Internal ballistics

Internal ballistics, a subfield of ballistics, is the study of a projectile's motion from the time its propellant's igniter is initiated until it exits the gun barrel. The study of internal ballistics is important to designers and users of firearms of all types, from small-bore Olympic rifles and pistols, to high-tech artillery.

General concerns

Hatcher breaks the duration of interior ballistics into 3 parts:

• Lock time, the time from sear release until the primer is struck
• Ignition time, the time from when the primer is struck until the projectile starts to move
• Barrel time, the time from when the projectile starts to move until it exits the barrel.

These times have significance for accuracy. If the weapon is moving, then a shorter lock time minimizes the effect of that motion. The consistency of the ignition and barrel times affect and relate to the muzzle velocity.

There are many processes that are significant. The source of energy is the burning propellant. It generates hot gases that raise the chamber pressure. That pressure pushes on the base of the projectile, and causes the projectile to accelerate. The chamber pressure depends on many factors. The amount of propellant that has burned, the temperature of the gases, and the volume of the chamber. The burn rate of the propellant depends not only on the chemical make up, but also on the shape of the propellant grains. The temperature depends not only on the energy released, but also the heat lost to the sides of the barrel and chamber. The volume of the chamber is continuously changing: as the propellant burns, there is more volume for the gas to occupy. As the projectile travels down the barrel, the volume behind the projectile also increases.

There are still other effects. Some energy is lost in deforming the projectile and causing it to spin. There are also frictional losses between the projectile and the barrel. The projectile, as it travels down the barrel, compresses the air in front of it.

Models have been developed for these processes.

These processes affect the gun design. The breech and the barrel must resist the high pressure gases without damage. Although the pressure initially rises to a high value, the pressure starts dropping when the projectile has traveled a distance down the barrel. Consequently, the muzzle end of the barrel does not need to be as strong as the chamber end.

There are five general equations used in interior ballistics:

1. The equation of state of the propellant
2. The equation of energy
3. The equation of motion
4. The burning rate equation
5. The equation of the form function

History

There was a time when interior ballistics didn't have a lot of information. The barrels would be built strong enough to survive a known overload (proof).

Muzzle velocity could be measured.

Then barrels were instrumented. Holes were drilled in the barrel, "crusher gauges" using copper pellets were attached, the gun was fired, and the pressure was measured indirectly by how much the copper pellet was deformed. The measurement only indicated the maximum pressure that was reached at that point in the barrel.

Later, piezoelectric sensors were used. They allow the instantaneous pressure to be measured. Also strain gauges on the barrel did not need a pressure port.

Instrumented projectiles were developed that could measure the pressure at the base of the projectile and the acceleration.

Priming methods

Main article: Primer (firearm)

Through the years, several methods of igniting the propellant were developed.

Propellants

Black powder

Main article: Gunpowder

Gunpowder (Black powder) is a finely ground, pressed and granulated mechanical mixture of sulfur, charcoal, and potassium nitrate or sodium nitrate. It can be produced in a range of grain sizes. The size and shape of the grains can increase or decrease the relative surface area, and change the burning rate significantly. The burning rate of black powder is relatively insensitive to pressure, meaning it will burn quickly even without confinement, making it also suitable for use as a low explosive. However, it is a very poor explosive compared to modern high explosives because it has a very slow decomposition rate, and therefore a very low brisance. It is not, in the strictest sense of the term, an explosive, but a "deflagrant", as it does not detonate but decomposes by deflagration due to its subsonic mechanism of flame-front propagation.

Nitrocellulose (single-base propellants)

Main article: Smokeless powder

Nitrocellulose or "guncotton" is formed by the action of nitric acid on cellulose fibers. It is a highly combustible fibrous material that deflagrates rapidly when heat is applied. It also burns very cleanly, burning almost entirely to gaseous components at high temperatures with little smoke or solid residue. The burning rate of nitrocellulose is dependent upon the pressure — a pile of uncontained nitrocellulose will burn slowly, with a high, bright flame, but when placed in a high-strength, sealed container, the same material will burn very quickly, bursting the container. Gelatinised nitrocellulose is a plastic, which can be formed into many shapes of gun propellants such as cylinders, tubes, balls, and flakes. The size and shape of the propellant grains can increase or decrease the relative surface area, and change the burn rate significantly. Additives and coatings can be added to the propellant to further modify the burn rate. Normally, very fast powders are used for light-bullet or low-velocity pistols and shotguns, medium-rate powders for magnum pistols and light rifle rounds, and slow powders for large-bore heavy rifle rounds. These are known as Single-base propellants.

