A History of Research and a Review of Recent Developments

174
Penetration and fragmentation
projectile speed do not produce a significant change in damage size. The maximum
lateral damage is a circle of radius 6 metres, when the impact velocity is just
over 1000 feet/sec.
Damage prediction techniques for fragments have only been properly
developed for high-velocity compact fragments of low density, typical of impacts
from surface/air missiles or high explosive projectiles. An expression proposed
by Avery, Porter and Lauzze is:
(7.29)
where L is the lateral damage size in inches; θ is the impact angle measured
between the flight path and a normal to the target surface; D is the maximum
projected frontal dimension of the fragment and t is the target thickness in inches.
7.5 FRAGMENTATION
Fragmentation was discussed in the previous section (7.4) in relation to the breakup
of the casing of conventional bombs, but the history of fragmentation analysis
is an interesting field in its own right. As before, students of the subject are indebted
to Christopherson [7.12], who dealt with advances in fragmentation prediction
during the Second World War. In 1943 Mott produced three research papers for
the UK Armament Research Department which included the theoretical treatment
of shell fragmentation (refs [7.60] to [7.62] inclusive). Mott argued that the number
of fragments (N) between mass W and W+dW should be given by
(7.30)
where M=W 1/2 and M A, B are constants for a given weapon. B was related to
the total fragmenting weight, W 0, by the equation , and the
parameter M A was given by M A=Gt 5/6 d 1/3 (1+t/d), where t=thickness of casing
(in) and d is the internal diameter (in). Experiments showed that for a TNT
filling inside a casing of British Shell Steel (carbon content approximately 0.4
to 0.5%), G=0.3. The fragment weights were measured in ounces.
It was pointed out by Christopherson that equation (7.30) and the formula
for M A were incompatible, but both had experimental support. The limited
range of weapons that could be examined by Mott’s theory was a greater
problem, and this was overcome by Payman [7.63]. His formula related the
weight of fragments (W) each of weight greater than w, to W 0 by the equation
–cw=log 10 W/W 0 ,
(7.31)
where the fragmentation parameter (c) was given by c=Kt –2.45 d –0.55 . The
coefficient K depended on the nature of the casing steel and the type of explosive.