RIFLING.] GUN MAKING 295 UP = PM, which shows that the shot, though rotating in either case with equal angular velocity on leaving the muzzle, has, up to that moment, with the parabolic twist turned through an angle half as great as would be the case with the uniform twist. The table below exemplifies the principle on which curves of rifling are, or should be, constructed. The first three columns speak for themselves ; the fourth is arrived at by multiplying the area of the shot s base by the gas pressure per square inch recorded on the gauges, and given in the 5th column. Columns 6 and 7 are worked out from formulas due to Captain Noble of Elswick ; in column 6 the pressures due to a uniform twist are given. Prea It will be seen that they bear a constant proportion to the on pressures of the gas recorded in columns 4 and 5, and that S 100 the maximum rises to a considerable height soon after the shot has begun to move, while at the muzzle little work is done. In column 7 the calculations are made to suit a curve consisting of a portion of a parabola, starting from the vertex where the groove is parallel to the axis of the piece, and rising to the required twist at one foot from the muzzle, thence proceeding uniformly. In this curve the maximum strain is greatly reduced, the pressure gradually Table showing Pressures of Grooves on Studs in the 38-ton Gun, with various Curves of Rifling. Charge, 130 ft. Cubical Powder of l 25-inch edge. Projectile, 800 K>. Calibre, 12 "5 inches. Travel of Shot through Bore. Time of Travel. Velocity acquired. Pressure on Base SQuare mc h O f of Shot. Base Pressure on Studs with Uniform Twist of 1 turn in 35 Cals. Pressure on Studs, Parabola, Twist to 1 in 35 Cals. Pressure on Studs, Semi-Cubical Pura- bola, 1 in 200 Cals. to 1 in 35 Cals. ft.
sees. ooooo f.s.
tons. 2000 (estimated) tons. 16 3 tons. 79-3 tons.
tons. 31-4 1 00143 140 2221 -3 181 88-1 1-65 22-6 5 00273 474 3320-3 27-0 131-6 15-6 59-8 1-0 00360 676 2060-6 16-8 81-7 26 -3 61-3 2-0 00490 869 1394-1 11-4 55-3 421 65-1 3-0 00598 987 1095-0 8 9 43-4 531 66-3 4-0 00695 1074 908-8 7-4 36-0 61-95 66-3 5-0 00785 1142 746-4 6-1 29-6 687 85-0 6-0 00871 1195 668-3 5-4 26-5 75-0 647 7-0 00953 1242 592-8 4-8 23-5 80-3 63-9 8-0 01032 1277 499-4 4-1 19-8 83-3 61 9-0 01109 1309 421-9 3-5 16-7 86-2 58-95 10-0 01184 1335 355-6 2-9 14-1 88-2 56-6 11-0 01258 1355 265-1 2-2 10-5 88-1 53-95 12-0 01331 1369 1887 1-5 7-5 87-3 48-8 13-0 01404 1379 131-6 1-1 5-2 ( 86-4 ) ( 5-2 i U5-2) 1 5-2 | 14-0 01476 1385 120-9 I O 4-8 4-8 4-8 rising with the increase of twist. The figures are derived from another formula worked out by Captain Noble. Column 8 shows the pressures required to give the neces sary rotation when the curve of groove is a semicubical parabola, having for equation x% = py. In the instance chosen, the early part of the curve is rejected, and it starts from 1 turn in 200 cals., arriving at the required twist at a foot from the muzzle as before. The figures are derived from a calculation worked out on the principle devised by Captain Noble. Here the maximum is yet further reduced, and some approach to uniformity of strain is made. The diagram in Plate IV. shows the pressures graphically. Let R=- rotation pressure between studs and grooves ; G = gas pressure on base of shot ; yu = coefficient of friction ; h = pitch of rifling ; k = tan. of angle made by groove with plane traverse to axis ; <f> = angle turned through by shot ; 6 = angle made by groove with line parallel to axis ; p = radius of gyration ; z-= travel of shot along v = velocity of shot ; W M = mass of shot = ; r = radius of shot. Then in a uniform twist (z = bore ; in a parabolic twist in a semicubical twist hr(k - .G; 2V z p Vz(3Vz + 2>) Lieut Younghusband, E. N. , gives the following formula, which is applicable to curves of any equation, and will be found much handier than the above by those familiar with differential calculus :
rl + tan 2 0) - tan (r 2 - A radical difference exists between the rifling of muzzle- loaders and that usually employed for breech-loaders. When the projectile has to be pushed down the gun from the front, it must be smaller than the bore ; when it is thrust home from behind, it may be rather larger than the bore. Hence the earlier muzzle-loading shells were provided with ribs or studs which fitted in the grooves, and guided the projectile in its rotatory course ; while the earlier . breech-loading shells were coated with lead, into which the lands of the bore bit sharply as the powder gas forced the projectile between them. All rifled ordnance were formerly rifled with a uniform twist ; indeed, it is clear that where ribs are cast or fixed on the projectile, or where they are formed in the soft envelope by the first action of the grooves, no alteration in the angle of rifling is possible, since the ribs can only make a constant angle with a line parallel to the axis of the piece, and cannot fit a groove making a varying angle with it. The smaller and earlier muzzle-loading rifled projectiles were fitted with two rows of studs, front and rear, and equal in size, so that a front and rear stud travelled in each groove, and practically con stituted the ends of a rib. As the guns grew, it was found Mod that the great strain of giving rotation at starting fre- of g quently forced the bronze studs out of the recesses machined for them in the sides of the shells, and scooped away the driving edges of the grooves even when the gun lining was of steel. The shell might have been cast with ribs on them, but certain difficulties of manufacture stood in the way, and the excessive strain would still have ex isted though its effects might have been mitigated. The increasing twist was therefore devised, and the rows of studs increased in number from two to three in the larger natures of projectiles. Three studs are allotted to each
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