Double-base propellants

Main articles: Ballistite, Cordite, and Smokeless powder

To further increase the energy of smokeless powder, nitroglycerin can be added in amounts up to 50%. These powders are called "double-base powders", since both their main components actively produce energy, and they have similar basic physical properties to single-base powders. The nitrocellulose serves to desensitize the highly unstable nitroglycerin, preventing it from detonating as a high explosive, and the nitroglycerin gelatinises the nitrocellulose and greatly increases the energy density of the resulting powder. Double-base powders burn faster than single-base powders of the same shape, though not as cleanly, and in general the higher the nitroglycerin content of a powder, the faster the burn rate.

In artillery, Ballistite or Cordite has been used in the form of rods, tubes, slotted-tube, perforated-cylinder or multi-tubular; the geometry being chosen to provide the required burning characteristics. (Round balls or rods, for example, are "degressive-burning" because their production of gas decreases with their surface area as the balls or rods burn smaller; thin flakes are "neutral-burning," since they burn on their flat surfaces until the flake is completely consumed. The longitudally perforated or multi-perforated cylinders used in large, long-barreled rifles or cannon are "progressive-burning;" the burning surface increases as the inside diameter of the holes enlarges, giving sustained burning and a long, continuous push on the projectile to produce higher velocity without increasing the peak pressure unduly. Progressive-burning powder compensates somewhat for the pressure drop as the projectile accelerates down the bore and increases the volume behind it.)

Solid propellants (caseless ammunition)

A recent topic of research has been in the realm of "caseless ammunition". In a caseless cartridge, the propellant is cast as a single solid grain, with the priming compound placed in a hollow at the base, and the bullet attached to the front. Since the single propellant grain is so large (most smokeless powders have grain sizes around 1 mm, but a caseless grain will be perhaps 7 mm diameter and 15 mm long), the relative burn rate must be much higher. To reach this rate of burning, caseless propellants often use moderated explosives, such as RDX. (Caseless ammunition might be considered a return to the mid-19th century, since the first practical cartridge repeater, the "Volcanic" pistol, used a charge of black powder in a cavity in the bullet base. This weapon was the direct ancestor of the Henry and Winchester rifles, though they switched to metal-cased ammunition. Some early rifles and revolvers also used combustible-paper cartridges, but they required a separate ignition system.) The major advantages of a successful caseless round would be elimination of the need to extract and eject the spent cartridge case, permitting higher rates of fire and a simpler mechanism, and also reduced ammunition weight by eliminating the weight (and cost) of the brass or steel case. While there is at least one experimental military rifle (the H&K G11), and one commercial rifle (the Voere VEC-91), that use caseless rounds, they are meeting little success. One other commercial rifle was the Daisy VL rifle made by the Daisy Air Rifle Co. and chambered for .22 caliber caseless ammunition that was ignited by a hot blast of compressed air from the lever used to compress a strong spring like for an air rifle. The caseless ammunition is of course not reloadable, since there is no casing left after firing the bullet, and the exposed propellant makes the rounds less rugged. Also, the case in a standard cartridge serves as a seal, keeping gas from escaping the breech. Caseless arms must use a more complex self-sealing breech, which increases the design and manufacturing complexity. Another unpleasant problem, common to all rapid-firing arms but particularly problematic for those firing caseless rounds, is the problem of rounds "cooking off". This problem is caused by residual heat from the chamber heating the round in the chamber to the point where it ignites, causing an unintentional discharge. Belt-fed machine guns or magazine-fed submachine guns designed for high volumes of fire usually fire from an open bolt, with the round not chambered until the trigger is pulled, and so there is no chance for the round to cook off before the operator is ready. Such weapons could use caseless ammunition effectively. Open-bolt designs are generally undesirable for anything but belt-fed machine guns and pistol-cartridge submachine guns; the mass of the bolt moving forward causes the gun to lurch in reaction, which significantly reduces the accuracy of the gun. Since one of the motivating factors for the use of caseless rounds is to increase the rate of fire to the degree that several shots can be fired to the same point of aim, anything that reduces the accuracy of those first shots would be counterproductive. Cased ammunition serves as a heat sink, to carry heat away from the chamber after firing; the hot case carries away much of the heat before it can transfer to the chamber walls, and the new case absorbs heat from the chamber, reducing the risk of cook-off.

