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ADB015617
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TOApproved for public release, distributionunlimited
FROMDistribution authorized to U.S. Gov't.agencies only; Administrative/Operationaluse; Dec 1976. Other requests shall bereferred to Naval Weapons Center, ChinaLake, CA 93555-0000.
AUTHORITY
USNWC notice 23 Jan 1979
THIS PAGE IS UNCLASSIFIED
NWC TP 5892
i-~ i
SDevelopment of Optimum TheoreticalWarhead Design Criteria
LA-byT. ZulkoWski
Propulsion Development Department
DECEMBER 1976
Distribution limited to U. 5. Guvernment agencies only; test and o•valuation; 30 ,aptember 19;(. OLnkh requestt for thisdocument must be r ferred to the Naval Weaponls LCnter. e4
Naval Weapons Center'w: '," ~~~~CHINA LAKE. CALIF-ORNIA 9355 bbb.. =•
Naval Weapons CenterAN ACTIVITY OF THE NAVAL MATERIAL COMMANDR. G. Freeman. III, RAdm., USN ............... ...................... Commander
G. L- Hollingsworth .............................................. Techflt-di Director
FOW .EWORD
This report describes an anpiyticai stud,. conducted during the period Januarythrough May 1976, to develop optimum theoretical warhead design criteria. This effortwas funded by the Naval Air Systems Command under Program Element 62332N,Subproject W-32-352-502.
R.G.S. Sewell has reviewed this report for technical ic'uracy.
Released by Under authority ofG. W. LEONARD, llead G. L. !HOLLINGSWORTHPropulsion Development 1)epartment Technical Director1 August 1976
NWC Technical Publication 5892
Published by ....... .............. .. Technical Information DepartmentCollation .................................... Cover, 19 leavesFirst printing ......... ................. 185 unnumbered copies
NATIONAL SECURITY INFORMATION: Unauthorized disclosure subject to criminal sanctions.
UNCLASSIFI ED ___
SECURIýYCL- AS',FICATION OF T,'s PAGE (wh.o Dw.r Enrof~d)
REPORT DOCUMENTATION PAGE BFREA INSTRUCTIN ORM
2.GOVT ACCESSION NO, 3. RECIPIENT'S CATALOG NiUMIUER
-(- ;TL.E *Ad l,,gi c .
DEVELOPMENT OF gP1I]MUM THEORETICAL WARHEAD Jawf-a tW976q!RESIGN CR)TE-R!A -G- im -nm OTNME
-~~~A dee. ~ueE
~FORMN~RUANIZATION NAME AND ADDRESS /~-NavoP WwponJIS Cur tar Programn Element 62332NChina~ Ljke, California 93555 Subproject VVF32-352-502
11I CONTROLLING OFF71CE NAME AND ADDRESS
NdvaI Ai, Systemýs COfmrn~d // ixir 1 DL9X
Wdshinlgtonl, DC 20360 .vfq v4
14 MONITORING AGýENCY NAME 6 ADORE55(i( dilterent fcror Co~ntOliri~ Ofil" IS SEUIYC-S
UNCLASSIF [EDiS. DECL ASSI I'lCATION. DOWNGRADING
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lh OIS-RIBUTION STATEMENT 'of this Report)
Distributioii lunjitd tu U.S. GeVerniuunt agericies only; tost ind evaluatio 30 SeptLme 1Io 9/6.Other requests fur thib dULtuIIIUIt must ho ruferred to the Naval Weapons Cel tuL
17. DISTRIBUTION STATEMENT (of thea bstract entered In Block 20, 21 different I'-, Report)
18 SUPPLEMENTARY NOTES
S19 KEY WORDS (Conciflue on favors@ aide It ntos-..y and Identify by block numbe')
Wcirhedd DesIyn
I rdgJIlnflt Kinutif. EnergyS.Ifid Cylinider
End LlftNtsI
20 ABSTRACT (Conlinuo, nn r.e'.rms. ide If nocammaty and Identify by block ub.r)-
So! r2vorsI ;idi(! of this to111.
DD 1473 FDIT1.,IOII I NO 15 15 OBSOLETE UNC LASSI FI LED h
SECURITY CLASSIFICATION OF THIS PAGE (Wfhen Dall.Xn
UNCLASSIFIED.,•I•Y' CLASSIFICATION OF THIS PAGE(When Dalt Enrered)
(U) Development of Optimum Theoretical Warhead Design Criteria, byT. Zulkoski. China Lake, Calif., Naval Weapons Center, December 1976.36pp. ( C TP 5892, publication UNCLASSIFIED.)
study was conducted to develop optinmum theoretical warheaddesign criteria. Weight, diameter and length constraints were considered basedon a solid cylinder with no end confinement. End effects were alsoconsidered and treated using correction factors in the form of exponentialfunctions of length-to-diaineter ratios. Using these paranmeters, three generalqualitative conclusions were drawn: (1) the greater the warhead length, thegreater its initial fragment kinetic energy, (2) the mathematical modelsdeveloped indicate that the optiinumrl charge-to-metal mass ratio (C/M) isgreatei than 1.4 and that a decreased length-to-diamete| ratio results in higheruptimuni ('/Ms; and (3) optimum warhead case material, from the standpointof initi-al fraginent kinetic energy, is a function of warhead weight, length anddiameter.
