Internal ballistics
Internal ballistics is the science of the process of firing a firearm from the process of igniting the propellant to the exit of the projectile from the barrel. See also Transitional ballistics, External ballistics, and Terminal ballistics. The study of internal ballistics is important to designers and users of firearms of all types, from smallbore Olympic rifles and pistols to designers of high-tech artillery.
Ignition
Priming methods
The first step to firing a firearm of any sort is igniting the propellant. The earliest firearms were cannons, which were a simple closed tube. There was a small hole, the touchhole, drilled in the closed end of the tube, leading down to the main powder charge. This hole was filled with finely ground powder, which was then ignited with a hot ember or torch. With the advent of hand-held firearms, this became an undesirable way of firing the gun. Holding a burning stick while trying to carefully pour a charge of black powder down a barrel is a good way to get maimed or killed. Also, trying to hold the gun with one hand, aim at the target, and look for the touchhole so you could put the burning stick against it with the other hand wasn't conducive to any degree of accuracy.
External priming--match, wheel, flint, cap, modern muzzleloaders
The first attempt to make the process of firing a small arm easier was the matchlock. The matchlock incorporated a "lock" (so called because of it's resemblence to door locks of the day) that was actuated by a trigger. The lock was a simple lever which pivoted when pulled, and lowered the match down to the touchole. The match was a slow burning fuse made of plant fibers that were soaked in a solution of nitrates, charcoal and sulphur and dried. This was ignited before the gun might be needed, and it would slowly burn, keeping a hot ember at the burning end. After the gun was loaded and the touchhole primed with powder, the burning tip of the match was positioned so that the lock would bring it into contact with the touchhole. To fire the gun, it was aimed, and the trigger pulled. This brought the match down to the touchhole, igniting the powder. The slow burning match could be kept going, with careful attention, for long periods of time, and the use of the lock mechanism made accurate fire (within the limits of the gun) possible.
The next revolution in ignition technology was the wheel-lock. It used a spring loaded, serrated steel wheel which rubbed against a piece of iron pyrite. There was a key which was used to wind the wheel and put the spring under tension. Once tensioned, the wheel was held in place by a trigger. When the trigger was pulled, the serrated edge of the steel rubbed against the pyrite, generating sparks. These sparks were directed into a pan, called the flashpan, filled with loose powder which lead into the touchhole. The flashpan was usually covered by a spring loaded cover that would slide out of the way when the trigger was pulled, exposing the powder to the sparks. The wheellock was a major innovation--since it did not rely on burning material as a source of heat, it could be loaded and kept loaded for extended periods of time. The covered flashpan also gave the gun some ability to withstand bad weather. Wind, rain, and wet weather would render a matchlock useless, but a wheellock that was loaded and waterproofed with a bit of grease around the flashpan could be fired under most conditions.
The wheellock enjoyed only a breif period of popularity before being superceded by a simpler, more robust design. The flintlock, like the wheellock, used a flashpan and a spark to ignite the powder. As the name implies, the flintlock used flint rather than iron pyrite. The flint was held in a spring loaded arm called the "cock", after it's resemblence to a rooster. The cock rotated through about a 90 degree arc, and was held in the tensioned or "cocked" position by a trigger. Usually, flintlocks would lock the cock in two positions. The "half cock" position held the cock halfway back, and used a deep notch, so that pulling the trigger would not release the cock. This was a safety position, used when loading and when storing or carrying a loaded flintlock. The "full cock" position held the cock all the way back, and was the position from which the gun was fired. The frizzen was the other half of the flintlock ignition system. It served as both a flashpan cover and a steel striking surface for the flint. The frizzen was hinged, and spring loaded so that it would lock in the open or closed position. When closed, the striking surface was positioned so that the flint would strike at the proper angle to generate a spark. The striking flint would also open the frizzen, exposing the flashpan to the spark. The flintlock mechanism was simpler and stronger than the wheellock, and the flint and steel provided a good, reliable sorce of ignition. The flintlock remained in military service for over 200 years, and flintlocks are still made today for historical reenactments and hunters who enjoy the additional challenge the flintlock provides.
