Page 266 - Dynamic Loading and Design of Structures

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Figure 6.5 Overpressure and dynamic pressure positive phase duration versus range (Biggs, 1964).

first are k times those of the second, then the peak pressure ps0 measured at any distance R
from the centre of the first charge will be equal to those measured at distance kR from the
centre of the second charge. The +ve impulse, energy and duration of the second will be k
times the corresponding quantities for the first at these related distances.
The characteristics vary with the size of the explosive charge and it is experimentally
observed that if two spherical charges are made from the same explosive, then the peak
pressures in the air blast waves produced by these charges will be equal at distances that are in
the same ratio as the cube root of the weight of each charge when the atmospheric pressures
are the same in the two cases. This cube root scaling allows empirical charts to be published
from the results of experiments using a wide variety of charge sizes.

(2) Cube root scaling
Since densities are presumed to be equal for the two charges of the same explosive, if one is k
3
times larger in its linear dimensions then its mass will be k times greater and the principle of
similitude can be stated using the cube root of the mass as the scaling factor.
If the masses of two geometrically similar charges of the same explosive are M and M 2
1
then the peak pressures at distances proportional to (M1) 1/3 and (M2) 1/3, respectively will be
equal and are said to occur at homologous times (i.e. corresponding but not necessarily equal
times).