APPROVED FOR PUBLIC RELEASE · 2016-10-21 · APPROVED FOR PUBLIC RELEASE APPROVED FOR PUBLIC RELEASE . This official electronic version was created by scanning the best avail able

APPROVED FOR PUBLIC RELEASE


I

● ☛ ● O*800 ●°0 : ●ge ●● ****● O* ●

. ...0:&M$lFIEn:●******90 800

● . ● *. 9** ● ** :00 ● m9*** ● 0

89*9 ● ***● 0 :● :

● e: ● *

● ●:0 : ●:e ● 99 ● O

3CK2-14 REPORT COUECTION

REPRODUCTIONCOPY

—-———.

● ☛☛ ● ●:0 ● *. . .●**● :

●:0● . .. ::

● m.:000: *b

9* 9** ● .* . . . :.. ● *



February 12,

● ✎ ● ✎☛ ✎ ✎ ✎ ● m* .0. ● .● ● 00

b : ● 0 ● 0 ::● m :*● :

● *

●● *●:0 : ●:* :.0 ● 0

~flcLt$$\&

1945

VERIFIED ~CLASIFIED

By CYC+4 5“/3 -7g

This dooument ccmtaina ugea

/

FROPAGAT10N OF DETONATION WAVES

ALONG THE INTMRFACE BETWJM TUO EXPLOSIVES

WORK DONE BY:

%. A. Bowers

REHWT %RITTEN BY;

??.A. Bowers

.



ABOUT THIS REPORT

This official electronic version was created by scanning the best available paper or microfiche copy of the original report at a 300 dpi resolution. Original color illustrations appear as black and white images. For additional information or comments, contact: Library Without Walls Project Los Alamos National Laboratory Research Library Los Alamos, NM 87544 Phone: (505)667-4448 E-mail: [email protected]

The ideal problea of a detonation wave propagating along the inter.

face between two semi-infinite explosives has been treated in the ease when tho

point of’ initiation is infinitely distant. In a coordinate system in which the

detonation fronts are stationary the pressures density and material velootties

behind the front are functions only of the angle with the detonation front. For.

a given ratio of normal detonation velocities three cases arise: (3) The anglo

betwcoa the detonation fronts assumes its””normalr?value (i.e. ita cosine ia the

detonation velocity ratio). and there i~ a rarefaction behind each front, {2) For

sufficient.lygreat ratio of density of fast explo~ive to Slow$ a shock is sent

from the fast to the slow explosive, which forces it to travel with greater than

its normal vel.’ocity,thus reducing the ‘refractive indexws (~) For auffloiently

small ratio of densities~ the opposite occurs~ i.e. the fast explo8ivc i6 speed-

oa Up$ thus increasing the %efractive index.n Graphs have been plotted show-

ing the limiting values of denci-tyre.tioat which case (1) goes over into eases

(~) and (z) respectively, as a function of normal refraction angle. Thio has

been done asauming (a) an Qdiabatio index ~ = j for reaction prsduct. M both

oxplusiveso (b) ~ = 2. (c) [ = 2 for slow and ~ =3 for fas%’explonivc. Graphs

have also been plotted showing the Jovi&tion from normal refracting angle as a

function of density ratio for some special casas. In a typical case$ assuming a

normal refractive index of 29 i~e~ refracting ar.gle=@”, the deviation is ~ero

from density ratio 008 to .555 above .5Ijit Salle Blowly te +.6° deviation.,

at density ratio 2000

..———————-.. . . ... ,-. ...Z

● 8* ●●’0 9:. ● . . . . ., ==- ... .. —---- ---——

● : :0 ● ● e

9 ● * ●● :0

:0::9*

● 9 ● ee ● 9* ●:0 :.. ● *

● bb ● ** ● ●:00 ● .*. . b ● 9*. ~wAss/F&l● ea● *.. :

● 00 .

● *.:*O.

89 *...● * 9**, ..* ●

,.

t,

I



● ✘ ● mo ●

1

● O***● eoee

Obo ●● 0090● O ● *O ●

● ✎ ● ✎ ✎ ✎ ✎ ✎

● 00.*O.

9** ● a. ● O● a..

