Firearms
Updated: 3/4/05
I corrected the section on rifle bullet
wounding/tumbling.
This is the section of the site where I collect information about
one of my many free time interests: guns. I am primarily
interested in firearms from an engineering standpoint, even though it
is indeed a recreation. Further, there is a great deal of
information available on the subject on the web, but much if not most
of this is disputable or suspect. Often opinion is too mixed with
data from web sources, and there is little distinction made between the
too. Therefore, not only will I endeavor to include as little
"opinion" or "bias" in this page, if either is necessary I will clearly
identify it as such.
I am by background a mechanical engineer, with MS and BS degrees
in that field. I am currently working on my PhD in mechanics of
materials (also ME). You may find a certain proclivity toward
materials and failure (damage) in the content. These are my main
interests; firearms are simply a platform. However, I am no
expert, so don't sue me based on anything contained or claimed on this
page.
Much of the cartridge information is inspired by www.chuckhawks.com,
and while I have made significant improvements and done my own
research, there is a resemblance. Therefore, make no copies of
this data while
I work to substantially improve and make unique this page.
Finally, this page is always under construction as I ferret out more
data and do original calculations myself. I will leave notes to
myself in italics for this purpose. If you have any questions or
content you'd like me to add, just email me.
Firearm Materials
Carbon Steel: AISI 4140
The material used for most barrels is AISI 4140 Cr-Mo
steel. This is one of the most excellent steels produced for
engineering applications. This alloy steel contains by wt.
%: C 0.4, Mn 1.0, Cr 1.0, and a number of other elements in
lesser amounts. This steel, and its popular cousin 4340, are very
popular because they have excellent properties and they are very
hardenable. Hardenability is a measure of the depth of material
that can be hardened during a quenching operation. High
hardenability means more uniform strength and possibly faster
throughput. This steel can be made fantastically strong (UTS 200
Ksi) and hard (Rockwell C 57). This material is used to make
bearing balls, and if you think about it a barrel is basically a
bearing, so this makes sense. This steel is easily machined,
welded, otherwise handled.
One thing it also does well is oxidize. Carbon steel barrels must
be protected from oxidation, since iron oxide (rust) does not form a
stable protection layer on the surface like chromium. Typically
barrels are "blued", which is the designation for any of the various
mixtures of chemicals used to change the color of the steel to a dark
blue/grey color. The blue color is actually oxidized iron, but it
is Fe3O4,
which is a stable layer much like the one that forms on chromium or
nickel. Bluing is also done on drill bits, and that is a very
high wear application. Blue, or multicolored sheen, can be seen on many
heat treated parts such as hacksaw blades. This grows on the
surface during heat treating. The color is dependent on the
thickness, like a soap film. Bluing is not perfect, and standard
Fe2O3 rust
can also form on a blued firearm. Parkerizing is a phosphating
process very similar to bluing. This finish is matte (black
usually) and more durable than bluing, and is preferred by the military
for these reasons. Also, since it does not leave a polished
appearance, the parts can be beadblasted or sandblasted in preparation,
increasing throughput. Incidentally, both of these processes can
be done by a hobbiest with a large stainless tub full of boiling water
and some chemicals which are easily purchased online.
Stainless Steel: AISI 416
Stainless steels have come a long way in this century, and
416 stainless is one of the best available. It can be heat
treated to be very strong (200 ksi) and hard (>50 Rc). It is
magnetic (some stainless materials are not, that is all beginning with
a 3xx) and easily machined due to a high sulfur content. 416 SS
contains (other than iron): <0.15% C, 12.0-14.0%
Cr, <1.25% Mn, <1.0% Si, <0.06% P, >0.15% S. It is
the high Cr content which makes it rust resistant, because the chromium
forms a hard stable oxide which protects the metal. This layer is
only a few molecules thick, so it is hardly detectable. The high
machinability comes at a slight cost of oxidation resistance. The
sulphur also prevents galling and binding which makes this material a
good candidate for bearings.
