Blast wave part 2, chapters 5 through 10

,., APPROVED FOR PUBLIC RELEASE ,, * ‘1 ——— ; APPROVED FOR PUBLIC RELEASE APPROVED FOR PUBLIC RELEASE ● o ** -’~ ‘UN(JNWFIED ~ ~ ,’ T ‘ .1’ BLAST ITAVE ‘“‘“‘ ~ ‘ “TA3LEOF CONTENTS , Chapter ~ 5.1 5*P 5.3 5J4 5.5 ~.6 507 Chapter General Pmoedure Gmeral Equat$ona The i%int SouruO Comparison of’the Point &mroe Results with the Ihrmt SCil\iti On The Case of the J.aothermalSphere Variakle Gluma The Waste Energy t’ Eiw13cT OF VARImI,? DENsITY M Tlia PROPAGATION OF m BUNT WAVE K, FuQhs ‘1 ‘/ introduction Method of !i~timating Energy R~bQao by Obtirimtiom of the,,&iOd( Radius Xntegratitx of the Bquatims ofMotion 6,3 Effeet of Variable:Density Ikar the Cmter on-the @r 6.)+ shock 6,5 Application to the Trinity Teat 2:; THE IBM SOI.JXON OF THE 13LASTWAVE mO13LEM K- FVcha lilt Foduotion ~a~ 7*3 7● 7.5 7*’T Chapter The Initial Conditions of the 13M Run The To+al Energy The IBM Run Results with,TMT Exploaim, Effieienwy of Bh@sar scaling UWB Bomb ASYMPTOTIC THEORY FOR SMALL BLAST FRl$SSURE R* Beth*; X, ihmhs APPROVED FOR PUBLIC RELEASE APPROVED FOR PUBLIC RELEASE “ ” ; Ghepter8 (Continued) ,.’ , :, 8*11 , ,“ (mi$erg The Contidmtim of the IHki.Run THE EF?JWT OF ALTITUDE -=X ~OhO ,’.,! 9* I 9@e 9* >.;:5 lntroduotion AQou8tio Theory TMory Inoluding itm?gy Diaaipa%ion Alternative Derivation l?valuationof Altltude Correotton Faators 4pplioation to Hiroshim and ?ltigatii TM! MACH lSFF3CTAND THE HEIGETOF”B~ST J von Ntmmarm, F* Reinea “, ‘::: “~-~ ~Qn6ideruti~~ m the Production of Bla@ lhmag~ Height of’Detonation end A,aalitative Discussim , ~,? T “’%heMaoh*~ff&t m RefIeot~on 10 Expmimental Determination of the Height of Burst 10.5 Conclusion: The Height of %ti i! , ., ,.; ~eto such a swthod is found in the very peculimr nature of the point source solution of ,/ Taylor and von l’?elmsnn.It is oharaeteristic for that 8olution that the density is extremly low in the inner regions and is high Onljr in the immediate neighborhood of the shock front, Similarly, the pressure is almost exactly constant inside a radi~s of about ●9 of the redius of the shook weve, It is particularly the first of’these facts that is relevant for constructa Jng a more general wt!-md, The physic~l situation is that the material behind the shock moves outward with a high velocity Therefore the swterinl strenms away from the center of the shock wave and oreates a high vacuwn nenr the centere The ab~enoe of any appreoimble amount of mterifil, together with the , moderate size of the nccelorationa~ immediately leads to the concllzsionthat the press’uremust be very nearly constant in tha of low density It is interesting to note that the pressure in that region is by no means zero, but is ~lmost 1/2 of the pressure at the shock front+ ,.,-., / /) APPROVED FOR PUBLIC RELEASE # APPROVED FOR PUBLIC RELEASE ●✎ ● *a ● *m ● ** ● ** ‘!q&+&**? pronounced for values of evaountion of the refiionna~rg “ the specifio heat ratio ~ It is w1l close to known thnt thu density at “%-.