● ***:0 ● b

● m●:0 :00 ● 0 ‘w$s/[/f.u

PROPAGATION OF DETONATION WAVES ALONG TEE INTERFACE 13XfWEEN IWO EXPLOSIVES

1. We consider here the problem of two semi-infinite explosive6 bounded by

a planes detonated an infinite distanoe away. We expect the detonation front

in the faster explosive to be a plane perpendicular to the interfaae. and that

in the slower explosive to be a plane making an angle a with the normal to

the interfaoe, where in %ho absenoe of persistence effeots we should have.

co~ a = ratio of norml detonation velocities in the tvm mediac We shall

invtmtigah in particular under what circumstances thi6 is true, and also

att6mpt to caloulate a

2. If we transform to

fronks are a-trest, we

in oases where this is not trueo

a system of co-ordinates in which the detonation

have a stationary phenomenon. iilththe a-mptions

6tated above the problem

and henee all quaxrtitiea

depend only on the angle

contains no constant of the dimension of a lengths

[pressure,density. material velecity~ oto~) can

~ measured from the plane of the fast explosive

detonation front9 with the origin at the intersection of the detonation

fronts and the interfaoeo If we denote the radial and tangential components

of makerial velooity by Ur and u ret?peotive2y0the equations of motione

~=om~) .

‘% “dur/d61=0

1*Ue @#@ +Ur) =.-

P de(2)

.● ✘☛ ●

1)0 Cf. ti-3&j, Section 12”:: : :● ●*

● *.“~”~:”~”~~: ~9* bee99*.:.:.O ● *

●* ●@a ●** ● ●● ● ● 9°0.● 90 ● ● ●** “:!nF$@● *** ● ●** .:● *9 ●0: ●

WIERL?fa$,

::0● m ● ** . . . ● -



● e 99* ● 0●.9*98: ●’* ●● **9* ● 00● mmb : ● ee ●:a *ma*.. ● . .

9*O ● ● 99.**

:: Muc14si6Enb* ,** ● *O 8** ● 00 ● *● **00

● 9:* ● b

● *●:O :00 ●*

~z==---- ‘-‘-— “—

and the continuity equation becomos$

du@ ‘Q g—+lar=e~ (3)

de

Hem p and p denote preamro and density respectivoly~ Using d~dp = 020

where o is sotmd velocity, (2) beaomes:

Combini.ngthis with (3) we

(uQ* - 02)

F+. (4.)has *W solutions:

=coos(Q+6), ur=c‘9 .

have:

dp/d#3= O

A) p = Oonstant,

Veloo.ityo B)Me = ~ c where the sign is

w now make the further assumption that

(a)

whioh clearly meano comfkant matewia2

to be chosen so that Q ie positive. If

the reaction products of’the explosive

Y 2 ~S~o and hencmobey an adiabotio law with index y :pfi,p~ 60 that c~,,p

[/(alp/p= 2y - l~do/o = W(Y = 1] duG..ue,eq. (%) becomes:

du.~+u#. uee2 ~ldu

55’- yr r +’ee

O, 7+1 WQymr ‘%=0

—.. -.

●9* ●●’* ●:* ● ** . .

● :90

:● . . .

:

● . .:0.::

● “ Iticllwla●0●00●00●:0:....●**9**● ●:’*.●*9●

● *e ● 99*.

● . . .●

:● e* .

● *.**.● 0:

● s● **

● am ● . . ,--



. . . . . . .*O ● I

T?itheq.

.

(1), this yields:

+-c #,= v~ =

This is the familiar

J(y +1)/(y - 1) Sir+l V4Y - Nl(-f +Q +6’) (9.

I

(ACcose y= I)/(y +1) +6 ){6) !