\I
UNCLASSIFIED
SECURITY CLASSIFICATION OF TI41S PAGiEr*h7r DOta Enrterad)
NWC TP 5892
CONTENTS
Introduction . . . . . . .. 3
M ethod . . . . . . . . . ... . 3Velocity Currection lFactor, . . . . . . . . . . . .. 4
Other InitiationI Tcchniques . 71 raglnic-.t Initial Kinetic I.)Energy . 8
R esults . . . . . . . . . . . . . . . . . . . . . . . . . . .. 1
('onclusion.s . . . .. 1 2
I!
I.I
I;4
NWC TP 5982
The following conversion factors are provided to allow the reader to convertstandard units used in this report to metric equivalents:
To convert from to Multiply by
inch meter 0.0254pound-mass kilogram 0.4535pound-mass/inch 3 kilogram/meter 3 27679.9slug kilogram 14.5939
2
NWC VP 5982
INTRODUCTION
Anl optimumi theoretical warhecad design is needed primarily during the earlystages of' warhead design. Sysitems analysts also need such informiation when they areattempting to evaluate systems performance in early systemis synthesis. In Cecent years,the p~rimarwy parameter for determining optimum warhead designs hias been anl energycriteria; initial fragment kinetic energy being one of' 11w first factvors of' concern.
T'he warlmeid enivironment is quite variable and all the conditionls imposed haveanl effect onl the energy chiaracteristics of' the warhecad. A study by R.G.S. Sewellconsidered several of' these conditions in determining anl optbiumw clbarge-to-mietal ratiuf'or both weight and voIlumle contrained warheads. 1 Ini making the determinations of'Op~tiln oml charge-to-metal ratios, SewCll used Gurney f~ormiulas to evaluate initialfr-agment velocities and kine-tic energies and, for the sake of" simplicity, accepted theassumiiption~s implicit in these formulas. The mnust significant of' these assumptionsrelative to practical warhecad designs is that there are no end effcts to modify themilhtal 1*raginlent Velocity anid, hecnce, no etffect onl initial Fragi ment k ine tic e nerpiy.H owever, past experience Willh cased cylindrical eýxplosive chiarges ha"s shlown that thlisis not the ease and that velocity variations ajt the ends of' the warliead are significantdueI to these end effects. Phus, to determine the initial f'raginen t kinetic energy, theseend eff*c~ts Must be included in thme warhead desipn consideration.
M L'lI 0 )
The study effort reported hecreini is basically a continuation and expansion of)Ithec work done by Sewell (see footnote 1). Hius work served b~oth as a baisi andostarting point For' this effort.
Thijs study, ais did Sewell's, considers veiglit constraints imposed onl thlewarhecad. But, instead of' a volume constraint being imposed, separate considerations of"
both diain eter and lengt Ii art- included. TO this hlas beenI added thle conside rationm of 'end e ffCtIs: these apea s comreel ion Fac tars in thle formn of' exponenialC~ Imii ctions (A'
lemigtb-to-diameter ratios. Althloughl Only kine~tic en~ergy (1/2 mv2) is of concern hecre,til SalICgenralIVOC(I-ies allbe sedoilotlvroptimization c.riteria such ats
mo10n11e1tLnin1 ( mv) or any otihe parameter involving niass and velocity, e.g.. niv-1Additionlally, onl1y a so)lid cylinder withi no end con fineme at is considered in thiis-Study. Any otlier con figuraticn, such as a hiollow cylinder or use of' appreciable endcon i 'nenien t, would re nire new correction I'ac lois since the mlodif'ied enld effects Iforeachi con figurationm would have to be de term miied.
Naval Ordnanice *Fest Stad i-1. FI'xed-W~eight and Vulume C'onstrainits On optimnum Ch/arge-i;o-Mt'tal Ratios ini War/wad I)L'ign, b~y R.6S,. Sewell, hmina Lake, Calif.- N(YUS, Marchl 19)(4. (NOTS'111 34.30, publication tINCI.ASSIFIFI).)
3
LO
NWC TP 5892
This is a relatively simple method. lHowever, it is highly dependent on tilequality of the input data. Because the data employed were not generated under thisstudy effort, appropriate references tor these data were used to generate correctionfactors for the velocity as a function of length-to-diameter ratios (L/D) at the initiatedand uninitiated ends of a cylindrical warhead. These velocity correction factors werethen combined with the Gurney equation for a solid cylinder and included as a partof the incremental energy equation. Integration of that equation resulted in the totalinitial fragment kinetic energy for a given set of input parameters. Depending uponwhich velocity correction factors were used, three different initiation schemes could heconsidered, as shown in Figure 1. Single-point, one end, center initiation (Figure a.)served as the baseline, while the center initiation (Figure lb) and simultaneousdual-end center initiation (Figure Ic) schemes were modeled by choosing the appro-priate combinations of correction factors.
VELOCITY CORRECTION FACTORS
Derivation of the velocity correction factors is the first step. Because therelease effects are difflerent on each end of a single end initiated cylinder, each end ofthe cylinder will be treated separately. Mathematically this assumes that the entirecorrection lfactor is thle product of two independent functions of length, i.e.,
"fa) Single point, one end, centerinitiation.
(b) Center initiation,
(c) Simultaneous dual end centerpoint Initiation.
FIGURE 1. hIntiation Schenws.
4 .I I I I I II III .. ........ "1-1 [1 I I IOmni •
NWC TiP 5892
Cf- = lK*(Qd) G(/d) (I)
where
CI is tile velocity correction factorý,/d is the position inl length- tv-diamieter ratio of' explosive charges
onl thle chargeIt V/d) is the correction at the inlitiated enid(;( Q/d) is the correction at 'thle uninitiated end
Thec problem, theni, becoines one vi determiining F(V/d) Lind G(V/d) for the c:ylinderCIs.
