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Gun Work

That depends on the gun. Different guns have different firing mechanisms.

Bullets, however, generally work the same way. A modern bullet cartrige contains 5 parts:

1. The bullet itself (this is the part that actually shoots out of the barrel)
2. The case
3. The propellant, usually gunpowder
4. The rim
5. The primer

When you pull the trigger on a handgun, the hammer snaps forward and a pin strikes the primer(5). This creates a spark, which ignites the gunpowder(3), and the explosion propels the bullet(1) out of the gun. In a semi-automatic pistol the extractor then grabs hold of the rim(4) and ejects the empty casing from the gun to make room for the next round.The speed of the projectile depends on the ammunition. Since gunpowder burns so rapidly, the gas generated by it allows the projectile to travel at a very fast pace. The gas also forces the slide back on the gun, ejecting the empty casing, and also loading another round that requires another trigger squeeze. Pressure is the key. High pressure means high velocity (usually). So when a piece of lead is launched out of the barrel, it travels so fast that when it strikes a target it penetrates (and expands), or goes completely through the target. The weight and shot placement of the projectile determine the lethality and "stopping power".

First of all , there are many types of guns. Different types of guns may have different ways to feed the bullet. Generally a revolver uses revolving cylinder mechanism to feed a new bullet after each shot.

There are different components in a revolver.
If you want to fire a bullet you have to pull the trigger , and the mechanism is designed in a way such that , hammer is pushed back which will compress the spring and at the same time the cylinder which hoses bullets in also rotated.
If you pull the trigger all the way back , the leaver inside the trigger will release the hammer and the whole potential energy stored in the spring is now being used to push the hammer forward.
So now hammer will make an impact at the back side of the bullet, which will activate the chemical reaction in the bullet.
Lets see how this chemical reaction makes a bullet run so fast.

A bullet has different components ,each component has a different function to perform.

At the back ,there is primer. Function of the primer is to ignite the spark after the impact of hammer.
Then this small spark generated from the impact of the hammer will activate the reaction in the powder propellant. Propellant is a mixture of two compounds . One is fuel and other is oxidizer. This reaction will form a huge volume of gases at very high speed ,which will force the bullet to go out of the gun at very high speed.
In the front ,there is a metal jacket ,which is responsible of the actual damage done by the bullet.
So that's how a gun fires a bullet at very high speed.

A firearm is basically a hyper-powered blow gun. Pressurized gas in a closed space pushes a projectile out of a tube.

Same principle between firearms and air rifles but different sources of pressurized gas.

Since many have already covered the topic of the firing mechanism and components of the modern fixed cartridge, there is also the mechanics of how semi-automatic and automatic firearms operate.

The most common auto-feed mechanisms are recoil (blowback) and gas operated.

Recoil operated is pretty self explanatory. Newton’s 3rd law says that for every action there is an equal and opposite reaction. So as the expanding gases accelerate the bullet/projectile down the barrel, there is a reciprocal push rearward, i.e. recoil. This is used to push the bolt back, eject the spent casing, cock the firing mechanism (hammer or striker), pick up a new cartridge from the magazine or belt and load it into the firing chamber. The cycle repeats after that.

Gas-operated actions are quite different in that the bolt is locked in the breech and does not immediately move back when the round is fired. The bullet must travel down the barrel to a certain point where there is a small hole called the gas port. Once the bullet passes by the gas port, the expanding gases vent into the gas port and push open the rotating bolt unlocking it from the breech allowing it to move back. From there it works much like the recoil operated action except that the bolt rotates and locks again at the end when the round is chambered.

There are two sub-types of gas operated actions: direct impingement and gas piston.

Direct impingement (DI) has a tube from the gas port that routes the gases directly back to the bolt/bolt carrier to unlock the breech and cycle the action. The M16/M4 is the most well-known example of a DI gas operated action.

Gas piston works by having the gas port go to a rod. The gas pushes the rod back which pushes on the bolt/bolt carrier to unlock the breech and cycle the action. The AK-47 is the most famous example of a gas piston action.

Recoil operated pros: simple. Generally low maintenance

Recoil operated cons: can be fussy about spring tensions and some muzzle velocity is lost because it is used to cycle the action. Think about diving off a floating platform in a lake. When you push off, the platform slides back and you lose some of your forward energy.

Gas operated pros: higher muzzle velocity and effective range

Gas operated cons: more complicated design, more parts, gas tubes and pistons can get quite hot

DI pros: can have a pretty high rate of fire, smoother action, lower weight and generally better accuracy due to fewer moving parts

DI cons: In shorter rifles, carbine length and shorter, can result in dirty actions and substantially more cleaning.

Gas piston pros: In shorter rifles, results in far less soot in the action, generally lower maintenance

Gas piston cons: Generally heavier and lower rate of fire due to additional mechanical linkage; the moving mass of the piston is noticeable which can result in decreased accuracy at longer ranges. It isn’t much, but at longer ranges it doesn’t take much to be off by a lot.

There is the final category of electric-powered machine guns, a.k.a. mini guns which are a class by themselves since they require external power to operate. These operate by an electric motor that simultaneously rotates the barrel group, feeds new rounds and ejects spent rounds.

The rotating barrel group assembly has gears and a cam that ejects the previous spent cartridge from the current barrel, loads a new cartridge, pushes into the firing chamber and fires it. Some mini guns have electric fired primers while others are standard primers that go off with a firing pin.

Mini guns have multiple barrels to reduce wear and heat by splitting the load between 6–8 barrels. This is how they can achieve extremely high cycle rates of 4000 rounds/min or more. For example, a 6 barrel mini gun firing at 2400 rounds per minute (40 rounds/sec) is only effectively firing 400 rounds per minute per barrel.

It’s a piece of tube closed at one end and open at the other. At the closed end of the tube is placed an explosive or propellant such as compressed gunpowder and a means of ignition such as a spring with a flint hammer that creates a spark. As the gunpowder is tightly compressed the spark will burn it. The gunpowder burns extremely quick and instantly turns into gasses far exceeding the volume of solid powder. Trapped with nowhere to go except out the open end of the gun barrel, if there happens to be anything in the barrel about the same diameter between the powder and the open end, the gasses from the fun powder will push it out the end really fast. That’s a simplified version of what the first guns were probably like.

Of course guns and bullets evolved. Out came the revolver, a reliable semi that nearly never jams and is famously used in a version of roulette with no possible winners. Rifles, machine guns, sub machine guns, and apparently 1 in 60 people in the world own an AK47.

A gun is for turning living moving things that might hurt you into bits of meat that can’t hurt you. If I throw a marble at a wolf as hard as I can it will bounce off. If I throw a 9mm piece of red hot metal at a wolf at 1000mph, it will drop on disintegrate its internal organs leave a bleeding hole where I hit it, and a massive hole out the other side.

That’s how a gun works. It’s a hollow tube with a lever that you squeeze that makes a one-way propellant explosion that allows you to effortlessly make small pieces of red hot metal fly towards whatever you want to fall over and die by transferring massive amounts of kinetic energy due to the velocity of the projectile. Momentum = Mass x Velocity. The mass of a bullet may be small, but bullets are fast, and guns are what give them momentum.

A gun launches a projectile at high velocity.

The two most common ways to propel the projectile are using gas produced by a chemical reaction of burning solid propellant such as gunpowder (firearms) and using compressed gas or air (airguns). There are also more exotic designs, such as a Gauss gun which uses magnetic fields, and the Gyrojet which had miniature rockets for ammunition.

Contrary to popular opinion, the process that propels the projectile in a firearm is not an explosion, but rather a very fast burn that releases hot gas. Black powder is only explosive under certain conditions and smokeless powder is not an explosive at all.

Generally, all firearms from the antique cannons to modern day rifles and pistols have the following basic components:

Projectile (bullet)
Barrel
Propellant (powder)
Ignition source (spark or flame)

A most basic gun consists of a barrel closed at one end and an ignition system of some sort. Earliest guns were matchlocks. They used a slow match - a smoldering piece of string. Then came flintlocks which produced sparks from flint striking steel, later to be replaced by percussion caps which used a small amount of chemical that ignited on impact from a spring-loaded hammer. The percussion caps then evolved into cartridge primers that use the same principle. Matchlocks and flintlocks also required the use of a small amount of very fast burning and easy to ignite powder called a priming charge to set off the main charge inside the barrel.

An interesting footnote to this is a modern muzzle-loading rifle made for hunting that uses an electric spark to set off the charge.

Modern guns use either a combination of a hammer and firing pin or a striker. The hammer or the striker are spring-loaded and held back by the sear. Pulling the trigger moves the sear out of the way allowing the hammer to fall on the firing pin or the striker to move forward and to smash the primer of a cartridge which produces a flame to ignite the propellant charge inside the cartridge case. The burning powder produces gas, which rapidly expands. The pressure from the gas expands the casing slightly making it seal the breech and pushes the projectile out of the case and down the barrel.

Barrels can be smoothbore or rifled. Rifling is spiral grooves cut into the inner surface of the barrel. Rifling makes the projectile spin, making it more stable in flight. Earliest guns were all smoothbore, and they were used both for single solid projectiles, and for a load of many small projectiles called shot. Today solid bullets are mostly fired from rifles, and smoothbore guns are shotguns.

Manual repeaters, such as bolt and lever action rifles are cocked through operating the action by hand. Semi-auto guns and auto guns either use some of the gases generated by cartridge, or energy of the recoil to operate the gun automatically.

An interesting exception to the above are the automatic cannons/large caliber machine guns mounted on tanks and airplanes. Some of them use electricity to set off the charge and some use electric or hydraulic motors to work the action rather than recoil or gas energy.

The Combine of Revolver

I know this is a tad overwhelming, but bear with me.

First, you load up a cartridge in whatever loading port that the weapon has. In this case, this pistol has a magazine (not a clip) that fits into the grip, which, since this is an HK USP 45 handgun, it holds about twelve rounds on average. This weapon takes .45 ACP cartridges, and other cartridges will not work in it.

This picture is of a Colt 1911, which is also .45 ACP, so the rounds from the USP can fit in here, but the magazines cannot be interchanged.

Once it clicks and is secure in the weapon, you charge it by pulling the top part back until it stops, the top part being called the slide. There is a slide catch that will stop it from moving back forward normally, so you can release it by pushing down on the catch. The slide will clack forward. Your first round is now loaded.

You aim the weapon. With most handguns, you put the front sight between the two rear sights and make the tops of the sights level with each other. The top of the front sight is where you are going to hit.

Once you pull the trigger, a pin inside of the weapon will strike the back of the cartridge in the middle (usually), which is the primer. That sets the primer off into a small explosion, which lights the gunpowder inside the cartridge, the burning of said powder sending the bullet out from the golden-looking cartridge (it’s made of brass, for the record, but can also be steel). The bullet flies at speeds upwards of one thousand feet per second, and impacts the target with immense force.

This is a slow motion gif of a Beretta handgun. Not the same ammo as the previous two guns, much smaller in fact.

The recoil causes the slide to cycle, meaning it flies backwards, then the spring throws it back forwards and loads the next round. (See gif above)

This is generally true for most modern guns, except for specifics. Old guns didn’t work this way. They had powder, but no cartridges, and before primers and after powder they had percussion caps. Really, a primer is a hyped up percussion cap, but cartridge ammo made guns more effective, and way more accurate.

A round of ammunition contains four basic components:

The casing, which holds everything together.

The bullet, which is just a shaped piece of metal.

The propellant, which is a basically an explosive, traditionally black powder, but now more sophisticated.

The primer, which is a small chunk of material which explodes when struck.

The process of shooting, then, is pretty simple. The ammunition sits in the gun barrel. When you pull the trigger, a pin hits the primer, causing it to explode. That ignites the propellant, causing a bigger explosion. That explosion forces the bullet down the barrel at huge speeds.

In essence, the function of the gun is to set off an explosion and focus it in one direction. Put a piece of lead in front of that explosion, and it's coming out fast.

Generally speaking, a "gun" works by channeling the explosive force of a propellant down a barrel, driving a projectile ("bullet") out of the barrel and towards a target..

The same forces are at work, whether using an antique muzzle-loader or a modern-day rifle or pistol.

Modern ammunition carries the primer, propellant, and projectile all in the same cartridge. The process of firing the gun starts when you load the cartridge into the firing chamber. After loading the cartridge, you aim the weapon and pull the trigger. The mechanics of the gun vary, but a firing pin eventually strikes the primer, which ignites the propellant. The hot explosive gases are channeled behind the projectile, forcing it down the barrel and out of the gun.

There are many variations of "guns," such as single-shot, revolver, and semi-automatic.

                                        XXX . XXX How Many Revolvers Work

What exactly happens between your squeezing the trigger and the bullet firing into your target?
The revolver is a pretty simple piece of combustion machinery originally conceived of in the mid-19^th century. The first concept allowing the shooter to fire repeatedly without having to reload, the revolver was considered a revolutionary concept at the time. Moving away from what were essentially miniature, one-shot cannons ignited with percussion caps, gun owners were ready for something a little more cutting edge.
The handgun revolver concept was not brand new when the forward-thinking Sam Colt drummed up the design, but it was the best. Many ‘repeating weapons’ were conceived prior to the Colt revolver, but they were much too large and complicated to find favor with the American public.

Colt refined, simplified and shrunk the repeating weapon concept a few thinkers before him attempted to mass produce.

Portable, simple and easy to use, the latest design quickly caught on as demand skyrocketed by the middle of the 1800’s.
The inspiration for the first handgun, according to Colt, was the nautical capstan design. A sailor by profession, Sam Colt found inspiration in these cylindrical barrels used to distribute degrees of force to ship sheets and anchor chains. And these barrels greatly influenced the reason we have the gun design we enjoy today.

This barrel housed 6 chambers to house ammunition, which are self-contained explosives. The four components to a bullet in addition to the slug itself include the propellant (gun powder), the rim (extractor), the primer and the case- or jacket- which holds the entire unit together. These are loaded into the aforementioned barrel chambers individually. Now applying explosive pressure behind the projectile is needed to force it down the barrel, the driving principle to every firearm available today.
This is where the trigger-hammer is important. When squeezed, the trigger forces down the hammer. The hammer then strikes the firing pin with spring force, directly striking the bullet primer on the ammunition round in the chamber. As soon as the primer is compressed, a chain reaction is set off, igniting the gun powder in the bullet casing to extract the slug from the cylinder and down the gun barrel. The ratchet then turns the cylinder, aligning the next live round of ammunition with the firing pin.
Now you know how a revolver works, it is imperative you know never to place your hand anywhere the forcing cone in front of the cylinder when firing. This can at the least severely burn your hand and at the very most blow your proximate fingers clean off. This is because, unlike enclosed pistols, revolvers are very external.

All the moving parts on a revolver, such as the firing pin and chamber cylinder, are visible.

This allows for faster cooling but at the same time requires an extra degree of caution. And though you should exercise the same degree of caution regardless of the caliber, understand the more powerful the gun, the larger degree of injury you are subject to. Whereas firing a .22 target pistol is sure to leave a burn, a .50 Desert Eagle will dismember.

XXX . XXX 4%zero Physics of firearms

From the viewpoint of physics (dynamics, to be exact), a firearm, as for most weapons, is a system for delivering maximum destructive energy to the target with minimum delivery of energy on the shooter. The momentum delivered to the target, however, cannot be any more than that (due to recoil) on the shooter. This is because the momentum imparted to the bullet is equal to that imparted to the gun-shooter system .

