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5814 *-ONIDE IALCOPY No. ~

Y" L R.festricted DISCRBETU

0 ~ L4O I

MINISTRY OF SUPPLY

-BY AUTHORIry OF/

DATE .~ BsY ________

ARMAMENT RESEARCH ESTABLISHMENT.

REPORT 58154

WTEAPONS RESEARCH DIVISION

Spatial Distribution of Fragments, 111.

T. L. WallSafety in Mines Research Establishment, Buxton

~:Best Available Cop

j~ONIPENIALDecemberFort HalsteadDICET15

DICRE 195

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A.R.E. REPORT 58/5%

Spatial Distribution of Fragments, III

by

T.L. Wall, B.Eng.

CONTENTS

SUmUny I

I. Introduction I

2. Experimental Method I

3. Results 2

4. Discussion 7

5. Conclusions 10

References 11

Appendix 12-31

Approved

.......... ....... .... for Director, S.M.R.E.

. ... .or Superintendent, A.R.E.

Buxton Report E216 February, 1955

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Establishment, Fort Halstead, Sevenoaks, Kent, if retention becomes no longer necessdry.IITTIAL DISTRIBUTION

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9-18 Director, SIRE

19 ALTM - DD20-21 - SFR22 C=D23 DGFV24 DRLE (M-7)25-26 MC of S27-28 Royal School of Tank Technology29-30 Sec. . Lethality Committeo (OB)31 Sec. OB32 - Artt. Y1r. Bishop33 Prof. Pocarson, University College, London

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66-81

OO0'4FIDNTIWISMEET

SUMMARY

The fragment speed and dispersion from scaledcylindrical casings has been examined for twodiameters of case and a range of 04) ratios foreach diameter. Four fragmentation zones wereobserved with long casings. A method of obtainingthe dispersion angle for fragments from the variousparts of the casing is suggested. The applicationof this method to the cases used leads to a maximundivergence of only 10 between observed and expectedangles. The results have all been obtained withcylindrical casings: no work has yet been done withother shapes.

Is IMODUCTION

In the first stage of the investigation on the spatial distribution offrajfents (Rif,. 1) a formula was derived which indicated that a fragment isdeflected from the normal to the inner surface of the casing by an amount 4where

sin _V cos(? + "e(.2 E If

where ot is the angle between the normal to the detonation wave and the axis,J is tRe angle betmen the normal to the casing and the axis, V is the speedof projection of the fragment, and U the velocity of detonation of theexplosive filling. The formula was tested by application to data fromcylindrical and barrel shaped model casings, to data from two full scaleG.W. warheads and to additional data from model cylindrical casings withvarious types of end confinement. It was found that expected distributionsdeduced from the formula agreed very well with the observed distributionsexcept at two sections along the casing. These sections consisted of alength equal to twice the internal diameter at the detonator end of thecasing, and a much shorter length at the opposite end of the casing, thelength of both sections being independent of the type of end restraint (Ref. 2).

Over the first of these two sections, i.e. at the detonator end, thereis a progressive increase in speed of projection of the fragments; at theend remote from the detonator there is a progressive reduction towards theend. That some other factor or factors must be taken into account isindicated by the fact that there is disagreement between observed and expectedangles of throw even when the lower measured fragment speeds are used in thecalculation.

The present series of experiments was designed to study the effect ofscaling the dimensions of the casings and has also yielded information on thedispersion of the fragments from the end near the detonator.

2. E=21CR ENTAL METHOD

The lay-out consisted, exactly as previously, of a surround of strawboardpacks arranged tangentially along two semi-circular arcs at distances of3, 5 or 10 ft. from the casing. The casing was suspended in the centre ofthe lay-out with its axis vertical, detonation of the charge being from thetop. Horizontal zones, each representing a 5 degree arc from the centre ofthe casing were marked on the strawboard packs. Multi-velocity screensconnected to an argon lamp chronograph were attached to the front of thepacks and were arranged in the various zones.

In order to assist correlation of both speed and direction of flightwith the origin of the fragments on the case, the cases were very lightlystamped. Examination of the collected fragments showed that the stampingdid not affect the break-up of the casing when the fragmentation was

COVFIYMIAI/DIScRT

controlled, and it is thought that due to the lightness of the stamping(under 0.005 in.) that it did not have any effect when the casings werenaturally fragmented. After detonation the position, mass and depth ofpenetration of each fragment were recorded together with an associated speedand an estimate of its original position in the casing whenever possible.

The experiments were carried out with scaled casings having insidediameters of 1J in. and 2j in. and lengths giving +/D ratios of 0.6, 1.0,2.0 and 4.0 at each diameter. The wall thickness, thickness of screwedend pieces and fragment length (for controlled fragmentation) were in theratio of the diameters. The charge weight ratio for all the casings wasapproximately 0.45, a small difference occurring between the controlled andnaturally fragmented casings due to the weight of explosive lost in formingthe grooves. Scaled casings having an inside diameter of 5 in. were alsoprepared, but these charges were too heavy to be fired at Buxton andfacilities were not immediately available elsewhere. These charges, therefore,have not yet been fired.

All casings were of mild steel normalized at 850 0 0 and were filled withcast CE/TNT 30/70 with an inset axial CE booster 0.55 in. diameter and 0.45 in.long at one end. At each diameter and each length two casings were naturallyfragmented and two others were fragmented with the grooved-charge method ofcontrol of the fragmentation. The grooved charges were pro7ae.iif by castingthe charges in fluted rubber liners in a mould, peeling off the rubber whenthe explosive had set and then inserting the charges into the particularcasings (Ref. 3).

A summary of all the experiments, with a full list of dimensions of the

casings is given in Table 6 (Appendix).

3. RESULTS

The data relating to spatial distribution are shown in Tables 6 to 67(Appendix). The data can be represented by weight histograms showingpercentage weight of fragments collected against angular zone measured fromthe centre of the casing (Figs. I and 2). From the histograms a comparisoncan easily be made between the results for controlled and naturallyfragmented casings.

It would seem that for all series except Nos. I and 2 the peak of thehistogram is more sharply defined and greater in magnitude with naturalfragmentation. It is impossible, however, to establish the point ofprojection of the majority of the individual fragments in the series withnatural fragmentation, and this is essential for a precise study ofdispersion. To compare the dispersion angles of the fragments from casingswith controlled and natural fragmentation a method has already been evolved(Ref. i) to obtain estimated values of the dispersion angles from all partsof the casing for natural fragmentation. Cumulative curves showing thepercentage weight of fragmented casing collected forward of angle 0 are shownin Figs. 3 and 4 for natural fragmentation. To compare with controlled.fragmentation each casing may be regarded as comprising the same number ofsections marked A, B .... from the detonator end as the correspondingcontrolled casings, and from the curves estimates of the dispersion anglesrelative to the centre of the case corresponding with each row can be deduced.From the geometry of the casing and the collecting arc, a correction mustthen be applied to each row to obtain the true dispersion angle with respectto the point of projection. This vas unnecessary in Series I as most of thefragments were the whole length of the casing and the remainder were easilyidentified. With controlled fragmentation the dispersion angle with respectto the point of projection was measured directly as the fragments were easilyidentified.

Similarly the speed of fragments with respect to the originating row(A,B, .... ) for the series with controlled fragmentation was measured directly,but the speeds so obtained were corrected to give the fragment speed on leavingthe casing. The corrected speeds were then plotted and a smooth curve drawnthrough the points; these smooth curves are shown in 3ig. 5 and the speeds aregiven in Table 1.

-3

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o '

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00

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0p 4 A O HC1oMMo co -

With the naturally fragmented casings the speeds relative to the centreof the casing were measured for the various dispersion zones and the probablesource of the fragments (sections A, B, etc.) on the casing was deduced by themethod previously discussed: the speeds from the different sections could thenbe deduced. Corrected speeds could not be obtained for this series since veryfew fragments could be associated with a particular speed measurement.

Estimates of speeds associated with the sections, taken from the smoothedcurves shown in Fig. 6, are given in Table 2.

TABLE 2

Comparison of fragment speeds, natural fragmentation. Deducea averagespeeds over a distance of 3-5 ft. from the casing, ft/c.so.

Section Series I Series 3 Series 5 Series 7 Series 9 Series 11 Series 13

A 3160 4040 4350 4280 3650 4.100 4090B 3540 4080 4500 4390 3650 4200 43000 3390 4080 4560 4460 361+0 4200 430D 4090 4570 4510 4180 45103 4070 4580 4550 4170 4570P 4590 4580 4610G 4600 4630 4640H 46oo 4660 46o1 4610 4680 46203 4600 4710 4590K 4720L 4730M 4+750N 47600 4770P 4770Q 4770R 4760S 4760T 4710

Expected dispersion angles for each row of fragments along the casings werecalculated by substituting the smoothed speeds in formula I and these arecompared in Table 3 with the observed angles for the controlled series and inTable 4 with the extrapolated angles for the natural series: they are showngraphically in Pigs. 7, 8, and 9, 10 respectively.

