2016

Ballistic Analysis of an Experimental .30 Caliber

Cartridge

NORTHERN ILLINOIS UNIVERSITY

DILLON GARDANIER

1 | P a g e

Contents List of Figures .................................................................................................................................. 2

List of Tables ................................................................................................................................... 3

List of Equations .............................................................................................................................. 4

Introduction .................................................................................................................................... 5

Calculation of Velocity .................................................................................................................. 10

Calculation of Propellant .............................................................................................................. 16

Design of New Casing .................................................................................................................... 19

Future Work .................................................................................................................................. 21

Appendix A: Government Print of Bullet ...................................................................................... 26

Appendix B: Calculation of Velocity .............................................................................................. 27

Appendix C: Volume Calculations ................................................................................................. 29

Appendix D: Calculations of Propellant ........................................................................................ 36

Appendix E: Calculations of Areas and Moments of Inertia ......................................................... 37

References .................................................................................................................................... 42

2 | P a g e

List of Figures Figure 1: Composition of a Cartridge .............................................................................................. 6

Figure 2: Geometry of .30-06 Bullet ............................................................................................. 10

Figure 3: Sub-Geometry ................................................................................................................ 11

Figure 4: illustration of Precession ............................................................................................... 13

Figure 5: New Casing Dimensions ................................................................................................. 19

Figure 6: New Casing Comparison ................................................................................................ 20

Figure 7: Target Analysis ............................................................................................................... 21

Figure 8: Hydraulic Shock .............................................................................................................. 24

3 | P a g e

List of Tables Table 1: Moments of Inertia about Y ............................................................................................ 12

Table 2: Moments of Inertia about X ............................................................................................ 12

4 | P a g e

List of Equations

Equation 1: 𝜔𝑝 =𝐼𝑠𝜔𝑠 sin 𝛼

𝐼𝑝 cos 𝛼 ............................................................................................................ 14

Equation 2: 𝑇𝑤𝑖𝑠𝑡 𝑅𝑎𝑡𝑒 = 3.5∗√𝑉∗𝐷2

𝐿 ............................................................................................ 14

Equation 3: 𝑉 = (𝜔𝑝

0.001489)

3

2.......................................................................................................... 15

Equation 4: 𝑃𝑎𝑣𝑔 = 𝑉∗𝑚

𝐴∗𝑡∗𝑔 .............................................................................................................. 16

Equation 5: 𝑃𝑎𝑣𝑔 ∗ 𝑉𝑝 = 𝑚𝑝 ∗ 𝑅𝑠 ∗ 𝑇 ........................................................................................... 17

Equation 6: 𝐾𝐸 = 1

2∗ 𝑚 ∗ 𝑉2....................................................................................................... 23

5 | P a g e

Introduction

Ammunition is defined as information, advice, or supplies to help defend or attack a

viewpoint, argument, or claim. (Dictionary.com, 2016) While ammunition can take up many

forms, its most common and relatable form would be that of the copper and brass cartridges

used in firearms. So what is this specific type of ammunition composed of in modern times? It

consists of four basic components: the casing, the bullet, propellant, and finally the primer,

together these form what is commonly known as a cartridge.

To begin there is the casing, the main housing for all the other components. It is

generally made of brass with a cylindrical shape and a hole at each end. At one end of the

casing the bullet is housed. The bullet generally consists of a lead core surrounded by a copper

jacket. This is the component that sails through the air, becoming a projectile. The other end

of the casing houses the primer. This is a metal compound that when struck abruptly, will

release a spark to ignite the propellant. Lastly is the component of the propellant, which is

created in a “powder like” substance that is highly flammable. It serves the purpose of

providing the necessary forces to propel the bullet through the barrel. The function of this

cartridge is that once the primer is struck it will ignite the powder. This powder will rapidly

burn, creating a hot and expanding gas. These gasses will push the bullet outward and through

the barrel of the firearm. A breakdown of the components can be seen in the below figure.

