Converting CUP to PSI

[Jim Watson]

You slipped in a ringer.
A strain gauge doesn't read out the same as a piezoelectric transducer, does it?
Any of them have to be calibrated. Since the strain gauge is glued to a gun barrel, you can't get at it to calibrate by dead load or hydraulic pressure.
Can you order SAAMI calibration ammo? I've not seen it offered.

For those of us without the instrumentation, it doesn't matter whether the maximum load is given in CUP or psi, it is still the maximum and we are well advised to "work up."

 

[Reloadron]

Just reloading for any of the common cartridges? Probably no need to make the conversion. There is indeed plenty of good data available.

On that note I figure things like understanding chamber pressure and the curves or area under the curve of different powders really comes into play when we start getting into cartridge development. Yes, it really has been that long Denton.

During my career I attended no shortage of trade shows and really enjoyed time spent talking to the representatives of the company which makes the transducers used by SAAMI for their pressure testing. PCB Piezotronics were the guys and they manufacture a wide range of sensors including their Ballistic Pressure Sensors which I had the chance to drool over. Something of interest is how exactly (procedure and method) we get the numbers. Years ago I was involved in some shock testing. This was similar to CUP and closer to LUP. We made small conical lead forms. Pretty much like casting a bullet but each alloy lot was carefully controlled.Here is what we got:



The cone on the right began like the center cone. A large steel dowel was swung back like a pendulum and released. It impacted a table with a product under test. When it hit it also struck a piston of known dimensions, much like the CUP method, which smashed our lead cone. Following a strike the height of the cone was measured. When each lot of the cones was made a few samples were pulled and a weight, actual several weights were dropped on them striking an identical piston and the results all noted and compared to previous lots. They had to fall within a window.

When cartridge CUP testing was done it was done pretty much similar but a copper slug was used. However, the test procedure and method was carefully followed. We had a CUP procedure and method and our friends across the pond also had their own procedure and method, each procedure and method were well defined. We have all seen those cool pictures of cartridge cases which were used for testing. Under the newer method, on our side of the pond, we have advanced to using a piezo sensor along with a different procedure and method. Much like the older CUP procedure and newer piezo procedure differ, so does the CIP method. All of the methods yield different numbers and all of them label the result as chamber pressure. The CIP list the Max Pressure of 308 Winchester as 4150 bar which works out to 60,190.66 psi while the new SAAMI method reflects 62,000 psi. My own thinking here is different methods measuring at different points using different procedure and methods will yield different results. This is a good overview showing the points where the measurements are taken.

Again, this is just my thinking on the subject and why I tend to lean towards the side which thinks there is no direct conversion but again, I admire all of the work, number crunching and time you have in all of this.

Ron

 

[Reloadron]

You slipped in a ringer.
A strain gauge doesn't read out the same as a piezoelectric transducer, does it?
Any of them have to be calibrated. Since the strain gauge is glued to a gun barrel, you can't get at it to calibrate by dead load or hydraulic pressure.
Can you order SAAMI calibration ammo? I've not seen it offered.

For those of us without the instrumentation, it doesn't matter whether the maximum load is given in CUP or psi, it is still the maximum and we are well advised to "work up."

Hey Jim, I believe you are referencing what is called "proof ammunition". Ammunition made with very accurate controls on the powder quantity and quality for determining pressure. It is only made in small lots and carefully distributed to those doing the testing.

No, a strain gauge transducer does not measure in the same manner as a piezo crystal transducer. Just off the top a strain gauge as used in a bridge requires external excitation (voltage) where a piezo crystal transducer generates its own voltage. Using a strain gauge system presents a whole bunch more variables in the equation. However, they are much less expensive and it is a system that many shooters can afford. Yes, once glued to a barrel there is no simple calibration method.

Ron

 

[Jim Watson]

Proof ammunition is for overload testing.
Reference ammunition is for qualifying test equipment.
Two different products.

You can't likely buy reference ammo.
The Pressure Trace folks say you can get along without it if... but not if...
So you will either have an instrumental estimate or a comparison with a garden variety factory load.

 

[Reloadron]

Proof ammunition is for overload testing.
Reference ammunition is for qualifying test equipment.
Two different products.

You can't likely buy reference ammo.
The Pressure Trace folks say you can get along without it if... but not if...
So you will either have an instrumental estimate or a comparison with a garden variety factory load.