Difficulty was experienced in the series ith controlled fragmentation inobtaining the individual speeds of fragments from the last few rows remotefrom the detonator. The fragments from the rows approaching the remote endare thrown forward at progressively smaller angles and strike the velocityscreens almost at the same level. Too much reliance cannot therefore be placedupon the speeds of fragments associated with each of the last three rows or uponthe expected angle of projection of these fragments for the longest casings.

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-7-

4. DISCUSSION

In the following discussion L represents the total fragmented lengthof the casing, 1 the distance from the detonator end to some position alongthe casing and D the internal diameter of the case.

Taylor (Ref. 6) has shown that the angle of projection of a fragmentfrom a point some distance along an infinitely long cylindrical casing isgiven by:-

;Ll 6 =X (2)2 2U

where V is the fragment velocity, U is the detonation velocity and 0 is theangle of coning. This formula was modified during the first stage-of thiswork (Ref. 1) to take into account the shape of the casing and the angle atwhich it is struck by the detonation wave (equation 1).

Even when these factors and the observed variation in fragment speedfrom the different parts of the casing have been taken into account, thereis still a divergence between the observed angles of throw and thosecalculated from equation I 9pr"the length of the case represented by valuesof !/D between 0 and 2 and also at the end remote from the detonator. Forthe remainder of the casing, provided L/D exceeds 2, the observed and expectedangles agree to within - : if L/D is less than 2 there is no agreementbetween the observed and expected angles.

The speed of projection of fragments from casings has been discussed byGurney (Ref. 4). He assumes for simplicity that the initial speed offragments from all parts of the case is the same and hence the speed obtainedfrom his formula is a mean. The formula contains an empirical constant Ewhich is different for each explosive and must be determined by experiment.In the report quoted, only the value for cast TNT is given: it is statedthat other values were to be found.

Analysis of the early results (Refs. I and 2) and the present resultsshows that there is a progressive increase in the speed of projection of thefragments at the detonator end of the casing, over a region extending fromthe end up to a distance equal to twice the internal diameter of the case(1/b equal to 2). At the end remote from the detonator there is a progressivereduction in speed over a much shorter length of the case. The lower speedof projection at the detonator end has been found to be more than 20 belowthe average maximum speed of projection of the fragments from the centre of thecase. Over the length of the case between 1/D equal to 2 and the last tworows of fragments the speed of projection has been found to be constant.

Fig. 7(d) shows the angles at which fragments are thrown from a casingwith an L/D ratio greater than 2. When the observed angles are plottedagainst log 1/t), shown in Fig. 12(d), three discontinuities are seen in theline.

The variation in fragment dispersion from different portions of thecase is to be expected from a consideration of the geometry of the expandingdetonation wave and the manner in which it impinges on the wall of the case.With initiation from a point at the centre of one end of a long case thewave becomes approximately hemispherical before reaching the wall: it thenimpinges normally. During this period detonation in the charge is buildingup and may not be fully established: the end of the casing is also beginning

to move and is absorbing and releasing some energy. Thus the fragments fromthe first portion of the wall are not only subjected to a weaker blow but are

also restrained differently at the two ends and they tend to be projected

backwards: their motion is affected considerably by the end restraint.

After the first few rows of fragments have been formed the end restraintoan no longer have any effect, but the wave is still not stable in shape.If unit time is taken to be the time required for the (spherical) detonationwave to expend a distance equal to the radius of the tube, it is found thatafter first impact on the walls the lengths of tube affected by the wave insuccessive unit intervals of time are 0,866D, 0.548D, 0.523D, 0.512D, andwhen the wave becomes essentially plane, 0,5D. Thus initially the rate offracture of the case is continually decreasing and the weight of chargeexploded relative to length of case fractured is increasing: the angle atwhich the wave approaches the wall is also varying.

It can be seen from the figures given above that conditions should becomeapproximately stable when the wave has travelled a distance along the casingof approximately two diameters. Thereafter, fragmentation should remainconstant indefinitely almost up to the remote end. Here, there will againbe differential restraint at the ends of the incipient fragments and therewill be some release of energy from the end.

Starting from the detonator end, the dispersion of the fragments fromthe first short length of case, examined previously, (Ref. 2) is affected bythe end restraint. The effect of end restraint found to extend for adistanoe of approximately 0.4. = J/D for all casings used in the presentseries but the angle of throw of fragments from this part of the case varieswith the 1/D ratio. This variation with the L/D ratio for the particulardiameters used is shown in Fig. 14. It is not possible to establish withobrtainty from the results that the angle of throw of fragments from thefirst row tends to become constant when the 1A ratio exceeds 4 for aparticular diameter, but from the shape of the curve it would appear that anyfurther variation in angle with increasing length of case would be small.

The second fragmentation zone extends from I/ = 0.4 to 2. The observedangle of projection of fragments is plotted against log I/D for all casings inthis series in Fig. 13 and a mean of the results for the previous series(Ref. 2) is also included. In Figs. 11 to 13 the curves for the individualseries are plotted, together with the expected angles from formula I andthose which would be obtained by using the Gur~ey calculated fragment speed.

The two main points of interest are as follows:

i. The slope of the line is constant Vithin experimental error for allcasings in the present series and for all casings used in the previous series.The oharge/weight ratio was the same in both series but the explosive wasdifferent. The mean slope of the lines for the previous series with RDX/TNT55/.5 filling is 8.64 and the mean slope for the present series with CE/1T30/70 filling is 8.94. This only affects the angle of throw by 12 minutes.

2. The position of the line is determined by the L/D ratio of the case andis independent of the actual diameter, For a given diameter the angle ofthrow of a particular fragment at a specified distance from the detonatortends to decrease as the L/b ratio of the case is increased. It is notcertain from these results whether the position of the line representingI/D = 7 for the previous work indicates a continued reduction of the angleof throw as the IA) ratio increases or whether it is due to the differentexplosive used.

Equations have been deduced for all lines by means of the method ofleast squares: they are given in Table 5. For the column headed "mean",an average slope has been calculated using all the lines and the value ofthe constant in the equation is the average value of the constant for eachpair having the same 4/D ratio but different diameters.

-9-

TABLE 5

Relationship between dispersion angle and point of originof fragment on the case for values of 1/b up to 2

44)1 in. dia. casings 2J in. dia. casings Explosive Mean

I Y: %50log10 X+ 94.70 Y= 8.90 log1oX +94.60 TE/TNT 30/70 Y= 8.89 10:1oX + 94.6584.00 = tan- 1 9.5 83.60 = tan- 1 8.90

2 Y=8.661ogOZx+ 94.06 y= 8. 77 logioX + 93.77 aE/TI 30/70 Y= 8.89 log oX + 93.9283.4P = tan-1 8.66 8350= tan 1 8.77

4 Y= &90logioX + 93.18 Y= 8.88JogloX+ 93,56 CE/TT 30/70 Y= 8.89 logjOX + 93.3783.60 = tani- 8.90 83.50 = tan-' 8.77

7 Y~w- 8A44kIO +92.46 iMikiW 55/4583.40 = ta71 8.6.

(Mean of experimentsreported in Ref. 2)

where y = angle of throw of fragmentX = value of l/D at the particular part of the case

When the L/D ratio of the casing exceeds 2 the angle of projection of thefragments reaches a constant value at the point I/D = 2 and this marks thebeginning of the third fragmentation zone present in long casings. It extendsalmost up to the end remote from the detonator, however long the casing may be.In this zone both the shape of the detonation wave and the mechanism of fractureof the case have become stable.

At the end remote from the detonator there is a short fourth fragmentationzone arising as a result of the end effect. The stable speed of projection inthe third zone is progressively reduced towards the end. The results do notpermit a precise estimate of the length of this zone but it appears to be notgreater than one half the diameter of the case.

Thus, for cases with a I/D ratio not greater than 0.6 the fragmentation isentirely governed by the combined end effects, and the fragments are projectedapproximately normal to the case with little more than 10 scatter.

When the L/D ratio lies between 0.6 and 2.0 the fragment dispersion isaccording to the first, second and fourth zones. The stable conditions of thethird zone are not attained and the length of case within the second zone willdepend on the L/D ratio.

For long casings, the first and fourth zones are negligible and the fragmentpattern may be obtained by consideration of the second and third zones. Thefragment speed calculated from the Gurney formula is substituted in equation 2and this immediately gives the angle of projection throughout the third zone.This angle is then plotted, and from a point in the case where l/D = 2 a line isdrawn with the mean slope indicated in the empirical equation given in Table 5.The fragment dispersion along the second zone is then defined.

The fragment dispersion predicted by this method for the casings used inthis series are shown in Figs. 11 to 13, together with the dispersion predicted

-10-

by the Gurney formula alone and by using equation I. It can be seen that,using the method described above, the difference between observed andcalculated angles of throw is little more than I degree at any point.

It must be remembered, however, that these equations have been derivedsolely from experiments with cylindrical casings having a constant E/c ratio.The effects of shape of casing and E/C ratio have yet to be examined. SomeAmerican results (Ref. 5) with cylindrical casings of different metalscontaining different explosives at different loading densities indicate thatsimilar curves were obtained for the relationship between fragment speed anddistance from point of initial expansion. The values of 1/D at the point ofchange-over from unstable to stable conditions appeared to vary from 11 to 2k,with an average value nearer the lower figure.

