Long
Distance Rifle Ballistics:
A Guide for the Competitive Rifleman
You never get a second change to make a good first
shot, and this book is indispensible for any long-distance rifleman who
needs to make their first shot count.
This handbook is designed to give the professional
and non professional long distance rifleman a functional understanding
of ballistics without obtaining a four-year degree in physics.
While much of the content of this book is supported by proven
science, we deliberately skip-over the dense math and over-generalize
and simplify each concept.
Starting with easy-to-understand elementary rifle ballistics principles
we illustrate each concept in plain English and easy to understand
illustrations.
Towards the end of the book we fill-in the blanks
and create a comprehensive view of rifle ballistics, complete with the
equations, and annotated with proven scientific studies.
High on pragmatism and short on theory, this is an
indispensible ballistics guide to the big game hunter, competitive
marksman and military sniper.
By the end of this book you will have a general
appreciation of every aspect of firearms ballistics and understand the
relative importance of each factor, all the way from the trigger pull to
impacting the target. The
concepts in this book provide insights that make the difference for any
competitive long-distance rifle competitor.
This is a must-read book for anybody who needs to
understand the physics behind firearms ballistics. If you are already an
expert marksman who needs that “competitive edge”, this is the book that
can make the difference between success and failure.
Introduction
Ever since the Chinese created the first
hand-cannons from large stalk of bamboo, people have been working out
ways to make firearms functional over longer and longer distances.
Even as late as the American Civil War, cannon
ballistics was an inexact science, an expensive trial-and-error process
that was both inefficient and dangerous.
Even in 21st century Afghanistan, U. S. military
studies show that it takes nearly a quarter million rounds to kill a
single terrorist.
It’s important to remember that every gun is unique
and that even tiny factors can make a huge different when shooting at
distances of 1,000 yards or greater:
Rifle
action and body
Every rifle is unique and has its own “signature”
for optimal ballistics.
Ammunition
Many professional marksmen used “match grade”
ammunition and target shooter will reload their own ammunition.
Trigger
A championship trigger should have a pull of less
than five pounds, with limited “travel”.
At trigger release time, the release should be “crisp”, like the
feeling of snot on glass.
Barrel wear
Barrels need breaking-in, just like a car.
Also barrels wear out, especially high caliber rifle chambers.
Barrel life is directly
influenced by the peak pressure in the barrel (near the chamber) and by
gas volume.
Bullets
Obviously, the shape, size and weight of a bullet
make a vast difference in accuracy.
The weight of a bullet is especially important when shooting a
living target. It’s not
just the velocity of the bullet that counts; the higher the weight of
the bullet, the higher the Kinetic energy.
Higher Kinetic energy increases the gyroscopic stability for long
distance shooting (usually shot from a rifle with a faster twist).
A higher Kinetic energy also improved the wallop at impact.
It’s like the different in impact damage after being hit by a
golf cart versus being hit by a dump truck.
This chapter will take a brief look at the history
of rifle ballistics so that we can appreciate the impact of technology
of long-distance shooting and understand that some fundamentals have not
changed in centuries.
Basic
Ballistics Terminology
Xxx
External factors:
Winds
A good marksman must be able to gauge “windage”,
the side-to-side variances in the bullet flight path caused by the speed
and direction of a breeze.
Over distances greater than half a mile there may be multiple winds,
each at a different direction and velocity.
Expert riflemen have a sixth-sense that has been dubbed “Kentucky
Windage” because it looks like magic.
Gravity
Normally gravity is a constant, but it the
real-world gravity is less at the equator than at the poles!
The earth is not round, it is pear-shaped and widen below the
equator. The centrifugal
force measurable reduced the pull of gravity at the equator (the
Coriolis effect <ADD CONTENT>) Gravity also plays a role at altitude.
For example, a 55 grain bullet at sea level will weigh less than
55 grains at 14,000 feet of altitude.
Because the rifle path must be arched-upward to
account for the pull of gravity, there will always be two spots where a
bullet will cross the target elevation.
For example, an AR-15 with “battle sight zero” will
sight at 38 yards and 300 yards.
Air Density
Dense air (barometric pressure) produces more
bullet “lift” and also helps by providing a mirage for you to gauge wind
direction and speed. This
is why high altitude mountain goat shooting is more challenging than big
game hunting at sea level.
Air
Temperature
Hot air is thinner than cold air, and all else
being equal, a bullet will travel farther and higher on a cold day.
