Copper units of pressure or CUP, and the related lead units of pressure or LUP, are terms applied to pressure measurements used in the field of
internal ballistics
Internal ballistics (also interior ballistics), a subfield of ballistics, is the study of the propulsion of a projectile.
In guns, internal ballistics covers the time from the propellant's ignition until the projectile exits the gun barrel. The s ...
for the estimation of chamber pressures in
firearm
A firearm is any type of gun designed to be readily carried and used by an individual. The term is legally defined further in different countries (see Legal definitions).
The first firearms originated in 10th-century China, when bamboo tubes ...
s. These terms were adopted by convention to indicate that the pressure values were measured by copper crusher and lead
crusher gauges respectively. In recent years, they have been replaced by the adoption of more modern
piezoelectric
Piezoelectricity (, ) is the electric charge that accumulates in certain solid materials—such as crystals, certain ceramics, and biological matter such as bone, DNA, and various proteins—in response to applied Stress (mechanics), mechanical s ...
pressure gauges that more accurately measure chamber pressures and generally give significantly higher pressure values. This nomenclature was adopted to avoid confusion and the potentially dangerous interchange of pressure values and standards made by different types of pressure gauges. For example, it makes little sense to describe a maximum pressure as 300 MPa, and in case the pressure has been measured according to the CUP procedure it should be denoted as 300 MPa (CUP).
Pressure
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...
is a fundamental physical parameter that is expressed in units of force divided by area. The unit of pressure in the
avoirdupois
The avoirdupois system (; abbreviated avdp.) is a measurement system of weights that uses pounds and ounces as units. It was first commonly used in the 13th century AD and was updated in 1959.
In 1959, by international agreement, the definiti ...
system is pound per square inch, while the unit of pressure in the
metric system
The metric system is a system of measurement that succeeded the Decimal, decimalised system based on the metre that had been introduced in French Revolution, France in the 1790s. The historical development of these systems culminated in the d ...
is the
bar
Bar or BAR may refer to:
Food and drink
* Bar (establishment), selling alcoholic beverages
* Candy bar
* Chocolate bar
Science and technology
* Bar (river morphology), a deposit of sediment
* Bar (tropical cyclone), a layer of cloud
* Bar (u ...
, and the unit of pressure in the modern
SI system
The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...
is
pascal
Pascal, Pascal's or PASCAL may refer to:
People and fictional characters
* Pascal (given name), including a list of people with the name
* Pascal (surname), including a list of people and fictional characters with the name
** Blaise Pascal, Fren ...
(equivalent to
newton
Newton most commonly refers to:
* Isaac Newton (1642–1726/1727), English scientist
* Newton (unit), SI unit of force named after Isaac Newton
Newton may also refer to:
Arts and entertainment
* ''Newton'' (film), a 2017 Indian film
* Newton ( ...
per square meter). A chamber pressure measured with a copper crusher gauge would there be expressed in
psi
Psi, PSI or Ψ may refer to:
Alphabetic letters
* Psi (Greek) (Ψ, ψ), the 23rd letter of the Greek alphabet
* Psi (Cyrillic) (Ѱ, ѱ), letter of the early Cyrillic alphabet, adopted from Greek
Arts and entertainment
* "Psi" as an abbreviatio ...
(CUP) in the English system, bar (CUP) in the metric system, and MPa (CUP) in the SI system.
Methodology
Estimation of pressure using CUP and LUP units is performed by a special ''crusher gun'', which uses pressure applied to a piston to crush a carefully manufactured and calibrated
copper
Copper is a chemical element with the symbol Cu (from la, cuprum) and atomic number 29. It is a soft, malleable, and ductile metal with very high thermal and electrical conductivity. A freshly exposed surface of pure copper has a pinkis ...
or
lead
Lead is a chemical element with the symbol Pb (from the Latin ) and atomic number 82. It is a heavy metal that is denser than most common materials. Lead is soft and malleable, and also has a relatively low melting point. When freshly cu ...
cylinder. The amount of deformation is compared to the amount of crushing produced by different pressures in pounds per square inch. Copper cylinders are used at high pressures, such as are generated by most
handgun
A handgun is a short- barrelled gun, typically a firearm, that is designed to be usable with only one hand. It is distinguished from a long gun (i.e. rifle, shotgun or machine gun, etc.), which needs to be held by both hands and also braced ...
and
rifle
A rifle is a long-barreled firearm designed for accurate shooting, with a barrel that has a helical pattern of grooves ( rifling) cut into the bore wall. In keeping with their focus on accuracy, rifles are typically designed to be held with ...
cartridges, and lead cylinders are used for low pressures such as are generated by
shotgun shell
A shotgun shell, shotshell or simply shell is a type of rimmed, cylindrical (straight-walled) cartridges used specifically in shotguns, and is typically loaded with numerous small, pellet-like spherical sub- projectiles called shot, fired thro ...
s. The crusher gun has a hole in the chamber that is linked to a piston, and upon firing, this piston is subjected to the pressure of firing. The piston then acts on the calibrated cylinder, crushing it slightly. The length of the crushed cylinder is measured and compared to a chart of lengths resulting from crushing cylinders with given amounts of pressure, and the corresponding force is the CUP or LUP pressure value.
