132 



THEORY OF THE SHOCK WAVE 



The solution after 27 steps for a charge of initial radius 30 cm. gave the 

 pressure distribution up to a time 700 ^isec. after detonation was com- 

 plete, at which time the shock front in the water had advanced to 174 

 cm. or approximately 6 charge radii. The shock wave at later times 

 was then estimated by approximate calculation of the "overtaking 

 effect," (see section 2.4), as a result of which the front of the wave is 



REDUCED DISTANCE R/a« 



Fig. 4.5 Pressure distribution around an 1,800 pound TNT charge, from 

 calculations of Penney and Dasgupta. 



determined by pressures behind the front at earlier times, the portions 

 nearer the front being lost by dissipation. The balance of the curve 

 was then estimated by assuming an acoustic decay with distance, and 

 the spreading of the wave predicted by the Kirkwood-Bethe theory is 

 therefore not taken into account. 



Penney' s original results were inaccurate because of the assumption 

 of adiabatic conversion for the initial conditions instead of the detona- 

 tion wave, and because the equation of state used for water was based 

 only on the available data at low pressures. An improved equation of 

 state was made possible by later data of Bridgman (see section 2.6). 

 Revised calculations were made by Penney and Dasgupta (85) using 

 this equation of state and initial conditions based on Taylor's calculation 

 of the spherical detonation wave in TNT (see section 3.6). The initial 

 pressure and particle velocity at the front of the shock wave shortly 

 after its generation were taken to be 60 kilobars and 1,420 m./sec, and 

 corresponded to a chemical energy of 800 cal./gm. of explosive. The 



