When SAAMI established the MAP (Maximum Average Pressure) for the new Transducer method they did so cartridge by cartridge using established standard ammo (regular and proof) that was measure both with the CUP system and the new Transducer system. They did measurements over as many CUP test barrels as they could get their hands on and then similarly as many Transducer barrels as they could and used that actual data specific to each cartridge to establish the new Transducer MAP. Sometimes they even went so far as to create special test barrels with both methods integrated into them to make conditions as close to the same as they could to help improve the data. This was done for each cartridge that received a new Transducer MAP limit directly with no conversions or empirical fitting.
So coming back to the formula that Denton shares in his first post. Being bored I went through the SAAMI documents and grab the MAP for every rifle and pistol cartridge that had both a CUP MAP and a Transducer PSI MAP established. I then ran the CUP MAP into Denton's formula (KPSI = 14.39 + .01716*KCUP^2) and looked at the error between the established Transducer MAP and what Denton's formula predicts. I got an average absolute error of 7.8% over the 72 cartridges I looked at. At first blush that seems decent. The scary thing is the outliers.
On the low side it predicted as much as 20% below the SAAMI Spec for 25 Auto that is 18,000 CUP vs 25,000 PSI but the formula predicts only 19,900 PSI. 257 Robers and 470 Nitro Express were two other notably low prediction of 9% and 13.6% respectively.
The scarier part is on the high side that could lead to an over pressure situations. 44-40 is 13,000 CUP vs 11,000 PSI but the formula predicts 17,300 PSI That is a scary 57% over pressure. That is substantially higher than Max PROOF pressure. But I could be persuaded to throw it out as it's an odd-ball super low pressure cartridge. But the formula does almost as bad with 357 Magnum cartridges and higher than I would be comfortable with in several other cartridges.
357 Mag 40.4% (That is proof pressure levels of over prediction)
7.62x39 27.3%
45 Colt 26.8% (everyone runs this hot so who cares
)
218 Bee 19.6%
38S&W 19.2%
41 Rem Mag 16.2%
44 Rem Mag 16.2%
Of the 72 cartridges I looked at the formula over predicts 16 by 10% or more, and under predicts 5 by 10% or more.
So I will ask if you have an old cartridge and old data for that cartridge that only has a CUP pressure data how will you know if the above formula is going to over or under predict a PSI pressure limit compared to what it would be if you had done the testing properly using test barrels with both methods and standard ammo? The formula over predicts cartridges spanning low to high pressure and both straight wall and bottle neck cartridges. I don't see how you would trust that formula since there is no way to know if it is going to over or under predict and by how much. IMHO the CUP method and the Traducer methods are too different to trust any type of empirically fit function for conversions. It's an interesting endeavor to try and might have some limited utility but please keep in mind the potential error such CUP to PSI formula unavoidable are going to include.
-rambling