Propellant charge

Load density and consistency

Load density is the percentage of the space in the cartridge case that is filled with powder. In general, loads close to 100% density (or even loads where seating the bullet in the case, compresses the powder) ignite and burn more consistently than lower-density loads. In cartridges surviving from the black-powder era (examples being .45 Colt, .45-70 Government), the case is much larger than is needed to hold the maximum charge of high-density smokeless powder. This extra room allows the powder to shift in the case, piling up near the front or back of the case and potentially causing significant variations in burning rate, as powder near the rear of the case will ignite rapidly but powder near the front of the case will ignite later. This change has less impact with fast powders. Such high-capacity, low-density cartridges generally deliver best accuracy with the fastest appropriate powder, although this keeps the total energy low due to the sharp high-pressure peak. Magnum pistol cartridges reverse this power/accuracy tradeoff by using lower-density, slower-burning powders that give high load density and a broad pressure curve. The downside is the increased recoil and muzzle blast from the high powder mass, and high muzzle pressure. The advantage is that the magnum pistol rounds can generate accuracy comparable to a good hunting rifle, and energy sufficient to take medium game at ranges out to 100 yards (100 m) and beyond.

Most rifle cartridges have a high load density with the appropriate powders. Rifle cartridges tend to be bottlenecked, with a wide base narrowing down to a smaller diameter, to hold a light, high-velocity bullet. These cases are designed to hold a large charge of low-density powder, for an even broader pressure curve than a magnum pistol cartridge. These cases require the use of a long rifle barrel to extract their full efficiency, although they are also chambered in rifle-like pistols (single-shot or bolt-action) with barrels of 10 to 15 inches (25 to 38 cm).

One unusual phenomenon occurs when dense, low-volume powders are used in large-capacity rifle cases. Small charges of powder, unless held tightly near the rear of the case by wadding, can apparently detonate when ignited, sometimes causing catastrophic failure of the firearm. The mechanism of this phenomenon is not well known, and generally it is not encountered except when loading low recoil or low-velocity subsonic rounds for rifles. These rounds generally have velocities of under 1100 ft/s (320 m/s), and are used for indoor shooting, in conjunction with a suppressor or for pest control, where the power and muzzle blast of a full-power round is not needed or desired.

Chamber

Straight vs bottleneck

Straight walled cases were the standard from the beginnings of cartridge arms. With the low burning speed of black powder, the best efficiency was achieved with large, heavy bullets, so the bullet was the largest practical diameter. The large diameter allowed a short, stable bullet with high weight, and the maximum practical bore volume to extract the most energy possible in a given length barrel. There were a few cartridges that had long, shallow tapers, but these were generally an attempt to use an existing cartridge to fire a smaller bullet with a higher velocity and lower recoil. With the advent of smokeless powders, it was possible to generate far higher velocities by using a slow smokeless powder in a large volume case, pushing a small, light bullet. The odd, highly tapered 8 mm Lebel, made by necking down an older 11 mm black-powder cartridge, was introduced in 1886, and it was soon followed by the 7.92 x 57 mm Mauser and 7 x 57 mm Mauser military rounds, and the commercial .30-30 Winchester, all of which were new designs built to use smokeless powder. All of these have a distinct shoulder that closely resembles modern cartridges, and with the exception of the Lebel they are still chambered in modern firearms even though the cartridges are over a century old.

Aspect ratio and consistency

When selecting a rifle cartridge for maximum accuracy, a short, fat cartridge with very little case taper will generally yield higher efficiency and more consistent velocity than a long, thin cartridge with a lot of case taper (part of the reason for a bottle-necked design). Given current trends towards shorter and fatter cases, such as the new Winchester Super Short Magnum cartridges, it appears the ideal might be a case approaching spherical inside. Target and varmint hunting rounds require the greatest accuracy, so their cases tend to be short, fat, and nearly untapered with sharp shoulders on the case. Short, fat cases also allow short-action weapons to be made lighter and stronger for the same level of performance. The trade-off for this performance is fat rounds which take up more space in a magazine, sharp shoulders that do not feed as easily out of a magazine, and less reliable extraction of the spent round. For these reasons, when reliable feeding is more important than accuracy, such as with military rifles, longer cases with shallower shoulder angles are favored. There has been a long-term trend however, even among military weapons, towards shorter, fatter cases. The current 7.62 x 51 mm NATO case replacing the longer .30-06 Springfield is a good example, as is the new 6.5 Grendel cartridge designed to increase the performance of the AR-15 family of rifles and carbines.

