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APPENDIX VII 
Dynamic Calibration of Copper Crusher Spheres 
and Cylinders with Freely Falling Weights 
by P. Newmark and C. kh, Niffonegger 
Several sizes of steel weights were released by an electromagnet from 
various heights and allowed to fall freely on copper spheres or cylinders 
which in turn rested on a hardened stecl anvil. Plots of the energies re- 
quired to produce: given deformations Against the deformations are showm in 
Pigs. VII-2, VII-3, VII-). The curves fit quite closely the following em- 
pirical equations in terms of E = energy (ft-lb) and D = deformation (1073 in.), 
For 3/8-in. spheres, 
BE - (330D + 0.27D2)* x 107° 
for values of D = 0 x 1073 in. through 150 x 1073 in. 
For 5/32<in, spheres, 
E = (190D + 0,87D2)* x 1078 
for values of D = 30x 10"3 in, through 110 x 1073 in, For copper cylinders 
(0.33-in. diameter, 1/2 ine long), 
E = (700D + 0..6D2)t+6 x roma 
for values of D = 0 x 1073 4n, through 110 x 1073 in, 
The calibrations were made on the machine shovm in Fig. VIi-l, or on 
one similar to it. No significant differences could be noticed between the 
calibrations from different machines, provided the concrete base is suffi- 
ciently large. 
Weights varying from 1/h lb to 10 lb, dropped from heights up to ft 
wore used in the present calibrations, Strain rates varied from 18.1 sec= 
to 195.0 sce"+ for the cylinders and from 62.3 sec7l to 257.5 sec-l for the 
spheres. 
In almost all cases the taro fuces of the deformed specimens were not 
parallel, the extent to which the faces were not parallel varied. Micron- 
eter measurements of deformations were taken across the centers of the two 
faces, and were reproducible to a high degree. 
Rebounds of the weights were studied by motion pictures at a speed of 
6), frames/see and were found to be significant. As the energy availabe 
from the dropping weight just before impact (input energy) was increased, 
Sie 
