Trajectory of Oblong Projectiles.—From the law of inertia, a rifle projectile moves through the air with its axis of rotation parallel to the axis of the bore. Hence it follows that an oblong projectile, fired under a low angle of projection, presents a greater surface toward the earth, and less parallel to it, than a round projectile of the same weight, consequently the vertical component of the resistance of the air is greater, and the horizontal component less, in the first case than in the second. The effect of this will be to give an oblong projectile a flatter trajectory and longer range than a round one.
Deviation of Projectiles.—The path described by the centre of inertia of a projectile, moving under the influences of gravity and the tangential resistance of the air, is called the normal trajectory. In practice, various causes are constantly at work to deflect a projectile from its normal path. All deviating causes may be divided into two classes,—those which act while the projectile is in the bore of the piece, and those which act after the projectile has left it. The first class includes all the causes which affect the initial velocity, and give rotation to the projectile; the second includes the action of the air.
Causes which affect Initial Velocity.—The principal causes which affect initial velocity are variations in the weights of the powder and projectile, the manner of loading, the temperature of the piece, and the balloting of the projectile along the bore. Rotation. The principal cause of the deviation of a projectile is its rotation combined with the resistance of the air. By balloting. If the projectile be spherical and homogeneous, rotation is produced by the bounding or balloting of the ball in the bore, arising from the windage. In this case the axis of rotation is horizontal, and passes through the centre of the ball; the direction of rotation depends on the side of the projectile which strikes the surface of the bore last. The velocity of rotation from this cause depends on the windage, or depth of the indentations in the bore, the charge being the same. By eccentricity. If, from the structure of the ball, or from some defect of manufacture, the centre of gravity does not coincide with the centre of figure, rotation generally takes place around the centre of gravity. This arises from the fact that the resultant of the charge acts at the centre of figure, while inertia, or resistance to motion, acts at the centre of gravity. For the same charge the velocity of rotation passes through the centre of gravity, and is perpendicular to a plane containing the resultant of the charge and the centres of figure and gravity. For the same charge, the velocity of rotation is proportional to the lever arm, or the perpendicular, let fall from the centre of gravity to the resultant of the charge. Knowing the position of the centre of gravity of the ball in the bore, it is easy to foretell the direction and velocity of rotation. In general terms the front surface of the projectile moves toward the side of the bore on which the centre of gravity is situated, and the velocity of rotation is greatest when the line joining the centres of gravity and figure is perpendicular to the axis of the bore.
The Effect of Rotation.—The effect of rotation in producing deviation may be discussed under three heads: 1st. When the projectile is spherical and concentric; 2d. When it is spherical and eccentric; and, 3d. When it is oblong. If a projectile be spherical and concentric, rotation takes place from contact with the surface of the bore around a horizontal axis, and the effect will be to shorten or lengthen the range, as the motion of the front surface is downward or upward. If the projectile be eccentric, the motion of the front surface is generally toward the side on which the centre of gravity is situated, and the deviation takes place in this direction. The extent of the deviation for the same charge depends on the position of the centre of gravity; the horizontal deviation being the greatest when the centres of gravity and figure are in a horizontal plane, and the line which joins them is at right angles to the axis of the piece; the vertical deviation will be the greatest when these centres are in a vertical plane, and the line which joins them is at right angles to the axis of the piece. If the axis of rotation coincide with the tangent to the trajectory throughout the flight, all points of the surface have the same velocity in the direction of the motion of translation, and there will be no deviation. This explains why it is that a rifle projectile moves through the air more accurately than a projectile from a smooth-bored gun. In accurate firing, therefore, it is important to know the true position of the centre of gravity. In ricochet firing over smooth water, the number of grazes may be increased or diminished by placing, in loading, the centre of gravity above or below the centre of figure.