Movement of
the earth
The earth constantly rotates to the East at a speed
of 750 miles per hour. We
do not notice this movement as wind because the atmosphere is also
rotating at an identical speed, but we do see evidence of this rotation
in the “jet stream” at high attitude.
The jet streams snakes eastward in the northern hemisphere in
direct reaction to the earth’s natural movement.
Water DOES NOT rotate in different directions at
each side of the equator.
The Coriolis Effect is too small to measure in most
cases, but long-distance projectiles must consider that the earth is
moving beneath them. In
most cases, only huge artillery (8 inch bore or greater) considered the
movement of the earth.
Relative
motion
Assume that we have a bullet fired backwards from a
jet fighter travelling at 2,000 miles per hour with a muzzle velocity of
2,700 feet per second (1,841 miles per hour).
The bullet would still maintain its speed through the air even
though the “real” speed of the bullet upon hitting a stationary object
would be negated by the elative motion.
Conversely, firing a bullet forward from a fighter
plane moving
would be
Bullshit? (page 106)
British Small Arms committee in 1886 said that the
movement of the earth
causes a 6 inch deviation at 1,000 yards in the Northern hemisphere and
a corresponding six inch left deviation in the southern hemisphere.
Maximum drift occurs when the bullet is fired
toward the Southeast and the minimum drift occurs when the bullet is
fired toward the northwest.
The amount of deviation due to the earth’s rotation
is varies according to the distance from the equator.
“Generally, the bullets curve will be about one
tenth of an inch in 125 yards in the central part if the US”. (Ricker,
p106)
Hollow-point bullets have the negative consequence
of shifting backwards of the center of gravity but they also improve
gyroscopic stability by decreasing the de-rotation effect.
Precession pg 90
Nutation (page 93)
Type of ballistics
·
Internal ballistics:
These are the machinations that occur between the chamber and the end of
the muzzle. These internal
ballistics are hidden and hence, very difficult to measure empirically.
·
External ballistics: External ballistics covers the distance from
the muzzle to impact and includes the flight path and aerodynamic
characteristics of the bullet.
·
Forensic ballistics:
The term” forensics” relates to a study of the law, and forensic
ballistics is used by law enforcement to measure the
All rifles from a .22 caliber plinker to a 50
caliber sniper rifle operate on exactly the same principles of
ballistics. Let’s start
with a simple review of the parts of a rifle:
·
Trigger
·
Chamber
·
Barrel: The barrel is an extension of the bullet chamber that holds
the gasses as they burn.
The barrel is exposed to tremendous pressure such that only metal is
strong enough to contain the pressure.
·
Muzzle: This is the
exit point where the bullet and gunpowder meet the open air.
There are several attachments that may be added to the end of a
muzzle including a silencer, a flash suppressor and a muzzle break.
·
Muzzle Brake: The
muzzle brake acts to deflect the upward pressure of the bullet, reducing
recoil and keeping the bullet at a flatter trajectory.
·
Rifling:
These are the “grooves” that are cut into the barrel to impact
spin. This spin acts like a
spinning top to give the bullet gyroscopic stability.
·
Flash Suppressor:
·
Gas valve:
Gyroscopic drift:
about 13 inches for a 30-06 at 1,000 yards.
We also need to cover the basic properties of
ammunition:
Barrel
Caliber
This is the measure of the diameter of a bullet and
barrel interior diameter, measured in 1/100th of an inch.
A .50 caliber bullet is one-half inch wide, and a .38 caliber
bullet is about 1/3 of an inch wide.
Bullet
The weight of a bullet is measured in “grains” with
7,000 grains per pound.
Table 1.1 shows the common weights associated with common calibers of
bullets.
Shell
casing
The Brass quality influences the bullet trajectory.
Some shell casing the not completely round, but slightly conical
shaped, wider at the primer-end and tapered by a few thousandths of an
inch where the bullet is seated.
Consider the difference between a .22 magnum cartridge and a
standard .223 cartridge (Figure x.x).
These buckets are essentially the same caliber, but the .223
bullet is 55 grains and the “shoulder” in the shell casing allows a much
greater diameter of powder in the chamber (Figure x.x).
This idea of having a cartridge that is of a larger
diameter that the caliber allows for increased pressure for the bullet,
but the slant of the shoulder is very important.
I short taper in the shoulder is ideal for
increasing bore life, while a longer taper will cut-down on the bore
life because of the way that the expansion of the gunpowder forces the
brass into the front of the chamber.