Prandtl=rdeyer

I

~~~ution for the problom of supersonic

f’lowaround,a corner.

3. Under certain cirWm8tinces a solution of the probiem exists of the

following nature: behind the detonation front in eaoh explosive there

is an expansion (iooo a Prandtl==Meyes region) which goes over at a certain

angle into a region of conl+m% density, material vebeity~ etct.o (Of. Fig. lj

dotted lines indioate c%pansion region Z and TV)G The mqybr width of a-h

expansion region,and the angle at which %M interfaoetbetween the two

explosives moves off, can be determined by requiring continuity of material

velooity and pressure at the boundary of each expan6ion rogion~ and con=

tinuity of pressure at the interface between tho two media. “’Onealso

obviously require8 the vanishing of the tangential material velocity CO-

ponent at the interfaoe~’in order to avoid mixing of the two mediaj the

radial oomponemt may however be disoontinuou8 (i~e.~the interface

‘slipstream”]”.

We shall now write down the solutions explicitly. Let ~

may be a

Ibe the angle

at which the expansion region behind the fast-explosive detonation front ends;

let ~be the angle at whioh t

+d”f*g;::,;;be:”g’ea’9**:**. ●00 ● ●●** ● ● 9 ●*9● *>9 ●● .96 ●9* .:● *. ● **cc:●9 9m*

●*99*.. .



● ☛☛ ● m●****O: ●** ●● *D** ● *9“be ● : bee e‘00000.0 ● 0...*8. a.9. e .*-“: ● 9 ●:0 ● 00 ● O. ..* . . unm4ss\F\@● ● *::●:.;,t$:: r ::8 ●**●** ●

whioh the expansion region of the slow explosive endu6 the slow.explosive

detonation front is at the angle ~ - ao Now at the fast=expl06ive detonation

frent we have. from the Chapnmn.Jougust oondition~ that the ~terial vel~ i~

is 9,/(y-1-1) and the sound velooity ix yi(y + 1) in units of the detonation

velodty ~ in our system of eo=.ordinates(detonation front at rest) this mean~

a material velocitiyof y/(y + 1)& since this is norml to the fronts we have.

that for e = 0’ % =Y/[Y+l), ~=o. redo= Y/(y + 1)o We have therefore

in region 1, (O= e ~~)

0 =‘o = Y+ OOs (em) (?4

—\

(P)

In region

the r6quiremcaxtof

oH.

q /& ‘a< b, we have constant pressure and velocity;

oontinutty gives:

(8a)

● O ● 9*● . .● *.● *..● **● * . . .

● ☛● ✎

✚✚

.

uKw$[FfEfl● 0. Oio-

● 0...



. . S89 **● ,0 ●°0 : ●e* ●● ***b ● **● *** : S**eta ● @@ ●ct.:*8 ● Oe*e O*mm

-7=

Similarly at the detonation front of the slow OXplOSiVea we have the

/material velocMy equal te cos a (y + 1), since we q.reassuming

here that the slow detonation frontiis at its “normal” position. Transforming

to our system of oo.ordinatesO we fin-dthat at the detomtion

‘e=”(y cos a)\(y +1)0 ur=aina, o = (y cos a)/(y +1)=

following solution in region 3V0 (P? < 63< x - a)

front wo have

This gives the

‘Ur=7$+7-+-‘ [ ) /=q”*Bb(@-~+a=n Y-1 (9b)\r+

“+ ““”’1.

requiremc3ntof continuity

‘III = ~~

ate= P’:

- “:”i “i”~:”:“!● 9 ● 00 ● ** .*. :00 ●.

● ☛ ● ☛☛ ● be ● ●●9..*.. ● ● ●°0● ** ●● . .. ●** .:● *. ● 9*● 0:● *

● *9● ***.** .

-{1OCI]



● m ● *9● me.9*9● @*● **● - ● *O

● m

●“c : ●°0 ●

● O*..● ● ● *@ ●

● ** ● *O*● ● 9*9**

● 00 ● ** :00 ● *● * ● 8● .00000

● e ● m

● *O ● 9e ● *L“”””8

equation betweenP

andP

~; the othem eqwtion must come from the continuity

M pressure at @ = i. We shall find the relation m30e*smy lmtmen 011 and.

CIIIin order !hat the pressure be continuous From 02 = Y’p/p9we hav%

assuming y the same in each medium ~011/c1~1)2 /= P1ll PII* Further, in each.