Firearm energy efficiency

From a thermodynamic point of view, a firearm is a special type of piston engine, or in general heat engine where the bullet has a function of a piston. The energy conversion efficiency of a firearm strongly depends on its construction, especially on its caliber and barrel length. However, for illustration, here is the energy balance of a typical small firearm for .300 Hawk ammunition:

Barrel friction 2%
Projectile motion 32%
Hot gases 34%
Barrel heat 30%
Unburned propellant 1%.

which is comparable with a typical piston engine.
Higher efficiency can be achieved in longer barrel firearms because they have better volume ratio. However, the efficiency gain is less than corresponding to the volume ratio, because the expansion is not truly adiabatic and burnt gas becomes cold faster because of exchange of heat with the barrel. Large firearms (such as cannons) achieve smaller barrel-heating loss because they have better volume-to-surface ratio. High barrel diameter is also helpful because lower barrel friction is induced by sealing compared to the accelerating force. The force is proportional to the square of the barrel diameter while sealing needs are proportional to the perimeter by the same pressure.

Force

Assuming the gun and shooter are at rest, the force on the bullet is equal to that on the gun-shooter. This is due to Newton's third law of motion (For every action, there is an equal and opposite reaction). Consider a system where the gun and shooter have a combined mass

M

and the bullet has a mass

m

. When the gun is fired, the two systems move away from one another with new velocities

V

and

v

respectively. But the law of conservation of momentum states that the magnitudes of their momenta must be equal:

MV+mv=0\qquad (1)

Since force equals the rate of change in momentum and the initial momenta are zero, the force on the bullet must therefore be the same as the force on the gun/shooter.
Gunshot victims frequently fall or collapse when shot; this is less a result of the momentum of the bullet pushing them over, but is primarily caused by physical damage or psychological effects, perhaps combined with being off balance. This is not the case if the victim is hit by heavier projectiles such as 20 mm cannon shell, where the momentum effects can be enormous; this is why very few such weapons can be fired without being mounted on a weapons platform or involve a recoilless system (e.g. a recoilless rifle).
Example: A .44 Remington Magnum with a 240-grain (0.016 kg) jacketed bullet is fired at 1,180 feet per second (360 m/s) at a 170-pound (77 kg) target. What velocity is imparted to the target (assume the bullet remains embedded in the target and thus practically loses all its velocity)?
Let

m

_$b$ and

v

_$b$ stand for the mass and velocity of the bullet, the latter just before hitting the target, and let

m

_$t$ and

v

_$t$ stand for the mass and velocity of the target after being hit. Conservation of momentum requires

m

_$b$

v

_$b$ =

m

_$t$

v

_$t$.

Solving for the target's velocity gives

v

_$t$ =

m

_$b$

v

_$b$ /

m

_$t$ = 0.016 kg × 360 m/s / 77 kg = 0.07 m/s = 0.269 kmph.

This example shows the target barely moves at all. That's not to say one couldn't stop a train by firing bullets at it, it's just completely impractical.

Velocity

From Eq. 1 we can write for the velocity of the gun/shooter: V = mv/M. This shows that despite the high velocity of the bullet, the small bullet-mass to shooter-mass ratio results in a low recoil velocity (V) although the force and momentum are equal.

Kinetic energy

However, the smaller mass of the bullet, compared that of the gun-shooter system, allows significantly more kinetic energy to be imparted to the bullet than to the shooter. The kinetic energy for the two systems are

{\begin{matrix}{\frac {1}{2}}\end{matrix}}MV^{2}

for the gun-shooter system and

{\begin{matrix}{\frac {1}{2}}\end{matrix}}mv^{2}

for the bullet. The energy imparted to the shooter can then be written as:

{\frac {1}{2}}MV^{2}={\frac {1}{2}}M\left({\frac {mv}{M}}\right)^{2}={\frac {m}{M}}{\frac {1}{2}}mv^{2}

If we now write for the ratio of these energies we have:

{\frac {{\frac {1}{2}}MV^{2}}{{\frac {1}{2}}mv^{2}}}={\frac {m}{M}}\qquad (2)

The ratio of the kinetic energies is the same as the ratio of the masses (and is independent of velocity). Since the mass of the bullet is much less than that of the shooter there is more kinetic energy transferred to the bullet than to the shooter. Once discharged from the weapon, the bullet's energy decays throughout its flight, until the remainder is dissipated by colliding with a target (e.g. deforming the bullet and target).

Transfer of energy

When the bullet strikes, its high velocity and small frontal cross-section means that it will exert large stresses in any object it hits. This usually results in it penetrating any soft object, such as flesh. The energy is then dissipated in the wound track formed by the passage of the bullet.
Bulletproof vests work by dissipating the bullet's energy in another way; the vest's material, usually Aramid (Kevlar or twaron), works by presenting a series of material layers which catch the bullet and spread its imparted force over a larger area, hopefully bringing the round to a stop before it can penetrate into the body. While the vest can prevent a bullet from penetrating, the wearer will still be affected by the kinetic energy of the bullet, which can produce serious internal injuries.

Terminal ballistics

Terminal ballistics (also known as wound ballistics) a sub-field of ballistics, is the study of the behavior and effects of a projectile when it hits its target and transfers its energy to the target. Bullet design and the velocity of impact determine the effectiveness of its impact .

Bullet parts: 1 Metal Jacket, 2 Lead Core, 3 Steel penetrator

General

An early result is due to Newton; the impact depth of any projectile is the depth that a projectile will reach before stopping in a medium; in Newtonian mechanics, a projectile stops when it has transferred its momentum to an equal mass of the medium. If the impactor and medium have similar density this happens at an impact depth equal to the length of the impactor.
For this simple result to be valid, the arresting medium is considered to have no integral shear strength. Note that even though the projectile has stopped, the momentum is still transferred, and in the real world spalling and similar effects can occur.

Firearm projectiles

Classes of bullet

There are three basic classes of bullets:

Those designed for maximum accuracy at varying ranges.
Those designed to maximize damage to a target by penetrating as deeply as possible.
Those designed to avoid over-penetration of a target, by deforming to control the depth to which the bullet penetrates, which as a by-product, deals more damage inside the wound.

The third class may limit penetration by expanding or fragmenting.

Target shooting

.32 ACP full metal jacket, .32 S&W Long wadcutter, .380 ACP jacketed hollow point

For short range target shooting on ranges up to 50 meters (55 yd), aerodynamics are relatively unimportant and velocities are low. As long as the bullet is balanced so it does not tumble, the aerodynamics are unimportant. For shooting at paper targets, the best bullet is one that will punch a perfect hole through the target. These bullets are called wad cutters. They have a very flat front, often with a relatively sharp edge along the perimeter. The flat front punches out a large hole in the paper, close to, if not equal to, the full diameter of the bullet.
This allows for easy, unambiguous scoring of the target. Since cutting the edge of a target ring will result in scoring the higher score, fractions of an inch are important. Magazine-fed pistols may not reliably feed wad cutters because of the angular shape. To address this, the semi wad cutter is used. The semi wad cutter consists of a conical section that comes to a smaller flat, and a thin sharp shoulder at the base of the cone. The flat point punches a clean hole, and the shoulder opens the hole up cleanly. For steel targets, the concern is to provide enough force to knock over the target while minimizing the damage to the target. A soft lead bullet, or a jacketed hollow-point bullet or soft-point bullet will flatten out on impact (if the velocity at impact is sufficient to make it deform), spreading the impact over a larger area of the target, allowing more total force to be applied without damaging the steel target.
There are also specialized bullets designed for use in long range precision target shooting with high-powered rifles; the designs vary somewhat from manufacturer to manufacturer. Research in the 1950s by the U.S. Air Force discovered that bullets are more stable in flight for longer distances and more resistant to crosswinds if the center of gravity is somewhat to the rear of the center of pressure The Match King bullet (which is still in wide use and holds many records) is a hollow point design with a tiny aperture in the jacket at the point of the bullet and a hollow air space under the point of the bullet, where previous conventional bullets had a lead core that went all the way up to the point.
The U.S. military now issues ammunition to snipers that use bullets of this type. In 7.62×51mm NATO, M852 Match and M118LR ammunition are issued, both of which use Sierra Match King bullets; in 5.56×45mm NATO, those U.S. Navy and U.S. Marine snipers who use accurized M16-type rifles are issued the Mk 262 Mod 0 cartridge developed jointly by Black Hills Ammunition and Crane Naval Surface Warfare Center, using a bullet manufactured by Sierra Bullets that was cannelured according to military specifications for this project.
For ultra long range precision target shooting with high-powered rifles and military sniping, radically designed very-low-drag (VLD) bullets are available that are generally produced out of rods of mono-metal alloys on CNC lathes. The driving force behind these projectiles is the wish to enhance the practical maximum effective range beyond normal standards. To achieve this, the bullets have to be very long and normal cartridge overall lengths often have to be exceeded. Common rifling twist rates also often have to be tightened to stabilize very long projectiles. Such commercially nonexistent cartridges are termed "wildcats". The use of a wildcat based (ultra) long-range cartridge demands the use of a custom or customized rifle with an appropriately cut chamber and a fast-twist bore.

Maximum penetration

For use against armored targets, or large, tough game animals, penetration is the most important consideration. Focusing the largest amount of momentum on the smallest possible area of the target provides the greatest penetration. Bullets for maximum penetration are designed to resist deformation on impact, and usually are made of lead that is covered in a copper, brass, or mild steel jacket (some are even solid copper or bronze alloy). The jacket completely covers the front of the bullet, although often the rear is left with exposed lead (this is a manufacturing consideration: the jacket is formed first, and the lead is swaged in from the rear).
For penetrating substances significantly harder than jacketed lead, the lead core is supplemented with or replaced with a harder material, such as hardened steel. Military armor-piercing small arms ammunition is made from a copper-jacketed steel core; the steel resists deformation better than the usual soft lead core leading to greater penetration. The current NATO 5.56mm SS109 (M855) bullet uses a steel-tipped lead core to improve penetration, the steel tip providing resistance to deformation for armor piercing, and the heavier lead core (25% heavier than the previous bullet, the M193) providing increased sectional density for better penetration in soft targets. For larger, higher-velocity calibers, such as tank guns, hardness is of secondary importance to density, and are normally sub-caliber projectiles made from tungsten carbide, tungsten hard alloy or depleted uranium fired in a light aluminum or magnesium alloy (or carbon fibre in some cases) sabot.
Many modern tank guns are smoothbore, not rifled, because practical rifling twists can only stabilize projectiles, such as an Armour-Piercing Capped Ballistic Cap (APCBC), with a length-to-diameter ratio of up to about 5:1 and also because the rifling adds friction, reducing the velocity and thus total force it is possible to achieve. To get the maximum force on the smallest area, modern anti-tank rounds have aspect ratios of 10:1 or more. Since these cannot be stabilized by rifling, they are built instead like large darts, with fins providing the stabilizing force instead of rifling. These sub caliber rounds, called Armor-Piercing Fin-Stabilized Discarding Sabot (APFSDS) are held in place in the bore by sabots. The sabot is a light material that transfers the pressure of the charge to the penetrator, then is discarded when the round leaves the barrel.

Controlled penetration

The final category of bullets is that intended to control penetration so as not to harm anything behind the target. Such bullets are used primarily for hunting and civilian antipersonnel use; they are not generally used by the military, since the use of expanding bullets in international conflicts is prohibited by the Hague Convention and because these bullets have less chance of penetrating modern body armor. These bullets are designed to increase their surface area on impact, thus creating greater drag and limiting the travel through the target. A desirable side effect is that the expanded bullet makes a larger hole, increasing tissue disruption and speeding incapacitation.
While a bullet that penetrates through-and-through tends to cause more profuse bleeding, allowing a game animal to be blood trailed more easily, in some applications, preventing exit from the rear of the target is more desirable. A perforating bullet can continue on (likely not coaxial to the original trajectory due to target deflection) and might cause unintended damage or injury. Frangible bullets, made of tiny fragments held together by a weak binding, are often sold as an "ultimate" expanding bullet, as they will increase their effective diameter by an order of magnitude. When they work, they work extremely well, causing massive trauma to the target. On the other hand, when they fail, it is due to under penetration, and the damage to the target is superficial and leads to very slow incapacitation.

Flat point

The simplest maximum disruption bullet is one with a wide, flat tip. This increases the effective surface area, as rounded bullets can allow tissues to "flow" around the edges. It also increases drag during flight, which decreases the depth to which the bullet penetrates. Older center fire rifles with tube magazines were designed to be used with flat-point bullets. Flat-point bullets, with fronts of up to 90% of the overall bullet diameter, are usually designed for use against large or dangerous game. They are often made of unusually hard alloys, are longer and heavier than normal for their caliber, and even include exotic materials such as tungsten to increase their sectional density.
These bullets are designed to penetrate deeply through muscle and bone, while causing a wound channel of nearly the full diameter of the bullet. These bullets are designed to penetrate deeply enough to reach vital organs from any shooting angle and at a far enough range. One of the hunting applications of the flat point bullet is large game such as bear hunted with a handgun in a .44 Magnum or larger caliber. More common than hunting is its use in a defensive "bear gun" carried by outdoorsmen. The disadvantage of flat point bullets is the reduction in aerodynamic performance; the flat point induces much drag, leading to significantly reduced velocities at long range.

Expanding

More effective on lighter targets are the expanding bullets, the hollow point bullet and the soft point bullet. These are designed to use the hydraulic pressure of muscle tissue to expand the bullet. The hollow point peels back into eight or nine connected pieces causing it to expand the damaged area. The hollow point fills with body water on impact, then expands as the bullet continues to have water pushed into it. This process is called mushrooming, as the ideal result is a shape that resembles a mushroom—a cylindrical base, topped with a wide surface where the tip of the bullet has peeled back to expose more area to create more drag while traveling through a body. A copper-plated hollow point loaded in a .44 Magnum, for example, with an original weight of 240 grains (15.55 g) and a diameter of 0.43 inch (11 mm) might mushroom on impact to form a rough circle with a diameter of 0.70 inch (18 mm) and a final weight of 239 grains (15.48 g).
This is excellent performance; almost the entire weight is retained, and the frontal surface area increased 63%. Penetration of the hollow point would be less than half that of a similar nonexpanding bullet, and the resulting wound or permanent cavity would be much wider.

Fragmenting

Example photo of the over-penetration of a fragmenting projectile.

This class of projectile is designed to break apart on impact, causing an effect similar to that of a frangible projectile, whilst being of a construction more akin to that of an expanding bullet. Fragmenting bullets are usually constructed like the hollow point projectiles described above, but with deeper and larger cavities. They may also have thinner copper jackets in order to reduce their overall integrity. For the purposes of aerodynamic efficiency the tip of the hollow point will often be tipped with a pointed polymer 'nose'. These bullets are typically fired at high velocities to maximize their fragmentation upon impact. In contrast to a hollow point which attempts to stay in one large piece retaining as much weight as possible whilst presenting the most surface area to the target, a fragmenting bullet is intended to break up into many small pieces almost instantly.
This means that all the kinetic energy from the bullet is transferred into the target in a very short period of time. The most common application of this bullet is the shooting of small vermin, such as prairie dogs. The effect of these bullets is quite dramatic, often resulting in the animal being blown apart upon impact. However, on larger game fragmenting ammunition provides inadequate penetration of vital organs to ensure a clean kill; instead, a "splash wound" may result. This also limits practical use of these rounds to supersonic (rifle) rounds, which have a high enough kinetic energy to ensure a lethal hit. The two main advantages of this ammunition are that it is very humane, as a hit almost anywhere on most small vermin will ensure an instant kill, and that instead of dangerously and uncontrollably ricocheting off surfaces, the bullet harmlessly breaks apart. Fragmenting bullets should not be confused with frangible bullets (see below).

