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Cratering Phenomenology and Yield EstimationEstimation of yield from crater diameters relies on several parameters. The mostimportant ones are (1) the depth of emplacement (2) The type of medium and the (3)type of explosive that is chemical high explosives (HE) or nuclear explosives (NE). Therelation between these various parameters was carried out by several people principally,M.D. Nordyke [1] and J. Toman [2] at Livermore Radiation Laboratory. These experimentswere carried out to evaluate possible use of nuclear explosives for peaceful purposes, orPNE’s. Let us summarize some of the conclusions of these authors.The Toman CurvesThe mechanism of crater formation in nuclear explosions(NE) and that caused byhigh explosives(HE) and various scaling laws has been studied in the fundamental papersby Nordyke [1] and Toman [2]. [1] contains an excellent review of the subject, while [2]discusses several technical aspects. Toman [2] introduces normalized parameters(scaledparameters) to study various types of explosions, HE and NE in different media. Weintroduce these parameters. First we have the scaled radius Rs defined as,Rs =RY 1/3.4(1)where R is the observed radius of the crater in meters or in feet, and Y the yield in kilotons.Next we have the scaled depth Ds,Ds =DY 1/3.4(2)where D is the depth of emplacement in metres or feet, and again Y the yield in kilotons.Toman plotted for various explosions (see [2] and also Nordyke [1] who reproduces Toman’scurves) the value of Ds along the x-axis and Rs along the y-axis. Toman [2] obtained thecurves presented in Fig. 1 in our article which is a reproduction of the plots on pg. 368 of[2].The following observations are immediate from the plots obtained by Toman.Effect of MediaIt is seen that the curves for hard, dry rock, are bounded above by the curve foralluvium. This is true for both HE and NE. That is for a given yield and same depth ofemplacement, the crater will be smaller for hard rock than for alluvium. In a sense thesemedia are the extreme cases and for any other media the curves have to lie between thetwo displayed extremes. This is the situation for the medium at Pokharan.Chemical or NuclearIt is seen from the curves that if the medium is either hard rock or alluvium theplots for nuclear explosions is enveloped by those for high explosives. Thus chemicalexplosions for a given yield and same depth of emplacement give a larger crater thannuclear explosions. That is the coupling is different. This is the result of various gasesand other chemical products produced in HE explosions. [2] has a discussion on pg. 3541
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explaining the fundamental differences between HE and underground nuclear explosions.One may also consult [8] for a further technical discussion on this point elucidating thedifferences between HE and NE and crater formation.Depth of emplacementIt is seen the curves for NE in hard rock decay sharply and cut the x-axis at theparameter value 60 where the depth of emplacement D is now measured in meters andwhere the scaled depth of emplacement Ds was plotted along the x-axis. The plots showthat for NE when Ds = 60 in hard, dry rock there will be no crater but a retarc ( areversed crater, a mound of rubble). This cut-off point is determined by the event Sulky.The mechanism of crater formation is explained in Toman’s paper. For a device buried ata shallow depth, first a small crater is formed since the bulk of the content escapes into theatmosphere or as ejecta. As the device is emplaced at deeper depths, the crater diameterincreases to a maximum, then again starts to decrease and then at a certain stage insteadof a crater a retarc is formed. Emplacing it deeper produces then no visible disturbanceon the surface. Thus from the Sulky event depths of emplacement D given by:D = 60(Y )1/3.4 meters(3)will produce a retarc in hard, dry rock. D is clearly larger in softer alluvium. Now for theevent S-1(Indian thermo-nuclear explosion of May 11, 1998), Y = 45. In hard, dry rockusing (3) we compute easily that the critical depth for producing a retarc is 194 metres,which is close to the shaft depth for S-1 stated by Chengappa in [3], pg. 427. In fact themedium for S-1 was wet [3], and somewhat softer and since Chengappa says [3] that theS-1 shaft was over 200 metres, the S-1 event did produce a small sand mound, consistentwith our equation (3).Maximum crater sizeThe cratering curves in [2] achieve a maximum at Ds = 40 and for this value of Dsthe corresponding Rs value in hard rock is 45 and 50 for alluvium. This means that for ashaft like S-1 with depth of emplacement D = 200 metres or thereabouts, the maximumcrater size will be obtained by a device whose yield is(200/40)3.4 = 237 kilotonsand this will produce a crater of radius 250 