The multiperforated grains in which American nitrocellulose of the larger sizes is made up, are an example of (iii.). The cylindrical grain has seven equal longitudinal perforations; a typical cross section is shown in fig. I.
One of the perforations coincides with the axis of the cylinder, and the others are disposed symmetrically about the axis, their centres orming a regular hexagon and being so arranged that the least dimension of the grain or " web thickness," which is the least distance between any two adjacent circumferences, is the same throughout.
During the first phase of the combustion, i.e. before the grain breaks up, the grain burns with an increasing surface, the thickness burnt through at any time being greater than the percentage of the whole weight of the grain consumed. When the web thickness is burnt through, the grain breaks up into twelve slender trian- gular prisms with curved sides known as " slivers." The slivers will burn with a decreasing surface in a very similar manner to long cords.
The less the percentage of the whole weight of the grain consumed compared with the percentage of the thickness burnt through, the more " progressive ' is the shape said to be. Fig. 2 illustrates the burning of different forms of grain in a gun.
It shows the pressure-space curves for a charge of the same weight made up of long cords, long tubes, and multiperforated grains; the diameter of the cord, thickness of the tube, and web thickness of the m.p. grain are so arranged that the whole charge is just completely consumed at the muzzle, 1 i.e. after the same travel of the shell; the same shell is supposed to be fired from the same gun with these three different natures of charge.
The muzzle velocity will be the same in each case, but the pressure curves very different. For the charge to be completely consumed at the muzzle the diameter of the cord and thickness of tube will be the same, but the web thickness of the m.p. grain will be considerably less, as after this is burnt through there are still the slivers to burn.
The maximum pressure is lower and the muzzle pressure higher with the tube than with the cord or m.p. grain, which are about level in this respect, but the point of maximum pressure with the m.p. grain occurs farther up the bore than with the cord, the point of maximum pressure with the tube being between the two.
The point where the web thickness of the m.p. grain is burnt through and the grain breaks up into slivers, is shown on the diagram. From this point the pressure drops rapidly, owing to the change from an increasing to a decreasing surface of combustion, until it runs into the curve for the cord which it follows to the muzzle.
If we increase the diameter of the cord and the web thickness of the m.p. grain (keeping the weight of the charge the same) the maximum pressure will be lower, but the muzzle velocity will also be lower as the charge will not be consumed in the gun.
Q Web thickn
ss burnt
10
20 TRAVEL
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FIG. 2.
30
40 calibres
In practice the maximum pressure is generally the limiting factor as we must not exceed the safe working pressure of the gun, and the endeavour is to get the required muzzle velocity combined with good regularity; for this it is desirable that the muzzle pressure should be low and the charge completely burnt well back in the gun.
The best practicable combination of form and weight of charge for this purpose is the problem of the designer.
1 This is only for illustrative purposes. In practice the charge should be completely consumed before the shell reaches the muzzle.
The main problem of Interior Ballistics may now be stated as follows: Given the necessary particulars of the gun, charge, and shell, to determine the corresponding values of the velocity of the shell (with special attention to the muzzle velocity), the pressure of the gases of the charge (with special attention to the maximum pressure), and the proportion of the charge burnt (with special attention to the point of complete combustion), at any point of the travel of the shell up the bore.
Various subsidiary problems of an inverse nature required for considering questions of design and analyzing firing results will also suggest themselves.
The physical phenomena, as will be readily understood, are of a very complex nature. Besides the energy expended in propelling the shell from the muzzle with a certain muzzle velocity, we have the work expended on the charge, on the gun and mounting (recoil) and in giving rotation to the shell ; work is also done in forcing the driving band into the rifling grooves (" engraving " the band), and in over- coming friction up the bore. There is also the heat lost by con- duction.
As regards the gun, besides the main dimensions (" calibre," " chamber capacity," and " shot travel "), variations in the design of the rifling and the state of wear of the bore generally may have an appreciable effect on the results. This does not exhaust the possible causes of variation, and in fact two guns of the same design even when new may not give the same muzzle velocity under conditions which have carefully been made as nearly identical as possible.
As regards the charge, in addition to the nature of the propellant and form of grain, we may have to take into account the circum- stances of the ignition and the temperature of the charge as fired. Two samples or " lots " of the same propellant, however carefully made to be as nearly identical as possible, may give different ballistics in the same gun, and even if they give practically the same results when new, the matter may be complicated later by the length and conditions of storage.
As regards the shell, besides the weight, the design of the driving band may have to be taken into account, as this may affect its resistance.
It must be understood that though all these causes and others not touched on may appreciably affect the results, they by no means all do so in all circumstances, from the point of view of their practical effect on shooting; indeed, some of them may require very refined experimental methods even to detect them. For this reason a due appreciation of their relative importance in any particular case is very desirable and can be obtained only by close study and wide experience.
From the extreme complexity of the physical phenomena, even under carefully standardized conditions, it may be doubted if a complete solution of the problem is possible, but various systems more or less complete for an approximate solution have been pro- posed and worked out. Some of these are referred to above. The underlying theory is of necessity difficult and the calculations involved laborious, the complications increasing rapidly with the degree of comprehensiveness attempted.
None of these systems up to date can be said to have gained general acceptance, and in fact serious divergencies on the most crucial points will be found in the different authorities. All that will be attempted here will be a short description of certain empirical formulae which have been and still are considerably used for prac- tical calculations of muzzle velocity and maximum pressure. They arc of the monomial type, and by their aid, given the muzzle velocity and maximum pressure known to be obtained with certain com- binations of gun, charge and shell, we can endeavour to predict the changes in ballistics which will result from variations in the data which give the known results.
The following notation will be employed:
d calibre in inches.
The calibre is defined as the diameter of the bore of the gun measured across the lands (the portions of the bore between the grooves of the rifling).
G= chamber capacity in cubic inches.
That is the volume of the portion of the interior of the gun which is behind the shell when rammed home. In the case of guns which use a metallic cartridge case allowance must be made for the space occupied by this.
S = shot travel in inches.
That is the distance moved through by the projectile from the time it starts to move till it leaves the muzzle. W = weight of shell in Ib. M = weight of charge in Ib. L = least dimension of the grain in inches.
That is the diameter of the cords, the thickness of the tubes or strips, or the web thickness of the m.p. grains of which the charge is made up.
V = muzzle velocity in feet per second (f/s). P = maximum pressure in tons per square inch (ton/in 2 ). In order to facilitate calculations and comparisons of results with guns of different calibres it is advantageous to introduce the principle pf " similar guns," and to reduce all particulars to those correspond- ing to a standard or unit gun of I in. calibre. The reduction of the data to those of the standard gun, in any particular case, is effected