Friction and inertia

Static friction and ignition

Since the burning rate of smokeless powder varies directly with the pressure, the initial pressure buildup has a significant effect on the final velocity, especially in cartridges with fast powders. The friction, holding the bullet in the case, determines how soon after ignition the bullet moves, and since the motion of the bullet increases the volume and drops the pressure, a difference in friction can change the slope of the pressure curve. In general, a tight fit is desired, to the extent of crimping the bullet into the case. In straight-walled rimless cases, such as the .45 ACP, an aggressive crimp is not possible, since the case is held in the chamber by the mouth of the case, but sizing the case to allow a tight interference fit with the bullet, can give the desired result.

Kinetic friction

The bullet must tightly fit the bore to seal the high pressure of the burning gunpowder. This tight fit results in a large frictional force. The friction of the bullet in the bore does have a slight impact on the final velocity, but that is generally not much of a concern. Of greater concern is the heat that is generated due to the friction. At velocities of about 1,000 ft/s (300 m/s), lead begins to melt, and deposit in the bore. This lead build-up constricts the bore, increasing the pressure and decreasing the accuracy of subsequent rounds, and is difficult to scrub out without damaging the bore. Rounds, used at velocities up to 1,500 ft/s (460 m/s), can use wax lubricants on the bullet to reduce lead build-up. At velocities over 1,500 ft/s (460 m/s), nearly all bullets are jacketed in copper, or a similar alloy that is soft enough not to wear on the barrel, but melts at a high enough temperature to reduce build-up in the bore. Copper build-up does begin to occur in rounds that exceed 2,500 ft/s (760 m/s), and a common solution is to impregnate the surface of the bullet with molybdenum disulfide lubricant. This reduces copper build-up in the bore, and results in better long-term accuracy.

The role of inertia

In the first few inches (centimeters) of travel down the bore, the bullet reaches a significant percentage of its final velocity, even for high-capacity rifles, with slow burning powder. The acceleration is on the order of tens of thousands of gravities, so even a projectile as light as 40 grains (2.6 g), can provide hundreds of pounds-force (over 1000 newtons) of resistance, due to inertia. Changes in bullet mass, therefore, have a huge impact on the pressure curves of smokeless powder cartridges, unlike black-powder cartridges. The loading or reloading of smokeless cartridges thus requires high-precision equipment, and carefully measured tables of load data for given cartridges, powders, and bullet weights.

Pressure

This is a graph of a simulation of the 5.56 mm NATO round, being fired from a 20-inch (510 mm) barrel. The horizontal axis represents time, the vertical axis represents pressure (green line), bullet travel (red line), and bullet velocity (light blue line). The values shown at top are peak values

Energy is imparted to the bullet in a firearm by the pressure of the gases produced by the burning gunpowder. While it seems to casual observers that a higher peak pressures should produce higher velocities, that is not always the case, since measures of peak pressure capture only a small fraction of the time the bullet is accelerating. To achieve maximum performance, the entire duration of the bullet's travel through the barrel must be considered.

There are hundreds of powders in existence because powders must be carefully matched to the case volume, case dimensions, bullet dimensions, bullet weight, barrel length, and special bullet features such as moly coating or driving bands. For example, long, heavy bullets are required to be seated so deep in the case that they displace powder, while at the same time requiring a slower powder which gives their greater mass more time to move down the barrel. If the bullet is banded or coated with a lubricant like moly, faster powders can be used as the bullet moves faster due to decreased friction with the barrel. All of these variables must be accommodated within the maximum pressure levels set for the platform. Finding the optimum combination is largely a trial and error process, and may take years to complete. New cartridges with significantly new internal ballistics often bring forth new powders engineered to maximize performance; examples of this are Accurate Arms 2230, designed for use in the .223 Remington, and #9, designed for use in magnum pistol cartridges.

Piobert's Law

Propellant burns by consuming the outer surface of each grain of the charge. The larger the surface of the propellant's grains exposed to burn, the faster the release of gases to the chamber and the higher the pressure buildup. This pattern of burning by external surfaces is known as Piobert's Law.

Pressure vs distance traveled

This graph shows different pressure curves for powders with different burn rates. The leftmost graph is the same as the large graph above. The middle graph shows a powder with a 25% faster burn rate, and the rightmost graph shows a powder with a 20% slower burn rate.

Using powder that is too fast creates a destructive pressure spike that usually has a very short duration. Using powder that is too slow produces poor energy and leaves a lot of unburned powder.