- ~ the shock inoreaaea by a factor (1) inite as ~ approaches unityo Therefore~ for ~ near the This ~ecomea inf’ assumption that all aaterial is oo~entrated near tlw shook front becomes “* be shown to behave as more and more valid● Tti density near the , +3/(2’-1)* The idea of the method proposed horo, is to W&S repeated use of the f aot that ths material is oonoentratod near the shook front AS a oonsequenoe of this fuet the velooity,of nearly ,allthe material will be the snnw as the veloeity of the =terial direatly behind the front* Moreover, if Y is near 1, the material mlocity behind the front is very nearly equal to the ! shock veloeity itself; the two quantities differ only by a faotor 2/(~+1~ ● The acceleration of almost all the meteriaL is then equal to the acceleration the shook wave J knowing the aoceleration one oan caloulate the pressure distribution in inside terms Of the a given radius● material coordinate, iDc~, the amount of air This calculation again is facilitated by the feet that nearly all the material is at th shook front and therefore has the same position in space (Eulerinn ooordinato~c + The,procedure followed is then simply this- W that alljmaterial is oo”~ntrated ●t tb shock f’ronte distribution~ From tb prewire relation bet-en and start from the assumption We obtain the pressure density along an adi- abatio8 IWOoan obtain ths density of each material element if we know its j ,- pressure at the present the , , 4- aa well as when it was first hit by the shock~ By intw~ration of the density W= ~~~ ~*yore aoourate value for the “ ● *W.*** ’ .* *”*1 ● *9 ●:* *** -** ** ~j j:”j“=j“”+; *;8 ●* 4’.’“’ -——— ~ — APPROVED FOR PUBLIC RELEASE —.——— —-— ,-., — -— ,-, , -.- , -,.-._- APPROVED FOR PUBLIC RELEASE it would then lend to a power series in powers of ~ -1 The method lesds directly to a relstion between the shook acceleration, the ehook pressure and the internal pressure wave ● the shook In o~der to obtsin a differential eountion for the position of the shock as a function of timeS we have to use two ad~itional facts One is the Hugoniot relntion between shook pressure end shock velocity The ot~r is energy eoneermtion applicfitionasuch as thnt to in some form: the point eource solution itself, we may use the conservation of the total energy which requires that the shook pressure decreases inwersely as the cube of the shock radiue (similarity law)● On the other hand, if there is a cen- tral isothermal sphere as described in the lnst chapter, no similarity law holds, but we ‘may consider the adiabatiu expansion of the isothermal sphere and thus determine the decrease of the central pressure as a function of the mdius of the isothermal spheree If we wish to ~pply the method to the ease of v~riabla ] without isothermal sphere,we may again uso the conservation of tohnl energy but in this case the pressure will not be simply proportional to l/YK not prevent the applimticn of our method is long as ‘he density ● , *.$, ,“”,,0 ● 9- -* - .* ● ** ●*U ● ● ** *-,~-a” c - APPROVED FOR PUBLIC RELEASE increase APPROVED FOR PUBLIC RELEASE ~ GENERAL EWATI CMi We shall denote the initial position of an arbitrary mass element by and the position at time t 1? The Do$ition of the shock wave The density at time t wi11 be denoted by Y ial density by PO by The pressure is p $S denoted byfl , the init- (r ,t ) and the pressure behind the shock iS pS ( Y ) The cont:lnuityeo~tion takes the simple fom (2) From this we have (3) “G ‘IM equation of motion becomes simpljj (4) dt~ The pressure for any given material elemefitis connected with its density by the adiabatic law (conservation of energy), The particular adiabat to be taken is determined by the condftf.onof the material element after it has been hit by the shock If we assume-constant z the adiabatic reldtion gives ‘k(r, t) =~~(r) i) @ x PJ$-) (r (5) We shall use this relation’mostly to determine the density from the given #- for the density behind the shock presw IT dist:rih~~ tion, Using ~tionDO*0 (1) ●* ● ** ● * P3 , and the continuity ~ua~?