Shot range estimation based on pellet distributionin shots with a pump-action shotgun

I. Cakira, G. Cetinb, H.B. Unerc,*, E. Albekb

aCouncil of Forensic Medicine, Ministry of Justice, TurkeybDepartment of Forensic Medicine, Cerrahpasa Faculty of Medicine, Instanbul University, Turkey

cInstitute of Forensic Sciences, Instanbul University, Turkey

Received 9 October 2002; received in revised form 6 January 2003; accepted 15 January 2003

Abstract

In the present study, shots from different ranges were fired using a non-choked pump-action shotgun (Hugsan) of calibre 12

with a bore length of 52 cm and pellets of various sizes. The aim of the study is range estimation from the distribution of pellets.

Usingpelletsof2,3.5,5and8 mmsize,5shots werefiredfrom:0.7,0.8,0.9,1,2,3,5,10,15,20and25 ms.Themaximumdistance

between the pellets in vertical and horizontal direction was measured. Statistical evaluation of the data revealed a highly significant

correlation for each pellet type; the constant values a and b were calculated to be used in the linear regression equation y ¼ a þ bx.

As a conclusion, the linear regression equation as well as table data may allow range determination within acceptable ranges

of error for the same barrel length and diameter for the same cartridge type. Under identical conditions they may also provide

information for pellets of comparable size.

# 2003 Published by Elsevier Science Ireland Ltd.

Keywords: Pump-action shotgun; Range estimation; Pellets; Distribution pattern

1. Introduction

In cases of firearm wounding and especially in those with

fatal outcome shot range estimation is of paramount impor-

tance for criminal investigations. For purposes of shot range

estimation, gunshot residues on the victim and/or his cloth-

ing may yield valuable clues [1–4]. In cases of wounding by

a shotgun, the distributional pattern of pellets on the target

may also allow shot range estimation [3–8].

In the present study experimental shots were fired from a

pump-action shotgun from different distances using pellets

of varying caliber in order to investigate the correlation

between the distribution pattern of pellets on the target and

the shot range.

2. Materials and methods

In this study, a pump-action shotgun of Turkish produc-

tion, trade mark Hugsan (12/76 Magnum, 52 cm cylinder

bored barrel) and cartridges (length: 70 mm) of Turkish pro-

duction, trade mark MKE (Machine and Chemical Industry)

containing 2, 3.5, 5 and 8 mm diameter lead pellets were

used.

� Shooting area: S.B. Police Training Center.

� Dimensions of the soothing area: 30 m � 10 m

� Environmental conditions: Clear sky, average temperature

18 8C, slightly windy, atmospheric pressure approxi-

mately 1 atm

� Target: Fabrics and wrapping paper of varying dimensions

in wooden frame.

Shots were fired from 0.7, 0.8, 0.9, 1 m, 5, 10, 15, 20,

25 ms distance in a right angle (908) toward the target, using

pellets of 2, 3.5, 5, 8 mm diameters by a professional person,

obeying the technical rules. The distribution of the pellets

was determined by measuring the maximum distance

between the pellets in the vertical and horizontal direction.

Abnormal deviations were not included in the calculation.

The statistical significance of the values was assessed by

the one way (ANOVA) method using post hoc Tukey HSD

test. The Pearson correlation coefficient was calculated for

Forensic Science International 132 (2003) 211–215

* Corresponding author.

E-mail address: hbuner@istanbul.edu.tr (H.B. Uner).

0379-0738/03/$ – see front matter # 2003 Published by Elsevier Science Ireland Ltd.

doi:10.1016/S0379-0738(03)00022-7

Table 1

Descriptive statistics of vertical distance, horizontal distance, pellet diameter and shot range

Pellet

diameter

(mm)

Shot

range

(m)

Maximal distance between pellets (mm)a

Shot 1 Shot 2 Shot 3 Shot 4 Shot 5 Mean distance

(N ¼ 5)

S.D.

