A History of Research and a Review of Recent Developments

144
Penetration and fragmentation
penetration and V. On this basis, Young discussed the following equation for
penetration into soil:
(7.5)
The units are reconciled in the constant terms 0.53 and 0.0031.
S is the soil constant and N a nose-performance coefficient, which takes
account of the nose shape, ranging from a flat nose (N=0.56), to a cone shape
having a length of cone equal to three times the diameter (N=1.32). Note
that, contrary to the theories of Poncelet and Perry, penetration in soil is
proportional to (Wp/A) 1/2 rather than Wp/A. Values of S and N were found
experimentally, and linked to broad ranges of soil type thus:
Rock: S=1.07
Dense, dry silty sand: =2.5
Silty clay: =5.2
Loose, moist sand: =7.0
Moist clay: =10.5
Wet silty clay: =40
Soft wet clay: =50.
Thus, all other things being equal, penetration in soft wet clay is about 50
times as far as in rock, and about 20 times as far as in dense, dry, silty sand.
Typical values of N are:
Flat nose N =0.56
Tangent Ogive 2.2 CRH =0.82
Tangent Ogive 6 CRH =1.00
Cone (L/D=3) =1.32.
Care must be taken not to give these figures a greater scientific accuracy than
they merit, since the scatter of penetration test results is notoriously wide.
Experimental data exists on penetration depths up to 220 feet and in Young’s
equations there is apparently no upper limit to the value of p for penetration
into homogeneous soil. There is a lower limit, however, and it is suggested that
the equations apply as long as the total depth of penetration is equal to ‘three
body diameters plus one nose length’. At lesser depths the mechanics of penetration
are not fully activated. Further, if the nose length is more than one-third of the
total penetrator length there is insufficient length of cylindrical section to ensure
stability, because the centre of gravity of the penetrator is too far aft.
It is useful to note that the practical range of Wp/A is fairly limited, and
ratios greater than 15 to 20psi are difficult to achieve. For solid steel, to take
an extreme example, a billet having a diameter 4 in and a length of 60 in, has
a value of Wp/A=17. There is also a practical range for velocity, V, in Young’s
equations. He suggests that at impact velocities less than 105 ft/sec, the
penetration depth is too shallow for reliable analysis.