An indicator diagram can be drawn for a gun (fig. 3) as for a
steam-engine, representing graphically by a curve CPD the relation between the volume and pressure of the powder-gas; and in addition the curves AQE of energy e, AvV of velocity v, and AtT 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 powder-gas as the shot advances AM is represented by the area ACPM, and this is equated to the kinetic energy e of the shot, in foot-tons,
| (1) e = | w | ( | 1 + | 4k2 | tan2 δ | ) | v2 | , |
| 2240 | d2 | 2g |
in which the factor 4(k2/d2)tan2δ represents the fraction due to the rotation of the shot, of diameter d and axial radius of gyration k, and δ 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 ¼πd2, the cross-section 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 l, the length in inches of the travel AB of the shot up the bore, gives the work realized in inch-tons; which work is thus equal to the M.E.P. multiplied by ¼πd2l = 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 powder-chamber.
Equating the muzzle-energy and the work in foot-tons
| (2) E = | w | V2 | = | B - C | × M.E.P. |
| 2240 | 2g | 12 |
| (3) M.E.P. = | w | V2 | 12 | . |
| 2240 | 2g | B - C |