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Assuming an evenly distributed charge and uniform casing wall thickness,
the following expression was developed for the initial fragment velocity
resulting from the detonation of a cylindrical container:
EQUATION:
Vo = (2E')1/2[W/Wc)/(1 + 0.5W/Wc>]1/2
(21)
where,
(2E')1/2
=
Gurney's energy constant, fps
W
=
weight of explosive (oz). In design calculations, W
= 1.2 times the actual explosive weight, as discussed
in paragraph 2 of this section.
Wc =
weight of casing, oz
Vo =
initial velocity of fragment, fps
(1) Figure 25 shows the variation of the normalized quantity
Vo/(2E')1/2, with W/Wc for this case. Table 2 contains expressions
for the initial velocity for other configurations. This table also contains
expressions for the velocity which is approached as a limit with increasing
values of the W/Wc ratio.
(2) An alternate fragment velocity expression was derived by R.I.
Mott, A Theoretical Formula for the Distribution of Weights of Fragments,
which gives a lower value for initial velocity than that predicted by
Gurney's equation. Therefore, for design purposes it is conservative to
base initial velocity calculations upon the Gurney equation.
b. Variation of Fragment Velocity with Distance. The primary concern
for design purposes is the velocity with which the fragment strikes the
protective structure. At very short distances from the detonation (about 20
feet), the striking velocity can be assumed to be equal to the initial
velocity. However, taking into account the effects of drag, air density,
and shapetoweight relationship, the striking velocity can be expressed as:
EQUATION:
Vs = voe kvRf
(22a)
where,
Vs = fragment velocity at a distance R from the center of the
detonation, fps
Vo = initial velocity of fragment, fps
Rf = distance from the detonation to the protective structure, ft
kv = velocity decay coefficient = (A/Wf)[rho]aCD
2.0844


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