C.U.P. Mathematical Calculation

Bohica793

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I want to be able to calculate the approximate CUP value for hand loads based on caliber, bullet type and weight, COL, powder type and charge weight. Does anyone know the mathematical formula for accomplishing this?
 
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I want to be able to calculate the approximate CUP value for hand loads based on caliber, bullet type and weight, COL, powder type and charge weight. Does anyone know the mathematical formula for accomplishing this?

I wrote up a recent thread where I found that guy had worked out a mathematical CORRELATION to convert the two. If I could find it and find out how I'd link you to it.

People treated it like a rattlesnake because there IS NO true conversion between the two. The formula will give you an idea of the pressure range but no reloading can depend on it.
If I can find it I'll put it up here.


Update: Here is the link. Again, IT IS NOT TO BE USED AS DATA FOR RELOADING.

http://www.shootingsoftware.com/ftp/psicuparticle2.pdf

The writer is pretty complete in his methods and explanations, but the formula is buried in the text and doesn't jump out at you. He also makes the point that all calibers don't fit his formula.
 
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I want to be able to calculate the approximate CUP value for hand loads based on caliber, bullet type and weight, COL, powder type and charge weight. Does anyone know the mathematical formula for accomplishing this?

The measurement "copper units of pressure" is based on a measurement of the length of a copper cylinder after it is crushed in a fixture in a test barrel. This measurement is then compared to a table supplied by the manufacturer of the cylinder. From this table comes the pressure in CUP. There is no mathematical formula that I know of to obtain CUP pressure.

Sorry, but I'm afraid you're out of luck.
 
Theoretical measurement that doesn't replace common sense and an understanding of pressure signs. Learn the differences in appearance between a primer fired at normal specs, a cratered primer and a pierced primer. Understand what the appearance of powder smudges on fired cartridge cases means. Clearly understand the differences between rifle and pistol cartridges. After all that, then worry about CUP numbers.
 
Theoretical measurement that doesn't replace common sense and an understanding of pressure signs. Learn the differences in appearance between a primer fired at normal specs, a cratered primer and a pierced primer. Understand what the appearance of powder smudges on fired cartridge cases means. Clearly understand the differences between rifle and pistol cartridges. After all that, then worry about CUP numbers.

I completely understand all of these things. What I am interested in is having some idea of what things may possibly happen prior to having to experience the actual physical pressure symptoms. The modeling of pressures, stresses and failure points has been a practice of engineering forever. It is a poor engineer who builds something without a solid idea of what and where the structural weaknesses are and what is the theoretical breaking point.
 
The measurement "copper units of pressure" is based on a measurement of the length of a copper cylinder after it is crushed in a fixture in a test barrel. This measurement is then compared to a table supplied by the manufacturer of the cylinder. From this table comes the pressure in CUP. There is no mathematical formula that I know of to obtain CUP pressure.

Sorry, but I'm afraid you're out of luck.


If this were the case, we would never have been able to put a man in space or have airplanes as we would never have been able to calculate potential stresses and pressures that would have been exerted on the airframes in flight. You can calculated air pressure, water pressure, hydraulic pressure.....why not CUP?
 
If this were the case, we would never have been able to put a man in space or have airplanes as we would never have been able to calculate potential stresses and pressures that would have been exerted on the airframes in flight. You can calculated air pressure, water pressure, hydraulic pressure.....why not CUP?

Actually, we build wind tunnel models known as "loads models", which are instrumented with several hundred pressure taps. The model is tested in a wind tunnel(s), and the data are used to obtain a pressure distribution on the model surface. The loads are then extrapolated to full-scale and the airframe is designed using these loads. We still build loads models today but there are other techniques, such as pressure sensitive paints, that can map the entire surface pressure, not just discrete points as is done with pressure taps.
 
Since the CUP reading varied from lot to lot of copper pellets and said manufacturer had to provide a correlation value for calculations, the resultant pressure reading could vary just by using a different batch of pellets.

Converting CUP to PSI is also another waste of time many have tried without much success. The two mentioned seem to be able to get ballpark estimates for rifles but don't work for pistols or some small rifle cases, so there are flaws in the method I for one wouldn't want to take a chance on.