Martensitic (400 series) SS has a marked ductile/brittle transition at
cold temperatures. Actually, the jump in properties is right near
room temperature, or below depending on what annealed/tempered state it
is in. When the material is brittle, it is still strong, it is
just more sensitive to cracking and fracture. This is most likely
a problem for high impact applications rather than high strength
applications. Wear is a complicated combination of strength and
hardness considerations, and considering the high speed and shock of
the load due to a bullet, firing a stainless rifle in the cold could
potentially be a problem. Low temperature wear of
400 series SS is undoubtedly a topic of research currently, and I will
look into it and update this section.
400 series SS is not very weldable, and does not behave particularly
well after heat treatment. Its toughness and resistance to
oxidation make it a good candidate for firearms applications,
notwithstanding a dramatic change in impact/wear properties in cold
ambient temperatures.
Natural Wood (walnut)
Wood makes a good engineering material, but is widely
maligned as being either insufficient or old fashioned. In
firearms it is used because it is both sufficient and old fashioned,
and very attractive. Walnut has a nice closed grain which makes
it less likely to absorb moisture, and also makes it tough. It is
strong (7 ksi) and durable. A popular problem that is perceived
with wooden stocks on firearms is that they can warp as they take on or
lose moisture from the environment. This is mitigated by sealing
the wood with laquer and the like, but it cannot be totally
avoided. As the wood deforms, it is thought that this can distort
the barrel and reduce the rifle's accuracy. Wood also has a
brittle/ductile transition temperature below freezing. Try
splitting wood in the summer vs. winter. The gummy material in
wood becomes brittle like glass below freezing and the wood can be
split with a wedge very easily. Rifle stocks will therefore split
in the winter much more easily than in the summer (due to impact or
crack initiation at a surface). I am looking into just how much this
warping can affect accuracy from an engineering perspective.
Laminated Wood
This material is very similar to plywood, except the
orientation of the plys is somewhat different. By filling the
wood grain internally with glue, the tendency for the wood to take on
moisture is nullified. Further, this improves the mechanical
properties of the wood somewhat. The laminated (stacked)
structure of the wood is sometimes used to create a layered
topographical look to the stock which is unique to the material.
Laminated wood is also laquered, although mostly for appearance.
This material is thought to be more dimensionally stable than natural
wood, since it is both impervious to water and the pores of the wood
are filled with glue. This material is less susceptable to
brittle failure than its natural counterpart.
Glass Reinforced Plastic
This is the "synthetic" material used in modern plastic
rifle and pistol frames. It can be injection molded and machined
very cheaply and accurately. The glass is added to give the
polymer added strength just from the mixture, but also impact toughness
due to some micro-scale strengthening mechanisms. Glass is also
more dense than plastics, and the resulting material is therefore more
dense. This material, unlike wood, is entirely homogeneous (above
the size scale of the glass) and therefore less susceptable to cracking
along grain directions. It does not change properties near room
temperature (this can be engineered somewhat) and can take a number of
surface finishes.
Firearms
Design and Operation
Basics
Bolt Action
Gas Operated Repeating
Recoil Operated Repeating
Other (of less interest to me)
Firearms
Manufacturing
Barrels
Bullet Dynamics and Design
Spin Stabilization
Ballistics
Expansion
Materials and Design
Firearm Recoil
All information in this table can be found by a combination of using Hornady's (and other
ammunition/bullet manufacturers' websites) toget bullet and MV
information, and this is fed into a ballistics
calculator. One such calculator can be found at http://www.biggameinfo.com.
Recoil is found using a formula found in reloaders handbooks, which
requires the input of the weight of the bullet, the powder charge, the
rifle, and there are some conversion factors thrown in since English
units
make no sense. (7000 grains to the pound (mass), 32.2 pounds (mass) in
one pound (force), when in gravity (32 ft/s^2)). Here is the
equation:
Vr=(Wb*MV+Wp*4000)/(32.2*7000)*(32.2/Wr) =
(Wb*MV+Wp*4700)/(7000 Wr)
Er = 1/2 (Wr /32.2) (Vr)^2=1/2(Wr/32) * [(Wb*MV + Wp*4700)/(7000
Wr)]^2
These can be derived by equating the momentum of the fired shot, with
the propelled mass and velocity balancing the recoil momentum. In
an explosion, or a collision, you cannot assume conservation of energy
of only these products because so much energy goes into heating the
system and producing noise. Note also how the light bullet, compared to
the
heavy rifle, moves so much more quickly than the rifle. Since
energy is related to the square of
velocity, the bullet gets much more of the available propellant energy
than the rifle.