In competition rifles with fully-packed cartridges (e.g. 308 at
1,000 yards) the forces in the chamber causes the barrel chamber to
become sub-optimal after only 1,100 rounds. (Figure (x.x):
Bullet
Crimp:
A tighter crimp of the bullet to the shell means
that more internal pressure is required to start the bullet moving down
the barrel.
Powder
The gunpowder is a mixture of chemical that can
burn at a very fast rate without the benefit of oxygen.
Primer
A primer is an unstable chemical such as “fulminate
of mercury” that create a fiery “flash” when struck by the trigger
firing pin.
Other Terms:
·
Muzzle Flash: This is
where un-ignited gunpowder residue meets with oxygen and buns.
A muzzle flash is impressive, but it gives-away a snipers
position, and from a ballistics viewpoint, a muzzle flash indicates
wasted energy.
·
Muzzle Velocity: This
is the speed (measured in feet per second (fps)) for a bullet as it
leaves the muzzle. The
muzzle velocity can range from 100,000 feet per second (about 682 MPH)
for a small .22 caliber plinker to over 3,000 fps (2,000 MPH) for a .50
caliber sniper rifle. The
muzzle velocity varies inversely with the mass of the bullet (small mass
= higher velocity), and the muzzle velocity varies directly with the
size of the caliber (greater caliber - greater velocity)
Barrel
A barrel must be both strong and flexible, and only
metal compound have the strength to hold the high pressure of the
gunpowder reaction and the flexibility to deal with the forces made by
the bullet. All else being
equal, a fat “bull barrel” is better at minimizing barrel movement, but
the extra weight makes it hard for soldiers.
Today, barrels are made from titanium and stainless
steel and no plastics or non-metal compounds can contain the pressure of
a gunpowder charge.
Gunpowder
Ballistics
Contrary to popular opinion, gunpowder does not
explode, it simple burns quickly.
While a firecracker is essentially black powder wrapped into a
tight paper tube, gunpowder burns at a fast rate but it does not
explode.
To understand this, let’s look at the relative burn
rates for C4 explosive vs. modern gunpowder:
xxx
Original black powder date back to the Middles Ages
and was created with simple ingredients:
·
Charcoal: This is the
“fuel” for the burn. (15%)
·
Saltpeter: Salt peter
is created by spreading line over animal feces and harvesting the
drainage, creating Potassium Nitrate (KNO3).
(75%)
·
Sulfur: This is the
only “mined” component of black powder. (10%)
In an ideal world, black powder gunpowder would
burn as a constant rate, but in reality, gunpowder burn rates are
influenced by are within the chamber (“squib” loads), moisture (“Keep
your powder dry”) and many other factors.
Pressure is also required for the chemical reaction
in gunpowder. At the
pressure peak (one inch or so from the chamber, the pressure can exceed
50,000 pounds per square inch (psi) while the pressure at the muzzle
exist drops to about 5,000 psi. (Figure x.x)
Figure x.x – Changes in pressure for a travelling
bullet
At the mid 19th century black powder started to be
replaced by “smokeless powder” a different chemical cocktail with
different burning properties. Smokeless powder was called “plastic
monopropellant” and it was very advantageous because it was less messy
and corrosive and allowed a shorter barrel, making for easier combat
with lighter rifles.
Alfred Nobel (of Nobel Prize fame) helped develop
modern gunpowder’s and it’s interesting that the ”fuel” for the
gunpowder chemical reaction was changed from charcoal to cellulose
fibers, originally carbohydrates or cotton fibers.
The smokeless powders also allowed manufacturers to create coated
particles with more uniform burn rates.
Today we see “fast powders” that burn to create
higher bullet velocities used in shotguns and pistols, while we see
“slow powders” that are used in long distance rifles.
·
Shotguns use a dense “heavy” powder
·
Handguns require a “fast-burning powder”
·
Long distance rifles use slow-burning
powder: All else being
equal, a slower gunpowder requires a longer barrel.
Modern gunpowder is very stable and will only
ignite at temperatures in excess of 300 degrees.
100 pounds of gunpowder has the same explosive energy as only 10
pounds ( xx gallons) of gasoline.
When machine gun barrels get hot from excessive firing (e.g.
combat) the barrel temperatures can cause the barrel to glow red-hot,
causing bullets to “cook off” and ignite spontaneously.
In general, standard ammunition has a ratio of one
grain of gunpowder for every three grains of bullet weight.
