've guessed the error was in the copper crusher method, which is fine for comparative data but not very precise for absolute pressures. Probably influenced by the rate of pressure rise and the duration of near-maximum pressure, as the piston's moving as the copper "crusher" collapses. I think there'd be issues of variability of copper's malleability in sudden vs. slow deformation as well. Dunno about all that. But I do know that the CUP method was problematic enough for the major ammo factories and load data developers to discard it 30 years ago.

Tha name of the report is "Firearms Pressure Factors". It's a series of articles that started in 1967, and continued on for several years. I believe they were published as magazine articles, and later bound together as a book. I don't have the original, but a friend kindly supplied me with a Xerox of the book.

Waitaminit's link is Brownell's graph, page 35. That's excellent!! I have not checked his graph against the formula, but Brownell was a careful worker, and they are bound to be similar. I only investigated the 28K-60K PSI portion of the curve, which is pretty linear. Brownell investigated from 10-100 KPSI. As far as I know, you might as well just print and use waitaminit's curve.

Jeffeoso, I believe you have correctly inverted the formula.

Richochet, you are quite right that the CUP system is not very precise. Unfortunately, the piezo PSI data you see published is not a whole lot better, because there is a key variable SAAMI does not properly control. The good news is that if you have a few dozen data pairs, and if each data is actually the average of 10 shots, the random error "averages down" quite a bit. Net of nets, the conversion formula is quite a bit better than the data it came from, because the random noise in the measurement systems is reduced through averaging. (Did I get enough syllables in that??)

Hi denton -
Net of nets, the conversion formula is quite a bit better than the data it came from, because the random noise in the measurement systems is reduced through averaging.
I copied that and distributed it over our network here, with a request for opinions from each employee. Man, talk about getting some blank looks.

R-WEST

R-West--

Here's a physical example that some people might be able to relate to.

The ocean is full of noise, and most of it is random. How to you find the sound of a Russian sub, over all that random noise? You know about how fast the Russian is turning his propeller, and you know how many blades it has. So you set your averaging interval to correspond to the appropriate amount of time, and average over 1,000 time intervals. The random noise decreases by the square root of 1,000, and suddenly you can hear the Russian propeller.

denton - I'll give them your example this afternoon. In the meantime, maybe they'll at least think a little bit about something, instead of spending all day on the 'net like me

R-WEST

My goodness, Steve!

I used to live in Hillsboro... 1330 SE Walnut. I understand it has changed a lot since I moved in 1980.

So are you with Intel? Tektronix (my alma mater)?

Heck, at 16 bits, the dynamic range and sampling noise cease to be much of a problem in most cases...

You really want to blow R-West an crew's minds tell them about noise shaping to reduce the noise floor or absolute dynamic range due to quantizing noise from the resolution of the measument system.



-Steve

Hey denton, just out of curiosity, what's the key variable that SAAMI doesn't control?

Denton,

Shoot that's just down the road from me. I live off Brookwood. Was raised in Aloha and grew up along 185th. I know all about how this area has changed!!

I used to work at Tek. My group was aquired by my current employer, Credence Systems, 1/1/91. I've been here since...


16 bits is nothing. We're seeing 24 bit stuff (non sigma-delta). But that's all specsmanship. As you and I both know it's really ENOB where reality is at. The real problem is that sampling and output/input frequencies are so high with incredable dynamic ranges.

As far as things like jitter measurements, were looking at femto-second (10e-15) RMS specs. I think that might be where God plays.


-Steve

I think a better example is that there are WAves, valleys, winds, high and low tides, extremes to both side (north winds for low tide, hurricanes for high) and tsunami's...

but everyone knows what sealevel is...

or, to reduce this into a mathmatical formula, that you can "slam" your buddies for their blank stares

ask em if they ever heard of "least squares" for finding the point/intercept formula for a slope, or cost/bennefit, or fixed and variable costs models..

Y=mX+b.


jeffe

Thank you, "denton." As it is, that book is on my "to find" list of firearms books. I've seen references to it by Steve Faber, who built strain gauge modules for measuring pressures in barrels. I was able to locate an ISBN and publisher for the book, but no copies on the used market nor for inter-library loan. The plot supplied by "waitaminit" is interesting.

You mentioned R^2 was about 0.93. If I recall, a least squares line can look rather iffy as plotted against the data when R^2 falls below 0.98, at least that's my memory of doing such work 20+ years ago.

It seems to me that the relationship of CUP to piezo is skewed some when considering straight wall and bottleneck cases. In the former, CUP and psi usually seem to be equal, whereas with the latter, they are not. Then there's the shorter, pistol cases...

Again, thanks for the reference. I might troll the used book sellers again tonight.

Karl

asdf, I sure wish I could direct you to one of those books. I did some work for RSI/PressureTrace, and they furnished me with the copy I have. I think they are scarce as hen's teeth.



Ricochet, the key variable SAAMI does not control is barrel/chamber temperature. They meticulously control ammunition temperature, requiring it to sit for 24 hours at the test temperature, but the control on barrel temperature is really loose ("Warm up the barrel, but don't let it get too hot."). If you fire your rifle single-shot style, and load and fire as quickly as you possibly can, barrel temperature is about 2-3X as strong a variable in pressure as ammunition temperature is... at least in the tests I have run.



Steve, I know the Brookwood area well. Very pleasant area when I knew it. 15 fempto-seconds? Ummm... long enough for light to travel about half a centimeter, if my mental calculations are correct. Yeah, that qualifies as low jitter!! 24 bits is a lot of dynamic range... (OOOPS! Moving the decimal, I left out "pico" between "nano" and "fempto"... just a small matter of 3 orders of magnitude... harrummmph.... as I was saying, 15 fempto seconds is long enough for light to travel a good .00045 cm.)



jeffeoso, that's a better example that people will relate to. Sea level makes a lot of sense.



And, finally, there are situations where you'd hope for an R^2 of .999, and there are places you're really happy to get .35. If you have large samples, .35 can give you a very statistically significant result... you just haven't explained very much of the variation. The number that tends to stick in a lot of people's minds is that with 30 samples (rarely the case), an R^2 of .68 is the point where you start to figure you might have had a lucky day, instead of a real effect.

See "The Varmint Hunter Magazine", issue 46, April 2003, for an indepth explanation on this subject. You might find the author's name familiar.

Elkhntr;
There are lots of conversion charts on www.reloadbench.com !

Hope this helps!

The standard SAAMI pressure for .45 Auto Rim was long ago set at a lower level (in CUP or PSI) than the .45 ACP. I'd have to hunt around a bit to find an authoritative statement of the SAAMI .45 ACP limit in CUP, but it's close to 20,000.

Clark, I should have been more careful in my statement. I have only investigated normal operating pressures for rifles. Over the range 28 KPSI to 60 KPSI, the formula given works pretty well. Except for the link waitaminit gave, I do not know how it works beyond that range. If it happens to give a right answer in that region, it is more attributable to good luck than management.



Brownell's conversion graph covers a much broader range, enough that curvature becomes important. If you want to convert a pistol cartridge, I'd suggest you follow waitaminit's link.



Also remember that neither measurement system is very repeatable. Plus or minus a couple of thousand PSI is common, due to random measurement error. In a 60 KPSI rifle cartridge, it isn't a huge deal. In a lower pressure pistol round, it's a lot bigger issue. And you will get that much error out of BOTH the CUP and piezo systems.