Nice article, very thorough.
I do see one clarification that needs to be made. The comments about 52,000CUP and 62,000PSI being equal need to be qualified. They may be equal in the .308 but they are not at all equal in the general case.
It is not possible in the general case to make such statements because a PSI measurement is a true pressure measurement while a CUP measurement involves, to some extent, measuring the area under the time vs pressure curve.
It is sometimes possible to come up with reasonably accurate approximations between CUP and PSI that work within a single chambering
or within a group of chamberings that operate in similar pressure ranges and have generally similar cases
but it is NOT possible in the general case. So it might be corrrect to say that both are the same pressure in the .308 but it is not correct to make the unqualified statement that the two figures are correct.
Dr. Ken Oehler determined this from his successful efforts to derive a model which converted electronic pressure (PSI) measurements to CUP. The results were reported in an Article in Sept 2006 Shooting Times. While he managed to make the conversion, it was only possible if the entire electronically measured pressure curve was analyzed. The two figures simply do NOT contain sufficient information to allow conversion between the two in the general case.
A direct quote from Dr. Oehler:
"...there is no way to predict CUP from a peak PSI reading, and there is no way to predict a peak PSI reading from a CUP reading."
Dr. Oehler research indicated in no uncertain terms that there is no way to come up with an accurate generic conversion algorithm that converts from PSI to CUP unless you take the entire pressure curve into account.
Dr. Oehler made a point of noting that it's not even possible to say accurately that PSI will be higher than CUP. His measurements under carefully controlled conditions showed that it is definitely possible for accurate PSI readings to be lower than accurate CUP numbers. There is no accurate general rule of thumb--there can be no accurate approximation. Peak PSI can NOT be accurately converted to CUP nor can CUP be accurately converted to peak PSI.
Therefore while 52,000CUP may be equal to 62,000PSI IN THE .308
, that is not a true statement in the general case. They're not
equal like 60mph is equal to 100kph.
Formulas that claim to convert CUP to PSI should be viewed with a jaundiced eye. Oehler's research indicated that such formulas, regardless of complexity, are simply NOT possible. It's not that the formula would simply be less accurate than desired--it's that it has no hope of being correct (or even of being a reasonable approximation) in the general case.
The only way to do a general conversion was to have access to a complete pressure vs. time curve. The single numbers simply can not be converted to the other except, perhaps within a single caliber and even then probably only within a limited range of pressures.
Bramwell's article is interesting but several statements he makes are in error. For example, he asserts that the reason it has been said that a conversion shouldn't be attempted was because "they are talking about the old, incorrect use of the term PSI, not the modern, correct use of PSI from strain gauges and piezoelectric pressure meters". That assertion is obviously mere speculation, with no basis in fact when viewed in light of Dr. Oehler's quoted research results. It's not about incorrect term usage it's about fundamental differences in the two readings.
Second, his comment that correlation automatically implies that an accurate conversion formula (or even a general approximation) exists is also in error. Dr. Oehler readily acknowledged that there was a correlation but at the same time stated in no uncertain terms that there was no possible way to convert accurately between the two numbers in the general case.
Likewise, Bramwell states that measurement error is part of what has led to the confusion. Dr. Oehler had very accurate equipment available and still came to the conclusion that the two measurements could not be accurately converted back & forth.
The bottom line is that Bramwell's entire premise indicates a basic misunderstanding about the difference in the two measurement systems. The reason that they can't be converted is that one (PSI) is a single measurement figure indicating a peak value or an average peak value while the other (CUP) is dependent on the entire area under the pressure vs time curve. It is not measurement error that causes the problem, it is that the two systems work in very different ways.
I would say that Bramwell's approximation is good for, and ONLY for exactly the numbers he poked into his correlation attempt. That is, it's a reasonably decent approximation for converting between the SPECIFIC
PSI/CUP numbers he used in his data fit. At best
it's a reasonable approximation when applied to generally similar cartridges in the specific pressure range he worked with. Taking it any farther is not at all wise given Dr. Oehler's conclusive results. I would also point out that Bramwell is fairly cautious and is careful to state that his formula is not a general formula but should only be used with certain caveats. Unfortunately it seems that few people read his material carefully enough to take note of the caveats he wisely provides.
Just to put things into perspective, Dr. Oehler gained the cooperation of "one of the ammo industry labs" and worked for "the better part of a year" on the research resulting in his evaluation. In addition, he is universally considered to be an expert in the field.