Frangible

The last category of expanding bullets is frangible bullets. These bullets are designed to break up on impact, which results in a huge increase in surface area. The most common of these bullets are made of small diameter lead pellets, placed in a thin copper shell and held in place by an epoxy or similar binding agent. On impact, the epoxy shatters and the copper shell opens up, much like a hollowpoint. The individual lead balls then spread out in a wide pattern, and due to their low mass to surface area ratio, stop very quickly. Similar bullets are made out of sintered metals, which turn to powder upon impact. These bullets are usually restricted to pistol cartridges, as the nonhomogenous cores tend to cause inaccuracies that, while acceptable at short pistol ranges, are not acceptable for the typical range at which rifles are used.
One interesting use of the sintered metal rounds is in shotguns in hostage rescue situations; the sintered metal round is used at near-contact range to shoot the lock mechanism out of doors. The resulting metal powder will immediately disperse after knocking out the door lock, and cause little or no damage to occupants of the room. Frangible rounds are also used by armed security agents on aircraft. The concern is not depressurization (a bullet hole will not depressurise an airliner), but over penetration and damage to vital electrical or hydraulic lines, or injury to an innocent bystander by a bullet that travels through a target's body completely instead of stopping in the body.
Also used are bullets similar to hollowpoint bullets or soft point bullets whose cores and/or jackets are deliberately weakened to cause deformation or fragmentation upon impact. The Warsaw Pact 5.45×39mm M74 assault rifle round exemplifies a trend that is becoming common in the era of high velocity, small caliber military rounds. The 5.45×39mm uses a steel-jacketed bullet with a two-part core, the rear being lead and the front being steel with an air pocket fore most. Upon impact, the unsupported tip deforms, bending the bullet nose into a slight "L" shape. This causes the bullet to tumble in the tissue, thus increasing its effective frontal surface area by traveling sideways more often than not.
This does not violate the Hague Convention, as it specifically mentions bullets that expand or flatten in the body. The NATO SS109 also tends to bend at the steel/lead junction, but with its weaker jacket, it fragments into many dozens of pieces. NATO 7.62 mm ball manufactured by some countries, such as Germany and Sweden, are also known to fragment due to jacket construction.
Other bullets in use by militaries are quite back heavy, due to a long, sharp point created in an attempt to get the maximum ballistic coefficient (see external ballistics). These bullets will flip over after impact, then settle into a stable, back first orientation before stopping. The Swiss military actually redesigned their 5.56mm assault rifle bullet to prevent this, to more fully comply with the spirit of the Hague Convention, though according to some sources the present GP90 5.56×45mm Swiss assault rifle ammunition was actually designed as an armor-piercing bullet, because, in the 1980s, it was perceived that the Soviets and their Warsaw Pact allies were going to issue soft body armor to infantry units on a wide basis, but after the end of the Cold War, the Bofors corporation, having spent a great deal of money on developing the new bullet, changed the sales pitch in order to sell it to the Swiss government.
It might seem that if the whole purpose of a maximum disruption round is to expand to a larger diameter, it would make more sense to start out with the desired diameter rather than relying on the somewhat inconsistent results of expansion on impact. While there is merit to this (there is a strong following of the .45 ACP, as compared to the .40 S&W and 0.355 in diameter 9×19mm, for just this reason) there are also significant downsides. A larger diameter bullet is going to have significantly more drag than a smaller diameter bullet of the same mass, which means long range performance will be significantly degraded. A larger diameter bullet also means more space is required to store the ammunition, which means either bulkier guns or smaller magazine capacities. The common trade-off when comparing .45 ACP, .40 S&W, and 9×19mm pistols is a 7- to 14-round capacity in the .45 ACP vs. a 10- to 16-round capacity in the .40 S&W vs. a 13- to 19-round capacity in the 9×19mm.
Although several .45-caliber pistols are available with high-capacity magazines (Para Ordnance being one of the first in the late 1980s) many people find the wide grip required uncomfortable and difficult to use. Especially where the military requirement of a nonexpanding round is concerned, there is fierce debate over whether it is better to have fewer, larger bullets for enhanced terminal effects, or more, smaller bullets for increased number of potential target hits.
The purpose of firing a large calibre projectile is not always the same. For example, one might need to create disorganisation within enemy troops, create casualties within enemy troops, eliminate the functioning of an enemy tank, or destroy an enemy bunker. Different purposes of course require different projectile designs.
Many large calibre projectiles are filled with a high explosive which, when detonated, shatters the shell casing, producing thousands of high velocity fragments and an accompanying sharply rising blast overpressure. More rarely, others are used to release chemical or biological agents, either on impact or when over the target area; designing an appropriate fuse is a difficult task which lies outside the realm of terminal ballistics.
Other large-calibre projectiles use bomblets (sub-munitions), which are released by the carrier projectile at a required height or time above their target. For US artillery ammunition, these projectiles are called Dual-Purpose Improved Conventional Munition (DPICM), a 155 mm M864 DPICM projectile for example contains a total of 72 shaped-charge fragmentation bomblets. The use of multiple bomblets over a single HE projectile allows for a denser and less wasteful fragmentation field to be produced. If a bomblet strikes an armoured vehicle, there is also a chance that the shaped charge will (if used) penetrate and disable the vehicle. A negative factor in their use is that any bomblets that fail to function go on to litter the battlefield in a highly sensitive and lethal state, causing casualties long after the cessation of conflict. International conventions tend to forbid or restrict the use of this type of projectile.
Some anti-armour projectiles use what is known as a shaped charge to defeat their target. Shaped charges have been used ever since it was discovered that a block of high explosives with letters engraved in it created perfect impressions of those letters when detonated against a piece of metal. A shaped charge is an explosive charge with a hollow lined cavity at one end and a detonator at the other. They operate by the detonating high explosive collapsing the (often copper) liner into itself. Some of the collapsing liner goes on to form a constantly stretching jet of material travelling at hypersonic speed. When detonated at the correct standoff to the armour, the jet violently forces its way through the target's armour.
Contrary to popular belief, the jet of a copper-lined shaped charge is not molten, although it is heated to about 500 °C. This misconception is due to the metal's fluid-like behaviour, which is caused by the massive pressures produced during the explosives detonation causing the metal to flow plastically. When used in the anti-tank role, a projectile that uses a shaped-charge warhead is known by the acronym HEAT (high-explosive anti-tank).
Shaped charges can be defended against by the use of explosive reactive armour (ERA), or complex composite armour arrays. ERA uses a high explosive sandwiched between two, relatively thin, (normally) metallic plates. The explosive is detonated when struck by the shaped charge’s jet, the detonating explosive sandwich forces the two plates apart, lowering the jets’ penetration by interfering with, and disrupting it. A disadvantage of using ERA is that each plate can protect against a single strike, and the resulting explosion can be extremely dangerous to nearby personnel and lightly armoured structures.
Tank fired HEAT projectiles are slowly being replaced for the attack of heavy armour by so-called "kinetic energy" penetrators. Ironically, it is the most primitive (in-shape) projectiles that are hardest to defend against. A KE penetrator requires an enormous thickness of steel, or a complex armour array to protect against. They also produce a much larger diameter hole in comparison to a shaped charge and hence produce a far more extensive behind armour effect. KE penetrators are most effective when constructed of a dense tough material that is formed into a long, narrow, arrow/dart like projectile.
Tungsten and depleted uranium alloys are often used as the penetrator material. The length of the penetrator is limited by the ability of the penetrator to withstand launch forces whilst in the bore and shear forces along its length at impact.

Stopping power

Stopping power is the ability of a firearm or other weapon to cause enough ballistic trauma to a target (human or animal) to immediately incapacitate (and thus stop) the target. This contrasts with lethality in that stopping power pertains only to a weapon's ability to incapacitate quickly, regardless of whether death ultimately occurs.
Stopping power is related to the physical properties of the bullet, but the issue is complicated and not easily studied. Although higher caliber has traditionally been widely associated with higher stopping power, the physics involved are multifactorial, with caliber, muzzle velocity, bullet mass, bullet shape, and bullet material all contributing. Critics contend that the importance of "one-shot stop" statistics is overstated, pointing out that most gun encounters do not involve a "shoot once and see how the target reacts" situation.
Stopping power is usually caused not by the force of the bullet but by the damaging effects of the bullet, which are typically a loss of blood, and with it, blood pressure. This is why in many instances a single gunshot wound (GSW), with slow blood loss, does not stop the victim immediately. More immediate effects can result when a bullet damages parts of the central nervous system, such as the spine or brain, or when hydrostatic shock occurs. The importance (or lack thereof) of hydrostatic shock and of momentum transfer in determining stopping power has long been controversial among gun users. Some have ascribed great importance to hydrostatic shock; some have tried to entirely discount it. Not every GSW produces it.
In response to addressing stopping power issues, the Mozambique Drill was developed to maximize the likelihood of a target's quick incapacitation.
"Manstopper" is an informal term used to refer to any combination of firearm and ammunition that can reliably incapacitate, or "stop", a human target immediately. For example, the .45 ACP pistol round and the .357 Magnum revolver round both have firm reputations as "manstoppers". Historically, one type of ammunition has had the specific tradename "Manstopper". Officially known as the Mk III cartridge, these were made to suit the British Webley .455 service revolver in the early 20th century. The ammunition used a 220-grain (14 g) cylindrical bullet with hemispherical depressions at both ends. The front acted as a hollow point deforming on impact while the base opened to seal the round in the barrel. It was introduced in 1898 for use against "savage foes",^[1]^{[note 1]} but fell quickly from favor due to concerns of breaching the Hague Convention's international laws on military ammunition, and was replaced in 1900 by re-issued Mk II pointed-bullet ammunition.
Some sporting arms are also referred to as "stoppers" or "stopping rifles". These powerful arms are often used by game hunters (or their guides) for stopping a suddenly charging animal, like a buffalo or an elephant.

The concept of stopping power appeared in the 19th Century when colonial troops (e.g. American in the Philippines during the 1889-1913 Moro Rebellion, British in New Zealand during the 1845-72 Land Wars) at close quarters found that their pistols were not able to stop charging native tribesmen. This led to the introduction or reintroduction of larger caliber weapons (such as the older .45 Colt and the newly developed .45 ACP) capable of stopping opponents with a single round.
During the Seymour Expedition in China, at one of the battles at Langfang, Chinese Boxers, armed with swords and spears, charged the British and Americans, who were armed with guns. At point-blank range, one British soldier had to fire four .303 Lee-Metford bullets into a Boxer before he ceased to be a threat. The American Captain Bowman McCalla reported that single rifle shots were not enough: multiple rifle shots were needed to halt a Boxer. Only machine guns were effective in immediately stopping the Boxers.^[2]
In the Moro Rebellion, Moro Muslim Juramentados in suicide attacks continued to charge against American soldiers even after being shot. Panglima Hassan in the Hassan uprising had to be shot dozens of times before he died.^[3]^[4]^[5]^[6]^[7] This forced the Americans phase out revolvers with .38 Long Colt caliber ammunition with Colt .45 Colt against the Moros.
British troops used expanding bullets against native tribesmen in the Northwest Frontier of India, and in the Sudan (see The River War by Winston Churchill). Britain voted against a prohibition on their use at the Hague Convention of 1899, although the prohibition only applied to international warfare.

Dynamics of bullets

A bullet will destroy or damage any tissues which it penetrates, creating a wound channel. It will also cause nearby tissue to stretch and expand as it passes through tissue. These two effects are typically referred to as permanent cavity (the track left by the bullet as it penetrates flesh) and temporary cavity, which, as the name implies, is the temporary (instantaneous) displacement caused as the bullet travels through flesh and is many times larger than the actual diameter of the bullet.^[12] These phenomena are unrelated to low-pressure cavitation in liquids.
The degree to which permanent and temporary cavitation occur is dependent on the mass, diameter, material, design and velocity of the bullet. This is because bullets crush tissue, and do not cut it. A bullet constructed with a half diameter ogive designed meplat and hard, solid copper alloy material may crush only the tissue directly in front of the bullet. This type of bullet (monolithic-solid rifle bullet) is conducive to causing more temporary cavitation as the tissue flows around the bullet, resulting in a deep and narrow wound channel. A bullet constructed with a two diameter, hollow point ogive designed meplat and low-antimony lead-alloy core with a thin gilding metal jacket material will crush tissue in front and to the sides as the bullet expands. Due to the energy expended in bullet expansion, velocity is lost more quickly. This type of bullet (hollow-point hand gun bullet) is conducive to causing more permanent cavitation as the tissue is crushed and accelerated into other tissues by the bullet, causing a shorter and wider wound channel. The exception to this general rule is non-expanding bullets which are long relative to their diameter. These tend to destabilize and yaw (tumble) soon after impact, increasing both temporary and permanent cavitation.
Bullets are constructed to behave in different ways, depending on the intended target. Different bullets are constructed variously to: not expand upon impact, expand upon impact at high velocity, expand upon impact, expand across a broad range of velocities, expand upon impact at low velocity, tumble upon impact, fragment upon impact, or disintegrate upon impact.
To control the expansion of a bullet, meplat design and materials are engineered. The meplat designs are: flat; round to pointed depending on the ogive; hollow pointed which can be large in diameter and shallow or narrow in diameter and deep and truncated which is a long narrow punched hole in the end of a monolithic-solid type bullet. The materials used to make bullets are: pure lead; alloyed lead for hardness; gilding metal jacket which is a copper alloy of nickel and zinc to promote higher velocities; pure copper; copper alloy of bronze with tungsten steel alloy inserts to promote weight.
Some bullets are constructed by bonding the lead core to the jacket to promote higher weight retention upon impact, causing a larger and deeper wound channel. Some bullets have a web in the center of the bullet to limit the expansion of the bullet while promoting penetration. Some bullets have dual cores to promote penetration.
Bullets that might be considered to have stopping power for dangerous large game animals are usually 11.63 mm (.458 caliber) and larger, including 12-gauge shotgun slugs. These bullets are monolithic-solids; full metal jacketed and tungsten steel insert. They are constructed to hold up during close range, high velocity impacts. These bullets are expected to impact and penetrate, and transfer energy to the surrounding tissues and vital organs through the entire length of a game animal’s body if need be.
The stopping power of firearms when used against humans is a more complex subject, in part because many persons voluntarily cease hostile actions when shot - they either flee, surrender, or fall immediately. This is sometimes referred to as "psychological incapacitation".
Physical incapacitation is primarily a matter of shot location; most persons who are shot in the head are immediately incapacitated, and most who are shot in the extremities are not, regardless of the firearm or ammunition involved. Shotguns will usually incapacitate with one shot to the torso, but rifles and especially handguns are less reliable, particularly those which do not meet the FBI's penetration standard, such as .25ACP, .32 S&W, and rimfire models. More powerful handguns may or may not meet the standard, or may even overpenetrate, depending on what ammunition is used.
Fully jacketed bullets penetrate deeply without much expansion, while soft or hollow point bullets create a wider, shallower wound channel. Pre-fragmented bullets such as Glaser Safety Slugs and MagSafe ammunition are designed to fragment into birdshot on impact with the target. This fragmentation is intended to create more trauma to the target, and also to reduce collateral damage caused from ricocheting or overpenetrating of the target and the surrounding environments such as walls. Fragmenting rounds have been shown to be unlikely to obtain deep penetration necessary to disrupt vital organs located at the back of a hostile human.