In trying to follow the derivation of this equation, it seems that the
"velocity" of the propellant charge is assumed to be 4000 ft/s on
average. This is fairly complicated since expanding gas is
slowing down, not all
of its energy is given up before the bullet leaves the barrel, and
other factors which lead to the assumption of 4000 ft/s instead of
something
related more directly to the muzzle velocity, or the actual expansion
speed of the powder. In any case, this is an approximation.
According to experts, 20 ft*lbs is about the limit for what
people will shoot well enough to bother. 15 ft*lbf is a better
threshold for fun shooting. 20 ft*lbf is about what is
experienced when shooting an M1
Garand. For reference, here are some approximate free recoil
figures for a number of common rifles and loads.
Rifle
Cartridge
|
Free Recoil
(ft*lbf)
|
.223
|
3
|
.243
|
8
|
6.5x55
|
11
|
.308
|
18
|
.30-06
|
21
|
.300 Win Mag
|
25
|
.338 Lapua
Mag
|
37
|
Some shooters seem to have no problem shooting above 20 ft*lbf for long
sessions, while others cannot. I, for one, do not prefer to shoot
high recoil firearms because I am somewhat bony and high recoil rifles
actually can percuss a nerve in my chest. Proper holding of the
rifle can mitigate some of this: if the rifle is held snugly it will
not have room to accelerate and then strike you like a hammer.
There is a limit to ways to accomodate high recoil though, and one
should examine exactly what they are getting in performance for the
increased recoil cost. This leads to the age old argument about
what cartridge is best, and I will revisit this in the lethality
section.
As for pistol recoil, the same equations are presented for use to
determine free recoil energy and velocity, but the fudge factor used to
compute the contribution of the powder is almost certainly wrong for
these cartridges. Here are some representative values.
Pistol
Cartridge
|
Free Recoil
(ft*lbf)
|
25 ACP
|
1
|
.380 ACP
|
2.5
|
9mm Luger
|
5
|
.357 Mag
|
9
|
.40 S&W
|
10
|
The effect of free recoil energy on pistol shooting is less
straightforward than in rifle shooting since the gun is free to move
after the shot. The increase in free recoil from 5 ft*lbf for 9mm
to 10 ft*lbf for 40 S&W probably does not accurately convey the
qualitative difference between the feel of shooting the two.
Nonetheless, the numbers stand as shown.
note: lbf is "pounds-force" and lbm is "pounds mass". One pound
of mass on Earth produces one pound of force. The true English
unit of mass is the Slug, which is not a pound-mass. Anyway, get
used to arcane
measures in shooting sports. Someday I will get my hands on some
SI data from Europe.
Extensive recoil data is presented in the data tables below.
Firearm Wounding and Lethality
The lethality of rifle and pistol bullets are both quantitatively and
qualitatively different. This is a highly controversial subject,
but is nevertheless a vital one if firearms are to be used properly as
tools. The discussion on this subject is based in large part on
the publication www.firearmstactical.com
. This site is maintained by the "Firearms Tactical Institute",
which seems nebulously connected to the FBI. In any case the
contributors are for the most part either combat trauma surgeons or
forensics experts that do work for the FBI, and much if not most of the
information has been published in peer-reviewed
scientific journals. FTI is mostly interested in
understanding pistol bullet would dynamics, as their purpose is to aid
law enforcement agencies choose adequate firearms for their
duties. I am certainly no expert in this field, but I will
attempt to paint a complete picture of what I have found on the subject
here so that others can check my conclusions. FTI information is
the work of the government, and therefore is not subject to copyright
in the US.
The idea behind bullet wounding and tissue damage involves several
modes of damage which occur at the same time. First, the bullet
pierces tissue and destroys the tissue which is crushed by its
passing. This is not dissimilar to a deep laceration, which
affects only the immediate area, and then bleeds profusely.
