DANIEL WEBSTER COLLEGE

SCHOOL OF ENGINEERING AND COMPUTER SCIENCE

Baseline Design of a Rifle Barrel

EG325 Mechanics of Materials II

Joshua Ricci

12/15/2013

i

Table of Contents List of Figures ................................................................................................................................................ ii

List of Tables ................................................................................................................................................ iii

1 Abstract ...................................................................................................................................................... 1

2 Background ................................................................................................................................................ 2

3 Preliminary Calculations ............................................................................................................................ 4

3.1 Static Analysis...................................................................................................................................... 7

3.2 Fatigue Analysis ................................................................................................................................... 9

4 Results ...................................................................................................................................................... 13

4.1 Final Static Stress Analysis ................................................................................................................ 13

4.2 Fatigue Life Analysis .......................................................................................................................... 14

5 Discussion ................................................................................................................................................. 16

6 Drawings of Final Design .......................................................................................................................... 17

7 Conclusion ................................................................................................................................................ 18

8 Appendix .................................................................................................................................................. 19

9 References ............................................................................................................................................... 23

ii

List of Figures Figure 1. Cut-away sideview of a gun barrel illustrating the expanding gas and a bullet being forced down

the barrel by the pressure. ........................................................................................................................... 2

Figure 2. Drawing of a 5.56 x 45 mm NATO round with all the necessary dimensions. ............................... 4

Figure 3. Chamber pressure versus time for the M193 5.56 x 45 mm NATO cartridge with 846 ball

powder. ......................................................................................................................................................... 5

Figure 4. Plot of the maximum pressure distribution, shown by the purple dashed line, as a function of x-

location along the barrel. .............................................................................................................................. 5

Figure 5. Simplified version of the P-versus-t curve for integration purposes. ............................................ 6

Figure 6. Diagram of a cylinder subjected to internal and external pressure. ............................................. 7

Figure 7. Stress distribution of a pressurized cylinder. ................................................................................. 8

Figure 8. Fatigue strength fraction, f, of Sut at 103 cycles. .......................................................................... 12

Figure 9. COMSOL static analysis result – safety factor along the inner surface of the barrel versus x. ... 14

Figure 10. Comparison of hand calculations of outer radius for static loading versus fatigue loading. .... 16

iii

List of Tables Table 1. Material properties for AISI 4140 Steel, oil quenched, 400°F temper. ........................................... 7

Table 2. Tabulated results for the static stress analysis. ............................................................................ 13

Table 3. Tabulated results for the fatigue life analysis. .............................................................................. 15

1

1 Abstract The goal of this project was to design and analyze a rifle barrel undergoing a cyclic pressurized

loading. It was also necessary to research certain geometry, such as the projectile dimensions, as well as

select the material to be used. This was a very rudimentary design; rifling and a corrosion-resistant layer

were not incorporated into the calculations or design. The round in question, and for which the pressure

data was provided, was the 5.56 x 45 mm NATO cartridge. The barrel length was fixed at 18 in, as

measured from the bullet tip to the muzzle. The local maximum pressure depreciates down the length

of the barrel, allowing for a slight taper of the outer surface. First, a barrel was designed based on a

safety factor of 2 for a static loading. Aside from hand calculations, a static analysis was also conducted

using the COMSOL software package. Then, the final design was based on achieving a fatigue life of

100,000 cycles, with one cycle being equivalent to reaching maximum pressure then back down to zero.

The final design resulted in a total mass of 0.75 lb with a selected material of AISI 4140 steel. Due to

time constraints, complete satisfactory results were not achieved. Some additional adjustments to the

final design would be beneficial.

2

2 Background A rifle barrel is subjected to large pressure forces due to the firing of a bullet. The pressure

distribution decreases along the length of barrel, with the maximum occurring inside the chamber and

the minimum at the muzzle. The chamber section of a rifle barrel is where the bullet cartridge is loaded.

It is also where ignition from the powder charge takes place and, as such, the chamber section

experiences the greatest pressure. The gas then expands and moves the bullet through the barrel. Some

of the work being done by the pressurized gases gets transferred into overcoming friction and drag, and

also into rotational energy of the bullet due to rifling, or small helical grooves on the inner surface of the

barrel. Figure 1 shows a schematic of a barrel undergoing pressure forces during the firing of a

projectile.

