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386 TABLE III.

Percentage alteration in muzzle velocity due to an alteration of + 70% in

Chamber Capacity.

Shot Travel.

Weight of Shell.

Weight of Charge.

Least Dimension of Grain.

->.c / <* 5 /o

+2%

-4%

M.D.T.+ 7 % N.C.T. +6% M.D. +6%

M.D.T.- 3 % N.C.T. -3% M.D. -1-5%

TABLE IV.

Percentage alteration in maximum pressure due to an alteration of +10% in

Chamber Capacity.

Weight of Shell.

Weight of Charge.

Least Dimension of Grain.

M.D.T.-io% N.C.T. -11% M.D. -i 1-5%

+6%

M.D.T. + i8% N.C.T. +16% M.D. +16%

M.D.T.-I4% N.C.T. -14% M.D. -8-5%

Example. A gun gives m.v. 1680 f/s for max. press. 15-5 ton/in 2 with a charge of 20 Ib. N.C.T. What decrease in charge will give a velocity of 1660 f/s, and what will be the corresponding pressure?

A change from 1680 to 1660 f/s is a decrease of 1-19%. From Table III. a decrease of 10% in weight of charge will decrease m.v. 6%. Therefore a decrease of 1-19% will correspond to a decrease . 10X1-19

in weight of charge of :

= 1-98% or 0-396 Ib.

From Table IV. 10% decrease in charge decreases P by 16%. Therefore 1-98% decrease in charge decreases P by 3-16% =0-49 ton/in. 2 Hence the maximum pressure for V = 1660 f/s will be about 15 ton/in. 2

For the experimental determination of any of the indices, say the velocity index m, we require a series of firing results in which the corresponding quantity M has alone been varied, and the muzzle velocities recorded.

The logarithms of the corresponding values of V and M are then plotted as ordinates and abscissae and a straight line fitted to the points as closely as possible. The slope of this line, as measured by the tangent of the angle which it makes with the axis of M, gives the value of the index.

As an example fig. 3 shows the plotting by this method of a number of firing results for a certain gun with different weights of charge, all the other particulars being kept the same.

The firing results plotted were:

M Ib.

Vf/s

6-12 1 6-62

816 1 865

7-69 959

8-0 991

9-0 1071

10-25 1164

JI-O 1222

The points obtained are shown by small circles.

It is then evident that a straight line as shown on the diagram can be drawn which will pass very nearly through all the points.

The best straight line could be determined mathematically by the " method of least squares," but in practice all that is necessary is to take a piece of thin black thread and move it about on the diagram estimating the best position by eye. Drawing the best straight line determined in this simple manner we can read off the index m. In the present case we thus arrive at the result that m =0-7, so that V

,-07

FIG. 3.

Connexion between Interior and Exterior Ballistics. When the shell leaves the muzzle of the gun and starts to describe its trajectory it enters the domain of Exterior Ballistics, but the condition in which it leaves the muzzle, particularly as regards initial velocity and steadiness and the round-to-round variations

in these conditions, will have an important influence on the behaviour of the individual rounds, and on the dispersion of a group of rounds fired from the same gun at the same elevation. These initial conditions are determined by what happens as the shell travels up the bore and at the moment it leaves it, and it is therefore appropriate to touch on them here.

Thus, if the shell leaves with a large initial " yaw " (inclination of the longer axis to the direction of motion of the centre of gravity), the range will in general be less than that which would be obtained if the initial yaw were small. Again, from the point of view of dispersion, even although all the shell were equally steady, the greater the round-to-round variation in the muzzle velocity, the greater would be the dispersion in range.

From the point of view of accuracy, as measured by the small dispersion of a group of rounds fired at the same elevation, the round-to-round variation in the initial conditions should be as small as possible. As far as regularity in muzzle velocity is con- cerned, the charge is a main factor, but the driving band and the state of the bore also have an effect.

. Considering the charge, the constituents of this should be, in the first place, as homogeneous as possible, both as regards com- position and dimensions. Further, for the same shape of grain the longer the travel of the shell before the charge is completely consumed, the more sensitive is the muzzle velocity to variations in size, etc., so that the further back the charge can be burnt the better, or the smaller the size that can be used the better. This is of course limited by the muzzle velocity required ; the smaller the size the less muzzle velocity can be obtained for the same maximum pressure.

When we come to consider the degree of steadiness with which the shell leaves the muzzle and the variations in this, while there is no question as to its importance, the conditions which govern it and their relative importance are by no means well estabh'shed.

The shell has to be given rotation, by means of the rifling grooves, in order to maintain an end-on position in its sub- sequent flight, and, in the first place, it is clear that it must be satisfactorily centred when rammed home, and that the design of the rifling grooves and driving band must be mechanically suitable for imparting the rotation in an efficient manner. Further we have as possible influences on the conditions of emergence, the effect of the blast of the gases as they are released at the muzzle, and the effect on the shell of the vibrations of the barrel. As to the former the violence of the blast effect will depend on the muzzle pressure, and the general practice is to keep this as low as possible so as to decrease the chances of trouble from this cause. As to barrel vibrations, although some experimental work has been done in the case of rifles, there is very little really known as to the behaviour of ordnance in this respect, and their influence on the state of departure of the shell. It is a matter which un- doubtedly calls for research, but the experimental and theoretical investigation bristles with formidable difficulties.

Bibliography. A list of some recent works and papers on the subject is appended. It is not intended to be complete but covers a good deal of ground, and may be useful in suggesting a course of reading which might be undertaken by anyone intending to study the subject seriously. G. Bianchi, Nozioni Fondimentali di Balistica Interna (1914, 2nd. ed., revised by G. Madaschi); P. Charbonnier, Balistique -Interieure (1908); Desmazieres, " Note sur 1'etat actuel de\a.ba.\istique'mterieure," Revue d'Arlillerie, vol. 85, April and May- June 1920; Gossot and R. Liouville, Les Ejfets des Explosifs (1919); A. G. Hadcock, " Internal Ballistics," Proceedings of the Royal Society, A, vol. 94, London, 1918; G. Sugot, " Les Formules de Charbonnier," Memorial de I'Artillerie Navale (1913); W. H. Tschappat, Text Book of Ordnance and Gunnery (1917).

(R. K. H.)

II. EXTERIOR BALLISTICS. Previously to the World War, and under the practice in vogue in 1910, guns proper were used only in direct fire at elevations below 20 degrees. Fire from guns, howitzers or mortars, above. 15 elevation was known as high angle fire, and fire from howitzers at angles of elevation below 15 was known as curved fire. Howitzers were fired at elevations up to 45; mortars were used at angles of elevation up to 65; but howitzers and mortars had low muzzle velocities, relatively short ranges, and the maximum ordinates of their trajectories were comparatively small.