The only way I know of from a formulaic view is one of those slide rule units (Powley Computer) that I believe only works with the IMR powders.
Even then , I think it's somewhat subjective.
You are referring to Copper Units of Pressure which is found by measuring a copper slug from a crusher in a pressure gun. Each batch of copper slugs had what was called a Tarrage Table which was to be used with the measurements from that particular lot of copper slugs taking into account their hardness/malleability. It only measures what is termed as peak pressure. Not the duration.
The measurement was then converted to a measurement in PSI.
In the late 60's however, an effort was made to move away from stating the results in PSI due to the confusion that would be caused in later and more wider use of the Transducer method of pressure measurement. The transducer is an electronic method of pressure measurement which it is also possible to plot the peak pressures and the duration of them in the cartridge under firing.
Someday, if someone comes out with a practical unit for the handloader to measure pressure on his own reloads, it will be a milestone.
There really is no accurate way to do it and know the exact pressures involved.
The closest I've come is with a form of pressure ring measurement but only particularly to the 444 Marlin case. It works quite well but is still in the area of an educated comparison and nothing more.
I hate to explain this, this way, but CUP and PSI are the same. CUP is just a way of getting the result. It is measured by measuring displacement of a copper plate. Unfortunately, it is non-linear and cannot really be related to true PSI. It gives a quantifiable result, but because, I might design my test different than you did, my CUP result and yours will most likely be different for the same load. That said there are standards for testing, so I believe one makers CUP test relates closely to another's, but not to a true PSI test measured with a strain gage. I think it has to do with the stress vs. strain curve being assumed linear, but it is really not exactly.
Wow, all that writing and it isn't any clearer! Sorry, but that is what all this schooling has done to me.
This is going to start just like Nathan's post, but, I hate to say it this way, but PSI and CUP are not the same thing, not by quite a lot. Nathan actually contradicts himself in the first paragraph by forst saying PSI and CUP are the same, and then a few sentences later says that one makers CUP result may relate closely to anothers result but NOT TO A TRUE PSI TEST MEASURED WITH A STRAIN GUAGE! You can't have it both ways.
Before the days of the piezo electric guages which are now used pressure was determined by using the copper crusher method. This was then expressed as PSI. When the Piezo electric method became available, it was found that in most every case the pressure which had been calculated from either the Copper (CUP) or Lead (LUP) was actually quite far from the new information. Since the strength of firearms is determined by analysis of the metal and mechanical testing it was found that much of the data determined by the crusher method actually resulted in pressures much higher than expected. This is a major reason why data in the more recent loading manuals has in many cases been revised down.
I know that this is a fun way to ask questions and share information. In many cases, this one particularly, the information is available in virtually any loading manual. The admonition to buy as many manuals as you can afford, and READ THEM, is still a very good rule.
All the above is available in any of the recent loading manuals. Do yourself a favor, when you have a question like this, go to the books for an answer.
Contender hit it on the head about the Powley Computer. This was a very useful sliderule device which calculated loads and velocities with an amazing degree of accuracy. The modern version of the Powley Computer is Wayne Blackwells "Load From a Disk".(LFD)
LFD is a computer software package which uses several easily determined variables to calculate powder charge, type, and resulting velocity and pressure. It also makes several ballistic calculations including drop, ballistic coefficient, bullet energy, drift, etc. The only shortcoming is that you need to have a computer!
It has been said many times before, but there are two items that any serious handloader needs to have. The first is a chronograph of which there are many available over a wide price range. The second is a computer with the LFD program. Once you have used either you will wonder how you ever got along without them! These will allow you to quit guessing and answer for yourself most of the questions posted.
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