A History of Research and a Review of Recent Developments

20
The nature of explosions
Figure 1.8 Relationship between shock front velocity and peak overpressure (from
Rankine, ref. 1.3).
The duration of the positive phase, t 0, is a function of p 0 and the total
energy yield of the explosion. The end of the positive phase has an overpressure
of zero, which is the characteristic of a sound wave, since a sound wave has
no shock front and only infinitesimal changes in pressure amplitude. So the
zero overpressure condition must move away from the centre of the explosion
at the speed of sound in air. This is a lower velocity than the shock front
velocity, ū, and means that the duration of the positive blast wave increases
with distance, reaching a limiting value when p 0=0.
Typical values of t 0 for high explosives can be found from the formula
(1.22)
where t 0 is in milliseconds and W is in kilograms. As before, z=R/W 1/3 but in
these units R is in metres.
For nuclear explosions,
(1.23)
where t 0 is now in seconds and W is in kilotonnes. The units of R are metres.
These equations are rather complicated, and we must turn again to the
work of Dr Philip for a simpler formula. When she conducted the tests to