A History of Research and a Review of Recent Developments

The analysis of detonation and shock in free air 9
explosive gases escape and form an incandescent zone that expands so rapidly
that a shock wave or pressure pulse is formed.
Taylor wrote many valuable papers [1.7], [1.8] on the dynamics of shock
waves for the Civil Defence Research Committee in the early days of the
Second World War, and it is from these that much of the analysis has been
taken. His work was summarized lucidly by D.G.Christopherson in 1945
[1.9] and the latter’s summary has been consulted frequently by the author in
writing the chapters of this book. In the summer of 1945 Christopherson
wrote his seminal report on the structural effects of air attack, the information
having been collected during the Second World War by the Research and
Experiments Department, Ministry of Home Security, and much of it coming
from experiments carried out on behalf of that Department by the Building
Research Station and Road Research Laboratory. Contributions were also
drawn from the work of the National Defence Research Committee in the
USA. Christopherson’s report, entitled Structural Defence, covered every aspect
of the subject from the theory of blast waves in air, earth or water to the
general theory of structural behaviour and the design of protective structures
of all types. Christopherson was educated at Oxford, was a fellow at Harvard
and then a postgraduate at Oxford before joining the Research and Experiments
Department of the Ministry of Home Security in 1941. He left, after writing
Structural Defence in the space of two or three months after victory in Europe,
to join the Engineering Department at Cambridge University in 1945. Since
then he has pursued an illustrious academic career and has been a major
influence in the teaching of Engineering subjects in the universities, as well as
in the management and control of universities and colleges.
The form of the overpressure/duration relationship for a high explosive or
nuclear explosion in air is shown in Figure 1.1, where p is overpressure (or air
blast pressure) and t is time. In the figure the decay of pressure after the first
instantaneous rise is expressed exponentially. There are other ways of denoting
the form of the pressure/duration relationship, as we shall see later, but for the
purposes of this chapter Figure 1.1 will be adequate. The value of the peak
instantaneous overpressure p 0 will depend on the distance of the point of
measurement from the centre of the explosion. Using imperial units, in a TNT
explosion p 0 might be 200 or 300 psi at the point of burst of the explosion, but
would rapidly diminish with distance. In a nuclear explosion equivalent to 1000
tons of TNT, the peak overpressure would be 2000 psi at 30 metres from the
centre of the explosion. The duration of the positive phase is t 0 units of time.
Theoretically, for a perfectly spherical charge in air, the relationship between
p 0, the distance of the point of measurement from the centre of the explosion
(R), and the instantaneous energy release (E), takes the form
1.1)
so that an important non-dimensional parameter is p0R 3 p =KE/R
0
/E. In imperial units E
is measured in ft lb, and in SI units in joules. Experiments show that the explosion
3 ,