1224 
== 
Von Neumann (Bureau of Ordnance Explosives Researcn Reoort No, 12: Oblique Reflection of Shocks) 
has shown theoretically that when two shock waves meet at an angle then if the intensities of 
the waves are large ana the angle oetween their two directions sufficiently small the two waves 
merge intc one, known as tne wacn wave (see Figure 5). 
Figures 18 and 19 are pressure oulse records at angles from 180 Jegrees to 0 deyrses and 
at distances of 37 ft. and 50 ft. from the Multiole Charge Tyoe 1a, As the angle cf measurement 
decreases from 180 degrees the time interval between the two distinct oulses recorded decreases 
from 300 microseconds to about 5 microseconds at 60 degrees. At angles of lees than 6C degrees 
the two pulses merge into one. 
Consiger figure 4 in which A and B reoresent the Initiator ano target charges respectively. 
Charge A is fired electrically at time 0 and as noted previously charge 3 detonates after the time 
the detonation wave requires to travel through 14 inches of C.£. primer ano T.N.T. Charge and 
through 47 inches of cordtex. The time interval between the detonation of charyes A and B as 
measured by the gauge at 90 degrees Is soproximately 90 microseconds. The oressure oulses from 
A and B initiated at times 0 and 90 microseconds respectively travel in all directions with the 
velocity of propagation of the cressure culse in water, For the gauge in the 180 degree 
direction the oulse from A leads the oulse from 6 by 90 microseconds clus the time for the 8 oulse 
to travel BA (incluging the extra time the B pulse requires tc traverse or diffract round the gas 
pupble of A). For the gauges at 150 degrees the pulse from A leads by 90 microseconds plus the 
time for the B oulse to travel the extra distance 48 cos 30°, For the gauges at 60 degrees tne 
oulse from A leads by 90 micrasecond@ minus the time for the A culse to travel the extra distance 
AB cos 60. For the gauges at 0 degrees the oulse from A leads by 90 microseconds minus the time 
for the A oulse to travel the extra distance AB. 
The reasoning in the preceding carajraoh explains why, for Multiole Charge Type 1A, the 
time Interval between the two distinct culses recordea decreases as the angle of measurement 
decreases from 180 degrees to 60 deyrees. At Jess than 60 degrees the two oulses merye into a 
Mach wave. 
For Multiple Charge Tyoe 18 the Mach Zone extends from 0 degrees to 100 degrees. For 
Multiole Charge Tyoe 2 the Mach zone extends from 60 degrees to 95 Jejzrees accroximately. 
Table 5 analyses the results from a Mach wave standpoint. 
Figure 5 illustrates tne formation of the Mach wave zone for the Multiple Charge Tyoe 2, 
Charge B detonates aocroximately 30 microseconds after charge A. Consider the hyoerbola, 
foci A and B, whos2 difference in focal distances °A minus 78 is equivalent to 30 microseconds. 
This hyperbola is the locus of intersection of the oulses from A ana 8. Lat P, be the ooint of 
intersection nearest tc the charges. If the angle a8 is sufficiently small for the intensity 
of the Intersecting cressure pulses a Macn wave will be formed. if a? ,8 is too large the two 
oulses will continue in tneir original directions undisturbed, It may be for some other ooint 
on the hyoerbola, that corresconding to tne intensity of the constituent pulses at that ooint, 
the angle A2B is smal] enougn for a Mach wave to be formed.  Sucoose Po is the ooint at which 
the mach wave is formed and et, and °.M, are positions cf the wave fronts from the charges A 
and B resoectively. at a later time the wave front from charge A is at Ql,» the wave front 
from charge B is at ROM and the Mach wave front is Ri Q5s The pesition of the three wave fronts 
at an even later time are Iet3» RAM, and R303 respectively and the Mach zone is the area bounded 
by the lines PRR, — and 740205 —_. 
When the time interval between the detonation of the charyes is zero the hyoerbola of 
intersection becomes the straight line in the 90 deyrees direction and the Macn zone is formed 
symmetrically about that line. When the time interval between the detonation of the charges is 
equivalent to the time for the oressure oulse to travel from A to B then the hyoerbcla of 
intersection becomes the straight line in the 0 degrees direction ana the Mach zone is formed 
Symmetrically about tnat line. The equations of the asymptotes to the hyperbola of intersection 
are 
where th xX axis is the 0 aegree direction 
the y axis is the 90 degree direction 
2b 
uv 
effective distance between the charges 
28 
distance lag of the two oulses. For 
esos 
