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„ NRTp, I (ApJ Ă 1)
G 1 +(r-H»)“eXPL(r+e)*Jj • ()
The various factors influencing P in the K-W equation may be assessed more readily when it takes the form of Eq. (7), in which the kt terms are eliminated, than had been the case with Eq. (4). As an example, the dependence of P on T resulting from the use of Mader’s “RDX parameters” is evaluated at various loading densities in Appendix A for a special case of Eq. (7).
IV. THE RUBY COMPUTER CODE
With the advent of the new high-speed digital computers, several more sophisticated methods of predicting detonation properties of high explosives from the Kistiakowsky-Wilson equation of state have achieved wide acceptance. Two related programs, the stretch jbkw code for use on the IBM-7030 computer11 and the ruby code1 for use on the IBM-7090 provide the comparison information against which predictions from the equations offered in the present paper will be judged. For the purposes of present discussions, ruby results
Explosive15 Po ¦iVruby Mrubyc Qruby ¦^oelo •Pruby diff ^o»lc ^RUBY %
Eq. (8) Eq. (9) diff
HMX<* 1.903 0.0338 27,20 1496 384.7 391.3 -1.7 9.157 9.238 -0.9
RDXd 1.712 0.0339 27.15 1496 311.9 306.0 + 1.9 8.512 8.437 +0.9
TNT' 1.468 0.0263 27.94 1258 165,5 161.2 +2,7 6.512 6.446 +1.2
Tetryl*1 1,643 0.0276 30.06 1411 239.1 235.9 + 1.4 7.548 7.508 +0.5
Explosive De 1.720 0.0285 28.27 1098 231.4 227.3 +1.8 7.312 7.250 +0.8
Picramide8 1.770 0.0265 29.89 1250 250.0 245.6 + 1.8 7.541 7.392 +2.0
if-salt* 1.520 0.0345 23.08 1397 223.0 221.2 +0.8 7.478 7.444 +0.5
DINAd 1.660 0,0335 26.93 1450 284.2 276.9 +2.6 8.203 8.143 +0.7
*H. Hurwitz, Ref. 16.
b See Appendix II for glossary of compound names and molecular formulas.
* Mruby is calculated from the relationship M =(I —12 Nt)/N-R\jby. d Computer results based on RDX parameters.
• Computer results baaed on TNT parameters.
as determined at the Naval Ordnance Laboratory16 and stretch bkw results differ only in minor regards.17 Unless otherwise specified, therefore, the term ruby shall hereafter encompass the results of both systems and ruby computations shall be considered as based on Mader’s most recent parameters and covolume factors in Eq. (4), with the heat of formation of solid carbon taken as zero.
The ruby code finds “exact” equilibrium compositions of the detonation products by sophisticated multi-iterative processes involving minimization of the Gibbs free energy of the total system. Complex input equations, derived through the equation of state, relate free energies of formation of the potential detonation products to temperatures, pressures, covolumes, and the compressibility of solid carbon. The current codes are equipped to consider as many as 16 gaseous products and two solid phases; improved codes are being designed to accommodate sixty gaseous species and five solid phases.18
Several pages of print-out are associated with a single ruby computation. Reported together with Z>, P, T, and VK at a given p0 (loading density) are the following quantities: AEq, the chemical energy of the detonation reaction (~Q); Ej~Eq, the change in internal energy across the detonation front; pj, the Chapman-Jouguet density; JV, the total number of moles of gaseous detonation products per gram of explosive; the number of moles of the individual gas species; Ë7â, the number of gram atoms of solid carbon or other solids; V& the
uruby results referred to in the present paper are by H. Hurwitz of this laboratory and have not yet been reported elsewhere.
We are grateful to Mr. Hurwitz for making this information ajfeil-able.
17 For reasons which are as yet unresolved, however, ruby and stretch bkw, given the same input information for the same explosive at the same loading density, will report slightly different Chapman-Jouguet densities. Though small, the differences are significant in their effects on C-J pressures, the problem being more pronounced (differences of several percent in P) with under-balanced explosives at higher loading densities. Compare, for example, the results from Refs. 11 and 16 for HMX and TATB in Table VI.
18 Dr. L. Seely, Stanford Research Institute (private communication) .
solid volume per gram atom of carbon; and the “gamma law” constant, 7 = (—3 In P/ä lnF)s. Although only P, D, and possibly T are subject to relatively unambiguous experimental verification at the current “state of the art,” ruby’s predictions of other of the above quantities provide a framework upon which much of the subsequent discussion is based.
V. SIMPLE EQUATIONS FOR ESTIMATING DETONATION PROPERTIES
We have found that estimates of detonation pressure and velocity, corresponding surprisingly closely to ruby predictions, are possible for C-H-N-0 explosives by means of relatively simple empirical equations. These equations imply that the “mechanical” properties of the detonation depend only on the number of moles of detonation gases per unit weight of explosive, the average molecular weight of these gases, the chemical energy of the detonation reaction (Q=—AHo), and the loading density, with the dependence in each case being relatively simple. The equations take the forms