5. CONCLUSIONS

I. The fragmentation of scaled cylindrical casings of two different diametershaving a constant charge/weight ratio but different I/D ratios has beenexamined. The fragment speeds and dispersion angles from different parts ofthe cases were found to scale with the linear dimensions.

2. In the fragmentation of long cylindrical casings four zones have beenobserved.

(i) Up to a distance 0.4D from the detonator end the fragmentation isaffected by the end confinement of the case and also by the ID ratio forvalues less than 4.

(ii) From this zone and up to a distance of 2D the dispersion may bedescribed by an empirical equation.

(iii) The third zone begins at a distance of 2D from the detonator endand extends up to a point approximately 0.5) from the remote end, howeverlong the case may be. In this zone stable conditions of detonation waveand fracture of case are attained. All fragments are projected at theangle deduced from the simple Taylor formula using a fragment speed calculatedaccording to Gurney,

(iv) In the final zone up to the remote end the dispersion is againaffected by end confinement.

3. If the I/D ratio of the case is less than 2 the third (stable) fragmentationzone does not occur and the second zone may be shortened. If the ratio isless than 0.6 all fragments are projected approximately normal to the case,with only about 10 scatter.

4. Similar results are obtained with both controlled and natural fragmentation.With natural fragmentation there appears to be more scatter about the meandispersion angle from a particular part of the case than with controlledfragmentation. Owing to ease and certainty of identification of fragments,hovever, the data with controlled fragmentation are mbre reliable than thosewith natural fragmentation.

CONFIDENTIAL/DISCREPET

- 11 -

REEECES

1. J.W. Gibson & T.L. Wall; Spatial Distribution of Fragments I.A.R.E. Report No. 19/52. Buxton Report E200

2. J.W. Gibson & T.L. Wall; Spatial Distribution of Fragments II.A.R.E. Report No. I0/54.' Buxton Report E205

3. W.C.F. Shepherd & J.W. Gibson; Controlled Fragmentation XXXI. Thedevelopment of rubber liners for the grooved charge methodof controlling fragmentation; A.R.E. Report No. 18/51,Buxton Report El 94

4. R. Gurney; B.R.L. Report 405

5. D.P. MacDougall & others; The Application of Flash Photography to theStudy of Explosion Phenomena. O.S.R.D. No. 5616

6. G.I. Taylor; Analysis of the explosion of a long cylindrical bombinitiated at one end. R.C. 193, A.C. 743

CONF3DETIAL/DISCREE T

- 12-

The Appendix contains the full experimental data from Series i to 16.Tables 6 and 7 give collected results and summaries and descriptions ofexperiments. Corresponding with each series there are four Tables; thefirst gives raw data classified into shots, collecting arcs and dispersionsones. Numbers and weights of fragments are shown; in the number column,the first number represents the total number of fragments collected and thesecond bracketed number represents the number of holes made in the strawboardpacks. The second Table in each series gives numbers and weights offre4pents corrected to 360 degrees from that part of the casing which liesbetween the end plugs. The third and fourth Tables show averages overcollecting arcs and experiments.

- 13 -

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-15 -

TABLE 8

Dispersion of fragments, Series I - NUmbers and weights of fragments

IA IB

Collecting Aro 3.-ft. 5' f 3-ft. 5-ft.

Zone of dispersion, Number Wgt.,. Number Wgt.,, Number Wgt.,. Number Wgt.,deges ...& __ _ __ _ .-

- 606o- 6565- 7070- 7575- 80 1~ j~- 1

80- 85 1.0585- 90 27 (17 16.61 9 (5) 5.24 7 (5) 5.97 31 (22 20.999o- 95 (8 6.3325 (17) 17.10 27 (22) 16.60 5 (3 1.5595-100 1(1 0.30 - i-

100-105 1 (1) 0.15105-1101o-is 1 (1 ) 1.10115-120 1 () 0.11

120sum 43 (26) 23.24 34 (22) 22.3 30 (27) 22.57 37 (26) 23.59

Dust 0.39 0.38 0.79 0.82

Total .63 22.72 23.36 24.41:Estimated weightof fraeented 52.0 52.0

part, g.__ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _

Dispersion of fragments, Series I - Numbers and weights oorrected to 3600

Experiment BIA 1_ _ii _ _ __... -l-ml ,, t .. .

Collecting Arc 3-ft. 5-ft. 3-ft. 5-ft.- - - - - -

Zone of dispersion, Number Wgt. , Number Wt., Number Wgt., Number Wgt.,dere __ % % %

80- 85 2 (2) 4.4585- 90 59 (37) 71.47 21 (i1) 23.46 16 (11) 26.45 66 (4) 88.9890- 95 33 (18) 27.24 57 (39) 76.54 60 (49) 73.55 11 (64) 6.5795-100 2 (2) 1.29.

TABLE 10

Dispersion of fragments, Series I - Averages over oollecting aros

Eperiment IA IB

Zone of dispersion, Number Wgt., Number Wgt.,degrees % %80- 85 1 () 2.2385- 90 4.0 (24) 47.46 41 (29) 57.7190- 95 45 29 51.89 36 40.0695-100 1 () 0.65

TABL 11

Dispersion of fragments, Series I - Averages over experiments

Collectin.g Ar .3-ft. 5-ft.

Zone of dispersion, Number Wgt., Number Wgt.,de rees _ .. ...80- 85 1 i[2.2385- 90 38 (24) 48.96 41+ (29) 56.2290- 95 47 (34- 50.39 34 (52) +1.5595-100 0 () 0.65

-16 -

TABLE 12Dispersion of fregents, Series 2 - Numbers and weights of fragments

Experiment ____2A. 2BColleoting Aro 3-ft. 5-ft. -3-ft. 5-ft.

Zone of dispersion, Number Wt., Number gt., Number Wgt., Number Wgt.,degrees g. g. . - . ... ;

-6060- 6565- 7070- 7575- 8080- 8585- 90 5 (5) 3.64. 19 (19) 15.09 17 (17) 13.54 3 (3) 2.2190- 95 20 (20) 16.52 10 (10) 8.0. 16 (5 11.60 22 (21) 19.1395-100

100-105105-110lio-115I115-120

sum 25 (25) 20. 16 29 (29) 23. 13 33 (31) i51 5 (24.) 21.34Dust 0.14. 0.16_ 0.11 0.09

Total 203 Z3- ,,l r52 2-I I I3

Estimated weigh-of fragmented 52 52

part, g.

Dispersion of fragwents, Series 2 - I'udbers and weights oorreoted to 360°

Exeien _______2A 2B

l . - -J]- 5I- -

Zone of dispersion, Nunber Wgto., Number Wgt., Number Wgt., Number Wgt.,.degrees - _-__%__%

85-90 I13 (ti) 18.06 42 (4.2) 65.24-35 (35) 53.86 7 (7) 10.3690-95 51 (51) 81.94 22 (22) 34.76 3.3 (31) 46.14 53 (51) 89.64

Dispersion of fragments, Series 2 - Averages over oollecting arcs

Experiment 2A. 2BZone of dispersion, Number Wit, Nuzber Wt.

degrees _ _

85-90 28 (28) 4.1.65 21 (21) 32.1190-95 37 (37) 58.35 4.3 (41.) 67.89

Dispersion of fragments, Series 2 - Averages over experiments

Collecting Aro, 3-ft. 5-ft.Zone of dispersion, Number Wt;., Number

degrees I __

85-90 24. (24.) 35.96 25 (25) 37.8090-95 42 (41) 64.0.. 38 (37) 62.20

-17 -

ft~ %.J.D CM 0 %a0 '.

r- W% "-

N N-

tf .. -00 U"*

4)%0

0%4 4

0 0 0 0

-P I' N

N RN

%0 1

C-4 0(V 0

0 C4

54~% 0 .I.'*; 0) 0j 0

N N

e - V % V.T 1 4x _ _ _

14 -P 0d b) N ,A I I I I lo0 0c

A, 0 co Ei-43 4)P 4 4

~~to 0os pq

ft 4.0 tcf

-18-

030

o 04tOA~~ __

a% - __ _

1.

