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X. A Method of Measuring th,- Pressure Produced in the Detonation of 

 Explosives or by the Impact of Bullets. 



/>'// BERTRAM HOPKINSON, F.R.S. 

 Received Octoter 17, Read November 27, 1913. 



THE determination of the actual pressures produced by a blow such as that of a 

 rifle bullet or by the detonation of high explosives is a problem of much scii-ntitir 

 and practical interest but of considerable difficulty. It is easy to measure the transfer 

 of momentum associated with the blow, which is equal to the average pressure 

 developed, multiplied by the time during which it acts, but the separation of theae 

 two factors has not hitherto been effected. The direct determination of a force acting 

 for a few hundred-thousandths of i second presents difficulties which may perhaps be 

 called insuperable, but the measurement of the other factor, the duration of the blow, 

 is more feasible. In the case of impacts such as those of spheres or rods moving at 

 moderate velocities the time of contact can be determined electrically with pomndambk 

 accuracy.* The present paper contains an account of a method of analysing experi- 

 mentally more violent blows and of measuring their duration and the pressures 

 developed. 



If a rifle bullet be fired against the end of a cylindrical steel rod there is a definite- 

 pressure applied on the end of the rod at each instant of time during the period of 

 impact and the pressure can be plotted as a function of the time. The pressure-time 

 curve is a perfectly definite thing, though the ordinates are expressed in tons and the 

 abscissae in millionths of a second ; the pressure starts when the nose of the bullet 

 first strikes the end of the rod and it continues until the bullet has been completely 

 set up or stopped by the impact. Subject to qualifications, which will l)e considered 

 later, the result of applying this varying pres- 

 sure to the end is to send along the rod a wave 

 of pressure which, so long as the elasticity is 

 perfect, travels without change of type. If the 

 pressure in different sections of the rod be 

 plotted at any instant (fig. l) then at a later 



time the same curve shifted to the right by a distance proportional to the time 

 will represent the then distribution of pressure. The velocity with which the wave 

 travels in steel is approximately 17,000 feet per second. As the wave travels over 

 any section of the rod, that section successively experiences pressures represented 

 * SEAUS, ' Proc. Camb. Phil. Soc., 1 vol. xiv. (1907), p. 257, and references there given. 



VOL. CCXIII. A 506. Publisl " d "P"*" 1 * J """ ry " 19U 



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