My bad, I took the definition from the PCB website, the guys making the sensors used. SAAMI clearly defines it in their glossary, "Ammunition used to qualify and/or calibrate velocity and pressure measuring systems". The word proof should have clued me in as in proof test. My read on reference ammunition was about what I mentioned, made in limited lots with limited distribution.

Ron

 

[Jim Watson]

I recall reading that careful as they are, reference ammo is not necessarily to exactly the catalog specification. So you get offset numbers for that lot of reference.

 

[denton]

You slipped in a ringer.
A strain gauge doesn't read out the same as a piezoelectric transducer, does it?
Any of them have to be calibrated. Since the strain gauge is glued to a gun barrel, you can't get at it to calibrate by dead load or hydraulic pressure.
Can you order SAAMI calibration ammo? I've not seen it offered.

For those of us without the instrumentation, it doesn't matter whether the maximum load is given in CUP or psi, it is still the maximum and we are well advised to "work up."

Strain gauges and piezoelectric sensors are indeed different critters.

The output of the strain gauge depends on its gauge factor, the applied current, the ID and OD of the chamber where the gauge is applied, and the properties of steel. All of those are easily obtained to 3 or 4 significant digits, which is more than enough.

A few years ago, Ken Oehler shared a data set from a barrel equipped with two identical strain gauge systems and two identical piezoelectric systems. What we found was the piezo and strain systems tracked each other very well. Initially, a pressure measurement technician had told Ken to use 7 KPSI to account for the adjustment for having the cartridge brass in the measurement path. Working from the strain gauge formulas, the actual adjustment is closer to 5 KPSI. Once that 2 KPSI difference was accounted for, the piezo and strain systems gave practically identical results, confirming the aforementioned calculations. We concluded that the systems are practically interchangeable for accuracy and precision.

 

[Reloadron]

Denton, have you done any experimenting with the Pressure Trace II system? This system uses a strain gauge and is much less expensive than trying to duplicate the SAAMI method and equipment. I have thought about placing a strain gauge on a barrel with less emphasis on how accurate the curve is but just a curiosity as to what the curves would look like. Based on Ken Oehler's findings I think it may be an interesting little science experiment.

Ron

 

[denton]

Yes, I've used the PressureTrace, and even contributed a little bit to the design. It's a very useful device in a few certain situations. I load for the 6.5x55 and the 7x57, which generally have loads that are far short of what a modern action will handle. When I started loading for the 243, I found large discrepancies in the loads for 100 grain bullets and used the PT to resolve which to use.

Early on, I put a gauge on a 30-06 and it was great fun to see the pressure curve.

Later, I put together my own system with dual traces, so I could see events in two places in their correct time relationship. I was also curious to see if I could replicate the fast transient pressure spikes that Brownell noted in his work. So I made my system with about 10X the bandwidth of current systems. It was a bust. There just wasn't anything to see but the plain vanilla pressure curve.

The piezo system is like opening a patient's chest and putting a manometer into his heart to measure blood pressure. The strain gauge system is like using a blood pressure cuff.

 

[Zendude]

Maybe the basic differences in the two devices for CUP and PSI is why I find such a wide variation in 38 special load data for the identical powder and bullet.

 

[Reloadron]

Yes, I've used the PressureTrace, and even contributed a little bit to the design. It's a very useful device in a few certain situations. I load for the 6.5x55 and the 7x57, which generally have loads that are far short of what a modern action will handle. When I started loading for the 243, I found large discrepancies in the loads for 100 grain bullets and used the PT to resolve which to use.

Early on, I put a gauge on a 30-06 and it was great fun to see the pressure curve.

Later, I put together my own system with dual traces, so I could see events in two places in their correct time relationship. I was also curious to see if I could replicate the fast transient pressure spikes that Brownell noted in his work. So I made my system with about 10X the bandwidth of current systems. It was a bust. There just wasn't anything to see but the plain vanilla pressure curve.

The piezo system is like opening a patient's chest and putting a manometer into his heart to measure blood pressure. The strain gauge system is like using a blood pressure cuff.

Thanks for sharing that. While I don't have Pressure Trace I have enough to try and duplicate what it does. Many years ago I did quite a bit of work with strain gauges and remnants linger around here somewhere. I had hoped to do this last summer but my wife is having some health issues which placed a dent in my range time. I have a bunch of gauges and the rest of what I need to complete a bridge, I have a strain gauge amplifier circuit and the data logger system. Not really worried as to the accuracy in pressure as I am just looking at the curves. Since I do not have any great expectations I should be happy with whatever I can plot.

Again, I want to pass along a thank you for what you have shared. Chamber pressures are just one of those things which have fascinated me over the years.

