52 Lecture 3 
At the Admiralty Research Laboratory the main use of explosion sources 
has been in the investigation of transmission loss. In order to deduce the abso- 
lute transmission loss from the signal level it is necessary to know the source 
level. One also needs to know the source differences between the charges of 
different sizes and types that may have to be used, together with the depth 
dependence of source level. Thus it became necessary to make a general study 
of explosion sources, including the measurement of absolute levels and differ- 
ences at various depths. 
It may be noted that the most important parameter is often the acoustic 
energy rather than the peak pressure, since the pulse energy should obey the 
same acoustic transmission laws as the intensity froma continuous wave source. 
The spectrum level of the acoustic energy which has flowed through a unit area 
is often quoted in db re 1 erg/cm*-cps. Actually, it is usually fp” dt (pis the 
pressure) which is measured, comparable to p* forthe C.W. source, and strictly 
speaking these quantities do not obey quite the same transmission law as energy 
or intensity (e.g., near a free surface). 
3.3. GENERAL IDEAS ON SCALING LAWS AND SPECTRUM SLOPES 
There is surprisingly little in the literature oncharge spectrum levels or on 
scaling laws, and what there is contains many misleading statements. Thus, the 
second part of the paper starts off with some general ideas which are applicable 
to any type of disturbance in a three-dimensional medium, and it is not essential 
to consider the mechanisms involved. However, to be specific, think of an explo- 
sion with charge weight W, so that total energy is proportional to W. Volume is 
also proportional to W, sothatthe linear scaling factor for both distance and time 
is w’%. More precisely one has identical pressure-time curves when these are 
plotted against reduced time tw /3 and measured at corresponding values of 
reduced range rW 4s This explosion-similarity principle is semitheoretical but 
confirmed by experiment. 
The scaling law may be applied to explosion spectrum levels, e.g., for a 
change from 1 1b to 50 lbwhere w'4 =3.68. It is necessary to make the additional 
assumption of spherical spreading, which leads to some appreciable though 
calculable errors, especially at the shorter ranges. Fig. 3.1 shows that the 
whole spectrum is shifted back in frequency by w 73 (3.68 in the example), 
corresponding to the w’4 time scaling. It is also raised in level by w’S (or 23 db 
in the example); the factor W comes fromthe change in total energy and the factor 
w’8 from the change in the bandwidth of any given portion of the spectrum. 
Consider now how the spectrum level depends on W at a given frequency. This 
dependency is a function of the spectrum shape, so that in general there is no 
simple scaling law for a fixed frequency. There is a simple law 
only in a region of constant spectrum slope (assuming a logarithmic plot), the 
index being the sum of the above 44 for general-level change plus the product of 
', (frequency change) times the index of the spectrum slope. Table 3.1 shows 
some of the important practical laws. 
To make use of the laws given in Table 3.1, it is necessary to know what 
spectrum slopes to expect, and Table 3.II illustrates some useful general rela- 
tions between pulse shape and spectrum slope, together with the predicted scal- 
