THE DETONATION PROCESS 85 



This method has been extensively applied to a number of organic 

 explosives at various densities with results that agree with experimental 

 detonation velocities to within experimental errors in nearly all cases. 

 The other calculated quantities are not readily determined with any 

 accuracy experimentally, and it is therefore difficult to judge how good 

 the computed pressure, etc., are. The assumed reactions for specific 

 explosives, comparison of experimental and calculated values for det- 

 onation, and the consequences of the results in determining the form 

 of the detonation wave and the initial conditions of an underwater ex- 

 plosion will all be dealt with in more detail in section 3.4. 



3.4. Calculated Conditions at the Shock Front 



In section 3.2 it was shown that from the point of view of hydro- 

 dynamics the progress of a detonation wave in an explosive is described 

 by the conditions of conservation of mass, momentum, and energy of 

 the explosive material as it changes from its initial condition to the re- 

 acted products on passage of the detonation wave. The further Chap- 

 man-Jouget condition relating the velocity of the front to properties 

 behind the front then fixes the detonation conditions at the shock front 

 in terms of the pressure-density relation for the products and the chemi- 

 cal energies (heats of formation, specific heats) involved in the reaction. 

 The detailed calculation of the velocity and initial state (pressure, vol- 

 ume, temperature) immediately behind the front is then possible for 

 specific explosives if sufficient chemical data are available. An exact 

 development from these principles is not possible because of two diffi- 

 culties: inadequate knowledge of the properties of gases at the high 

 pressures and temperatures existing behind the detonation front, and 

 difficulty of accounting exactly for the variety of molecular combinations 

 possible. The first of these difficulties is perhaps the more serious 

 fundamentally, although the second presents the problem of determin- 

 ing with a tolerable amount of effort a reasonable final composition. It 

 has already been suggested that the composition in chemical equilibrium 

 at the final pressure and temperature is a plausible approximation on 

 the basis of detonation velocity in gaseous mixtures, and for want of re- 

 action rate data to suggest a better criterion, this condition has been 

 assumed in the calculations to be described. 



Two approaches to the determination of a suitable equation of state 

 were outlined in section 3.3. The first is the approximation of Jones 

 for TNT in which interaction effects of all molecules in dense phases 

 were taken to be the same and represented by an equation suggested by 

 the theory of solids fitted to experimental data for nitrogen, the pres- 

 sure-density relation at lower pressures being represented by a virial 

 equation. The second procedure, developed by Brinkley and Wilson 

 (11), uses an empirical equation of state in which "covolume" constants 