Besides a long hole behind the bullet, there is a permanent cavity
which is an expansion of the bullet trail as the result of the high
stresses around the bullet. This is typically only a couple times
the size of the bullet. There is also a temporary cavity,
which exists only for a couple of milliseconds after the bullet passes,
and occurs because animal tissue is very elastic, more than many
rubbers! The tissue recoils from the shockwave of the passing
bullet, and then crashes back together. Other materials, like
jugs of water or phonebooks, do not exhibit a temporary cavity because
they are not so rubbery. It is the temporary cavity which is the
cause of much of the controversy over bullet wounding.
Rifle vs. Pistol
There is a magical velocity watershed which is considered to separate
bullet wounding from rifle wounding; bullets below 1800 fps are pistol
bullets, above are rifle bullets. A quick flip through a military
emergency medicine manual will give plenty of evidence of the
difference between a rifle wound and a pistol wound. There is
extensive remote damage around the bullet track of a rifle bullet,
commonly assumed to be caused by a "shockwave", since rifle bullets are
supersonic. First, rifle bullets travel faster than the speed of
sound (of air, c=1100 fps) (and so do most pistol bullets), but the
speed of sound in a solid or liquid (water, c=4900 fps) is much higher
than the speed of a bullet. Thus, it is a misconception to
imagine the damage due the the same process by which jets make a "sonic
boom".
Why then does a rifle bullet cause
so much damage? After a search through the literature, I have
uncovered the answer. Bullets mainly only cause damage to the
tissue which they impact. This is largely due to the fact that
bullets are made to be aerodynamic, and therefore are so streamlined as
to pass through the body easily as well. Expanding bullets become
less hydrodynamic, but also stop quickly, and may fragment and lost too
much momentum to penetrate. Rifle bullets tend to be long and
narrow, like an arrow, and in this way are very aerodynamic for the
mass of the projectile. However, when they are passing through
tissue, any very small deflection puts a pressure force on one side of
the bullet, which tends to further deflect it. When a bullet
turns sideways inside the body like this, it is called
"tumbling". This is the source of massive damage in rifle
wounds. As a bullet tumbles, the non-aerodynamic disturbance
greatly increases the size of permanent and temporary cavities, not to
mention the actual penetration cross-section. Handgun bullets are
short and fat, and if they tumbled they would not really be any
different in cross-section during the passage.
As an example, consider the feared 7.62x39 (AK47) bullet. This
bullet travels at "rifle" speed, but in ballistic tests (and in
surgical observations) is shown to not begin tumbling after contact
with a soft medium in less than a foot. Therefore, the bullet
passes through the body quickly and cleanly, without causing much of a
mess. Bullets such as the 7.62 NATO do indeed tumble inside the
body, but the initiation of tumbling is dependent on the
manufacture. US made bullets tend not to tumble, compared to
other NATO made bullets. Hollow point or soft point bullets cause
massively more damage, both through tumbling, enlarging, and
fragmenting.
As a final note, competition grade bullets are now made with "Boat tail
hollow point" designations, supposedly making them more accurate.
There is something to this. The hollow point moves the center of
mass to the rear of the bullet, making it more able to resist the yaw
causing pressures which cause tumbling in the body, and inaccuracy in
flight. This is also why competition bullets are explicitly not
for hunting use, as they are designed not to tumble and generally pass
right through a target.
Penetration
Therefore, while rifle bullets can have devastating effects due to the
huge region of damage caused, pistol bullets only really damage what
they touch. Ignoring the marginal effect of fractions of an inch
in wound diameter, the only important factor in pistol wounding
potential is how far the bullet travels in the body. If it passes
all the way through, then it will have pierced everything in its path,
and this is the maximum amount of damage possible. Several shots
may be necessary to pierce a vital site and cause enough trauma to
force physiological incapacitation. There has been a second
school of bullet wounding which calls for a rapidly expanding bullet,
or even better a pre-fragmented bullet, with the idea that the bullet
will get much larger and disrupt more tissue by an increased effective
diameter. At the extreme is the Glaser, which is essentially
epoxied shot shaped into a bullet and partially jacketed. These
expand and explode, causing a nasty mess. However, they only
penetrate a couple of inches, and are unlikely to make it into a vital
organ. If the intention is to let some poor mammal die slowly due
to infection, this is the way to do it. It does cause a lot of
damage, but superficially, and not in a way which is particularly
useful.
