Indoor ballistics

from Wikipedia, the free encyclopedia

The ballistics describes the sequences during the firing of a projectile from a gun in the period from release of the shot to exiting of the projectile from the barrel .

Numerous parameters are involved in the development of the shot, with parameters of thermodynamics , thermochemistry , fluid mechanics and mechanics playing a role. The pressure curve of the burn of the propellant charge , the energy of the propellant charge, the barrel length of the weapon, the caliber , the projectile mass and the structural features of the weapon and, if applicable, the cartridge are taken into account.

The best combination of bullet type, powder type and powder quantity for a specific weapon can generally only be determined in shooting tests because of the numerous determining parameters. The data determined in this way are published in the form of loading boards in which the permissible powder quantities, powder types, dimensions and weights for each type of cartridge are listed.

Shot release

In modern handguns, the shot is triggered when a firing pin hits the primer in the bottom of the cartridge after the trigger is pulled . The impact-sensitive ignition charge in the primer detonates when the energy is supplied; a hot gas jet passes through the ignition channels to the propellant charge and ignites it. The propellant charge should completely ignite as quickly as possible. There are different types of primers that are used depending on the amount of powder or the volume of the powder chamber.

Start of bullet movement

After the propellant has been ignited, its combustion produces large quantities of hot gases in a short time. These gases are under pressure and exert a force on the base of the projectile, which depends on the pressure (in Pascal ) and the cross-sectional area of the projectile (in square meters): (in Newtons ) For example, a .30-06 cartridge with typical load will produce after of ignition within 500 nanoseconds, gases whose normal volume corresponds to 14,000 times the volume of the propellant charge, with temperature and pressure rising to 2700 ° C and 3600 bar, respectively  .

A certain minimum force (pull-out resistance) is required to move the bullet, as the bullet is firmly seated in the case mouth. This withdrawal resistance can be up to 1000 N for fully automatic rifles with belted cartridges, with other cartridges it is usually 300 N to 600 N. The pressure in the cartridge increases until the withdrawal resistance of the bullet is exceeded and the bullet is accelerated. The counterforce of this acceleration is transferred to the cartridge base by the high pressure gases, which causes the recoil effect of the weapon.

Influencing variables of the projectile acceleration

Schematic representation of the pressure wave when a projectile is fired at supersonic speed

After the projectile has been driven out of the case, it moves in the transition cone between the cartridge chamber and the drawn part of the barrel in a so-called free flight without form-fitting guidance through the barrel. It then reaches the drawn part of the barrel and is pressed into the cables that give it the twist . Depending on the design, the bullet can reach the trains before it has completely emerged from the case. When the bullet has passed the muzzle, it is accelerated over a short distance by the powder gases, which are still under high pressure and which flow in, whose sudden pressure equalization to the air pressure creates the muzzle bang.

With a known barrel length (in meters) and known muzzle velocity (in meters per second), the mean projectile acceleration can be calculated: (in meters per square second )

The acceleration time can also be calculated from the muzzle velocity and the barrel length : (in seconds)

The acceleration force that acts on the projectile can be calculated from the projectile mass (in kilograms) and the projectile acceleration: (in Newtons)

Bullet resistance and barrel vibrations

The resistance that the bullet opposes to the acceleration results not only from its ability to persist, but also from the other mechanical resistance caused by its movement. First and foremost, this is the frictional resistance between the bullet and the barrel wall, but other variables such as air resistance inside the barrel or barrel deformations inhibit the bullet's movement.

The barrel is set in vibration by the forces acting during the launch. The extent of these vibrations has an influence on the spread of hits that can be achieved with the barrel . The barrel oscillates in the direction of the barrel core and in the direction perpendicular to the barrel core, and the counter-torque of the twist generates a torsional vibration . Weapons that are designed for the highest possible shooting precision, such as sniper rifles , therefore usually have heavy barrels with significantly reinforced barrel walls.
In guns about a reproducible, systematic bending steps out during firing of the pipe upwards or downwards, which as a departure angle error included in the calculation of the target data. Depending on the design, the bend typically ranges from -20 '( minutes of arc ) to about + 1 ° 10'.

