Elements of Ballistics
The term ballistics is derived from the Latin word ‘ballista’ which refers to a crossbow-like device for throwing stones using twisted ropes.
To understand the elements of ballistics, it is divided into three parts and these parts are as follows:
• Internal ballistics
• External ballistics
• Terminal ballistics
Internal ballistics is the study of what happens within the barrel of a weapon from the moment the firing pin hits the primer to the time the bullet exit from the barrel.
It includes primer ignition time, primer pressure, time curves, and temperature, etc. It deals with the motion of projectiles, commences as soon as the first grain of the propellant is ignited, and subsists till the projectile leaves the muzzle end of the weapon. The study includes all details concerning the impulse, which makes the projectiles move out from the muzzle in the air.
When the projectile remains in the firearm, it obtains its energy during the period, and it can be divided into three parts:
• Lock time
• Ignition time
• Barrel time
Lock time is the time interval between the release of the sear and the impact of the striker on the percussion cap. A short time interval is advantageous in rapid-fire. The lock time can be measured in several ways, in one such system, the use of linear motion sensors and the oscilloscope is made.
Ignition time is the duration or interval between the striking of the firing pin to blow the ignition of the first grain of powder. The ignition, under normal conditions, takes place at an interval of about 0.002 seconds.
Barrel time is the time interval from the pressing of the trigger to the exit of the bullet from the muzzle end.
Internal ballistics is limited to happenings, which occur inside the barrel of the firearm. Internal ballistics, as well as external ballistics, both are important in the forensic field. External ballistics is concerned with the firing of police to disperse the crowd, use of improvised firearms (country-made weapons) used in criminal cases involving homicides and murders. It contributes much during war times. In peacetime, it plays an important role in space travel where the atmosphere is absent and the projectile move in a vacuum.
Horizontal Range Determination
The horizontal range is the distance traveled by the bullet horizontally. If a bullet is fired with a velocity V at an angle of elevation µ. Its components in the vertical direction and horizontal direction would be V sinµ and V cosµ respectively when air resistance is not taken into consideration.
Experimental Determination of Trajectories
The test-firing for the trajectory determination is done from a machine test or a bench test after ascertaining the proper functioning of the baseline. The heights of various ranges from the baseline of various screens give the height of the trajectory at distances of the screens platting the distances and heights gives the trajectory of the projectile. There should be a large number of shots to ensure better accuracy.
Another method for trajectory determination is to have fired in a large and wide uninhabited area of appropriate dimensions to cover a range of projectiles of which the trajectories are required to be determined with necessary precautions to ensure that no accidents due to stray bullet takes place.
The angle of Firing
The angle of fire is the angle at which the barrel axis line with the baseline. When the angle of elevation/firing (measured in minutes) is one minute, then the line of fire and baseline will get apart by a distance of over one millimeter at four meters and about thirty centimeters at one thousand meters.
The angle of elevation is generally low. Especially in cases of hunting purposes these angles can have lowered values and this also holds good for normal cases. However, if the target animal is at a higher pedestrian, the position may be different.
The angle of elevation at which maximum range is attained is called the critical angle. There is no accurate way of determining the maximum range of a bullet.
When the firing is at an angle, the elevation may give rise to an area that may be called a safe zone along the trajectory because the projectile will be moving over the heads of the persons standing along the baseline. When the sights are set to a target range of fewer than 300 meters then the rifle is fired within .303” and there would be practically no safe zone throughout the entire range.
At greater ranges, however, there will be safe zones. Safe zones are determined with the help of a graph. The heights of the trajectory at various distances for the given elevation are plotted against the distance. The safe zone for the given elevation is the portion of the trajectory where the height is over and above the height of the target, two meters from the ground in the case of a human target.
Internal ballistics include the study of several phenomena
• Burning of propellants
• The geometry of gun powder
• Pressure and its measurement
• Atmospheric conditions
• Shape of cartridges
• Density of loading
• Twist of rifling
• Bullet fit and velocity of bullet at a muzzle
• Heat generation and problems
• Strength of barrel
• Corrosion or rusting of the barrel
• Bullet of the weapon
• The recoil of the weapon
• The phenomenon of busting of barrel
The priming compound explodes when the firing pin strikes the hammer. It has a great velocity causing a jet of flames of an extremely high temperature to pass through the flash hole into the propellant chamber. This jet of flame with a temperature of about 2000 degrees ignites the propellent which burns at high speed to form a large volume of high-pressure gas which accelerates the bullet down the barrel and out of the muzzle end.
Burning of Propellents
The burning process is a chemical reaction that involves oxidation. The shorter the period during which a given quantity of propellent burns, the more explosive will be production and expansion of gases. Propellent is a chemical compound that contains both fuel and oxidizer. It should be chemically and physically stable in normal conditions.