There are various methods for determining the pressure inside the chamber. One example is the

Copper Crusher Method. A hole is drilled in the chamber and the wall of a test cartridge, and a crusher

chamber is attached to the hole. The pressure resulting from the powder ignition causes a precisely

machined piece of copper to become deformed within the crusher chamber. The amount of

deformation correlates to a specific pressure based on standardized measurements. The unit of

pressure in this way is the Copper Unit of Pressure (CUP). Measurements using this method will typically

vary by ±5%.

Another method is the Piezoelectric Method, and is the most commonly used method today.

This is similar to the copper crusher method with the exception that it uses a quartz crystal transducer in

place of a copper piece. Applying pressure to the crystal changes its electrical properties, which can be

measured and recorded with very sensitive equipment. The pressure when measured this way is usually

reported in units of pounds per square inch (psi). These measurements are typically accurate to within

±3%.

A third example is the Strain Gauge Method. A strain gauge is placed on the outside of the barrel

near the front of the chamber. The internal pressure causes the barrel to expand slightly, and

CHAMBER

r Figure 1. Cut-away sideview of a gun barrel illustrating the expanding gas and a bullet being forced down the barrel by the

pressure.

3

consequently the small wire of the strain gauge becomes stretched. This change in length of the wire

changes its electrical resistance. These changes are measured and recorded by sensitive equipment, and

are used to provide a good indication of the pressure magnitude. The pressure is also reported in units

of psi. The strain gauge method is the least expensive, but is not as reliable as the first two methods.

Because the pressurized gas expands to occupy a larger volume as the bullet travels down the

barrel, the pressure decreases with bullet distance. In other words, the maximum pressure experienced

by the local material decreases with increasing distance x along the barrel. From an engineering

standpoint, this means the local material undergoes less stress towards the end of the barrel. The barrel

can then be designed with a slight taper, gradually reducing the radial thickness from the chamber

section to the muzzle. Thus, the weight of the barrel can be significantly reduced.

4

3 Preliminary Calculations Some preliminary calculations were performed under the following assumptions:

• Inertia effects (rapid pressurization in front of the bullet and propagation of the stress wave) are

negligible.

• Pressure at any specific location along the barrel is cyclic, varying from zero to maximum value and

back to zero.

• Material is isothermal and at room temperature.

• Entire barrel is made of a single material with constant density.

• Temperature effects (thermal expansion, etc.) on the material properties are negligible.

• Barrel is absent of rifling.

• Energy consumed by friction and drag forces is ignored.

• Rotational energy is ignored.

To begin designing the barrel, it was first necessary to find the geometry of testing round to

estimate the internal dimensions of the chamber section. The round in question was the NATO 5.56 x 45

mm cartridge. After a little research online, the schematic of Figure 2 was found. The notches located at

the rear of the cartridge, and at the front of the collar where the projectile is housed, were ignored to

avoid complicated stress concentrations.

Figure 2. Drawing of a 5.56 x 45 mm NATO round with all the necessary dimensions.

5

A typical plot of the chamber

pressure versus time for the 5.56 x 45 mm

NATO cartridge is shown in Figure 3. It should

be noted that this is for the local pressure

inside the chamber only. From the plot, the

maximum and minimum pressures were

determined to be 53,600 psi and 11,800 psi,

respectively. A good approximation for the

pressure distribution down the barrel’s

length can be made by assuming the

pressure at the start of the barrel (x = 0) is

equal to pmax and the pressure at the muzzle

(x = L) is equal to pmin. A third point is

required for an accurate curve fit, which was

chosen to be 53,000 psi at 0.5 in. For this

study, the barrel length was fixed at 18 in, as

measured from the front of the casing to the

muzzle. The resulting plot of the maximum

pressure versus x-location is shown in Figure

4 along with the curve fit equation.

P(x)= -64.127x2 - 1167.9x + 53600 psi

0

10000

20000

30000

40000

50000

60000

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Pre

ssu

re (

psi

)

x (in)

Maximum Pressure Distribution Down the Length

of the Barrel

Figure 3. Chamber pressure versus time for the M193 5.56 x 45 mm NATO

cartridge with 846 ball powder.

Figure 4. Plot of the maximum pressure distribution, shown by the purple dashed line, as a function of x-

location along the barrel.