Gas pressure and combustion behavior of the propellant charge

The projectile is primarily accelerated by the gas pressure. It is not accelerated uniformly during the shot development because the pressure developed by the propellant charge is not constant during the shot development. The pressure increases to a maximum value after ignition and decreases again until the bullet passes the muzzle. The permissible upper limit of the pressure is determined by the strength of the barrel and the breech and must not be exceeded.

Although the gas pressure is not constant, the effect of a constant mean gas pressure (in Pascal) can be assumed, which would lead to the same muzzle velocity. Values ​​of around 40% to 60% of the maximum gas pressure can be assumed as practical values ​​for the mean gas pressure. A purely arithmetical derivation of the mean gas pressure from the projectile mass, projectile cross-section and acceleration is not possible, since the actual projectile resistance during launch can only be determined through experiments. If the bullet resistance (in Newton) is known, the mean gas pressure can be calculated: (in Pascal)

The bullet resistance can be calculated with a known mean gas pressure and known muzzle velocity : The bullet resistance reduces the efficiency of the energy conversion of the propellant charge.

In order to adapt the gas pressure and the gas pressure curve to the respective weapon type, the projectile type, the projectile mass and the barrel length, the amount and burn rate of the propellant charge are adapted to the respective purpose. The burning rate of propellant charge powders can be determined via the chemical composition, the surface properties, the total surface area per unit volume and the shape of the powder grains. Common forms are platelets, sticks or tubes with sizes adapted to the respective area of ​​application. The burning rate can also be influenced by coating the powder grains with graphite , for example.

The smoother the individual powder grains, the smaller their surface and the smaller the surface of the powder per unit volume (coarse grain size), the slower the powder burns. Fast burning powders are offensive powders , slower burning powders are progressive powders . Offensive powders are used when there is only a short way to accelerate the projectile (handguns) or when relatively light projectiles are fired from a long weapon.

The pressure generated by a propellant charge also depends on the bullet mass. With the same caliber, a heavy bullet opposes the expansion of the propellant gases with a higher resistance due to its inertia, so that the pressure and temperature of the propellant gases increase, which with modern nitro powders can further increase the burning rate and thus the pressure development. This can lead to undesirably high gas pressure when firing. A light bullet, due to its lower mass inertia, leads to a lower pressure and temperature development and thus to a slower burn. This means that the energy of the propellant charge can be converted less effectively into projectile energy.

Heavy projectiles are therefore preferred to be fired with propellant charges made from progressive powders, conversely, propellant charges made from offensive powders are used for light projectiles. For short barrels, more aggressive powders are used, since if the combustion is too slow, unburned powder may leave the barrel muzzle and be lost as a source of energy.

Pressure progression with different combustion behavior, the colored areas under the curves correspond to the work done (W) and are ideally the same size, the final velocity v is always the same.

The energy content of the propellant charges is hardly dependent on their burning behavior. With the same barrel length and powder charge, a bullet can be brought to the same speed from an offensive and a progressive powder. The offensive powder creates a higher gas pressure, which acts on the projectile for a shorter period of time, so that the work done is ideally the same.

When firing, around a fifth to a third of the energy of the propellant charge is converted into kinetic energy of the projectile. The rest of the energy is lost primarily through heat dissipation and in the form of the residual energy of the propellant gases.

Especially with indirect artillery shooting, the muzzle velocity has a significant influence on the hit location, as it also determines the range of fire in addition to the angle of the attachment. A reproducible hit position can only be achieved with the smallest possible deviation of the muzzle velocities within a series of shots. Since the temperature of the propellant also influences its burning behavior and thus the muzzle velocity, it is included in the calculation of the guide data here. In the case of fortress guns or large mobile guns such as the Dora cannon , the propellant charges were therefore partly stored in air-conditioned rooms or chambers. During the service life of a gun, the volume of the cartridge chamber in the gun barrel increases as a result of the action of the gas pressure, which reduces the gas pressure that can be achieved with a certain charge and thus the muzzle velocity. The influence of this expansion on the range is determined by shooting tests.

Cartridge ammunition is usually loaded by the loader with the most favorable propellant charge for the respective purpose before the shot . The propellant charge is brought into the cartridge in the form of pre-packed bags. The full charge is only fired at firing ranges close to the maximum range in order not to unnecessarily burden the gun.

