MEASUREMENT OF PRESSURES 151 



mine Pm as a function of kSm and the product oid. In this apphcation, 

 the gauge gives a measure of peak pressure provided d is known at least 

 approximately. The ratio tm/Trj^ = co/^/tt and the deformation fac- 

 tor Pm/kSm are plotted in Fig. 5.2 as a function of cod. It is seen that 

 if cod is not too small the deformation factor is not too sensitive to vari- 

 ations in 0^6. Hence, although the gauge does not, strictly speaking, 

 measure peak pressure Pm without a priori information about 6, it per- 

 forms this function reasonably well for sufficiently large charges if 6 is 

 known approximately. 



Several complications have been tacitly ignored in the simple dis- 

 cussion of the ball crusher gauge which complicate the reduction of its 

 readings to more fundamental quantities. It has been assumed that 

 the pressure P(0 acting on the gauge is the same as the free field pres- 

 sure which would exist in the absence of the gauge and diffraction effects 

 due to its presence are thus neglected. The magnitude of these effects 

 has been estimated both theoretically and experimentally, with indi- 

 cations that they are not serious for conditions in which the gauge re- 

 sponds primarily to peak pressure. A second source of difficulty is the 

 fact that the deformation of the copper crushers depends not only on 

 the magnitude of the force but on the rate of its application, experi- 

 mental itests by Seitz et al. (100) indicating that this "speed effect" may 

 increase the constant k by as much as 15-20 per cent for strain rates 

 {1/S)AS/At of the order 1,600 per sec. Corrections can be made on 

 the basis of such tests but the existence of the effect makes the interpre- 

 tation of observed depressions more uncertain. A third difficulty is the 

 assumption of a specific form of pressure-time curve. While an ex- 

 ponential decay is certainly the best simple mathematical description 

 of a shock wave in water, it is by no means true that it is always a good 

 one. For example, the pressure-time curves in certain directions around 

 cyHndrical charges have multiple peaks (see Fig. 7.15, Chapter 7). The 

 response of the gauge to such pressure could in principle be computed 

 from the known form of the curve, but this approach obviously con- 

 stitutes an investigation of the gauge rather than the pressure acting 

 on it. 



As a purely empirical device for comparison of different explosives 

 or different conditions, the ball crusher gauge has very real value be- 

 cause of its reproducibihty and simplicity in use and because one has at 

 least a rough picture of what it is measuring. Comparison with the 

 more detailed results obtained by electromechanical gauges which give 

 a continuous record of pressure have confirmed the essential validity of 

 the simple theory presented here. With this background the ball 

 crusher gauge forms a useful tool in explosive investigations.^ 



3 Detailed discussions of the use of ball crusher gauges and precision of measure- 

 ments are given in reports by J. S. Coles (22), and by R. H. Brown (12). 