14 u %i-. V

E-4 44r--

'00

0.4 .rbi.

o~P 0 la4pS~g

14 42 I

0 0 rd43 ,(-i. HO

C qC*

0~ ~~ 0 - - _ _

E-1 WN t 4 bOi U 4'.0COC - oto-

W0ft

~~~ 14P0

o 00*0

0 #4-0

0"

pa\ %

U% 00CC

0 00 G\ ON 44

0 T

- 19=

TABLE 20

Dispersion of fragments, Series 4. - Numbers and weights of fragments

Experiment 4k ______ 4.BCollectin A ______._t 5-ft. 3-ft. 5-ft.

Zone of dispersion, Numbr Wgt., Number Wgt. , Number Wgt., Number Wgt.,

degrees gog. g.

6o60- 6565- 7070- 7575- 8080- 85

90- 95 28 (28) 18.87 31 (31 Z3.07 31 (31) 24 .o+ 34 (33 26.7995-100 1 (1 0.75 1 (1 0.57

100-105 1 (1) o.2)105-1101.0-115115-120

120sum 4(4)3".725_2 _2)39.746 46)J73M4 WT+) 38.81

Dust 0 0.4.9 0.56 0.43 o.4Total 5235.21 .40o30 37.81 39.25

Estimated weightof fragmented 86.0 86.0

part, g.__ _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _

Dispersion of fragments, Series 4 - Numbers and weights corrected to 3600

Experiment 4B

Collecting Arc 3-ft. 5-ft. 3-ft. 5-ft. -

Zone of dispersion, Number Wgt., Nwmber Wt., Number Wgt., Number Wgt.,degrees % .... % %

85- 90 46 (Q6) 4.5.65 1.3 (43) 4-0.06 34. (34) 35.27 29.50

90- 95 68 (68) 54.35 66 (66) 58.05 71 (71) 64.73 75 (72) 69.03

95-100 2 (2) 1.89 .. ... 2 (2) 1.4 7_ _ _ _ - -,i- - - -i

TAKLE 22

Dispersion of fragments, Series 4. - Averages over collecting aros

Experiment 4A 4B

Zone of dispersion, Number Wgt., Number •,degrees %____IT

85-90 +5 (4.5) 42.86 33 (33) 32.3990- 95 67 (67 56.20 73 (72 66.88

95-100 1 (1) 0.94. 1 .(, 0.73

TABLE 23

Dispersion of fragments, Series 4 - Averages over experiments- - - --

Colleoting Aro 3-ft. 5-ft.

Zone of dispersion, Number Wgt., Number gt.,

degrees %

85-90 40 (40) 40.46 37-(37 3-7890- 95 70 (70) I59.54. 72 (69) 63.34

- 20 -

Dispersion of fragments, Serie! 5 - Numers aa weights ot fragments

Bverient{ 5A - BColleotiug Aro 3...te 5-ft. 3-ft. I 5-ft.

Zone of dispersio., Number Wgt.,, Nistbr W'' 4 . umberW-' Nube-Idegrees . . .- g°

6060. 6565-7070- 7575- 8080- 85 1 ( 0.4885- 90 7(7) 3.57 10 1 3.60 6 (6 1.67 . (3 2.15

95-100 6 (5 2.09 3 (31 0.32 9 (7)I 5.75 7 (5 4.08110-105 --+ ..-.-.105-110110-115115-120

-120 ____

sun 97 (58) ]-75 96 M 6 0.73 9 6 5) 4.7 1014. 59)Du......94st ..... .3.76 - 3.97 5.03

Total -. 50.. 3, 64.19 -7. -Estimated weight

of fragmented 173 173part, g.

TABR ,rDispersion of fragments, beries 5 - ibers r weights oorreoted to 3600

Ezerinnt5A 5BColleoting Aro 3-t. 5-ft. 3-ft. 5-ft.-= , = 0 - .; .- - -' J + - -" -"

Zone of dispersion, Number Wgt., Number Wt., Nlumber Wgt., 1Number Wgt.,deee - %80- 85 -3) 0_7985- go 24. (24) 7.52 27 (27,i 5.93 18 (18) 3.05 9 (7 3.1190- 95 288 (158) 88.07 220 (139) 92.75 239 (127 86.42 217 (119) 90.9895-100 21 (17)4.)1 8 (8) 0.53 27 (21) 10.53 16 (12 5.91100-105 .....

TALU 26Dispersion of fragments, Series 5 - Averages over oollecting arcs

I I l p~t p 5A

Zone of dispersion, Number Wgt., Number Wgt.,ef e es - _ +- % %

80- 85 2 (2 -,1o

85- 90 26 (265 6.72 14 (13) 3.0890- 95 254(1.9) 90,41 228 (123) 88.7095-100 15 (13) 2.47 22 (17) 8.22


Colleoting Arc 3-fZone of dispersion, NtmoIr Wgt., Number Wgt.p

de'ees __ _2_ ,9I

80- 85 2 (2 0.4085- 90 21 (21) 5.28 18 (17 4.5290- 95 264 Q3 87.25 209 (129 91.8695-100 24 (19) 7.47 12 (101 3.22

100-105

- 21 -

TAMUE 28Dispersion of fragments, Series 6 - Nmnbers and weights of fragments

Experiment 6A 6BCollectins Arao 3-ft 5-ft. 3-ft. 5-ft.

Zone of dispersion, Number Wgt., Number Wgt., Nwnber Wgt.,, Number Wgt.,degrees _ g. - g.

6060- 6565-7070- 7575-8080- 85 2 '(2) 1.78 1 (i) 0.2085-90 22 (22) 18.20 22 (22) 18.84 20 0 1605 17 17 14.4090-95 46 (46) 35.4.6 4.6 (46)36.55 57 57 38.56 38 38 28.94.95-100 21 21)15.42 314 34.) 23.95 25 2 16.7)+ U Z3 17.09100-105105-11o110-115115-120

120

SM 91 (91) 70.86 103 (103) 79.54 T02 (101) 71.35 78 (78) 60.43

Dst 0.57 _ ___0.6- ___._ 1.06 0.89... .. . - f- ... .8o1- -- - -.. -Total 171. 80M7 _____72.41 161.32i1- - --

Estimated weightof fragmented 173 173

TABLE, 29Dispersion of fragments, Series 6 - Numbers aaA weights corrected to 3600

_ _ _ e _t 6 _ _"_ _6B .. .

Coll_.ting Ara 3-f. 5-ft... 3-t 5-f.Zone of dispe:rsion, Number W'gt., Number We.., Number Wgt., Number Wgt.,

80-8 5 5 (5) 2 51 2 (2) 0,2585- 90 .53 (53) 25.68 4.7 (4.7) 23.69 4.8 (48) 22.49 50 (5o 23.8390- 95 111 (111) 50.04 99 (99) 45.95 136 (136 54.04 107 (107) 47.8995-100 51 (51) 21.7? 73 (73)i 30.11 60 (57 23:1+7 65 (65) 28.28

Dispersion of fragments, Series 6 - Averages over oolleoting arcs

Experiment 6A 6B

Lone of dispersion,, Number Wt., ubr Wtdem'ees -....

80- 85 4. () 1.3885- 90 50 (50 24.68 49 (49) 23.1690- 95 105 (105 48.00 122 (122) 50.9695-100 62 (621 25.94 63 (61) 25.88

Dispersion of fragments, Series 6 - Averages over experimentsCollecting Arc 3-ft. 5-ft.

Zone of dispersion, Number Wgt,, Number Wtdegrees % -

80-85 3 (3) 1.25 1 (1 0.1385- 90 51 (51) 2.09 49 (49 23.7690- 95 124 (124.) 52.04 103 (103) 46°9295-100 _ _i56 (54) 22.62 69 (69) 29.19

- 22 -

Dispersion of fragments, Series 7 - Numbers and weights of fragments

ri-ent 7A 7B

Collecting Ac 3- . .. - - . 3-ft. 5-ft.Zne ce fdtipeb, Number Wgt , Number Wgt., Number Wgt., Number Wgt.,

degrees _ g. _ _ g. .g.

6060- 6565-17070- 7575-18080- 8585- g0 27 (17 10.33 24 19 9.36 29 (19) 15.04. 2 (14) 12.6690- 95 94+ (33) 12.00 103 50 54.77 62 2 0.14 76 (52) 43.5695-100 111 (43) 53.79 124 (58) 63.52 96 31 3.15 146 (65) 78.26

100-105 I 1 0.10105-110110-115115-120

120_ _ __ _ _ _

sum 232 (93)10o6.12 251 (127) 127.65 188 (79) 108.4-3 a4 (131) 13)+4&~.

Dust 8.64____ 10.36 _____ 9.82 _____12.18

Total ..... .. 114.76 138.01 118.25 146.66

kimated weightOf fragmented 3"346

part. g. _

Dispersion of fragments, Series 7 - Numbers and weights oorreoted to 3600

..... ... .. _ _.... . . _ _ _ T7A ... .. . ... . ._ 7B

Colleoting Arc 3 5-ft. 3-ft. 5-f.

zce C' t i Number Wgt , Number Wg., Num. Wgt., N r Wt.degrees - % % -

85- 90 81 (51 9.73 60 (48) 7.33 85 (6) 13.87 50 (33 9°4190- 95 283 (9 39.58 259 (126) 42-918 (73) 27.80 179 (123 32.3995-100 335 (130) 50.69 312 (146) 49.76 281 (9) 58.24. 342 (153 58.20

100-105 _ _... . 3 (3) 0.091 ,

Dispersion of fragments, Series 7 - Averages over collecting aros

BxprimntIA -7B

