8J^ THE DETONATION PROCESS 



in calculating detonation front conditions with an equation of state 

 fitted to available phj^sical and chemical data other than values from 

 explosion measurements. The adiabatic relation for the burnt gases is 

 also obtainable from these calculations. The two sets of results will be 

 considered in more detail in sections 3.4, 3.5. 



C. The Wilson-Kistiakowsky equation of state. A somewhat dif- 

 ferent approach to the problem of the equation of state was developed 

 by Wilson and Kistiakowsky (64), who assumed an equation of the 

 form 



(3.14) PV = ^^ [1 + xe^-] 



with a; = Y.iNih/T^'VM) 



where Ni is the number of moles of product i, ki is an empirical param- 

 eter with dimensions of volume which may be called a covolume, and 

 a and jS are constants. In the original development, Wilson and 

 Kistiakowsky took a = 0.33, jS = 1.0, Y^Nrki = K, but better results 

 were later obtained using a = 0.25, /3 = 0.30. This form of equation 

 does not apply very well at low densities and it is therefore necessary 

 to determine the ki in some other manner than from the data at low 

 temperatures. Instead of fitting a form suggested by theory of solids 

 to compressibility data, as Jones does, a less fundamental but widely 

 appHcable procedure was adopted in which the h were determined to 

 give agreement with detonation velocities at a number of initial (load- 

 ing) densities for several explosives, a sufficient number being taken to 

 include significant effects of the various possible product species. (It 

 will be noted that the variation of D with the loading density should be 

 a good measure of the ki, as for perfect gas behavior with the kt all zero 

 the velocity is, from Eq. (3.13), independent of initial density.) 



Actual calculations of the detonation velocity, and values P and V 

 at the front, with this equation of state are carried out by numerical 

 methods which are too involved to be more than very generally de- 

 scribed here. The first step of the calculation is computation of a 

 hypothetical detonation velocity D* for products obeying the ideal gas 

 law, in the manner already outlined for gaseous explosions. In the 

 next step, the ratio D/D* is computed with the ideal gas results as a 

 starting point, using the equation of state (3.14) and corrected thermo- 

 chemical data. The equilibrium composition to be used is computed 

 from equilibrium constants versus temperature and stoichiometric con- 

 ditions by successive approximations or by approximate rules for the 

 reaction which give surprisingly good results. The pressure, density, 

 and particle velocity of the products also result from these calculations 

 and the properties of the front are thus all determined. 