6 | P a g e

So how did society reach this level of projectiles? It first started with the creation of

black powder. The invention of this flammable powder was the main driving force for the

industrialization of projectiles. Traditionally projectiles were launched through tension of wood

and rope such as the bow and arrow, or through momentum transfer like that of a trebuchet,

where a large weight would swing an arm containing the projectile. The problem with these

techniques is that they were very inefficient. Meaning large amounts of energy were required

to propel and object sub-par distances. By the application of black powder, an individual could

send a projectile sailing at extremely high velocities with very little effort. The first attempts of

this motion simply took a metal tube that was blocked at one end, then pour powder down the

tube, followed by the desired projectile. The user would then ignite the powder through a

touch hole with some sort of match like device. While this was successful to some extend it left

a multitude of problems in its wake. The most major of these problems was safety, there was

no standard for amounts of powder and often led to the tube exploding and harming the

Figure 1: Composition of a Cartridge

7 | P a g e

operator. This style of firearm was used for quite some time, however, there were several

changes made to the tube itself, transforming it into a more recognizable firearm. However,

with these changes the ammunition style stayed the same.

The big changes to ammunition occurred with the creation of the musket. The main

change here was the use of wadding as well as a new ignition system. Wadding was simply a

piece of cloth wrapped around the desire projectile to create a better seal. With the projectile

well seated, the musket allowed for the operator to apply powder to a small tray near the

firearms barrel and use a flaming wick to ignite this tray and then send the projectile outward.

This style again persisted for quite some time with more modifications being made the rifle

itself, however powder was still simply poured down the barrel followed by the projectile. This

was finally modified by the creation of the first cartridge. However, these were far from what

are seen today. These first cartridges were a forged bullet surrounded in paper tube that was

filled with the powder. Now an operator could simply tear the back of the paper, send the pre-

measured amount of powder down the barrel and follow it with the bullet using the paper as

wadding. This was a huge step forward as it significantly reduced the time and difficulty of

reloading the rifle, while increasing consistency in powder measurements.

The next major invention was the snap cap. This is very similar to the modern primer

and consists of a metal compound that will send a spark when struck abruptly. These were

however not used on the cartridges themselves but used to replace the trays on the sides of the

muskets. However, this new technology allowed for the experimentation which led to creating

a casing that allowed for the entire contents of the bullet to be held in one convenient package.

8 | P a g e

With this new modernized case, new manufacturing methods needed to be created to

produce these now precise instruments. The main manufacturing components that needed to

be implemented was that of cold hammer forging. Small copper blanks are cold hammered to

be stretched into a thin copper cup. Then a molded lead core can be inserted. The shape at

this stage is not crucial because the overall shape is mechanically induced after the two parts

are brought together. Once the proper shape has been formed any excess lead that has leaked

out of the copper jacket from forming is trimmed, leaving the bullet ready to be inserted into

the casing. The casing is formed similar to that of the copper jacket. It begins as a base brass

slug and is heated and stretched to shape. After the main shape is formed, several oxidizers

have entered the metal, thus a solution cleaning and tumbling is conducted to help purify the

metal. Next the required features are machined into the casing, such as the extractor lip. Also

the flash hole is punch and the markings are stamped into the rear of the casing. To finish the

round, the neck is annealed to allow it to be malleable for the insertion of a bullet. (NRApubs,

2012)

Once manufacture of these cartridges was mastered, it led to the design of several other

types of bullets. These types are known as calibers and are what distinguish different cartridges

from one another. Several general calibers are now being produced in large quantities for all

types of use. However, it can often be seen that one of the mass produced calibers does not

meet the requirements of the operator. Meaning that the bullet size may be too big or small,

or the speed it travels is too slow. For situations like this, a hobby known as Wildcatting was

formed. Wildcatting is essentially a homebrewed bullet. Meaning a firearm enthusiast decided

to create their own custom caliber. The catch is that these custom calibers are seldom forged

9 | P a g e

from scratch and usually an adaptation of one of the traditionally marketed calibers. That is

similar to what will be seen in this project. For the case of this study, the .30 caliber bullet is

investigated to be manipulated. The .30 means that the copper jacket of the bullet itself is

roughly 0.300 inches in diameter. The .30-06 Springfield and the .308 Winchester are that of

the two most common .30 caliber cartridges and have been selected to be the base cartridge.