You could compile a bunch of min & max reading from all the published manuals to get a general idea of what specific powder charges & bullet weights produced for selected cartridges in typical guns or lab test equipment over time but you would not be able to apply that to your own field testing.

I'd say if you want to know that info, go buy one of the RSI pressure test setups and save yourself a lot of time and guesswork.
 
Bohica
you may get some clues in an article titled "Chamber Pressure Revelations" that Terry Weiland wrote in Handloader magazine December 2012 [hl281full]. The article discusses a series written by Lloyd E. Brownell, PhD and included his "General Equation".

I too have some curiosity on this subject and it has lead me to reading about internal ballistics. Its very complex - but interesting - and then that lead me to what ChuckS1 suggested.
I'm still reading about pressure curves, etc. but found it prudent to also study observable pressure signs. Sorta thinking like a doctor first - before thinking like an engineer.
 
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One good reason

If this were the case, we would never have been able to put a man in space or have airplanes as we would never have been able to calculate potential stresses and pressures that would have been exerted on the airframes in flight. You can calculated air pressure, water pressure, hydraulic pressure.....why not CUP?

A piezo pressure transducer like they use in ballistics testing measures the pressure at an instantaneous time. The copper unit crushes before, during and after the the peak of pressure but doesn't tell you WHERE that peak is.

The results cannot be precisely matched up point for point, so there is no direct conversion.

However, if the results are linearized by a math process, then an APPROXIMATE correlation (not a conversion) gives an estimate of equal pressures.

That''s the point of the link I put in my post.

Another area where there is no correlation between points is viscosity of liquids because the methods of testing are too different and different types of shear give different readings and you can't convert between all units of viscosity.
 
It is a poor engineer who builds something without a solid idea of what and where the structural weaknesses are and what is the theoretical breaking point.

The answer: A current reloading manual:D. All the details are taken care of with sufficient precision. Sometimes it is as simple as read the book and follow the instructions.

This is even covered by a military engineering specification: MIL-TFP-41c.

You are welcome. :)
 
I'm old fashioned, when I started reloading all the pressure data was given in CUP. When they started changing over to the transducer method and PSI my mind would lock up and reject these new pressure readings.
(its the old dog and new trick thing)

Download the link below and all standard rifle and pistol ammunition pressures are given in both CUP and Transducer PSI.(I use this SAAMI data to cross reference CUP and PSI pressure data)

http://www.saami.org/specifications_and_information/publications/download/205.pdf

Below military pressure requirements for 5.56MM, BALL, M193 ammunition given in CUP and PSI.

And this is "WHY" so many people think there is 10,000 psi difference between the .308 and 7.62x51 because TM43-0001-27 list both pressures as PSI (this is because both methods are "STILL" pounds per square inch)

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.

What even adds more confusion is when NATO EPVAT pressure testing standards are used based on European CIP standards and pressures are measured at the case mouth increasing the reading further. (higher than American SAAMI CUP and tranducer PSI readings for the same exact pressure)

NOTE: European cup sizes are in centimeters and will give Americans a false measurement reading.
(and much smaller handfuls) :eek:
 
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I've looked at Powley which is why I believe the formula actually exists, but without his source code it remains a mystery.

Powley Computer

The javascript formulae are viewable in the page source code.
Most browsers will let you view this.
In Firefox it's: Tools/Web Developer/Page Source.

These are very old formulae and that page has a limited number of options.
If you want the most comprehensive internal calculator, use the
other one you pasted (although it's readouts are all in PSI).

quickload quicktarget software

I am thinking about getting this just to play with and see what
effects the reduced volumes of 445 brass made from rifle rounds have
compared to the commercial stuff.

To read an example of how it can be used to develop a new load,
read Jim Taylor's articles on the 480 Achilles at:

Jim Taylor's articles of leverguns, the cartridges, the nostalgi & campfire stories of hunting ,handloading

Internal ballistics is a fascinating and complicated topic. It can
also be frustrating to try and master all the inter-related formulae
folks come up with. I know I never have :)

---
Nemo
 
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