Page:EB1911 - Volume 03.djvu/295

278
BALLISTICS

The result is plotted in figs. 8 and 9, in a curve showing the relation between p and D the gravimetric density, which is the specific gravity of the P lb of powder when filling the volume C, cub. in, in a state of gas; or between p and v, the reciprocal of D, which may be called the gravimetric volume (G. V.), being the ratio of the volume of the gas to the volume of an equal weight of water.

 Fig. 7.

The results are also embodied in the following Table:—

TABLE 1
G.D. G.V. Pressure in Tons per sq. in.
Pebble Powder. Cordite.
0.05 20.00 0.855 3.00
6 16.66 1.00 3.80
8 12.50 1.36 5.40
0.10 10.00 1.76 7.10
12 8.33 2.06 8.70
14 7.14 2.53 10.50
15 6.66 2.73 11.36
16 6.25 2.96 12.30
18 5.55 3.33 14.20
20 5.00 3.77 16.00
22 4.54 4.26 17.90
24 4.17 4.66 19.80
25 4.00 4.88 20.63
26 3.84 5.10 21.75
30 3.33 6.07 26.00
35 2.85 7.35 31.00
40 2.50 8.73 36.53
45 2.22 10.23 42.20
50 2.00 11.25 48.66
55 1.81 13.62 55.86
60 1.66 15.55 63.33

The term gravimetric density (G.D.) is peculiar to artillerists; it is required to distinguish between the specific gravity (S. G.) of the powder filling a given volume in a state of gas, and the specific gravity of the separate solid grain or cord of powder.

Thus, for instance, a lump of solid lead of given S. G., when formed into a charge of lead shot composed of equal spherules closely packed, will have a G.D. such that

(4) ${\displaystyle {\frac {\mbox{G.D. of charge of lead shot}}{\mbox{S.G. of lump of solid lead}}}={\frac {1}{6}}\pi {\sqrt {2}}=0.7403;}$

while in the case of a bundle of cylindrical sticks of cordite,

(5) ${\displaystyle {\frac {\mbox{G.D. of charge of cordite}}{\mbox{S.G. of stick of cordite}}}={\frac {1}{6}}\pi {\sqrt {3}}=0.9067;}$

 PRESSURES OBSERVED IN A CLOSED VESSEL WITH VARIOUS EXPLOSIVES Fig. 8.

At the standard temperature of 62° F. the volume of the gallon of 10 lb of water is 277.3 cub. in.; or otherwise, 1 cub. ft. or 1728 cub. in. of water at this temperature weighs 62.35 lb, and therefore 1 lb of water bulks 1728÷62.35=27.73 cub. in.

Thus if a charge of P lb of powder is placed in a chamber of volume C cub. in., the

(6) ${\displaystyle G.D.=27.73P/C,\quad G.V.=C/27.73P.\,}$

Sometimes the factor 27.68 is employed, corresponding to a density of water of about 62.4 lb per cub. ft., and a temperature 12° C., or 54° F.

With metric units, measuring P in kg., and C in litres, the G.D.=P/C, G.V.=C/F, no factor being required.

From the Table 1., or by quadrature of the curve in fig. 9, the work E in foot-tons realized by the expansion of 1 lb of the powder from one gravimetric volume to another is inferred; for if the average pressure is p tons per sq. in., while the gravimetric volume changes from v-½Δv to v+½Δv, a change of volume of 27.73 Δv cub. in., the work done is 27.73 p Δv inch-tons, or

(7) ${\displaystyle \Delta E=2.31p\Delta v{\mbox{ foot-tons}};}$

and the differences ΔE being calculated from the observed values of p, a summation, as in the ballistic tables, would give E in a tabular form, and conversely from a table of E in terms of v, we can infer the value of p.

On drawing off a little of the gas from the explosion vessel it was found that a gramme of cordite-gas at 0° C. and standard atmospheric pressure occupied 700 ccs., while the same gas compressed into 5 ccs. at the temperature of explosion had a pressure of 16 tons per sq. in., or 16×2240÷14.7=2440 atmospheres, or 14.7 lb per sq. in.; one ton per sq. in. being in round numbers 150 atmospheres.

The absolute centigrade temperature T is thence inferred from the gas equation

(8) ${\displaystyle R=pv/T=p_{0}v_{0}/273,\,}$

which, with p=2440, v=5, p0=1 v0=700, makes T=4758, a temperature of 4485° C. or 8105° F.

 PRESSURE IN A CLOSED VESSEL OBSERVED AND CALCULATED Fig. 9.

In the heading of the 6-in, range table we find the description of the charge.

Charge: weight 13 lb 4 oz,; gravimetric density 55.01/0.504; nature, cordite, size 30.

So that P=13.25, the G. D.=0.504, the upper figure 55.01 denoting the specific volume of the charge measured in cubic inches per lb, filling the chamber in a state of gas, the product of the two numbers 55.01 and 0.504 being 27.73; and the chamber capacity C=13.25×55.01=730 cub. in., equivalent to 25.8 in. or 2.15 ft. length of bore, now called the equivalent length of the chamber (E.L.C.).

If the shot was not free to move, the closed chamber pressure due to the explosion of the charge at this G.D. (=0.5) would be nearly 49 tons per sq. in., much too great to be safe.

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=3/2C=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 8×¼πd2×3.225=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.