~m -0 ● **wj e“=&~ ***.*? ** ● ~(2\, APPROVED FOR PUBLIC RELEASE ‘ APPROVED FOR PUBLIC RELEASE (6) The three conservation laws, (2), (4) and (~)$ must ~ , the.Hugoqiot equations at th8 shock fwit which am ccmsequenaem of the gqme conservation MO’ kn~ supplemented by to Mq$hm-lvw These 2wAkt4cn6 glb for the density at the shock frdnt the result ahwwiy quoted inl!$qua~im (1), for the and for the relation between the material velocity behind the shock, ~, and -4%: qdv : L’”> j ,‘ (“$J the shock velocity, ~ s / ,~~ :~:= ‘2 ;/(%+1) (8) The prc}blemwill now be to solve these eight equations for particular cases with the assumption that ~ is close to 1, T&m #quatiOn (4) reduces to Ck!the”right hand side of thfs equation we have used the fact diacusaed the Last section that practically all the ~terial frcnt Therefore the position R the shock in is very near the shock can be Mantified with the position of “~ with the shock acceleration ~ Y’, and the accelerate~ S@m the right hand side of Iiquati m $ immediately to give of r it tntagrates ‘ (9) is WMqpmdant \ # (lo) If we use the Hugoniot relation (7) and put ~ = in that relation we find further k ● ,, *CI n 4,, ** = +-+ e.● m , -! ● , !m.* *F ,, **- APPROVED FOR PUBLIC RELEASE **9 APPROVED FOR PUBLIC RELEASE V-6 (11) This equation gives the pressure distribution at any time in terms of the position, velocity and acceleration of the ehocka Of particular interest is the relation between the shock pressure aridthe pressure at ting’ r,., = the center of the shock wave O This rehtl.on is obtained by put- in Bquation (10)0 Then we get “(M) , The press~re near the center is in gene7al smaller than the pressure at the shock because ‘; is in genexnl negative It can be seen that the derivation given here is even more general than was stated In cartic~~lar,it applies also to a medium which has i’nitialSy ,* non-uniform density It is only necessary to replace < ,, rs by tha ma’ss en \ closed in tha sphere r (except for the factor 4~/3) From thelpressure distribution (11) we can obtain the density or the ~ position R using llquation(6)0 Thy r%maining%problem is now to calculate this densiti~distribution explicitly, and to determine the of the shock wave in particular cases ,+ The simplest application of the general theory developed in the last , sect.icnia to a point source explosion, In this case, the the~ry of von Neumann a,ndG, Taylor is available for comparison , Equation (12) gives a relation between various quantities referring ,“ ,,, to the shock and the pressure at the center of the shock wave To make any further pro~xwss we have to use the conservation of total energy in the APPROVED FOR PUBLIC RELEASE —— ——.—-— ,.,-— —— - — —.,.,, ——- —— ——.——— — —— —— “, >7: -., APPROVED FOR PUBLIC RELEASE v “8 1.4 With t~ 3CW; ●261 : i I 1.96 ; 2.05 -.*-U ,- *,& *,& “ , ,, ,- , ” _. J relation of internal and shock pressure known, w can now eal- culat$ the-t@tal petential energy content We knuw that the potential energy @or unit v~lun@ is P/( x -l)● We further knew from ncpntfen (11) that the pressure is constant and ●qual to ly Moreowwr,wa know that a11 the matter is free of a very thin abll P(O) ovur the entire region which ia nearin conoentratec! near the shock front* Therefore,with the exception of a very amall~fractiun of the volum occupied by the shock waves the pressure ia enual t: t?w intorlcw pressure The totel energy is then a #J s (17) -$-n_ ( of* Eq*ticn In the