Peak vs area

Energy is defined as a force exerted over a distance; for example, the work required to lift a one-pound weight, one foot against the pull of gravity defines a foot-pound of energy (One joule is equal to the energy used to move a body over a distance of one meter using one newton of force). If we were to modify the graph to reflect force (the pressure exerted on the bullet multiplied by its area) as a function of distance, the area under that curve would be the total energy imparted to the bullet. From this, it can be seen that the way to increase the energy of the bullet is to increase the area under that curve, either by raising the average pressure, or increasing the distance, the bullet travels under pressure (in other words, lengthen the barrel).

Propellant burnout

Another issue to consider, when choosing a powder burn rate, is the time the powder takes to completely burn vs. the time the bullet spends in the barrel. Since the burn rate of nitrocellulose-based powders increases with increasing pressure, this can be a very difficult interaction to guess, and requires careful testing with gradual changes. Looking carefully at the left graph, there is a change in the curve, at about 0.8 ms. This is the point at which the powder is completely burned, and no new gas is created. With a faster powder, burnout occurs earlier, and with the slower powder, it occurs later. Propellant that is unburned when the bullet reaches the muzzle is wasted — it adds no energy to the bullet, but it does add to the recoil and muzzle blast. For maximum power, the powder should burn until the bullet is just short of the muzzle.

Since smokeless powders burn, not detonate, the reaction can only take place on the surface of the powder. Smokeless powders come in a variety of shapes, which serve to determine how fast they burn, and also how the burn rate changes as the powder burns. The simplest shape is a ball powder, which is in the form of round or slightly flattened spheres. Ball powder has a comparatively small surface-area-to-volume ratio, so it burns comparatively slowly, and as it burns, its surface area decreases. This means as the powder burns, the burn rate slows down.

To some degree, this can be offset by the use of a retardant coating on the surface of the powder, which slows the initial burn rate and flattens out the rate of change. Ball powders are generally formulated as slow pistol powders, or fast rifle powders.

Flake powders are in the form of flat, round flakes which have a relatively high surface-area-to-volume ratio. Flake powders have a nearly constant rate of burn, and are usually formulated as fast pistol or shotgun powders. The last common shape is an extruded powder, which is in the form of a cylinder, sometimes hollow. Extruded powders generally have a lower ratio of nitroglycerin to nitrocellulose, and are often progressive burning — that is, they burn at a faster rate as they burn. Extruded powders are generally medium to slow rifle powders.

Muzzle pressure concerns

From the pressure graphs, it can be seen that the residual pressure in the barrel as the bullet exits is quite high, in this case over 16 kpsi / 110 MPa / 1100 bar. While lengthening the barrel or reducing the amount of propellant gas will reduce this pressure, that often is not possible due to issues of firearm size and minimum required energy. Short-range target guns usually are chambered for .22 Long Rifle or .22 Short, which have very tiny powder capacities and little residual pressure. When higher energies are required for long-range shooting, hunting or anti-personnel use, high muzzle pressures are a necessary evil. With these high muzzle pressures come increased flash and noise from the muzzle blast, and, due to the large powder charges used, higher recoil. Recoil includes the reaction caused not just by the bullet, but also by the powder mass and speed (with the residual gases acting as a rocket exhaust).

General concerns

Bore diameter and energy transfer

A firearm, in many ways, is like a piston engine on the power stroke. There is a certain amount of high-pressure gas available, and energy is extracted from it by making the gas move a piston — in this case, the projectile is the piston. The swept volume of the piston determines how much energy can be extracted from the given gas. The more volume that is swept by the piston, the lower is the exhaust pressure (in this case, the muzzle pressure). Any remaining pressure at the muzzle or at the end of the engine's power stroke represents lost energy.

To extract the maximum amount of energy, then, the swept volume is maximized. This can be done in one of two ways — increasing the length of the barrel or increasing the diameter of the projectile. Increasing the barrel length will increase the swept volume linearly, while increasing the diameter will increase the swept volume as the square of the diameter. Since barrel length is limited by practical concerns to about arm's length for a rifle and much shorter for a handgun, increasing bore diameter is the normal way to increase the efficiency of a cartridge. The limit to bore diameter is generally the sectional density of the projectile (see external ballistics). Larger-diameter bullets of the same weight have much more drag, and so they lose energy more quickly after exiting the barrel. In general, most handguns use bullets between .355 (9 mm) and .45 (11.5 mm) caliber, while most rifles generally range from .223 (5.56 mm) to .32 (8 mm) caliber. There are many exceptions, of course, but bullets in the given ranges provide the best general-purpose performance. Handguns use the larger-diameter bullets for greater efficiency in short barrels, and tolerate the long-range velocity loss since handguns are seldom used for long-range shooting. Handguns designed for long-range shooting are generally closer to shortened rifles than to other handguns.