Gas pressure measurement

The typical maximum gas pressure for handguns is between 550 bar ( shotguns ) and about 3900 bar for magnum hunting cartridges. The gas pressure can be measured using a pressure stamp. A cartridge drilled at the side is loaded into a barrel with a special, drilled cartridge chamber. The side hole is closed by a piston that acts on a copper cylinder. The copper cylinder is plastically deformed by the gas pressure during the shot . The amount of deformation allows conclusions to be drawn about the maximum gas pressure that has occurred.
The gas pressure can also be measured by a piezo sensor, which is used instead of the copper cylinder. The piezo crystal is elastically deformed by the pressure . In this case, an electrical voltage proportional to the pressure profile is generated, from which, in addition to the maximum pressure, the time profile of the pressure can also be derived.

Cross-sectional loading

The projectile acceleration depends on the acceleration force (in Newtons) and the projectile mass (in kilograms): (in meters per square second) The acceleration force in turn depends on the gas pressure and the cross-sectional area of ​​the projectile. At a given gas pressure, which should not exceed certain values ​​for structural reasons, the projectile acceleration and thus the muzzle velocity that can be achieved from a weapon is determined by the cross-sectional area and the projectile mass. Inside ballistic, a light projectile with a large cross-sectional area would thus be advantageous for achieving a high muzzle velocity. The parameter that specifies the ratio of cross-sectional area and projectile mass is the cross-sectional load . A projectile with a low cross-sectional load, which can be easily accelerated by the gas pressure, is, however, also easily decelerated again after being fired by the air resistance , which reduces the effective range of the projectile. For most applications today, full-caliber long bullets are sufficient , which have a relatively high cross-sectional load due to the favorable external ballistic properties and can nevertheless be brought to a practically high muzzle velocity by choosing the appropriate propellant charge and barrel length.

In some fields of application it is necessary to maximize the muzzle velocity, for example in order to achieve a high penetration power with military weapons . A more favorable compromise between the inner and outer ballistic optimum of the cross-sectional loads can be achieved here with additional design effort. One possibility is to shoot crushed bullets or cuff bullets from barrels with a conical bore. The caliber of these barrels is greatest at the chamber and narrows to the barrel muzzle, whereby the bore narrows either continuously or in a section of the barrel. When the propellant is ignited, the gas pressure acts on a larger area, which enables higher projectile acceleration. At the same time, the volume of the powder chamber can be increased, since the sleeve can be larger because of the larger initial diameter. The bullet is then squeezed together until it reaches the muzzle, which reduces its diameter and thus increases the cross-sectional load as desired.
Conical barrels were only used in a few anti-tank weapons such as the Panzerbüchse 41 or the 7.5 cm PaK 41 and have not left the experimental stage for handguns.

Artillery sabot projectile

Another possibility to change the effective cross-sectional loading of projectiles before and after launching is the use of sabot . Due to the sabot, the projectiles have a low average density and thus a low cross-sectional load which is favorable for internal ballistics. As a result, the projectiles can be accelerated to significantly higher speeds than heavier massive projectiles with the same gas pressure and the same barrel length. After leaving the barrel, the light sabot remains and the actual, under-caliber projectile continues the flight alone. These projectiles are usually very long and made of very dense material, which means that they have the high cross-sectional load necessary for a long range and penetration effect. Sabot bullets are the state of the art, especially when it comes to fighting tanks.

Muzzle velocity and muzzle energy

Grenade cal. 914 mm of the Little David mortar with twist guide ring

The muzzle velocity is dependent on the acceleration of the projectile and run length : The muzzle energy is dependent on the muzzle velocity and the projectile mass.

There are certain limits to the muzzle velocity that can be achieved. The projectile acceleration depends on the gas pressure and, via the cross-sectional load, on the projectile mass; the structural properties of the barrel bore and the projectile also have an influence on the projectile acceleration.

The gas pressure cannot be increased at will because the strength of the barrel and breech are limited, and the cross-sectional load cannot be reduced at will. The barrel length also has limits, since the longitudinal stability of a barrel and thus the accuracy of the shot can only be ensured up to a certain caliber length with reasonable effort. The lifespan of rifled barrels also decreases disproportionately from a certain muzzle velocity.

