A History of Research and a Review of Recent Developments

158
Figure 7.16 Penetration simulation by SAMPLL (from Schoof et al., ref. 7.19).
A further investigation of the accuracy of Young’s equation was reported
in 1989 by Taylor and Fragaszy [7.20], who used a centrifuge to carry out soil
penetration tests at accelerations greater than 1 g. Spherical projectiles were
shot into clean quartz sand which was controlled tightly on density and
uniformity. The projectiles were made of brass, with diameters of 5.69, 7.82,
9.09 and 10.92 mm, and entered the sand at velocities of about 300 m/s. A
Thompson Contender pistol was used to fire the projectiles.
The authors questioned several features of Young’s equation (see Eq. (7.5)),
which, for velocities greater than or equal to 61 m/s, can be written as
p=0.117KSN(W p /A) 0.5 (V–30.5)
Penetration and fragmentation
(7.12)
(when p is in cm, Wp in kg, A in m 2 , V in m/s).
They were unhappy about the mass scaling factor, K, which they considered had
no theoretical basis, and they also questioned the dimensional correctness of the equation
and the exponent 0.5 used with the mass/area ratio. We have discussed earlier the
variation between Young’s work and other early theories with regard to this exponent.
They also felt the soil penetration index, S, was rather qualitative—a problem already
understood and discussed at the time when Young’s work was first presented.
As a result of about 80 centrifuge model tests, the authors produced the
following ‘best fit’ equations:
Dense Ottawa Flintshot sand,
p=0.00282(Wp/A) (7.13)
0.915 ,