Interior ballistics covers the events inside a gun that occur from the time the firing pin strikes the primer until the bullet exits the muzzle. While the internal ballistics of large cartridges such as cannons are reliably predictable from mathematical considerations, interior ballistics for small arms are difficult to predict at least by reasonable calculation procedures. In the past, ballistic data for small arms have been found primarily by velocity and pressure tests or empirical methods rather than by calculation.
The familiar kinetic energy equation (E = 1/2mv2) when equated to the energy available from the powder charge driving the bullet down the gun barrel will allow the calculation of bullet velocity with reasonable accuracy.
A pound of single-base rifle powder has an energy content of about 1,246,000 ft-lbs of energy or about 178 ft-lbs per grain of powder. In actual practice only a fraction of this energy is available to accelerate the bullet. Julian Hatcher in HATCHER'S NOTEBOOK reported the energy distribution for the Browning Machine Rifle as follows:
You will note that the energy imparted to the bullet is only about 29% of the total powder energy available. While this is typical of many small arms cartridges, actual efficiencies may range from 17 to 37 percent or more. The actual efficiency is basically a function of expansion ratio and charge weight to bullet weight ratio.
THE SHOT AND PROCESSES, ACCOMPANYING IT
The shot is the composite phenomenon, which is accompanied by a series of physical and chemical transformations. When the shot occurs, the chemical energy of gunpowder quickly turns at first into a thermal energy and then into a kinetic energy of a shell and some of mechanical parts of the gun. Part of the energy is used for operation of automatic mechanisms, and also is spent for heating of the weapon.
Energy of gunpowder can be used not only for operating of mechanisms, but also for return of relative parts of the weapon to an initial standing. The phenomena occurring in a bore at a shot, are studied by the science called interior ballistics. The processes occurring in a bore at a shot, are divided into four periods. The forcing period lasts from the moment of the primer-break prior to the beginning of the motion of a shell. There is an inflaming practically by all surface of gunpowder grains at moment of primer-break, and then, the process of the burning is spread in the depth of the grains. At the initial moment of time the gunpowder burns in constant volume, because shell needs some energy for riping the driving band in a rifling grooves.
The first ballistic period includes time from the beginning of a motion of a shell till the moment of combustion of all gunpowder and corresponds to burning of gunpowder in variable volume. In the beginning, volume, in which gunpowder is burning, is incremented slowly because the shell at this moment has small velocity, but the process of a gas distension goes very quickly. Thus, pressure of the gunpowder-gas rapidly increases and at some moment gets of the peak value. Maximum values of gas temperature and shell acceleration also correspond to this moment.Then the shell velocity gets such value, at which the magnification of volume behind a shell goes faster, than the process of a gas distansion at a burning gunpowder.
Thus the bore pressure (pressure inside the bore) begins to decrease even before the gunpowder ends burning. The second ballistic period comes after combustion of gunpowder, when the inflow of new gases stops. However, gases which reside the space behind a shell, still have a major reserve of energy. Being dilated, they keep incrementing a missile velocity. In the second ballistic period the pressure in a bore is monotonously decreases. This period comes to end when the shell leaves the barrel. The burrel-pressure of gas and the burrel-velocity of the shell correspond to this moment. The aftereffect period begins from the moment when the shell leaves the barrel and is prolonged so long as gunpowder-gasees prolong to exert influence on a motion of a shell, giving it extra velocity. The increment of a missile velocity in this period is rather insignificant and makes no more than 2,5 %, but it influences the operation of weapon mechanisms and compensators of force of recoil. Estimating the efficiency of these devices, the aftereffect-period is critical.