(N ¼ 5)

VD HD MV VD HD MV VD HD MV VD HD MV VD HD MV VD HD VD HD

2 0.7 20 16 18 20 20 20 21 20 20.5 20 19 19.5 20 20 20 20.2 19 0.45 1.73

0.8 21 21 21 22 21 21.5 22 21 21.5 22 21 21.5 21 21 21 21.6 21 0.55 0.00

0.9 23 24 23.5 24 24 24 26 25 25.5 24 23 23.5 24 23 23.5 24.2 23.8 1.10 0.84

1 30 28 29 30 30 30 31 30 30.5 30 30 30 30 29 29.5 30.2 29.4 0.45 0.89

2 53 53 53 53 61 57 54 54 54 62 65 63.5 59 65 62 56.2 59.6 4.09 5.81

3 110 98 104 100 110 105 100 110 105 110 115 112.5 110 105 107.5 106 107.6 5.48 6.43

5 232 233 232.5 210 200 205 239 235 237 216 225 220.5 235 233 234 226.4 225.2 12.66 14.60

10 480 440 460 470 480 475 470 490 480 470 492 481 472 480 476 472.4 476.4 4.34 21.09

15 700 740 720 702 740 721 760 740 750 730 720 725 732 740 736 724.8 736 24.76 8.94

20 998 995 996.5 982 986 984 983 1007 995 980 930 955 982 970 976 985 977.6 7.35 29.84

25 1290 1238 1264 1244 1193 1218.5 1192 1205 1198.5 1245 1210 1227.5 1242 1230 1236 1242.6 1215.2 34.70 18.46

3.5 0.7 22 20 21 20 20 20 21 20 20.5 22 20 21 20 20 20 21 20 1.00 0.00

0.8 20 22 21 22 23 22.5 25 23 24 24 22 23 23 22 22.5 22.8 22.4 1.92 0.55

0.9 24 23 23.5 22 21 21.5 22 24 23 25 20 22.5 25 24 24.5 23.6 22.4 1.52 1.82

1 23 22 22.5 24 23 23.5 26 23 24.5 25 24 24.5 23 27 25 24.2 23.8 1.30 1.92

2 50 49 49.5 49 47 48 39 45 42 50 49 49.5 50 50 50 47.6 48 4.83 2.00

3 85 88 86.5 84 85 84.5 60 85 72.5 83 85 84 83 85 84 79 85.6 10.65 1.34

5 168 165 166.5 175 170 172.5 165 170 167.5 170 172 171 170 175 172.5 169.6 170.4 3.65 3.65

10 360 380 370 410 400 405 380 390 385 400 397 398.5 396 392 394 389.2 391.8 19.58 7.69

15 670 620 645 640 700 670 602 605 603.5 599 602 600.5 605 615 610 623.2 628.4 30.98 40.69

20 880 832 856 884 840 862 742 880 811 850 860 855 852 861 856.5 841.6 854.6 57.82 18.97

25 950 1015 982.5 960 1063 1011.5 990 985 987.5 980 960 970 910 924 917 958 989.4 31.14 52.99

5 0.7 22 21 21.5 22 20 21 24 22 23 20 22 21 21 22 21.5 21.8 21.4 1.48 0.89

0.8 21 22 21.5 22 22 22 20 28 24 24 20 22 22 22 22 21.8 22.8 1.48 3.03

0.9 25 25 25 24 25 24.5 23 23 23 26 25 25.5 25 25 25 24.6 24.6 1.14 0.89

1 22 20 21 24 22 23 28 24 26 25 23 24 26 25 25.5 25 22.8 2.24 1.92

2 38 38 38 38 39 38.5 36 39 37.5 38 40 39 38 40 39 37.6 39.2 0.89 0.84

3 70 74 72 70 70 70 60 48 54 60 55 57.5 80 78 79 68 65 8.37 12.88

5 167 165 166 165 160 162.5 155 160 157.5 160 150 155 146 160 153 158.6 159 8.44 5.48