metres. Thus one can conclude that a devicewith yield 230 kilotons could have been emplaced in the shaft S-1. But this would haveproduced a gigantic crater, the largest ever if one looks at the table of PNE explosionscompiled by M. Nordyke that appears in Toman’s article [2]. This is Fig. 2 in this article.The largest crater in a US conducted PNE experiment was the event Sedan (see the tablein Fig. 2) which was emplaced in a shaft 194 metres deep in desert alluvium and produceda crater of radius 185 metres. In fact Nordyke [1] recommends using Ds values between40 and 50 for digging craters and in fact suggests using NE in a fantastic scheme to digout a secondary Panama Canal. The aim of POK-2( Indian nuclear explosions of May 11,1998) was not the creation of craters of maximum radii which would be consistent witha PNE type of shot, but the weaponization of devices. Furthermore it would have been2
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ludicrous to test such massive yield devices with the device relatively shallowly emplaced.One could ask the question what Ds value would BARC be comfortable with. To answerthis question we recall POK-1(Indian nuclear explosion of May 18, 1974). We will seein an instant that its Ds value is around 52 thus it qualifies as a PNE, but we will usethe terminology MCE, maximal cratering experiment. In fact for POK-1, the depth ofemplacement was 107 metres[6] and the yield 12 kt. Using (2),Ds =107121/3.4= 52.Thus POK-1 is a genuine MCE. Now the shaft for S-1( the thermo-nuclear device at POK-2) was supposedly over 200 metres [3]. Thus let us compute the maximum allowed yieldfor a device that is to be emplaced in a shaft exactly 200 metres long and with scaleddepth of emplacement parameter chosen so that Ds = 52. We pick Ds = 52 since thisis the parameter picked by BARC for a maximal cratering experiment on May 18, 1974.Thus BARC used this parameter confident that there would be no release of radio-activegases and at the same time to produce the largest possible sub-surface effect, a PNE whichis consistent with the geology of the Pokharan site. Thus using Ds = 52 and depth ofemplacement D = 200 metres, we compute using (2),52 =200Y 1/3.4.Solving for Y the permissible allowed yield for shaft S-1 we get, Y = 100 kilotons. Forthe Ds value 52 the corresponding value for Rs is Rs = 30 where we have taken a pointbetween hard, dry rock and alluvium. This would have produced a crater of radius 138metres. This is a far more reasonable assumption of what the shaft S-1 could have carriedmaximally. Thus the shaft S-1 was at most capable of a maximum of 100 kilotons.R. Chidambaram’s Lecture at IISc(Indian Institute of Sciences)In notes taken by Dr. Shiv Sastry [4] at a lecture by R. Chidambaram at IISc, (alsosee [5]) the following points were made by Dr. Chidambaram.(a) For a 1 kt. device a burial depth of 150 metres is needed to prevent crater forma-tion. The meaning of this is now clear from the Toman plots. The emplacement depthChidambaram refers to is clearly in alluvium. Thus in alluvium the critical burial depthDcritical satisfies the relation,Dcritical = 150(Y )1/3.4.(4)(b) Chidambaram also made the statement that the burial depth at Pokharan is abouthalf. One thus suspects that the strength of the material at the depth at which the S-1device was emplaced is roughly double that of alluvium. Thus the material has a strengthmidway between alluvium and hard, dry rock. Thus the critical depth of emplacementwhere only a retarc will be produced at Pokharan isDcritical = 75(Y )1/3.4.(5)3
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Now using the announced yield of S-1, Y = 45 kilotons, we easily compute using (5) thatDcritical = 229 metres. Thus if S-1 was buried at over 200 metres as per Chengappa[3], pg.427, S-1 would have produced a small subsidence crater or a retarc. This was indeed thecase, pg. 431, [3].Pokharan-1, The Indian PNE of May 18, 1974As seen above the Ds value for POK-1 was 52. The curves of Toman show thatfor a medium that has the strength midway between hard, dry rock and alluvium thecorresponding Rs value is approximately, 30. Since the yield of POK-1 was 12 kilotonswe see that POK-1 would have produced a crater of radius, (12)1/3.430 = 62 metres. Thisagrees very well with the crater radius stated in [6], [7].C. Sublette’s analysis of the Pokharan-1 eventSublette[6] has made an analysis of the crater data for the Pokharan explosion of May1974. However, there are serious errors in his analysis. We now point out these flaws.(a) In arriving at the plot, Fig. 1 in [6] Sublette has completely ignored the effect of themedium and essentially assumed that cratering effects are the same in all media, thus theplot in [6] consists of a single curve as opposed to the plots in [2] where multiple curvesare obtained for different media.