Review of' UVailablC litCr-aturHc wouldC ildicaIC o11lY Very limited work has beenIdonec inl this area. A plot of' correctionl factor ver-suS lengLth inl L/t) (FigLrcC 2)1'tar
si e poi lit enld unitkiationl \as fon. h aaWere used because of' theirconivenient formo and availability. It was asiiumed that thet correct ion factor applied toiliitial Velocity at vaIrioul.s lo in t- onl the cylinder rathier than average velocity of' theovcrill cylinder- :mld that the charge umass to meltal MaSS raUtio Was so Ificiient y hiigh thiattlie mnetal eawe thnickess wa.- Nmall c0l)pa1-Vd t-o thle me1tal eaISe outside dianmeter.
A muodified least squatres fit was done to thle curve to puit thle data inl thet lorilnof' anl eq nat iOn. TIIi rsl-SIt iS also plotted inl Figu re 2. The for-ili 01 eqluationl uISed as ac-orrect ionl factor is,:
FV)= I cA (V/ d (2)
Where
1PtQ(I =? correct ion I'c tarQd= position onl tilie case inl terms of length-to-diameter ratio oi the
explosive char-geA - constant =-2.3017
Once thme corre~ctionl lactor, F(VAO/d, has been determined. it becomes niecessary todetermiime the correction fllCt or For tile uinitiiinit otd end, ( N Wd ). The Ballistics 1< eseareliLaboratories (BRU. ) had pub fished dat a3 Which we cmuiipoycd for1 this purilpose. ForfliItire- simlll)icity, Wje Will saIy that ((d) (Nxwhere x =X( kid). x is thle distanlceFroim the tni initiat ed cuid. Introducing this change of' variable will niake the proccssintj.01' time 13RI. dalk. mm1Lieli easier. A least sq~uares tit of, tile data (0oy several diffe- renltexponiential equai~tionls resuilted inl
2 FNIC (to pouiiijn. 171c Husirc \/2E. by Doiiald R. Kenniedy. lO'enrsc Thluiittogv
.3AjicimcaiuI hLi'lh( PTIMIMltehres' Asstwiai oil. l'tmeeohuig rf the First ln1tunmarfuiall
Sump'I nilmo Ikallisi(N. 13-1t5 Noo'uutwi 19074. '(AClclation il tO Eniguen Velociuic.s Flom
hI' z~iiic'itl lol Muriimi "" hI Ri~* '. R. lKdrpp anid Vt. %V. Piv-edlonr Balltistics Rescarch Lrbnra-Ltruies
I publticationi UNtT'JASSI 1:1 l.I
S
NWC T11 5892
+ - BY EQUATION
0- 0.8F-,
z
F-
0.4
0.2
r.0
0 0.4 0.8 1.2 1.5 2.0LENGTH-TO-DIAMETER RATIO
FIGUR[ 2. Correction E~actur Comnparison, F(V/d).
GAX) 1 e - (3)
where
B constant =0.28806C Constant -4.603x distance in charge diameters from uninitiated end
Now x can be converted back to a fuinction of W/d such that
X ý X(R/d) = (L - W)d (4)
which simply places the position of' the point of interest relativc io the initiation end.
6
NWC 'Ill 5892
The form of (iWx was selcctcd oil the basis of the best correlation coefficientre1sulting from the least squares lit. The total correction factor f~or velocity as afun1ction Of' position in explosive charge diameters is now
(I-~ 2 .3617 t/d -O2 tie4.603( 1.- )d)
Multiplying this and thle GurNey eqjuation should provide a reasonable velocitNprediction along the lengthi of' a solid cylindrical, metal encased. explosive charge whichhas been point initiated on one end at the center.
To be completely rigorouLs, it Should be pointed out that I~quationi 5 is a.or-rection tal-ctor for Fragment speed. It cannot be used for velocity sinice velocity is avector qunantity anid speedv misoly thle mnagn ituode and says not hing ahouit direct ion offragments.
ONILER INITIATION TLI`CINIQU1IS
By combining IN (/d j and G(N;)~/ in two other ways with small chAanges in thlevariable, time initiation methods shown in Figures lb and Ic call be approximated. [lierationiale and correction facItors arc p~resented inl this section.
Inl the case of' center point initiation, as shown in F~igure lb. we find that thlerelease effects at either enld of tile charge arc idenltic~al, In addition, they are the sameas tilie uninlitiatedI end o I thle Single end initiated charge. Th is means that the endcorrect ion facýtor- for all tlin iitiatedI end Canl be utilized for both ends if' an appropriateChange is mlade in thle form11 of' thle equation. This Change allows treat ing the velocityffoni a refecrence end correspomnding to thle initiated end inl thle first case, i.e., Q/d =U
Thus, for this enld of* I le Charge.
()/d) I ,). 288the4 l (o)
whmile onl the other end, where V/d I L/I, thle correction factor is simply I'Auatioi 3..Heknee, this correCUO. Lionfctor is
C, = (] - .2880ove4.003td)( I - 0.2S88O)ce4b6 3 ( L- !/d 1) (7)
Thie centecr region of' tihe clmmrgi: Ior tliis con figuration is assumed, in thmismimodle]. to be unaffected by the in itiat ion point location. This is a reasonableaSSUmnlltiOll aS long as onl1Y thle Iiagn 1itUde of' thme velocity is of' interest. It is notcorrect if diricet ion is of' conkcril since an appropriate treatment of, thle Vc~tor prob~lenmin nSt also he Made. II owever, our concern1 is with minagnitude only. thbus, we need oinly
justifyV that the velocity nmagiimittitl is Unchanged. It Was determinedI,* from11 ho100thooretical and experimental information, that normal impact of' tile detonation waves
PerlSonal tliscussiniis heiwecin11 ihic athor' .111L MI. R.G.S. SCviell A' TWC.