Ron

 

[ATLDave]

Common sense tells us there must be a correlation between the two. The amount of pressure created doesn't change, only the units of measurement. Kinda like the difference between Fahrenheit and Celsius. 32 degrees Fahrenheit,

No. F° and C° can be and are measuring the same thing and are measured with the same methods - they just report on a different scale.

CUP is measuring one thing as a proxy for the thing that PSI purports to measure/characterize directly, and does so with different instruments/methods. The proxy may be good enough to allow some rough conversion/prediction between the two, but it is NOT like F° and C°.

 

[denton]

Thanks for sharing that. While I don't have Pressure Trace I have enough to try and duplicate what it does. Many years ago I did quite a bit of work with strain gauges and remnants linger around here somewhere. I had hoped to do this last summer but my wife is having some health issues which placed a dent in my range time. I have a bunch of gauges and the rest of what I need to complete a bridge, I have a strain gauge amplifier circuit and the data logger system. Not really worried as to the accuracy in pressure as I am just looking at the curves. Since I do not have any great expectations I should be happy with whatever I can plot.

Again, I want to pass along a thank you for what you have shared. Chamber pressures are just one of those things which have fascinated me over the years.

Ron

That can be a fun project.

When I did my dual trace version, I put the full Wheatstone bridges on the barrel using a gauge and three hand selected resistors. Since then, I've seen full bridge gauges for around $10, and that's probably a better way to go.

If you're using one of the inexpensive digital oscilloscope front ends for a phone or tablet, it's best to keep the signal in a differential channel until you're up into the low single digit volts. It's also a good idea to use plus and minus supplies for the bridge, usually 2.5 V, and to use dual power supply for the amplifiers. The ground on a computer is really dirty, jumping up and down and cluttering the signal with noise. Staying differential helps manage both that and environmental noise, plus it fixes some potential problems with some diff amps.

Most pressure measuring equipment rolls off at about 10 KHz. More can be better, especially if you're looking for things that other systems might filter out.

There really isn't any reason you can't get accurate pressure out of such a system. You know the gauge factor, you know the applied voltage, you know the gain of your amp chain. The result you'll get will be calibrated in microstrains. Those can then be converted to PSI with just a bit of added information. If you want to do that, PM me your email address and I'll send you an article that shows how to do that.

 

[Reloadron]

Thanks Denton, yes I have some Micro Measurements strain gauges dating back before they became part of the Vishay group. About 30 years ago I took a course on surface prep. I have found 350 and 120 Ohm versions and I know I have more buried around here somewhere. They include the gauge factors. I can either make the bridge or I also have an Omega BCM-1 bridge completion module. I will use my laptop with a data acquisition module, I have a few which are pretty fast with good sensitivity. I would like a stable 10V excitation and think I have a few solutions for that. Sort of like I have all the pieces so it's just a matter of finding them, dusting them off and putting things together. All I really need is some decent weather.

Thanks
Ron

 

[mcb]

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

 

[Zendude]

The other variable when comparing max CUP to max PSI on old cartridges is who is making the judgment regarding what is max? Engineering standards often change over time in a variety of fields.

 

[Jim Watson]

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.

Since most of us lack pressure test equipment, we have no way of getting a real number whether 11000, 13000, or 17000.
So two gauges at a factory and a correlation equation do not accomplish anything.

All I can do is look in the book and don't put more than about 8.5 grains of Unique in a period .44-40. (Lyman does show a "group II" up to 19000-21000 CUP for stronger guns like 1892 Winchester. This is approaching the old High Velocity loads that gunzine writers like to warn us against, as though we were buying 50+ year old ammo at the general store.)

 

[mcb]

The other variable when comparing max CUP to max PSI on old cartridges is who is making the judgment regarding what is max? Engineering standards often change over time in a variety of fields.

But if we are talking about SAAMI MAP then the CUP MAP and the Transducer MAP for a particular cartridge are effectively the same thing. SAAMI or a SAAMI member company did the testing and are certifying that if a ammunition manufacture creates ammo to SAAMI specs (all not just pressure) and tests it using either method (per SAAMI spec) and are at or under MAP for the testing method they are using it will be safe for gun designed for that SAAMI cartridge.

Since most of us lack pressure test equipment, we have no way of getting a real number whether 11000, 13000, or 17000.
So two gauges at a factory and a correlation equation do not accomplish anything.