For example, a 60 grain bullet would require approximately 20
grains of gunpowder.
It is not necessary to completely fill the shell
casing to the bullet, and you can create lighter loads called “squib
loads”. Squib loads can be
used for practicing and help with barrel longevity in large caliber
target rifles. When using
Squib loads it’s important to pack the powder down at the primer-end
using an inert substance such as Dacron or Kapok.
A 15% decrease in the volume of the gunpowder will reduce stress
at pack pressure (immediately outside of the chamber) and translate into
a 25% increase in barrel life.
Firing
Ballistics
At firing time, the following sequential steps
occur:
Trigger time
Ignition time: Internal combustion
As the gunpowder burns there is a rapid increase in
volume, but this pressure is not uniform.
Initially, the pressure builds to a point where the bullet begins
to travel from the shell casing, but in less than a quarter inch, the
pressure drops off. This
drop is pressure is a function of the bullet acceleration and the energy
required to start the spinning through the rifled groves of the barrel.
By the time the barrel leaves the barrel the bullet can spinning
at over 250,000 RPM and travelling at over 1,000 feet per second.
Only 30% of the gunpowder energy goes to the
bullet. Another 30% is
wasted as heat energy and 40% is wasted on noise and recoil.
Greasing a bullet shell can cause less space in the
chamber and cause the brass to slide forward into the chamber causing a
30% increase in chamber pressure. In general, it’s not a good idea to
polish or grease a chamber as some friction is required to properly seat
the shell casing.
Recoil begins while the bullet is still in the
barrel.
If you disable
the gas valve in a semi-automatic rifle, the recoil increases but the
muzzle velocity will decrease by 15%.
(page 69)
Pistol
Caliber
Bullet Charge
muzzle velocity
.22
40
01.1
800 fps
.32 auto
50
00.9
760 fps
.38
88
03.8
990 fps
.357 mag
158
16.0
1,235 fps
.45 Colt
250
08.5
860 fps
Rifle
Caliber
Bullet Charge
muzzle velocity
.223
55
27
3,240 fps
.308
150
47
2,820 fps
.3030
170
32
2,200 fps
Bullet
Ballistics
A bullet shrinks in diameter as it moves down the
barrel.
Studies have shown proven that this bullet
shrinkage is related to barrel length:
A) A bullet is fired into water and the bullet
retrieved and measured with a micrometer.
B) One inch is cut-off from the muzzle end of the
barrel and the test is repeated
In each successive trial, the lossage in caliber
decreases
Chapter x:
Barrel Ballistics
The pressure of the bullet moving through a rifled
barrel creates centrifugal force.
Even in a rifle with a slow twist, exist spinning can exceed
250,000 RPM, placing a huge outward force on the bullet.
A new barrel needs to be “broken in”, using a
method called fire-lapping.
For competition high-powered rifle barrels, a complete log of every
round fired is required and barrels are replaced every 1,100 rounds.
When a barrel is replaced, it is because the chamber-end has
become sub-optimal (CARL WHY?)
A used barrel can be removed and a new chamber
drilled, making a useful barrel that is several inches smaller than the
original barrel.
The length of the barrel influences the exit
pressure (muzzle velocity).
This data for a 30-06:
Barrel
Length
Muzzle Velocity
24 inches
2,700 fps
30 inches
2,850 fps
There are limits to effective barrel length.
A .22 rifle is most efficient at a 18” to 22”
barrel length.
Barrel whip
and bulge
As the bullet moves through the barrel, a “whip”
effect is imparted. It’s
like holding a fishing rid horizontal and quickly flipping it upward.
The end of the fishing rid quickly moved downward and then reacts
and begins moving upwards.
As the bullet moves through the barrel, a bulge is formed immediately
before the bullet. This
“swelling” move down the barrel ahead of the bullet and the expanding
gasses, ending with the bullet traveling slightly upwards as it exist
the muzzle.
The rifling also imparts torque on the barrel, in
the opposite direction as the rifling.
A 30-06 will show as two inches left (from a right-hand rifling
twist) at 500 yards.
As the bullet leaves the muzzle, this centrifugal
spin can cause the bullet to “yaw”, creating a spiral helix pattern.
Anyone familiar with the “double helix” of DNA knows the look of
a spiraling bullet flight path.
In long distance rifles, this spiraled flight path
is quite small, not exceeding the diameter of the bullet.
In some long range bullets it takes 200 yards for the bullet to
become completely stabilized.
