Page:EB1911 - Volume 20.djvu/227

HISTORY AND CONSTRUCTION] resulting pressure on the engraved ribs of the driving band rises suddenly to a maximum which, in high velocity guns, the driving band is unable to resist. For this reason the straight portion at the commencement of the rifling has been discarded, and with high power guns firing a slow burning propellant uniform rifling has again found favour.

It is evident that in order that a projectile may have a definite amount of spin as it leaves the gun a determinate amount of work must be imparted to rotate it during its passage along the rifled portion of the bore. Put briefly, this work is the sum of the products of the pressure between the engraved ribs on the driving band and the lands of the rifling in the gun multiplied by the length of the rifling over which this pressure acts. Sir Andrew Noble has proved theoretically and experimentally (see Phil. Mag., 1863 and 1873; also Proc. Roy. Soc. vol. 50) that the rotating pressure depends on the propelling pressure of the powder gas on the base of the projectile and on the curve of the rifling. If this curve was so proportioned as to make the rotating pressure approximately constant along the bore, the result was an increasing or progressive curve partaking of the nature of a parabola, in which case it was usual to make the last two or three calibres of rifling at the muzzle of uniform twist for the purpose of steadying the projectile and aiding accuracy.

In uniform rifling the curve is a straight line and the rotating pressure is consequently mainly proportional to the propelling gas pressure. The pressure for rotation with uniform rifling therefore rises to a maximum with the propelling pressure and falls as it becomes less towards the muzzle.

With increasing rifling, owing to the angle of twist continually changing as the projectile travels along the bore, the ribs originally engraved by the rifling on the driving band are forced to change their direction correspondingly, and this occurs by the front surface of the ribs wearing away. They are therefore weakened considerably, and it is found that with high velocities the engraved part of the band often entirely disappears through this progressive action.

It will thus be seen that although an increasing twist of rifling may be so arranged as to give uniform pressure, it is evident that if wear takes place, the engraved rib becomes weaker to resist shearing as the shot advances, and the rate of wear also increases owing to the increase of heat by friction. With the very narrow driving bands used for low velocity guns this action was not so detrimental.

With the long modern guns and the high muzzle velocities required, the propelling gas pressures along the bore rise comparatively slowly to a maximum and gradually fall until the muzzle is reached. The pressure of the gas at all points of the bore is now considerably higher than with the older patterns of B.L. guns.

For modern conditions, in order to obtain an increasing curve giving an approximately constant driving pressure between the rifling and driving band, this pressure becomes comparatively high. The maximum rotating pressure, with uniform rifling, is certainly somewhat higher, but not to a very great extent, and as it occurs when the projectile is still moving slowly, the wear due to friction will be correspondingly low; the pressure gradually falls until the muzzle is reached, where it is much lower than with increasing rifling. The projectile thus leaves the gun without any great disturbance from the rifling pressure. Further, as the band is engraved once for all with the angle it will have all along the bore the pressure is distributed equally over the driving face of the engraved ribs instead of being concentrated at the front of the ribs as in progressive or increasing rifling.

The following formulae showing the driving pressures for increasing and uniform rifling are calculated from Sir Andrew Noble’s formula, which Sir G. Greenhill has obtained independently by another method.

Let R＝total pressure, in tons, between rifling and driving band. G＝gaseous pressure, in tons, on the base of the projectile. 𝑟＝radius, in feet, of the bore. ＝coefficient of friction. ＝radius of gyration of projectile. ＝angle between the normal to the driving surface of groove and radius. ℎ＝the pitch of the rifling, in feet. 𝑘＝cotangent of angle of rifling at any point of rifling. M＝weight of the projectile in pounds. 𝑧＝the length, in feet, travelled by the projectile.