Deviation of Oblong Projectiles.—The cause of the deviation of an oblong rifle projectile is quite different from one of spherical form. An oblong projectile moving in the air is acted upon by two rotary forces, viz.: one which gives it its normal rotary motion around its axis of progression, and another the resistance of the air, which, in consequence of the deflection of the axis of progression from the tangent to the trajectory by the action of gravity, does not pass through the centre of inertia, but above or below it; depending on the shape of the projectile. From a law of mechanics, a body thus circumstanced will not yield fully to either of the forces that thus act upon it, but its apex will move off with a slow uniform motion to the right or left of the vertical plane, depending on the relative direction of the two rotary forces. If the action of these forces be continued sufficiently long, it will be seen that the axis of the projectile before referred to describes a cone around a line passing through the centre of inertia and parallel to the direction of the resistance of the air. Owing to the short duration of the flight of an ordinary projectile, it is only necessary to consider the first part of this conical motion. If the projectile rotates in the direction of the hands of a watch to the eye of the marksman, and the resultant of the resistance of the air pass above the centre of inertia, as it does in the service bullet with a conoidal point, then the point of the projectile will move to the right, which brings the left side of the projectile obliquely in contact with the current of the air. The effect of this position with reference to the air will be to generate a component force that will urge the projectile to the right of the plane of fire. This peculiar deviation was called by the French officers that first observed it, “derivation,” or “drift.”
Summary of Deviating Causes.—The following summary may be considered as embracing nearly all the causes of deviation of cannon and small-arm projectiles: 1st. From the construction of the piece. These causes are, wrong position of the sight; bore not of the true size; windage, etc. 2d. From the charge of powder. Improper weight; form of grain and variable quality of the powder, etc. 3d. From the projectile. Not of the exact size, shape, or weight; disfiguration in loading, or on leaving the bore; eccentricity. 4th. From the atmosphere, etc. The effect of wind; variations in the temperature, moisture, and density of the air; position of the sun as regards the effect on the aim; difference of level between the object and the piece; and rotation of the earth. It is found that a projectile will deviate to the right of the object in the northern hemisphere whatever may be the direction of the line of fire, and at a distance from it, depending on the latitude of the place, and on the time of flight and the range of the projectile.
Projectiles, Effects of. The effects of projectiles, and particularly that of penetration, depend on the nature of the projectile, its initial velocity, and the distance of the object. The effects of the various kinds of projectiles upon iron and steel plates are not yet thoroughly understood, and experiments are still being made, particularly in England, to determine the best combinations of wrought and cast iron, and steel, to resist the penetration of the enormous projectiles of the present day. Their effects upon wood, earth, etc., are, however, better understood.
Effect on Wood.—The effect of a projectile fired against wood varies with the nature of the wood and the direction of the penetration. If the projectile strikes perpendicular to the fibres, and the fibres be tough and elastic, as in the case of oak, a portion of them are crushed, and others are bent under the pressure of the projectile, but regain their form as soon as it has passed by them. In consequence of the softness of white pine, nearly all the fibres struck are broken, and the orifice is nearly the size of the projectile; for the same reason the effects of the projectile do not extend much beyond the orifice; pine is therefore to be preferred to oak for structures that are not intended to resist cannon projectiles, as block-houses, etc.
Effect on Earth.—Earth possesses advantages over all other materials as a covering against projectiles; it is cheap and easily obtained, it offers considerable resistance to penetration, and to a certain extent regains its position after displacement. It is found by experience that a projectile has very little effect on an earthen parapet unless it passes completely through it. Wherever masonry is liable to be breached, it should be masked by earthworks with natural slopes. Gen. Gillmore states that the powers of resistance of pure, compact, quartz sand to the penetration of projectiles very much exceed that of ordinary earth, or mixture of several earths. The size of the openings formed by the passage of a projectile into the earth is about one-third larger than the projectile, increasing, however, towards the outer orifice. Rifle projectiles especially are easily deflected from their course in earth, hence their penetration is variable. Unless a shell be very large in proportion to the mass of earth penetrated, its explosion will produce but little displacement,—generally, a small opening is formed around an exploded shell by the action of the gas in pressing back the earth. Time-fuzes, being liable to be extinguished by the pressure of the earth, are inferior to percussion-fuzes, which produce explosion when the projectile has made about three-fourths of its proper penetration. The penetration in earth of oblong, compared to round projectiles, when fired with service charges, and at a distance of about 400 yards, is at least one-fourth greater. This difference, however, is less at short and greater at long distances. The penetrations of similar projectiles into a given substance, are proportional to the squares of the velocities of impact and to the diameters and densities of the projectiles.
Penetration in Water.—The penetration of a rifle projectile in water depends much on the direction of its axis with respect to penetration; for instance, penetration rapidly diminishes at long distances, as the axis of the projectile strikes the surface of the water under a diminished angle.