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.
[Illustration: _Elevation._
FIG. 102.]
[Illustration: _Plan._
FIG. 103.]
=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.
[Illustration: FIG. 104.]
=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.
[Illustration: FIG. 105.]
=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 |[infinity](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_.
[Illustration: FIG. 106.]
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.
[Illustration: _Actual Intersection of Sheaf._
FIG. 107.]
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 ⅓ 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.