In order to increase the muzzle velocity for a given gas pressure and barrel length, the mass of the projectile must be reduced. Since the acceleration time is reduced with the higher projectile acceleration, a faster burning (offensive) propellant charge must be used to achieve the same gas pressure.

If the muzzle velocity is to be increased with the same bullet mass and barrel length, an increase in the mean gas pressure is necessary. As the acceleration time is reduced, a more offensive powder must also be used in this case. The muzzle energy increases by the square of the muzzle velocity for the same projectile mass, so that when the muzzle velocity is doubled, the projectile has four times the muzzle energy. Correspondingly, to double the muzzle velocity with the same projectile mass, the mass of the propellant charge would ideally have to be quadrupled.

If the projectile mass and gas pressure are given, the duration of the gas pressure and thus the barrel length must be increased to increase the muzzle velocity. Since the projectile receives a higher muzzle energy here too, a correspondingly larger propellant charge is necessary.

In order to achieve a higher muzzle velocity through constructive measures, in addition to the use of crush and sabot bullets, concepts were also implemented that primarily aim to reduce bullet resistance. The bullet resistance can be reduced by using bullets with twist guide rings. These rings have grooves that are adapted to the rifling of the barrel and guide the bullet in the rifling, so that the rifling does not have to cut into the guide rings with high resistance and wear and tear when firing. Such projectiles can also extend the life of a gun barrel. The production of such projectiles is complex, so that they are only used in a few types of guns.

Lubricants can also be used to reduce bullet drag. A more recent development is a coating with the dry lubricant boron nitride (BN) in its hexagonal variant. By applying BN powder to rifle bullets, when the maximum gas pressure is reduced, an increase in the muzzle velocity and an improvement in the accuracy of the shot is usually achieved. Other coatings, such as molybdenum disulfide , tungsten disulfide or lubricating greases (for lead bullets), on the other hand, primarily serve to improve precision and reduce bullet wear. Molybdenum disulphide must also be sealed with a layer of wax, as the substance can have a decomposing effect on NC propellants.

Some guns have a Paradox bore, a special choke where the tensionless, polished running at the mouth in a slightly constricted section with trains passes. If shotgun bullets are fired with it, they achieve a higher muzzle velocity due to the low bullet resistance of the smooth barrel and still get a twist from the pulls , which improves precision. Such barrels were first used in heavy hunting rifles from around 1880, as they offered a favorable compromise between the highest possible bullet energy and precision.

Propellant charge and case shape

The more energy a projectile should receive, the greater the mass of the propellant charge must be. The volume of the powder chamber is subject to design limits relative to the size of the caliber. One way of accommodating a large propellant charge is to extend the powder compartment. If the space becomes too long, however, the propellant charge may no longer ignite evenly, which can lead to a loss of energy and deviations in the muzzle velocity.
High-performance cartridges are often bottle-shaped and therefore have a diameter that is greater than that of the barrel bore. The powder space can be enlarged without the sleeve becoming too long. At the case shoulder, there are flow losses when firing, which also limit this type of volume increase.

literature

  • Willi Barthold: Hunting weapon knowledge . 6th edition. VEB Verlag Technik Berlin, 1984.
  • Karl Heinz Martini: The weapon specialist book . 14th edition. DWJ Verlags GmbH, 2004, ISBN 3-936632-02-2 .
  • David Harding (Ed.): Weapons Encyclopedia . 2nd Edition. Motorbuch Verlag, 1995, ISBN 3-613-01488-2 .

Individual evidence

  1. ^ David Harding (Ed.), Waffen-Enzyklopädie, Motorbuch Verlag, ISBN 3-613-01488-2 , 2nd edition, 1995, p. 113
  2. Satoru Shoji: BALLOTING IN A FRENET FRAME , 2007 (PDF, 254 kB) ( Memento from May 10, 2018 in the Internet Archive )
  3. Willi Barthold, Jagdwaffenkunde, VEB Verlag Technik Berlin 1969, edited edition 1979, p. 194
  4. ^ Günter Hauck, Äußere Ballistik, Militärverlag der DDR, 1st edition 1972, p. 525
  5. Caliber Edition 11/12 2009, VS Medien GmbH, Michael Fischer: Magic means for better precision? New coating for rifle bullets, pp. 72 to 77
  6. Visier Special 47, Magnum short and long weapons, Vogt-Schild Germany 2007, p. 39