Zone of dispersion, Number Wgb., Number Wgt.degrees %___ %___

85- 90 71 (50 8.53 68 +5 14.6490- 95 271 (113) 41.24 180 (98 30.0995-100 324 (138) 50.3 303 (126 58.22

100-105 . 2 .(21 0.05

TANZ 3


Collecting Arc 3-ft. 5-ft.

Zone of dispersion, Number t', Number Wt.p. .. ..degtees .. ..

85- 90 83 (54) 11.80 55 (41) 8.3790- 95 232 (86) 33.69 219 (125) 37.6595-100 308 (115 54.47 327 (150) 53.98

100-105 2 (2) 0.04

- 23 -

Dispersion of fragments, Series 8 - Numbers ard weights of fragments

.perimlnt 88B

Collecting Arc 3- 5-ft. . 3-. 5-ft.Zm ccerad=u, Number Wt., Number Wt., Number Wgt., Number Wt.,

degrees g. ._.,_. g. .. g..60

60- 6565- 7070- 7575- 80

80- 85 6 (6) 5A17 2 (2) 1.63 11(11) 9.98 T3 13 2.5385- 90 28 (28) 22.57 32 (32) 26.06 24. (24 19.11 33 (33) 2.6.3990- 95 42 (4) 3507 58 58) 42.25 1 54 38.40 64 (64 48.1895-100 73 (71 50.90 91 (89) 77.02 90 (90 64-.19 97 94) 69.59

100-105 1 1 0.73 ...... .105-110110-115115-120

120

Sum 149 (146) 113.71 183 (181) 146.96 177 (177) 132.4.1 197 (194) 146.69Dust 1.06 1.37 1.31 1.46

Total 114.77 148.33 _ .133.72 ...... _ 148.15Estimated weightof fragmented 346 346

-part, _go _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

Dispersion of fragments, Series 8 - Numbers and weights corrected to 3600

Experiment 8A 83

Collecting Aro 3-ft. 5-ftt. 3-ft. f5-ft.SEne cediset~m, Number Wt, Number W6t. Number W.. Number

degres r____ T __%____

80- 85 1818) 4555 (5) 1.11 28 28 7.54 7(7) 1.7285-90 84 (84. 19.85 75 (75) 17.73 62 (62 14.43 77 (77 17.9990- 95 127 (124 30.84 135 (135) 28.75 132 (132 29.00 149 (149) 32.8.95-100 220 214 44.76 212 (208) 52.-1 233 (233 48.48 227 (220) 47.45

100-105 ..... 3 (31 0.55 -

TABLE 8Dispersion of fragments, Series 8 - Averages over colleoting aros

Experiment 84 8BZone of dispersion, Number Wgt., Number Wgt.,

degrees 1.. •%

80- 85 12 1 2.83 18 (18 4.6385- 90 80 80 18.79 70 (70 16.2190- 95 131 (1301 29.79 141 (141 30.9295-100 166 (211) 48.59 2.30 (227 47.96

100-105 1 2 (2 0.28


Collecting Arc 3tZone of dispersion, Number Wgt., Number Wgt.,

dege s ........ .... . %

80- 85 23 (23 6.o 6 (6 1.4285- 90 73 (73 17.14 76 (76) 17.8690- 95 130 (130 29.92 14.2 (142) 30.7995-100 227 (224 46.62 220 (214) 49.93

100-105 2 (2 0.28_____

-24-

Dispersion of fragents, Series 9 - Numbers and weights of fragnts

Zzpimnt9A 9B____ e~!,,t,,, 3- . -T:Aq --I-- -........... ,Oolleatiag Aro 3-___ '74t 3-ft. 5-ft.

Zone of dispersion, Nmvber Wgt., Number wgt., Number Wgt., Number Wgt.,degrees _"_____ __ g. . S.

6060- 6565- 7070-7575- 8080- 8585- 90 56 (28) 14.2.97 29 (21) 41.90 36 (i6) 60.37 37 (20) 106.57-90- 95 7 ( t 0..0 63 (36) 157.14 4.7 (26 0123.75 36 o22 95.4995-100

100-105105-110110-115115-120

120 ....---Sum 63 (31) 156.97 92 (57) 199.0. 83 (4.2) 184.,12 73 (42) 202.06

Dust 2.60, 2.30 ___ 2.98 ___ 2.02

Total __ __159.57 201-34 ___ 187.10 204-.08

Zstimated weightof fragmeented +.15

pa~rt.. .____

Dispersion of frag ents, Sdries 9 - Numbers and weights correoted to 360P

Experiment 9A _ ______9B

Colleting Aro 3-ft. 5-ft. 3-ft. 5-it.Zone of dispersion, Number Wgt., umber W . r Number . -. ,

Ldegrees %__ _%__ %_

85- 90 14.6 (73) 91.08 6 (43) 21.05 80 7(35) 32.79 75 (4i) 52.74.190- 95 18 (8) 8.92 130 (74) 78.95 101+ (58) 67.21 73 (45) 47.26

Dispersion of fragments, Series 9 - Averages over oolleoting aros

Ex-periment 9A 93

Zon of dispersion, Number Wgt.., Number Wt.,degrees % ,%85-90 103 (58) 56.07 78 (38) 42.7790-95 74 (41) 43.93 89 (52) 57.23


Cofleoting Aro 3-ft. 5-ft.Zone of dispersion, Number Wgtt Number Wgto,

degrees % ___ %

85-90 113 (51+) 61.93 68 (42) 36.8990-95 61 (33) 38.07. 101 (60) 63.11

-" 25 -

TA~~4

Dispersion of fragments, Series 10 -+N-inhzs and weight+s of fragentX

Collect!i.ng Ar. 3-... Jir 3t.

Zone of dispersion, Num~ber Wg., Kvmbar Wgt., Nwiber Wgt, Ni;;ber Wt,,evees S. --

6060- 6565- 7070- 7575- 80s0- 85 2 (2j 0.29 1 1 7.7585- o 12 (12) 54.52 18 18 57.17 14+ "1 .8 ,1 ( ,.6,

90- 95 20 20 107.4.9 26 2k% 10.,6 13 13 7005 24 . 10i6.49

95-100 1 (1) 0.15 1 () 0.5 (10 0o13 1 (I 0.17100-105 + .105-110110..115115-120 4. (.1 0,47

125 1 1 0.15 1 0 -o

am33 (33)102.16 47 (45) 162.-67 28 (28)1154-97 44 4)170.02

Dust__ 1.67 1 .68 2.29 2.51

Total 16 .3~~C.5- _172 _172.3Betinated weight

of fragmented 41t5 4.15

part, g. ------

TA L

Dispersion of fragments, Series 10 - Numbers en. waights correoted to 36O

_______________ 5-ft______ 10

Oolleoting Ar o3t 5-3tf. - 3-ft. 5-ft.

Zone of dispersion, Num er Wgt., Number gt., Numbar Wgt., Number Wgt.,deg'ees %I %

SO- 8 ( IA8 2 (2. 4.56

85- 90 30 (3o ) 33.6247 (7) 35.14. 37 (37) 54.71 43 (3) 32.7190- 95 50 (so) 66.29 66 (61 64.52 35 (35) 45.20 58 (58) 62.6395-100 2 (2) 0.09 2 (2) 0.16 2 (2) 009 2 (2) 0.10

100-105

Dispersion of frapents, Series 10 - Averages over oollecting acos

fzperiment lOt. lOB

Zone of dispersion,, Nuber NNu2Kabr Wgt,degrees 0- r

80- 85 3 (3) 0,09 1 (1) 2.2885- 90 39 (39) 34.38 40 (40 43-719- 95 5 (6)65.01 4 77 53.9295-100 2 .(2) _0.121_ 2 () 0.0

Dispersion of fragments, Saries 10 - Averages over experime~nts

Collctin Aro5-ft.Zone of dispers:ion, Number IWt, Number t.

so-853 (3) 2.3785- 90 33 (33) 44-17 45 (45) 33.9290- 95 43 (43) 55.74, 62 (M0 63-58

195-100 2 (2) 0.0j 2 (2) 0.13

- 26 -

TABU~ 48

Dispersion of fragmets, Series 11 - Numbers and weights of fragments

Experiment 1 A 1tB

Coflooting Aro 3-ft. -5-ft. 3-ft. 5-rt.am cespzasion, Number Wgt., Number gt., Number Wgt., Number Wgt.,

de_ ,-es g. - --- - -

6060- 6565- 7070- 757 5- 8 0 ( 1 0_0 _

80- 85 5 1 .'0.55 1 (1 0.1085- 90 21 (21 36.46 36 28 56.35 31 (21) 4.93 18 (16 22.3790- 95 74. ( 178.4 83 ( 183.37 82 (42) 157.8. 119 (72 216.0395-100 2 (1 0.43 2 2 1.21

100-105 .1 11 0.10 ....

105-110 1 (1 0.25 3 3 0.34 2 (2) 0.48110-115 1 2 040 1 1 0.16115-120 7 (7) 2.65 1 1 0.21

120 1. (14 7.31 9 191 2.25 -

Sam 98 (61 215.48 122 )21.03 116 (66) 203.32 138 (89) 238.50

Dust 1 2.35 2.63 2.58 3.15

Total 1217-83 243.66 205.801 1251.73

Estimated weight(f fragmented 691 691

part, g. __ _ __ ___.. . .._ _

TA=I _49Dspersion of f!I1nts. Series 11.- Numbers and weightcs orreoted to 3600

Experiment 11A I__B,_,,A1

Col.eoting Aro 3-ft. 5-ft. 3-ft. 5-f.