21

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10 330 320 325 380 360 370 380 375 377.5 340 341 340.5 330 310 320 352 341.2 25.88 27.01

15 565 563 564 560 535 547.5 525 543 534 460 480 470 633 565 599 548.6 537.2 63.11 34.46

20 830 780 805 830 760 795 820 762 791 804 838 821 820 725 772.5 820.8 773 10.64 41.44

25 895 980 937.5 800 990 895 860 989 924.5 970 930 950 860 860 860 877 949.8 62.21 55.95

8 0.7 25 25 25 25 25 25 22 25 23.5 26 25 25.5 23 23 23 24.2 24.6 1.64 0.89

0.8 28 25 26.5 25 26 25.5 23 25 24 28 25 26.5 26 25 25.5 26 25.2 2.12 0.45

0.9 26 26 26 26 26 26 24 26 25 26 27 26.5 26 27 26.5 25.6 26.4 0.89 0.55

1 30 30 30 30 30 30 29 28 28.5 31 28 29.5 30 30 30 30 29.2 0.71 1.10

2 34 33 33.5 33 32 32.5 32 33 32.5 34 34 34 35 34 34.5 33.6 33.2 1.14 0.84

3 50 50 50 50 45 47.5 43 45 44 50 45 47.5 55 60 57.5 49.6 49 4.28 6.52

5 90 100 95 80 100 90 90 90 90 91 92 91.5 89 92 90.5 88 94.8 4.53 4.82

10 170 162 166 173 170 171.5 173 164 168.5 173 175 174 186 165 175.5 175 167.2 6.28 5.26

15 250 220 235 255 300 277.5 190 300 245 200 210 205 230 210 220 225 248 29.15 47.64

20 390 230 310 335 360 347.5 370 355 362.5 264 290 277 240 330 285 319.8 313 65.50 54.04

25 400 460 430 425 400 412.5 450 342 396 490 500 495 470 480 475 447 436.4 35.64 64.69

a VD, vertical distance; HD, horizontal distance; MV, mean value.

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the distance variable of the pellets. A linear regression model

was constituted for each pellet type.

In the present study experimental shots were fired from a

pump-action shotgun within 11 different ranges, using pel-

lets of 4 different diameters. The distribution pattern was

determined in the horizontal and vertical direction.

3. Results and discussion

In firearm fatalities shot range estimation is of paramount

importance for the reconstruction of the event and for origin

determination. This is especially true if there are no eye-

witnesses, the testimonies are contradictory or there exist

incongruencies between the testimonies and other case

related findings.

If rifled weapons are used or slugs fired from shotguns,

shot range estimation beyond the reach of gunshot residues

or of the wad of the cartridge is not possible. Here, the only

possible range estimation is that of a distant range shot;

if in contrary, pellets are used, a relationship between the

pellet distribution on the target and the shot range may be

established, thus allowing shot range estimation [3,8].

In case of shotguns, type of the weapon, barrel length and

diameter choke, type of the cartridge, powder and relevant

properties of the pellets as well as the physical circumstances

under which the shot was fired will influence the distribution

pattern of the pellets on the target. Thus experimental shots

under standardized conditions have to be performed in order

to establish a correlation between the variables allowing a

reliable shot range estimation [3–8].

We used for our experimental shots a pump-action type

shotgun frequently involved in firearm fatalities as well as

pellets of widely used diameters.

The experimental shots started from a distance of 0.7 m

on. As is seen in Table 1 a distribution pattern applicable

for practical purposes is observed beyond the range of 1 m.

In distances under 1 m, the pellets did show no distribution, a

result consistent with the literature on the subject [3,5,7].

Beyond the distance of 1 m, the pellet distribution in the

vertical and horizontal direction showed an increase, pellets

of small diameters dispersed over a greater arc. The high

number of small pellets in the cartridge causes a decrease

of kinetic energy load per pellet, so that the reduction of

the velocity by the air resistance leads to a considerable

dispersion.

