256 
Sec. 20 ~45- 
tabulate t/t' as a function of x for a fixed value of by (Cv /rR). From 
this and a knowledge of To and xo, T’ can be read. This table is found in 
the appendix (Table A-IV). Likewise, the variation of b, with temperature 
was ignored in computing log P/P’ as a fiumction of x from Eq. (136). This 
is also tabulated in the appendix (Table A-IV). From it and a knowledge of 
Po and xo , log P’ is read off. Hq. (157) can next be employed to obtain 
Uz as a function of x. The integral in Eg. (157) can be tabulated (Table IV), 
so that little labor is involved in carrying out these computations. When 
U3 and P5 have been computed for several values of x, Py oan be plotted 
against U3 , and this curve compared with the corresponding curve for shock 
waves. 
The approximation of ignoring the variation of heat capacity is probably 
not too serious. At the high temperatures involved the variation is not 
great; furthermore its effect partly cancels out. 
e. A sample calculation. As an example consider tetryl at_a density 
of 1.2 g./ec. Here M = 267, h = 11.5, Ty = 3950 and D,; = 2.35 10° om./sec., 
according to the methods of Part II. We could also compute the other re- 
quired properties theoretically but to avoid compounding errors, it is better 
to make use of the measured detonation velocity, D = 5.9 x 10°, at re = 1.2. 
Then D/D, = 2.50. Examination of the heat capacity of the products shows 
that Table A-ITI with Cyi = 7 is the right one to use, whence we get x; = 
1.67 , Xo = 2.246, To = 3520. From 4 (850), Po = 10.7',x 101° dynes/s4. 
cm» (over 10? atm.?). Then using Table A-IV we get log P = 8.22427] and 
T' = 1180. Also w = 1.51 x 102 cm./sec. from Eq. (86). 
These numbers may now be inserted in Eq. (137), mking use of Table 
A-IV to obtain the values of the integral. The result is a Table of values 
of UZ against the final x. From Table A-IV also one can obtain log 3 vs x 
knowing log P’. Therefore log Ps can be plotted against Uz , a8 shown in 
Fig. 20-1. On the same plot is shown 1 vs for the shock wave in 
air, these points being from Table 16-1. he intersection of the shock 
wave curve with that for the burnt gases gives the predicted mass-velocity 
» which enables D' to be found, again from Table 16-1. The result in 
this case is D' = 7' 50 meters/sec. for air. The experimental value is 
7900 me /sec. It should be emphasized that these are only the initial 
shock wave velocities; they will decrease as the shook wave proceeds. 
f. Other results. Little experimental data exists with which to 
compare calculations of initial shock wave velocities. Some of the avail- 
able data is summarized in Table 20-1 below, together with the velocities 
computed as above. The agreement is all that could be expected. 
Table 20-1. Calculated and observed Initial Shock Wave Velocities in Air. 
(Experimental results from Cairns )3 
Explosive Density D'calc.: D'obs. $ 
PETN 0.5 6120 6500 5.8 
¥ 1.2 7880 8100 Ay 
Tetryl 1.0 7500 7700 2.6 
es 1.2 7730 7900 2.2 
* For values beyond the limits of Table 16-1, the table in Sec. 4b was 
provisionally used. 
