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#526372 10/18/18 10:42 AM
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KDGJ Offline OP
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Hodgdon is listing a load with pressure in LUP instead of PSI. The pressure is 7100 LUP. How does this relate to PSI?

I searched this site, but didn't get any hits on LUP.

Thanks,
Ken

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The Hodgdon pressure is PSI (Pound-force/square inch) as measured by Lead Crushers (LUP = Lead Units of Pressure).
PSI as measured by modern piezoelectric transducers would be 10-14% higher.
There is no mathematical conversion.

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Crusher pressure measurements (e.g. CUP, LUP) are an expression of the entire area under the pressure curve. Transducer pressure measurements (i.e PSI) are an expression of the single highest amplitude of pressure in the pressure curve.

Unfortunately, crusher pressures are sometimes inaccurately given as PSI. They aren't, and this kind of nonsense just confuses the issue.

Crusher methodology measurements and transducer methodology measurements cannot be meaningfully compared, nor can a pressure measurement from one method be meaningfully converted to a measurement in the other method.

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The problem is, if you go back to the pre-transducer days, crusher measurements WERE referred to as psi. We all need to remember that when we look at older information referring to pressure. Doc Drew does a good job of pointing that out in his posts when referring to old pressure data.

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Quote:
Crusher pressure measurements (e.g. CUP, LUP) are an expression of the entire area under the pressure curve. Transducer pressure measurements (i.e PSI) are an expression of the single highest amplitude of pressure in the pressure curve.


I will have to respectfully disagree with this statement. Both systems, Crusher or Transducer, measure the Max pressure. "IF" each in a system where you were measuring static pressure they would both read the same. The reason they do not read the same in this application is the transducer reads instantaneously while it takes a period of time to collapse the crusher. Admittedly it is an extremely short time, but never-the-less the time of the max pressure being applied is not enough to fully compress the crusher. The crusher will never show a higher pressure than the transducer, assumong it is properly calibrated.


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The long version

British Crusher Gauge illustration
https://books.google.com/books?id=inQCAAAAYAAJ&pg=PA29&dq
Tarage Table
https://books.google.com/books?id=inQCAAAAYAAJ&pg=PA37&dq

Wallace H. Coxe, in “Smokeless Shotgun Powders: Their Development, Composition and Ballistic Characteristics” published by E.I. du Pont de Nemours & Co., 1927, “Measurement of Pressures”
The common method of taking pressures in small arms in this country is known as the Radial Pressure system. A housing is built around the barrel, and a hole drilled through the housing and barrel into the chamber at a distance of 1 inch from the breech and at right angles to the axis of the bore. The hole is then bushed and drilled to a uniform diameter of 0.2250 inch. Then a piston is made the length of the piston hole and 0.2250 inch in diameter. Next the piston hole is lapped to permit the piston to fit snugly without either sticking or getting out of alignment.
In firing the gauge, the piston is inserted and seated, then a lead crusher cylinder is placed on the head of the piston and held firmly in place by a screw and anvil attachment built into the housing. When the cartridge is fired, a portion of the same gas pressure that pushes the bullet through the barrel drives the piston against the lead cylinder and compresses it.
The length of the lead crusher cylinder after compression is naturally less than before the shot was fired and the difference between the original length and the length after compression therefore represents the amount of pressure which has acted upon the lead. Thee exact pressure is read from a table giving a pressure reading for every remaining length reading and commonly called a Tarage Table.
Pressures that are determined at ballistic laboratories are merely relative values and are not absolute values.

NOTE: The Tarage Table conversion may be for pressure expressed as Tons / Sq. Inch or Pounds/ Sq. Inch (PSI). Coxe clearly converted psi to tons simply by dividing by 2240 for some of his published pressure curves.

September 1931 American Rifleman. “Standard Shotgun Pressure Barrels”, by Merton A. Robinson, Ballistics Engineer, Winchester Repeating Arms Co. The article described in detail the crusher method of pressure testing, with images of pressure barrels then in use by Peters, Hercules, Western, Remington, Winchester, Du Pont and Federal. Although the barrels were of somewhat different designs, they were ALL crusher barrels, without evidence of piezoelectric transducers. (Courtesy of Larry Brown)