All I can do is look in the book and don't put more than about 8.5 grains of Unique in a period .44-40. (Lyman does show a "group II" up to 19000-21000 CUP for stronger guns like 1892 Winchester. This is approaching the old High Velocity loads that gunzine writers like to warn us against, as though we were buying 50+ year old ammo at the general store.)

Agreed. For most the formula is fairly useless and the safe way is to stay with publish data from trusted sources. But there are always a few out there that want to do something for which there is no data (try to find load data for 38/200). And where I see a danger is if someone has a copy of Quickloads and trying to put in some old cartridge that only has CUP data available and tries to use one of these conversion formula to convert the old CUP to a PSI measurement to use there. It could lead to dangerous loads.

 

[denton]

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

Most people assume that the measurement systems we use and have used are better than they are.

The best estimate I've been able to come up with for the standard deviation of the random error in the CUP system is about 1800 PSI. And that's one technician, on one day, with one set of equipment. If you move from lab to lab, it's worse than that. Often a lot worse.

Using piezo or strain gauge equipment, a technician drawing 10 cartridges from a large lot and measuring their pressure, and then drawing another 10 from the same lot can easily arrive at an average 1000 PSI different, and 2000 PSI is entirely possible.

The question is not whether the available measurements are perfect. They are not. But, for the most part, they are adequate to allow us to keep possession of our fingers, nose, and eyes.

Once you know how much error the systems have, especially the CUP system, you shouldn't be shocked by the differences you found. Add in human intervention and decision making, and what you're seeing is to be expected.

 

[mcb]

Most people assume that the measurement systems we use and have used are better than they are.

The best estimate I've been able to come up with for the standard deviation of the random error in the CUP system is about 1800 PSI. And that's one technician, on one day, with one set of equipment. If you move from lab to lab, it's worse than that. Often a lot worse.

Using piezo or strain gauge equipment, a technician drawing 10 cartridges from a large lot and measuring their pressure, and then drawing another 10 from the same lot can easily arrive at an average 1000 PSI different, and 2000 PSI is entirely possible.

The question is not whether the available measurements are perfect. They are not. But, for the most part, they are adequate to allow us to keep possession of our fingers, nose, and eyes.

Once you know how much error the systems have, especially the CUP system, you shouldn't be shocked by the differences you found. Add in human intervention and decision making, and what you're seeing is to be expected.

I am fairly familiar with the process and equipment use for the Transducer method (I understand the crusher method though I have never used that one) and the 1000-2000 psi variation due to all the experimental variables in the pressure testing is only a few percent error relative to the peak pressure we are typically worried about. The conversion formula for CUP to PSI has errors over 10% in 21 of the 72 cartridges I found specification for in both methods. In a few case the conversion resulted in dangerously high values. And if you only have one data type there is no way to know if the conversion formula is going be accurate or not.

I think the conversion idea is interesting and a tempting thing to do but it is simply not accurate enough to be useful. This is not just my opinion but many experts that work in the industry say there is no reliable mathematical conversion from CUP to PSI. Quoting SAAMI, "This is important, since the pressure values determined by one method cannot be mathematically converted to values for another, despite claims to the contrary. Likewise, the limiting pressure values for the different systems are not interchangeable."

Another interesting and related set of data we can add to this conversion. Look up the proof pressures in the SAAMI specs. For a fair number of the cartridges in the SAAMI spec not only can you get the MAP Service pressure in both CUP and PSI but you can get the Minimum Proof pressure and the Maximum Proof pressure in both units. That gives you three data points for each individual cartridge, and if we assume that zero CUP equals zero PSI (a safe assumption I think) you have four data points for each cartridge that has a SAAMI spec under both methods. Pick a few cartridges and plot those four data point for each and do a linear fit. You will see that each set of data within one particular cartridge is very linear. But you will find as you go from cartridge to cartridge the slope of that CUP to PSI conversion will vary between ~.78 to ~1.38. Since we assumed the zero CUP equals zero PSI there is no intercept just a slope.

Given that each cartridge has a very linear conversion from CUP to PSI but they all have fairly different slopes from cartridge to cartridge sort of points to the fact that your never going to have a reliable conversion from CUP to PSI independent of the cartridge.

 

[denton]

Quoting SAAMI, "This is important, since the pressure values determined by one method cannot be mathematically converted to values for another, despite claims to the contrary. Likewise, the limiting pressure values for the different systems are not interchangeable."

The sun came out today, the temperature soared to 50 F, and I ditched all the things I should have done and went to the range. I hope your day was equally agreeable.