The objective was to determine the highest speed a .30 caliber bullet could travel within some

constraints of rotation. Once that is determined the amount of propellant needed to push the

bullet to this speed was determined, and lastly the size of the case needed to hold such amount

of powder was designed.

10 | P a g e

Calculation of Velocity

The first objective was to determine the geometry of the bullet to be used. This was

chosen to be the 150 grain .30-06 Government Issue round that saw use in the M1-Garand rifle.

The reason for this choice is that it is a very common bullet with very traditional geometries.

The dimensions of the bullet can be seen below, with the original government print be listed in

appendix A. (M1-Garand-Rifle.com, 2016)

With this geometry chosen some very important values were able to be obtained.

These values are that of centroid location, and moment of inertia. The centroid of the bullet is

the location of balance. Meaning that the same amount of mass will be above the centroid as

below, or to the left as to the right. Whereas the moment of inertia can be described as the

bodies resistance to rotation. To calculate the moments of inertia several sub geometries had

to be created. This is due to the fact that Inertia equations are defined for simple geometries

such as a rectangle or triangle. The division of the bullet into these sub geometries can be seen

in the below figure. Note that only half of the bullet was divided and calculated. This is

possible because of the bullets symmetry which allows for these half values to be doubled.

Figure 2: Geometry of .30-06 Bullet

Figure 4Figure 5: Sub-GeometryGeometry of .30-06 Bullet

11 | P a g e

With these simplified geometries created the moment of inertia for each one is able to

be evaluated. It is important to note that the inertia is taken about a certain axis. These axes

are that of the x and y axis created at the point of the centroid of the bullet. The quantities of

these calculations can be seen in the following tables. As well as the location of the centroid in

the x direction. Once again due to symmetry the y location was not needed to be calculated for

the centroid. It is located along the center line of the bullet.

Figure 3: Sub-Geometry

12 | P a g e

Due to the odd geometries of the bullet, the half circle segments near the tip of the

bullet were assumed as triangle in order to calculate an approximated moment of inertia.

Table 1: Moments of Inertia about Y

Figure 10: New Casing Comparisonout X

Table 2: Moments of Inertia about Figure 11: Target Analysisnts of Inertia about X

Table 2: Moments of Inertia about X

13 | P a g e

These values tell the bullets resistance to rotation about the vertical and horizontal axes

centered at its centroid. While conceptually these values do not seem comprehensible they

allow for the calculation of the extremely important concept, gyroscopic precession.

Gyroscopic precession tells the wobble of the bullet. This can be easily visualized by the flight

of an American football. When the ball is thrown it is seldom a perfect spiral, there is usually a

wobble, meaning that the tip of the football can be seen traveling up and down as it travels

through the air. This precession can be seen in the figure below. The football is traveling about

the blue line, and it can be seen that the red line, representing the axis of rotation of the

football, is rotating about the line of travel. (Boal, 2001)

So with this concept of wobble being defined it now needs to be calculated. This is

calculated through a relatively easy equation. However this equation is specifically for torque

free precession. This was used because while the bullet does feel torque within the barrel, it is

Figure 4: illustration of Precession

14 | P a g e

also unable to wobble within the barrel. Thus when it exits the barrel and is now flying free of

torque it is allowed to wobble.