Major Sir Gerald Burrard published an estimated Lead Crusher (LUP) (Long) Tons/ Sq. Inch (TSI) to piezoelectric transducer Pounds/ Sq. Inch (PSI) conversion formula in the Third edition of The Modern Shotgun, 1955, Vol. 2 derived from simultaneous crusher and transducer pressure readings in a test barrel. He observed the under-reporting of pressure by (crusher) LUP compared to piezo transducer gauges:
“A most interesting outcome of pressure measurements on shotgun cartridges using the piezoelectric gauge has been the comparison of the maximum pressure readings with those of the lead crusher gauge. By mounting the “Two Gauges” on opposite sides of the same gun at one inch from the breech face “Simultaneous” readings on the same cartridge were possible. As had been known for some time, the crusher readings were less than those given by the piezoelectric gauge due to the time lag in the plastic deformation of the lead-the piezoelectric gauge piston only moves about 1/100,000 inch when subjected to 2.5 tons per sq in and is thus free from this error. Over the ranges of pressures usually encountered at the one inch position in shotguns the readings given by the two gauges are related by the equation;
P = 1.5L - 0.5 tons per sq inch X 2240
Where;
P = the maximum pressure (PSI) indicated by the piezoelectric gauge
L = the maximum pressure (TONS) indicated by the lead crusher gauge”

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Quote:
Over the ranges of pressures usually encountered at the one inch position in shotguns the readings given by the two gauges are related by the equation;
P = 1.5L - 0.5 tons per sq inch X 2240
Where;
P = the maximum pressure (PSI) indicated by the piezoelectric gauge
L = the maximum pressure (TONS) indicated by the lead crusher gauge”


Excellent post Drew. I will just add a comment or so, note this formula only applies to
"The ranges of pressures usually encountered at the one-inch position in shotguns".
Also further note that Burrard stated this formula would not give an "Exact" conversion, but within the criteria given it was extremely Close & would not give a serious error.

Using "The Formula" a 3-ton LUP would convert to a 4 ton PSI. It should be extremely obvious that a gun safe with 4-ton PSI would not necessarily be safe with 4-ton LUP. Multiplying by 2240 (Long Ton) gives 3-ton = 6720 & 4-ton = 8960 or a 33% increase.

A 4-ton lup would convert to 5.5-ton psi or 12,320 psi. It should be obvious when comparing pressures it is imperative to stay within the same methods of measuring.
Note that none of this contradicts what Drew wrote, just putting in some actual figures. Even though a 3-ton LUP pressure converts to 4-ton psi, there is a world of difference between a 3-ton & 4-ton when Both are LUP. The conversion equates to a 33% increase in Reading, while the latter is an actual 33% increase in Pressure.


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I don't know that I buy into Burrard's formula.

I was looking at data for International the other day, and Hodgdon still publishes pressures using both systems in the same chart.

Apparently, they are unable to convert and don't want to re-shoot old loads just to get PSI.

Interesting that they can assure SAAMI standards with loads published in LUP.

Comparing very, very similar loads within .1 grain of charge and with primers considered by most to be so similar as to be interchangeable, the difference is indeed 'in the area' of 15%.

I don't find anything approaching 33%.


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To convert PSI as determined by LUP (converting a measured mechanical change to an estimated pressure) to PSI as measured by modern piezo transducers, add 10-14%

To convert TONS as determined by LUP to modern transducer PSI use Burrard's formula.

UNLESS, like Coxe, you used a Tarage Table for PSI and to get TONS simply divided by 2240, or vv. frown THEN add 10-14%

Which is what these numbers are; published some time after 1920



and these in 1927



Ballistite 4.9 Tons X 2240 = 10,976 psi + 10 - 14%


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The 1954 Rules of Proof “Highest Mean Service Pressure” equivalent transducer values as converted from LUP by Burrard’s formula:
3 tons = 8,960 psi
3 1/4 tons = 9,800 psi
3 1/2 tons = 10,640 psi
4 tons = 12,320 psi

Conversion provided by the Birmingham Proof House 2001 - similar but as Miller observed less so with increasing pressures
3 tons = 8,938 psi
3 1/4 tons = 9,682 psi
3 1/2 tons = 10,427 psi
4 tons = 11,917 psi

Mr. Roger Hancox, Proof Master, Birmingham Proof House, 2008
A basic “Rule of Thumb” conversion of tons to CIP transducer pressure (is) multiplying the tons per sq inch by 2240 to obtain psi, and then by a factor of 1.33 to obtain the approximate CIP pressure.

INTERESTING
3.5 tons X 2240 = 7840 X 1.33 = 10,427
4 tons x 2240 = 8960 X 1.33 = 11,917
It appears that the proof house simply converted the numbers and did not do simultaneous transducer tons and transducer psi, kg/cm2, or BAR measurements!

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