THE USE OF TRIGONOMETRY IN BLOOD STAIN PATTERN

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THE USE OF TRIGONOMETRY IN BLOOD STAIN PATTERN

Sowmiya .R¹, Kaviyasri .V², Naveenapriya .D³, Sujata Barman⁴, Sangeetha .R⁵

1,2,3,4,5PG scholars, Sri Krishna Arts and Science College, Kuniyamuthur, Coimbatore, Tamil

Nadu, India.

Abstract

A case study on blood stains pattern or blood spatter is analysed. Though trigonometry play a vital role in blood stain pattern during crime. In this paper we analyze the blood spatter by using Rossmo’s formula to find angle of impact via trigonometry. The recognition and analysis of blood spatter can yield useful crime investigative information. The most probable scenario resulting in blood spatter on walls and floor can be reconstructed during crime using trigonometric analysis.

Forensic science considers physical evidences relating to criminal activity. Some numerical examples were given to show the effectiveness of the proposed theory.

Keywords:Bloodstain pattern Analysis, Forensic Science, Applications, Rossmo’s formula.

1. Introduction:

Trigonometry confide on shoal of mathematical procedures to organize, summarize and interpret numerical data during crime. Catching serial criminals is a daunting problem for law enforcement officers around the world. Investigate the field of forensic science is called bloodstain pattern analysis. The Bloodstain pattern analysis is the study and analysis of blood at a known or suspected crime scene with the purpose of drawing conclusion about the nature, timing and other details of crime. It is the interpretation of bloodstains at a crime scene in order to recreate the actions that caused the bloodshed. For example: the shape of blood droplets might be used to draw conclusion as to how far away the victim was from a gun when they were shot. In this paper rossmo’s formula and use of trigonometric is our case study .in which we will show the criminal distance from the crime scene by using the impact of angels with the same function at same buffer zone.

2. Kim’s Rossmo’s Formula:

The formula was developed and patented in 1996 by criminologist Kim Rossmo and integrated into a specialized crime analysis software product called Rigel. It is developed by the software company Environmental Criminology Research Inc. (ECRI). The Rossmo’s formula is use to obtain the probability of the crime. The map of the crime scene into the grid scene with i rows and j columns.

The probability of criminal located in i and j Pij=k∑ ^∅

(2B)^f

Tc=1 +^(1−∅)(B^g−f)

(2B−2D)^g (1) Where,

2D=2B-(|xi-xc|- |yj-yc|) K is scalling constant

T is the total number of crimes.

∅= the metric which puts more weights on one metric than the others B is the radius of buffer zone.

f = g= 3.2

However, (1) describe about the crime scene and where the criminal is located, If for any crime scene xc and yc. If we take equality of 2B=(|xi-xc|- |yj-yc|) and it is satisfied. Then we found that the denominator of term ^(1−∅)(B

g−f)

(2B−2D)^g is zero then it must be undefined. And also if the region as the crime then ^∅

(2B)^f is undefined. It is seeks to focus on the possible conduct of an unknown criminal

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based on the data collected from the past. In this paper we have taken our own data to satisfy the Rossmo’s formula.

Figure 1: same radius of buffer zone in different distance at same function (f = g= 3.2).

Figure [1] shows that distance from the crime scene at the same function with same radius of the buffer zone (i.e. 2B =8). We refer reader for table [1].

EXAMPLE:

Figure 2.

3. ANGLE OF IMPACT:

The acute angle formed between the direction of a blood drop and the plane of the surface it strives.

The length of bloodstain is the hypotenuse while the width is opposite side of angle of impact.

Sinθ=^opp

hyp

sin θ=^w_l Where,

w= width (minor axis) l= length (major axis) θ= angle of impact

distance, 1, 55

distance, 2, 65

distance, 3, 85

distance, 4, 33 distance,

5, 73

radius, 1, 8

radius, 2, 8

radius, 3, 8

radius, 4, 8 radius, 5, function, 8

1, 3.2

function, 2, 3.2

function, 3, 3.2

function, 4, 3.2 function,

5, 3.2

Buffer zone of rossmos formula^distance ^radius ^function

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Figure 3. Angle of impact

1. Consider the stain with actual major axis of 85mm and the minor axis of 45mm. find the angle of impact.

Given:

W=45mm L=85mm Soln:

sin𝜃=^𝑤

𝑙

𝜃=𝑠𝑖𝑛^{−1 𝑤}

𝑙

=𝑠𝑖𝑛^{−1 45}

85

=32°

2. Determine the angle of impact when we see a spot of blood on a wall. It is the shape of an ellipse. The major axis has length 12mm and the minor axis has length 6mm.

Given:

W=6mm L=12mm Soln:

sin𝜃=^𝑤_𝑙 𝜃=𝑠𝑖𝑛^{−1 𝑤}

𝑙

=𝑠𝑖𝑛^{−1 6}

12

=30°

3. Calculate the angle of impact when the length is 2.57mm and the width is of 0.47mm.

Given:

W=0.47mm L=2.57mm Soln:

𝑙

=𝑠𝑖𝑛^{−1 0.47}

2.57

=10.5°

4. Consider the bloodstain with actual major axis of 95mm and the minor axis of 65mm. find the angle of impact

Given:

W=65mm L=95mm Soln:

𝑙

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=𝑠𝑖𝑛^{−1 65}₉₅ =45°

5. Calculate the angle of impact when the length is 75mm and the width is of 60mm.

Given:

W=60mm L=75mm Soln:

sin𝜃=^𝑤

𝑙

𝜃=𝑠𝑖𝑛^{−1 𝑤}_𝑙

=𝑠𝑖𝑛^{−1 60}₇₅

=53°

4. Angle of convergence:

The area containing the intersecting generated by lines drawn through the long axes of individual stains that indicates in two dimensions the location of blood source.

tan𝜃=^{𝑜𝑝𝑝𝑜𝑠𝑖𝑡}

𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡

tan𝜃=^ℎ_𝑑

Where,

h= height d=distance

Figure 4. Angle of convergence

To solve angle of convergence we have to find height tan𝜃*distance=height

By taking 𝜃from the angle of impact and using it in convergence formula.