6

The muzzle velocity of the bullet can be determined by performing some simple integration of

the P-versus-t graph of Figure 3. First, the graph was broken down into two separate curves, and

imported into Excel where trendlines could be fitted to obtain their respective equations. The result is

shown in Figure 5.

Figure 5. Simplified version of the P-versus-t curve for integration purposes.

Now, the muzzle velocity was determined using the equations found above:

Equation 1

��� = � ��� � = � �� �153143 − 22971 ��.��.�

+ � �58333� − 165262 + 122671 ��.��.�

���

�

where m is the mass of the bullet, Ve is the muzzle velocity, and A is the cross-sectional area of the bullet

that the pressure is acting on. The mass of the bullet in question is 0.004 kg, or approximately 0.009 lb.

Performing the integration and solving for Ve reveals that the muzzle velocity is about 3884 ft/s.

According to Small Arms Defense Journal, the muzzle velocity for the round and a barrel of this length

should be around 2900 ft/s, based on experimental data. The theoretical result is much larger than the

published data due to the gross assumptions where large frictional and drag forces were neglected, as

well as the energy required to generate the rotation of the bullet.

P(t) = 153143t - 22971 psi

P(t) = 58333t2 - 165262t + 122671 psi

0

10000

20000

30000

40000

50000

60000

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2

Pre

ssu

re (

psi

)

Time (ms)

Chamber Pressure Versus Time

7

It is of interest to the engineer to estimate what the angular velocity of the bullet would be in

the presence of rifling using the muzzle velocity calculated from Equation 1. Based on a rifling scheme of

“one twist per nine inches”, the angular velocity was found using Equation 2.

Equation 2

! = ��1#$%9&' (12&'1) * (

60,1�&'* � (3884), *

1#$%9&' (12&'1) * (

60,1�&'* � 310,700#.�

Published data could not be found for the angular velocity to compare this with.

Based on the demanding strength requirements, and after doing some research on typical gun

steels, the material selected for the barrel was AISI 4140 steel quenched and tempered. This steel has

both a very large ultimate strength and yield strength, as well as being relatively light-weight. The

material properties are summarized in Table 1 below.

Property Value Unit

Ultimate tensile strength, Sut 260.3 ksi

Yield strength, Sy 219.7 ksi

Elastic modulus, E 29.7 Msi

Poisson ratio, ν 0.29 1

Density, ρ 0.284 lb/in3

Table 1. Material properties for AISI 4140 Steel, oil quenched, 400°F temper.

Figure 6. Diagram of a cylinder subjected to internal and external pressure.

3.1 Static Analysis

An initial sizing of the barrel was performed based on a static stress analysis of the pressure

distribution of Figure 4. It was assumed that the pressure was uniform in the chamber section

equivalent to the pressure at x = 0 in. Referring to Figure 6, it can be shown by performing force

equilibrium on a differential element of a thin ring with thickness dr that the equations for tangential

and radial stress are given by:

8

Equation 3

/� = .0#0� − .1#1� − #0�#1��.1 − .0 #�⁄#1� − #0�

Equation 4

/3 = .0#0� − .1#1� + #0�#1��.1 − .0 #�⁄#1� − #0�

In this study, po is equal to zero since the internal gauge pressure is given, and the stress was examined

at the inner surfaces only since that is where their magnitudes are the greatest, as shown in Figure 7.

Thus, with po = 0 and r = ri, Equation 3 and Equation 4 reduce to:

Equation 5

/��4 = #0���4#1� − #0�

51 � #1�#0�6

Equation 6

/3�4 = −��4

Equation 5 and Equation 6 are now functions of x, where the internal pressure has been substituted

with the pressure function P(x) of Figure 4.

Figure 7. Stress distribution of a pressurized cylinder.

Since there is no shear stress at this orientation, the tangential and radial directions are the

principal axes. Therefore, σt and σr are the principal stresses, and the complete state of stress can be

9

represented by a single variable, known as the von Mises stress. For plane (2D) stress, the von Mises

stress is given by Equation 7.

Equation 7

/7 = 8/�� − /�/3 + /3�

Finally, the factor of safety against yielding is the ratio of the yield strength to the applied stress, as

shown in Equation 8.

