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d by authority of the U. & Atomic Eucrgy Commissio14

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BY REPORT LIBR_X ““%5 ~

?.priliO, 1945

(’HIOUIWSHOCK RESULTING 7RO:IN3TONATIONS ON OR ABOVE THE SURFACE - Pi8Ll&.Y flElsiwu. —— . .

!?nsignGo T.,Reynolds

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‘ COPY

J.33eariier discussion *J indicated that a oharge of a given weighL det~i.+

&ted on the surfaoe of ths ground should be about as e.t’feotivein producj.~ zrow.:.

shook as a O-bargeequal to 1S percent to 25 peroent the ~ivan wei~ht~ if thi:,

smaller ohar~e was detonated at ltoptimuiidepth~i~ (The O@ilIIUM depth

o.fburial which results in the msximum orater diameter. The optimum

any oharge is given by

5A-41%) ii is in feet and W is the oharge weight.in pounds.) This enalysi[~was

c~.rricdout On the basis of energies in~ol~d in aratering~ The method was cr~dei

lw~ tho results

eom-parisoneand

e?feoi;iveas 20

.

have agreed well with tho few oases that have been suitable for

tinegeneral assumption i8 now tit a surfaoe oharge is about as

percent of its weight would be if buried at the so oalled optimum

depth defined above. The purpose of the calculation was to

&zta on ground shocks~ mo8t of whia~ is for buried ~~rges~

the effeots of surfaoe detonationa~ St has reoently beoome

.

to predi~t the ground effects due to aharges

oribed below is admittedly very crude and i8

ri~nitude of the results~

allow the aucnunulated

to be used in predicting

desirable to atl;eirtpt

detonated in air, The method dom

designed only to indioate the order Gf

Any attempt to use orater volumes tt8 an indication of ground energies

must admit that as the holght of’the charge inoreases the geometry beoomes less 4.)

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the uxtrapola%ion of the best crater ourves available at pro8art 2, indicate

onztors of zero diameter under oonditio!38such that there is still some energy

getting into the groundo !thi8meano that t??oa8mmption that a fixed percmhx%ge

of the earth shock goe8 into oratering lead8 to a lower limit for tho energy in

the earth from an air burst. The crater is an indication of energy in the aen6e

that a oertain amount of earth is removed and lifted to a oertai.nheightg Thi8

is di80us8ed in l). For the purpose of applying data collected for oortain weights

of oharge to oharge8 of other weights, it will be assumed

dimensions goes as “ii1~3 where W is the aharge weight.

fled, linear dimensions will be in feet and charge weight

2) law agrees with the data on hand ~ The energy involved

that sealing of linesw

(Unless otherwise speoiin pounds). This scaling

in cratering i8 not

strictly proportional to the volume of the water since it depend6 on tho volume

times the height to whioh this is lifted. Beoause of the ohanging geometry as the

height of tho charge inorea8es, the vertioal height to whioh the earth is thrown

probably doefinot saale direotly and the energy on the water assumption is likely

to be proportional to between the third and fourth power of’the orater diameter,

Ileoo@izi~ that mater volumes indtaate a lower timit for ground

energies, anclare as ~ood a ?:asisas is availablo for a limited range of oharge

heights, there i6 another method which #ves a orude estimate of ground energies

for greater heights and w~ioh can be tied into the orater method at

heights. This method is based on an integral whioh is proportional

reaohing the ground in the blast wavep The assumption is then that

intermediate

to the energy

the reflection

ooefi’ioientis independent of the changin~p_ geoxcetryreeultin~ f’romahauges

height of the fsharge~ The method is admittedly crude, but should serve as

in the

an upper

limit for tho energy in the :~round~ _Y..-.. ——-

2) NDRC Div 2: Weapon Data~” Data sheets 3131and 37jla~

.

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An illustration of the use of these methods is given here for the

c=

heiRht of oharge in feet of .47 (moo-?: at

(charge woi~ht in pound8] 1A

ft},

The method uses reference 1.

Xl =

~

The sealed diameter = 2*7 for

,.

using an intermediate point at ,24 (50!X)-Tat 50 f’t]~

The scaled oxater diantetorfor a surface detcoation is

diameter of crater in feet = 3.?.a

(charge weight in”pounds) 1/3 ~

the scaled haight of ~24~ the rat%o of diamekoue ia

thus 3.7 = 1.370 Raised to the third power this is = 2055 + raised to the fourth

power it is ‘3.S. Thus the crater

gets into the earth when the oharge

charge is detonated on the surfaoe.

of ;24 by the

If the sooond

follows; The

wave is taken

same method Indicates

method indicates that about 1/3 as muoh avargy

is at a Sealed height of 024 as does when the

Comparing the Sealed height of 047 with that

a further reduc%ion by a faotor of about l/10~

method is used to make the same compariqoa the prooedure is c;3

quantity representing the energy incident on the earth in ths blast

as the product ptv where p is the peak pressure, t the duration

and v the wave velocity. Thi8 can equally well be taken as

impulse. Choosing the 50Q0-T ease, the impulse on the ground

roughly (sealed from data sheet 3a2 in referenoe 1) 45 pound

Iv where I is the

under the charge is

seconds per sq,. k.

for the ~24 sealed height, and’24 pound seconds per sq. in. for the 047 scald

height, !fhevelooities are about 9100 I% per second and 8800 i% per seeond respect-=

ively. This indicates that the ratio of energies is about 1/2 as the charge height

is Inoreased from *24 to ~47. A consideration of the solid angles of importance

in imparting energies to the ground oan be mado by assuming that energy is not

isnpartedto any significant degree when the pressure on the ground is less than a

certain valuee Assuming that the flat maxima ezmountered in the Maoh effects

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indiuate that very rou~hly the areas involved on the ground are about tha aam

far the two heights, the ratio of solid angles is about 1/4.

Considering all of the above results the following ratio of ef’fsctiva

weights is su~gested for a 5000-T shot$

DEPTH EFFECTIVE WTe

z~

1.0 = 1/1

i“’.’ . - - ,*, ‘,9*

6.”

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
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APPROVED FOR PUBLIC RELEASE