Then for parabolic rifling

$$\text{R} = 2\rho^2(\text{G}z+\text{M}v^2)$⁄${\frac{(r^2 k^2+4\rho^2 z^2) \sin \delta}{(4z^2 \sin^2 \delta+k^2)^{\tfrac{1}{2}}} + \frac{2\mu_1kz(\rho^2 - r^2)}{(4z^2 + k^2)^{\tfrac{1}{2}}}}$|undefined$

For uniform rifling

$$\text{R} = 2\pi\rho^2\text{G}$⁄${\frac{\mu_1(2\pi^2k-rh}{(1+k^2)^{\tfrac{1}{2}}} + \frac{2\pi\rho^2+rhk) \sin \delta}{(k^2 + \sin^2\delta)^{\tfrac{1}{2}}}}$|undefined$

For modern rifling ＝90°; therefore sin ＝1; by which the above expressions may be considerably simplified.

For parabolic rifling

R＝$2^{2}(4z𝑧^{2}+𝑘^{2})^(G𝑧 + Mv^{2})⁄𝑘𝑟^{2}(𝑘−2_{1}𝑧)+2^{2}𝑧(2𝑧+_{1}𝑘)$.

For uniform rifling we can write ℎ𝑘＝2𝑟 and the expression reduces to

R＝$^{2}(1+𝑘^{2})^⁄_{1}(^{2}𝑘−𝑟^{2}⁄𝑘)+^{2}z)+𝑟^{2}$.G.

EB1911 - Ordnance Fig 31.png . 31 —Pressure Curves (uniform and increasing twist).

Fig. 31 shows graphically the calculated results obtained for a 4·7-in. 50-calibre gun which has a shot travel of 17·3 ft.; the pressure curve A is for a rifling twist increasing from 1 in 60 calibres at the breech to 1 in 30 calibres at the muzzle; curve B is for rifling having a uniform twist of 1 in 30 calibres.

It must be remembered that this comparison is typical for modern conditions; with old-fashioned guns firing black or brown powder the maximum rotating pressure for uniform rifling could attain a value 50% above that for increasing rifling.

In this example, with the increasing twist there is a loss of energy of about 11% of the total muzzle energy, and for the uniform rifling a loss of about 8%. This explains the reason for uniformly rifled guns giving a higher muzzle velocity than those with increasing rifling, supposing the guns to be otherwise similar.

The pitch of the rifling or the amount of twist to be given to it depends altogether on the length of the projectile; if this is short a small amount of twist only is necessary, if long a greater amount of twist must be arranged for, in order to spin the shell more rapidly. Sir G. Greenhill has shown that the pitch of the rifling necessary to keep a projectile in steady motion is independent of the velocity, of the calibre, or of the length of the gun, but depends principally on the length of the shell and on its description, so that for similar projectiles one pitch would do for all guns.

Table I., on following page, has been calculated from Greenhill’s formula.

In most modern guns the projectile varies in length from 3·5 to 4 calibres, so that the rifling is made to terminate at the muzzle with a twist of 1 turn in 30 calibres, which is found ample to ensure a steady flight to the projectile. In the United States a terminal twist of 1 in 25 calibres is often adopted; Krupp also uses this in some guns. With howitzers the projectile may be 4·5 calibres long, and the rifling has to be made of a quicker twist to suit.

If the gun has, as is usually the case, a right-hand twist of rifling the projectile drifts to the right; if it has a left-hand twist the drift takes place to the left. The drift increases with the range but in a greater ratio; further, the greater the twist (i.e. the smaller the pitch of rifling) the greater the drift. On the other hand the smooth B.L. projectiles drift less than studded M.L. projectiles.

To find the angle, usually called the permanent angle of deflection, at which the sights must be inclined to compensate for the drift, a number of shots are fired at various ranges. The results obtained are plotted on paper, and a straight line is then drawn from the point representing the muzzle through the mean value of the plotted curve.

The early guns were fired by inserting a red-hot wire into the vent, or by filling the vent with powder and firing it by a red-hot iron. Slow match held in a cleft stick afterwards took the place of the hot iron, and this again was replaced by a port-fire. Filling the vent with loose powder was inconvenient and slow, and to improve matters the powder was placed in a paper, tin or quill tube