PHYSICS

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP80-00809A000600200197-3
• Release Decision: RIPPUB
• Original Classification: R
• Document Page Count: 6
• Document Creation Date: December 22, 2016
• Document Release Date: June 29, 2011
• Sequence Number: 197
• Publication Date: July 27, 1948
• Content Type: REPORT

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PLACE
ACQUIRED
CENTRAL INTELLI
(JFQRMAT
IIIMI.. In ull. a.NDMICIgII OI MI. IOR. I! m "V aU.I..Ol.
M'1I* SD D*1on 00.71.MID III.6.1 or I.a IOU w} ..TIIIIW
FS amemi
REPORT
DATE DISTR. 27 JU1!.* 1948
NO. OF PAGES (
NO. OF ENCLS.
(LISTCO BELOW)
SUPPLEMENT TO
D CD r, T Dill
`rHIS IS UNEVALUATED INFORMATION FOR THE RESEARCH
USE OF TRAINED INTELLIGENCE ANALYSTS
SOURCE Riweian periodical, ]k~kledy Akademii Nancy Vol LV, No 7, 1%?, (FDB Per Abe
REFILECTION OF A PJANE MO:UiTIOH wA)7E
Ye. B. Zel'dovich
Corresponding G9ember
AcaIony of Sciences of the D:4SR
and K. P. Stanyukow;? oh
es referred to in the text are eppended. 11m. bars in parentheses
refer to the bibliograp'*~J
The law of adiabatic expansion pw . coat (1") is approximately cor-
( ?t~ dt of dctonstion of condensed explosives etith high denoitiea
Studying the reflootion of the front of a strong detonation we from
an abaci stable asl~., it is pocciLlto to areive at forurtlas (), v~hiah
give the pressure and density in the first moment,
5rr1+ 17V r2 t 2rta
p2 - Ph - b a (1)
9,2-?.+ (r- 1) I7r2r 21
i1
2 h 9Y2r2r+ (Yr 1) 17x2,-2r -1 ~ (2)
P
D2 x w2 (? - 1) D,
wn Ph
where 7 Is the polytropic index, In out case equal to 3;<
CLASSIFICATION p 1 -
)uw S NSRB DISTRIBUnoN
STAT
STAT
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Ph x~?1 is the pressure on the front of the detonation wave; 100 : i
?
the density S3, vh is the specific volume on the front of the detonation
wave; p2 and v2~are the pressure and apocific volume on the front of the re
flected percussion wave; D is the speed of the front of the detonation rave;
and D2 is the speed of the front of the reflected wave.
These formulae are obtained from the standard theory of p.,rcusaion
Pe PC
waves on the assumption E _ --r w3Lh,~' = 3 (see te.ble, ;). This
r- 1
de-
sioonFitn%wonuldle lead to a detsia s eedlof de equation ti n s ecPnst a ae r dsduceri tro
pending upon ys m
experimental data on the dependence of the speed of detonation upon the
density D8. It is possible to solve the same problem, assigning pQ3 coast
not only. to the ieentrope, but also to the Gyugonio adiabatic curve of a
perc.as.on wave and using the exact formulae of the theory of percussion
waves,
12
. 11 11', p2Pl and
D = ul vl v v2
u u7 = ' (P2 ' Pl) (vl -. v2) (see table, IX).
Finally, it is possible to examine appros?iroately the changes o:' the
state and speed of a percussion rave, using the correct formulas for a u;ca-
bination of acoustic waves du = o dr ? ?, do = do (with r;~ 3) and
their integral I url - x:21=j01 - cPj leas table, zIi). '
All three give very similer results for the state in, the initial nonant,
p2/pl
2387
2347
2370
v2/V1
0760
0753
0750
e2/ol
1347
1329
1,333
3ucsh agreement is the result of the small ratio of the speed to the
speed of oomid ul/o = 3/3 in the current which is not runaing to the wall,
which leads to a o3 seneas of the percussion rave to the acoustic and, in
particulae, to a small change of entropy (4). It is curious that this takes
place with a significant change of the pressure of almost 2.5 times. (it can
be shown that with any po3ytswpie index, including r ? 1, the entropy changes
very little i the reflection of the detonation wave.)
This eirembtnnoo with r m 3 makes it very simple to solve i:..e problem
of the reflection of a detonation wave, using the acoustic bond U and g.
STAT
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I
erall solution of t'o :;nt:.atic:: c' , IWOtoan cr :e .; el ;?~, at s io ha<
3 (L r c) r .'1 (i t C); i/..
