Page:Encyclopædia Britannica, Ninth Edition, v. 11.djvu/308

294 GUN MAKING [ORDNANCE. riflia; the bore the less is the breech pressure required to produce a given muzzle velocity, and the less is the maximum strain thrown upon the studs, gas check, or other rotating agent ; next, the more forward the general disposition of the metal, the farther from the breech end will be the centre of gravity, j and consequently the trunnions, a position which favours steady shooting and absence of jump; thirdly, a siege ! howitzer, being always fired under cover, is little exposed except near the muzzle, which should therefore be made as strong as possible to avoid injury from anything less than a direct hit by unburst shell. Rifling. Spherical projectiles fired from smooth-bored guns seldom or never pursue the mean trajectory. The centre of the ball s figure will rarely coincide exactly with the centre of gravity, and the pressure of the air during flight will then act with unequal effect on different parts of the surface. This inequality will be increased by accidental imperfections or roughness. The difference between the diameter of the bore and that of the projectile is termed " windage "; when this is considerable, it is a principal cause of error in shooting, as the ball rebounds from side to side against the walls of the piece as it is driven along, its actual direction of departure depending on the effect of the last bump before it leaves the muzzle. Accuracy of manufacture may greatly mitigate these errors, but will never entirely remove them ; it is therefore found necessary to cause the projectile to rotate rapidly round an axis coincident with the axis of the gun ; by this means the inequalities in the action of the pressure of the air, due to the imperfections above mentioned, take effect in all direc tions in turn as the projectile rotates, and hence neutralize ea^h other. Extending this principle, the stability im parted to a shot by its moment of rotation is such that elongated projectiles can be employed and driven point first j .at high speed through the air. The course of the projectile from the time of its leaving the muzzle to the end of its flight belongs to GUNNERY (q.v.). Here we have to con- Princi- sider the modes in which the interior of the gun is made to pies of impart rotation to the projectile. Rotatkm is usually ex pressed in angular velocity ; a shot is said, in popular language, to make so many turns per second. Mathemati cally, the unit of angular velocity consists of rotation through the unit of circular measure in one second; the unit of circular measure is the angle subtended by an arc equal to radius, viz., 57 17 44" 48" . If we call this angle w, a complete rotation will be expressed by 27rw. In consider ing the energy stored up in a shot s rotation, or, what is the same thing, the work done in producing that rotation, the weight of the projectile W, and its radius of gyration p, must be taken into account. The energy of a travelling body is ; the weight of a rotating one is supposed to be concentrated at the end of the radius of gyration ; then if O be the angular velocity, the velocity of a travelling body will correspond with pfi in a rotating one, and the energy W of rotation will be expressed by p 2 fi 2 . The propor tions of service projectiles differ for different guns, the thicknesses of sides and base and the shape of head varying ; but roughly for common shell the value of p may be taken as 40c (d = diameter), for Palliser projectiles as - 38cZ, and for shrapnel as 36c For artillery purposes a pro jectile is said to turn once in so many calibres, that is, to make one complete revolution in travelling a distance equal to so many times the diameter of the bore. Supposing a given length of groove in the bore to make a known angle with a line parallel to the axis of the gun, determining the arc through which the surface of the shot must turn while advancing the length of the groove, it is evident that the angular velocity attained by the shot will entirely depend on the velocity of translation or forward movement. Again, the greater the diameter of the bore the less will be the proportion borne by the arc turned through to the whole circumference ; consequently the bigger the gun the less the angular velocity of the projectile, if the angle of rifling and the velocity of translation remain constant ; the velocity of rotation of a point on the surface will, under these condi tions, always be uniform. It is generally considered that with studded muzzle-loading service projectiles, having a length equal to about 2 to 3 times their diameter, the velocity of rotation of a surface point of about 110 f. s. is sufficient to keep them steady, allowing for loss of spin by atmospheric friction up to any probable range. Supposing the interior of the gun to be opened out and laid flat, the groove (of a uniform twist) will be straight, and since the shot guided by it makes a complete revolution in n calibres, the angle made by the groove with a line parallel to the gun s axis may be expressed by tan -. In designing the ?t piece, the muzzle velocity is determined on, and also the velocity of rotation to be communicated to the projectile; the combination of the two fixes the final angle of the groove. Now it is easy to see that the spin of the shot on leaving the bore depends only on the conditions immedi ately preceding. The rate at which the work of giving rotation is done during the travel of the projectile from breech to muzzle is an entirely different question. If a shot be rotating, its tendency is, putting friction aside for the moment, to continue to rotate with the same velocity. No work is done in keeping up this rate of rotation, but work would be done in accelerating or retarding it. Thus in apportioning the work done on the shot in giving rotation Umf< at different parts of the bore, we have to consider, not the aiul i actual angular velocity, but the increments of angular "^ velocity. The work then can be distributed at pleasure over the whole length of the groove, by varying the angle it makes with a line parallel to the gun s axis, as it runs along the bore. Supposing, as before, the interior surface of the gun to be opened out and laid flat, then OU (fig 47) will represent a groove having a uniform twist, that is Fig. 47. making a constant angle with a line OM parallel to the axis of the piece. O denotes the commencement of the rifling at the breech end of the bore, UPM the muzzle. Guns are rifled with any number of grooves exceeding two, but it is not necessary to consider more than one. With the groove OU, every increment of angular velocity im parted to the shot is due to an increment in the velocity of translation ; and therefore the pressure between the sides of the grooves, and the studs, gas check, lead coating, or whatever fitting on the shot is employed for the purpose, bears a constant relation to the pressure of the powder gas on the base of the shot driving it forward. The table given below shows the result of this with great clearness. In order to mitigate the unevenness of strain, recourse was had to the increasing twist ; and a curved groove was employed which, when developed as in fig. 47, forms the parabola OP, begin ning at the point O, parallel to OM, and terminating at P, parallel to OU. The equation to OU is x=py that to OP is x 2 = py. Since OP is a parabola having its vertex

at O, and since the tangent at P is parallel to OU therefore