Theoretical Gunnery. Definitions. General Principles. Probability of Fire. Burst of Shell. Burst of Shrapnel.

DEFINITIONS.

INTERIOR BALLISTICS.

Interior Ballistics.—The effects produced on a projectile in the bore of a gun, and on the gun, when subjected to the action of the products of combustion of gunpowder or other explosives.

Gunpowder Explosion is the rapid conversion of gunpowder into gases and solids with evolution of heat.

Ignition is the raising of the temperature of some point of a grain of powder to 300° C.

Inflammation is the spread of the ignition from point to point on the surface of the grain or mass.

Combustion is the burning of the grain from the ignited surface, inward or outward, as the case may be.

Density is the ratio of the weight of a grain of gunpowder to that of an equal volume of water under standard conditions. It varies from 1.68 to 1.90, rarely exceeding 1.85.

Gravimetric Density is the ratio of a given volume of powder to that of an equal volume of water under standard conditions.

Density of Loading is the ratio of the weight of a charge of gunpowder to the weight, under standard conditions, of the volume of water that would fill the powder-chamber. Its value is 27.68 W/C, in which W is the weight of the charge in pounds, and C the volume of the chamber in cubic inches.

Initial Air-space is the portion of the chamber in a loaded gun or shell unoccupied by solid matter before firing.

The Reduced Length of any volume in the bore of a gun is the height of a right cylinder of the same volume, but with a diameter equal to the calibre of the gun.

An Adiabatic Transformation is a change that takes place in the state of a gas within an envelope impermeable to heat, or which occurs in such a short space of time that no heat is received or lost by it.

Detonation is exceedingly quick explosion.

Slow Powders are those which are not entirely burned when the projectile leaves the muzzle.

Velocity of Emission is the ratio of the amount of a unit weight of powder, burned in air in a small increment of time, to the time itself.

The Sectional Density is equal to the weight of the projectile divided by the square of its diameter.

Spherical Density is the ratio of the weight of the projectile to that of a sphere whose radius is equal to that of the right section of the projectile.

Similar Guns.—Two guns are similar when all their homologous lineal dimensions are proportional to their calibre.

Similarly Loaded.—When the weight of charge and projectile are proportional to the cube of the calibre, and the grains of powder are alike in form and composition, with dimensions proportional to the calibre.

EXTERIOR BALLISTICS.

Exterior Ballistics treats of the motion of a projectile in air after it has left the piece.

Trajectory.—The curve described by the centre of gravity of the projectile during its passage through the air. (Figs. 102 and 103.)

Line of Fire.—The prolongation of the axis of the piece.

Plane of Fire.—The vertical plane containing the line of fire.

Line of Sight.—The straight line passing through the sights and the point aimed at. (Figs. 102 and 103.)

Plane of Sight.—The vertical plane containing the line of sight.

Angle of Sight.—The angle made by the line of sight with the horizontal. (s in Fig. 102.)

Line of Departure.—The line in which the projectile is moving when it leaves the gun.

Angle of Departure.—The angle made by the line of departure with the horizontal. (d in Fig. 102.)

Angle of Elevation.—The angle made by the axis of the piece with the horizontal. (q in Fig. 102.)

The Jump.—The difference between the angle of elevation and the angle of departure, owing to the movement of the gun at discharge. (j in Fig. 102.) (The jump of 3.2 in. and 3.6 in. guns varies from 20 minutes at 1 degree to 30 minutes at 10 degrees elevation.)

Initial Velocity.—The velocity of the projectile at the muzzle.

Remaining Velocity.—The velocity at any point of the trajectory.

Final Velocity.—The velocity at the end of the range.

Range.—The horizontal distance from the muzzle to the point where the projectile strikes.

Drift.—The departure of the projectile from the plane of fire. With guns having a right-handed twist it is to the right, and its extent varies nearly as the square of the range.

Direct Fire is from guns with service charges at all angles of elevation not exceeding 15°.

