1090 
pressures from ball crusher deformations used in this report is described 
in kef. 7, Appendix I. The equation for peak pressures from 3/8 inch 
copper balls is 
4 *n 
= 7-62 x 10 —_— 
¥ (6) 
where is an average deformation in inches of the four gauges in one 
block, and values for W, the relative response (as defined in Ref. 7), 
are based on the @ obtained from piezoelectric results (see Fig. 3). 
As can be seen from Fig. 10 the ball crusher peak pressures agree 
very well with the piezoelectric peak pressures in the lower portion of 
the curve, but they are about 11% lower than the piezoelectric at the 
highest pressures measured. Several considerations neglected in the 
above calculations may tend to lower the peak pressures calculated from 
large ball crusher deformations: 
(1) The calibration curve for the copper spheres is assumed to be 
linear throughout, although it deviates appreciably from the linear for 
deformations above about 0.09 inchese For shock waves of the type dis- 
cussed in this report, the time constant is of the order of 300 micro- 
seconds and the correction factor (%&) is approximately 0.80. Con- 
sequently, calculated pressure values above 8500 1b/in.? would be lowered 
by the assumption of a linear calibration curve. 
(2) The rate of strain increases with large deformations. 
(3) It is possible that, under the velocities of the piston attain- 
ed during deformation of the sphere, there could be an increase in the 
frictional effect sufficiently great to account for a part of this dis- 
crepancy. 
V. SUMMARY 
If the equations for peak pressure, impulse, and energy are re- 
presented by the equations; 
p= x W/S/pye (1) 
1 = y w/3 (wl/3/p)P (2) 
pe zwi/s (W/3/R) S (3) 
Table I shows a comparison of the parameters for TNT based on 
piezoelectrio and ball crusher gauge results from tests on spherical 
chargese The constants for the Kirkwood theoretical curves for TNT are 
also shown. 
