237 
Sec. 11 -26- Eq. 83-8 
gases. The assumption was then tried that K is an additive function of K's 
characteristic of the different product molecules. The principal product 
species are No, CO, 05, COs, WhO, Hp and solid carbon. It was found that 
values of Ky. could be assigned to these substances so that very satisfactory 
agreement is obtained between the values of K obtained from the measured 
velocities and those computed from the additive rule: 
a 2 ae (3) 
Table 11-2 shows the nature of this agreement, while Table II of the 
Appendix gives the values of K, used. This success is quite pleasing since 
it gives us confidence that this method can be used to predict detonation 
velocities for other substances made of similar components. 
ad. Calculation of pressure, etc. Furthermore, this success gives us 
faith in the calculations of pressure, temperature, density and mss velocity 
in the explosion which can be made using the theory. The necessary auxiliary 
quantities K, x5, D etc., can be calculated theoretically from a knowledge of 
the composition as shown above, or if D has been measured for the given 
density, the following scheme may be used. First calculate Dy (see Sec. 
(9)). Then from D/D; work backwards in Table ILI (Appendix) to xo, Tp/To4 
and x,;. Then, from the definition of x , 
(iri 7) ea (84) 
The pressure can be obtained from either the equation of state 
Py = noRTnx(l4xe @*)/(xr” ™ ), (85) 
or from Iq. (42) 
Sep etna eerie (a) (850) 
which should give the same value (units are dynes/sq.cm if c,g,8, units are 
used for D, Py). 
he mass-velocity of the burnt gases is given by 
Up = D(1-x, /xz) (86) 
which comes from the law of conservation of mass, Iq. COs with U,=0. Values 
of Po, Up, and Tp for some important explosives are given in Table V of the 
Appendix. 
e. Limitations. It should be stated here that this method does not 
work too well when solids or liquids are present in the hot decomposition 
products. This means that the results are somewhat in error for TNT and TNB, 
for example. This defect can doubtless be eliminated and efforts are being 
made to do so, 