Indirect or Curved Fire is from guns with less than service charges, and from howitzers and mortars, at all angles of elevation not exceeding 15°.

High-angle Fire is from guns, howitzers, and mortars, at all angles exceeding 15°.

Front or Frontal Fire is that which is directed perpendicularly, or nearly so, to the general line of troops fired at.

Oblique Fire is that which is directed obliquely to the line fired at; it is more searching than front fire.

Enfilade Fire is that which rakes the enemy's line of troops, the gun being on the prolongation of the line. It is the most effective fire.

Flanking Fire is one directed along the front of, or nearly parallel to, the line to be flanked or defended.

Reverse Fire is when the object is fired at from the rear.

Cross-fire is where the projectiles from guns in different positions cross one another at a particular point of ground. (See Fig. 105 for these cases.)

PROBABILITY OF FIRE.

Absolute certainty of hitting the same spot at each round is impossible of attainment; and accuracy of fire is therefore a comparative term.

The Probability of Fire measures the chance of hitting a given target. It is determined for any gun by firing a certain number of shot at a given range, measuring carefully the ranges and dividing the sum by the number of shots, which gives the mean range.

Subtract each range from this mean range thus obtained, and the results obtained will be the errors in range for each shot. Add these errors together and divide their sum by the number of shots, and this will give the mean error in range. Multiply this mean error by 1.69, and the product will be the depth in the direction of the range of a belt or zone which will probably contain one half the whole number of shots fired.

In the same way the width of the probable zone, laterally, may be obtained, and also the height of the probable zone vertically. The origin of reference for the points of impact of the shots in the last two cases is generally taken at the lower left-hand corner of the target.

The intersection of the first two zones will give a rectangle which will contain 25 per cent of all the shots.

Similarly we may consider only the vertical and lateral errors, thus obtaining a vertical in lieu of a horizontal rectangle containing 25 per cent of all the shots.

The 50 per cent "breadth column" should, in practice, generally be neglected, as most of the errors in shooting are always over and under, and not lateral, ones.

The Point of Mean Impact is the intersection of the lines of mean range and mean lateral deviation.

The Probable Rectangle is one which contains 50 per cent of all the shots.

To find the probable rectangle for any gun, multiply the mean error in range by 2.637 for the side of the rectangle parallel to the range, and the mean error in lateral deviation by 2.637 for the side perpendicular to the range.

In all range tables for guns the 50-per-cent zones for length, breadth, and height should be given; and by means of them and the following table of probability factors the dimensions of zones of other percentage, and also the percentage due to certain dimensions at different ranges, can be obtained.

PROBABILITY FACTORS.

Percentage.	Factor.	Percentage.	Factor.	Percentage.	Factor.
1	.02	25	.47	60	1.25
3	.06	30	.57	70	1.54
5	.09	35	.67	80	1.9
10	.18	40	.78	90	2.44
15	.28	45	.89	95	2.91
20	.38	50	1.00	100	8 (say 4)

First.—Opposite any given percentage, say 20, we find in the contiguous column a factor, .38. If we multiply the dimensions of the 50-per-cent zone, given in the range table, by this factor .38, we will obtain the corresponding dimension of the 20-per-cent zone.

Second.—Suppose for a particular range the dimension, say height of the 50-per-cent zone, is given in the range table as 4 feet, and we wish to know what percentage of shots will probably strike a zone 7.6 feet high. If we divide 7.6 by 4, we obtain 1.9, and from the table we see that the factor 1.9 corresponds to 80 percentage. Therefore we may assume that 80 per cent of the shots at that particular range will probably strike a zone 7.6 feet high.

For all practical purposes we may consider that the factor of the 80-per-cent zone is 2, of the 95-per-cent zone is 3, and of the 100-per-cent zone is 4.

SHELL.

A shell is a hollow projectile containing a bursting-charge of gunpowder, or some high explosive, and a fuze to ignite the charge at some point of its flight, or on impact. Its penetration into earth at 850 yards may be taken at 12 to 15 feet for field-guns. It is invariably fired with a percussion-fuze, and is used against material.