1.

Where,𝛩 = 32°

d=55mm

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Soln:

h= d*tan 𝜃 =55* tan 32°

=34.3mm

2

Where, 𝜃 =30°

d=65mm Soln:

h=d*tan 𝜃 =65*tan 30°

=37.5mm

3.

Where, 𝜃 =11°

d=85mm

Soln:

h=d*tan 𝜃 =85*tan 11°

=16.5mm

4.

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Where,𝜃 = 45°

d= 33mm Soln:

h=d*tan𝜃

=33* tan 45°

=33mm 5.

Where, 𝜃 = 53°

d= 73mm Soln:

h= d*tan 𝜃 =73*tan 53°

=96.8mm

Table 1: The table reveals the value for plotting the graph.

S.NO DISTANCE(mm) ANGLE(𝜃) HEIGHT(mm)

1 85 11° 16.5

2 55 32° 34.3

3 33 45° 33

4 65 30° 37.5

5 73 53° 96.8

Figure 5: angle of convergence which is considered from the angel of impact.

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5. Different shapes of spatter:

Bloodstain pattern can occur on a variety of surfaces according to their surfaces or spatter direction. The types of surfaces that free falling blood strikes affect the appearances of the resulting spatter. A blood drops on a smooth surface will make a more uniform, regular or circular shape and rough surface will make an irregular stain with rough or jagged edges. The shapes of the stains vary from circle to oval depending on the impact of angles from 90ᵒ to less than 90ᵒ. The different surfaces of spatter are:

5.1 Low velocity spatter 5.2 Medium velocity spatter 5.3 High velocity spatter 5.1 Low velocity spatters:

Low velocity spatter can cause by blood dropping and it falls at the speed or force of normal gravity. These spatter fall from an open wound or from the surface is saturated with blood. For example: a blood dripping from a forehead. The force of the blood hitting a surface for low velocity spatter is 5 feet per second or less. This causes the blood droplet to be large in diameter (between 4 and 8mm).

5.2 Medium velocity spatter:

It is produced with more energy i.e. blunt object or force than gravity. The force of this spatter cause the blood to break into smaller size patterns relative to the amount of force applied.

y = 9.1143x + 19.933 R² = 0.3046 y = 13.117x - 9.56

R² = 0.559

Height

distance

Series1

Series2

Series3

Linear (Series1) Linear (Series2)

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This type is usually seen in blunt force, stabbing and secondary spatters. For example:

someone beaten by cricket bat or stone. The force of medium velocity spatters hitting between 5 and 100 per second. This causes the blood in smaller spatter with diameter of 2-4 mm.

5.3 High velocity spatters:

It is caused by a gunshot, explosions and high sped collisions. High velocity spatter takes on a “mist like” appearance. The force of blood hitting a surface is over 100 feet per second. Each tiny droplet in a high velocity blood patter less than 1mm in diameter.

6. Forensic science:

In the actual spatter analysis, a forensic investigator determines the trajectory of the blood where the blood came from and how it spread over the surface. With the evidence, the forensic investigators determine how blood spatter is useful in piecing together what took place, identifying the victim and determining who was responsible for the crime. Because of this forensic science community, it is imperative to have scientists who are accurate to produce reliable results.

6.1Applications:

The application of the forensic science is a broad spectrum of science to answer the legal questions.

Forensic science is science used in public, in a court or in the justice system. Today forensic science is a high technology field using electron microscopes, lasers, ultraviolet, advanced analytical chemical techniques and computerized databanks to analyze and research evidence. Modern forensic science has a broad range of applications. It is used in civil cases such a forgeries, fraud or negligence. It is used in monitoring the compliance of various countries with such international agreements as the nuclear non-proliferation treaty and chemical weapons convention are developing secret nuclear weapons programs.

7. RESULT AND DISCUSSION:

From the same buffer zone we have found the Rossmo’s formula of the terms is zero so it is undefined .And seeks the unknown criminal. Second bloodstain evidence is most often associated with violent acts such as assault, homicide, abduction suicide or even vehicular accident. Because of this, we exploring computerized method of finding angle of impact and convergence could fulsomely improve the classic of science and reduce the amount of false convictions.

REFERENCE:

[1] V.T. Bevel and R. M. Gardner. Bloodstain pattern analysis: with an introduction to crime scene reconstruction. CRC Press, 2^nd edition, 2001.2.

[2] Yonder, Anita. “Trigonometry in bloodstain pattern evidence, math use in question”. Elsevier, 2011.

http://www.sciencedirect.com/science/article/pii/B9780123704825500586 [3] http://www.crimescene-forennsic.com/spatter_VS_Transfer.html

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[4] Freeman, Shanna. “How bloodstain pattern analysis works” 24 April 2008. How StuffWorks.com. http://science.howstuffworks.com/bloodstain-pattern-analysis.htm 28 April 2014.

[5] Wonder, A.Y. “Blood Dynamics” Forident, 2008.

http://homespat.com/terminology/index.php?cat=projected&sub=LVIS

[6] National Forensic Science Technology Center “A simplified guide to bloodstain pattern analysis”

2013.

http://www.crime-scene-investigator.net/SimplifiedGuideBloodstainPatterns.pdf

[7] Riley, Pat, “Blood Drop Analysis” 2013 http://www.youtube.com/watch?v=DKW5agx-Cqw