Ratio of propellant to projectile mass

Another issue, when choosing or developing a cartridge, is the issue of recoil. The recoil is not just the reaction from the projectile being launched, but also from the powder gas, which will exit the barrel with a velocity even higher than that of the bullet. For handgun cartridges, with large bullets and small powder charges (a 9x19 mm, for example, might use 5 grains (320 mg) of powder, and a 115 grain (7.5 g) bullet), this is not a significant force; for a rifle cartridge (a .22-250 Remington, using 40 grains (2.6 g) of powder and a 40 grain (2.6 g) bullet), the powder charge can make for the majority of the recoil force. There is a solution to the recoil issue, though it is not without cost. A muzzle brake or recoil compensator is a device which redirects the powder gas at the muzzle, usually up and back. This acts like a rocket, pushing the muzzle down and forward. The forward push helps negate the feel of the projectile recoil by pulling the firearm forwards. The downward push, on the other hand, helps counteract the rotation imparted by the fact that most firearms have the barrel mounted above the center of gravity. Overt combat guns, large-bore high-powered rifles, long-range handguns chambered for rifle ammunition, and action-shooting handguns designed for accurate rapid fire, all benefit from muzzle brakes. The high-powered firearms use the muzzle brake mainly for recoil reduction, which reduces the battering of the shooter by the severe recoil. The action-shooting handguns redirect all the energy up to counteract the rotation of the recoil, and make following shots faster by leaving the gun on target. The disadvantage of the muzzle brake is a longer, heavier barrel, and a large increase in sound levels and flash behind the muzzle of the rifle. Shooting firearms without muzzle brakes and without hearing protection can eventually damage the operator's hearing; however, shooting rifles with muzzle brakes - with or without hearing protection - causes permanent ear damage. (See muzzle brake for more on the disadvantages of muzzle brakes.)

Powder-to-projectile-weight ratio also touches on the subject of efficiency. In the case of the .22-250 Remington, more energy goes into propelling the powder gas than goes into propelling the bullet. The .22-250 pays for this by requiring a large case, with lots of powder, all for a fairly small gain in velocity and energy over other .22 caliber cartridges.

Accuracy and bore characteristics

Nearly all small bore firearms, with the exception of shotguns, have rifled barrels. The rifling imparts a spin on the bullet, which keeps it from tumbling in flight. The rifling is usually in the form of sharp edged grooves cut as helices along the axis of the bore, anywhere from 2 to 16 in number. The areas between the grooves are known as lands.

Another system, polygonal rifling, gives the bore a polygonal cross section. Polygonal rifling is not very common, used by only a few European manufacturers as well as the American gun manufacturer Kahr Arms. The companies that use polygonal rifling claim greater accuracy, lower friction, and less lead and/or copper buildup in the barrel. Traditional land and groove rifling is used in most competition firearms, however, so the advantages of polygonal rifling are unproven.

There are three common ways of rifling a barrel, and one emerging technology:

• The most basic is to use a single point cutter, drawn down the bore by a machine that carefully controls the rotation of the cutting head relative to the barrel. This is the slowest process, but as it requires the simplest equipment, it is often used by custom gunsmiths, and can result in superbly accurate barrels.
• The next method is button rifling. This method uses a die with a negative image of the rifling cut on it. This die is drawn down the barrel while carefully rotated, and it swages the inside of the barrel. This "cuts" all the grooves at once (it does not really cut metal), and so is faster than cut rifling. Detractors claim that the process leaves considerable residual stress in the barrel, but world records have been set with button-rifled barrels, so again there is no clear advantage.
• The last common method used is hammer forging. In this process, a slightly oversized, bored barrel is placed around a mandrel that contains a negative image of the entire length of the rifled barrel. The barrel and mandrel are rotated and hammered by power hammers, which forms the inside of the barrel all at once. This is the fastest (and in the long run, cheapest) method of making a barrel, but the equipment is prohibitively expensive for all but the largest gun makers. Hammer-forged barrels are strictly mass-produced, so they are generally not capable of top accuracy as produced, but with some careful hand work, they can be made to shoot far better than most shooters are capable of.
• A new technique being applied to barrel manufacture is electrical machining, in the form of Electrical discharge machining (EDM) or Electro chemical machining (ECM). These processes use electricity to erode away material, a process produces a highly consistent diameter and very smooth finish, with less stress than other rifling methods. EDM is very costly and primarily used in large bore, long barrel cannon, where traditional methods are very difficult, while ECM is used by some smaller barrel makers.