A high statistical significance was found between pellet

diameter and distribution for shots from different distances

(P < 0:001). Correlation coefficients were calculated for

each pellet diameter (Table 2).

The formula y ¼ a þ bx allows the estimation of the shot

range; here, y the shot range (in m), a the constant, b the

coefficient, and x the maximum distance between two pellets

Table 2

Pearson correlation coefficients among vertical distance, horizontal

distance, mean value and shot rangea

Pellet diameter

(mm)

Direction Shot range

2 Vertical distance 0.999

Horizontal distance 0.999

Mean value 1.000

3.5 Vertical distance 0.996

Horizontal distance 0.997

Mean value 0.997

5 Vertical distance 0.992

Horizontal distance 0.996

Mean value 0.996

8 Vertical distance 0.983

Horizontal distance 0.979

Mean value 0.989

a P < 0.001 for all coefficients.

Table 3

Linear regression analysis including R, R2, and standard error of estimate

Pellet diameter

(mm)

Direction a constant b coefficient R R2 Standard error

of estimate

2 Vertical distance 0.5638 0.0197 0.999 0.999 0.3174

Horizontal distance 0.5087 0.02 0.999 0.999 0.3104

Mean value 0.5336 0.0199 0.999 0.999 0.2644

3.5 Vertical distance 0.5275 0.0243 0.996 0.992 0.7739

Horizontal distance 0.5539 0.0237 0.997 0.994 0.6692

Mean value 0.5296 0.024 0.997 0.994 0.6393

5 Vertical distance 0.6264 0.0259 0.992 0.984 1.0782

Horizontal distance 0.7036 0.0256 0.996 0.992 0.7435

Mean value 0.638 0.0258 0.996 0.992 0.7597

8 Vertical distance �0.1122 0.0586 0.983 0.966 1.5691

Horizontal distance �0.1519 0.0588 0.979 0.959 1.7220

Mean value �0.258 0.0597 0.989 0.978 1.2606

214 I. Cakir et al. / Forensic Science International 132 (2003) 211–215

in the vertical and horizontal direction or the arithmetical

mean (in mm). R indicates the regression coefficient and its

square (R2) explains the percentage that how maximum

distance between pellets contributes to the variation in the

shot range. In know cases R2 values exceeded 95% (Table 3).

However the values are smaller for larger pellets. With the

formula proposed, pellets with a diameter of 2 mm are

associated with a small error in distance estimation. This

error increases whit pellet over 2 mm diameter. The formula

is not applicable under a shooting distance of 1 ms for 2, 3.5,

and 5 mm pellets and of 2 ms for 8 mm pellets, respectively.

We, however, think, that range estimation is also possible

just with the help of tables without the use of the formula.

One should, of course, always keep in mind, that the results

thus obtained represent only an estimation of the shot range.

As mentioned in the chapter material and method, the data

obtained in this study are valid exclusively for shots fired to

the target under the right angle. In shots under angles other

than the right, the distributional pattern would be ovoid

rather than circular. In this case, the inter-pellet distances

vertical to the shot direction should be determined for a

correct calculation.

The method we present can also be used if there are

aberrant pellets not striking the target; if they are high in

number, however, the reliability of the method would suffer

due to the increased error factor. The method should also not

be applied in cases where a hindrance is interposed between

pellets and target. There, a highly aberrant distributional

pattern due to the billiard ball-effect would result [3,9–11].

Highly aberrant pellets should also not be taken into con-

sideration, because they would increase the acceptable error

range.

Ideally, correlation coefficients should be determined for

all pellet diameters. For diameters other than those used in

this study range estimation with an acceptable error is still

possible if mean values are used. The tables, however, should

not be used in shots from shotguns of different barrel length

and diameter.

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Yontem, Doktora Tezi, Istanbul Universitesi Adli Tıp

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