To shall exa;aine sech t: erobl e: Let '.;.a e or e, , ~, rn bo,lin a ; t?
n Crary ~c as.
a
ui do
2-
.,here u is tho icoel greed of the c~cmon~, o? aa; a ;a ' he local Q;:'' id of scz
F' F n',
r if? C
by thersa same eguatie;as (Fi'vre 1, '.rj jar xuir a: c roeree) d:'. the :me: t Of "si
The moveaaont of produc?i.o of deLonaaticn ;^:aich d1of?r`.og'atc to :f ,a .aft
xl t,l i)%: u
From the oonditlon' ths't x a, e z 3, rr..J that oii :he .''rant of thr; ro?.
We noticed that the aped of x e&c :.n +hca re21cct d rz.ve hru, a sil n tshi:t
is the opFeeita of that of the 3pood of brreac on - ie e9ri?,onctioz ware. Since
are fulf i.led, we doternirea the val'm of th: crbittrary :unctions F1 anel F2.
F7 (u + a) _ tot In - a, F, ('a - C) " a - C2 D = 0; fror thZn ,:~~ hnc?-
u2 Z. e^. 1P which with r z 3 erd &-,x v !',no nif givo
D2 r 02 _- L'1.
From this,
Integrating azad remembetring tint with t = a/L, x ?- a, w. ibta-
which gives the 1a`v of the distri`?w-ti^n f' `hc fo?~
ot ze
c .r t? iec,
?2q;ULf a
2
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J'j
Do - -~ ^' g ?} ?
We novice that the relative amplitude of the wave in this solution in-
creases according to the measure of its diffusion, as a result of which the
error of the allowances which arc:?.made also dner,ases. lb ,the cane of an exact
solution which considers the change of the ortropy, the reflected wave would
have to overtake the left front of the expanded products of detonation with
t --f.w (p -i0). The solution which we have found indicates that the meeting
win take p3aer with x . DTh/2 = - Dt/2 - 1/2 E -!-2a, from which t = 16 a/D
and x = -8a. The pressure on the call in this will be 64 ~~,,,,
i.e,
6
pM'
0?OQ0
27 i6
4
14 will ftti4~[ia.:y w =U eraely small. 'U j6," 4116 iit`au~:iu-ac:y 16 wav u.tutt lai5~
t, when pis very small, i.e, in the field which is of no interest to us phys
ically. -The distribution of the speed of the current and the speed of sound
in the reflected wave at different moments of tire is illustrated in Figure 1;
the density is p- o, the pressure is -c3. %The upper pair of curves gives
the distribution of products of detonation in scattering until the wave reach3c
the mon.)
complete impluso of. the pressure acting on the wall:
We calculate the
e
pxlt 7 P i )3 dt . 6N1} a .D 3?'aB2-1
tuJh '/b
A curve of the pressure with ar explosion of an equal charge at the wall.,
such that toe detonation move would be distributed from the wail tc the open.
and of the charge is iilujtrate'l in article (5). Curves of pressure on the wall,
in both cases are compared in Figure 2; the maximum pressure in the case of
reflection (the continua curve) surpasses by eight tines the pressure on the
wall for the front of the wave separated from the wall (the broken ctnvvm); ho?x
over, the complete impulse of pressure in both cases is the sase.
Finally, oxamining the case of an ordinary explosion (ecmpare(8)), i.e,
instautsnuous reaction of an entire "-rlosive with the formation in the first
rlowent of a layer of immobile explosion products of a constant density, weob?-
fain a pressure curve of the typo p = pb; ttl
and, depending upon the assumption, the following nrmerical results,.
1. Letting.E - 'rv/2, we find for the pressure, of the explosion p
P CO Y 3/8 ; do : V 3"j?_ 1035 J.
2. Letting pv5 - coast, not only along the isentrope, but
p, - ~cf P? = 0.42 P t ; c0 D r2 5 J =
The corresponding ourvee p (t), not shows in Figure 1"(in order not to
encumber it), are represented by a horizontal straight line between the axis
of the ordinate and the fa ling arm of the continuous curve and practically
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BiblioMvhv
1. L. D. Landau and K. P. Stanyukc'ich, D 399, 1945
2. ?Q. I. Pokrovskiy and K. P. Stanyukavich, DAN 2, 33, 1946
3. S. P. Starqukovich, DF.N 52, 777, 1914
4. Ya. B.'Zel'dovioh, IMM Of ues on avo and &aMZdMtIgn
G ea 1946
5. K. P. Stang avioh, DAN , 523, 1946
6. A. A. Crib, Pt,1ltladaass~te~atika i rAekanika, 8, 273, 1944
,Appended figures follov?7
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