Sec. 9 -19- Eq. 52-54 
elements are present in the explosive) are formed, 
(4) Oxygen reacts quantitatively with carbon to form CO, the excess 
forms quantitatively H50 and what is left over reacts to form C05. 
The question of whether a real pressure and temperature range exists 
in which al}. these assumptions hold is entirely immaterial for the follow- 
ing, because D; and other "ideal" quantities resulting from these calcula- 
tions are merely convenient steps to reach the real detonation velocity D. 
The second step is the calculation of D/D,;. In this step any 
inadequacy of the conditions defining the ideal state must be corrected. 
The discussion in Sec. 7 shows that the ideal state should agree quite well 
with the real condition of the burnt gases except for the use of ideal gas 
behavior. 
b. Decomposition equations. The detailed procedure for the numerical 
calculation of D; will now be given. This is particularly simple for a 
special class of compounds with general formula 
C,H,O,N, such that a¢s¢2q + r/2. 
This class includes most of the common organic explosives, except TNT and 
nitroglycerin. Then the application of the general rules shows that such 
compounds will decompose according to one of the following equations. 
Cage A, a+ r/2 Ss. My = = (24+ r+ t). 
Cgl.Cgily = aCO + (q-str/2)iy + (s-q)Hp0 + t/2 Mo. (52) 
Case B, a+ r/2 6. » Np = 2 (2a+r+t). 
CgH.Ogl, = (s-q-r/2)COp + (2q-str/2) CC + 
(r/2)Hp0 + +/2 No. (53) 
For explosives not of this type the ceneral rules above must be applied 
in each case in order to determine the composition of the products. 
c. Heat capacity equations, In order to calculate the ideal temperature 
T,, it is necessary to lmow the mean heat capacity of the products as a func- 
tion of temperature. Tortunately the heat capacities of simple molecules can 
be calculated theoretically with considerable accuracy. The available 
information has been incorporated in empirical formulas of the type. 
= T 
rt ea os C,aT = AFBI, (OE) 
T-300 J, 
500 
in which A and B are numerical constants given in Table I of the Appendix. 
These equations are correct to about 1% for the temperature range 2000 to 
5000°. From these tabulated constants for the individual gases, constants 
A and B for the mixture can be obtained as explained in Table I. 