SHRAPNEL.

A shrapnel consists of a collection of lead balls in an envelope, and bearing a small bursting-charge, which, by action of the fuze, ruptures the envelope at some point of the projectile's flight, and leaves each bullet free to describe its own path, and the paths thus described, taken together, form the cone of dispersion.

TIME-SHRAPNEL.

This shrapnel is used entirely against animate objects, its main purpose being to cover a given area with a powerful and effective bullet-fire, and must have, at the instant it bursts, a terminal velocity of 500 ft.-sec. to be effective. The trajectory of shrapnel until it bursts is identical with that of shell. On its bursting the bullets spread in every direction, and form a cone of more or less denseness. This cone will increase in size as the range increases, because the velocity of translation decreases more rapidly than the velocity of rotation. On the other hand, the area of the oval formed by the intersection of this cone with the ground will decrease as the angle of fall increases. This oval has its greatest depth in the direction of fire, and its broadest end furthest away from the gun. Its depth diminishes as the range increases, and for short ranges it is much greater than for long ones. The breadth increases as the distance short of the object at which the burst takes place increases. The nearest bullet (that is, the one which has travelled the shortest distance) will have the highest striking velocity, and the bullet that travels furthest will have the lowest striking velocity, the bullets between striking with proportionate velocities. As the distance short of the object at which the shell bursts increases so will the distances between the bullets on striking increase.

When firing at a horizontal target, the bullets are not uniformly spread over the whole of the oval of dispersion, those on the nearer side of the minor axis being more crowded together than those on the farther side. Of course the ricochets more or less endanger the omitted spaces, but as these are dependent on the hardness of the ground and on the angles that the strikes make with the actual surface of the ground with which they come in contact, they cannot be relied on. On favorable ground all the bullets will ricochet at all ranges, but the ricochets of those that fall short of the axial bullet will be about the only ones that will be effective.

The following rules should be observed:

1. When the object has depth, the fire cannot be too direct.

2. When the object has frontage and little depth, the more oblique the angle of fire is to the front the greater is the area affected.

3. Time-shrapnel is peculiarly adapted to objects moving toward or from the battery. In the first case the fuzes are set rather short, in the second rather long.

4. The best position generally for the point of burst is about six yards above and fifty yards in front of the target. A good rule for the height of burst is the height of burst in feet = the number of hundred yards in range. Thus for 1800 yards' range it would be 18 feet (6 yards).

5. The spread may in general be reckoned as ¼ to ? the distance of burst.

It must be borne in mind that a variation in the length of burst at any particular range may alter the frontage covered considerably, but it hardly affects at all the depth covered by effective bullets. This depth may be taken as 500 yards for ranges of about 1500 yards, 400 yards for ranges of about 2500 yards, and 300 yards for ranges of about 3300 yards, irrespective of the length of short burst.

PERCUSSION-SHRAPNEL.

With shrapnel of this kind the cone of dispersion has an ascending angle which will be much greater than the angle of descent, and would vary with the conditions of the ground struck. The velocity is very much impaired by the retardation on graze, and the smallest irregularity may cause the projectile to bury itself, or rise at a very considerable angle.

The effect being so greatly inferior to time-shrapnel, they would only be used on particular occasions.

CANISTER.

Canister is a collection of bullets contained in a can, which is ruptured in a gun by the shock of discharge, the bullets thereby forming a cone of dispersion with its apex at the muzzle of the gun. The can, or envelope, in the U. S. service is known as the Sawyer, and is made of malleable cast iron, weakened by spiral cuts.

Canister is essentially a close-quarter projectile for employment against personnel and horses, and under the most favorable circumstances is effective up to nearly 500 yards; up to 300 it is annihilating.

Effective ricochets are necessary for maximum results, and can only be obtained at short ranges, and then only over smooth water, or on a hard level surface not intersected with obstacles.

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