Instlix in hat expre8aicm (13) ) of Table ~*3Jabove, We gin the exact nuumric~l factor in (17), according to calculations of Hirschfeldor~ It ia seen that this facitoris very O1OU* to 2R/3, for all values of 104s This itidue to n compensation of varicma errors up to The Internal pressure is ●c%ually lb~s than l/2 of the shook pressure, but this is compensated by the fact th@ttb @ pressure near the shook front is higlwr than the internal pressure Ir@@ed the ratio of the volume average of the pressure to the shook pressure b mush oloser to 1/2 than the corresponding ratic for the internal pressure (cf*Eqwt%On# 31a, 31b~? ~ade in ~’uation (17~ A further error wh:ch hme been is thnt the factor 2/( M +1) hes been neglected in APPROVED FOR PUBLIC RELEASE APPROVED FOR PUBLIC RELEASE I —J .-.-.–l-= – —. _ -, ‘+- —.— -“: -$‘::‘-g-” “: ;-” 3j-]’::-’ ! ; ‘-: —! ——_.— — —— — ——- ——- - —— - — + _ ——- ‘- - - “ ‘“’”’-’~~ : :._ _ f-,;~::~, ; ?j ,f~: :: —_ -r Illlllilll III - l/lh=lll — t7c=i.5 ‘ -–t––– / / —— / h.=2 @ - / — — ‘-” ““-””-~ —— .—— 1“2 D - HORIZONTAL ( PROJEGTEC)) DISTAN~~ APPROVED FOR PUBLIC RELEASE f=RCj~ ~~A~~~ 10 (f~.) II 12 APPROVED FOR PUBLIC RELEASE * lt-90 ● J !, Height,Of buret -~U6 horlsontaldi8tWOe fOr a @stem height and ovarpmmra + -8=llb TWl!’ D = horlsontalpro$mted distance hc= cha~geheight (feet) a b= *1.400 ft ;80 C21 X*63 d= 46 s a ●S7 faK ,, (fa8t) =-i% 29“’ ; ~ ,~:: 20 j = :: k= g = ● APPROVED FOR PUBLIC RELEASE ”.- “- APPROVED FOR PUBLIC RELEASE _— — —-— —— ““”-” i “i~ —— I !5 , 4’ 22-=JJ 6- , -k I I { I h i JT , [0 12 * 14 16 1$ D (ft) APPROVED FOR PUBLIC RELEASE ‘ 20 22 24 26 APPROVED FOR PUBLIC RELEASE x- 91 the peak px%ssurehas a prescribedvalue.(19)mis valuewill, in general,be (19) It might be statedthat a betterschemenow existsthan thatwhich was used for obtainingthe pressure(on the ground)versusdistancecurves for an elevatedpuclsarbomb ‘Iheidea is~ deduce the reflection coefficientsfor chsen overpreseures and angles of incidencefr~ the measurmenta made on ‘lNTand thenapply theseresultsto the free air blast curvefrom the nuclearbomb The main reason thiswas not dme in determiningthe heightof burst is that the IBM runs which give the free air overpreeaure, diotancecurvesfor the nuclearbomb were not @t carriedout when the heightof burst tableawere made up In the regionof Mach reflection If we choose~ instead,to determinew height of burstby requiringthat the etem of the Mach Y have a prescribed height,y, at a given peak pressure,then for this value of hc it is, in general, true that U < Din= The advantagegainedby basinghc on y is that the pressure is Increased,noL only on the groundbut over a verticalregioncoinciding with the Mach Y as well In thisway, the averagepressureexertedby the blast on a structureis increased,resultingin incraeed destructicmin regions where the pressureis marginal Ihe problemis somewhatcomplicatedby the variationof pressurealong the stem of the Y A 15 to 25 per cent decrease in pressureoccuj?s in traversingthe stem of the Y from the ground to the triple point 13ecause of thisvariationthe mean pressurealong a chosenvertical strip is not rigorouslymaximizedby making the etem of the Y Just tall enough to cover it As a workingapprcucimaticn, however,we will choosethe height of burst so as to achievea desiredstem l$ightat a chosenpeak cwerpreaswe By usinga W1/3 scalefactor,ldbles10 4-2 (~), 10*4-2(b),werepreparedfor ‘ varioustonnagesof TNT ‘Wesetablesgive the heightsof burst necessary to obtainstem heightsof 30 and 100 feet at variouschosenpeak overpreesures The distancesat which thesestem he~hts are obtainedare also listed ,“”-’., APPROVED FOR PUBLIC RELEASE APPROVED FOR PUBLIC RELEASE X*”* Ta#le 1o*4-2(IU~ , ,,- Heightof Burst and Radiusat Whioh *em of IdaohY = 30 fto and I 16hd I 800 ~ ‘1960 ., ,, ; [ ,, ‘$, :, ;) ,,, ‘ , r, ,, , .