The purpose of the barrel is to provide a consistent seal, allowing the bullet to accelerate to a consistent velocity. It must also impart the right spin, and release the bullet consistently, perfectly concentric to the bore. The residual pressure in the bore must be released symmetrically, so that no side of the bullet receives any more or less push than the rest. The muzzle of the barrel is the most critical part, since that is the part that controls the release of the bullet. Some rimfires and airguns actually have a slight constriction, called a choke, in the barrel at the muzzle. This guarantees that the bullet is held securely just before release.

To keep a good seal, the bore must be a very precise, constant diameter, or have a slight decrease in diameter from breech to muzzle. Any increase in bore diameter will allow the bullet to shift. This can cause gas to leak past the bullet, affecting the velocity, or cause the bullet to tip, so that it is no longer perfectly coaxial with the bore. High quality barrels are lapped to remove any constrictions in the bore which will cause a change in diameter.

A lapping process known as "fire lapping" uses a lead "slug" that is slightly larger than the bore and covered in fine abrasive compound to cut out the constrictions. The slug is passed from breech to muzzle, so that as it encounters constrictions, it cuts them away, and does no cutting on areas that are larger than the constriction. Many passes are made, and as the bore becomes more uniform, finer grades of abrasive compound are used. The final result is a barrel that is mirror-smooth, and with a consistent or slightly tapering bore. The hand-lapping technique uses a wooden or soft metal rod to pull or push the slug through the bore, while the newer fire-lapping technique uses specially loaded, low-power cartridges to push abrasive-covered soft-lead bullets down the barrel.

Another issue that has an effect on the barrel's hold on the bullet is the rifling. When the bullet is fired, it is forced into the rifling, which cuts or "engraves" the surface of the bullet. If the rifling is a constant twist, then the rifling rides in the grooves engraved in the bullet, and everything is secure and sealed. If the rifling has a decreasing twist, then the changing angle of the rifling in the engraved grooves of the bullet causes the rifling to become narrower than the grooves. This allows gas to blow by, and loosens the hold of the bullet on the barrel. An increasing twist, however, will make the rifling become wider than the grooves in the bullet, maintaining the seal. When a rifled-barrel blank is selected for a gun, careful measurement of the inevitable variations in manufacture can determine if the rifling twist varies, and put the higher-twist end at the muzzle.

The muzzle of the barrel is the last thing to touch the bullet before it goes into ballistic flight, and as such has the greatest potential to disrupt the bullet's flight. The muzzle must allow the gas to escape the barrel symmetrically; any asymmetry will cause an uneven pressure on the base of the bullet, which will disrupt its flight. The muzzle end of the barrel is called the "crown", and it is usually either beveled or recessed to protect it from bumps or scratches that might affect accuracy. A sign of a good crown will be a symmetric, star-shaped pattern on the muzzle end of the barrel, formed by soot deposited, as the powder gases escape the barrel. If the star is uneven, then it is a sign of an uneven crown, and an inaccurate barrel.

Before the barrel can release the bullet in a consistent manner, it must grip the bullet in a consistent manner. The part of the barrel between where the bullet exits the cartridge, and engages the rifling, is called the "throat", and the length of the throat is the freebore. In some firearms, the freebore is all but nonexistent — the act of chambering the cartridge forces the bullet into the rifling. This is common in low-powered rimfire target rifles. The placement of the bullet in the rifling ensures that the transition between cartridge and rifling is quick and stable. The downside is that the cartridge is firmly held in place, and attempting to extract the unfired round can be difficult, to the point of even pulling the bullet from the cartridge in extreme cases.

With high-powered cartridges, there is an additional disadvantage to a short freebore. A significant amount of force is required to engrave the bullet, and this additional resistance can raise the pressure in the chamber by quite a bit. To mitigate this effect, higher-powered rifles tend to have more freebore, so that the bullet is allowed to gain some momentum, and the chamber pressure is allowed to drop slightly, before the bullet engages the rifling. The downside is that the bullet hits the rifling when already moving, and any slight misalignment can cause the bullet to tip as it engages the rifling. This will, in turn, mean that the bullet does not exit the barrel coaxially. The amount of freebore is a function of both the barrel and the cartridge. The manufacturer or gunsmith who cuts the chamber will determine the amount of space between the cartridge case mouth and the rifling. Setting the bullet further forward or back in the cartridge can decrease or increase the amount of freebore, but only within a small range. Careful testing by the ammunition loader can optimize the amount of freebore to maximize accuracy, while keeping the peak pressure within limits.