7
NWC T11 5892
under the conditions existing in this probhoni do not change the maximum or initialvelocity; only the acceleration profile of' the fragmentation is modified. This is becausethe actual imlpulse remains about constant in this region for either normal or sweepingdetonation waves. The higher pressures from a normally impacting detonation wave arealso of shorter duration. Conversely, longer durations and lower pressures are char-acteristic of a sweeping detonation wave: hence, the resulting change in accelerationprofile with tile same limiting "velocity".
In the case of simultaneous dual end initiation, as shown in Figure 1c, bothends are initiated. Utilizing the same considerations as before, we find the correctionfactor at the reference end to be EqLuation 2 only. Now using x in place of Q/d forthe opposite end, and making appropriate substitutions, the correction lactor becomes
Ct = (I - e- 2 ' 30 17ldt)(1 c-?.4 61 7(Lk-)/d) (8)
The main assumption in this case is that the center interaction zonc, where thedetonation waves Meet, does not change the velocity magnitude of' the fragmentationsystem. Supporting this assumption is the width of the reaction zone in the explosive;on the order of 0.1-0.2 inch thick. Conversely, limited test data would indicate that,although the explosive interaction zone is very narrow, the effect on fragmnentationvelocity is significant over a much larger percentage of the warhead length. For ourpurpose, the assumption will be considered valid. However, this model should beconsidered, at best, useful only For generation of trends because of the apparent lackof' validity of this assumption.
FRAGMENT INITIAL KINETIC INERGY
There now exist correction factors which, applhed to the Gurney equation for asolid cylinder, will predict initial velocities at any point along the length of thecylinder. And this, in t LIrn, can hC used to predict f•_,iinent initial kinetic energy orpotential energy within a solid cylindrical configuration fot any of the variousinitiation systemis shown. Figure 3 will be referred !o in the following section as anaid in developing the appropriate equations. It consists of a constant diameter (d)explosive chaige having length (I.) and encased within a constant wall thickness metalsleeve.
The energy of that cylinder can be determined as follows. First, the energy atany point along the cylinder is:
d1 = ',dmv- (9)
where the incremental mass, din, of the metal case is defined as
din I III7r( 4) dt, . . )
8
NW( TI1 '589)
dd
t _ / \\ýL I
d11 iipl 7(I d Ld
TheeC ~ desity veocityl metail Lqa tin rqiStec. ~~i~i~ f'Iqain5t
tl-G IHC e( j Ut io ti T cnhe relorittenquateioin now tbevoimbes: a olos
Where
yydy 1)2 - c1
Fi OnTia veo ity 7(V in Lqmton') eursteaplctolf[qltyl5heGnic e atin.Ie eoci Vej aio owbenms
9J
NW(" TP 5892
Substituting Equation 12 into Lquation 13,1I)2 dt2 ('/M • fY 2.361
~~~~ a .. -4 W"O .~~c a5i( o[N-e- 7y
0 0.28806C4.o3(Y ))- Jy (14)
The integral itself is simple but tedious to evaluate. By expanding, integratingterm-wise, and reducing to its simplest form, we have the integral
f [(1 - e 2 .3(17y)(I 0.2880n(e- 4 ý0° 3 (Y-Y))] dy - 0.75128 + Y
+ l.3367c2, 3o17Y 5.1740e- 4 . 0 3Y +4.5918e- 4 .7 23 4 Y
0.00328c ,!.2 06Y (15)
The last term is so small that for any practical application it can be ignored.Substitutinig Equnation 15 into E'iquation 14 for the integral results in
2 = 2 ll -4 d (l M (-0.75128 + L/d + 1.33o"c 2.36 17L/d
5.1740c 4.,O31 Id 4 4.5918c4.7 2 3 4 1 -/d (1((
One additional algebraic manipulation must be done. That is :in expression forthe explosive charge diameter in terms of the more commonly specif'icd parameters ofweight (W), length (L). UIId ontidc diameter (D). Writing the expression for W:
W = 7T.. 4m+rr2. 4e(7( 4)2 d2 ) Lp1 + dT (11)0
Solving EqnUation 17 for d:
d4 ' p11)/( p+1)],,' (d -= [41 - Phil) I Pill + •P,2 1[12
iknd finally the chargeito-imass (('/M) ratio becomes
('/M = Ip ,7rr .(d -/iA )J/ [ f) 7 " L, 4 Q1 )
o)r
('/M = - _1)2d2
10
! • I i I I I I I I I I i i i , . . . . ..
NWC ITf 5892
This same procedure can bc applied to the other initiation techniques shown inFigure I as well. Fhe only changes made will be in the correction factors alreadydeCeloped and discussed, e.g., Lquations 7 and 8. lience, only the integral portion ofELuation 14 needs to be redone for tI cases considered here. For the centerinitiation, Figure 1b and Eiquation 7, the integral becomes
f 1(1 - 0.22880oc 4 .'0 3Y)y I 0.28806e 4.0 3(Y-y))dy = Y 0.2503+(0
+ 0.1782 + 0.33 19Y)e 4. 03Y -+ (0.02077 + 0.00688Y)e'' t.2' 06Y (20)
Once again the last term is significant only for Y << 1; there fore, we can ignore itand substitute Iiquation 20 fo r thle integral in Equation 14.