I am familiar with SAAMI's statement. Since the R^2 for the conversion is .96 and the P value is 0, the formula is a conversion from one to the other. I posted a scatterplot of CUP vs. PSI. That scatterplot is from SAAMI's own data. The scatterplot and SAAMI's statement cannot be reconciled. Which do you choose to reject?

You can argue that you don't find the conversion useful, or that you don't think it is accurate enough for your purposes, and that's completely fair. I have no problem at all with that.

But you cannot successfully argue that it doesn't exist or isn't real. The scatterplot, the R^2, and the P value establish it beyond question.

 

[mcb]

The sun came out today, the temperature soared to 50 F, and I ditched all the things I should have done and went to the range. I hope your day was equally agreeable.

I am familiar with SAAMI's statement. Since the R^2 for the conversion is .96 and the P value is 0, the formula is a conversion from one to the other. I posted a scatterplot of CUP vs. PSI. That scatterplot is from SAAMI's own data. The scatterplot and SAAMI's statement cannot be reconciled. Which do you choose to reject?

You can argue that you don't find the conversion useful, or that you don't think it is accurate enough for your purposes, and that's completely fair. I have no problem at all with that.

But you cannot successfully argue that it doesn't exist or isn't real. The scatterplot, the R^2, and the P value establish it beyond question.

Spent too much of the day upgrading to the latest version of Solid Works and getting my interface back they way I like it so it could have been better.

I think you you might put too much weight on you R^2 and P Values. I am far from a statics expert but as I understand it you can have a high R^2 and still have a bad model that does not properly fit the data. For the rifle data you use do a linear equation and in the second larger all center fired data set you use a parabolic equation. Why? What under lying fundamental physics makes either of those equation the correct model for the system being analysed? Why not use a 6th order polynomial, or maybe a logarithm or trig based equation? I fit a 6th order polynomial to the data for the 72 cartridges I have and I manage to get a R^2 value of .958 but I honest don't think that is the right model as there is unlikely anything going on in that data set that is that high of order.

If your model is as good as you say it is then why does it do very well with some cartridges and totally misses with other cartridges that are within the range you say the conversion is good for? A model that only works some of the time is not a good model. 357 Mag is the real eyesore there but I listed several other cartridges up thread that end up being way off when put into the equation. I don't think the 40% error in 357 Mag and the over 15% error in several other cartridges is sufficiently explained by experimental error in the measurement methods especially with how large of samples SAAMI did to create those specifications. The fact that you have a high R^2 value and yet the equation clearly fails to proper predict a subset of the data accurately would seem to point to the idea that the equation/model you have selected may not be the right one assuming a right one exists.

-rambling

 

[denton]

R^2 is a measure of how much of the total variation the equation explains. And the P value tells what the chances are that you could get a result this strong just by random chance. P = 0 and R^2 = .96 is your basic statistical slam dunk. There is a strong mathematical relationship between CUP and PSI. Since both systems measure the same thing, the only way you could end up with no conversion is if one or both systems just plain didn't work, and that doesn't seem to be the case. Well, some people aren't so sure about CUP, but....

It's easier to just look at the scatterplot. If the data appear to be clustered around an obvious line or curve, the input and output variables are connected. If it looks like someone spilled a bowl of marbles, then not so much. The scatterplot using SAAMI data says the two are connected.

Now why did I use a quadratic term instead of something else? Well, I tried that, and got an R^2 of .96. That means that whatever else I did, there was only 4% of the variation left to explain. So going after that 4% would be a lot of work for very little benefit. Also, I knew before the fact that there was curvature in the line because the higher the pressure, the more that CUP underestimates it. That strongly indicates a squared term.

Trying to cover a range that great with one equation might be overly ambitious. The linear model that I made a few years ago, with limited range, works better.

With the large random error in PSI, and the even larger random error in CUP, it's not hard to stack up measurement system errors of plus and minus a few thousand PSI. When you get down into the low end of the scale, that's a large percentage, where on the upper end of the scale the percentage is smaller.

 

[murf]

Which do you choose to reject?

obvious which one I reject.

don't think it is accurate enough for your purposes

it is inaccurate enough to be dangerous.

establish it beyond question.

nothing is beyond question.

stick with published loads folks.

murf

 

[denton]

obvious which one I reject.

it is inaccurate enough to be dangerous.

nothing is beyond question.

stick with published loads folks.

murf

Murf, you're going to have to help me out here. Do you reject SAAMI's statement that there is no relationship between CUP and PSI, or do you reject the scatterplot of SAAMI's data that says that there is?