The American standards organization
Sporting Arms and Ammunition Manufacturers' Institute
The Sporting Arms and Ammunition Manufacturers' Institute (SAAMI, pronounced "Sammy") is an association of American manufacturers of firearms, ammunition, and components. SAAMI is an accredited standards developer that publishes several Americ ...
(SAAMI) published CUP pressure level standards for many cartridges.
Comparing units
While CUP and LUP numbers were intended to be comparable to the crushing power of a given pressure in psi (
lbf
The pound of force or pound-force (symbol: lbf, sometimes lbf,) is a unit of force used in some systems of measurement, including English Engineering units and the foot–pound–second system.
Pound-force should not be confused with pound-m ...
/in
2), the numbers are not equivalent. Since a longer duration, lower pressure pulse can crush the cylinder as much as a shorter duration, higher pressure pulse, CUP and LUP pressures frequently register lower than actual peak pressures (as measured by a
transducer
A transducer is a device that converts energy from one form to another. Usually a transducer converts a signal in one form of energy to a signal in another.
Transducers are often employed at the boundaries of automation, measurement, and contr ...
) by up to 20%. For example, the
SAAMI
The Sporting Arms and Ammunition Manufacturers' Institute (SAAMI, pronounced "Sammy") is an association of American manufacturers of firearms, ammunition, and components. SAAMI is an accredited standards developer that publishes several Americ ...
maximum pressure for the
7.62×51mm is given as 52,000 psi (CUP), or 62,000 psi (430
MPa
MPA or mPa may refer to:
Academia
Academic degrees
* Master of Performing Arts
* Master of Professional Accountancy
* Master of Public Administration
* Master of Public Affairs
Schools
* Mesa Preparatory Academy
* Morgan Park Academy
* Mound ...
); the
.45-70, on the other extreme, is listed as 28,000 in both CUP and psi (190 MPa). SAAMI standards for a given cartridge may be expressed in CUP units, LUP units, or in standard units of pressure (psi or MPa).
Although no accurate conversion formulas are possible, for converting between true pressures and crusher indicated pressures, linearized approximation conversion equations do exist over narrow ranges of pressures for estimating piezo pressure readings given crusher pressures.
For example, Denton Bramwell has published a conversion approximation formula, covering only SAAMI crusher pressures between 28,000 and 54,000 CUP:
:piezo = 1.52 × crusher − 18,000
Likewise, there is a conversion approximation formulas for estimating between CIP (European) crusher pressures (which are recorded in multiples of 50 bar) and piezo ratings, consistent with different assumptions for CIP vs. SAAMI crusher test conditions:
:piezo = 1.21 × crusher − 2.8
In addition to these linear approximations, there also exist exponential conversion approximation formulas for estimating from about 0 to about 60
ksi
Olajide Olayinka Williams "JJ" Olatunji (born 19 June 1993), known professionally as KSI, is an English YouTuber and rapper. He is a co-founder and member of the British YouTube group known as the Sidemen. He is the CEO of Misfits Boxing and ...
crusher values to psi values, and these are sometimes used up to around 67 ksi, but with significantly increasing errors.
CUP and LUP pressures vs. transducer pressures
Until the invention of measurement transducers in the 1960s, crusher guns were the only reliable method for estimating chamber pressures. With the availability of inexpensive, reliable transducers since the 1960s for actually making chamber pressure measurements, the industry almost universally has begun to move away from crusher guns for estimating chamber pressures, towards favoring making actual measurements. Transducers are also faster to use in practice, as they do not require the careful measuring of the copper or lead cylinders after firing. Additionally, transducers are capable of recording instant-by-instant pressures through the entire firing cycle. Hence, in the long run, using a transducer is less expensive, as it does not require using expendable metal cylinders in a crusher gun, and also reduces the labor required to analyze test results.
One outcome from this transition to using measurement transducers is, for example, that a
Speer
Speer is a surname.
: Ashkenazim (): a spelling variation of ''Speyer'', a name indicative of origin from the German city of Speyer
: Middle High German and Middle Dutch (): ''sper'', meaning "spear"
: Scottish and northern Irish : a spelling va ...
reloading manual from 1987 lists all SAAMI pressures in CUP, while current references list nearly all pressures in PSI. Another outcome is that design margins are now better determined, which has the effect of increasing the long-term safety of firing multiple thousands of rounds in a gun. With estimates based on crusher guns, actual safety margins could never be accurately assessed, short of actually firing tens of thousands of rounds in a sample gun.
References
External links
Chamber Pressure Measurementby Terry Hart
of SAAMI pressure levels for common cartridges, in PSI or CUP.
A studydone that shows a statistically significant correlation between CUP and PSI for rifle cartridges.
* Speer Reloading Manual Number 11, Omark Industries, 1987 {{No ISBN
Units of pressure