Free Boring
The idea of free boring was to leave an un-grooved
area for a few inches past the chamber with no rifling.
This was supposed to give the bullet a “head start” down the
barrel before the rifling kicked-in to impart a spin.
Free boring does not work
For the best accuracy, the rifling should meet the
chamber, and the bullet actually touching the rifling at trigger time.
Gain twist
A Gain twist happens when the rate of twist
increases toward the muzzle end, increasing the acceleration of the
bullet spin at the end of the rifling.
Measuring
rifling twist
It’s easy to measure rifle twist.
All you need is a standard brass cleaning rod, a “sharpie” marker
and a measuring stick.
1 - If possible, clamp-down the gun to remove
movement.
2 – Thread a cleaning rag through to open hole in
the flat side of the rod plunger.
3 – With a
sharpie, draw a line down the length of the brass cleaning rod.
4 - As you start the plunge, mark the barrel at the
point where the rag begins to twist into the grooves of the rifling.
5 – As you continue to plunge the rode down the
barrel, you will observe the brass rod twisting as it progress.
When the rod reaches the point of a full-twist (as denoted from
your first mark on the barrel), make another “cross mark” on the rod and
withdraw it.
5 – Now, simply measure the distance between the
end of the rod to your cross mark.
This distance will be the travel for a single
rotation. If the length is
7 inches, you have a 1:7 twist.
If you have 12 inches, you have a 1:12 twist.
Optimal
rifle twist
It is a common misconception that it is the weight
of a bullet determines the optimal gyroscopic twist rate twist rate.
The gyroscopic stability varies as the square of the rifling
twist, such that a small change in twist creates a big change.
This is because the velocity is a function of the square of the
rotational speed, such that a small increase in rotational speed results
in a large decrease in velocity.
The Greenhill equation is named after Alfred
Greenhill, a ballistics researcher in the late 1800’s.
He developed a fairly accurate equation for estimating the
“optimal” twist for a barrel based on the bullet length and the caliber.
The Greenhill equation uses a constant of 150 for muzzle
velocities under 2,000 feet per second and 180 for muzzle velocities
greater than 2,000 fps.
Greenhill says that it’s the LENGTH of the bullet
that matters, not the WEIGHT (even thought the length and weight are
correlated). Important
note: A linger bullet
requires more gyroscopic stability (a faster spin).
Hence, a longer bullet is more susceptible to a “tumble” at long
distances than a short bullet od equal weight.
A pointed bullet has more aerodynamic stability
than a round-nosed bullet but it has an increased risk of tumble.
A U. S. Army study in 1880 using .45 caliber round nose rifle
bullets (500 grains) at 3,500 yards (almost two miles) showed that the
fat round tip bullets did not tumble at great distances.
At 3,500 feet, the bullet was exhausted and had an impact angle
to the ground of 65 degrees, but the bullet was still tip-forward!
All else being equal, pointed tip bullets will
tumble at this distance.
Given:
30 caliber bullet = .308 inches in diameter
Bullet length (inches) = 1.125
Optimal Twist = (150 / (Bullet
Length/Caliber))*Caliber
= (150 / (1.125/.308))*.308
= (150 / 3.65)* .308
= 41.09 * .308
= 12.65 twist
If two bullets have the same spin and speed, a
longer, heavier bullet will keep gyroscopic rotation better then a
short, light bullet.
If you control velocity with handloading, you can
stabilize a bullet coming from a slower twist barrel.
Too much twist
“Because of tumbling”, some experts say that when
the M-16 rifle barrel twist was change from 12 to 14, the killing power
was reduced” – (Rinker, p 145)
The 30’06 used to have a 10 twist, perfect for
heavy long bullets (over 125 grains), but that was changed to 12 or 14
to accommodate lighter bullets.
Switching to a longer or heavier bullet require a
faster twist, resulting in less accuracy at long distances.
Effect of
specific gravity of the bullet
Weight of dry bullet minus weight of bullet
submerged in water.
The .22 short (with 30 grain bullet) always
performs best with a 1:20 inch twist
The .22 Long Rifle (with a 40 grain bullet) always
perform best with a 1:16 inch twist
Barrels and
Ballistics
Initial drilling is .01 inches larger and final
reaming takes down the barrel to the caliber size.
Periodic heat-treating during manufacture relieves metal stress
and makes a target barrel more accurate.
