DESIGNING.] GUN MA KING 293 Let W = weight of projectile in tons ; r = radius of do. in inches ; v = velocity of do. in feet per second ; Vv 2 = energy of do. in foot tons t = thickness of plate perforated in inches; then 1-xr This formula tells the gun-designer what energy is neces sary to overcome the resistance of the plate. Guided by experience, he assumes for the moment a striking velocity; the other component of the energy, the weight of the projectile, is then directly arrived at. The proportions of armour-piercing shell are the same for all guns, so that the weight guides the dimensions, and the calibre of the gun follows. Should this appear to be in no way unsuit able to the length already laid down in the conditions, the gun-designer calculates the loss of velocity in the given range and from the striking velocity deduces the muzzle velocity and the muzzle energy. The excellent Work labours (Researches on Explosives) of Captain A. Noble, lone by F.R.S., of Elswick, and Professor Abel, F.K.S., have shown in ~ how to calculate the amount of work done by a pound of powder for every volume of expansion its gas undergoes; the results of many careful experiments and much intricate calculation are embodied in the accompanying table, which B B ~C~ Total work Gun c Total work Gun where B=content powder is capable where B=content powder is capable of bore in cub. in., of performing per of bore in cub. in., of performing per and C=vol. of Ib of charge burned. and C=vol. of Ib of charge burned, charge at 277 in foot -tons. charge at 27 7 in foot-tons. cub. in. per Ib. cub. in. per Ib. TOO o-o 4-0 82-1 1-02 1-9 4-5 87-1 1-04 3 8 5-0 91-4 1-06 5-5 5 5 95-2 1 -OS 7-2 6-0 98-6 1-10 8-9 6-5 101-7 1-1-2 10-4 7-0 104-6 1-14 11-9 7-5 107-2 i-16 13-3 8-0 109-6 1-13 14-7 8-5 111-8 1 "JO 16-1 9-0 113-9 1-25 19-2 9-5 116-0 1-30 22-1 10-0 117-8 1-35 24-9 11-0 121-2 1-40 27-4 12-0 124-2 1-45 29-8 13-0 127-0 1-50 32 -0 14-0 129-6 1-55 341 15-0 132-0 1-60 36-1 16-0 134-2 1-70 39-8 17-0 136-2 1-80 43-1 18-0 138-1 1-90 4G"2 19-0 139-9 2-00 49-1 20-0 141-6 2-50 60-6 25-0 149-0 3-00 69-3 30-0 154-8 3-5.0 76 -3 35-0 159-7 affords the means of determining the total work performed by any charge in any gun. A certain portion of this work is expended in heating the gun and projectile, in giving rotation, and so forth ; the remainder appears as the energy of translation of the shot on leaving the muzzle. Large guns realize a greater proportion of the total work than small ones ; the gunmaker knows very approximately by experience what percentage may be expected from certain classes of ordnance with certain descriptions of powder. Roughly the factor of effect may be put within the following limits: for mountain guns, 45 to 50 per cent ; field guns, 60 to C5 per cent.; medium guns, 70 to 80 per cent.; heavy guns, 85 to 95 per cent. The method of calculation will be best understood from an example. Suppose a charge of 425 ft> of P 2 powder is to be fired from the SO-ton gun chambered to 18 inches diameter; the projectile weighs 1700 ft>, and the space behind it is 14,450 cubic inches. The whole content of the bore is 60,400 cubic inches, and the volume of the charge is (425 x 27 7) 11,773 cubic inches, the number of expansions therefore is 5 13 ; the table shows that powder gas expanding to this extent from a density equal to that of water can perform work amount- ing to 92 4 foot-tons per ft). Since, however, the charge burns up in and has to fill (425 x 34) 14,450 cubic inches before doing work, the energy due to this extent of expan sion (1-227) is lost, and 17 7 foot-tons per ft) must be deducted, leaving (92 4- 17 7) 74 7 foot-tons per ft) as the total work the charge is capable of performing under these conditions. It is known from the preliminary tests of the powder that in the 80-ton gun between 92 and 95 per cent of the total work will be realized. Hence the energy of the projectile will lie between 29,210 and 30,155 foot-tons, and its muzzle velocity between 1581 and 1600 f. s. A reference to the table on p. 292 will show that the result actually arrived at lies nearly midway between these limits. In this manner the charge required to impart the necessary energy to a shot of given weight hi a given length of bore, and, conversely, the length of bore which will contain the re quisite number of expansions of a given charge, are easily found ; hence the charge required to produce the necessary energy is readily found ; the air-space and the dimensions of the powder chamber follow, and the inside of the gun is settled. The gun designer now has to put walls round his bore. Guided by the knowledge previously mentioned as derived from the crusher gauge and the chronoscope, he lays down the pressures at each point of the interior, and calculates the amount and strength of the metal to be used, according to the special system of construction employed, and thus the exterior of the gun is settled. To give another instance : let it be required to construct the most powerful howitzer that can be made for the siege train. The conditions are given thus : recoil (of piece only) must not exceed 20 feet per second ; weight of piece must not exceed 70 cwt.; limiting purposes are to breach at 1500 yards, with not more than 5 elevation, and to bombard at 5000 yards, with not more than 35 elevation. A piece weighing 70 cwt. and running back at 20 f. s. velocity gives 156,800 units of momentum (in pounds and foot- seconds); the initial momentum of the gun in recoiling is practically equal to the momentum of the shot on leaving the muzzle. Hence the shell must have 156,800 units of momentum, which may be composed of high velocity and light weight, or low velocity and heavy weight. For breaching purposes, accuracy and penetration are essential qualities ; a shell varying in length from two and a half to three times its diameter will be suitable for the purpose. We have now a neat problem in ballistics, viz., To find the calibre of a shell of the proper length, of such a weight that, with the muzzle velocity required to give a range of 1500 yards at 5 elevation, the muzzle momentum shall be 156,800 units. This problem is readily solved by the methods indicated in the article GUNNERY, and it is found that a shell 80 in. in diameter, weighing 170 ft), and having a muzzle velocity of 940 f. s., will be slightly on the safe side of the limits. Proceeding in a similar manner, a shell 8-0 in. in diameter, weighing 230 ft), starting with a velocity of 675 f. s., satisfies the conditions of bombard ment. The calibre being thus settled, the proportions of the piece remain to be worked out. As there is no difficulty in obtaining a velocity so low as 940 f. s. with a small charge and low pressure, the length of the bore and the disposition of the metal can be adjusted to suit, not only the strain of discharge, but the conditions of service. In the gun now under consideration, the bore is made as long as possible, and the weight of metal thrown as far forward as possible consistently with preserving due strength at the breech. The reasons for this are threefold : finst, the longer Actic f d <
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