552 
a he 
by the impact of fragments of the charge case against the pressure end of the bar. 
Discussion of the results and compartson with theory. 
The results of the experiment within the limits t = 0.035 and t = 0.143 milliseconds can be 
compared with previous calculations of Penney and of Penney and Dasgupta. The Calculations given 
relate to a spherical charge of T,N.T. of radius 50 cm, packed to a density of 1.5 gm./c.c.; with 
this value for the density of T.N.T., the volume of our charge is 548.8 c.c , whilst the internal 
volume of the charge case used in this experiment is about 550 c.c. These two values of the volume 
of the charge are in good agreement and the radius of a sphere of volume 548,8 C.c. i$ 5.08 cm = 
2 inches; this sphere is shown in section in Figure 1 by the circle drawn in dotted lines with Its 
centre at the centre of the charge case. The ratio of the radii of the charge used in the experiment 
and in Penney's calculation is 10.16; when comparing the results of the experiment with the 
calculation, it will be sufficiently accurate to take this ratio to be 10,00, since the errors in the 
experiment and in the calculation both exceed 1.6%. 
Let F, and v be the values of a pressure and a velocity at time t* (say) reckoned from the 
beginning of an explosion and at a distance r (say) from the centre of the charge when the radius i 
(say) of the charge is 50 cm.; it follows from the similarity relationship that if ro = 5 cm, the 
pressure and the velocity will have the values Py and v when the time is t'/10 and the distance is 
t/10. 
Using this relationship, the curves shown in Figure u, relating to ro = 5 cm, have been 
calculated from the data given elsewhere. In this diagram, time t’, reckoned from the instant of 
detonatlon is plotted as abscissa, and distance r from the centre of the Charge as ordinate. The 
horizontal straight lines of ordinates 5.08 cm. and 19.79 cm. represent respectively the surface of the 
charge, assumed spherical, and the pressure end of the bar. The curve labelled "shock wave" gives 
the relationship between time t' and the distance r of the shock wave surface from the centre ef the 
Charge. This curve has been calculated from the values of the shock wave velocity U given by Penney 
and Dasgupta, the value of the shock wave pressure Py (say) corresponding to a given value of r being 
calculated from the equation 
Ph = ¥6r, eto (P, in TONSAINSS) Ie Meise: tees, eee ee (4,1) 
iP r 
The curve labelled "|Interface" in Figure 4 shows the relationship between time t’ and the distance, 
from the origin, of the interfate separating the gas bubble and the water; the data for this curve 
is taken from Penney's calculations. 
Figure 4 shows that the shock wave arrives at the pressure end of the bar when t' is 
approximately 0.065 milliseconds; the corresponding value of Py Calcylated from equation (4.1) is 
19.7 tons/sq.in. The time of arrival of the bubble at the pressure end of the bar cannot be 
Calculated with any degree of accuracy since the data available does not extend beyond t' = 0.130 
millisecond, and as t' increases the radial velocity of the interface decreases. if, however, we 
assume that the radial velocity of the interface remains unchanged at the value (245 m./sec.) 
corresponding to t* = 0.130 milliseconds, then the bubble would reach the pressure end of the bar 
at time t' = 0,49 milliseconds. 
The subsidiary curves (1) ... (4) of Figure 4 show the distribution of pressure over the 
lower partion of the bar when the shock wave has travelled different distances from the pressure 
end; curve (1), for example, relates to time t' = 0.085 milliseconds, and the pressures (in tons/ 
sq-in.) at the different points on the bar at this instant are represented by the horizontal 
distances between the curve and the vertical line through 0, Curves (1), (2) and (3) have been 
derived from the last two curves in Figure 7. Curve (4) has been extrapolated from curve (3), 
assuming that the shock wave pressure is given by equation (4.1) and that the pressure behind the 
shock wave falls off according to the ordinary theory of sound. The curves (1) ... (%) show that 
as t* increases from t' = 0,065 millisecond, the pressure distribution along the bar undergoes 
considerable variations. when t' = 0.065 milliseco d, the cylindrical surface of the bar is free 
from stress whilst the plane end-surface facing the charge is subjected to a normal pressure of 
19.7 TONS cece 