Wounding effects

Physical

Permanent and temporary cavitation cause very different biological effects. A hole through the heart will cause loss of pumping efficiency, loss of blood, and eventual cardiac arrest. A hole through the liver or lung will be similar, with the lung shot having the added effect of reducing blood oxygenation; these effects however are generally slower to arise than damage to the heart. A hole through the brain can cause instant unconsciousness and will likely kill the recipient. A hole through the spinal cord will instantly interrupt the nerve signals to and from some or all extremities, disabling the target and in many cases also resulting in death (as the nerve signals to and from the heart and lungs are interrupted by a shot high in the chest or to the neck). By contrast, a hole through an arm or leg which hits only muscle will cause a great deal of pain but is unlikely to be fatal, unless one of the large blood vessels (femoral or brachial arteries, for example) is also severed in the process.
The effects of temporary cavitation are less well understood, due to a lack of a test material identical to living tissue. Studies on the effects of bullets typically are based on experiments using ballistic gelatin, in which temporary cavitation causes radial tears where the gelatin was stretched. Although such tears are visually engaging, some animal tissues (other than bone or liver) are more elastic than gelatin. In most cases, temporary cavitation is unlikely to cause anything more than a bruise Some speculation states that nerve bundles can be damaged by temporary cavitation, creating a stun effect, but this has not been confirmed.
One exception to this is when a very powerful temporary cavity intersects with the spine. In this case, the resulting blunt trauma can slam the vertebrae together hard enough to either sever the spinal cord, or damage it enough to knock out, stun, or paralyze the target. For instance, in the shootout between eight FBI agents and two bank robbers on April 11, 1986 in Miami, Florida (see FBI Miami shootout, 1986), Special Agent Gordon McNeill was struck in the neck by a high-velocity .223 bullet fired by Michael Platt. While the bullet did not directly contact the spine, and the wound incurred was not ultimately fatal, the temporary cavitation was sufficient to render SA McNeill paralyzed for several hours. Temporary cavitation may similarly fracture the femur if it is narrowly missed by a bullet.
Temporary cavitation can also cause the tearing of tissues if a very large amount of force is involved. The tensile strength of muscle ranges roughly from 1 to 4 MPa (145 to 580 lbf/in²), and minimal damage will result if the pressure exerted by the temporary cavitation is below this. Gelatin and other less elastic media have much lower tensile strengths, thus they exhibit more damage after being struck with the same amount of force. At typical handgun velocities, bullets will create temporary cavities with much less than 1 MPa of pressure, and thus are incapable of causing damage to elastic tissues which they do not directly contact.
Rifle bullets that strike a major bone (such as a femur) can expend their entire energy into the surrounding tissue. The struck bone is commonly shattered at the point of impact.
High velocity fragmentation can also increase the effect of temporary cavitation. The fragments sheared from the bullet cause many small permanent cavities around the main entry point. The main mass of the bullet can then cause a truly massive amount of tearing as the perforated tissue is stretched.
Whether a person or animal will be incapacitated (i.e. "stopped") when shot, depends on a large number of factors, including physical, physiological, and psychological effects.

Neurological

The only way to immediately incapacitate a person or animal is to damage or disrupt their central nervous system (CNS) to the point of paralysis, unconsciousness, or death. Bullets can achieve this directly or indirectly. If a bullet causes sufficient damage to the brain or spinal cord, immediate loss of consciousness or paralysis, respectively, can result. However, these targets are relatively small and mobile, making them extremely difficult to hit even under optimal circumstances.
Bullets can indirectly disrupt the CNS by damaging the cardiovascular system so that it can no longer provide enough oxygen to the brain to sustain consciousness. This can be the result of bleeding from a perforation of a large blood vessel or blood-bearing organ, or the result of damage to the lungs or airway. If blood flow is completely cut off from the brain, a human still has enough oxygenated blood in their brain for 10–15 seconds of wilful action, though with rapidly decreasing effectiveness as the victim begins to lose consciousness.
Unless a bullet directly damages or disrupts the central nervous system, a person or animal will not be instantly and completely incapacitated by physiological damage. However, bullets can cause other disabling injuries that prevent specific actions (a person shot in the femur cannot run) and the physiological pain response from severe injuries will temporarily disable most individuals.
Several scientific papers reveal ballistic pressure wave effects on wounding and incapacitation, including central nervous system injuries from hits to the thorax and extremities.^[ These papers document remote wounding effects for both rifle and pistol levels of energy transfer.
Recent work by Courtney and Courtney provides compelling support for the role of a ballistic pressure wave in creating remote neural effects leading to incapacitation and injury.^[19]^[20] This work builds upon the earlier works of Suneson et al. where the researchers implanted high-speed pressure transducers into the brain of pigs and demonstrated that a significant pressure wave reaches the brain of pigs shot in the thigh. These scientists observed neural damage in the brain caused by the distant effects of the ballistic pressure wave originating in the thigh. The results of Suneson et al. were confirmed and expanded upon by a later experiment in dogs which "confirmed that distant effect exists in the central nervous system after a high-energy missile impact to an extremity. A high-frequency oscillating pressure wave with large amplitude and short duration was found in the brain after the extremity impact of a high-energy missile ..." Wang et al. observed significant damage in both the hypothalamus and hippocampus regions of the brain due to remote effects of the ballistic pressure wave.

Psychological

Emotional shock, terror, or surprise can cause a person to faint, surrender, or flee when shot or shot at. Emotional fainting is the likely reason for most "one-shot stops", and where people have instantly dropped unconscious when the bullet only hit an extremity, or even completely missed. Additionally, the muzzle blast and flash from many firearms are substantial and can cause disorientation, dazzling, and stunning effects. Flashbangs (stun grenades) and other less-lethal "distraction devices" rely exclusively on these effects.
Pain is another psychological factor, and can be enough to dissuade a person from continuing their actions.
Temporary cavitation can emphasize the impact of a bullet, since the resulting tissue compression is identical to simple blunt force trauma. It is easier for someone to feel when they have been shot if there is considerable temporary cavitation, and this can contribute to either psychological factor of incapacitation.
However, if a person is sufficiently enraged, determined, or intoxicated, they can simply shrug off the psychological effects of being shot. During the colonial era, when native tribesmen came into contact with firearms for the first time, there was no psychological conditioning that being shot could be fatal, and most colonial powers eventually sought to create more effective manstoppers.
Therefore, such effects are not as reliable as physiological effects at stopping people. Animals will not faint or surrender if injured, though they may become frightened by the loud noise and pain of being shot, so psychological mechanisms are generally less effective against non-humans.

Penetration

According to Dr. Martin Fackler and the International Wound Ballistics Association (IWBA), between 12.5 and 14 inches (318 and 356 mm) of penetration in calibrated tissue simulant is optimal performance for a bullet which is meant to be used defensively, against a human adversary. They also believe that penetration is one of the most important factors when choosing a bullet (and that the number one factor is shot placement). If the bullet penetrates less than their guidelines, it is inadequate, and if it penetrates more, it is still satisfactory though not optimal. The FBI's penetration requirement is very similar at 12 to 18 inches (305 to 457 mm).
A penetration depth of 12.5 to 14 inches (318 and 356 mm) may seem excessive, but a bullet sheds velocity—and crushes a narrower hole—as it penetrates deeper, while losing velocity, so the bullet might be crushing a very small amount of tissue (simulating an "ice pick" injury) during its last two or three inches of travel, giving only between 9.5 and 12 inches of effective wide-area penetration. Also, skin is elastic and tough enough to cause a bullet to be retained in the body, even if the bullet had a relatively high velocity when it hit the skin. About 250 ft/s (76 m/s) velocity is required for an expanded hollow point bullet to puncture skin 50% of the time.
The IWBA's and FBI's penetration guidelines are to ensure that the bullet can reach a vital structure from most angles, while retaining enough velocity to generate a large diameter hole through tissue. An extreme example where penetration would be important is if the bullet first had to enter and then exit an outstretched arm before impacting the torso. A bullet with low penetration might embed itself in the arm whereas a higher penetrating bullet would penetrate the arm then enter the thorax where it would have a chance of hitting a vital organ.

This photo demonstrates the overpenetration of a projectile against a synthetic ordnance gelatin.

Over penetration

Overpenetration occurs when a bullet passes through its target and out of the other side, risking damaging something or someone else beyond and preventing the bullet from transferring all of its energy to the intended target.

Other hypotheses

These hypotheses are a matter of some debate among scientists in the field:

Energy transfer

The energy transfer hypothesis states that the more energy that is transferred to the target, the greater the destructive potential.
Kinetic energy is a function of mass and the square of velocity. Generally speaking, it is the intention of the shooter to deliver an adequate amount of energy to the target via the projectiles. Projectiles such as rifle bullets, high velocity handgun bullets and shotgun slugs can over-penetrate. Projectiles such as handgun bullets and shot can under-penetrate. Projectiles that reach the target with too low a velocity or bird shot may not penetrate at all. All the above conditions affect energy transfer.
Over-penetration is detrimental to stopping power in regards to energy. This is because a bullet that passes through the target does not transfer all of its energy to the target. Despite decreased tissue damage due to loss of transferred energy on an over-penetrating shot, the resulting exit wound would cause increased blood loss and therefore a decrease in blood pressure in the victim. This effect on both persons and game animals is likely to be incapacitating over the length of the entire shooting event.
Under-penetration is also detrimental to stopping power. Projectiles that do not transfer enough energy to the target may fail to create a fatal wound cavity. Also vital organs may not be reached, thereby limiting the amount of tissue damage, blood loss or loss of blood pressure.
Non-penetration of projectiles may only deliver enough energy to create bruising, punctures and or blunt force trauma. All of which may result in internal injury solely through the force of the impact but not stop the target. A notable example of projectiles designed to deliver stopping power without target penetration are Flexible baton rounds (commonly known as "beanbag bullets"), a type of reduced-lethality ammunition.
As mentioned above, there are many factors that affect "stopping power". Within this theory energy transfer is related to destructive potential; however, the importance of energy transfer in determining the stopping power of projectiles (when compared to other factors like location of the wound and wound cavity size) is a controversial topic.
The force exerted by a projectile upon tissue is equal to the bullet's local rate of kinetic energy loss, with distance

\mathrm {d} E_{k}/\mathrm {d} x

(the first derivative of the bullets kinetic energy with respect to position). The ballistic pressure wave is proportional to this retarding force (Courtney and Courtney), and this retarding force is also the origin of both temporary cavitation and prompt damage (CE Peters).

Hydrostatic shock

Hydrostatic shock is a theory of terminal ballistics that wounding effects are created by a shock wave in the tissues of the target. It is argued that evidence of such shock can be seen in ultra-high-speed images of supersonic bullets passing through various objects such as fruit; the fruit explodes due to the shock waves caused by the bullet passing through at high speed. Proponents of the theory contend that damage to the brain from hydrostatic shock from a shot to the chest occurs in humans with most rifle cartridges and some higher-velocity handgun cartridges.

Knockback

The idea of "knockback" is a subset or simplification of energy transfer theory, and states that a bullet of sufficient mass at sufficient speed which transfers all its energy and thus momentum to a subject has enough force to stop any forward motion of an attacker and knock them backwards or downwards. It follows from the law of conservation of momentum that no "knockback" could ever exceed the recoil felt by the shooter. The idea was first widely expounded in ballistics discussions during American involvement in Philippine insurrections and, simultaneously, in British involvement in the Caribbean, when front-line reports stated that the .38 caliber revolvers carried by U.S. and British soldiers were incapable of bringing down a charging warrior. Thus, in the early 1900s, the U.S. reverted to the .45 Colt in single action revolvers, and later adopted the .45 ACP cartridge in what was to become the M1911A1 pistol and the British adopted the .455 Webley caliber cartridge in the Webley Revolver. The larger cartridges were chosen largely due to the Big Hole Theory (a larger hole does more damage), but the common interpretation was that these were changes from a light, deeply penetrating bullet to a larger, heavier "manstopper" bullet.
Though popularized in television and movies, and commonly referred to as "true stopping power" by uneducated proponents of large powerful calibers such as .44 Magnum, the effect of knockback from a handgun and indeed most personal weapons is largely a myth. The momentum of the so-called "manstopper" .45 ACP bullet is approximately that of a 1 pound (0.45 kg) mass dropped from a height of 11.4 feet (3.5 m).^[21]^{[note 2]} Such a force is simply incapable of arresting a running target's forward momentum. In addition, bullets are designed to penetrate instead of strike a blunt force blow, because, in penetrating, more severe tissue damage is done. A bullet with sufficient energy to knock down an assailant, such as a high-speed rifle bullet, would be more likely to instead pass straight through, while not transferring the full energy (in fact only a very small percentage of the full energy) of the bullet to the victim.
An actual "knockback" effect is however frequently observed in real-life shootings^,and can be explained as a physiological and psychological reaction to the shot. Humans encountering a physical hit, be it a punch or a bullet, are conditioned to absorb the blow by moving in the same direction as the force. The physical effect against a non-penetrating weapon is to reduce the force felt by the blow, and in addition, retreating from an attack increases the distance such an attack must cover, which in the case of non-projectile weapons such as fists or a knife, places the target out of range of further attack. In addition, there is a theoretical sociological explanation, that in modern civilization, with far greater separation by most individuals from violence, hunting, and combat, normal individuals may simply recoil, buckle, or fall backward when hit by a bullet, even when in pure physiological terms they are perfectly capable of continuing to charge.

One-shot stop

This hypothesis, promoted by Evan P. Marshall, is based on statistical analysis of actual shooting incidents from various reporting sources (typically police agencies). It is intended to be used as a unit of measurement and not as a tactical philosophy, as mistakenly believed by some. It considers the history of shooting incidents for a given factory ammunition load and compiles the percentage of "one-shot-stops" achieved with each specific ammunition load. That percentage is then intended to be used with other information to help predict the effectiveness of that load getting a "one-shot-stop". For example, if an ammunition load is used in 10 torso shootings, incapacitating all but two with one shot, the "one-shot-stop" percentage for the total sample would be 80%.
Some argue that this hypothesis ignores any inherent selection bias. For example, high-velocity 9 mm hollow point rounds appear to have the highest percentage of one-shot stops .Rather than identifying this as an inherent property of the firearm/bullet combination, the situations where these have occurred need to be considered. The 9 mm has been the predominantly used caliber of many police departments, so many of these one-shot-stops were probably made by well-trained police officers, where accurate placement would be a contributory factor. However, Marshall's database of "one-shot-stops" does include shootings from law enforcement agencies, private citizens, and criminals alike.
Critics of this theory point out that bullet placement is a very significant factor, but is only generally used in such one-shot-stop calculations, covering shots to the torso.
Since 2006, after the conviction of retired school teacher Harold Fish in Arizona for second degree murder during a self-defense shooting, some CCW holders in the United States have elected to switch from carrying hollow-point bullets, and especially 10mm Auto caliber weapons with perceived higher one-shot stopping power, to carrying smaller caliber weaponsFish's conviction for killing a homeless man with a history of dangerous violent behavior and mental instability who attacked Fish while hiking on a remote trail, was obtained through a jury trial by stressing that Fish overreacted, through choosing to use the increased stopping power of 10 mm hollow point bullets. State law in Arizona has subsequently been changed, such that the state now has the burden to prove that a self-defense shooting was not in self-defense, whereas the burden previously, before the Fish incident, was that the shooter on trial had to prove that the shooting was in fact, done in self-defense. The conviction has since been thrown out by the Arizona Court of Appeals. CCW training classes often advise the use of bullets that are identical to those used by local police, in type (FMJ or hollow point) and caliber, to prevent an overreaction prosecution.