Equation 8

'9 = :9/7 = 219.7;,&/7

The initial sizing was designed to achieve a safety factor against yielding of 2 at all inner surface

locations.

3.2 Fatigue Analysis

Next, the sizing based on finite life fatigue loading was determined similarly to the process

described above, with a few extra steps. The endurance strength is a material property that describes

the limit below which that material is said to last an infinite number of cycles, and is denoted by S’e. The

apostrophe represents that the data is based on a pristine, controlled laboratory specimen. Typically for

steels with an ultimate tensile strength greater than 200 ksi, the endurance limit is estimated to be S’e =

100ksi, based on empirical data. The actual endurance limit of the test specimen is estimated from

Equation 9:

Equation 9

:� = ;<;=;>;?;�;@:�7

where the k’s are modification factors to account for deviations of the test specimen from the pristine

specimen. This is known as the modified endurance limit.

The surface condition modification factor, ka, is to account for the fact that the surface of the

pristine specimen is highly polished. It is a function of the surface finish of the actual part and the tensile

strength of the material, and is given by

Equation 10

;< = A:B�=

where a and b are determined based on empirical data. For a machined or cold-drawn surface finish,

factor a and exponent b are 2.7 and -0.265, respectively. Thus, from Equation 10

;< = �2.7�260.3C�.�D� � 0.6184

The size modification factor, kb, accounts for the difference in diameter or for non-circular parts.

However, this only applies to bending and torsion. Since the barrel only experiences axial loading, radial

and tangential, the size factor is kb = 1.

10

A cycle involving rotating bending, axial, or torsional loading has varying endurance limits with

tensile strength. The load modification factor for axial loading is kc = 0.85. However, as will be shown

later, this factor is taken into account when the von Mises stress is calculated.

The temperature modification factor, kd, is for operating temperatures above or below room

temperature. Because the yield strength reduces rapidly at elevated temperatures, this factor was taken

into account. The equation for kd, based on a fourth-order polynomial curve fit, is

Equation 11

;? = 0.975 + 0.432�10CEFG − 0.115�10C�FG� + 0.104�10CHFGE − 0.595�10C��FGI

Research revealed that a typical gun barrel could easily reach temperatures over 500°F. Thus, from

Equation 11

;? = 0.975 + 0.432�10CE�500 − 0.115�10C��500� + 0.104�10CH�500E− 0.595�10C���500I = 0.9963

The reliability factor, ke, takes into consideration the scatter of data. Most endurance strength

data are reported as mean values. With an assumed reliability of 90%, ke = 0.897.

Lastly, the miscellaneous-effect modification factor, kf, takes into account a reduction in the

endurance limit due to all other effects not mentioned above, such as corrosion. To be conservative, a

modification factor of kf = 0.9 was used.

Now the modified endurance limit is calculated from Equation 9.

:� = �0.6184�1�1�0.9963�0.897�0.9�100 = 49.7 ;,& The tangential, radial, and von Mises stresses are calculated in the same manner as in the static

analysis. Due to the “on-off” nature of the cyclic loading, the mean and amplitude are both calculated

from Equation 12 below.

Equation 12

/< = /J = /J<K2

where σmax is equivalent to the von Mises stress as determined from Equation 7. The mean and

amplitude von Mises stresses for fatigue loading are calculated from Equation 13 and Equation 14,

respectively.

Equation 13

/J7 = LM/J,=�N?0NO + /J,<K0<PQ� + 3MRJ,�13S01NQ�T� �⁄

Equation 14

/<7 = UV/<,=�N?0NO + /<,<K0<P0.85 W� + 3MR<,�13S01NQ�X� �⁄

Because the stress state is purely axial (i.e. no bending or torsion), the above equations reduce to

11

Equation 15

/J7 = /J

Equation 16

/<7 = /<0.85

The finite life is determined from a completely reversed (zero-mean) stress magnitude. In this case, the

mean stress is non-zero. Therefore, an equivalent reversed stress must be determined. Using the

modified Goodman failure criterion, the reversed stress is

Equation 17

/3�Y = /<1 − /J:B�

Then the number of cycles, N, is calculated from Equation 18.