The next major leap in ignition technology was the invention of the chemical primer, or "cap", and the mechanism which used it, called the "caplock". The caplock appeared just before the American Civil War, and was quickly adopted by both sides as it was even simpler and more reliable than the flintlock. The main reason the caplock was so quickly adopted was its similarity to the flintlock. The flashpan and frizzen were removed, and replaced by a "nipple" which the cap fit onto. The cock was replaced by a "hammer", which also had half cock and full cock positions for the same reasons. When fired, the hammer would hit the cap, crushing it onto the nipple. The cap was a thin metal cup that had in it a small quantity of pressure sensitive explosive. When crushed, the explosive would detonate, sending a stream of hot gas down a hole in the nipple, and into the touchhole of the gun. In the process of firing, the cap generally split open, and would fall off when the hammer was moved to half cock position for loading. The caplock system worked well, and is still the preferred method of ignition for hunters and recreational shooters who use muzzleloading arms.
Internal priming--berdan, boxer, rimfire
Chemical primers, advanced metallurgy and manufacturing techniques all came together in the 1800s to create an entirely new class of firearm--the cartridge arm. Flintlock and caplock shooters had long carried their ammunition in paper cartrdiges, which served to hold a measured charge of powder and a bullet in one convenient package (the paper also served to seal the bullet in the bore). Still, the source of ignition was separate. With the advent of chemical primers, it wasn't long before all sorts of systems were invented, with a multitude of different ways of combining bullet, powder, and primer into one package which could quickly be loaded from the breach of the firearm. The three systems which have survived the test of time are the rimfire, the berdan primer, and the boxer primer.
Rimfire cartridges use a thin brass case with a bulge, or rim, around the back end. This rim is filled during manufacture with an impact sensitive explosive. When the rim is crushed by the hammer or firing pin, the explosive detonates and ignites the powder charge. Rimfire cartridges are single use--after firing, they cannot practially be reloaded. Also, since the rim must be thin enough to be easily crushed, the pressures generated in the case are limited by the strength of this thin rim. Rimfire cartridges used to be available in calibers up to .44, but all but the small .22 caliber rounds died out. The .22 Long Rifle (which is also fired in pistols) is the most popular recreational caliber, because it is inexpensive, quiet, and has very low recoil. The most inexpensive brands can be bought for less than US$0.02 per round in boxes of 500, and even Olypmic class ammunition is around US$0.20 per round.
The remaining types of priming, Berdan and Boxer are both considered "centerfire" to differentiate them from the rimfire rounds. Centerfire priming methods are interchangeable--the same firearm can fire both Berdan and Boxer primed rounds. Berdan primers are named after their American inventor, Hiram Berdan. These are very similar to the caps used in the caplock system--they are small metal cups with pressure sensitive explosive in them. The Berdan primers are pressed into the primer "pocket" of a Berdan type cartridge case, where the fit flush with the base of the case. Inside the primer pocket is a small bump, the "anvil" that rests against the center of the cup, and two small holes that allow flash from the primer to reach the interior of the case. Berdan cases are reusable, although the process is rather involved. The used primer must be removed, usually be hydraulic pressure or a lever that pulls the primer out the bottom. A new primer is carefully seated against the anvil, and then gunpowder and a bullet are added. Berdan priming is used by nearly all militaries and most civilian manufacturers, with the ironic exception of the USA.
Boxer primers, named after their inventor, British military officer Edward M. Boxer, are similar to Berdan primers with one major change--the anvil. In a Boxer primer, the anvil is a separate piece that sits in the primer cup. Because of this, the primer pocket has the flash hole centered. This makes little or no difference in the performance of the round, but it makes fired primers vastly easier to remove. A think metal rod is pushed through the mouth of the case, and it pushes the primer out. An new primer, anvil included, is then pressed into the case. Since the primer and anvil are sold as one part, the anvil depth is correct for the primer that is being inserted, so that the primer does not ignite during loading (although priming is done as the first step, before the powder is added, just in case). This is the main reason that Boxer priming is still popular in the USA, as there are a large number of shooters who reload their ammunition. Boxer primed ammunition is slightly more complex to manufacture, since the primer is in 2 parts, but the slight increase in initial cost is more than made up for by the decreased cost of firing reloaded rounds.
Electrical
Lock time considerations
Nearly all firearms today still use essentially the same technology that was developed for the caplock--a spring loaded hammer or striker is used to crush the primer, which causes a small detonation that ignites the powder charge. Since this system is mechanical, there is a small but significant lag, called the "lock time", involved between the pull of the trigger and the ignition of the cartridge. This is usually only a few hudredths of a second, but when you consider that the bullet leaves the barrel in a few thousandths of a second after ignition, the lock time is the major source of delay. When the shooter is trying to time a shot to fire between heartbeats, those hundredths of a second can mean the difference between a gold medal and no medal at all. Another place where lock time is critical is in the multibarrel Gatling guns used by militaries, which have rates of fire as high as 100 rounds per second. Many high speed Gatling guns, and a growing number of civilian arms are switching to electrical primers. Electrical primers in civilian arms use a battery pack and a capacitor to build up an electrical charge that is then sent through a transformer to increase the voltage to 150 to 200 volts. This charge is then sent through the primer where it ignites the explosive and thus sets off the propellant charge. Larger bore military weapons use thousands of volts to create a spark which detonates the primer.