It applies to the reaction of solid propellant grains to generate hot gas. Where the surface of the grain regresses, layer by layer, the burning takes place by parallel layers that are normal to the surface at every point.
The French general Guillaume property in 1839 explained this law that is, to explain the behavior of gun powder, but it has subsequently been applied to another solid propellant.
The progression is attributed to heat transfer from the surface of the solid of energy necessary to initiate the reaction in the case of single-phase propellant grains. The heat transfer rate increases with pressure. Smokeless powder reaction rates vary with a pressure that is described by paul Vieille in 1893.
In some weapons like shoulder arms, pressure should not develop suddenly, it should be gradual. It is a dense and bulk powder, and when ignited, it burns rapidly with the result that the projectiles receive a big push. The gradual development of pressure not only provides better velocities but also prevents quick wearing out of the barrel. A type of powder that contains grains that have multiple perforations.
In the case of degressive powders the shape and size of grains are kept such that, like the burning of propellent progresses, the rate of burning goes on decreasing. It is a type of solid grain which having no perforations that are also termed as non-perforated powder grains.
The ammunition is manufactured in the industries that give the desired velocities and pressures at a particular atmospheric temperature. If the temperature differs only slightly at the place of the use, the ballistic aspects are not seriously affected. But, if temperature variations are significant, they affect the ballistic aspects of the ammunition.
The Shape of the Cartridge Case
In hot places, the firearm may burst when the pressure developed at an excessive rate. In cold places, the ammunition may develop low velocities. There is variation in velocities because of temperature is about one meter per second.
The density of loading and combustion rate
S = U/V * 100
U is the volume that is occupied by the powder
V is the volume of the cartridge case
S is the density of loading
In the rifle’s cartridge, the loading density varies from seventy-five to ninety-five. Higher densities are more useful. Because they permit uniform burning, proper development of pressure, economical, and give rise to regular velocities. Low loading densities may result in giving hang fire. Sometimes, improper loading density materially affects the range and aim of a shot.
Heat problems and combustion of propellants
During the combustion of propellants, the temperature is often taught to 3000 degrees celsius. Sometimes a barrel of a firearm melts at these temperatures if gases at this temperature remain in the barrel for a long time. But fortunately, the time for which the hot gases are in contact with the barrel is about 0.001 seconds.
Chamber pressure is the pressure exerted by a cartridge case’s outside walls onto the inside of a firearm’s chamber when the cartridge is fired. It is generally expressed in pounds per square inch or copper units of pressure.
Pressure development inside the barrel depends upon certain characteristics which are given below;
• Quantity or quality of powder charge
• Available space for expansion
• Speed of initiation and burning
• Chemical nature of the powder
• Surface area
• Pressure determination
The pressure developed by ammunition is always measured to find out if the same is within the safe limits or not. Generally, this is done in the ordinance factory.
The formula for pressure determination;
P = KW
W is the weight of powder in grains
K is the constant value
There are three methods generally used to determine the pressures.
• Crusher technique
• Piezo technique
• Strain gauge method
The measurement of maximum chamber pressure is carried out with a pressure gun. For the adjustment of this pressure gun in a firearm, a hole is made in the barrel with a driller at the top of the chamber. Then clamped it over this hole. In this, a solid cylinder of standard dimensions and purity made of either lead or copper is used. The pressure developed inside the cartridge allowed to crush the cylinder. The decrease in length due to crushing, measures the pressure develop.
It is the most common method and is similar to the crusher method. It uses the quartz crystal transducer is inserted and attached to sensitive measuring equipment. This method generally yields a more accurate reading than the copper crusher and is more cost-efficient because the transducer can be reused.
Strain Gauge Method
It is the least accurate method but has the advantage of being the least expensive and requires no permanent modifications to the firearm. A strain gauge is attached to the barrel and at the time of firing the barrel stretches briefly, and this stretch is measured by the gauge.
This method is generally reserved as a way of relatively comparing different cartridge loads as the strain gauge reading is not as accurate as a crusher or Piezo test.
It means the backward movement of firearms. It is similar to Newton’s third law of motion. the width which the ejecta moves forward is the same with which the firearms move backward. Sometimes it injures the shooter if the weapon is not held properly or recoil velocity is excessive.
Total recoil velocity
Vr = (m1+Km2)V / M
Vr is the total recoil velocity
m1 is the mass of the projectile
m2 is the mass of the powder residues
V is the muzzle velocity of projectile and gases.
For reducing recoiling cut compensators are used. It helps in eliminating recoil due to blast, sometimes muzzle brake devices are also used for reducing recoil.