But the shot advances during the combustion of the cordite, and the chief problem in interior ballistics is to adjust the G.D. of the charge to the weight of the shot so that the advance of the shot during the combustion of the charge should prevent the maximum pressure from exceeding a safe limit, as shown by the maximum ordinate of the pressure curve CPD in fig. 3.
Suppose this limit is fixed at 16 tons per sq. in., corresponding in Table 1. to a G.D., 0.2; the powder-gas will now occupy a volume b = 3/2 × C = 1825 cub. in., corresponding to an advance of the shot 3/2 × 2.15 = 3.225 ft.
Assuming an average pressure of 8 tons per sq. in., the shot will have acquired energy 8 × &FRAC14;πd2 × 3.225 = 730 foot-tons, and a velocity about v = 1020 f/s, so that the time over the 3.225 ft. at an average velocity 510 f/s is about 0.0063 sec.
Comparing this time with the experimental value of the time occupied by the cordite in burning, a start is made for a fresh estimate and a closer approximation.
Assuming, however, that the agreement is close enough for practical requirement, the combustion of the cordite may be considered complete at this stage P, and in the subsequent expansion it is assumed that the gas obeys an adiabatic law in which the pressure varies inversely as some mth power of the volume.
The work done in expanding to infinity from p tons per sq. in. at volume b cub. in. is then pb/(m - 1) inch-tons, or to any volume B cub. in. is
|m - 1||B|
It is found experimentally that m = 1.2 is a good average value to take for cordite; so now supposing the combustion of the charge of the 6-in. is complete in 0.0063 sec., when p = 16 tons per sq. in., b = 1825 cub. in., and that the gas expands adiabatically up to the muzzle, where
|(10)||B||=||216 + 25.8||= 3.75|
|b||2.5 × 25.8|
we find the work realized by expansion is 2826 foot-tons, sufficient to increase the velocity from 1020 to 2250 f/s at the muzzle.
This muzzle velocity is about 5% greater than the 2150 f/s of the range table, so on these considerations we may suppose about 10% of work is lost by friction in the bore: this is expressed by saying that the factor of effect is f = 0.9.
The experimental determination of the time of burning under the influence of the varying pressure and density, and the size of the grain, is thus of great practical importance, as thereby it is possible to estimate close limits to the maximum pressure that will be reached in the bore of a gun, and to design the chamber so that the G.D. of the charge may be suitable for the weight and acceleration of the shot. Empirical formulas based on practical experience are employed for an approximation to the result.
A great change has come over interior ballistics in recent years, as the old black gunpowder has been abandoned in artillery after holding the field for six hundred years. It is replaced by modern explosives such as those indicated on fig. 4, capable of giving off a very much larger volume of gas at a greater temperature and pressure, more than threefold as seen on fig. 8, so that the charge may be reduced in proportion, and possessing the military advantage of being nearly smokeless. (See Explosives.)
The explosive cordite is adopted in the British service; it derives the name from its appearance as cord in short lengths, the composition being squeezed in a viscous state through the hole in a die, and the cordite is designated in size by the number of hundredths of an inch in the diameter of the hole. Thus the cordite, size 30, of the range table has been squeezed through a hole 0.30 in. diameter.
The thermochemical properties of the constituents of an explosive will assign an upper limit to the volume, temperature and pressure of the gas produced by the combustion; but much experiment is required in addition. Sir Andrew Noble has published some of his results in the Phil. Trans., 1905-1906 and following years.
Tartaglia, Nova Scientia (1537); Galileo (1638); Robins, New Principles of Gunnery (1743); Euler (trans. by Hugh Brown), The True Principles of Gunnery (1777); Didion, Hélie, Hugoniot, Vallier, Baills, etc., Balistique (French); Siacci, Balistica (Italian); Mayevski, Zabudski, Balistique (Russian); La Llave, Ollero, Mata, etc., Balistica (Spanish); Bashforth, The Motion of Projectiles (1872); The Bashforth Chronograph (1890); Ingalls, Exterior and Interior Ballistics, Handbook of Problems in Direct and Indirect Fire; Bruff, Ordnance and Gunnery; Cranz, Compendium der Ballistik (1898); The Official Text-Book of Gunnery (1902); Charbonnier, Balistique (1905); Lissak, Ordnance and Gunnery (1907).
(A. G. G.)