Propellant
Black powder--constant burn rate, not very efficient, very dirty
Black powder was the first chemical propellant and the first explosive recorded by history. Black powder is a mix of sulphur, charcoal, and potassium or sodium nitrate. It acts more like an explosive than a propellant, since its burn rate is not effected by pressure, but it is a very poor explosive because it has a very slow decomposition rate and therefore a very low brisance. This same property that makes it a poor explosive makes it useful as a propellant--the lack of brisance keeps the black powder from shattering the barrel, and directs the energy to propelling the bullet. The main disadvantages of black powder are a relatively low energy density (compared to modern smokeless powders) and the exremely large quantities of soot left behind. During the combustion process, less than half of black powder is converted to gas, the rest ends up a dense white smoke, and a thick layer of soot inside the barrel. In addition to being a nuisance, the residue in the barrel is hydrophilic and an anhydrous caustic substance. When moisture from the air is absorbed, the potassium or sodium oxide turn into hydroxides, which will eat away the barrel. Black powder arms must be well cleaned inside and out after firing to remove the residue. Black powder differs from the smokeless propellants in that its burn rate is not significantly affected by pressure. The size of the granules of powder and the confinement determine the burn rate of black powder. Finer grains result in a closer mix of the ingredients, which results in a faster burn. Tight confinement in the barrel causes a column of black powder to burn from end to end, which is the desired method. Not seating the bullet firmly against the powder column can result in the loose powder burning all at once, which can create a dangerous overpressure condition. It is difficult to overload a black powder arm, as any excess powder will simply be blown unburned from the end of the barrel. In fact, that is a traditional method for determining the optimal loading for a black powder musket or rifle--fire it over a patch of virgin snow with gradually increasing powder charges, and look for the appearance of unburned powder grains in the snow to indicate too much powder. The lack of pressure sensitivity means that the mass of the bullet makes little or no difference to the amount of powder used. A full charge of black powder seated by just a small wad of paper, with no bullet, will still burn just as quickly as if it had a full weight bullet in front of it. This makes black powder very well suited for blank rounds, signal flare rounds, and rescue line launching rounds.
Nitrocellulose--burn rate proportional to pressure, clean, high density
Nitrocellulose is formed by the action of nitric acid on cellulose fibers. Nitrocellulose is a highly combustible plastic that deflagrates rapidly when heat is applied. It burns very cleanly, converting almost entirely to gaseous components at high temperatures. 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. Since nitrocellulose is a plastic, it can be formed into many shapes of gunpowder, such as cylinders, tubes, balls, and flakes. The size and shape of the powder grains can increase or decrease the relative surface area and change the burn rate significantly. Additives and coatings can be added to the powder to further modify the burn rate. Very fast powders are used for low velocity pistols and shotguns, medium rate powders are used for magnum pistols and light rifle rounds, and slow powders are used for large bore heavy rifle rounds.
Double base propellants--nitrocellulose plus nitroglycerine, high energy fast burn
To further increase the energy of smokeless powder, nitroglycerin can be added in amounts up to 50%. These powders are called double base powders, and they have the same basic physical properties as single base powders. The nitrocellulose serves to desensitize the high unstable nitroglycerin, and the nitroglycerin greatly increases the energy density of the resulting powder. Double base powders burn faster than single base powders of the same shape, and in general the higher the nitroglycerin content of a powder, the faster the burn rate.
Solid propellants--moderated explosives
A recent topic of research has been in the realm of caseless cartridges. 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 glued to the front. Since the single propellant grain is so large (most smokeless powders have grain sizes around 1 mm, 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. While there is at least one military rifle (the H&K G-11) and one commercial rifle (made by Voere) that use caseless rounds, they are not having much sucess. The caseless ammunition is by necessity not reloadable (a major disadvantage in civilian markets where reloading is common) 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 problem peculiar to autoloading arms firing caseless rounds is the problem of rounds "cooking off". This 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 designed for high volumes of fire are designed to fire from an open bolt, which means that the round is not chambered until the trigger is pulled, and so there is no chance for the round to cook off before the operator is ready. Open bolt designs are generally undesirable for anything but belt fed machineguns and pistol sized submachineguns. The reason is that 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 both carry heat away from the chamber after firing and to cool the chamber when chambered, reducing the risk of cookoff.