Pistol rounds are generally classified according to how many inches a
particular bullet will penetrate into a person, and 12" is a good
depth. One way this is done is using a powerful charge, and then
designing the bullet to expand and slow down at a rate which causes it
to stop about 12-16" into a target. Not all tissue resists
penetration the same, and it has been shown that the rear layer of skin
on a person is ballistically equivalent to about 4" of muscle, due to
it being so elastic and tough. Therefore, if a bullet can
penetrate 16" of tissue, and it has traveled 13" when it gets to the
rear layer of skin, it won't exit but instead will come to rest just
under the skin. Many bullets are found lodged just under the far
hide of an animal, and this is the reason why. The first layer of
skin can't stretch and slow down the bullet because it is stretched
over the body; it is instead crushed. A simple experiment with a
plastic wrapped pound of ground burger shows this phenomenon well, just
pierce all the way through it with a finger and see how easy the front
and hard the back is to penetrate.
One example of how penetration and collatoral damage is important comes
from the design of the .223 Remington bullet. Military bullets
must have a full metal jacket, which means that they are essentially
armored and will not expand inside a body in order to cause increased
damage due to expansion or fragmentation. If these bullets are
very sharp, they can pass through the body without leaving much of a
damage wake. The .223 Remington was designed to get around this
problem. When entering the body the light, long, high velocity
bullet immediately begins to tumble and break apart. This causes
a damage zone similar to a pre-fragmented bullet. This does not
make it more lethal necessarily, but it does get more tissue damage
done compared to a light bullet which stays together. (.223 wounds show
up as long bright debris tracks on x-rays) Keeping in mind that
this is a military cartridge, this highly desireable because now the
enemy has an inconvenient and messy casualty to deal with. The
main competitor to this round, the 7.62x39 (AK-47 round) causes
relatively little secondary damage and exits the body cleanly and
almost undeformed. This was used in an infamous school shooting
in California, and the facts of the damage of the 7.62x39 were totally
blown out of proportion. Bullet deformation does determine to a
great extent whether it leaves the body and what it is capable of while
it is in motion. This can result in counterintuitive outcomes,
like the lame little .223 being quite effective exactly because it
explodes and makes a mess. An excellent discussion of this by
Col. Martin Fackler, MD can be found here
(as a crude copy, I'm collecting some papers on the subject).
On this subject, there have been designed some experimental bullets
which do not have nice convex tips, but in fact have concave sides
designed to direct impinging tissue off to the side like a snow
plow. These can be optimized to cause remote damage without
relying on any kind of expansion. These may not have as much of
an effect in pistols as in rifles. Given the dominance of
cavitation in the total wounding potential of a bullet, bullets
designed to cause more cavitation are an obvious and overdue
development.
Shotgun pellets will slow down in the body very fast due to their high
surface area and low mass. Therefore these don't penetrate
targets enough to be guaranteed to cause critical damage. The
huge amount of damage and trauma done is not to be put down
though.
Psychological Factors
According to Firearms Tactical physicians, the greatest factor
contributing to "stopping power" is the psychological impact on the
target when they are hit. Most people quit fighting as soon as
they are shot, and not because they have been rendered physically
incapacitated. Without trying to cite too many examples, there
are some extreme cases which can clarify this. Soldiers on the
battlefield can routinely operate with whole limbs blown off or several
bullet wounds to the chest, and policemen in a firefight have been put
down by a single shot from a 22LR pistol to the upper arm. While
the psychological factors governing what one does after getting shot
are not fully understood, one hypothesis goes that people give up or
fall down because they are somehow conditioned to believe that is what
they should do. When someone is sufficiently motivated to keep
fighting they can ignore all such impulses and continue to act after
being shot many times. It is these people that police must be
prepared to face, and it is this scenario for which their firearms are
optimized. The only way to guarantee that a motivated attacker
will stop is to either destroy the nerve center (head/spine shot), or
to cause enough critical damage that they bleed enough to pass
out. It is this scenario that totally fails pre-fragmented
ammunition.