Equation 1

𝜔𝑝 =𝐼𝑠𝜔𝑠 sin 𝛼

𝐼𝑝 cos 𝛼

The above equation specifically calculates the rate of precession or the rate at which the

nose will rotate about the line of motion. Within this equation Is is the moment of inertia about

the symmetric axis, Ip is the moment of inertia about the perpendicular axis, ωs is the rotation

rate of the body, α is the angle of the wobble, and lastly ωp is the rate of precession. For this

equation the inertia values have already been calculated as seen above. Next to be calculated

is that of the body rotation rate.

This is a concept that is achieved by the twist rate of the barrel. This is the measure of

the spiral seen within a firearm barrel. They are usually given in a value like 1 in 10. Meaning

that the spiral will complete one full rotation in ten inches of travel. However this value has a

general formula to calculate idealized values. (Hawks, 2012)

Equation 2

𝑇𝑤𝑖𝑠𝑡 𝑅𝑎𝑡𝑒 = 3.5 ∗ √𝑉 ∗ 𝐷2

𝐿

Within this equation V is the projectiles velocity, D is the projectiles diameter, and L is

the length of the barrel. Traditional barrel lengths for .30 calibers are 20in, 24in, and 26in. A

26in barrel will be used for the purposes of this project, due to the fact that longer barrels

generate larger velocities. This is due to an increased time that the bullet experiences force. By

15 | P a g e

multiplying this equation by another velocity term V, the rotation rate of the bullet as it exits

the barrel can be calculated. With ωs now solved for symbolically a limiting factor needs to be

determined for α. This was chosen to be one degree. This means that the bullet will be limited

to only allow for the axis of rotation to move one degree off of the line of travel. By

substituting these values into equation one, it can be rearranged to solve for the desired

variable of velocity.

Equation 3

𝑉 = (𝜔𝑝

0.001489)

32

The calculations of equation three can be seen in appendix B. This now allows for

velocity to be calculated as a function of the precession rate. This was chosen as a limiting

factor similar to that of the angle of precession. The value was chosen to be two. This means

that the bullet is only able to wobble twice around the line of travel. From this relation a

rounded value of 4100 ft/s was able to be determined for the bullet velocity. At this speed the

projectile will be able to travel across 1000m in roughly 0.8s. This means that although the

precession rate was set to two, it only has enough time to wobble 1.6 times before reaching its

target. 1000m was chosen as a test range because it is often considered the iconic distance for

long range shooting. Any closer ranges results in even less wobble.

16 | P a g e

Calculation of Propellant

With the desired velocity now discovered, the propellant details of the cartridge may be

investigated. To begin this process the pressure related to such a speed is determined.

Equation 4 displays a relation for the average pressure experienced on the system. This

equation was simply derived from both the definition of acceleration and pressure, as well as

Newton’s second law of motion.

Equation 4

𝑃𝑎𝑣𝑔 = 𝑉 ∗ 𝑚

𝐴 ∗ 𝑡 ∗ 𝑔

This leaves average pressure as a function of the end speed V, the mass of the projectile

m, the cross-sectional area of the bullet A, time in which it is experiencing the pressure t given

as 0.0032s, and lastly the gravitational constant g = 32.2 lbm ft/ lbf s2. (Lowry, 1968) All units

were converted to the foot measurement, and calculated to find the average pressure needed

to propel the bullet to 4100ft/s. The pressure was found to be 1,637,209.236 lbf/ft2, this is

roughly 11,000psi. This value was deemed acceptable as a rifle chambers routinely reach

pressures of 50,000psi. One thing to be noted is that this 11,000psi is an average pressure, thus

over the course of the 0.0032s the pressure must increase from zero to a peak value and then

decrease back down to essentially zero. In this time there is a large spike in pressure which can

equal about five times that of the average pressure. Making the correct number to compare to

the 50,000psi be 55,000psi. Which is again well in the range of acceptable pressure.