1lt• 1 (1)-2 d 2 \/C/M \[ -. 5CMI, = () .-d ' - /d - 0.2503
+ (0.1782 + 0.331(P/LI)c 4.'003 1./d] (21)
Using this same p'ocCd ure tr tiec dual end initiation, the integral in Fquation 20bt.eComles
[(1 e 17 )(l 3.3, 7 Y-y))](y
..... 1 ... N'+( -4.72'34Y ( 2
=Y - 1.27027 + 4Y- >C lT +(y+ I.27027)e (22)
With this now inserted hack into the original equation
1. -1 41)2 - d% + m L/d 1.27027 A- 4 1 2.3,17 1/d7r ( . - Lt Ct I L/ CI
+ (L/d + 1._27027,c 4.723 4 L /dl
RESU LTS
There 11Ow CXist thrCe sets Of eqLiat ions which will predict the initial fragmentkinetic energy outpu)0t Iroin a Solid cylindrical, metal encased, explosive charge of 'inkielength and having no cld confincment. A set ofl parameterized variables were selectedand each set of equations applied. The results are shown in tFigures 4 lhrough 2I.FigUres 4 through 9l arc for a single end initiated ch arge ds shown in I igure I a.
SI I
NWC TP 5892
Equations 14, 18, and 19 were used to generate those figures. Similarly, Figures 10through 15 are for a center initiated cylinder and utilized Equations 18, 19, and 21.Figures 16 through 21 are the maxlnuma energy plots for the parameters consideredfor each initiation method. The parameters used to generate these figures were: weightsranging from 10 to 30 pounds in 5-pound increments, outside diameter ranging from 5to 8 inches in 1-inch increments, and Pm = 0.283 in/lb 3 (i.e., steel). The length interms of the ratio of length to overall outside diameter was parametrically varied foreach pair of the above parameters (see Figures 4-8, 10-14, and 16-20). The peakenergy values determined for each set of parameters were then plotted in Figures 9,15. and 21. As summarized in the preceding graphs, these data indicate the L/D and('/M values for maximum El/a2 to the nearest 0.025. It can be seen that the optimum(/M increases as L/t) decreases and in none of the cases considered did the C/M everdrop to 1.4. Also note that increased L/l) with correspondingly decreased diameterresiilts in an increase in energy even though weight and volume constraints remain thesame. This is to be expected as the end effects become less of a factor on the totalenergy consideration fLur the longer warheads. What is surprising is the degree to whichthis effect is noticed. In some cases considered, the energy varied by more than anorder of magnitude (hie to a change in diameter of less than a factor of two.
In Figures 22 through 25, the impact of fragment density (P.1) on initialfagnient kinetic energy is considered. Using dif'ferent Pm values impacts the outputenergy in a linear fashion, as indicated by Equations 10 and 14, but it also affects theresults coming out of ltluations 18 and 19). It is interesting to note that the energy furthe low L/l)s is highest at the lowest densities while the opposite is true for largeL/Ds, i.e., high p, results in higher energy. In effect, there is a L/D region where casedensity will make little difference in energy as well as L/D regions where it will makea significant differcin,. This is not surprising since the correction factors used whenapplying this mode, to each initiation technique would be expected to produce,qualitatively, such an effect. What is surprising is the apparent effect, quantitatively, atthe short l./Ds. It can be seen by looking at Figures ), 15, and 21 that, for veryshort L/Ds, the eff'2ct is very significant. This leads one to consider that sub-calibers,or diameters smaller than the missile outside diameter, may be a desirable way todesign warheads simply to increase L/l) ratio and, hence, net total energy. However,the increase in unnecessary weight required to design a sub-caliber warhead must alsobe considered before making such a decision.
CONCLUSIONS
The considerations and resulting curves presented here may prove useful in thedesign of guided missile warheads by allowing the designer to define the optimum"initial energy" packaging envelope. They do not, however, consider any of the otherfactors necessary in the design of a warhead such as fragment size or weight, ejectionanglle, or any other factors affecting hit probability. Therefore, they do not provide allthe necessary information for designing a warhead. Although an attempt was made to
12
- - .
NWC TIP 589)2
consider different types of' initiation methods, the assumptions and approximaitionsUsed are limited. The least ac~cuiate model is that of' the simultaneous dual enld
j ~initiation with the interact ion zone ill the center. Although thec miodel c~an be used toge je rate trends, its aCercLI,-y is (ILneSt jOna He.
Three general ConIcIIluioS canm be drawn 1'rvi this effort, First, the greater thewarhecad length, the greater its initial tragment kinetic energ-,y. Note once again thatthiS Nays no0thinge abou the distrib ittion of' tha t energy. Second. these ma tl-mtenica I
models all inldicate that thle opt uin'l11 C/M ratio is greater than 1 .4 anld that decreasedLIDI resullts inl higher ('/NI. Thlird, thle op~t imu~in ease material, f'rom the stand point ofinitial t'ragnenta kinetic v ie rgy, is a f'unet ion of* warhead weigh~t, len~gth. a il LI LHiwi]e r.A ISU, there is no reason to believe thai chianges inl optinmization design Criteria, e.g..iliotnentuili1 or Illy"' /2Will resullt ill the samel deCsignIs prIoving Iop tanIM. Indeed, the
iNpIeIII execise ()I' ninitient iii1 opt i iizilt ion will sflow this not to lhe tile case. Thisreport nerelý exeiniphi ties the ploccdnreS neCeýssar-y to accoplll)iSh SUChI optimlitationIwhatever tilie optinli/ation criteria.
