The object of rifling is to cause the projectile to travel point first through the air without wabbling. To obtain this result, the form and twist of the rifling grooves, and the dimensions and position of the rotating band, must be such that the projectile leaves the gun with its axis practically coincident with that of the bore, animated with a rotation of suitable velocity about that axis, and having no other material angular velocity.
PITCH OF RIFLING.—The pitch of rifling is either constant, in which case its developed curve is a straight line, or increasing, in which case its developed curve is usually a parabola. It is usually defined by the number of calibers of travel along the gun's axis which would correspond to one complete revolution of the groove, as, for example, a rifling beginning with 1 turn in 180 calibers and ending with 1 turn in 30 calibers.
The final pitch which will insure stability in flight for any given projectile can only be fixed empirically: To compute its value we must know the moment of the total air resistance about a transverse axis through the center of gravity of the projectile, which we cannot with our present knowledge determine. In modern practice the final pitch of the rifling of high-power guns is I turn in from 30 to 25 calibers, the corresponding angle of the grooves with the axis of the bore being from 6° to 7°; while with guns used for high-angle fire it is somewhat greater, even as much as 1 turn in 15 calibers in the case of mortars firing very long shell.
EQUATION OF DEVELOPED GROOVES.—The first step in the rifling of a gun consists in laying down the developed curve of the groove, and for this purpose its equation must be found.
In a similar way the equation to the developed groove may be found if it is a circular arc, or has any other specified form.
The final pitch being fixed, two considerations should govern the selection of the curve of the rifling;—(1) The maximum Pressure between the driving edges of the grooves and the rotating band must not be so great as to shear or crush the bearing surfaces of the band; (2) the frictional resistance to motion along the bore caused by the rifling should be as small as practicable. So far as the strength of the gun is concerned the effects upon it of the forces developed by the action of the rifling are so small as to be negligible.
These conditions, however, are contradictory, since, as will be shown, the frictional resistance is least with a constant pitch rifling, while the maximum rotating force is least when the pitch increases at such a rate as to cause the rotating force to be constant.
THE ROTATING FORCE.—We will deduce the general expressions for the rotating force and the frictional resistance, and then apply them to particular cases.
Let m be the mass of the projectile, p its radius of gyration (about the axis of rotation), v its velocity of translation, w its angular velocity, and G the total pressure on its base; a being the radius of the bore, ? the inclination of the grooves, and ? the Coefficient of friction. Also let Q be the sum of the radial pressures between gun and rotating band (due to the compression of the latter), and R the sum of the tangential pressures, normal to the driving edges of the grooves, both these forces being uniformly distributed around the circumference.
THE FORCING.—Besides giving rotation to the projectile, the band serves the purpose of a gas check, preventing the free escape of gas past the projectile and the consequent loss of energy and rapid erosion of the bore, and to this end it is made of a diameter exceeding the diameter of the gun from groove to groove. Thus, in U. S. Naval guns, which have rifling grooves 0.05" deep, the diameter of the rotating bands is from 0.12" 10 0.16" greater than the caliber, with a view to their maintaining a close contact with the bottom of the grooves when the bore is expanded by the powder pressure.
The forcing of the band also serves useful purposes, (a) by delaying the first motion of the projectile until the pressure in the chamber has risen to a point which insures the complete inflammation of the charge, (b) by the hardening effect of the compression upon the metal of the band, increasing its resistance to the crushing action of the driving edges of the rifling. The increased muzzle velocity which results from excessive forcing can, however, be obtained with less strain upon the gun by the use of a quicker powder, and weakness of the rotating band is best remedied by increasing either its width or the number of rifling grooves.
The maximum diameter of the band, then, should only exceed the diameter of bore from groove to groove by an amount equal to, or very slightly greater than, the expansion of the bore under the action of the powder pressure, i. e. from 0.015" to 0.03" according to the caliber. Moreover, the width of groove should be at least twice the width of land, and the wider the rotating band the more important is it to make the lands narrow.
THE VALUE OF ?Q.—Such experimental measurements as have been made of the pressures required to force banded shell through the bores of rifled guns indicate very high values for the total radial pressure (Q) between bore and band, but to what extent this condition is altered when the bore is expanded by the powder pressure and when, instead of being very slowly forced into and through the bore, the projectile starts with a great acceleration and moves with high velocity, we do not know. There is little doubt, however, that in the case of many, if not most, guns and projectiles of modern design, a pressure in the neighborhood of two tons per square inch on the base of the projectile is required to force it into the rifling, and a pressure little if any below one ton per square inch to overcome the frictional resistance to its further motion through the bore, and this independent of the force required to overcome the friction caused by the rotating action of the rifling.
When the rifling is of increasing pitch, the distortion of the metal of the band due to the changing inclination of the lands must add considerably to the resistance to the motion of the projectile, but including this in the frictional resistance designated by ?Q, and supposing the latter to have a mean value of q tons per square inch of the projectile's base, we may say that with increasing pitch and considerable forcing the value of q is about one, while with uniform twist and the lightest practicable forcing its value is probably at least one-half.