Stopping Power
A great deal is made over the concept of "stopping power", particularly
in pistols. The idea is manifold, but there are several main
thrusts which can be addressed separately. First, there is the
idea that more energy imparted to the bullet necessarily means that it
will be more effective at killing a target on impact. A corrolary
to this says that if a bullet exits the body, it wastes some of this
precious energy. This argument completely ignores the idea of
effective damage, and assumes that a target is a homogeneous sausage
full of vitals which simply need to be disrupted by damaging
energy. Obviously this is not so, especially with pistols.
More energy might seem also to be able to knock down a target.
Given that momentum is conserved in a gunshot, the amount of recoil
felt by a shooter is exactly the momentum felt by the shot. If a
target got knocked over, so would the shooter.
The second, and more widely adhered to, concept of stopping power comes
from the work of Marshall and Sanow on what is commonly called
"One-Shot-Stop"ing power. This is what the guys at the FBI rail
against so much, and I'll try to present the problems with the idea
here (leaving out such issues as conflict of interest and ethical
complications in the work). Basically, the idea is that while lab
technicans and ballistics experts might be able to measure certain
quantities and make predictions as to the effectiveness of a cartridge
or bullet, that real statistics on lethality resulting from real
shootings is the only real laboratory for judging life-or-death
effectiveness. This is not a bad premise, at least from the
standpoint that all data is useful to an investigator. The idea
progresses from there not to a measure of overall effectiveness in a
fight, but particularly how likely one shot of a cartridge is to render
a target incapacitated or dead immediately. This too seems like a
reasonable metric for effectiveness, on the surface. The
investigators claim to have interviewed hundreds of policemen involved
in shootings and visited morgues to look at damage from firefights, and
present a complete (and continually updating) catalogue of the one-shot
effectiveness of every round. This has been widely disseminated
and touted for years.
There are two main problems with this research though. Similarly
to the energy argument, there is no mention of where each subject was
shot, and we are left to wonder if a shot in the shoulder with a .357
magnum has a 90% chance of incapacitation. What about the
leg? This is not semantic. We are not told how this
statistic was reached. If two bullets have struck a target in
non-lethal areas, a third in the chest will have a dramatically
different effect than if it were the first. Also, what were the
circumstances of the shooting? Was the subject fleeing?
Were they on drugs? There is no relative basis for just what this
number means. The psychological part of being shot is such a
large influence that it is hard to believe that a mechanical statistic
of this nature has any real applicability. The second problem has
to do with statistics, and I alluded to it just a minute ago. In
order to get a good, fair picture of what happens in gun fights an
investigator would have to sample randomly from all of them without
knowing the outcome or circumstances. This includes consideration
of how many shots were fired. This is impossible due to how many
happen, and how slowly they are catalogued. Further, one would
have to take so many samples that all the different scenarios in which
shootings happen would be fairly represented, for every bullet in the
study! This is easily billions of data points. The Marshall
and Sanow study accomplishes neither of these basic requirements.
They examine an extremely limited number of cases, in which certain
factors are known to be present, and miraculously their expected
conclusions are borne out in the data. They will not release
their data, and their claims have been contradicted by people cited as
submitting factual information for the study.
Finally, the Marshall study is not in any way Mechanistic, meaning
there is nothing to understand or not understand. Penetration,
wounding, permanent and temporary cavities, these are quantities which
are independently verifiable. While experience gets a great deal
of credit in the firearms world, experience cannot overcome the laws of
physics, even though perception and memory can seem to. The
science which drives firearms effectiveness is the subject of this
entire page, and the motivating factor to keep the page complete and
factual stems from the lessons of the stopping power debate (and the
gun control debate too).
Firearms Safety
DATA TABLES
This is a very large table, including bullet energies,
trajectories, and recoil figures.
An excel version of this table can be downloaded here. This version is better since the
headings are locked at the top of the screen, and it is easy to
manipulate things.
Rifle Cartridge Data
Here is a data table with several calibers each with several
loads. There is less detail in this table.
Pistol Cartridge Data