Zone of dispersion, Number T Number T Number TO Number TOdegees - -

80-85 3 3 .07 10 10 .27 3 0oM85- 90 67 (67 16.92 102 (79) 23.38 104. 71 22.10 4.9 (4) 9.3890- 95 235 (121 82.81 235 (159) 76.08 275 (14.1) 77.63 327 (198) 90.5895-100 6 (31 .20 6 (6) 0.50100-105 3 . 3) 0.04 i , , _

TANA~ 50

Dispersion of fragments, Series 11 - Averages over OcoLeoting aros

Experiment 1IA 113

Zone of dispersion, Number Wt., Number Wgt.,degrees %%

80- 85 2 (2 0.03 7 7 0.16

85- 90 85 (73 20.15 127 (75 15.74g0- 95 Z3 10 79-45 255 (150 84.1095-100 6 0.35 3 3100-105 2 (2 0.02 2 (2

TABLE 51Dispersion of fragments, Series 11 - Averages over experiments

Collecting Aro 3-ft. 5-ft.

Zone of dispersion, Number T , Numberdegrees,

80-85 "7 (7) 0.17 2 (2) 0.0285- 90 86 (69) 19.51 76 (62 16.3890- 95 255 (131) 80.22 281 (179) 83.3395-100 3 (2) 0.10 3 32 0.25

100-105 2 I 0.02 _J

- 27 -

Dispersion of fr&aents, Series 12 - Numiers and weights of fragments

EZxperiment 12A 12BColleoting Ara 5fZone of dispersion, Number Wgt,, Number Wgto , Number Wgt., Number Wgt.,

d ee g - g, . - ..,60

60- 6565- 7070- 7575- 80 1 0.14 J 1 0.16 -

80- 85 2 (2 0.22 6 (5 1.08 0,18 1 (1 0.2085- 90 11 47.12 14 ( 61.61 9 14.52 2. (22 115.9390- 95 19 18 98.00 27 (275 112-07125 (25 96.78 30 (30 121.7495-100 8 (8) 31.28 2 (2) 0.251 5 (5) 12.00 1 (1 0.25100-105 3 (3) 0,45 1 1 6.16105-11.0 1 1 0.25 1 (t ) 0.10 2 (2) 0.29110-115 1 1 0.37 -- ___

115-120 2 23 0.4.5 / 4 082-. .120 ... 2 21 0.55 (3) 0.38 3 3 0.65

Sum 40 (39) 176-62 52 (51) 175.4.6 41 (41) 129.64 56 (54) 238.12Dust 4..35 4.32 _ 3.10 5.70r n- ---: - - ,i j

Total 180.97 179.78 132.74 24-3.82Estimated weightof framnted 691 691

part;, _-_

Dispersion of fragments, Series 12 - Numbers and weights correoted to 3600Experiment _I____" 2A . 12B

Collecting Arc ~ f,5-ft. 3-ft. 5-ft.Zone of dispersion, Number Wgt., Number Wgt.., Number Wgt., Number Wgt.,

deea %_ % _%%__

80-85 8 (8 0.12 2 9 0.62 5 (5 0.14 3 ( 00985- 90 42 (2)26.68 54 () 35.11 47 (47) 1.20 68 (62) 48.6890- 95 73 (69) 55-49 104 (101) 63o87 130 (130 7465 85 (85 51.1295-100 31 (3) 17.71 8 (8) 0.14 26 (26) 9.26 3 (3 O.1l100-105 12 (12) 0.26, 5 (5) 4.75

TABLE 5Dispersion of fragments, Series 12 - Averages over oolleoting aros

_eriment t2k 12B

Zone of dispersion, Number Wgt., Number Wgt.sdeffees % % _

80- 85 16 14) 0.37 4 (4) 01285 90 48 30.90 58 (55 29.9490- 95 89 87 59.68 108 (08 62.8895-100 20 20 8.92 15 (15) 4.68

100-105 6 (6. 0.13 3 (3) 2.38


Colleoting Ara 3-ft. 5-ft.

Zone of dispersion, Number Wgt.,, Number Wgt.,degees % %

80- 85 7 (7) 0.13 13 (11) 0.3685- 90 45 (45) 18.94 61 (58) 41.8990- 95 102 (ioo) 65.07 95 (95 57.5095-100 29 (29) 13.48 6 (6) 0.12

100-105 3 3 2.38 6 (61 0.131

- 28 -

TABLE 56Dispersion of fragents, Series 13 - Numbers and weights of fragments

Experiment 13J 13B

Co.eotin Ar 10 ft. 5 ft. 10 ft. 5 ft.Zone ofdispers1= Number Wgt., Numberj Wgt., Number Wgt., Number Wgt.,

de r es g - , . ._ _ a60

60. 6565- 7070- 7575- 80 1 (1) 0.114.

80- 85 2 (2 0.41 9 (8) 1.55 1 (1) 0.12 3 (3 0.9985- 90 35 (23 58.12 63 5l% 99.14 18 (14.) 36.55 59 (48) 103-3695-100 1 1 0.39 100 56 218.62 14 11) 11.21 119 (71 202.20

100-105 2 (2 0.31 ' (1) 0.10 1 (1) 0.20

105-110 1 (1) 0.17 6 (6 0.87110,-15 2 2 0.28115-20 2 2 0.29

120 2 (2) 0.26 10 (1)i 1.58

136 (85) 233.o10 199(301) 633o32 135 (82) 224.96 34.3 (228) 635.83

Dust 1.88 5.12 3.14

Total 234.. 98 1638.44 226.07 638.97

Estimated weightof fragnented 1382 1382

p a r t , g .. ..... .... ... .. ...

Dispersion of fragments, Series 13 - Numbers and weights corrected to 360P

Experiment 13& 1.B _.

Collecting Arc 10 ft. 5 ft. 10 ft. 5 ft.

Zo of dispersion, Number Wgt. , Number Wt., Number Wgt., Number Wgt.,degrees % _ %

80- 85 12 (12) 0.18 19 (17) 0.24 6 (6) 0.05 6 (6) 0.1685- 90 206 (135) 24-.93 136 (117 15.65 110 (86) 16.26 128 1 ) 16.2690- 95 565 (335) 74.59 277 (173 49.56 62,.(1.2) 78.72 38 (227 51.7595-100 (6) (6) 0.17 216 (121 3.-.52 86 (67) 4.98 257 (5) 31.80

100-105 12 (12) 0.13 2 (21 0.03 2 (2) 0.03

TABLE 58Dispersion of fragnents, Series 13 - Averages over collecting arcs

Zone of dispersion, Number Wt., Number Wt.degrees % %

80- 85 16 (1'5 0.21 6 (6 0.1185- 90 171 16 20.29 119 (95~ 16.2590- 95 4.21 254.~ 62.07 4+86 (285 65.24~95-100 m1 (64 17-35' 172 (111 18.39

100-105 7 (7) 0.08 1 ( 0 .01

TABLE 592Dispersion of fragnents, Series 13 - Averages over experiments

Collecting Arc 10 -ft. 5 ft.Zone of dispersion, Number , .dogmas We. .degrees tr

96: 5 9 0.11 13 (12 0.2085- 90 158 (111 20.59 132 (11 15.9690- 95 5 956 (,3 76.66 313 (200 50.6595-100 2.57 237 (138 33.1

1 00-105 6 6 0.07 .1 ( 1 0.031

- 29 -

TABLE 60

Dispersion of fragments, Series 14 - mber and weights of fragmts

Zaerimt 14A. 1 iB_____________ 10 i-ft.-. 5-.ft I0ft 5-ft.

Zone of dispersion, Number Wgt., Nbofr Wgt. Nuber Wgtj, Number Wgt.,degees .. go g0 .9.

6060- 6565- 7070- 7575- 80 1 (I 0.10 _

80- 85 1 (1) 0.31 2 (2 13.67' 7 (7 48.84.185- 90 10 (10) 41,6 24. 24.) 1067.18 11 (1 1 77.15 27 (27 180.45g0- 95 35 (34 146:.08 50 48 305o41 31 (30 179.83 54 54. 330.8095-100 17 (6 40,27 A4 206.25 4 (4- 25 .39 29 29 179.80

100-105 _7___-0__

lO5-Io i (1) 0.13110-115115-120

120 1 (1) o.1oSum 63 (61) 228.66 108 (io6) 678,84. 48 (47) 296.M 117 (117) 739.89

Dust 1.73 5.13 1.71 4.27Total _2.39 1897 27.75 744.16

Estimated weightof fragmented 1382 1382

part, g. _ _ _ ___

TABI 61Dispersion of fragments, Series 14 - Nubera cI± weightes oorreted to 3600

Ezri1t __t__ IB

Cofleoting Aro 10-ft. 5-ft. 10-4. 5-f.

Zone of dispersion, Number sigt. Number Wt., Nwmber Wg , Number W 8todegrees ___ ___ %

80- 85 -6 (6) 0.141 9 (9) 4.62 13 (ii) 6.6085- g0 60 (60) 8.19 48 (4 241.3 51 (51 26.06 50 0 24,3990- 95 210 (201. 64.06 i ( 1 97 44.99 144 (1 60. 100 (100 44.71

95-1006 102 (96) 17.61 69 W 3.38 19 (19) 8.58 + 54(54 24.30

1000,105

T.ABL 62Dispersion of fragments, Series 14 - Averages over colleting arcs

Experiment -4 1- 5-

Zone of dispersion, Number Wgt., Numberdegrees % _T_.......

80- 85 3 (3) 0.07 11 (ii) 5.6185- 90 54 (54 21.41 51 (1) 25.2290- 95 156 (151) 54.53 122 (120 52.7395-100 86 (83) 23.99 37 (37) 16.44

100-10 ____

Dispersion of fra ts, searies 14 - Average._over experimentsCofleoting Arc 10-ft. 5-ft.