Equation 18

Z = V/3�YA W� =⁄

where a and b are constants defined by specific points on the S-N diagram. Substituting these points

yields

Equation 19

A = �):B��:�

Equation 20

[ = − 13 log ():B�:� *

where f is the fraction of Sut represented by (S’f)103 cycles. A plot of the fatigue strength fraction is shown

in Figure 8. From this figure, the fraction was estimated to be f = 0.77 based on a tensile strength of

260.3 ksi, which is off the chart.

12

Figure 8. Fatigue strength fraction, f, of Sut at 103 cycles.

Now, from Equation 19 and Equation 20:

A = �0.77 ∗ 260.3�

49.7 = 807.7 ;,& [ = − 1

3 log (0.77 ∗ 260.349.7 * = −0.2018

13

4 Results

4.1 Final Static Stress Analysis

Using the method and equations outlined in Section 3.1, several iterations were performed on

the outer radius at each location to obtain a yield safety factor of 2. The results of those iterations are

shown in Table 2 below.

x [in] ro [in] ri [in] pi [ksi] σt [ksi] σr [ksi] σ' [ksi] SF

Chamber Section

NA 0.457 0.177 53.6 72.5 -53.6 109.6 2

NA 0.327 0.127 53.6 72.6 -53.6 109.7 2

Rifled Section

0 0.286 0.1115 53.6 72.8 -53.6 109.9 2

1 0.270 0.1115 52.4 73.9 -52.4 109.9 2

2 0.255 0.1115 51.0 75.1 -51.0 109.9 2

3 0.241 0.1115 49.5 76.5 -49.5 110.0 2

4 0.229 0.1115 47.9 77.7 -47.9 109.8 2

5 0.217 0.1115 46.2 79.3 -46.2 109.9 2

6 0.206 0.1115 44.3 81.0 -44.3 110.0 2

7 0.197 0.1115 42.3 82.1 -42.3 109.6 2

8 0.187 0.1115 40.2 84.5 -40.2 110.2 2

9 0.179 0.1115 37.9 85.9 -37.9 109.9 2

10 0.171 0.1115 35.5 88.0 -35.5 110.2 2

11 0.164 0.1115 33.0 89.7 -33.0 110.0 2

12 0.157 0.1115 30.4 92.1 -30.4 110.5 2

13 0.151 0.1115 27.6 93.7 -27.6 110.1 2

14 0.145 0.1115 24.7 96.1 -24.7 110.5 2

15 0.140 0.1115 21.7 96.8 -21.7 109.2 2

16 0.135 0.1115 18.5 97.9 -18.5 108.3 2

17 0.130 0.1115 15.2 99.9 -15.2 108.3 2

18 0.125 0.1115 11.8 103.7 -11.8 110.1 2 Table 2. Tabulated results for the static stress analysis.

14

A static analysis was also performed in COMSOL. This was accomplished by modeling the barrel

as a “cylinder” with internal boundary loads corresponding to the pressure distribution. The result is

plotted in Figure 9.

Figure 9. COMSOL static analysis result – safety factor along the inner surface of the barrel versus x.

4.2 Fatigue Life Analysis

Using the method and equations outlined in Section 3.2, several iterations were again

performed on the outer radius at each location to obtain a fatigue life of at least 100,000 cycles. The

results of those iterations are shown in Error! Reference source not found. below.

15

x

[in] ro [in] ri [in]

pi

[ksi]

σt

[ksi]

σr

[ksi]

σ

[ksi]

σa

[ksi]

σm

[ksi]

σ'a

[ksi]

σ'm

[ksi]

σrev

[ksi]

N

[cycles]