Big hole school

This school of thought says that the bigger the hole in the target the higher the rate of bleed-out and thus the higher the rate of the aforementioned "one shot stop". According to this theory, as the bullet does not pass entirely through the body, it incorporates the energy transfer and the overpenetration ideals. Those that support this theory cite the .40 S&W round, arguing that it has a better ballistic profile than the .45, and more stopping power than a 9×19mm Parabellum.^{[citation needed]}
The theory centers on the "permanent cavitation" element of a handgun wound. A big hole damages more tissue. It is therefore valid to a point, but penetration is also important, as a large bullet that does not penetrate will be less likely to strike vital blood vessels and blood-carrying organs such as the heart and liver, while a smaller bullet that penetrates deep enough to strike these organs or vessels will cause faster bleed-out through a smaller hole. The ideal may therefore be a combination; a large bullet that penetrates deeply, which can be achieved with a larger, slower non-expanding bullet, or a smaller, faster expanding bullet such as a hollow point.
In the extreme a heavier bullet (which preserves momentum greater than a lighter bullet of the same caliber) may "overpenetrate", passing completely through the target without expending all of its kinetic energy. So-called "overpenetration" is not an important consideration when it comes to wounding incapacitation or "stopping power", because: (a) while a lower proportion of the bullet's energy is transferred to the target a higher absolute amount of energy is shed than in partial penetration, and (b) overpenetration creates an exit wound.

Other contributing factors

As mentioned earlier, there are many factors, such as drug and alcohol levels within the body, body mass index, mental illness, motivation levels, body part strike (e.g., "armpit hold") which may determine which round will kill or at least catastrophically affect a target during any given situation.

XXX . XXX 4 %zero null 0 1 2 What is valve lock in a pneumatic gun?

Two things drove me to this posting today. We had a reader from Hawaii whose AirForce Condor is not performing as it should, and another reader named baldtrucker asked what happens when a multi-pmp pneumatic like a Benjamin 397 is over-pumped. I did a search and couldn’t find where I had addressed this question before; but, even if I have, it’s time to do it again.
How does an impact pneumatic valve work?
The most common valve is the impact type or knock-open valve, and that’s the one that has a problem with over-pressurization. When a hammer strikes the end of the valve stem of an impact valve, it forces it to momentarily lift the valve face off the valve seat. When that happens, air can flow through or past the valve stem and out into the breech of the airgun.
The valve face is held against the valve seat by a return spring. Also, any air pressure inside the reservoir where the valve face and seat are located pushes against the back of the valve face, forcing it against the valve seal. These two forces (the return spring and air pressure) are what keep the valve closed.
The hammer has to strike the valve stem with enough force to unseat the valve momentarily, allowing air to flow from the reservoir. The weight of the hammer and the strength of the spring that pushes it have been calculated to open the valve when the pressure inside is at its maximum. For most multi-pump guns made today, the valve allows all the stored air to be released. That’s easy because their reservoirs are very small. But, precharged pneumatic reservoirs are larger and only a portion of air is released. The next time the valve opens, the pressure inside (pushing against the valve face) is slightly lower, so the valve remains open slightly longer. A little longer flow of air at lower pressure is released, giving the same velocity to the pellet. This is always easier to control when the barrel is longer, so long-barrelled rifles are generally the most consistent, though a valve can be tuned for any barrel length.
What happens when a pneumatic is over-pressurized?
When the air pressure inside the reservoir is higher than the design of the action can accommodate, the hammer cannot open the valve as far as it should, so less air escapes. That is exactly what is happening to the Condor out in Hawaii. The Condor valve face is HUGE! It has to be, to allow as much air as possible to move through the valve. However, such a large surface area means the valve is also EXTREMELY sensitive to air pressure. Any over-pressurization will hold the valve shut, so the pellet gets very little air to push it.
When you put air into an airgun, it is nothing like putting gasoline into the tank of a car. Even then, more gas doesn’t make the car go faster, does it? What a pneumatic gun needs is air FLOW, and that happens only when the valve remains open as long as it was designed to.
Condors do not like to be filled to 3,000 psi. I have seen only a few that would tolerate it. Most like to be filled to around 2,800 psi. And I have seen a few that liked to be filled to just 2,600 psi. No matter what pressure you fill them to, as long as it is their maximum pressure, they will all give you about 20-25 VERY powerful shots when the power setting it set on high. That may seem counter-intuitive to some, but consider this: A NASCAR race is not won by putting more fuel into the car. It’s won by making the most of the fuel that is put into the car.
The same thing happens when a multi-pump is over-pumped. I hear stories all the time about how so-and-so pumped up his Sheridan Blue Streak 20 times, and it cracked like a .22. I just smile and keep my thoughts to myself, and now you know why. A gun that is supposed to be pumped a maximum of eight times isn’t going to crack like a firearm with 20 pumps. It isn’t going to do much of anything; and if it does, that gun is already worn out and powerless.
Crosman had the answer!
In the 1950s, Crosman came out with a pneumatic valve that couldn’t be over-pressurized – at least not easily. They put it in the Crosman 140 rifle and the 130 pistol and touted it as the answer to over-pressurization and valve lock, as this problem is commonly known. The valve did work as advertised, however, it had a few drawbacks. As the pressure increased, the trigger became harder to pull. It was impossible to fix that, and the triggers were always second-rate. This type of valve had the habit of opening on its own when the pressure was still low. I’ve had guns fire while I was filling them – so this valve type was not the solution to valve lock that it promised to be. They also had the problem of the pliable parts of the valve extruding through the valve ports under pressure.

Button rifling

We explained how cut-rifling works, but I didn’t include the high-speed modern way of doing it, which is the rifling broach. Instead of just one cutting surface, a broach has cutters for every rifling groove, so it cuts them all at the same time. And, a gang broach, like the one shown, has progressively deeper (higher) cutters behind one another, so the entire barrel can be fully rifled in a single pass. Broach rifling is the modern, cheaper way of doing cut-rifling, however, the cutting broach takes a long time to make and must be sharpened often on all cutting surfaces. A small shop making all different calibers still cuts the grooves one at a time.

This gang broach can rifle a barrel in one pass. It is a chore to make and keep sharp.
Button rifling – faster and cheaper
Another way to rifle barrels is the most popular method used today. The button rifling method doesn’t cut the rifling pattern – it irons it into the barrel! A carbide tool called a button is either pushed (most common) or pulled through the barrel. As it moves, the hydraulic head also turns at the desired rifling twist rate. It is correct to say the button engraves a reverse of itself inside the bore, but it doesn’t do it by cutting. Instead, it displaces metal, actually hardening and smoothing the inside of the barrel as it goes.

A rifling button irons the bore into shape. This one is for microgroove rifling.
Rifling buttons wear just as broaches do, but because of how they are shaped and how they work, the wear is slower. Also, they leave a mirror surface behind them. Many of today’s custom barrel makers use the button method, as do many high-volume barrel makers.
Metal stresses
Unlike the cut-rifling method, the button method sets up stresses in the barrel. These have to be dealt with, or the barrel will “walk” as it heats up during firing. You can always tell a cheap barrel; as it heats up, it starts spraying shots in an ever-expanding pattern. A good button-rifled barrel has been properly stress-relieved and can group as well as a cut-rifled barrel. While it may take an hour to cut-rifle a barrel with a modern barrel making machine, a button-rifled barrel can be rifled in about a minute. More time will then be spent on relieving stress (or not), but the total doesn’t add up to the man hour that’s invested in a cut-rifled barrel. And, remember, if the man running the machine makes $20/hour, the barrel will have to include $100 just to cover his cost. The cost of the blank, of drilling the hole and of reaming and lapping are all extra. A good cut-rifled barrel will retail for $400 and up, while quality button-rifled barrels may start at $150.
Longer life
As the button irons the bore, it hardens the steel, resulting in a barrel that can outlast a cut-rifled barrel. Further steps, such as cryogenic treatment and plating with hard chrome, will add even more wear resistance. That’s a strong sales point, as long as the stresses have been properly relieved. In air guns, there are no hot combustion gases to worry about; but, in a firearm, the gases actually vaporize the steel of the bore over time. Button-rifled bores are more resistant to this. Also, they usually do not need to be lapped after rifling, though the top custom makers still do.
XXX . XXX 4%zero null 0 1 2 3 4 5 6 7* Calculating Bullet RPM — Spin Rates and Stability

Most serious shooters can tell you the muzzle velocity (MV) of their ammunition, based on measurements taken with a chronograph, or listed from a manufacturer’s data sheet. (Of course, actual speed tests conducted with YOUR gun will be more reliable.)
www.kurzeit.com

Bullet RPM = MV X 720/Twist Rate (in inches)
Photo by Werner Mehl, www.kurzzeit.com, all rights reserved.
However, if you ask a typical reloader for the rotational rate of his bullet, in revolutions per minute (RPM), chances are he can’t give you an answer. Knowing the true spin rate or RPM of your bullets is very important. First, spin rate, or RPM, will dramatically affect the performance of a bullet on a game animal. Ask any varminter and he’ll tell you that ultra-high RPM produces more dramatic hits with more “varmint hang time”. Second, RPM is important for bullet integrity. If you spin your bullets too fast, this heats up the jackets and also increases the centrifugal force acting on the jacket, pulling it outward. The combination of heat, friction, and centrifugal force can cause jacket failure and bullet “blow-ups” if you spin your bullets too fast.
Accuracy and RPM
Additionally, bullet RPM is very important for accuracy. Nearly all modern rifles use spin-stablized bullets. The barrel’s rifling imparts spin to the bullet as it passes through the bore. This rotation stablizes the bullet in flight. Different bullets need different spin rates to perform optimally. Generally speaking, among bullets of the same caliber, longer bullets need more RPM to stabilize than do shorter bullets–often a lot more RPM.
It is generally believed that, for match bullets, best accuracy is achieved at the minimal spin rates that will fully stabilize the particular bullet at the distances where the bullet must perform. That’s why short-range 6PPC benchrest shooters use relatively slow twist rates, such as 1:14″, to stabilize their short, flatbase bullets. They could use “fast” twist rates such as 1:8″, but this delivers more bullet RPM than necessary. Match results have demonstrated conclusively that the slower twist rates produce better accuracy with these bullets.
Calculating Bullet RPM from MV and Twist Rate
The lesson here is that you want to use the optimal RPM for each bullet type. So how do you calculate that? Bullet RPM is a function of two factors, barrel twist rate and velocity through the bore. With a given rifling twist rate, the quicker the bullet passes through the rifling, the faster it will be spinning when it leaves the muzzle. To a certain extent, then, if you speed up the bullet, you can use a slower twist rate, and still end up with enough RPM to stabilize the bullet. But you have to know how to calculate RPM so you can maintain sufficient revs.
Bullet RPM Formula
Here is a simple formula for calculating bullet RPM:
MV x (12/twist rate in inches) x 60 = Bullet RPM
Quick Version: MV X 720/Twist Rate = RPM
Example One: In a 1:12″ twist barrel the bullet will make one complete revolution for every 12″ (or 1 foot) it travels through the bore. This makes the RPM calculation very easy. With a velocity of 3000 feet per second (FPS), in a 1:12″ twist barrel, the bullet will spin 3000 revolutions per SECOND (because it is traveling exactly one foot, and thereby making one complete revolution, in 1/3000 of a second). To convert to RPM, simply multiply by 60 since there are 60 seconds in a minute. Thus, at 3000 FPS, a bullet will be spinning at 3000 x 60, or 180,000 RPM, when it leaves the barrel.
Example Two: What about a faster twist rate, say a 1:8″ twist? We know the bullet will be spinning faster than in Example One, but how much faster? Using the formula, this is simple to calculate. Assuming the same MV of 3000 FPS, the bullet makes 12/8 or 1.5 revolutions for each 12″ or one foot it travels in the bore. Accordingly, the RPM is 3000 x (12/8) x 60, or 270,000 RPM.

Implications for Gun Builders and Reloaders
Calculating the RPM based on twist rate and MV gives us some very important information. Number one, we can tailor the load to decrease velocity just enough to avoid jacket failure and bullet blow-up at excessive RPMs. Number two, knowing how to find bullet RPM helps us compare barrels of different twist rates. Once we find that a bullet is stable at a given RPM, that gives us a “target” to meet or exceed in other barrels with a different twist rate. Although there are other important factors to consider, if you speed up the bullet (i.e. increase MV), you MAY be able to run a slower twist-rate barrel, so long as you maintain the requisite RPM for stabilization and other factors contributing to Gyroscopic Stability are present. In fact, you may need somewhat MORE RPM as you increase velocity, because more speed puts more pressure, a destabilizing force, on the nose of the bullet. You need to compensate for that destabilizing force with somewhat more RPM. But, as a general rule, if you increase velocity you CAN decrease twist rate. What’s the benefit? The slower twist-rate barrel may, potentially, be more accurate. And barrel heat and friction may be reduced somewhat.
Just remember that as you reduce twist rate you need to increase velocity, and you may need somewhat MORE RPM than before. (As velocities climb, destabilizing forces increase somewhat, RPM being equal.) There is a formula by Don Miller that can help you calculate how much you can slow down the twist rate as you increase velocity.
That said, we note that bullet-makers provide a recommended twist rate for their bullets. This is the “safe bet” to achieve stabilization with that bullet, and it may also indicate the twist rate at which the bullet shoots best. Though the RPM number alone does not assure gyroscopic stability, an RPM-based calculation can be very useful. We’ve seen real world examples where a bullet that needs an 8-twist barrel at 2800 FPS MV, would stabilize in a 9-twist barrel at 3200 FPS MV. Consider these examples.
MV = 2800 FPS
8-Twist RPM = 2800 x (12/8) x 60 = 252,000 RPM
MV = 3200 FPS
9-Twist RPM = 3200 x (12/9) x 60 = 256,000 RPM
Of course max velocity will be limited by case capacity and pressure. You can’t switch to a slower twist-rate barrel and maintain RPM if you’ve already maxed out your MV. But the Miller Formula can help you select an optimal twist rate if you’re thinking of running the same bullet in a larger case with more potential velocity.