Now that the velocity has been calculated and allowed for the pressure to be found, the

project moves on to the volume of propellant required to create such pressures. This can be

17 | P a g e

very easily calculated by the ideal gas law. Within this equation, a specific universal gas

constant is used which allows for the use of the propellant weight instead of a molecular

weight. The specific ideal gas law is as stated below.

Equation 5

𝑃𝑎𝑣𝑔 ∗ 𝑉𝑝 = 𝑚𝑝 ∗ 𝑅𝑠 ∗ 𝑇

Here the Vp represents the volume of propellant required to create the pressure, mp is

the mass of an individual grain of propellant, Rs is the specific gas constant equaling 53.3533 in

English units, and finally the temperature T at which the reaction takes place; this temperature

is given as 4860R. (Xiaogang Huang, 2005) With this now formed equation the only value left in

contention is that of the mass of the individual propellant particles. This however became very

difficult to quantify. While it was very easy to locate the weight per cubic centimeter of

propellant there was no value of a specific granular. In order to combat this issue individual

particles were measured by hand. This once again led to problems. The particles were so small

that it was difficult to get accurate measurements. Also it was noticed that from these

measurements the sizes of grains were very dis-similar; because of this a new method to

calculate propellant volume needed to be determined.

The investigation for this solution led to the values of powder weight per cubic

centimeter, as well as reloading guides for different bullets. With this new found information it

was discovered that a specific powder needed to be chosen. In this case the IMR 4895

propellant was chosen due to its more desirable weight to size ratio. It was able to be

determined that 13.736 grains of powder was able to fill one cubic centimeter of space.

18 | P a g e

(Tacticool Products, 2007) A grain is a measuring unit of weight, it can be converted as one

pound is equal to seven thousand grains. With this known, the power of the propellant was

determined through the use of reloading knowledge. Pre-existing experimentation of IMR 4895

powder with a 150 grain bullet is readily available. From three selected loads an average value

of FPS/Grain could be calculated. This means that for each grain of powder the projectile will

fly a certain speed. This figure came out to be 62.8917 FPS/Grain. By combining the knowledge

of 13.736 Gr/cm3 and 62.8917 FPS/Gr it can be determined that 0.2896in3 of propellant are

required to produce the correct amount of feet per second, or 65.2 grains of powder.

19 | P a g e

Design of New Casing

This now leads to the production of the case that is capable of holding the required

charge. A general rule of thumb is that the casing should only be filled up to about 91% of its

capacity. Thus by dividing the volume of powder by a factor of 0.91 it can be found that the

casing needs to be capable of holding 0.3183in3 of volume. As discussed before Wildcatting

usually uses a modified base cartridge, thus to create a casing of adequate size the .308

Winchester cartridge was chosen as the base cartridge. Appendix C shows how the volume of

the .308 casing was calculated. (Sporting Arms and Ammunition Manufacturers Institute, 2016)

Its final value came out to be 0.2474in3, thus resulting in a casing needing to be roughly 30%

larger. For ease of testing the case geometry was decided to remain the same, the new space

would be created by simply elongating the center section. Appendix C also shows how the new

length requirement was derived based off of the geometry given by the .308 casing. The

tradition round had a midsection length of 1.360in whereas the new design required a

midsection length of about 1.7828in. The new resulting case can be seen in the figures below.

Figure 5: New Casing Dimensions

20 | P a g e

This above figure displays the finished cartridge, seen on the left, to the Springfield .30-

06 in the center and the Winchester .308 on the right. It can clearly be seen that the new

cartridge is quite a bit longer than that of the .308 casing, however it is quite similar to that of

the .30-06. With this new found casing, a quantity of 65.2 grains of IMR 4895 powder will be

capable of pushing a 150 grain .30 caliber bullet at a speed of 4100 feet per second through a

26 inch barrel.