meiliumOwe have p = Pc(P/Pc)y whel’eP. wid p aro the Chapxnan.Jouguetvalwmo

of pressure and densikyn rmpectively.> Using p. = @ + I)/y]PoP l..=e P.

i6 tho normal dcxmityo and D2 = (y -i-l)pc/po, where D is the normal detonation

vetiocityo this becomes:

Continuity of pressure themefoqe requires:

acre P5 and Pt moan the normal density of tho slow and fast explosive

respackively~

& Ifwe nawcorisider the special caoey =3, we have

(Ilb)

be ● 00 ● ** ● ●

● *C ●*e ● ● ● ●9*● s*** ● 00 ●

● 8*** 9*O● ● ● ●ms ~ .● 9O● m ● 2* ● O



● 0● m● *● *● *● m

● *b ● ● ● e

● ..:::O● am* ●

● e**.*@● ● *O ● boe●eam O*****

●✚✎● 00 ●:0 :00 ● 0●

● ●0000::● *b: ● *

● m

●:0 : ●:0 ● 00 ● 0

-90

or u~ing 8a and lCa;

[/7 )-1 .

where V= @ tan1

{ 3 tan a)

For a Siven detonation velooity ratio and density ratio of two explosives

therefore [12) md (13) may be solved for ~and #loO

Fig. 1 shows the flow lines in a typical caao~ the dotted

indioato the ragionrnof rarofaction behind the detonation fronts.

lines

In that

oaseo which corresponds to a detonation ~elocity ratio 1.6 and density ratio

O.~O one obtains ~=49.55”, b=9@’, ~’=121.q”,a=5~.30.

~. For certain ranges of values of pf/p60 It turns out that eqs. (12) ;md

finds that ae the ratio is IncreasedO ~ and ~ g both increaae~ i.e.~ the

expansion region in the’fast ex~losive inweaOes and that in the slow

OXPIOSiVO dacreasesO until finally Q = n -P

a (the slow exploeiva oxpanaion

region disappears)~ and similarly if p#’pe in deoreasod~~ andP S deorease

until finally /0= [O the fast explosive expzxmion region disappears). That

this 8houZd be the case ia p3ausible Oripisy8ical grounds; a fast explosive

of great density tends to push int~ the slow.explosive region~ and one of

small density is itself proye.#@ fr~ti:6x@-@ingby a dense 61OW explosive~

-:. ~A:~~



● 9 ● ** ● 0● *9 ●°0 : :.: ●

● 0000 ●

● 9*9 : ● ** ●

● *O 600 90**909000000 ● 00

The limiting valuca of p#’p8 for which a

oan be foundO ure easily calculated from

P=;00 and eliminating ~g (lCW density

solution of the typo di8cusoed above‘

equationm (32) and (13) by setting

ratio limit) or by setting.

B“=’” a and eliminating ~ (hi@ ~..si~ ra%io limit). The resulting

Gurves in tha caaey =3 in both explosives am she@ in Fig. 2, curve NOO 10

Curve No. II Rives similar limits for the case wheny = 3 in the fast eXplCXiVCJ

and y = 2 in the slow. The calculation for y $ 3 everywhere is exactly the

same as in the original one. except that the form of the coK~ditionreWiring

continuous pre8sure at fl=$issom~bt more complicated. Onehasinfaatp

inetead of (Ilb) the following condition:

Eq. (13) is chan~;edonly

sideo

There have been

by in~erting fiin place of @on the right=hand

inserted in Fig. 2 points corresponding t~ several

real explosives. Shoe not tao much is known about the value ofy to be

assigned to these axplosivea . if in fact the assumption ofa Dower law

that type is itself at all valid - one cannot draw

however that Baronal used with either pentolite or

probably behave “normally”~ the other combinations.

the allowed regions.

&5C in case the density rtatio pf/p= i8 outside tihe

many conolusions~ it

composition’B should

of’

a&mls

may be a little outside

allowed region one may

calculate what happens in the following fashion: Since too high values of’

Pj/Ps mp=erxbly nom that th~@<asta.?xp&of;veis9’0 99*0 :00

● -.*. :09** :: Giiiiir” ‘he ““W