* ,, .-,, ii — — —.—- APPROVED FOR PUBLIC RELEASE , APPROVED FOR PUBLIC RELEASE X“* Heightof llurstand Rad5.usat which ~%m of Mauh Y = 100 ft- and 0wqwe8suiw ExoeedsGimn Valuesfor VariousKilXms ofll!?l :, !18 hc (ft)~ 1.50 ; 200 50(-J j 300 d (Pt), 600 800 II(N3 + 1500” i_-,– . , ,-., -,’ —.-., ,, -+ -, “ 300 460 200 I ‘m t d &(lo 300 !9h* 1100 350 d 1200 ! - 1000 1400 , 4s0 650 1400 :,, 500 ‘ 1800 ~ ~mo ! f 2600 J J,., ,,.,, “/ : %foo ; 2000 2800 “’ 600 : ~ 1200 1600 23oO j ; 2000 4900 ‘ 2700 ., ;.-~ 1100 : MOO 2900 %0 - 800 \ 1200 S3Q0 5QO0 ,! , 4300 ?500 ‘km ! M& - Sfxlo 3600 4700 82OO 23(20 4300 ho 400 550 d 1300 1700 2200 4000 6200 9000 ‘ 7hc 450 600 900 “ l!klo 2500 4600 d J , h~ 1400 1900 2500 3400 4400 5700 10030 600 700 1000 1600 2000 2800 ~ 2100 2800 > +- ,m ; ) d 1600 p I /6ho 550 , I 1900 600 11s0 800 : 260(3 ; 3300 , , - - ,, 1250 \ “ I I , 5000 : 2300 , 1700 ~ 4600 i - / woo 2000 I : 3900 ( d 1700 I APPROVED FOR PUBLIC RELEASE 6000 ~ - ~ 5206 6603 11600 $lOC -* 7800 ‘: :- APPROVED FOR PUBLIC RELEASE X-94 ‘10,5 CONCLU$IC4J:‘iHEH3XGHT C@ 3UI?ST In this concludingsectionwe win bring the -Wial dismmed in tha precedingfour sactims to bear on theIproblemof 6Wemining thk heightof burst which restiLts in the greatestaraa of blas~ damage lhereare two d ? argumentswhich favoran air burst quite apart from the influenceof oblique reflection Fir(st, a bomb burst close to the groundis accomp&ied by crateringami meltingof the groundarxlhence a 10SS of energyto the blast Second,an air burst avoidsmuch shieldingof one structureby another An undesirablefeatureof air burst is, of txxmse,the fact that the bomb i8 furtherremovedfrom the targetthan it would be if it were burst on the ground A compe&ating featUrOis the fact that the high ~0$8Ure regionof a bomb burst on or close to the groundwould over-destroythe target in the near vicinityof the bomb This localoverdestructicm representsan unnecessary expenditureof energyon nearbyparts of the targetregienwhich decreasbsthe dsatruct’ion infl~ctedon &ore remotestructures 3he reductfonin blast pregsuredue to oletvating the bomb is of aoume more ueriouafor parts of the targetwhichw-h in immediatec-tactwith the groundburatb@ becomeremovedbyat least the he%ght they of beret For mOre dis~nt partu of”the , targetthe eff#etof raisingke b~off the ground Is lees important,and at distanceswhich are two or three timesgreaterthan the heightof bUr8t the changein dis~oe from bomb to targetdue to elevat$ngthe bomb is caapletely %’ unimportantin its effeet on’the pressureat the target Jud~ from the results,obta$.ned in the low b-t @@ feet) at Trinity, it is possibleto set reasonablelower limitson the height of burst required to minimizesome of.the ab~e the bla8~ reducing effectsdue to the proximityof ground .