13
NWC TP 5892
SINGLE END INrrIATION1 _'_
L/DWT: 10 LB EI/ 2
C/M
10-1
[0.325 0.750 1 1.250.386 X 10-2u /0.138 X 10-1 10.245 X 10-1
,2.639 12.320 1.980
0.475• 2S0.729•x~c-
2
S 6.705
"102
, , 6-1 .O D8-.IN. 0I' ,-IN. OD
0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
I:I;IRI 4. [ ragielit Initial Kinetic Einiergy [nvelopes it) Indicated \Vcighi, Single Fiid lIniliatlil.
14
I I I I -•' ' l I I I I i i - 1 -i- i' i i ... . .. 'i--'i
NWC TP 5892
SINGLE END INITIATION
WT- { L/D.
WT: 15 LB E/l"ClM
10 - ____ ____
1.825 1{0,488X l1,
0.7001,7730.192 X 10-t 2,19/
1.1000.475 {0.323X1¶
2329
,-AN O .D.
0 0.5 I II.I5 2.0 2.5 3.0 3.5
L/D
dI-I I !RI: 5. [ragmenti Ini~ia K inell trg 1:1IjIvel 101 Iiiilcaicýd NVNgIlt. Y411gIL [ic 1;1( 1IIlaiol .
15
NWC TP 5892
SINGLE END INITIATION
L/DWT: 20 LB E10,2
7 -- [C/M1~
_ I_.425 0-748 X 10 -
.. J:3~ '• 361• X.22,9 100-
2. 1
U.62b
-14
LU
o2110-2
-;: .5-IN. OID
7-IN. OD
110-3 .. ..OD0 0.5 1.0 i.b 2.0 2.5 3.0 3.5
""LDI:(;t. ILF h. Iragimnuil Initial Kinhtic licigy 'nvelopes lEi 1.dilcoted Weight, Single Find Initiahulu.
16
i i i i i i i~ i .. .i- i i - • .. ..
NWC TP 5892
SINGLE END INITIATION
WT: 25 LB Ej Ec 2
IC/M
-10
LU
w I
&-IN, OD
10 3
0 OU 1. l~b L 2.0 253.0 3.5
L - /D
NWC TP 5892
SINGLE END INITIATION
WT: 30 LB E/62'I I Clci
I[3.525 _
0.17 7X 102.100 1520.155X 101.350 -1}•_1.733\
0.790 X I
6-IN. O)
10 S0.925 .S0.544 X 10-1
2.061
C,,
-0 1 -LU
-IIN. OD0
7-IN. 00
0 0.5 1.0 1.5 2.0 2.5 3.0 3.b
L/D1 (,(IRI X. |,ragnicn I nitial Kinclic I'Icrgy Fivehlopes I<•r Inidicatud WVeight, Siingie hid linitiajlin.
18
S... • . ,, F.•
NWC TP 5892
SINGLE END INITIATION _______
300
1k-.AN 0 __
230_LB
1 ooo
-DIAMETER
WEIGHTI
0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
LID
NWC TP 5892
CENTER INtTIATION
4 m
WT: 10 LB E,/ 2
10-10.300 0.450 0.700 1.1750.219 X 10-1 0 288 X 10-1 ~0.*359 X 10-1 0.426 X 10-1I1.844 11881a 1,.733 11.552
1-2
C,,
B--IN. OD
10- 3
0 0.5 ; 01.5 2.0 2.5 3,0 3.5
LIDI I( ;[ R tF 1 0 . Fr alg m e ntl I niti ail K i n cic'l t F nl e rgy FI- v el o•p e s li• hI nd ic at ec d W e ig h t. C'e n l e i In i ti at io n] .
20
S.. ." | "N
NWC TP 5892
CENTER INITIATION
WT: 15 LB E/L2
0.6500.527 X 10-1 /11.750X 10-
/ 1.622 1.512
- 0.434 X 10
1.844ýZ, 1.025 1
0.617 X 10-11.580
10 2
LA-N. 00
N1 00
8-7-NN 00D
0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
-[;IGH ,l: I I. Fia~gllenH Initial Kineic Filergy t'livehflws Io•t Indicatied Weight, CL-'n1el hjhllillj
21
I._
NWC TP 5892
CENTER INITIATION
1
WT: 20 LB E/a 2
, -- ,C,/MK
0.8750.781 x 10- 1.683
1 6 3 1 ,3 E50i 2 .3 2 50o.600 U o88 1 X loI U_ 0.958 x O10
-- '0.669 X 10 -1' .1510 • 1.492
-NJ
10-2
6-IN. OD
8 8-IN. OD
10--3
0 0.5 1.0 1.5 2.0 2.5 3.0
L/D
I(;{ I' 12. ragm ntm Initial Kil lik' I Tie , Envelopes I'M Ildi,::}lL2 Weight, (2t'ntl Initiation.