Testing by Eric Johnson of Hoffman Arms Vo. showed
that the optimal velocity was a function of barrel length and the “best”
barrel length for a 22 LR bullet was only 18 inches. (Rinker, p118).
The wide “Bull barrel” style is fat all the way
from the chamber to the muzzle, where some target barrels are even
fatter at the chamber-end.
Bullet
design
Ever since the American Civil War, soldiers are
vary of the “splatter effect” of the 50 caliber lead mineballs, bullets
that left massive wounds.
(figure x.x)
Figure x.x:
A lead mineball
The hippies in Europe decided that the world needed
“clean kill” bullets and many people mistake that the Geneva Convention
created the idea of the “steeljacket” bullet, a soldiers bullet with
less expansion upon impact.
In reality, it was the Hague convention that mandated the use of
steeljackets and America refused to sign this declaration.
However, ballistics studies have shown that steel
jackets have enhanced flight properties and today’s bullet jackets are
not uniform. They are
thickest at the base and back side, and the jacket wall tapers towards
the point (see Rinker, p 210)
Most of today’s bullets go supersonic before they
exist the barrel, expect for some small .222 caliber sub-sonic bullets.
The effect of air drag are very important to a supersonic
projectile, whether it is a jet fighter of a sniper bullet, a pointed
head helps reduce drag and increase gyroscopic stability.
The boat
tail bullet base
The study of supersonic rifle bullets led to the
implementation of the “boat tail” base (a.k.a. a “tapered heel”) as seen
in Figure x x.
Figure x.x:
A regular and a boat tail bullet
The boat tail bullet can reduce air drag by as much
as 20%. This is only
helpful for supersonic bullets with long-range shooting (at least 200
yards). For example, a
small caliber supersonic bullet at 200 yards will have a very short
flight time, and a 20% air drag reduction would not have a statistically
significant effect on the impact velocity of the bullet.
The boat tail design has several competing
characteristics:
·
Positive: The boat tail
taper helps reduce the partial vacuum that exists behind the bullet.
The boat tail also reduces the deflection from crosswinds,
especially at ranges of 1,000 yards or greater.
·
Negative: During supersonic flight a ripple effect can be seen, and
this shockwave can impede accuracy.
The optimal compromise between these competing
effects is a boat tail taper diameter of .4 inches of the caliber (or
less). (Figure x.x) (Rinker
p 205)
·
A .308 bullet might have a boat tail of
(.308 * .6) = 18 caliber diameter at the base of the boat tail.
·
A .50 caliber bullet might have a boat
tail of (.5 * .6) or about 30 caliber.
At distances of 1,000 yards or greater a boat tail
bullet is mandatory for accuracy, and the boat tail reduces wind
deflection such that a 10 MPH cross wind will cut the bullet deflection
by three to four feet (Rinker p 204).
Bullet
ogive design
The “ogive” of a bullet is the shape of the nose of
the bullet, expressed as the straight line originating from the
curvature of a circle (Figure x x):
The ogive is expressed as the radius of the line that intersects
the imaginary center of the circle.
Note that bullets are never purely conical-shaped, and the ogive
only measure the straight-line taper of the nose of the bullet.
The ogive length is equal to the caliber of the bullet multiplied
by half of the square root of the quantity 4*(caliber_radius)-1.
The meplat
Competition rifle bullets never have a completely
sharp nose because if issues with semi-automatic guns.
Instead, a small flat spot exists at the most called the
“meplat”, a flat surface
What is a “spitzer”
shape?
Bullet
characteristics
All else being equal:
Expert competition shooter will always hand-load
their cartridges. No
factory ammunition can match the care required to make multiple bullets
with the exact same loads and precision.
Lighter bullets create faster muzzled velocities
and flatter trajectories.
Heavy bullets have a lower muzzle velocity but they
are more stable and have greater impact momentum.
Heavy bullets must also be carefully matched to the barrel twist,
and heavy bullet requires a faster twist.
For example, many competition shooters of .223 rifles with use a
1:7 twist, and use heavier bullets.
Using a heavy bullet with the “standard” 1:9 twist in a .223
would cause the heavy bullet to lose gyroscopic stability at long
distances and tumble, creating a “key hole” shaped impact hole.
Blunt-nosed bullets are not appropriate for
distances greater than 200 yards and blunt noses are more susceptible to
wind drift than pointed nose bullets.
The
insanity of “illegal” bullets
By great Grandpa Jonathan Hardister was shot by a
“mine ball” at the battle of Gettysburg and it tore a massive hole in
his side. It took him years
to recover from a wound that would not have been life-threatening if it
had been a “jacketed” bullet that did not expand or splatter on impact.