#” , ~ If it is desiredto avoid fusingearthand structuralmaterials,then since the radiusof the ar&l over which the earthwaa fusedat Trinitywas APPROVED FOR PUBLIC RELEASE , APPROVED FOR PUBLIC RELEASE x i *S * .’, - about 1,000 fswk, the he~ht of burst hf mh$.ehwill avoid aueh f%dng is * hf > 18000 fae~i’” -~ (35) This number.isfor an ener~ releasein the form of radi4mtenergyof kil+ tom of W,T‘did,sinceone may use am lnwnwe @#kre ‘@w for such radiative @ffects, W, heightof burstwhich will avoid tonnagerekm)ed aa wKU be relatedto the flxs~ radimt en@gy Ur (kilotonsI!JJT) by the inequality hg > l,CXD () + ‘3 (36) r This Calculatiohh aasunwsno atten~thn of the bw due to absorption It be released is not possibleto statewhat propmtion of the nuclearenergywill as radiantenergywithoutknowingthe designdeta$.ls of the bomb To date no such maculation has been @rried out becauseof the extreske canplwity of the lki.nity figuresgive a usefulIndicationof the the problem Hcnvever, proportionof energythat appear8as radiation (37) AC =* ~b + As a rough rul~ then,to avoid fusing t , , -,,.” /,, ‘%f”:”’$””’””; ‘ (4?q$““2’ + -.) ,, where hf ~ heightof burst ti feet to avoid fusings ~ = blast energy in kilotcm TIVT The availableevidenceon cratering frca air burat bemba is very frag- @entary Indeed,becauseof tb extmnely high presstiesa@ greatduration pf the’bl~st frcm a nuclearexplosionit is not possiblein our presentstate , ., of knotile~eto interpret,in any completmway, data on cratering from ordinary , explosives,s0that it will apply to nucluarexplosives ?he only data on ,, ,,’ APPROVED FOR PUBLIC RELEASE APPROVED FOR PUBLIC RELEASE X-96 + “ crateringby a nuclearexplosionis that abt8inedat Trinitywhere the bo& was detaated at,a heightof 100 feet: A compressioncrater10 feet deep in the centerand 500 feet in radiuewas formedIn the close packedeand of the New Mexico desert Using this pointand~the data in the WeaponsManual as a guide,It a pearsaxtrmdy unlikelythatany crateringat all would have ? occurredhad ths chargebeen detonatedat a height of 250 feet w) It is not poesibleto match everywherethe blastfma a nuclearexplosion by the blastf’ruaa suitablequantityof TNT At small~staneea the in the nuclearexploaicAgreatlyexc&d my ~eeauros pressures cleveloped developedin a chemicalexplod.on In addition,the nuclear+aqkmica 16 very much more rapid than a chemicalexplosionand does not featureafterburningof the conetltutentsso characteristic of the latter Becauseof this,and the finitesize of the mass of TNT as opposedto that of the nuclearexplosive,the shape of the blastwave anp hence its decayas it travelsoutwardis also diffwent in the two cases Deapitm this,it is possibleto find (cf Section10.4) a quantityof TNT which is equivalent “tothe nuclearexplosim in the sense that the peak overpremmre,distance characteristic is nearly the same overa emallrange of overpressure, s~ frmn to LO poundsper Squareinch The TrinityvalueWb ~ 10 kilotcms INT equivalent is for distanceswhere the overpress ure is in the range to 20 poundsper squareinch Since the ground was close, the energy effectiveh producinga craterwas greaterthan 10 kilotcmsand hekce the assumptionof 10 kilotonsamountsto sayingthat the groundis easier to crater lhe value for hn ●C is thereforeprobablytoo high scalingfor an axploeicmof blast tonnageWb (kilotonsTNT) hnot.> , (39) 120 Wbl/3 wherehn,c = height of burst @ feettO avoid craterlng ‘theheight of bursth~n to minimizethe From the above ccmsiderst~ons”’ reductionin blaatdue to the pratity of the ground~ be estfmatedaa ,., , , ‘kin> ‘n.co or hf, whtcheveris greater (40) The questicmof the value of h requiredto mfnimizeoverdestruction of the APPROVED FOR PUBLIC RELEASE - APPROVED FOR PUBLIC RELEASE ;0y2”9?= i ;::“:” *9 :., *● **O:: : ●: * “** be9 ** ** * * targetis sensitivelydepend~~ & ~he ~e@il~ $f the target Given the * ** 9** * pressurewhich is consideredas the Mmit beyondwhich overdesbructimsets ● ,.