Zone of dispersion, Number Wgt.V Number Wgtop

80 58 (8) 2.38 7 (7) 3.3085-9056 (56) 22.13 49 (41~9) 24-51

90- 95 177 (172) 62.40 101 (99) "4.8595-10061 (58) 13,09 62 (62) 27.34

100-105_ _ _

30

Diapersion of fraZments, Series 16 N en & n weights of fragments

Ezpariment ________IG 16BColsoting Are 5-n. IOf t. 5-r. 10-ft.

... _ _.. e1._._. _ .s .a a . .. -. ,Zone of dispersion, N~ber 'Wgt. , Numb~er Wgt,, Nnber Wgt., Nusber 1gb.,

go so60f]

6o- 6565- 7070- 7575- 880-85 9 (9 64. 27 3 1 21.83 12 12 77.18 3 .13 20 .04.85- 9o 21 (21 141.82 5 5 32-831 1 (9)128.29 7 (7 47.4990- 95 35 341 223.53 18 (13 115.90 36 (36) 27.30 17 ( 111.7195-100 69 (67) 42)+.32 33 (%35) 203.92 73 (73) 43.66 32 (31) 203.78

100-105 13 (13) 56.82 15 15) 91.99105-11011o-115115-120

120t.. _- - -_- - - - -

sum 14.7 (44) 10.76 59 (59) 374-.50 155 (155) 978 .2 59 (58) 383.02-- -o - -

Dust__________

Total 910.7 374-.50 9-A 421 383.02

Estimated weightof fragmented 27 64. 2764g.

part "g.___________ ___

TAW~I 65Dispersion of fr ets, Series 16 - Nmabor an weights of fragentis

Experime~nt 16A,____ _ _ 1 6BCollecting Ara 5-=b 10-ft. 5-ft. 10t.

_ egees . ...--- =.=-.-- -. " f - ... .- - -Zone of dispersion, Wvmer Wgt., Nvmber Wgb., Nvmber Wgb., Nunber Wgt.,,

6o- 6565- 7070- 7575- 8080- 85 27 (27) 7.061 22 (22 5.83 34.(4 7.89 22 (22) 5.2385-90 64. 15.7 37 (7 8.77 ( 13.11 51 (5112.4090- 95 106 (03) 24,.,% 133 (133) 30.95 102 (02 24-.25 12.3 (123) 29.1795-100 209 (203) 46.59 14. (241) 54.4,5 206 (206) 45.34 231 (2&g 53-20

100-105 39 (39) 6.24 42 (42 9.41105-110110-115115-120

- 31 -

TABIX 66

Dispersion of fragmnts, Series 16 - Averages over oolleoting aros

16L 163

Zone of dispersion, Nuber Number N- ge t

60- 6565- 70

70-7575-80s0- 85 25 (25) 6.45 28 (28) 6.5685- 90 52 52 12.17 53 M 12.7690- 95 120 (118) 27.75 113 (113 26.7095-100 227 (22) 50.51 219 (215 49.27

100-105 20 (20) 3.12 21 (21) 4.71105-110110-115115-120

120


Colleotig Are 5.-ft. 1-t

Zone of dispersion, Nuber Wgt., Number Wgt.,degrees % %

6060- 6565- 7070- 7575- 8080- 85 31 (31) 7.47 22 (22) 5.5385- 90 59 59) 14.34 J44 (44a.J 10.5990- 95 104 (103) 24.40 128 28 30.%0195-100 208 (205) 45.96 238(28 53.84.

100-105 41 (41) 7.83105-110110-115115-120

120II I__ -- -... .

CONFIDENTIAL - DISCREITPACKS

3 FT SFT 3 FT 5FT90.1 ~ -__ __" 1 .... ___

90 i i

60 ..

40 .

I-.I

2 0 160 80 i00 120 60 80 I002 6o0 00 12060 0 10

_o __- - ,r -- __ ____

90.. I60.

40-

S20----

Or l, O- I I60 80 100 120 60 80 100 120 60 80 100 12060 80 10 120

90 11 - 1~

3: 60-- - _ _ _

40-

20.

0- II I 60 m ji260 80 100 12060 80 100 120 80 1 2060 80

90N FO -

so- I

60- ,-

20 ,

6b 80 100 120 iO Bb I00 120 60 80 t00 12060 80 100 120

DISPERSION ANGLE MEASURED FROM CENTRE: DEGREES

NATURAL FRAGM,,ENTATIO,----.. I CONTROLLED FRX.MtENTATION-.

PERCENTAGE WEIGHT OF CASINGFRAGMENTED INTO ANGULAR ZONES

FIG.I

CONFIDENTIAL - DISCREETPACKS

3 FT 5 FT 3 FT 5 Ft

so0 SIS9 [SIS1

60- -- .. J__

40-

20-- - - - I - --!

60 90 100 12060 80 io0 120 60 80 100 120 60 80 100 12090 - 11 -t II I I

so- !-- SERIES2

60 --

40- - -

20- --

0 r- T - - ,

Z 60 80 I00 12060 8 100 120 60 60 100 12060 80 100 120u 0 FT S FT 0 FT S FT

(Z 90 ... II[Il

0-

20S40.-

60 80 I00 120 60 o 100 120 60 80 1O0 120 60 80 100 120

DISPERSION ANGLE MEASURED FROM CENTRE: DEGREES

1.-- NATURAL FRAGMENTATION l-.CONTROLLED FRAGMENTATION- 4

10 FT 5 FT

90 -_ _ _ _

so- FSRIES 161

60-

40- J20

60 go IOO 120 60 sO 100 120

DISPERSION ANGLE MEASUREDFROM CENTRE: DEGREES

-- CONTROLLED FRAGMENTATION----

PERCENTAGE WEIGHT OF CASINGFRAGMENTED INTO ANGULAR ZONES

FIG 2

CONFIDENTIAL- DISCREET

PACKS3 FT 5 FT 3 FT 5 FT

60 -------

080

2 02

607 --- -7-'

40 -

85 90 95 100 85 90 95 100 85 90 95 100 85 90 95 100

SERIES 3 I

Z 60 -- - -IlluU

~40 -

20

20

0 5 85 9 0 95 10 5 95 100 85 90 95 100 85 90 95 100

h SIS5 SEIS 6

I-- 60 -0

40 -- _ __

2020 -I- --

0 7-:- I .AE I ____85 90 95 100 85 90 95 100 85 90 95 100 85 90 95 100

100 -- _

SIES7

60

40 -

0 i85 90 95 100 85 90 95 100 85 90 95 100 85 90 95 100

DISPERSION ANGLE MEASURED FROM CENTRE: 9 DEGREES

NATURAL FRAGMENTATION "1 CONTROLLED FRAGMENTATION-

PERCENTAGE WEIGHT OF CASING FORWARD OF 0

FIG.3

CONFIDENTIAL- DISCREET

PACKS3 FT S FT 3 FT S FT

100

so

60 _ --

40 ---

20

40 - - -- , ---- __

85 90 95 I00 as 90 95 100 85 90 9S 100 85 90 9S 100

100 - --60

to .zwU 40

0. 20

. 65 90 95 100 as 90 95 1008 s 90 95 100 s 90 9s ,oo0 S FT 1OFT 5lFT 10 FT

0100

80 ELA. I [SERIES 13) /" [SERIES 14J

6 0

202

40

85 90 95 100 85 90 95 100 85 90 95 100 85 90 9s 100

5 FT l0 FT

60

40

20- _ _

80 85 90 95 100 lOs 80 85 90 95 00 lOS

DISPERSION ANGLE MEASURED FROM CENTRE: 0 DEGREES

PERCENTAGE WEIGHT OF CASING FORWARD OF 0

FIG.4

CONFIDENTIAL - DISCREET

DIAMETERImin 2 in

5000 F - ....-5 0 0 1 L/D RA -rO 0 6SERIES 2 SERIES 10

4500

4000

3500

3000 LJ I JA B C A B C

5000 L / AI -SERIES 4 SERIES 12

0

W 4000uj)

ci. 3500 -.

uw 3000LA A B C D E B C D E

to 5000 1 11-' -__-~~~~

w.I SEI 6D RATIO 2.0w SERIES 6 SERIES 14V) 4500 I__-

w 4000-

< 3500i,

3000-A 8 C D E F G H I J A B C D E F G H I J

SERIS 8 SERIES 16

400 RATIO 4-4500,'I '

3500

3000 .. . ..... ... . . . .. JLL. , ., , L,.,, ,,ABCDEFG H I J KLMNOPQRST A BCDEFGHI J KLMNOPQR ST

SECTIONS ALONG, LENGTH OF CASING

VARIATION OF SPEED ALONG LENGTH OF CASINGFIG. 5

CONFIDENTIAL - DISCREETDIAMETER

14 In 2i In5000 _ 1 1 - I

SERIES I L/D RATIO 0"6] SERIES 94500- ___-_

4000-

3500 - -3000

A B C A B C

5000 ~ _ _SERIES 3 _ R _ SERIES If

z 45000

4000....... i -

W 3500I-

W 300 0WA a C D E A a C D E

4500 11-

Z 4000

tc( 3500- - _ _

30 SERIES 5 LID RATIO 20 SERIES 1330 0 - I I I I

A.B C D E F G H I J A 1 C D E F G H-I J

4500

4000

3500 -ISERIES 7 L/D RATIO 4.01

3000 1 1 . ... I ,, I ,ABCDEFGHIJ KLMNOPQRST

SECTIONS ALONG LENGTH OF CASING

VARIATION OF SPEED ALONG LENGTH OF CASINGFIG.6


KS 0

U)

- z

z 0

-0- a(

I-.u UC-L w

Z wK * -i Zo

- K -0 -I,* <AKS0 twO

-K- __ _ _ zo 0.

0, x10 0 w

w LLw 0n

U))

-0 a0

90

0

S3313030 :31IONV NOISd3dSIO3


0

z

U w

ex z

U. >

K z

31 U

I-

1C3 LL

wiwh

-K- -e o 0.

0~~ x -0 a~~~ :y0N NOSUdI


IC 0 -.

-0-

AL >

