A History of Research and a Review of Recent Developments

48
The detonation of explosive charges
Their work was reported by the Office of Scientific Research in a series of
publications. Starting from slightly different assumptions, Kirkwood and
Brinkley [2.29] produced the formula
(2.15)
for R/W 1/3 >13 ft/lb 1/3 .
This gives good agreement with tests at the higher range of R/W 1/3 , because the
parameters of the theory were obtained directly from these tests. A comparison of
calculated pressures for TNT has been made by Cole [2.22] and is shown in
Figure 2.17. It was generally accepted that the Penney and Dasgupta analysis was
more satisfactory for calculating the initial formation conditions for the shock
wave. From Eq. (2.15) we can calculate impulse, which for R/W 1/3 >13 is given by
I=2.11W 1/3 /R (I in lb m · sec/in 2 ).
(2.16)
This equation is identical in form to that for explosions in air, see for example
Eq. [1.25], but the underwater impulse for the same charge is about thirty
times as large.
Kirkwood and Brinkley [2.29] calculated that the energy in the underwater
shock wave diminishes rapidly as the wave progresses outwards, about 30%
is dissipated within 5 radii of the charge and 48% within 25 radii. Energies
found from experimental pressure/time curves are generally 25% lower than
these calculations predict. The effect of substituting TNT with other types of
explosive was examined, and generally it was found that the differences are
Figure 2.17 Comparison of calculated pressures for TNT (from Cole, ref. 2.22).
R=distance travelled by shock wave; a 0 =original charge radius.