EXPERIMENTAL DATA.—The following experimental results, bearing on the question of the friction caused by rifling, were obtained by Captain Noble. Three 12 cm. guns, alike in all other respects, were rifled with grooves of the same profile; one with no twist; the second with constant twist of I turn in 35 calibers; and the third with twist increasing from 1 in 102 to I iii 35 calibers, the developed groove being a semi-cubical parabola. As the mean of 15 rounds from each gun, using the same powder charge, the muzzle energies were respectively 1408, 1387 and 1356 foot tons, showing a loss of 1.52% due to the constant pitch rifling and a loss of 3.78% due to the increasing pitch rifling. The difference of energy in favor of constant over increasing twist, 31 foot tons, as will be seen from our previous discussion, is only partly due to the less friction from the rotating action; the greater part of the difference is probably due to the fact that with the constant twist no further distortion of the rotating band occurs after it has once fully engaged the rifling.
THE NUMBER AND DEPTH OF GROOVES.—AS a general rule the number of grooves is proportional to the caliber, and their depth is the same for all calibers; for example, the U. S. sea-coast artillery guns have six grooves per inch of the caliber, 0.06" deep, while U. S. naval guns have four grooves per inch of caliber, 0.05" deep. This practice, however, is only justifiable if the width of the rotating band is increased proportionally to the caliber. For, since the value of R increases with the square of the caliber, the bearing surface between band and driving edges should increase in the same ratio, which it does not do unless either width of band or depth of groove, as well as number of grooves, is made proportional to caliber.
This is the most serious objection to the use of increasing twist rifling, that with it a broad rotating band cannot be used without excessive frictional resistance and increased liability to stripping.
Slipping of the band in its seat around the projectile, as well as the stripping or shearing of its outer surface, must be prevented, and to this end the band seat should be scored, parallel to the axis of the projectile, with cuts or notches not greatly less in number and depth than the rifling grooves of the gun. The frictional resistance to slipping of the band is always very considerable, but it should not be relied upon altogether, even in the case of small caliber projectiles, much less in the case of those of large caliber. If the width of bands was proportional to the caliber, which the common use of increasing twist rifling has prevented from being the case, the radial pressure between bore and band would probably vary approximately as the square of the caliber, and then the frictional resistance to slipping of the band would have the same relative value for all calibers. Actually, the larger bands are relatively less wide than the smaller ones, and so the greater the caliber the less friction can be relied upon to prevent slipping.
THE POSITION OF THE ROTATING BAND.—Extensive experiments carried out under the direction of the Gavre Commission from 1876 to 188o showed that with the French guns and projectiles then in use the position of the rotating band had a marked effect upon both range and accuracy of fire. The guns used were of BD, 14, 16 and 24 cm. caliber, and for each of them the distance from base of projectile to rear edge of band which gave the best results was found to be from 38 to 42 mm. As a result of these experiments a distance from base of projectile to band of 1.5 inches has been adopted for all U. S. Naval projectiles (excepting for guns using fixed ammunition in which the insertion in the cartridge case governs the position of the band), and practically the same position of band is now almost universally used.
If a projectile has insufficient rotation when it leaves the gun, either because the final pitch of the rifling is too small or because the rotating band has slipped or stripped, the resistance of the air speedily gives it a wabbling motion, like that of a dying top, and the amplitude of this motion rapidly increases until, if the flight is long enough, the projectile tumbles end over end.
But this motion of precession which we call "wabbling" often occurs even when the velocity of rotation imparted by the rifling is known to be sufficient, though in such cases the amplitude of the motion appears not to increase during the flight of the projectile and the latter does not "tumble." If the rotating band is of inadequate strength, so that, though it imparts the full velocity of rotation, it is nearly stripped in so doing, and especially when the wearing away of the lands of the rifling at its beginning, due to continued firing of the gun, has increased the tendency of the band to strip (on account of the diminished hold of the rifling on the band), wabbling, accompanied by loss of range and accuracy, is sure to occur. Under such circumstances the sound which accompanies the projectile's flight ceases to be smooth and steady, and becomes harsh and undulating.
The wabbling motion just referred to is the result of the projectile's having an angular velocity about a transverse axis imparted to it in the gun, and the remedy lies in having a profile of rotating band which will offer great resistance to such angular motion. The greater the width of the band, the less likely is wabbling to occur, and, since very wide bands cannot well be used with an increasing twist, this is another important element of superiority of rifling of uniform pitch over that of increasing pitch.
CONCLUSIONS.—From the foregoing, the writer draws the following conclusions:
(a) Uniform twist rifling is superior to variable twist in all important respects, and should be adopted in our future gun construction.
(b) With a depth of groove of 0.03", four grooves to the inch of caliber is an insufficient number with the high muzzle velocities now common. We should increase the number of grooves in our guns to six to the inch of caliber.
(c) The width of the bearing surface of the rotating bands of our large projectiles (certainly the 12" and 13" and probably the 10" as well) is insufficient, especially when the rifling is somewhat worn by firing.
(d) Increasing the diameter of the rotating bands will to some extent produce the same beneficial effects upon flight as increasing their width, but the former will accelerate the progressive wearing away of the rifling bands. The diameter of the bands should be no greater than necessary to prevent escape of gas past them; their material should be pure copper, thoroughly annealed; and, if practicable, their rubbing surface should be lubricated during their passage through the bore.
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