Understanding Bullet Stability (Twist Rate and MV)

Berger bullet SG MV twist rate stability Litz

Berger bullet SG MV twist rate stability Litz

produced an informative new video on the subject of bullet stability. The video explains how stability is related to spin rate (or RPM), and how RPM, in turn, is determined by barrel twist rate and velocity. For long-range shooting, it is important that a barrel have a fast-enough twist rate to stabilize the bullet over its entire trajectory.
We explains the key concepts involved in bullet stabilization “Bullet stability can be quantified by the gyroscopic stability factor, SG. A bullet that is fired with inadequate spin will have an SG less than 1.0 and will tumble right out of the barrel. If you spin the bullet fast enough to achieve an SG of 1.5 or higher, it will fly point forward with accuracy and minimal drag.”

Berger bullet SG MV twist rate stability Litz

There is a “gray zone” of marginal stability. Bryan notes: “Bullets flying with SGs between 1.0 and 1.5 are marginally stabilized and will fly with some amount of pitching and yawing. This induces extra drag, and reduces the bullets’ effective BC. Bullets in this marginal stability condition can fly with good accuracy and precision, even though the BC is reduced. For short range applications, marginal stability isn’t really an issue. However, shooters who are interested in maximizing performance at long range will need to select a twist rate that will fully stabilize the bullet, and produce an SG of 1.5 or higher.”
Berger Twist-Rate Stability Calculator
On the updated Berger Bullets website you’ll find a handy Twist-Rate Stability Calculator that predicts your gyroscopic stability factor (SG) based on mulitiple variables: velocity, bullet length, bullet weight, barrel twist rate, ambient temperature, and altitude. This very cool tool tells you if your chosen bullet will really stabilize in your barrel.

Twist Rate Stability Calculator

This twist rate stability calculator can be used to determine your gyroscopic stability factor (SG) based upon the Miller Twist Rule.

NOTE ABOUT FLAT BASE SG CALCULATIONS

The Miller stability formula is most accurate for boat tail bullets, and typically underestimates stability for flat based bullets. In other words, if this stability calculator indicates low stability for your flat based bullet and barrel twist, it’s because the formula is not accurate for flat based bullets.

Bullet Library
Select a bullet from the list or enter in the properties below

Bullet Parameters
BC Ballistic Coefficient Ballistic Coefficient (BC) to either the G1 standard or the G7 standard. If both G1 and G7 data are provided, it is best to choose the G7 value for HPBT type bullets.		G1 G7
Caliber The diameter of the bullet as provided by the manufacturer.
Weight The weight of the bullet as provided by the manufacturer.		grains
Length The length of the bullet as provided by the manufacturer. If unknown, mulitiply bullet diameter by 4.2.

Gun and Atmospheric Parameters
Muzzle Vel. How fast the bullet leaves the rifle as measured by a chronograph. For very accurate results, remember to account for the velocity lost in the 10-15 feet between the muzzle and the chronograph. As a rule of thumb, a bullet looses 5-15 fps in this short distance.
Barrel Twist How many “inches per turn” is your rate of rifling twist. This number is used along with other inputs to determine the stability and related trajectory metrics. Typical value for this input is between 1:7″ and 1:13″.		inches
Temperature The atmospheric temperature. Because there is a great sensitivity to atmospheric temperature, it is recommended that this data be provided by using a local weather station or handheld weather meter.
Altitude The altitude at which the shooter is at. The ICAO standard is used to find the standard atmospheric pressure at the given altitude and temperature.

Stability Analysis

Your bullet is STABLE.

Your bullet is flying with full stability. You can expect good groups and your BC is optimized.

XXX . XXX 4% zero null 0 1 2 3 4 5 6 7 8 9 X LED ( Loving Enter Day )

Bullets Light concept ( RENEINSTEIN GUN )

Hasil gambar untuk concept led bullet lights

QUANTA AND WAVE-PARTICLE DUALITY

- Introduction
- Early Developments in Atomic Theory
- Quanta and Wave-Particle Duality
- Probability Waves and Complementarity
- Superposition, Interference and Decoherence
- Quantum Tunnelling and the Uncertainty Principle
- Nonlocality and Entanglement
- Spin and the Pauli Exclusion Principle
- Conclusion

The earliest steps in the development of quantum physics arose from the investigation into something as mundane as why metal glows red when hot. The great German physicist Max Planck had been studying the problem of black body radiation in the late 1890s. The “problem” Planck was dealing with was the observation that the greatest amount of energy being radiated from a black body (or any perfect absorber) actually falls near the middle of the electromagnetic spectrum, rather than in the ultraviolet region as classical theory suggested.
While Planck’s initial black body radiation law described the experimentally observed black body spectrum quite well, it was not perfect, and it was Planck’s genius to realize that the only way the law could work perfectly was to incorporate the supposition that electromagnetic energy could be emitted only in “quantized” form (i.e. restricted to discrete values rather than to a continuous set of values). In 1900, he proposed that light and other electromagnetic waves were emitted in discrete packets of energy, which he called "quanta", which can only take on certain discrete values (multiples of a certain constant, which now bears the name the “Planck constant”). He concluded that the energy radiated from a black body could only be a multiple of an elementary unit, E, where E = hv (where h is the Planck constant, and v is the frequency of the radiation).
In effect, Planck showed that the very structure of nature is discontinuous, in the same way as the population of a city, for example, can only change in discrete increments (i.e. whole number of people). Although, quantization was a purely formal assumption in Planck’s work at this time, and he never fully understood its radical implications (that had to await Albert Einstein’s interpretations in 1905), it has come to be regarded as the first essential stepping stone in the development of quantum theory, and the greatest intellectual accomplishment of Planck's career, for which he was awarded the Nobel Prize in Physics in 1918.

Emission of electrons from a metal plate (photoelectric effect)

Building on this earlier research by Planck and by Philippe Lenard, Einstein became, in 1905, the first person to clearly realize that light was made up of photons. He saw it as the only way to make sense of the so-called "photoelectric effect" (the phenomenon whereby certain metals, when exposed to light, eject electrons).
Einstein found that, no matter how bright the light shone on the metal, only light above a certain frequency caused electrons to be given off. Above that point, as the frequency of the light is increased, the energy of the electrons given off also increased. Furthermore, he noted that all the electrons were emitted instantaneously, with no delay whatsoever, which could not happen if the light was a wave sweeping over the metal, but only if the electron emissions were caused by individual particles of light.
Einstein, therefore, extended Planck’s discovery by theorizing that energy itself (not just the process of energy absorption and emission) is quantized. Light, he concluded, must consist of tiny bullet-like particles, now known as photons. In fact, it was for this work on the photoelectric effect in 1905 that Einstein was awarded the 1921 Nobel Prize in Physics, not for his better known work (in the same year) on the Special Theory of Relativity.
In 1913, the Danish physicist Niels Bohr further built on Planck’s insights and on the recent discoveries of J. J. Thomson and Ernest Rutherford about the structure of atoms. Bohr introduced the idea that electrons can only orbit an atom's nucleus at certain discrete distances (or "shells"), orbits that are different for different elements. This happens because electrons are also waves of specific frequencies, and the waves only fit (without interfering with themselves or cancelling each other out) on orbits of certain sizes. Electrons closer to the nucleus have lower energy than those further away (even though they are travelling faster).

Quantum jump of an electron from one energy level to another

However, although an electron can only exist in certain discrete energy levels (or "quantum states"), it can move from one energy level to another. For example, if an atom is heated or forced to collide, the energy imparted can cause an electron to move to a higher energy level (we say that the electron is "excited"). Bohr noted that it did not gradually pass through a continuum of energy levels in between, but rather there was a "quantum leap" or “quantum jump”, and the electron instantly leaped from one energy level to the next. A useful analogy is that of climbing a set of stairs, where it is possible to stand on any given step, but not somewhere in between two steps.
He also discovered that when an electron drops from a higher energy orbit to a lower one - which it will do whenever there is a lower energy state available for it to occupy - it emits in the process a photon (an individual quantum, or packet, of electromagnetic radiation) with energy exactly equal to the difference between the energy levels of the two orbits. Conversely, if light with the right energy strikes an atom, then its electrons will be excited and rise to a higher energy state, and the light will be absorbed.
This phenomenon is essentially why a heated object glows: the heat causes electrons to jump into excited states; then, when they drop back down to the "ground" state, the atom gives off photons of light. It is also the basis for the invention of the laser: in a nutshell, energy is pumped into atoms, thereby exciting them, and then, when the electrons drop down in energy, the photons emitted are collected and focussed.
It had been observed for some time (dating back to Anders Jonas Ångström in 1853) that, as atoms were heated, light was emitted not as a diffuse, blurred smear but in distinct and separate bands of colour (i.e. different wavelengths), with each element producing its own unique spectral pattern, its own distinct "spectral fingerprint", but it had always been beyond the explanatory powers of classical physics. Bohr's revelation, that an electron jumps from one distinct state to another, neatly explained why the light was emitted in distinct bands of colour, as electrons with specific energy levels within different elements changed their quantum states. For example, an electron moving from the third orbit of an atom to the second orbit emits red light, from fourth to second creates blue-green light, from fifth to second violet light, etc, all corroborated by Bohr's model.
This arrangement of the electrons within atoms also has some very useful practical applications. Because of the very structured and regular arrangement of atoms in solids, the energy levels of electrons within constituent atoms combine to form continuous energy bands (known as valence bands) separated by band gaps. The band structure of a material determines several characteristics, in particular the material's electronic and optical properties (e.g. some materials have very close, or even overlapping, bands so that electrons can easily move between them, which makes them good conductors of electricity; other materials have very large band gaps which makes them good insulators; etc).
So, the early stepping stones towards a fundamentally new type of physics (which was to become known as quantum theory or quantum mechanics) were gradually falling into place, and it was becoming clear that an essential element of it was the conception of light (and indeed all radiation and all matter) as composed of discrete quanta or particles.

Wave interference in Thomas Young's double-slit experiment

However, it had already been demonstrated beyond doubt that light was in fact a wave. Thomas Young’s experiments with his “double-slit” apparatus at the beginning of the 19th Century had shown that light caused interference, a characteristic property of waves, and he was even able to determine its wavelength, which he established was less than a thousandth of a millimetre. This had seemed at the time to settle forever the dispute which had been raging since the 17th Century between those (such as Christiaan Huygens) who favoured a wave theory of light and others (such as Sir Isaac Newton) who favoured a corpuscular or particle theory of light.
The developments by Einstein and Bohr in the early decades of the 20th Century, therefore, meant that physicists had to come to terms with the idea that light was both a wave AND a particle, and that sometimes it behaved like a wave and sometimes it behaved like a particle, an idea which became known as wave-particle duality. In an absolute sense, then, light is actually neither a particle nor a wave, but only exhibits wave or particle properties, depending on the experiment being performed.
Such an idea, however, was totally incompatible with all physics that had gone before, and particularly with the whole edifice of Maxwell’s theory of electomagnetic waves which had become by that time the orthodoxy of classical physics. It was also impossible to visualize and totally counter-intuitive at first glance. Perhaps wave-particle duality may be most easily understood by analogy: consider, for example, that a novel is both a story and a collection of individual words; or that the mind consists simultaneously of both thoughts and a series of electrical impulses.
But there was more to come. In 1923, Arthur Compton’s famous “Compton scattering” experiment showed how x-rays (generally understood as waves of electromagnetic radiation) can be observed to bounce off electrons, thus exhibiting particle-like properties, just like billiard balls impacting with other billiard balls. He also showed how this particle-like characteristic of electromagnetic radiation could be measured by its frequencies, previously considered a characteristic property only of waves.
Furthermore, in 1924, the French physicist Louis de Broglie showed that wave-particle duality was not merely an aberrant behaviour of light, but rather was a fundamental principle exhibited by both radiation and ALL particles of matter. According to de Broglie’s findings, then, at least in theory, everything (a baseball, a car, even a person) has a wavelength, although their wavelengths are so small as to be not noticeable. Just as Planck and Einstein had shown that waves can have particle-like characteristics, de Broglie showed that particles can have wave-like characteristics.
These counter-intuitive claims were backed up by double-slit experiments using electrons insead of light, in which the same kind of wave-like interference patterns were demonstrated as in Thomas Young's early experiments with light. In a strange twist of fate, George Thompson received the 1937 Nobel Prize in Physics for definitively proving the wave properties of the electron, just as his father had won the 1906 Prize for his discovery of the electron as a particle.
Thus, it became clear that a particle like an electron (or even an atom) could in some way interfere with itself, and was in some sense "spread out", or at least was able to be in many places at once. It should be noted, though, that this is not to say that an atom can spread itself out in a broad beam of some sort: the wave we are talking about is a wave of information, of what can be known about the atom, a probability wave Essentially, the wave is not the particle itself but a measure of the probability attached to its particle nature

PROBABILITY WAVES AND COMPLEMENTARITY

- Introduction
- Early Developments in Atomic Theory
- Quanta and Wave-Particle Duality
- Probability Waves and Complementarity
- Superposition, Interference and Decoherence
- Quantum Tunnelling and the Uncertainty Principle
- Nonlocality and Entanglement
- Spin and the Pauli Exclusion Principle
- Conclusion

The acceptance of light as composed of particles (or photons) led to another shocking realization. For example, if light shines on an imperfectly transparent sheet of glass, it may happen that 95% of the light transmits through the glass while 5% is reflected back. This makes perfect sense if light is a wave (the wave simply splits and a smaller wave is reflected back). But if light is considered as a stream of identical particles, then all we can say is that each and every photon arriving at the glass has a 95% chance of being transmitted and a 5% chance of being reflected.
The actual behaviour of any individual photon is therefore totally random and unpredictable, not just in practice but even in principle. Although the tossing of a coin, for example, is random in practice, if we knew precisely everything about the force, angle, shape, air currents, etc, we could, in principle, predict the outcome accurately. The behaviour of a sub-atomic particle, however, is random on a whole different level, and can never be predicted.
Thus, it is not possible to predict a single definite result for an obervation, only a number of different possible outcomes, each with a particular likelihood or probability. Physics had therefore changed overnight from a study of absolute certainty, to one of merely predicting the odds!
The reason we do not see the effects of this on a more macro scale is that everyday objects are composed of billions or trillions of sub-atomic particles. Although the position of each individual particle may be highly uncertain, because there are so many of them acting in unison in an everyday object, the combined probabilities add up to what is, to all intents and purposes, a certainty.
In order to reconcile the wave-like and particle-like behaviour of light, its wave-like aspect needs to be able to “inform” its particle-like aspect about how to behave, and vice versa. It was the Austrian physicist Erwin Schrödinger, along with the German Max Born, who first realized this and worked out the mechanism for this information transference in the 1920s, by imagining an abstract mathematical wave called a probability wave (or wave function) which could inform a particle of what to do in different situations. Erwin Schrödinger proposed a ground-breaking wave equation, analogous to the known equations for other wave motions in nature, to describe such a wave. Born further demonstrated that the probability of finding a particle at any point (its "probability density") was related to the square of the height of the probability wave at that point.