● 0 ● -a ● OO ●:0 :00 ● 0

● 0 ● O9 ● ** ● ●

● 9* :00 ● ● ● ●**● e* ● ● ** ●● *O**●e*e*: ●::@9* ● ** ● ● ● ● m



● O 9*O ● *● ** ●.9 : ●9* ●

●*.***:.: ●.● 8*9● ** ●00 : b**o● m 9** 999 **9

● 0 ● 00 ● 00 ●:0 :00 :*e●

● :

:: ~

4011 P :0 ● ●

● O*● :**● ● 00 ● ●:0 :00 ● 0

eitplosiveni~o. the hi~h pressure behind the faat explosive is forcing the

presuure behind the slow explosive above ita normal valW, one my assume

that the slow ezplosiva detonation is foroed to travel faster than ita normal

velooityO iooao a ia reducodo In the opposite ca8eo O#P* too :Q~l one could

argue eimilarly that the fast explosive i6 forced to travel faster than normal;

but this seems doubtful physically. In this case one probably has to know

more about the struoturo of the detonation front itself~ in order to say what

happens at the intersection of the front~ in the fast and slow explosives.

Sinco however the lower limite of p&~p~ a6 shown in Fig. 2 are so Small$ the

question is of little practical imyortance~ and we shall not attempt to

treat it further here. but will limit

too high).

The equation of the Hugoniot

ourselves to the first caf3e (pf/p8

. .

curve (i.e. the curve of posaiblo

pres8ure - density conditions behind the detonation front) oanbe written:

P = po/~: + 1) v/v. - (y - lj’j (15)

where p. is the norsml~ GhapmtiJouguet detonation pressure~ v iS the

speoifio wolumeo and To the normal specifio volume of the explosive= From

the Hugoniot conditions we have further that the detonation velooity D

Iis given by:

~2=pvo/(l - v/vo)

Since the normal detonation velooity Do is:

D02 = (y + 1)Povo

(16)

(17]

● ☛ ● om ● a* ● ● ●● *9 f. ● ● ***● ** ● ● *9 ●● **O* ● **● * ● ● m : ● **● e ● 00 ● ● ● ● b



i% ham for

● ☛ ● mm ● ● m

9*9 .OO:::O.00000 ●

● *bO ● om

● ** ● 0: ● *C:.9 **...=. ● *=

The new value

2008 Ct=

the slow explosive:

whero a~ is the

velocity at the

of a is therefore given by:

(Da/Df)2 = (Da/Dao)20 (D~o/Dfo)2

and the

0

Oc

ma%erial

(18)

‘fnormaln refractive anglea Similarly we have the sound

310w detonation front c2 = Tp/P or:

~2 =

(y 1-1) v/v. - (y - 1]

(0/D~] 2= (G/D~o)2 [DSo/Df)2 (2!0)

2Coq U.

[y 1- I)-y’ - .1)

velooity u at the slow detonation

~2 “= p(vo - V) (21)

2

-=+‘f

● 00 ● .8* ● b. ,0●’* ● O* ● 9

● :000 ● *9*** 999*

● ** : ● *● * 9*. .*. ..* :0. ●.



● ☛ ● m* ● ● 0

● 00 ●°0:::0● *a*** ●

● *9**.* ●

49* 9** ● **:.m. mm b.m. ..*

Transformin~’to our system of co-ordinates, we have, in units of

=- (vo/v)cos a, u= = Sin a, c =cos a ~ ~y(v/vo)(l - T/vo)‘e

slow detonation front. If we assume we have no expansion region

the slow detonation front~ (which is reasonable since we arrived

‘f:

at the

behind

at this

ease by going beyond the limit in whiah ~aacha region disappeared)~ Vm have

threo regions instead of the previous four. Regions I (0< ~<~) and

11 ( ~< ~ < $) have precisely the mme solutions as before (i.e.. squaticma

7a, b,=d8 ate@). For region 11X [$4 43~ ~- a)$ we now have:

W have again the condition oII = 6111°

This gives one equation between

the threo unknowns P ~ a, v/v.; Eq. (19] gives another; the third must

again come from omrtinui%y of preseure at 9 = b. This gives. by a oak

mlat ion simikr to that at the end of Section 30 the following equations

which reduaes to (Us) when Vlvo = Y/of



{234

and UBing oq. (19) for mm a and aimplifyingo wo have finally ~

(23b)

