12 



THE DETONATION PROCESS 



front which throw considerable Hght on the matter. Before describing 

 his results it is worth-while to consider simpler arguments which have 

 been advanced to make the condition plausible and a natural assump- 

 tion. A rarefaction wave behind the front of a detonation wave travels 

 with the velocity c -\- u and if the velocity D of the front were less than 

 this any such wave could catch up with the front and weaken it. Such 

 a rarefaction will result if, for example, the detonation is initiated by a 

 piston which later comes to rest, and in general a rarefaction will result 

 from any cause which abstracts energy from the reaction products. 



Fig. 3.1 Rankine-Hugoniot curve for a detonation wave. 



Some such disturbance must therefore take place and unless the velocity 

 of the detonation front is at least equal to c -\- u it will be weakened by 

 rarefaction waves. The existence and maintenance of a detonation 

 wave therefore requires that D have a value equal to or greater than 

 c -\- u. 



The general picture is conveniently considered in terms of the pres- 

 sure volume diagram required by the Rankine-Hugoniot equations. 

 The actual computation of this P-V relation for practical explosives is 

 a complicated chemical problem, discussed briefly later in this section 

 and in section 3.3, which we assume here to give a result of the general 

 form indicated in Fig. 3.1. The point A representing the initial con- 

 dition of the explosive material must lie below the Rankine-Hugoniot 

 curve for possible states of the products after detonation. From Eq. 

 (2.29) the detonation velocity is related to the pressures and volumes 

 Po, Vo and P, V of the initial and final states by the ecjuation 