Figure 6: New Casing Comparison

21 | P a g e

Future Work

The final product of this project provides a fantastic basis for a round that may even be

capable of starting some testing. Creating a few of the proper sized casings and chambering a

custom barrel for the round would be able to provide several crucial notes of data. The most

important of these would be that of stability. Theoretically based off of this analysis the bullet

would be able to fly in a stable pattern meaning it has that minimum wobble of one degree.

However, if this were to be false, a range test would point this out immediately. Signs of this

occurring would be reduced accuracy of the round, so that the target would be littered with

holes instead of a tight grouping. Also the holes shape would be a good indication of this. If

the holes shape is a tight circle with tearing on the edges it means that the bullet entered

correctly with the tip first. However, if they holes are long lines, it means that the bullets was

tumbling in flight and hit the target sideways. In the figure below, circled in blue shows the

correct way the entries should look in a target, whereas circled in red shows what a tumbling

bullets entry would look like.

Figure 7: Target Analysis

22 | P a g e

Once testing was conducted there would be several factors that would be able to be

investigated for future iterations, provided the new caliber failed. To begin, air resistances

were not taken into consideration for this analysis. The main factor for air resistance would be

that of deceleration. A poor bullet geometry which includes a lot of resistance may show

promising results of speed when fired through a chronograph placed at the muzzle, however

down range it may have slowed drastically. This problem can be caused, in this case, due to the

flat shaped back of the bullet. This will cause a pocket of low pressure air behind the bullet

which produces a lot of drag. By changing the geometry of the bullet to a boat tailed design,

meaning there is a sloped cone shape on the rear of the bullet as well as the front, this pocket

of air will be removed allowing for the bullet to streamline through the air.

Apart from deceleration, if as discussed about the bullet was not stable there are a few

aspects to be changed. Two of these main factors are the twist rate of the barrel as well as the

length of the bullet. Traditional twist rates are that of 1 in 10 or 1 in 12 for a drawn out helix, or

a 1 in 7 to 1 in 9 for tighter helixes. By altering the twist rate the bullet stability can be heavily

influenced. However, this does not act alone. In direct correlation is the length of the bullet

itself. If stability was achieved through twist rate alone, a change in bullet length would most

likely result in a loss of this stability. Thus several different tests would need to be conducted

to determine the best pairing of bullet length to twist rate.

What would be the purpose however, of creating this new round? To start off the

trajectory of the bullet would be extremely favorable compared to that of the traditional

rounds. To visualize the trajectory imagine when a rock is thrown. It travels through the air

and slowly arcs downward as gravity pulls it back to earth. In ballistics the flatter the trajectory

23 | P a g e

the better, because this results in less corrections needing to be made before shots are taken.

No matter what the speed of the bullet is, it will always be experiencing the same amount of

gravitational. Thus by having this higher velocity it can travel a father distance while being

pulled down the same amount, creating these flatter trajectories. Another application in which

this higher velocity is favorable is that of the engagement of a moving target. By minimizing the

flight time of the bullet, one would minimize the chance for the target to move out of the line

of travel. The next component of why this round may be created is that of puncture and armor

piercing capabilities. When given the proper core to generate such effect, by having this

greater velocity the bullet now imparts a higher energy. This can be seen in the equation for

kinetic energy.

Equation 6

𝐾𝐸 = 1

2∗ 𝑚 ∗ 𝑉2

Kinetic energy is a function of the mass of the object m, and the velocity V. Not only is it

a direct relation, but the velocity term is squared meaning that it is the prime contributor to the

energy of the bullet. The higher end of .30 caliber bullets using this powder will see an energy

of around 97,000 ft-lbs, whereas the new round sees about 180,000 ft-lbs of energy. That is

about a 44% increase. This will correlate to the round being able to penetrate not only denser

materials but also thicker. Lastly would be the concept of great controversy, and that is the

hydraulic shock created behind the bullet. This hydraulic shock is what creates a large amount

of the damage caused by gunshot wounds. Basically as the bullet enters a soft material such as

clay or ballistics gel, it will only puncture a small hole for it to move through. However, there is

24 | P a g e

a large shockwave that trails the bullet and this will force a large mass of air through the hole

which will tear open a large cavity.