The “humane” steeljackets
The Geneva Convention came up with the idea of the
steel-=jacketed bullet for humane reasons, a reason to have a clean kill
and less agony for near misses.
In concept, the steeljacket is fine when you are up against an
honorable enemy as in WWII where the Japanese and Germans adhered to the
steel-cased bullets.
But today we deal with a morally-corrupt and
Godless enemy who has no problem using their own women and children for
suicide killings.
American soldiers need an equalizer, and it’s sad
that we must lose the lives of our young people to adhere to a higher
moral standard than the dastardly terrorists.
My nephew is a master sergeant in the Marines who
teaches close-up defense, and by the time a Marine needs to pull their
sidearm, they are in dire straights; being overwhelmed by the enemy at
close range. The military
has traded the higher stopping power of the .45 caliber semi-automatic
1911 pistol for the higher capacity of the Beretta and ??? 9mm bullets.
The 1911 holds (x + 1) while the 9mm holds xx + 1 bullets).
It’s important to note that using hollowpoints and
exploding bullets are not intended for machinery and thick-skinned big
game. These technologies
are designed or thin-skinned prey (deer and terrorists), and the
hollowpoints do not have the penetrating power for karee game with thick
hides..
Hollow
Points
Creating a hollow point in any handgun bullet has a
negligible effect upon the ballistics and increase the propensity of the
bullet to expand upon impact.
Mushrooming
The term “mushrooming” refers to the curling-back
of the point of the bullet upon impact forming a mushroom-shaped
appearance (Figure x.x).
Mushrooming is allowed (and encouraged) for personal defense and law
enforcement loads. Today,
civilian ammunition allows for “moderate” killing power in home defense
loads. For example, the
Hornady home defense loads have a hollow point filled with a plastic tip
that allows for expansion and “mushrooming” of the bullet upon impact
(Figure x.x). The law
allows for moderate mushrooming, but not as far as the technology will
allow.
·
Radioactive bullets: In
the military, the 50 caliber anti-tank bullets use heavy metal nuclear
waster uranium ??? to allow the bullet to penetrate the heavy steel case
of the tank and then explode. (Figure x.x).
However, there have been deliberate limits placed
upon the killing power of handgun bullets.
Illegal loads
I believe that American soldiers and law
enforcement should have access to special handgun shells that have
explosive power on impact.
There have been several cases of posthumous Medal of Honor recipients
(get names) where the soldier died in panic being killed by an
overwhelming force. It does
not have to be this way. We
have the technology to create a pistol bullet that explodes on impact
and will cut a terrorist in half, stopping them immediately.
Our soldiers deserve this “edge”;
Ever since Henry Shrapnel discovered that a bomb
could be placed inside a cannonball, ballistics experts have known that
a small explosive charge can be placed within a projectile (Figure x.x):
Henry
Shrapnel and the exploding projectile
Henry Shrapnel’s legacy is easily miniaturized and
can be used in medium and large caliber handgun bullets.
Some illegal concepts include:
·
Steel balls in hollow points: You can place a hardened steel bearing
inside the cavity of a lead hollow-point bullet causing the ball to be
thrust backwards at impact, causing the bullet to greatly increase in
diameter (mushrooming) (site book).
·
Mercury in hollow points:
Mercury embedded inside the nose of a bullet will create an
explosive effect upon impact.
·
Disintegrating bullets:
Some brittle metals have the properties if fragmenting upon impact,
leaving hundreds if tiny shards in the prey.
Allowing these “illegal” technologies for law
enforcement and the military would negate the effect of switching from
the lower capacity 1911 .34 semi-automatics to the higher capacity 9mm
handguns because an exploding 9mm round would have the take-down power
to stop a bad guy in their tracks.
The speed
of sound
Every child is taught to estimate the speed of
sound when estimating the distance between seeing a lightening flash and
hearing the crack of the lightening.
Counting “one-thousand-one, one-thousand-two) gets the number of
seconds, and multiplying by 1,130 gives the distance in feet.
For example, if it is 5 seconds between seeing a lightening flash
and hearing the crack, you know that the lightening hit about a mile
away.
In combat ballistics, the same principle applies.
If you see a sniper bullet crack a tree branch in front of you,
and you hear the rifle crack 1 second later, you can estimate the
distance by estimating the average velocity of the incoming bullet.
