AMIDE 17
16!1 , ,
15 :
steamengine, representing graphically by a curve CPD the relation between the volume and pressure of the powdergas; and in addition the curves AQE of energy e, AvV of velocity v, and MT of time t can be plotted or derived, the velocity and energy at the muzzle B being denoted by V and E.
After a certain discount for friction and the recoil of the gun, the net work realized by the powdergas as the shot advances AM is represented by the area ACPM, and this is equated to the kinetic energy e of the shot, in foottons,
(I) e=224 (1I d22tan2S) 2a,
in which the factor 4(k2/d2)tan2S represents the fraction due to the rotation of the shot, of diameter d and axial radius of gyration k, and S represents the angle of the rifling; this factor may be ignored in the subsequent calculations as small, less than 1 %.
The mean effective pressure (M.E.P.) in tons per sq. in. is represented in fig. 3 by the height AH, such that the rectangle AHKB is equal to the area APDB; and the M.E.P. multiplied by ;,rd2, the crosssection of the bore in square inches, gives in tons the mean effective thrust of the powder on the base of the shot; and multiplied again by 1, the length in inches of the travel AB of the shot up the bore, gives the work realized in inchtons; which work is thus equal to the M.E.P. multiplied by ird2l=B—C, the volume in cubic inches of the rifled part AB of the bore, the difference between B the total volume of the bore and C the volume of the powderchamber.
Equating the muzzleenergy and the work in foottons w V2 B C
(2) E=2240. 2g — I2 XM.E.P.
V2
w (3) M.E.P. = 2240 2g B?2C.
Working this out for the 6in. gun of the range table, taking L=216 in., we find B—C=61oo cub. in., and the M.E.P. is about 6.4 tons per sq. in.
But the maximum pressure may exceed the mean in the ratio 012 or 3 to I, as shown in fig. 4, representing graphically the result of Sir Andrew Noble's experiments with a 6in. gun, capable of being lengthened to 100 calibres or 50 ft. (Proc. R.S., June 1894).
On the assumption of uniform pressure up the bore, practically realizable in a Zalinski pneumatic dynamite gun, the pressurecurve would be the straight line HK of fig. 3 parallel to AM; the energycurve AQE would be another straight line through A; the velocitycurve AvV, of which the ordinate v is as the square root of the energy, would be a parabola; and the acceleration of the shot being constant, the timecurve MT will also be a similar parabola.
If the pressure falls off uniformly, so that the pressurecurve is a straight line PDF sloping downwards and cutting AM in F, then the energycurve will be a parabola curving downwards, and the velocitycurve can be represented by an ellipse, or circle with centre F and radius FA; while the timecurve will be a sinusoid.
300
250
200
1500
100
0.4 CORDITE
3000
 CORDITE rr_ 2800
03~ _ORDITE _~;36 CORDITE ~ . _. _ • —_
c . 2800
~  ~— p.2 CORDITE
~ _.  2400
4 CORDITE 2200
 
~_ 16—00
. 0.05
E CCORDITE
~~ ''
' RIFLORDITE
W 0.4 Cordite l 36 3
0.2 (0
r
(0
a J 1 CO
a 006 „ 86 a
Plugs 7 B 0 10 11 12 3 14 h Rifle
„ 9 „ I
15 to
8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 Velocity Curves, from Chronoscope experiments in 6 inch gun of soo calibres, with Cordite.
employed the steel spheres of bicycle ballbearings as safetyvalves, loaded to register the pressure at which the powdergas will blow off, and thereby check the indications of the crushergauge (Proc. R.S., March 1895).
Chevalier d'Arcy, 176o. also experimented on the pressure of powder and the velocity of the bullet in a musket barrel; this he accomplished by shortening the barrel successively, and measuring the velocity obtained by the ballistic pendulum; thus reversing Noble's procedure of gradually lengthening the gun.
But the most modern results employed with gunpowder are based on the experiments of Noble and Abel (Phil. Trans., 1875—1880—1892—1894 and following years).
A charge of powder, or other explosive, of varying weight P Ib, is fired in an explosionchamber (fig. 7, scale about g) of which the
0234 e 2 4 Travel in feet.
But if the pressurecurve is a straight line F'CP sloping upwards, cutting AM behind A in F', the energycurve will be a parabola curving upwards, and the velocitycurve a hyperbola with center at F'.
These theorems may prove useful in preliminary calculations where the pressurecurve is nearly straight; but, in the absence of any observable law, the area of the pressurecurve must be read off by a planimeter, or calculated by Simpson's rule, as an indicator diagram.
To measure the pressure experimentally in the bore of a gun, the crushergauge is used as shown in fig. 6, nearly full size; it records the maximum pressure by the compression of a copper cylinder in its interior; it may be placed in the powderchamber, or fastened in the base of the shot.
In Sir Andrew Noble's researches a number of plugs were inserted in the side of the experimental gun, reaching to the bore and carrying crushergauges, and also chronographic appliances which registered the passage of the shot in the same manner as the electric screens in Bashforth's experiments; thence the velocity and energy of the shot was inferred, to serve as an independent control of the crushergauge records (figs. 4 and 5).
As a preliminary step to the determination of the pressure in the bore of a gun, it is desirable to measure the pressure obtained by exploding a charge of powder in a closed vessel, varying the weight of the charge and thereby the density of the powdergas.
The earliest experiments of this nature are due to Benjamin
Robins in 1743 and Count Rumford in 1792; and their method volume C, cub. in., is known accurately, and the pressure ', tons per has been revived by Dr Kellner, War Department chemist, who ~ sq. in., was recorded by a crushergauge (fig. 6).
278
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
End of Article: AMIDE 

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