This figure shows the effects of this hydraulic shock in a block of ballistics gel. The

bottom image is a subsonic round that does not create a shockwave and only pierces a hole

that the bullet can fit in. Whereas on the top image it can be seen that this air being forced in

can have devastating effects. This concept can be cause for some debate, whether it is better

or worse to have more of such a phenomenon. In the case of hunting many people may agree

that it would be cruel to take an animal with such a violent act, however, on the contrary some

may believe it is more humane as the large shock will be able to take the animal quicker and

without the need for suffering. This same type of discussion may be made for the potential

penetration capabilities of this round as well. Although the biggest advocate to penetration is

the bullet composition itself which is heavily regulated by the government.

Figure 8: Hydraulic Shock

25 | P a g e

In conclusion, this is an experimental cartridge based off of the .30 caliber round. The

base calibers that were adapted are that of the Springfield .30-06 and the Winchester .308.

This new wildcat cartridge sees a 30% increase in case size comparted to the .308 and a 44%

increase in kinetic energy. It will push a 150 grain projectile at 4100 fps. Future work for this

project would include prototyping and field testing. With this data, concepts of projectile

geometry and barrel twist rates could be optimized for an accurate and producible round.

26 | P a g e

Appendix A: Government Print of Bullet

27 | P a g e

Appendix B: Calculation of Velocity

28 | P a g e

29 | P a g e

Appendix C: Volume Calculations

30 | P a g e

31 | P a g e

32 | P a g e

33 | P a g e

34 | P a g e

35 | P a g e

36 | P a g e

Appendix D: Calculations of Propellant

37 | P a g e

Appendix E: Calculations of Areas and Moments of Inertia

38 | P a g e

39 | P a g e

40 | P a g e

41 | P a g e

42 | P a g e

References Boal, D. (2001). Torque Free Rotation. PHYS 211 Lecture, 1-5.

Dictionary.com. (2016). Ammunition. Retrieved from Dictionary.com:

http://www.dictionary.com/browse/ammunition

ECUSW (Director). (2013). Moment of Inertia Examples [Motion Picture].

Gardanier, C. (2016, November). Discussion of Bullet Composition. (D. Gardanier, Interviewer)

Hawks, C. (2012). Rifling Twist Rate. Retrieved from ChuckHawks.com:

http://www.chuckhawks.com/rifling_twist_rate.htm

Lowry, E. (1968). Interior Ballistics: How a Gun Converts Chemical Energy into Projectile Motion.

Doublesay and Company.

M1-Garand-Rifle.com. (2016, November). .30-06 Springfield. Retrieved from m1-garand-rifle.com:

http://www.m1-garand-rifle.com/30-06/

Nosler. (2016). 308 Winchester Load Data. Retrieved from Nosler.com: http://load-

data.nosler.com/load-data/308-winchester/

NRApubs (Director). (2012). How Ammo Is Made [Motion Picture].

Research, W. (2016). Circular Segment. Retrieved from efunda.com:

http://www.efunda.com/math/areas/circularsegment.cfm

Sporting Arms and Ammunition Manufacturers Institute. (2016). 308 Winchester. Retrieved from

saami.org: http://www.saami.org/pubresources/cc_drawings/Rifle/308%20Winchester.pdf

Tacticool Products. (2007, February 01). Smokeless Powder. Retrieved from tacticoolproducts.com:

http://www.tacticoolproducts.com/powder.pdf

The Engineer. (2006, October 20). Centroids of Common Shapes. Retrieved from engineering.com:

http://www.engineering.com/Library/ArticlesPage/tabid/85/ArticleID/109/Centroids-of-

Common-Shapes.aspx

Xiaogang Huang, J. G. (2005). Thermal Analysis for a 37-mm Gun Chamber. Army Research Laboratory.