Load density and consistency, note low density detonation
Load density is the percentage of 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 that survived from the black powder cartridge era (examples being .45 Colt, .45-70 Government) the case is much larger than needed to hold the maximum charge of high density smokeless powder. This allows the powder to shift in the case, piling up near the front or near the back of the case. This can cause 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 slower. This change has less impact with fast powders, so 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 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 generate accuracy comparable to a good hunting rifle, and energy sufficient to take medium game at ranges out to 100 yards (100 meters) 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 high density 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. The mechanism of this phenomenon are not well known, and generally it is not enountered except when loading very low velocity subsonic rounds for rifles. These rounds generally have velocities under 500 ft/s (195 m/s) and are used for indoor shooting or 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 .30-30 Winchester was one of the first rounds to be designed to use smokeless powder, and it has a distinct shoulder that closely resembles modern cartridges, even though it dates back to the 1890s. Modern cases have shorter necks, sharper shoulder angles, and a rimless design which give better efficiency and feeding, but the .30-30 cartridge and the Winchester model 1894 rifle still account for more game in North America than any other rifle and cartridge combination.
Aspect ratio and consistency, functional considerations
When selecting a rifle cartridge for maximum accuracy, a short, fat cartridge will generally yield a higher efficiency and consistency than a long, thin cartridge (part of the reason for a bottlenecked design). The ideal shape would be something near spherical, but this would be impractical to build. Target and varmit hunting rounds, which require the greatest accuracy, tend to be short and fat, with sharp shoulders on the case. These cartridges do have disadvantages, however. The fat rounds take up a lot of space in a magazine, and the sharp shoulders do not feed easily out of a magazine and into the chamber. For this reason, rounds that do not require the utmost accuracy, but do need to be chambered in repeating arms (such as military rifles) tend to have longer cases with shallower shoulder angles.
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 generates a large quantity of friction. 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 1000 ft/s (390 m/s) lead begins to melt and deposit in the bore. This lead buildup 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 1500 ft/s (585 m/s) can use wax lubricants on the bullet to reduce lead buildup. At velocities over 1500 ft/s (585 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 buildup in the bore. Copper buildup does begin to occurr in rounds that exceed 2500 ft/s (975 m/s), and a common solution is to impregnate the surface of the bullet with molybdenum disulfide lubricant. This reduces copper buildup 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 (over 1000 N) 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. This makes loading or reloading smokeless cartridges require high precision equipment and carefully measured tables of load data for given cartridges, powders, and bullet weights.
Pressure curve
This is a graph of a simulation of the 5.56mm NATO round being fired from a 20 inch 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.
Peak vs. area
Energy is defined as a force exerted over a distance; for example, the force required to lift a one pound weight one foot against the pull of gravity defines a foot-pound of energy (lifting one newton one meter gives one newton-meter of energy). If we were to modify the graph to reflect pressure as a function of distance, the 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 presser (in other words lengthen the barrel).
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 a faster burning powder does yield a higher velocity, but at the cost of a much higher peak pressure. A slower burning powder gives a wider curve, but the lower pressure peak drops the energy. If the case could handle the increase in volume, a larger quanity of slower powder might give the same pressure peak as the medium rate powder, but with a wider curve to increase the overall energy transferred to the bullet.
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. Propellent 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 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 fairly small surface area to volume ratio, so it burns fairly slowly, and as it burns its surface area to volume ratio decreases. This means as the powder burns, the burn rate slows down. To some degree this can be negated by the use of retardant coatings on the surface of the powder, which slows the inital burn rate further 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 very high surface area to volume ration. 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 nitroglycerine 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 is can be seen that the residual pressure in the barrel as the bullet exits is quite high--in this case, over 16kpsi. While lengthening the barrel or reducing the amount of propellant gas will reduce this pressure, this is often not possible due to issues of firearm size and minimum required energy. Short range target guns are generally chambered in .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 antipersonnel use, high muzzle pressures are a nessesary evil. With this 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 for not just the bullet but also for the powder mass.
General concerns
Bore diameter and energy transfer
Ratio of propellant to projectile mass
Accuracy and bore characteristics
Autoloading firearms
Gas operated firearms
Recoil operated firearms
Blowback firearms
Hooks to transitional ballistics
Recoil and recoil control
Muzzle blast and flash
Large bore concerns
Boosters for primers
Categories: Ballistics