_ _ _ _ _ _ _ _ _ _ _ _ _ 0

101 - -0- '

L J- Z 0

Nz 0 0

N 0

50. < .( uL__

w_ ___ in_ __ 0

N-- 0 4W 0

N (n Lii

000

N- 0 0

U u 0

0A_ _ _ _ _ __ _ _ _ _ _ _ _ _ _U

N -uQ

NI 0

V a-

S3~3)( :3-15NV N0ISkI~dSIGl


9" 1- I t

SERIES 9 SERIES II SERIES 13 x x x

95 - -- _ _ - . - K -

x x

94 -

w93

w0

,92 -

z

z 91 --0

9 iO(.1) 0C

890

(a) (b) (c)

A B C A B C D E A B C D E F G H I J

SECTIONS ALONG LENGTH OF CASING

OBSERVED oEXPECTED X

COMPARISON OF EXPECTED ANGLES

WITH OBSERVED ANGLES

FIG. 10


96 I / ISERIES 2 / SERIES 10//

/

/ /94 I/ '! /93

/ /

92 /

910-/ I

Z 96I

"' I I I

12 95 - SERIES 4 SERIES 12

0. I/ /S94 ,

93 / I__ /92

91

90 ./

89 /(b) //

--1.0 -0-5 0 05 -10 -0.5 0 oS

LOG L/b

DISPERSION VELOCITY USING GURNEY FORMULA ... ... ,,

EXPECTED DISPERSION ANGLE USING FORMULA IOBSERVED DISPERSION ANGLE. ........................-----EXPECTED DISPERSION ANGLE USING EMPIRICAL FORMULA

COMPARISON OF OBSERVED ANGLE ANDANGLE PREDICTED BY DIFFERENT FORMULAE

FIG.II


97 96 SERIES

496v SERIES 14

/ 094 -

91. /I

90 -/"

" °) ,/ , / ._ _ _ _ _wI

3 -1-0 - 0-5 0 O-5 -1.0 -0-5 0 0-5

z VELO.ITY U.IG .Y F L .. .O 96O ... ...-

CO PRIO SER ESERE 8NL N

.SERIES 16

94

93

92

891

90 I

-10 -O05 0 0-5 -1.0 -0.5 0 0-S

LO G L/D

DISPERSION VELOCITY USING GURNEY FORMULA....... -' -EXPECTED DISPERSION ANGLE USING FORMULA I ... ........ '6--

OBSERVED DISPERSION ANGLE---......................

EXPECTED DISPERSION ANGLE USING EMPIRICAL FORMULA----

COMPARISON OF OBSERVED ANGLE ANDANGLE PREDICTED BY DIFFERENT FORMULAE

F IC,. 12


97

96 0

95t)wwCC 94u/0 /1

Li93

zz ______/____

0 9 1

w /0. 90-(n/

8 9 DISPERSION VELOCITY USING GURNEY FORMULA.... ,

EXPECTED DISPERSION ANGLE USING FORMULA I..

as 0BSERVED DISPERSION ANGLE .. .

1EXPECTED DISPERSION ANGLE USING EMPIRICAL FORMULA~-

87 1- 1.0 - 0.5 0 0.5 1.0

LOGIo L/D

97

96

t 5

Cr 94

87

97

w

Z 92

z0 93w i

0. 90 - MEAN DISPERSION ANGLES

/' ~- IY4IN.DIA.I ,, : C.E,). N.T 30/70IS9 4, -- --...- WN.DIA.C/D:I CE/TN.T 30/70

14- -I IN. DIA.L/D =2 C.E/T.NT" 30/76..... 2, 'eN.DIA.I.D =2 C.F.T'30/70

a.. I IN.DIA.I.D :4 CEITNT 30/7088 -- - -- 2- W N.DIAAI/D= 4 C.FE/.N.T 30/76

.... I4 IN.DIA.I/D -7 Rt.Dx/TNT55/45

:7 1 1I

-1I'0 - 0.5 0 0'5 1.0

LOG L/D

FIG.13


91

90- 1 _ _ _ _ _ _ _ _ _ _

LU

wI0

89

zz x088s

w0

87 X

86 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

0 I2 3 4

L/D

1 V IN. DIAMETER CASINGSX 2Y2 IN. DIAMETER CASINGS

VARIATION OF DISPERSION ANGLEOF FI RST FRAGMENT ROW WITH

L/D RATIO

FIG .14

For Indexing

OO)NFIDXNTIM4/DISaRET62-493:623.565.32 Spatial Distribution of Prag-

ments, II.

A.R.E. Report 58/54 T.LoWallo December 1954.

The fragment speed and dispersion from scaled cylindricalcasings has been examined for two diameters of case and a rangeof +/D ratios.for each diameter. Four fragmentation zones wereobserved with long casings. A method of obtaining the dispersionangle for fragments from the various parts of the casing issuggested. The application of this method to the cases usedleads to a uximtm divergence of only 10 between observed andexpected angles. The results have all been obtained withcylindrical casings; no -wrk has yet been done with othershapes.

31 pp. 14 figs. 67 tabs. 6 refs.

OONFI=IAIADISfCEET

62-49,7623.56A.R.E.

Tcasingof I/observanglesuggesleadsexpectcylindshapes

31 pp.

CONFIDENTIAL/DISCREETAlvmnent Research Establisument 62-3: IA.R.E. Report 58/54 623.565.32

Spatial Distribution ot Fragments, III.T.LWall. December 1954

The fragment speed and dispersion from scaled cylindrical casings Ihas been exmined for two diameters -f case and a range of L/D ratios foreach dlamter. Four fragmentation zones vrre observed with long casings.A method of obtaining the dispersion angle for fragments from the varlousparts of the casing Is suggested. The application of this method to the Icases used leads to a msxinmm divergence of only 1° between observed and Iexpected argles. The results have all been obtained with cylindricel casings; Ino work has yet been done with other shapes.

31 pp. 14 figs. 67 tabs. 6 rats. I

CONFIDENT IAL/DISC FEET

COWF IDENT IAL/DISCREET

Arimient Research Establishment 62-493A.R.E. Report 58/54 623.565.32

Spatial Distribution of Fragments, I1. December 1954

T.L.Walle

The fragment speed and dispersion from scaled cylindrical casings hasbeen examined for two diameters of case and a range of L/D Patios for Ieach diameter. Four fragmentation zones were observed with long casings. IA method of obtaining the dispersion angle for fragments from the various Iparts of the casing is suggested. The application of this method to the Icases used leads to a maximum divergence of only I between observed andexpected angles. The results have all been obtained with qlindrical I

Icasings; no work has yet been done with other shapes.

31 PP. 14 figs. 67 tabs. 6 refs. I

CO IDENTIAL/DISCREET

Idstil

Defense Technical Information Center (DTIC)8725 John J. Kingman Road, Suit 0944Fort Belvoir, VA 22060-6218U.S.A.

AD#: AD0083867

Date of Search: 8 Jun 2009

Record Summary: DEFE 15/2139Title: Spatial distribution of fragments, IIIAvailability Open Document, Open Description, Normal Closure before FOI Act: 30 yearsFormer reference (Department) ARE Report 58/54Held by The National Archives, Kew

This document is now available at the National Archives, Kew, Surrey, UnitedKingdom.

DTIC has checked the National Archives Catalogue website(http://www.nationalarchives.gov.uk) and found the document is available andreleasable to the public.

Access to UK public records is governed by statute, namely the PublicRecords Act, 1958, and the Public Records Act, 1967.The document has been released under the 30 year rule.(The vast majority of records selected for permanent preservation are madeavailable to the public when they are 30 years old. This is commonly referredto as the 30 year rule and was established by the Public Records Act of1967).

This document may be treated as UNLIMITED.

Documents

AUTHORITY THIS PAGE IS UNCLASSIFIEDexcept at two sections along the casing. These sections consisted of a length equal to twice the internal diameter at the detonator end of the casing,