R. Meyer J. Köhler A. Homburg Explosives

25 Ballistic Bomb
z(p/pmax) = p/pmax/{1 + x(1 – p/pmax)} (4)
and
p(z) = F * z / (1 + xz). (5)
Accordingly, the maximum gas pressure achieved at the end of burnup
(z = 1) is calculated as
pmax = F / (1 + x). (6)
The dynamic liveliness L is calculated from
L = S(0) ˙e(pref)
* f(z) * *
V(0) pref [ p
pref] a–1 1 + x
*
(1 + xz) 2
S(0)/V(0) is the ratio of the initial surface area to the initial volume of
the powder,
f(z) is the shape function of the powder, which takes account of
the geometrical conditions (sphere, flake, cylinder, N-hole
powder) during the burn-up (f(z) = current surface area /
initial surface area)
˙e(pref) is the linear burning rate at the reference gas pressure pref
pref
is the reference gas pressure and
a is the pressure exponent, which for many powders is close
to 1.
To evaluate Eq. (7), z should be replaced by p/pmax using Eq. (4).
Figure 3 shows the time profile of the pressure in the manometric
bomb for a typical 7-hole powder. Initially the pressure is increasingly
steep, since burn-up takes place more quickly the higher the pressure
and in addition the burning surface of the powder becomes greater as
Fig. 3. Pressure-time graph p = f(t)
(7)