Probability density plots of some hydrogen atomic orbitals

Schrödinger worked out the exact solutions of the wave equation for the hydrogen atom, and the results perfectly agreed with the known energy levels of these atoms. It was soon found that the equation could also be applied to more complicated atoms, and even to particles not bound in atoms at all. In fact, in theory it applies to ALL matter, although massive objects exhibit very small wavelengths, so small that it is rather pointless to think of them in a wave fashion. But for small objects like elementary particles, the wavelength can be observable and significant.
Like light, then, particles are also subject to wave-particle duality: a particle is also a wave, and a wave is also a particle. Using Schrödinger's wave equation, therefore, it became possible to determine the probability of finding a particle at any location in space at any time. This ability to describe reality in the form of waves is at the heart of quantum mechanics. In 1926, Schrödinger published a proof showing that Heisenberg’s matrix mechanics and his own wave mechanics were in fact equivalent, and merely represented different versions of the same theory.
The Danish physicist Niels Bohr, who, along with Heisenberg and Schrödinger, was integrally involved in the early development of quantum mechanics, tried to come to grips with some of the philosophical implications of quantum theory in the early 1920s. He felt that the classical and quantum mechanical models were two complementary ways of dealing with physics, both of which were necessary, an idea he called “complementarity”. This idea of complementarity formed the basis of what became known as the “Copenhagen interpretation” of quantum physics, a deeply divisive idea in the world of physics at the time.

The collapse of a probability wave function

Bohr felt that an experimental observation “collapsed” or “ruptured” the wave function to make its future evolution consistent with what we observe experimentally (an idea that will become very important in our subsequent explanations of quantum effects such as decoherence, entanglement and the uncertainty principle). As soon as a photon, for example, is observed or detected in a particular place, then the probability of its being detected in any other place suddenly becomes zero. Up until that point, the particle's position is inherently uncertain and unpredictable, an uncertainty that only disappears when it is observed and measured. This immediate transition from a multi-facted potentiality to a single actuality (or, alternatively, from a multi-dimensional reality to a 3-dimensional reality compatible with our own everyday experience) is sometimes referred to as a quantum jump.
However, Bohr also believed that there was no precise way to define the exact point at which such a collapse occurred, and it was therefore necessary to discard the laws governing individual events in favour of a direct statement of the laws governing aggregations. According to this model, there is no deep quantum reality, no actual world of electrons and photons, only a description of the world in these terms, and quantum mechanics merely affords us a formalism that we can use to predict and manipulate events and the properties of matter.
The Copenhagen interpretation, then, is essentially a pragmatic view, effectively saying that it really does not matter exactly what quantum mechanics is all about, the important thing being that it “works” (in the sense that it correlates with reality) in all possible experimental situations, and that no other theory can explain sub-atomic particles in any more detail.
Albert Einstein, whose work had been instrumental in much of the early development of quantum theory, had grave philosophical difficulties with the Copenhagen interpretation, and carried on an extensive correspondence with both Bohr and Heisenberg on the matter, arguing that the physical world must have real properties whether or not one measures them, famously claiming in 1926 that “I, at any rate, am convinced that He [God] does not throw dice". He took particular exception to Bohr’s claim that a complete understanding of reality lies forever beyond the capabilities of rational thought. Both Einstein and Erwin Schrödinger published a number of thought experiments designed to show the limitations of the Copenhagen interpretation and to show that things can exist beyond what is described by quantum mechanics.
Einstein's position was not so much that quantum theory was wrong as that it must be incomplete. He insisted to his dying day that the idea that a particle's position before observation was inherently unknowable (and, particularly, the existence of quantum effects such as entanglement as a result of this) was nonsense and made a mockery of the whole of physics. He was convinced that the positions and quantum states of particles (even supposedly entangled particles) must already have been established before observation. However, the practical impossiblity of experimentally proving this argument one way or another made it essentially a matter of philosophy rather than physics.

SUPERPOSITION, INTERFERENCE AND DECOHERENCE

- Introduction
- Early Developments in Atomic Theory
- Quanta and Wave-Particle Duality
- Probability Waves and Complementarity
- Superposition, Interference and Decoherence
- Quantum Tunnelling and the Uncertainty Principle
- Nonlocality and Entanglement
- Spin and the Pauli Exclusion Principle
- Conclusion

In the same way as it is possible in the everyday world to get big rolling waves in the sea with tiny ripples superimposed on them, it is also possible in the sub-atomic world for a combination or superposition of waves to exist.
Schrödinger’s theory of probability waves permits the existence of two or more waves. In the example from the previous section of light shining on an imperfectly transparent sheet of glass, one wave would correspond to a photon passing through the glass and another wave would correspond to the photon bouncing back. But it is also possible for both waves to have superposed waves, which leads to the possibility of the photon being both transmitted AND reflected, and therefore being on both sides of the glass simultaneously!
In fact, this leads to the possibility of a potentially unlimited number of superposed waves, which means that microscopic particles can theoretically be located in a potentially unlimited number of places at once, and to behave in a potentially unlimited number of different ways. Just one of the intriguing possibilities this idea suggests is in the realm of computing, for example, where a "quantum computer" (still largely hypothetical at this time) could take advantage of an atom’s ability to be in a superposition of states to produce prodigiously increased power and speed of calculations.

Double-slit experiment with a single photon

Interestingly, a modern incarnation of Thomas Young’s double-slit experiment using a very feeble light source that spits out one photon at a time, leads to the same evidence of interference, even though there are no waves as such to interfere with each other. The only way the single photons can experience interference, then, is if each photon somehow goes though both slits simultaneously (due to superposition) and interferes with itself! The entire experiment can in fact be performed with electrons, atoms or other sub-atomic particles instead of light, demonstrating that ALL particles manifest both wave and particle aspects (this interference is the mechanism by which a hypothetical quantum computer would combine its multiple calculations into one answer).
In 1978, John Wheeler proposed a variation of Young’s double-slit experiment (and Richard Feynman’s later refinements of it), often referred to as the "delayed choice” experient. He posited that the detection of a photon even AFTER passing through a double slit would be sufficient to change the outcome of the experiment and the behaviour of the photon. Therefore, if the experimenters know which slit it goes through, the photon will behave as a particle, rather than as a wave with its associated interference behaviour. This somewhat counter-intuitive hypothesis was finally verified in a practical experiment in 2007.
It should be noted that, in reality, superpositions can never actually be observed - all we can see is the consequences of their existence, after individual waves of a superposition interfere with each other. Thus, we can never observe an atom in its indeterminate state, or being in two places at once, only the resulting consequences, and physical reality is not determined until the act of measurement takes place and “solidifies” the situation into one state or another.
Part of the problem of observing and measuring superpositions is known as decoherence. Any attempt to measure or obtain knowledge of quantum superpositions by the outside world (or indeed any kind of interaction with their environment, even with just a single photon) causes them to decohere, effectively destroying the superposition and reducing it to a single location or state, and also destroying the ability of its individual states to interfere with each other. Decoherence, then, results in the collapse of the quantum wave function and the settling of a particle into its observed state under classical physics, its transition from quantum to classical behaviour.
Decoherence is also the main reason that quantum theory really only applies in practice to the sub-atomic world: in the large-scale world in which we live, it is all but impossible to isolate anything from interaction with its environment, especially given the countless trillions of photons bouncing off every object all the time. Even an object made of just 60 atoms requires extreme cold to prevent it from becoming “classical” rather than "quantum". It is the interaction of quantum objects with the environment that produces what we understand as classical objects, such as cats and tables. Thus, in practice we never observe a quantum system directly; we only observe its effect on its environment.

Artist's impression of Schrödinger's Cat thought experiment

In 1935, the Austrian physicist Erwin Schrödinger devised his famous thought experiment or paradox, known as “Schrödinger’s cat”, to graphically illustrate the problem of decoherence (and to illustrate the general bizarreness of quantum mechanics). He proposed a scenario with a cat in a sealed box, where the cat's life or death was dependent on the state of a particular sub-atomic particle. According to the Copenhagen interpretation, the cat is in a kind of limbo represented by a wave function which contains the possibility that the cat is dead but also the possibility that it is alive. The cat, then, remains both alive AND dead until the box is opened, i.e. a superposition. This is usually taken as a demonstration of the way that quantum physics breaks down when dealing with large objects.
Although the best known and most popular view, the Copenhagen interpretation is, however, not the only interpretation of the quantum world. Some scientists, going back to Hugh Everett III in 1957 and subsequently championed by Bryce DeWitt and many others, have hypothesized that each possible state of a superposition actually exists in a totally separate parallel reality, which are all part of a potentially infinite multiverse, the so-called “many worlds” interpretation. Thus, every indeterminism in a quantum system generates a multifoliate reality in which the universe is continually branching into myriads of physically disconnected (but equally real) parallel universes.
This view purports to explain many of the apparently inexplicable properties of quantum theory. For example, the experimentally-proven phenomenon whereby individual photons going through a slit mysteriously experience interefence, may be explained in the many worlds interpretation by interference from photons in other parallel universes. It may also provide explanations for some of the more intractible problems of the Big Bang theory - for example, see the section on Superstrings and Quantum Gravity.
Unlike the Copenhagen interpretation (in which consciousness actually influences reality), the many worlds intepretation requires no observers to shape reality, since it is not necessary to collapse a wave function to actualize the universe, and every reality that CAN conceivably exist is automatically created. On the down side, however, the many worlds hypothesis is about as extravagant as it is possible to get, quite the opposite of the principle of parsimony, often referred to as Occam’s Razor, which dictates that theories should be constructed using the least possible number of principles and assumptions. And, of course, if parallel universes are independent and separate from our own, there is not, and indeed never will be, any way of practically proving their existence.

Illustration of the transactional interpretation of quantum mechanics

In 1986, John Cramer proposed another alternative interpretation of quantum physics, which many people feel overcomes the drawbacks of both the standard Copenhagen interpretation and the many worlds interpretation, and resolves many quantum paradoxes. Known as the "transactional interpretation", Cramer described quantum interactions as involving both a wave going forwards in time and a wave gong backwards in time.
According to the transactional interpretation, in any quantum transation (such as the propagation of an electromagnetic wave between two particles, for example), the receiving particle’s backward wave reinforces the emitting particle’s forward wave so long as it is between the particles, but it cancels out the emitting particle’s own backward wave (which is why a backward wave is not seen before the emission); and the receiving particle’s forward wave also cancels out the emitting particle’s forward wave (which is why a forward wave is not preceived after the receiving particle has absorbed it). Thus, the particles interact in the way called for by quantum physics (including the “collapse of the wave packet”, etc) without requiring an act of measurement by an external observer, allowing for the existence of a "real world" out there independent of us. The interpretation has it critics, but has gained much traction since its initial proposal.
There are also many other competing interpretations of quantum theory, including the consistent histories interpretation, the ensemble interpretation, relational quantum mechanics, stochastic mechanics, objective collapse theories, the many minds interpretation, the modal interpretation, and several others. It remains a highly active (and controversial) area of modern physics.

QUANTUM TUNNELLING AND THE UNCERTAINTY PRINCIPLE

- Introduction
- Early Developments in Atomic Theory
- Quanta and Wave-Particle Duality
- Probability Waves and Complementarity
- Superposition, Interference and Decoherence
- Quantum Tunnelling and the Uncertainty Principle
- Nonlocality and Entanglement
- Spin and the Pauli Exclusion Principle
- Conclusion

One of the consequences of light having a wave-like aspect is exemplified by its apparent ability to jump gaps. For instance, light penetrating through a block of glass at a shallow angle is effectively trapped within the glass by the barrier of air at the far side, unless a second glass block is placed close to it (but not touching). Because of the spread-out nature of the wave, some of it penetrates the air barrier and if encounters more glass beyond it can continue, thus apparently jumping the air gap and escaping its prison.
A similar thing happens at the sub-atomic scale, when alpha particles try to escape from unstable nuclei during radioactive decay. The particles are effectively held in the nucleus by the nuclear forces and, in principle, should not be able to escape. However, escape they do, using a process known as quantum tunnelling, which makes use of the wave-like aspect of the particles, but also of a more general phenomenon known as "uncertainty" (which we will look at in more detail below).
Due to the wave-like aspect of particles, and the ability to describe an object by means of a probability wave, as we have seen, quantum physics predicts that there is a finite probability that an object trapped behind a barrier (without the energy to overcome the barrier) may at times appear on the other side of the barrier, without actually overcoming it or breaking it down. For instance, if an electron approaches an electric field and is repelled by it, there is nevertheless some probability, however small, that it will find itself on the other side of the field (see image below).

Quantum tunnelling through a barrier

This possibility of being detected on the other side of a barrier has become known as tunnelling, although there is certainly no actual physical digging going on. It can perhaps be best visualized by imagining a broad wave approaching, and then slightly overlapping, a barrier. Although the main part of the wave may never penetrate the barrier, a small part of it does, allowing for the possibility of the particle which is generating the wave suddenly being located on the other side of the barrier.
The uncertainty principle was first recognized by the German physicist Werner Heisenberg in 1926 as a corollary of the wave-particle duality of nature. He realized that it was impossible to observe a sub-atomic particle like an electron with a standard optical microscope, no matter how powerful, because an electron is smaller than the wavelength of visible light. He conceived of an imaginary microscope which used gamma rays (which have a wavelength much smaller than an electron) rather than visible light. But, because gamma rays are so much more energetic than visible light, they would have the effect of changing the speed and direction of the electron in an unpredictable and uncontrollable way. So, in solving one part of the problem, another problem is necessarily created.
In fact, through his famous “microscope” thought experiment, he realized that a similar thing was happening to some extent even within a standard optical microscope. To measure the position and velocity of a particle, a light can be shone on it, and then the reflection detected. On a macroscopic scale this method works fine, but on sub-atomic scales the photons of light that hit the sub-atomic particle will cause it to move significantly. So, although the position may have been measured accurately, the velocity of the particle will have been altered, and, by learning the position, any information previously known about the velocity has been rendered useless. In other words, the very act of observation affects the observed.

Heisenberg's microscope thought experiment to illustrate the effects of the uncertainty principle

Heisenberg realized, then, that the values of certain pairs of variables cannot BOTH be known exactly, so that the more precisely one variable is known, the less precisely the other can be known. If the speed (or, more strictly, the momentum) of a particle is known exactly, then its location must be uncertain; conversely, the more certainly its location is known, the less certain is the particle’s speed (or momentum). Likewise, if the energy state of a particle is known with certainty, then it can not be determined how long it will remain in that state (and vice versa). In slightly more mathematical terms, he showed that the uncertainty in the position of a particle times the uncertainty in its velocity times its mass can never be smaller than a certain quantity, known as the Planck constant.
With the advent of the uncertainty principle, then, particles could no longer be said to have separate, well-defined positions and velocities, but only a “quantum state”, a combination of position and velocity. If it is not possible to know the values of all of the properties of the system at the same time, then those properties that are not known with precision must be described by probabilities. The principle effectively overturned in one fell swoop the whole doctrine of scientific determinism which had been implicitly assumed since Newton and Laplace in the 17th Century, and redefined the task of physics as the discovery of laws that will allow us to predict events UP TO THE LIMITS set by the uncertainty principle.
In a way, the uncertainty principle exists to protect quantum theory, in that if the properties of atoms and particles could be known with certainty, then they would decohere and their wave behaviour and their ability to interfere would thereby be destroyed. There is therefore a built-in limit to our knowledge of the microscopic world, and nature does not permit us to measure precisely all we would like to measure. However, it should be noted that this is not due to imprecise measurements in practice (technology is advanced enough to hypothetically yield correct measurements); rather, the blurring of the measurable quantities of a particle (mass, velocity and position) is a fundamental property of nature itself, and does not depend on the type of particle or the method of measurement.