Chamber Section

NA 0.493 0.177 53.6 69.5 -53.6 106.9 53.4 53.4 62.9 53.4 79.1 100,292

NA 0.377 0.127 54.6 68.6 -54.6 106.9 53.5 53.5 62.9 53.5 79.1 100,092

Rifled Section

0 0.311 0.1115 53.6 69.4 -53.6 106.8 53.4 53.4 62.8 53.4 79.1 100,563

1 0.290 0.1115 52.4 70.5 -52.4 106.8 53.4 53.4 62.8 53.4 79.1 100,555

2 0.271 0.1115 51.0 71.8 -51.0 106.9 53.4 53.4 62.9 53.4 79.1 100,364

3 0.254 0.1115 49.5 73.2 -49.5 106.9 53.4 53.4 62.9 53.4 79.1 100,129

4 0.239 0.1115 47.9 74.6 -47.9 106.9 53.4 53.4 62.9 53.4 79.1 100,205

5 0.226 0.1115 46.2 75.9 -46.2 106.7 53.4 53.4 62.8 53.4 78.9 101,263

6 0.214 0.1115 44.3 77.3 -44.3 106.6 53.3 53.3 62.7 53.3 78.8 102,073

7 0.203 0.1115 42.3 78.8 -42.3 106.5 53.2 53.2 62.6 53.2 78.7 102,763

8 0.192 0.1115 40.2 81.0 -40.2 106.9 53.5 53.5 62.9 53.5 79.1 100,081

9 0.183 0.1115 37.9 82.6 -37.9 106.8 53.4 53.4 62.8 53.4 79.0 100,949

10 0.175 0.1115 35.5 84.0 -35.5 106.3 53.2 53.2 62.6 53.2 78.6 103,474

11 0.167 0.1115 33.0 86.1 -33.0 106.5 53.2 53.2 62.6 53.2 78.7 102,655

12 0.160 0.1115 30.4 87.7 -30.4 106.1 53.1 53.1 62.4 53.1 78.4 104,648

13 0.153 0.1115 27.6 90.1 -27.6 106.6 53.3 53.3 62.7 53.3 78.8 102,156

14 0.147 0.1115 24.7 91.6 -24.7 106.1 53.0 53.0 62.4 53.0 78.4 105,108

15 0.141 0.1115 21.7 93.9 -21.7 106.4 53.2 53.2 62.6 53.2 78.7 102,945

16 0.136 0.1115 18.5 94.3 -18.5 104.8 52.4 52.4 61.7 52.4 77.2 113,107

17 0.131 0.1115 15.2 95.2 -15.2 103.7 51.8 51.8 61.0 51.8 76.1 121,269

18 0.126 0.1115 11.8 97.0 -11.8 103.4 51.7 51.7 60.8 51.7 75.9 123,039 Table 3. Tabulated results for the fatigue life analysis.

16

5 Discussion Figure 10 plots the barrel profile (outer radius) for both analyses based on yielding and fatigue.

It can be seen that the thickness significantly increased at the beginning of the barrel where the

pressure and greatest. At the muzzle end the difference between yield and fatigue is negligible. Thus, at

small stress levels the geometry need not be adjusted to accommodate fatigue loading if a static stress

analysis has already been performed with a reasonable safety factor. However, at large stress levels the

effects of fatigue loading on the ultimate strength cannot be ignored.

Figure 10. Comparison of hand calculations of outer radius for static loading versus fatigue loading.

The COMSOL plot of Figure 9 displays some large variations in the safety factor. As expected, it

hovers around 2 towards the chamber section of the barrel, and then steadily decreases. At the end of

the barrel the safety factor drops off dramatically. This is likely due to the extremely small thickness

there, and the mesh sizing cannot accurately capture the local stress state.

0.000

0.050

0.100

0.150

0.200

0.250

0.300

0.350

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Ou

ter

Ra

diu

s [i

n]

x [in]

Barrel Outer Radius Versus Position

Yield

Fatigue

17

6 Drawings of Final Design

18

7 Conclusion Ultimately, a barrel mass of 0.75 lb was achieved. With more time, further analysis could have

been performed using COMSOL to obtain more reliable data. It would also be preferable to perform

fatigue analysis in COMSOL; however, this module was not available at the time. The final barrel design

has such a small radial thickness (0.0145 in) at the muzzle that it would not be practical for an actual

barrel. Also, the precise machining required to produce the taper would likely cost more in time and

labor that could not justify the weight reduction. Instead of varying the outer radius at every inch

location, a constant taper from one radius at the chamber to a smaller radius at the muzzle would be

more practical.

19

8 Appendix

20

21

22

23

9 References Budynas, Richard G., J. Keith. Nisbett, and Joseph Edward. Shigley. Shigley's Mechanical Engineering

Design. 9th ed. New York: McGraw-Hill, 2011. Print.

"Barrel Length Studies in 5.56mm NATO Weapons." Small Arms Defense Journal. N.p., n.d. Web. 13 Dec.

2013.

"Metallic Cartridge Chamber Pressure Measurement." Metallic Cartridge Chamber Pressure

Measurement. N.p., n.d. Web. 13 Dec. 2013.