Internal ballistics


Internal ballistics, a subfield of ballistics, is the study of the propulsion of a projectile.
In guns, internal ballistics covers the time from the propellant's ignition until the projectile exits the gun barrel. The study of internal ballistics is important to designers and users of firearms of all types, from small-bore rifles and pistols, to artillery.
For rocket-propelled projectiles, internal ballistics covers the period during which a rocket motor is providing thrust.

General concepts

Interior ballistics can be considered in three time periods:
  • 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.
The burning firearm propellant produces energy in the form of hot gases that raise the chamber pressure which applies a force on the base of the projectile, causing it to accelerate. The chamber pressure depends on 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 on the chemical make up and shape of the propellant grains. The temperature depends on the energy released and the heat loss to the sides of the barrel and chamber.
As the projectile travels down the barrel, the volume the gas occupies behind the projectile increases. 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, which adds resistance to its forward motion.
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 some distance down the barrel. Consequently, the muzzle end of the barrel does not need to be as strong as the chamber end.
Mathematical models have been developed for these processes. The four general concepts which are calculated in interior ballistics are:
  1. Energy - released by the propellant
  2. Motion - the relation between the projectile acceleration and the pressure on its base.
  3. Burning rate - a function of the propellant surface area and an empirically derived burning rate coefficient which is unique to the propellant.
  4. Form function - a burning rate modifying coefficient that includes the shape of the propellant.

    History

Internal ballistics was not scientifically based prior to the mid-1800s. Barrels and actions were built strong enough to survive a known overload. Muzzle velocity was surmised from the distance the projectile traveled.
In the 1800s test barrels began to be instrumented. Holes were drilled in the barrel and fitted with standardized steel pistons which exerted pressure which compressed standardized copper cylinders when the firearm discharged. The reduction in the copper cylinder length is used as an indication of peak pressure, known as "Copper Units of Pressure", or "CUP" for high pressure firearms. Similar standards were applied to firearms with lower peak pressures, typically common handguns, with test cylinder pellets made of more easily deformed lead cylinders, hence "Lead Units of Pressure", or "LUP". The measurement only indicated the maximum pressure that was reached at that point in the barrel. Piezoelectric strain gauges were introduced in the 1960's, allowing instantaneous pressures to be measured without destructive pressure ports. Instrumented projectiles were developed by the Army Research Laboratory that measures the pressure at the base of the projectile and acceleration.

Priming methods

Methods of igniting the propellant evolved over time. A small hole was drilled into the breech, into which a propellant was then poured, and an external flame or spark applied. Percussion caps and self-contained cartridges have primers that detonate after mechanical deformation, igniting the propellant.

Propellants

Black powder

is a finely ground, pressed and granulated mechanical pyrotechnic 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 and predictably even without confinement, making it also suitable for use as a low explosive. 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)

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. Gelatinised nitrocellulose is a plastic, which can be formed into cylinders, tubes, balls, or flakes known as single-base propellants. 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.

Double-base propellants

can be added to nitrocellulose to form "double-base propellants". Nitrocellulose desensitizes nitroglycerin to prevent detonation in propellant-sized grains,, and the nitroglycerin gelatinises the nitrocellulose and increases the energy. Double-base powders burn faster than single-base powders of the same shape, though not as cleanly, and burn rate increases with nitroglycerin content.
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.

Solid propellants (caseless ammunition)

"Caseless ammunition" incorporates propellant 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, the relative burn rate must be much higher. To reach this rate of burning, caseless propellants often use moderated explosives, such as RDX.
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 of the brass or steel case.
While there is at least one experimental military rifle, and one commercial rifle, that use caseless rounds, they have met with 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 durable. 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.
To minimize the risk of cartridge cook-off, machineguns can be designed to 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 machine guns; the mass of the bolt moving forward causes the gun to lurch in reaction, which significantly reduces the accuracy of the gun, which is generally not an issue for machinegun fire.

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 ignite and burn more consistently than lower-density loads. In cartridges surviving from the black-powder era, 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.
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 with barrels of 10 to 15 inches.