Internal Ballistics covers the mechanical reactions from primer ignition though the bullet leaving the rifling of the gun barrel.

Priming

Modern firearms are primarily primed via centerfire boxer or berdan primers, the obvious exception being the popular small caliber rimfire cartridges like .22 long rifle.

Centerfire

The identifying feature of centerfire ammunition is the primer - a metal cup containing a primary explosive inserted into a recess in the center of the base of the cartridge. The firearm firing pin crushes this explosive between the cup and an anvil to produce hot gas and a shower of sparks to ignite the powder charge. Berdan and Boxer cartridge primers are both considered "centerfire". Various priming mixtures have been used in different sized primers to effect prompt ignition of the powder charge. Particles with relatively high heat capacity are required to promptly ignite smokeless powder deterrent coatings. Cartridges for military use require stable priming formulations so war reserves of small-arms ammunition will dependably function after years of storage.

Propellants

Nitrocellulose (single-base propellants)

Nitroselusoe 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, 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.

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 8mm 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 Mauser and 7 x 57 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 odd, highly tapered 8 mm 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 varmit 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 NATO case replacing the longer .30-06 Springfield is a good example.

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.

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 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. If we were to modify the graph to reflect pressure 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

As the bullet exits the barrel, the residual pressure can be as high as 16,000PSI. 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 (the residual gases acting as a rocket exhaust).