Revolver-specific issues

The defining characteristic of a revolver is the revolving cylinder, separate from the barrel, that contains the chambers. Revolvers typically have 5 to 10 chambers, and the first issue is ensuring consistency among the chambers, because if they aren't consistent then the point of impact will vary from chamber to chamber. The chambers must also align consistently with the barrel, so the bullet enters the barrel the same way from each chamber.[41]

The throat in a revolver is part of the cylinder, and like any other chamber, the throat should be sized so that it is concentric to the chamber and very slightly over the bullet diameter. At the end of the throat, however, things change. First, the throat in a revolver is at least as long as the maximum overall length of the cartridge, otherwise the cylinder cannot revolve. The next step is the cylinder gap, the space between the cylinder and barrel. This must be wide enough to allow free rotation of the cylinder even when it becomes fouled with powder residue, but not so large that excessive gas is released. The next step is the forcing cone. The forcing cone is where the bullet is guided from the cylinder into the bore of the barrel. It should be concentric with the bore, and deep enough to force the bullet into the bore without significant deformation. Unlike rifles, where the threaded portion of the barrel is in the chamber, revolver barrels threads surround the breech end of the bore, and it is possible that the bore will be compressed when the barrel is screwed into the frame. Cutting a longer forcing cone can relieve this "choke" point, as can lapping of the barrel after it is fitted to the frame.[41][42][43]

A consistent lockup is important to keep all these parts in line, and revolvers are prone to abuse that can damage these parts, adversely affecting the accuracy and even safety of the revolver. This lockup consists of two parts, the crane to frame lockup, and the cylinder bolt to cylinder lockup. Many swing-out cylinder revolvers only support the cylinder securely at the rear, and flipping the cylinder open and closed can bend the crane and prevent the cylinder from lining up parallel to the bore. The cylinder bolt, which engages the bottom of the cylinder through a slot in the frame, should provide a relatively tight lockup, and not drag the cylinder during rotation or pop loose when the hammer is cocked at a reasonable speed. Fanning a revolver can batter the cylinder bolt and prevent a solid lockup.[43]

See also

• External ballistics
• Percussion cap, for an early history of priming powder and percussion caps
• Terminal ballistics
• Transitional ballistics
• Physics of firearms

References

• Army (February 1965). "Interior Ballistics of Guns". United States Army Materiel Command. AMCP 706-150. http://www.dtic.mil/dtic/tr/fulltext/u2/462060.pdf. 
• Baer, Paul G.; Frankle (December 1962). "The Simulation of Interior Ballistic Performance of Guns by Digital Computer Program". Aberdeen Proving Ground, MD: Ballistic Research Laboratories. BRL Report No. 1183. http://www.dtic.mil/cgi-bin/GetTRDoc?AD=AD0299980. 
• Hatcher, Julian S. (1962). "Hatcher's Notebook". Harrisburg, PA: Stackpole Company. ISBN 8117-0614-1. 
• NATO (May 22, 2000). "Thermodynamic Interior Ballistic Model with Global Parameters". North Atlantic Treaty Organization. STANAG 7367. http://www.tradoc.mil.al/Standartizimi/Downloads/4367Eed02.pdf. 

External links

• Gonzalez Jr., Joe Robert (1990). "Internal Ballistics Optimization". AD-A225 791. http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA225791&Location=U2&doc=GetTRDoc.pdf. 
• Horst, Albert W. (November 2005). "A Brief Journey Through the History of Gun Propulsion". Aberdeen Proving Ground, MD: United States Army Research Laboratory. ARL-TR-3671. 
• Mader, Charles L. (2008). "Numerical Modeling of Explosives and Propellants". CRC Press. ISBN 978-1-4200-5238-1. 
• A (Very) Short Course in Internal Ballistics, Fr. Frog
• Mungan, Carl E. (March 9, 2009). "Internal ballistics of a pneumatic potato cannon". pp. 453–457. Digital object identifier:10.1088/0143-0807/30/3/003. Archived from the original on March 16, 2013. http://web.archive.org/web/20130316071639/http://www.usna.edu/Users/physics/mungan/Publications/EJP5.pdf. 
• QuickLOAD Ballistics Software