Sunday, January 9, 2011

Testing Firearms: Measuring Chamber Pressures

In this post, we will look into the technique of measuring pressures inside a barrel, when a firearm is discharged. It is important for people to determine pressures of a firearm with various types and brands of ammunition, because some ammunition may produce too much pressure and therefore cause the firearm to explode. A system that enables one to determine the pressure is therefore very useful to determine which ammunition types may be safely used by a firearm.

The maximum pressure is exerted at the breech end in the firing chamber and decreases further down the barrel tube. That's why published numbers usually only list the chamber pressure. It must be noted that there are a couple of different standards in exactly how the pressure is measured. In our first post about proof testing, there were two organizations mentioned, CIP and SAAMI, that publish firearms data. Unfortunately, they have slightly different ideas about how chamber pressures should be measured. We will study these differences a little while later down in this post. Suffice it to say that CIP doesn't care about the shape of the cartridge when deciding which point to take the pressure reading from, whereas SAAMI has different locations to measure the pressure from, based on the shape and diameter of the cartridge. Therefore CIP and SAAMI numbers don't match up for this reason.

The classic method of measuring pressures goes back to the 1800s and early 1900s. It was the method most in use until about the 1960s. It uses crusher gauges to determine pressures.

It consists of a device that allows mounting of a gun barrel. The gun barrel is drilled at various points where pressure measurements are desired. To each of these holes is pushed a tight fitting stopper and the other end of the stopper is held in place by a precisely machined cylindrical piece, which in turn is supported by a steel screw. The precisely machined cylindrical piece is of uniform density and made of copper or lead, depending on the firearm type. For lower pressure weapons such as shotguns or smaller pistols, a lead cylinder is used, whereas copper cylinders are used for higher pressure applications such as rifle or most handgun cartridges. When the cartridge is fired, some of the gas pushes upwards and drives the stoppers out of their holes. This has the effect of squeezing the copper (or lead) cylindrical pieces against the steel screws holding them in position. The amount of deformation of the copper or lead cylinders is measured very precisely and compared with a chart of similar cylinders which were deformed previously under known pressures and the corresponding value is called the Copper Unit of Pressure (CUP) or Lead Unit of Pressure (LUP) value.

While CUP or LUP values are meant to be compared with the crushing power of a known pressure, this is not always the case. For example, the same amount of deformation can occur from a short duration high-pressure pulse as from a longer duration, but lower pressure pulse. Also, these numbers tend to be a bit lower than peak pressures measured using transducers. Therefore, when measurements are made using crusher gauges, the pressure is listed in mega-pascals (MPa - the SI standard unit of pressure) or pounds per square inch (psi - the imperial standard unit of pressure) followed by the letters CUP or LUP to indicate that the measurements were done using crusher gauges.

The crusher gauge method was the only reliable method of measuring chamber pressures until the 1960s, when cheap piezoelectric devices became available. This method is called the Conformal Transducer method or Piezo method. A piezoelectric transducer (a.k.a. sensor) has the property that it generates electricity as it is crushed. The setup is similar to the crusher gauge method, except that instead of a copper cylinder, a quartz crystal transducer is used. Quartz is a material that exhibits piezoelectric properties. Thus, when the cartridge is fired, the transducer transmits electricity, which can be measured and then compared against values generated by similar transducers, when subject to known amounts of pressure. This method has the advantage of measuring pressures at different instants of time, as the bullet leaves the barrel. Measurements by this method generally read about 15-20% higher than those shown by the crusher gauge method. As piezoelectric sensors have become much cheaper now, this is the method of choice for measuring chamber pressures, though crusher gauge measurements are still around as well.

Here's where the differences between the CIP and SAAMI standards show up. CIP uses a transducer made by the Swiss firm Kistler and requires a hole be drilled into the cartridge case and fired by a specially prepared barrel. SAAMI uses a different transducer, called a conformal sensor, mostly made by a US Company PCB Piezotronics. These sensors don't need holes drilled in the case, but they are more expensive as each one needs to be designed based on the diameter of the cartridge.

CIP standards state that the transducer should be positioned 25 mm. from the breech face, when the cartridge is long enough. If the cartridge is too small, then CIP decides to position the transducer at a shorter distance from the breech face, based on the cartridge model. CIP standards do not care what the shape of the cartridge is.

SAAMI, on the other hand, does care what the cartridge is shaped like. For bottle-necked cartridges, the center of the transducer is placed 0.175 inches (4.4 mm.) behind the shoulder of the cartridge for large diameter (0.250 inches, 6.4 mm.) transducers and 0.150 inches (3.8 mm.) behind the shoulder of the cartridge for small diameter transducers. For cylindrical cartridges, the transducer is located behind the base of the seated bullet at a distance of (0.5 * transducer diameter + 0.005 inches)

Since the two standards have different methods and different points from where to take measurements, therefore the CIP and SAAMI pressure numbers are different from each other for the same cartridge type.

Using a transducer is less expensive than using crusher gauges because the same transducer can be reused over and over again, as long as the cartridges used are the same type. So if a tester wants to repeat the test multiple times to get an average pressure reading, he or she only needs one transducer, if using the piezo method. Compare this to the crusher gauge method where each test needs a new copper cylinder and the costs begin to add up.

The third method involves using a strain gauge. This is a thin, flat piece of wire whose electrical resistance changes as it is stretched or strained. The strain gauge is attached on the outside of the barrel near the front of the chamber. When the firearm is discharged, the barrel expands slightly, which stretches the strain gauge and the change in the electrical resistance can be measured and the pressure calculated. This method is fairly accurate, but not as reliable as the other two methods. However, it has the advantage of being the cheapest method of the three and not requiring as much special equipment as the other two methods.

It must be noted that no test can give a truly accurate pressure reading because there is no way to know what the actual pressure should be. Even if the tester uses 100 identical cartridges with equal amounts of propellant and using the same firearm and test setup, the tester can expect up to a 5% variance in pressure values from cartridge to cartridge, when using the crusher gauge method to measure pressure. With the conformal transducer method, the variance is up to 3% from cartridge to cartridge. This is why the conformal transducer method is proclaimed as more accurate than the crusher gauge or the strain gauge method.

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