359 
= rich 
(a) Variations of loading densities and energy release. 
By interpolating between Kirkwood's curves(3) for T.N.T. density 1.59 and T.N.T. density 
1.40, we conclude that an overall reduction of the order of 10% should be made in the peak pressures 
for a density of 1.59 to compare them with a density of 1.50. This would give much better agreement 
with the step-by-step results, but we ought logically to apply a similar correction process to the 
T.N.T./Aluminium results, and this would worsen the agreement because Kirkwood's density is less. 
It is difficult to know how to correct Penney and Dasgupta's curve to allow for the fact that they 
assumed too small an energy content. The discrepancy in energy was 19%, so the discrepancy in peak 
pressure is unlikely to be more than 10%, and will probably be less, owing to the fact that the wastage 
of energy in the shockwave increases faster with peak pressure than does the energy given to the water. 
(b) Variations of the equation of state of the gas. 
We may deduce from Kirkwood's(2) work that variations in the composition, equilibrium, etc., 
of the exploded products makes relatively little difference to the pressure in the water. The 
step-by-step calculations give no evidence on this point. 
(c) Variations of the equation of state of the water. 
. 
It will be seen from Figures 3 and 5, comparing Penney's original work with the present 
calculations, that the peak pressure distance curve is only affected by the change in the equation of 
state in the region very near the charge. However, the pronounced minimum in the pressure-time curve, 
which was such a disquieting feature of Penney's original results, has disappeared. It was suggested 
by one of us that this minimum had appeared due to Penney’s original equation of state giving too small 
a compressibility of water at high pressures, which surmise seems to be confirmed. 
kirkwood's (3) work indicates that minor changes in the constants of the equation of state, due 
to temperature and salinity changes, are of practically no importance. 
(d) Variations of the assumed initial conditions. 
Figure 4 gives a straight comparison of our calculations with those of Penney and Dasgupta. 
Apart from the fact that the equation of state for the gas is slightly different, the only change that 
has been made is that we have replaced the “detonation wave" conditions by the assumption that the gas 
is initially at rest. It will be noted that Penney and Dasgupta's curve crosses ours twice, and this 
would remain true even if one made a correction of the order of 5 or 10% to allow for the energy 
difference already referred to. On account of the fact that higher peak pressure in the water involves 
a more than proportional rate of wastage of energy at the shock-front, it is clear that this phenomenon 
of crossing over is to be expected. In another report it has been suggested by one of us that an 
affect of this kind (different detonation velocities and pressures) may account for the anomalous results 
observed with Torpex and Minol ||, Torpex being apparently better at great distances, while Mino) 11 
gives bigger deflections on the box model (small distances). An attempt is made to correlate this with 
the detonation properties, Torpex being a sensitive explosive, whereas Minol || is difficult to detonate. 
(e) The effect of adding Aluminium. 
Neither our calculations nor Kirkwood's(2) throw any light on the question of whether or not the 
effect of aluminium is due to “after—burning", i.e., to the time of reaction of the Aluminium with the 
other explosion products being comparable with the time of expansion of the gas Subble. In the 
calculations of the adiabatics it is assumed that the reaction of the Aluminium is virtually completed 
before the expansion begins. Leaving aside this point, it is clear from Figure 3 and Table VI that 
Kirkwood finds that the addition of Aluminium has hardly any effect on the peak pressure but lengthens 
the time-constant, while we find an appreciable increase in the peak pressure but practically no effect 
on the time-constant. Indeed, at 5 charge radii the time-constant for the aluminised explosive drops 
below that for T.N.T., this presumably being associated with the fact that the ratio of peak pressure 
is increasing in this region. At 30 charge radii our curves for peak pressure are approaching one 
another rapidly. and we should expect this decrease in the peak pressure ratio to be associated with 
an increase in the ratio of time constants, although we have no definite figures to bear this out. 
\f so, it means that the step-by-step and Kirkwood methods give similar predictions at large distances, 
in agreement with the experiments, which indicate practically no effect of the Aluminium on the peak 
pressure, but an increase in the time constant. 
At weeee 