(b) More seriously the plot in [6] has been obtained by combining data from both NE andHE. Thus Sublette assumes that the coupling for NE and HE is the same. This is false asis clearly seen from Fig. 1 in this article which is taken from [2]. Both [1], [2] emphasizethat one cannot combine data from HE and NE to arrive at cratering curves. Furthermore,computer simulations by Burton et al[8] clearly show that coupling is markedly differentfor Nuclear and High explosives and one cannot estimate yields by combining data fromboth types of explosions.(c) To arrive at his plot [6], Sublette uses the Sulky event which produced no crater but aretarc, (see Nordyke’s table, Fig. 2 in our article). In fact [2] contains a photograph of theretarc formed by Sulky,on pg. 361. Furthermore the Sulky event defines the point wherethe cratering curve for NE in hard, dry rock crosses the x- axis in Fig. 1, that is producesno crater. Thus one is baffled as to how Sublette assigns a crater radius to Sulky in hisplot.(d) To arrive at his plot Sublette uses another event, Palanquin. As is seen from Nordyke’stable Fig. 2 in our article, Palanquin, was emplaced at 24 metres, and had a yield of4.3 kilotons. It was supposed to produce a retarc. However, a failure of the stemmingmechanism occured and thus a crater of radius 36.4 metres formed. This failure of theexperiment has been explained on pg. 375, [2]. Thus Palanquin was a flawed experiment.However, Sublette has used data from this event to construct his plot. It also clear thatin the all important steep part of the graph from where yield estimates for the POK-1event are deduced, Sublette uses only two data points from nuclear explosions, one theflawed experiment Palanquin and another event Sulky which did not produce a crater butto which Sublette nevertheless assigns a crater radius.The effect of failure to be careful and address the issues pointed out in (a)-(d) aboveis that Sublette produces a plot that is markedly shifted to the right in comparison with4
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the plots in [1] and [2]. Thus the conclusion one would obtain using Sublette’s plot is aclear underestimation of yields due to the rightward shift of the plot. This is the origin ofSublette’s lower estimate of the yield of Pokharan-1.Further Comments(a) The surface features of the S-1 shaft after the explosion coupled with information ofits burial depth indicate that the yield of S-1 is in agreement with crater and emplacementdata.(b) The data of 7,000 sq. metres of steel sheets to line shafts as claimed by Chengappa[3], pg. 40 is now seen as the amount needed to line both shafts S-1 and S-2.(c) Finally, we address the question as to why BARC did not test a 100 kt device in shaftS-1. The aim was to test a Agni configured device with the sole opportunity provided tothe weapons design team. Thus to fit a package into the requisite dimensions probablycalled for a device design with yield of about 45 kt. If there were no constraints, mostlikely a test of 100 kilotons would have been likely with the attendant large crater.(d) Lastly a perusal of Fig. 2 shows PNE experiments for craters were either sub kiloton,sub-sub kiloton or within 2 kilotons. Only two experiments were large. These were Sedanalready mentioned above and Schooner at 35 kilotons at 135 metres emplacement. Thisproduced a crater of, 130 metres radius.(e) The reader who is more mathematically minded perhaps will gain a better under-standing of this topic in the context of the Pokharan events by studying the articles [9],[10].
REFERENCES[1] Nordyke, M.D., Peaceful Uses of Nuclear Explosions, IAEA-PL-388/12, 49-107, PeacefulNuclear Explosions, Phenomenology and Status Report, Proceedings of a Panel, Interna-tional Atomic Energy Agency(IAEA), Vienna, 2-6 March 1970.[2] Toman, J., Results of Cratering Experiments, IAEA-PL-388/16, ibid, 345-375.[3] Chengappa, R., Weapons of Peace, Harper Collins, India, 2000.[4] Sastry, S., Notes taken at R. Chidambaram’s lecture at IISc, Strategic Affairs Archivesat http://www.bharat-rakshak.com[5] Chidambaram, R., The May 1998 Pokharan Tests: Scientific Aspects,
http://www.saag.org/papers5/paper451.html[6] Sublette, C., What are The Real Yields of India’s Tests?
http://nuketesting.enviroweb.org/hew/In ... lds.html[7] First Nuclear Test In Pokaran in 1974,
http://www.fas.org/nuke/guide/india/nuk ... -pix.htm[8] Burton at al, Computer Design of High Explosive Experiments to simulate subsurfaceNuclear detonations, Nuc. Tech., 26, 1975, p.655
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[9] Ranga Rao, M.P., Cavity Radius Estimation for Contained Peaceful Nuclear Explosions,An analytic approach, Proc. Indian Acad. of Sciences, Section A, 87A, 1978, 13-21.[10] Chidambaram, R., et al, Phenomenology of the Pokharan Peaceful Nuclear Experi-ment, Pramana, 24, 1985, 245-258.
