6.1.1 The
effects of a non-contact underwater explosion are described in Vol 1, Pt 4, Ch 2, 5 Underwater explosion (shock). Whilst the initial shock
wave described in that section initiates whipping to some degree it
is the pulsation of the bubble which leads to the majority of damage
to the hull. The initial shock wave causes local hull damage and shock
damage to the vessels equipment. In the strain history shown in Figure 2.6.1 Deck strains from hull whipping the initial shock wave
can be seen to be not just the free response of an elastic system
to an impulse as the amplitude continues to increase. There is a typical
second kick to the system which stems from the first bubble pulse
and which increases the response for several more cycles.
Figure 2.6.1 Deck strains from hull whipping
6.1.2 The
nature and behaviour of the gas bubble are dependent upon the warhead
charge size, the explosive composition, the detonation depth and the
influence of boundaries such as the sea bed.
6.1.3 The
maximum radius of the bubble at the end of the first expansion phase
is given by:
where
W
|
= |
bare
charge equivalent weight of TNT, in kg |
H
|
= |
depth
of the charge at the time of detonation, in metres. |
6.1.5 Even
a relatively modest warhead charge size can produce a bubble which
displaces a large mass of water in a very short time frame. The momentum
associated with this rapid incompressible flow of a sizeable volume
of water constitutes a major loading mechanism for any structure within
its sphere of influence.
6.1.6 The
effect on the hull is a large amplitude vertical bending and vibration.
This first introduces high shear forces at the quarter points which
may cause shear wrinkling, this damage will probably not be catastrophic
and the hull will go on to develop high compressive forces in the
keel. These may cause buckling especially as the bottom structure
may already be damaged from the initial shock wave. For extreme cases
whipping may lead to the ‘back breaking’ and total loss
of the ship.
6.1.7 An estimate
of the hull natural frequency for steel ships is given by:
where
L
OA
|
= |
the overall length of the ship, in metres. |
6.1.8 The
risk of a whipping response from a particular threat can be determined
using the approximation for the natural frequency and the bubble characteristics
of Vol 1, Pt 4, Ch 2, 6.1 General 6.1.4.
6.1.9 If the
threat is closer to the hull than 2R
bub then
the bubble loading is to be specially considered.