22
NWC TP 5892
CENTER INITIATION1-
L/DWT: 25 LB E/ac2
IC/M
L 0.725• .0 75 1.700 2.9001.618 0.4 100.1 X1 0.122 X 101.616 X01.576 .11.552 ,,/ 1.480
_______ ~ ~ 4N 00 __ ___5-N
c'J
10_2___ 7-tN. 0D
6.-I N. 00
-3
0 0.5 1.0 1.5 2.0 2.5 3.0 3.5L/D
jj(;IRIJ 13. Fra-iluilt. Initial Kinmelic 'iiergy Il'tvlopes for Indicaied Weight, (enter lnitiation.
"23
I
NWC TP 5892
CENTER INITIATION
WT: 30 LB EMD2
.. {C/M
0.2753.47
0.117 x1
'10*--
" 7-N.5 .I
0 0 1. 1. 2 \
10
0.510152.0 .53.0 3.5
24
....... "1.- - .I-.I-rI I-- -1
NWC TP 5892
CENTER INITIATION
-IN.N OIDS-4N. CID. 30 LB
S..-. ~25 LB ,•"'
10.-1 _____ B
.J -- ,."• 10 LS
)_2
-DIAMETERWEIGHT
10-3 -
0.5 1.0 1.5 2.0 2.5 3.0 3.5
L/D•I(;GURF 15. Muaxinjui 1hiti Kinctic 'icigy iovtpcs hi ('enur ]llilijujjuti(jn it I F:Illl h 1j
WelighL t iil Ia)iai,,clc.
25
L i -- -
NWC TP 5892
SIMULTANEOUS DUAL END INITIATION
L/D""WT: 10 LB E/o-2
-e I10-1 _______ _______
C..'
1.3250.115 X 10-1
12.579
0.5 1.0 1.5 2.80 253.
0.372 X 10-2I 3.231
I0.100 x1-
10~~ -3 L 7-o O
0 G~b 1.0 1.5 2.0 2.5 3.0 3.5L/D
FI(;(!RI; I. Fiaginent Initial Kinetic 'hiirgy Invelopes fo- indicated Weight, Siuhltanel',us DialFIld lnitiation.
26
NWC TP 5892
SIMULTANEOUS DUAL END INITIATION
1(
-
1
10-1 _ _ _ ___ _ _11.925 X.0.2.219
j 0.134 X 10-
o.•1 1o7 -15
2.77
i0.164 X 1 -3.013 /0.750
/,lj i0 .48 6• x 10 -2
SG-I u. 00: 5-IN .O
N-N. OD
10 -3 B-IN OD
1 30 0.5 1.0 1.5 2.0 2.5 3.0 3.b
L/D
FI(H; I ,I. 17. haginitif'l Initial Klinviik' knlilgy Ihive'l opes hl Ilitlicaiit'd Wcii, l,ý .Silmllillmiclil " Dullll
27
NWC TP 5892
SIMULTANEOUS DUAL END INITIATION
WT: 20 LB E/aC/M
10-1S10-1 -- 2.500 :
S• ' 0.545 X 10-1
S, •kJ 1.979S....1.525 • 1
0 60.291 X 10-
-250
0.97b
,- 0.125x io- 1 • . "I
II
(%1 0 .675 \ !/•II \'I -0.486 X 10" X
6-INN. OD
' '•2•'6- N_. Ci D10-3
1,~~ ~ ~ 1-m (AIoo:19 Ian Intal-KN.orchcg ieoe IM Idctdcgl.SlulnosDm
28
L66m- New.-III I I
NWC TP 5892
SIMULTANEOUS DUAL END INITIATION
L/D
Wl-: 25 LB E/Ll2S-- I [C/Ni
3.050
0.800 X 10-1.792
1-J
0o- 82b -
00.491 X 10--
2.18I 5-iN. OD
00. 2. X 10 - 12
0.105 X 10 1-
2.855
SI I7-IN. 00
SGU-IN. OD
10 -3 B-IN. 6Lu
0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
L/D
I.I;I RI( I• I~'at',~l'll l it~d in lit Ittc .')+ Filve chpe hI t hlth,.';4lt' W elgh ,.ill ll, ~ it'ttX lt:
Enld Initiattion.
• 29
NWC TP 5892
SIMULTANEOUS DUAL END INITIATION
L/DWT: 30 LB E/c,
2
C/A
2.200 1j.20.719 X 10- 0.106 X 102.098 1.125
10 6-IN. 00)
1.425U.400 X 10--
2.383
1.000 1.- , 0.190 X 10- '
C14 3.013
10- 2
7-IN. 00
10-3.. .1
0 0.5 1.0 1.5 2.0 2.5 3.0 3.5L/D
FI(;JURE 20. FrlagnicrII Initial Ki. [incrgy |InvUIopC S l,,)(11OW• IIl Weight. SiiruiltrliiWHis D)11alI nd Initiation.
30
m I m • i ... ....... i .... - i. . ... . .. i . . . . .T ... ....... .. ...... .... 7
NWC TP 5892
SIMULTANEOUS DUAL END INITIATION ___ ____
10-i
0 L
6CN CDhIN I
-LL
102 LB_
0 ~ ~ ~ ~ ~ ~ -N 0.CID .52025 . .
0( 1 L
NWC TP 5892
5 IN. SINGLE END INITIATION __.,__
-1 10-1
6 0.100S.3 1 ~0.163
0 0.280
102
0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
LiDFI(GUIRE- 22. ['llcct ol I'rag•,uHI I)a;ity on Maximum Initial Kinetic L-,'Žrgy Ihiivelops .as a
~UllCtion ol" Dialmu'lc :;md I./i).