An energy-losing electron should fall into the nucleus

Returning, then, to the earlier question (introduced back in the section on the Early Developments in Atomic Theory) of why orbiting electrons do not lose energy and spiral into the nucleus of an atom, it is the uncertainty principle that prevents electrons from approaching the nucleus too closely. If an electron gets too close then its location in space would be very precisely known, and its velocity would therefore be very uncertain and it could acquire enormous speed, enough to ensure that it did not stay confined in the nucleus.
In the same way, the uncertainty principle explains how an alpha particle is able to escape the nucleus of a radioactive atom. Trapped in the nucleus, the alpha particle is very localized in space, and its position is pinned down with great accuracy. In that case, according to the uncertainty principle, its velocity must be very uncertain, possibly much greater than we would have expected, and possibly enough to escape the pull of the nucleus.
A similar situation in reverse explains how nuclear fusion is possible in the Sun, when the temperatures in the Sun are actually about a thousand times cooler than the massive temperatures which are theoretically needed to provide the incoming protons with enough energy and speed to overcome the strong repulsive electromagnetic force of the receiving hydrogen atoms. By virtue of quantum tunnelling and Heisenberg’s uncertainty principle, the protons can “tunnel” through the barrier even given the apparently insufficient temperature and energy.
The uncertainty principle also explains why a typical atom is over 100,000 times bigger than the nucleus at its centre. Strictly speaking, the uncertainty principle holds that it is a particle’s position and its momentum (its mass times its velocity, as opposed to just its velocity) which cannot be simultaneously be known with certainty. Because an electron is about 2,000 times less massive than the protons in a nucleus, and because the repulsive electromagnetic force it is subject to is about 50 times weaker than the strong nuclear force in the nucleus, these two factors together result in the need for about 100,000 times as much space for the electron to move around in.

Virtual electron-positron pairs appearing at random near an electron

In fact, the uncertainty principle can be reformulated in yet another way to say that it is impossible to simultaneously measure the energy of a particle and the interval of time for which it has been in existence. Over a very tiny interval of time, there can therefore be a large uncertainty in the energy content of a particular location, and energy or even pairs of fundamental particles (known as "virtual particles", because they exist for such a short time that they are not considered part of everyday reality) could even appear out of nothing in the apparently empty vacuum of space and exist for a split-second before disappearing again. The more energy that is put into a vacuum, the more particles causelessly pop out of it. It appears, then, that there is no such thing as empty space.
Such a phenomenon (particles constantly popping in and out of existence), unlikely though it may sound, is well documented and has actually been indirectly observed through observations of the changing energy of existing electrons which are buffeted by such appearances and disappearances. In effect, the energy needed to create these virtual particles can be "borrowed" from the vacuum for a period of time, but the net energy from the reaction is still zero. Because overall they cancel each other out, they cannot be said to even exist in the classical world, nor to break any of the laws of classical physics.

NONLOCALITY AND ENTANGLEMENT

- Introduction
- Early Developments in Atomic Theory
- Quanta and Wave-Particle Duality
- Probability Waves and Complementarity
- Superposition, Interference and Decoherence
- Quantum Tunnelling and the Uncertainty Principle
- Nonlocality and Entanglement
- Spin and the Pauli Exclusion Principle
- Conclusion

Another of the remarkable features of the microscopic world prescribed by quantum theory is the idea of nonlocality, what Albert Einstein rather dismissively called “spooky actions at a distance”. This was first described in the “EPR papers” of Einstein, Boris Podolsky and Nathan Rosen in 1935, and it is sometimes referred to as the EPR (Einstein-Podolsky-Rosen) paradox. It was even more starkly illustrated by Bell’s Theorem, published by John Bell in 1964, and the subsequent practical experiments by John Clauser and Stuart Freedman in 1972 and by Alain Aspect in 1982.
Nonlocality describes the apparent ability of objects to instantaneously know about each other’s state, even when separated by large distances (potentially even billions of light years), almost as if the universe at large instantaneously arranges its particles in anticipation of future events.
Thus, in the quantum world, despite what Einstein had established about the speed of light being the maximum speed for anything in the universe, instantaneous action or transfer of information does appear to be possible. This is in direct contravention of the "principle of locality" (or what Einstein called the "principle of local action"), the idea that distant objects cannot have direct influence on one another, and that an object is directly influenced only by its immediate surroundings, an idea on which almost all of physics is predicated.
Nonlocality suggests that universe is in fact profoundly different from our habitual understanding of it, and that the "separate" parts of the universe are actually potentially connected in an intimate and immediate way. In fact, Einstein was so upset by the conclusions on nonlocality at one point that he declared that the whole of quantum theory must be wrong, and he never accepted the idea of nonlocality up till his dying day.

An entangled pair of particles can be seen to have complementary properties when measured

Nonlocality occurs due to the phenomenon of entanglement, whereby particles that interact with each other become permanently correlated, or dependent on each other’s states and properties, to the extent that they effectively lose their individuality and in many ways behave as a single entity. The two concepts of nonlocality and entanglement go very much hand in hand, and, peculiar though they may be, they are facts of quantum systems which have been repeatedly demonstrated in laboratory experiments.
For example, if a pair of electrons are created together, one will have clockwise spin and the other will have anticlockwise spin (spin is a particular property of particles whose details need not concern us here, the salient point being that there are two possible states and that the total spin of a quantum system must always cancel out to zero). However, under quantum theory, a superposition is also possible, so that the two electrons can be considered to simultaneously have spins of clockwise-anticlockwise and anticlockwise-clockwise respectively. If the pair are then separated by any distance (without observing and thereby decohering them) and then later checked, the second particle can be seen to instantaneously take the opposite spin to the first, so that the pair maintains its zero total spin, no matter how far apart they may be, and in total violation of the speed of light law.
Despite Einstein's misgivings about entanglement and nonlocality and the practical difficulties of obtaining proof one way or the other, Irish physicist John Bell attempted to force the issue by making it experimental rather than just theoretical. Bell’s Theorem, published in 1964, and referred to by some as one of the most profound discoveries in all of physics, effectively showed that the results predicted by quantum mechanics (for example, in an experiment like that described by Einstein, Podolsky and Rosen) could not be explained by any theory which preserved locality. The subsequent practical experiments by John Clauser and Stuart Freedman in 1972 seem (despite Clauser's initial espousal of Einstein's position) to definitively show that the effects of nonlocality are real, and that "spooky actions at a distance" are indeed possible.
In theory, the concepts of entanglement and nonlocality may have applications in communications and even teleportation, although these ideas are still largely hypothetical at this stage. Due to the effects of the uncertainty principle, the mere act of observing the properties of particles at a quantum level (spin, charge, etc), disturbs the quantum system irrevocably, and this would appear to prevent us from using this system as a means of instantaneous communication. However, Anton Zeilinger's work at two observatories in the Canary Islands has shown promising indications that entangled particles can indeed be reconstituted in a different place (although the leap from this to a teleportation device of the kind envisaged in Star Trek is a profound one).

SPIN AND THE PAULI EXCLUSION PRINCIPLE

- Introduction
- Early Developments in Atomic Theory
- Quanta and Wave-Particle Duality
- Probability Waves and Complementarity
- Superposition, Interference and Decoherence
- Quantum Tunnelling and the Uncertainty Principle
- Nonlocality and Entanglement
- Spin and the Pauli Exclusion Principle
- Conclusion

To return to the property of spin of fundamental particles, mentioned briefly in the previous section, spin can perhaps be most easily thought of as a rotation of particles around their own axis, although this is in fact something of a simplification, and in reality it is impossible to tell whether something as small as an electron is spinning at all. In general, though, spin obeys the same mathematical laws of angular momentum as do spinning objects in classical physics (such as the Earth, for instance), and there are really only two important aspects to consider: the speed of rotation and the direction of the axis it rotates about (referred to as “up” and “down”).
When spin was first discovered in 1922 by Otto Stern and Walther Gerlach, however, their experiments indicated that the intrinsic angular momentum, or spin, of a particle such as an electron was quantized i.e. it could only take certain discrete values. The spin of composite particles (such as protons, neutrons and atomic nuclei) is just the sum of the spins and orbital angular momentum of the constituent particles, and is therefore subject to the same quantization conditions. Spin is therefore a completely quantum mechanical property of a particle, and cannot be explained in any way by classical physics.

Artist's representation of the spin and charge of an electron

Now, it turns out that there are two sub-categories of particles: those with “integer” spin, which are known as bosons, and which include photons, gluons, W and Z bosons and hypothetical gravitons; and those with “half-integer spin”, which are known as fermions, and which include electrons, neutrinos, muons, and the quarks which make up composite particles like protons and neutrons. Another way of describing the difference between bosons and fermions is that bosons have symmetric wave functions while fermions have antisymmetric wave functions. The concept of a particle with half-integer spin is just another example of the apparently counter-intuitive nature of sub-atomic particles: crudely speaking, a fermion such as an electron has to spin around TWICE before it presents the same face as before.
The significance of this distinction for quantum theory is that the probability waves of bosons “flip” or invert before they interfere with each other, which effectively leads to their more “gregarious” nature, which in turn can lead to collective behaviour like that of lasers, superfluids and superconductors. Fermions, however, do not flip their probability waves, which, among other implications, leads to their “unsociable” nature. Thus, the spins of particles have to be added together very carefully using special rules for addition of angular momentum in quantum mechanics.
This discussion of the property of spin leads us to one of the most important principles in quantum physics, the Pauli exclusion principle (formulated by Wolfgang Pauli in 1925), which states that no two identical fermions may occupy the same quantum state simultaneously (although two electrons, for example, may acquire opposite spin in order to differentiate their quantum states). Another way of stating the principle is that no two fermions in a quantum system can have the same values of all four quantum numbers at any given time. This principle effectively explains the continued existence of very high density white dwarf stars, but also the very existence of different types of atoms in the universe and the large-scale stability and bulk of matter.

Electron shell diagram for the element uranium (using the Bohr model of the atom)

To understand why, it is necessary to know that, according to the Bohr model of the atom, electrons in an atom (which exist in the same quantity as the number of protons in the nucleus of the particular atom, so that the overall electric charge is zero) are constrained to occupy certain discrete orbital positions or “shells” around the nucleus. The closer electrons are to the nucleus, the more strongly the electric force is pulling them in and the more energy would be required to free it from the clutches of the nucleus (or, looked at another way, the more energy of its own an electron has, the less additional energy it needs in order to escape). The innermost shell can accommodate just two electrons, one with spin “up” and one with spin “down” in order to differentiate their quantum states. The next shell out, in a higher energy level, can accommodate a further eight, the next a further eighteen and the next thirty-two.
Actually, more recent research has yielded a more accurate “refined” Bohr model of the atom with each energy level composed of a certain number of sub-shells (named s, p, d and f) which can each hold only a certain number of electrons. For instance, the s sub-shell can only hold 2 electrons, the p sub-shell can hold 6, the d sub-shell can hold 10 and the f sub-shell can hold 14. The number of available sub-shells increases as the energy level increases, so that successive shells can hold a total of 2, 8, 18 and 32 electrons.

Depiction of an atom of nitrogen (using the refined Bohr model)

It is the Pauli exclusion principle which dictates this arrangement and effectively forces electrons to “take up space” in the atom through this arrangement of shells. By recognizing that no two electrons may occupy the same quantum state simultaneously, it effectively stops electrons from "piling up" on top of each other, thus explaining why matter occupies space exclusively for itself and does not allow other material objects to pass through it, while at the same time allowing light and radiation to pass.
It also explains the existence of the different atoms in the periodic table of elements and the sheer variety of the universe around us. For example, when an atom gains a new electron, it always goes into the lowest energy state available (i.e. the outermost shell). Two atoms with “closed” shells find they cannot form a chemical bond with each other because the electrons in one atom find no available quantum states in the other which it can occupy. So, the arrangement of electrons, particularly of the electrons in the outermost shell, also affects the chemical properties of an element and how atoms are able to bond and combine with other atoms (the basis of chemistry), and therefore the way in which molecules interact to form gases, liquids or solids, and how they aggregate themselves in living organisms.
Another effect of the Pauli exclusion principle is that, if two identical particles are forced (for instance, by an extremely strong gravitational force) to try to have the same quantum numbers, they will respond with a repelling outward force, known as "degeneracy pressure" or "Pauli repulsion". A type of star called a degenerate white dwarf is held up entirely by this force.
The Pauli exclusion principle is one of the most important principles in quantum physics, largely because the three types of particles from which ordinary matter is made (electrons, protons and neutrons) are all subject to it, so that all material particles exhibit space-occupying behaviour. Interestingly, though, the principle is not enforced by any physical force understood by mainstream science. When an electron enters an ion, it somehow mysteriously seems to "know" the quantum numbers of the electrons which are already there, and therefore which atomic orbitals it may enter, and which it may not.
CONCLUSION

This has been a necessarily abbreviated and condensed foray into the wonderful, and sometimes bizarre, world of quantum mechanics. If a couple of fundamental principles of quantum physics were to be singled out from all of the above, they would probably be the dual wave-like and particle-like behaviour of matter and radiation, and the prediction of probabilities in situations where classical physics predicts certainties.
For many, even those in the scientific community, these are difficult concepts to come to terms with, and even Albert Einstein had serious philosophical problems with a universe which behaves in an apparently totally random manner at the sub-atomic level, repeatedly claiming that “God does not play dice” (although Einstein is widely considered to have “lost” the extensive public debates he carried on with Niels Bohr on the subject). For a better or more comprehensive understanding of this complex and confusing subject, there is a copious amount of literature on the subject, both for the beginner and the expert alike, a few of which are mentioned on the Sources page.
Despite its difficulties, however, quantum theory remains an essential part of the bedrock of modern physics. It is arguably one of the most successful theories in all of science, and, despite its seemingly esoteric nature, it is primarily a practical branch of physics, paving the way for applications such as the laser, the electron microscope, the transistor, the superconductor and nuclear power, as well as explaining at a stroke important physical phenomena such as chemical bonding, the structure of the atom, the conduction of electricity, the mechanical and thermal properties of solids and the density of collapsed stars.
However, successful as it is in predicting and describing the world around us, quantum theory only successfully explains three of the four fundamental forces: electromagnetism, the strong nuclear force and the weak nuclear force. It does not explain the workings of gravity.
As has been mentioned in other sections (see here, for example), the way forward for physics seems now to rest with attempts to combine quantum theory with the General Theory of Relativity in a unified theory of quantum gravity (or quantum theory of gravity), the so-called “theory of everything”, which it is hoped will make sense of the entire universe. Candidates like superstring theory and loop quantum gravity, however, still need to overcome major formal and conceptual problems before such a claim can be made.
In parting, let me just mention one other interesting field of speculation related to quantum theory. It has been suggested that, if the whole universe (space, time, energy and everything else) is quantized and consists of indivisible fundamental particles, then it has a finite number of components and a finite number of states, like the bits and pixels of a computer program. In theory, this makes the universe "computable", and has led some to hypothesize that perhaps all of reality as we perceive it might actually be part of a huge Matrix-like computer simulation, individual parts of which only assume definite form when observed. Speculation only, perhaps, but an intriguing one nonetheless, and one which seems increasingly difficult to disprove as the details of quantum theory are ironed out.


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