‘7. If we consider again the special case y = 3, this equation gives:

r“ 9 -11/?l

1 I

C08 (#@) = ~ o ~*Q--— “’-“04 v/v. - 2)

2 20@s 008 a.

a. =4(1 - VAO) (4 T/v. -

(24)

For given values of a. /ad p8/pf (Acre Pa Pf

limiting value of curve No. Is Fig. 2)~ these

a~ #? and V/VoQ To cal~ulate the refractive angle a a8 a function of

is to be chosen above the

equations may be 6olvod for

the GXwRpman==Jougue%value 3/40 (corresponding to higher than normal

pressures in the slow detonmt-ionfront); from these calculate a from (~);



● m ● a* ● *

● oo ●b. : ●** ●

● O.**= ● 00. ...0 99* ●

IM![4SSIFIFB

. .

rasul% of such a calculation for the ca8e a. = &o, iOe O “normal“

refraoticm = 2. Acoording to this curves the angle of refraction

almost linearly from &l” at p~p~ = 055 ~0 about 5404° at p~~p~ =

index of

deoreaae~. .

200.

These deviations are therefore quite appmoiable and should be observod

oxporimentally~ if

explmive reaction

3StRte -pNp ].

It tihould

deviation8 aro to

I

our assumptions about the equation of state of the. .

products are not too far wrong (i.e. equation of

%Iso be remarked

bo expeoted only

that in an experimen’td setup. these

in the neighborhood of the interfaoe~

in fact for a distxmce of the order of the width of the explosives. Beyond

suoh a distance. the detonation waves will have their normal velooitieau

and will be curv6d* since it is only in the ideal ease of infinite extent

of explosivo and infinite age of the detonation.

all 8traight line60

wave that the fronts are

.

. .“,.-. _-.. .’,,.*>,S. . -7

.ee ● ● 00 ● *9 ● 9

●°0 ● ● : ● : :● *9 ●

● *:O ● mO*

● : ● *

● * ●:9 ● 9* ● 00 :,e ● * Ulillliui,.m.

“s c ● ** ● *me99b** ●’* ● ● ***● *9** .*O ●

● *eem9 .9*

.9 .**.* ● O*

● a ● O* ● eO*



● ☛ ● 9* ● *

● O* coo : ●*8 ●

● 0s0s ● ● 60

● 9S ● ● ● ** ●

● *o ●** ●..O : : ●.0● . ● 9*

-, . . . .

FAST EXPLOSIVE

12’EFRA-CTI O N

?2= !. G

Pf/P 6 = :9$* ●

● : :9 *.9●

● 0 ●:0 :00

● * ● **● O* (0● O*beeoe● O.*.● * ● *O ●

c

\

SLOW EXPLOSIVE

c DETONATION WAVE

. ** -ss● 09 ● *e ● e

:0 ● e● ..ma -- ‘Q=2



3,

3.

3.

.—

2.

2.

2

2.

2.

1.

t.

f.

1.

t.

.

.

.

.

‘w., .....,;........:...’,.:-, .

. ..

.-, ”I,.,.. . ... ....... ... .---t,..;.,..,.1.:!,..

)11::.... ;..:,.,...

;“i ‘ .’ ‘::’; !::

I

x’. . ..’;..QQ

I

i; ’.:,’ “

a-=’s. : :’:..; :;, :

,-d I I I

Hif,,.....

,’ . .. . .. . . .—

I... . . ., . ..,.,. . . . .. .

.,. .,. :1 ‘T

---T-- ‘ ‘ ~~\ 1,

! I. ,. “1

+ I

.- 1I -

Wi’:””’1”,,. I I I

0 1.1 ‘/.; ‘ r f.3

. . —.— . .

● 0...

+=

.-. 9 .****,. 9* ●

I

I ... ,,

““1qqw-gf-.... . . .-.,.., . . . .x. . . . . . PEFiTOLI”

I ! i

..-.

.,, . 1. . .

—,, . . .

.,. . [[/.: .,,.,.“- ‘“ -s,,. :. I “.:.: .“ .: ., i 1..1-.L .:l L

., ,.;

i!: ,L. :;’ ! -:. ‘;!“~ ~?-! I ; ; .~,: ,; ;..;}

i--+-l i

.

: -,.. ..I u .-

1 II

.-.. :. ,,

.’”

,!

-

. .

-

——

.

L---—.. .

....

.,!

\

. ----

@

,.’.

T“!,,

—..J

-—

!id.---l-

a .,,,.I

__Li.L

I

Lj..

. .

. . . .. .

.

.

. .

‘mI

l!.#oSLjGAE ,

—-

.

+ ““ “:I I

.:1 I

=-Ll-=UI.l.l ”-i

--!WI< -.:,‘,”

1>1“ J.— i \’I t

I

,, ,uiE“!: ”/..’-: ;_–_.—-----V

--J-II,4 2.2 2.3 2.4

tfiil&[F~~e,...----- ---- -—.— —.. —___ . _ .-— — . . . .-





Documents

APPROVED FOR PUBLIC RELEASE · 2016-10-21 · APPROVED FOR PUBLIC RELEASE APPROVED FOR PUBLIC RELEASE . This official electronic version was created by scanning the best avail able