32
LW-
NW( I'P 5892
10--1 6 IN. SINGLE END INITIATION
I--I
.,,00.100
SeN 0.697
110-
00.5 1,.0 1.5 2.0 2.5 3.0 3.5i./D
IIII
33
_. • ,.-.• A
I• .--- ... " ... ' '" ""-" "'-" ""• " i-i"......0"-i 0, . , .. ... . . .. ... i .. i "-T .. .... . .. .. ." '--- I- IL I. 3 ~ . 6
NWC TP 5892
7 IN. SINGLE END INITIATION
10-
e0.100p(LB/ 0.163
I ( 0.2800.697
10-3 .,0 0.5 1.0o 1.5 2.0 2.5 3.0 3.5
L/D
H(II(JL1 24. FL1fect oI Itligmelcit J)ceiisLity tuii Ma'jijiuin Inlitial Kinctic Energy EnvlCopei sa
34
': P(LBIN'3 -- EL3 .28
_7. 0.697
NWC TP 5892
8 IN. SINGLE END INITIATION
0--
S 0.100
p (LB/IN InkA 0.163SN 0280
0 0.697
10-2IIII0 0.5 1.0 1.5 2.0 2.5 3.0 3,5
L/D
1: 1 ( ; I I1 •, 1 2 5 . I !l l e c' t ol F~ l a. g ll l c il l D ec n s i t y ( I I M a x i lm i l l I n it i a l K i nli•' • c l h i i' g y F v klln\ ,t' q ¢ nl • a
I l-ull (ith ,D i:1linctel midK I./1).35
I.i -- -" •.. ...- .. ".%J.-- .. •. -...
NWC TP 5892
INITIAL DISTRIBUTION
14 Naval Air Systems ConaroundAIR-03P2 (1)AIR.-Y)E3A (1)AIR-350 (2)AIR-5108 (1)AIR-510813 (1)AIR-.5109131 (1)AIt,.5109C2 (1)AIR-532 (1)AIR.5323 (1)AIR-5324 (1)AIR.53242 (1)
AIR-954 (2)0 Chief ol Nav'l Operations
OP.031[(; (1)Ol1-342 (1)OP-50¢o( I)OP.-50o6 (I)
OPSn:(1)(I1P-987 ( I
L)P)'tX2LE42 (I1)
7 Naval Sea S>steums CommandSI.A-U33.3 (I)
SEA-t)411 (1)SIA-Ut)G32 (21
SLA-0543 (I1)SLA-(i54J(' (I1)
PMS-4o(J)22 (I)I Chief of Naval Research, Arlin•ton (ONRR-46 1)I Cormmandant of the Marine Corps (Code AAW-l)2 Marine Corps D)cvelopment arid Education Conmmand, Quantico
Mobility Support Division, Major Thorp (1)Waj (aiecs Division, Mai ine Coips Landing Forc 1)cvelopment Center (1)
I Air Test and Evaluation Squadron 5I N'aval Aintiiionl i)cOi, Earle1 Naval Ano|mt|ition Djep)t, lawthorne (Code 05, Robert Dempsey)I Naval Coastal Systems Laborat(ory, Panama City (Code 772)1 Naval Explosive Ordnan,:ce Disposal Facility, Indian HeadI Naval Intelligence Support Center (Code OOXA, Cdr. Jack Darnell)
I Naval Ordna,ice Station. Indian Ilcad (Technical Library)I Naval School Explosive Ordnance Disposal, Naval Ordiianie Station, Indiin HeadI Naval Special Warfare Croup, Atlantic (RDT&I)I Naval Special Warfare Group, Pacific (RU)T&E)
36
J[ P' - . ... . ••" 7 • "m e' • •.... ;-' . ......-7C '- ....-
13 Nv,val Surface Weapons Center, White Oak
Code 0431, G. Klanim (t)Code ESE, S. Mason (1)Code GWA (I)Code KM (1)Code NS (J)Code T (1)Code W (1)Code WR-12
L, A,.derson (I)M. Stosz (1)
Code WERCode WR-13, N. L. Coleburn (1)Code WR-102, 1. Kuibik (1)Code WWB (1)Code XWF (i)
I Naval Undersea Center, Sari Diego (Code 133)I Naval Weapons Station, Yoretown (Research and Development Division)I Naval Weapons Support Center, CrineI Navy Ships Parts Control Center, MNlchariicsburg (Code AMb)
I Nucicar Weapons Training Center, AtlanticI NucL'ar Weapons Training Center, Pacific (Conventional Weapons Employment Cu',rse)2 Pacilic Missile Test Center, Point Mugu
Code N322 (1)Code NI 124(1)
I Naval Intelligence Support Center Liaison Officer (LNN)
4 Army Armnaent Command, Rock Island (AMSAR-SF)I Army Combat Development Command, infantry Agency, Fort BenningI Army Materiel Command (AMCRD-J)
I Army Ballistics Research Laboratory, Aberdeen Proving Cround (AMSRD-BTL, C. Kingery)12 Picatinny Arsenal
SA RPA-AD-D-W (2)SMID, Concepts Branch (4)SMUPA-D (3)SMI fA-DM2 (1)SMUPA--P, Dr. Norman Slagg (1)SMUPA-VE-5 (1)
I Headquarters, U.S. Air Forcc (AFCSAM-I)1 Air Force Logistics Command, Wright-Patterson Air Force Base (MCMTM)4 Aui Force Systems Command, Andrews Air Force Base
DL(1)DLPI (I)DLW (1)SDW(1)
4%I