The speed of sound is important for long distance
rifle shooting because of the unique aerodynamic turbulence that occurs
between Mach .9 and Mach 1.1.
A rifle bullet goes supersonic while still in the barrel and the
“crack” of the bullet exceeding the sound barrier can be heard in the
forum of a 70 degree cone emanating from the end of the muzzle (Figure
x)
Figure x x:
The cone of hearing a bullet exceed the speed of sound
Note that this is the reason why you cannot use a
silencer with a high powered rifle.
The silencer cannot control the sound waves that are created
inside the barrel when the bullet goes supersonic.
It’s all Hollywood, like putting a silencer on a revolver, not
knowing that the space between the cylinder and the barrel emits a huge
sound!
Avoiding the instability of this “transonic” mode
is very important, especially at long distances when a bullet degrades
beck to subsonic. At
trigger time, the newly-supersonic bullet many be unstable for up to 200
yards until it shakes off the turbulence of the sound barrier, but these
shakes will reoccur when the bullet degrades below 1,300 feet per second
downrange and the shockwaves reoccur.
Avoiding the trans-sonic range is why many .22
competition bullets are deliberately subsonic because the momentum is
offset of the turbulence.
Hence, the impact velocity should always be
supersonic if possible, keeping at least 1,130 feet per second.
The denigration into the trans-sonic range causes huge air drag
and possible loss of gyroscopic stability and bullet tumbling
end-over-end.
Velocity
The maximum velocity with conventional powders if
6,500 feet per second, with 4,500 fps as a practical maximum velocity.
In a nutshell, a bullet can never move faster than the expansion
rate of the propellant (Rinker, p 167)
(look up
“wildcat” cartridges.)
Sectional Density
A higher sectional density (high weight) gives a
flatter trajectory. A lower
sectional density has a greater velocity loss, a higher trajectory arch.
A heavy bullet is also less susceptible to wind.
On impact, a heavier bullet will have more penetration.
The speed of sound is not a constant; it varies
according to several factors all related to the density of the air.
These factors are listed in order of importance):
·
Attitude:
The speed of sound slows slightly at greater altitude.
·
Temperature: The speed of sound slows
slightly at hot temperatures.
·
Humidity The speed of sound slows
slightly at in dense air.
Note that this difference is too small to be of
much importance. For
example, at 10,000 altitude shooting a target at 300 yards, only a 1/2
MOA downward adjustment would be required. (Rinker, p 157)
Velocity
All else being equal, the temperature affects the
velocity of a bullet. For
example, a 30 degree drop in temperature will cause a corresponding loss
of over 50 feet per second.
Air
pressure and air drag
The air pressure at sea level is 14.7 pounds per
square inch and this varies according to barometric pressure.
The air drag over a bullet is called “”skin
friction” or “parasitic” drag” and air drag is on of the most important
factors in the flight of a bullet.
For example, consider a 30’06 bullet fired straight
up. The bullet starts at
2,700 feet per second and it will slow rapidly until it reaches its peak
altitude at only 10,000 feet before it briefly stops and begins its fall
back to earth. In a vacuum
without air drag and only gravity to slow-down the bullet, a 30’06 would
travel straight-up to over 100,000 feet before dropping.
It’s counter-intuitive that gravity is far more
important that air drag. In the real-world, air drag is 90% more
important than air drag.
Interestingly, that same bullet falling from 10,000 feet would quickly
reach its terminal velocity of about 400 feet per seconds, again, due to
the air resistance. As the
bullet approaches sea level where the air is denser and the terminal
velocity becomes slower.
Remember, the vertical pull of gravity is not as
important you might think.
In The American Rifleman (Dec 1982) author William Davis noted that the
difference between dropping a 30’06 bullet from a high of five feet was
almost the same! The shot
bullet travelled 1,310 feet downrange, yet it only hit the ground a half
second faster than the un-shot bullet that was dropped from five feet!
1 A 30 caliber M72 match bullet will travel 1,000
yards in 1.66 seconds
Terminology
Dram:
A dram is a unit if weight equal to 27 grains
Slug:
A unit of mass
References:
Kelley & Reno, Exterior Ballistics, by McShane,
1953
Lowry, E. D., Exterior Ballistics of Small Arms
Projectiles, Winchester Western Division
Rinker, Robert, Understanding Firearms Ballistics,
Mulberry House Publishing, 1998
Range & Ballistics tables
RE-start at
Chapter 17