- ● ● ● ● ● ● ● ● in, a reasonablevalue of the minimumheightof burst can be obtainedfrom the pe~8’Wd ‘&s@nce curve in free air (cf Chapter? of Ma WO~ J and the mult~plication of pressureon reflecticnfrom the ground,consideringthe blast wave to be normallyincidenton a r~id ground the effectof reflectionon the pressurein the NOWAlot us consider # blast~~ from a bomb burst high (h > hc) in the air Directlyunder the bc@ ,., a ref?le~tion from the ground partly compensates for the 10s8 in over~essure due to the incrf?ase in distancefrom the boqb to the targetarea which accompanies air burst me gati in overpressure occasionedby the reflection of a normally incidentshockis a factorwhichwould be M the shockwere weak~and between2 and if the shockis of finitestrength(cf Figure21, Section10.2) For shockstrengthin the interestingregion,5 to 10 pounds per squareirich~, this factoris only a l~ttIeabove ~is, then,is the efgec$of head-onreflection A8 one departsfrom the point immediatelyunder the bomb, the incrmse in the 6verpt@Wwareg@as even more favorablebecause - of the propertiesof obliquereflectionmentioned~eviously The highest amplificationocmrs”’soonafterMach reflecti~ sets In After this it drops again as incidencabecomesmore and more.glancing Since t&e blast decays with d~st&nceand the free air peak overpressure dr0p8$it is olearlymost ,,~ dvmta&@ew to get the greatestboostingfactor,wherethe blast Pressureis * juet&j@al fc~rthe desiredtype of damage One should,therefore,choose * thQ hei&t of burst so that the maximumamplification occursat that point ,S$n* the opm amplif’icatlon occursfor earl.g ** heightof burst is to be deterdmed reflecticmthe by the #requirement thatMac% reflection sets in at aboat the limit of B damage.~21~ At &is point the amplification ● *IR* we.-’” *“ ‘ ● am aeanm~” abilityof 0.95, thatthe nuclearefficiencywill ke.:greater J, (24) than 1/2 the rated efficiency [: :.+ -, \ -f lhis was’cah’u~t~ by R F Christyfor a Christytype gadget,but is senai#AveQdependenton the specificimplosiondesign not One f~turo which-kes the choice of ,, dependent on,the at w~ich ,, for -pie, feet, defined above facts is the relative h8ight8 the abm’k bod is burst A variati~ of burst insensitivity over tiich the pressureexceedsa certain the area height the in of the prescribed height of burst gressure region to’”0 pound~per seriously value value producesno more thana 233per cent variatjon the less of to the of k L50 in the area sqwre inch for blast 20 kilotons In view of this fact,and those citedabove,a ,, very coci@aFratire limit on?the accuracyto which Lhe.bombshouldbe burstwhen : tonnages al 10 K used in ●re ●ttack is ~ 2S0 feet IX) NOT CIRCUMTE I?etentim COpY , ,,,, , ,/ @k5S\l\\D APPROVED FOR PUBLIC RELEASE r- - “+ APPROVED FOR PUBLIC RELEASE , 1, ‘ + $ .! ,“ * IJNCIAS$IFIED , ., T ,pJ-1 ,~,, M!a?M &$ #JJ ~A-fl - . ” ~,; -41 , APPROVED FOR PUBLIC RELEASE ... PUBLIC RELEASE ● o ** -’~ ‘UN(JNWFIED ~ ~ ,’ T ‘ .1’ BLAST ITAVE ‘“‘“‘ ~ ‘ “TA3LEOF CONTENTS , Chapter ~ 5. 1 5* P 5. 3 5J4 5. 5 ~.6 50 7 Chapter General Pmoedure Gmeral Equat$ona The i%int SouruO... 3(X-1) O( (r) ,[ d~~~ (55 ) ‘Y> rl the irite~,:m Bquation (54 ) reduces to - (Y) : Y + f ‘1 %&-) & In order to solve this equation’wa prooeed in two &p80 culsticm8 in Sect:ion5 -5 In the first step... end A,aalitative Discussim , ~,? T “’%heMaoh*~ff&t m RefIeot~on 10 Expmimental Determination of the Height of Burst 10 .5 Conclusion: The Height of %ti i! , ., ,.;