130 



THEORY OF THE SHOCK WAVE 



MacDougall and Messerly of the shock front velocity near cyhndrical 

 sticks of 50/50 pentohte^ which agree within 3-6 per cent with vahies 

 predicted from calculated peak pressures over the range 1-6 charge 

 radii. The agreement is not necessarily this good, as the measured 

 velocities may have been somewhat low. 



iS£C/CM) 



10 QK 



(SEC /cm) 



3 10 30 100 



REDUCED DISTANCE R/Qq 



Fig. 4.4 Calculated time constants at the side of a cylindrical TNT charge. 

 The dashed hnes and dotted Hnes have the same significance as in Fig. 4.3. 



300 



4.5. Penney's Theory Based on the Riemann Equations 



The differential equations for finite amplitude spherical waves have 

 been solved numerically by Penney (83) and later Penney and Dasgupta 

 (85) in the case of TNT. As was shown in section 2.3(c), these equa- 

 tions can be reduced to a form convenient for stop-by-step integration 

 by use of the Riemann functions A^ and Q, defined as 



^ These experiments, carried out at the NDRC Explosives Research Laboratory, 

 are reported in UE Interim Report #13 (114). 



