Materials Included In Kit

Additional Materials Required

Prelab Preparation

Bullet 1/Suspect 1

1. Place bullet hole 1 78" above the ground.
2. Place footprint 1 57" from the wall.
3. Repeat steps 1 and 2 twice with the two remaining copies of bullet 1 and shoe 1.

Bullet 2/Suspect 2

4. Place bullet hole 2 81.5" above the ground.
5. Place footprint 2 68" from the wall.
6. Repeat steps 4 and 5 twice with the two remaining copies of bullet 2 and shoe 2.

Bullet 3/Suspect 3

7. Place bullet hole 3 60" above the ground.
8. Place footprint 3 22.4" from the wall.
9. Repeat steps 7 and 8 twice with the two remaining copies of bullet 3 and shoe 3.

Safety Precautions

This laboratory activity is considered nonhazardous. Please follow all laboratory safety guidelines.

Disposal

All materials can be saved for future use.

Lab Hints

• Enough materials are provided in this kit for 15 student groups. There are three different bullet holes and shoe prints that are reconstructed that represent three different suspects. The 15 student groups will need to rotate so that each group visits stations 1, 2 and 3. For convenience, three copies of each bullet and shoe print are included in the kit so there can be three stations for each suspect (to minimize student wait times).
• You may wish to provide the major and minor axis of each bullet hole to students if step stools are not available for them to accurately measure the height of the bullet holes. The bullet holes may also be copied and placed on a lab table where the students can measure them more easily.

  Bullet Hole 1: Minor Axis = 18 mm, Major Axis = 19 mm
  Bullet Hole 2: Minor Axis = 24 mm, Major Axis = 25 mm
  Bullet Hole 3: Minor Axis = 22 mm, Major Axis = 24 mm

• Each student group will need access to a tape measure. It is advised that student groups be planned in advance and at least one student in the group should plan to bring a tape measure on the day of the activity.
• This lab may be performed more easily using a wall in the hallway, gymnasium or outdoors. In the lab there may be lab tables and other items obstructing accurate measurement.

Teacher Tips

• Enhance the story by allowing students to perform the other lab kits in the Flinn Forensic Files Series
  • FB2094 Flinn Forensic Files—Fingerprint Exploration
  • AP7745 Flinn Forensic Files—Ink Inspection
  • FB2096 Flinn Forensic Files—Finding Evidence in Fibers
  • AP7752 Flinn Forensic Files—Footwear Evidence

Answers to Prelab Questions

1. Calculate the angle of elevation in the triangle below if the impact angle is 42°.
   {12493_Answers_Figure_6}

   The three interior angles must add up to 180°. Therefore, the angle of elevation is 180 – 90 – 42 = 48°

2. Determine the shoulder height of a shooter based on the sketch below. The bullet hole is 85" from the ground. The shooter’s footprints are 92" from the wall and the impact angle is 77°.
   {12493_Answers_Figure_7}

   First the angle of elevation must be calculated; 180 – 90 – 77 = 13°. From there the height of the y-axis can be determined. Tan(13) = y/92. y = 22" The bullet hole is 85" above the ground. The shooter’s shoulder height is determined by subtracting the y from the height of the bullet hole. Therefore, 85" – 22″ = 63" shoulder height.

3. Based on the information calculated in Question 2, what is the overall height of the shooter, assuming the head is the height provided in the Background section?

   The Background section says that the head is assumed to be 8" taller than the shoulder height. Therefore if the shooter has a 3" shoulder height + 8" head his/her total height would be 71".

Sample Data

Answers to Questions

1. Based on the measurements obtained in the table, calculate the impact angle (to the nearest degree) for each bullet. Show work and record final value in the table.

   Bullet 1: sin (i) = 18/19

   i = sin^–1(18/19)
   i = 71°

   Bullet 2: sin (i) = 24/25

   i = sin^–1(24/25)
   i = 74°

   Bullet 3: sin(i) = 22/24

   i = sin^–1(22/24)
   i = 66°

2. Calculate the angle of elevation/depression for each bullet hole (to the nearest degree). Based on tests with dowel rods and lasers done by the investigators, bullets 1 and 2 are angles of elevation (above the shooter’s shoulders) and bullet 3 is an angle of depression. Show work and record final value in the table.

   Bullet 1 = 180 – 90 – 71 = 19°
   Bullet 2 = 180 – 90 – 74 = 16°
   Bullet 3 = 180 – 90 – 66 = 24°

3. Calculate the height of each of the three shooters. Assume the height from the shoulder to the top of the head is 8".

   Bullet 1 Shot fired above shoulder (angle of elevation)

   tan(19) = y/57
   y = 19.6"
   Height of the shooter’s shoulder = Distance from the floor to bullet hole center–y-axis of triangle
   = 78" – 19.6"
   = 58.4" tall at shoulder
   = 58.4 + 8" head = 66.4" tall or 5'6"

   Bullet 2 Shot fired above shoulder (angle of elevation)

   tan(16) = y/68
   y = 19.5"
   Height of the shooter’s shoulder = Distance from the floor to bullet hole center–y-axis of triangle
   = 81.5" – 19.5"
   = 62" tall at shoulder
   = 62 + 8" head = 70" tall or 5'10"

   Bullet 3 Shot fired below shoulder (angle of depression)

   tan(24) = y/22.4
   y = 10"
   Height of the shooter’s shoulder = Distance from the floor to bullet hole center + y-axis of triangle
   = 60" + 10"
   = 70" tall at shoulder
   = 70 + 8" head = 78" tall or 6'6"

4. The bullet hole found in Marty Higgins’ bedroom wall was 45" from the ground. Based on the dowel rod tests it is an angle of depression. The shooter was estimated to have been 130" away from the wall. The impact angle was measured and found to be 84°. Determine which of the three suspects could have possibly been the shooter.

   The angle between the floor and the wall is 90° and the impact angle is 84°, therefore the angle of depression is 6°, since the interior angles must add up to 180°. The y-axis of the triangle must be calculated to determine the height of the shooter.

   tan(6) = y/130
   y = 130tan(6)
   y = 13.6"
   The height of the shooter’s shoulder would be 45" + 13.6″
   = 58.6" = 58.6" + 8" head = 66.6", which is very close to the height of the shooter who shot bullet 1.

5. Explain other variables that could alter the accuracy of results.

   One factor that could alter the accuracy of results is the shoe the suspect was wearing at the time. Some shoes, especially women’s, have thick soles which could make the suspect appear taller than they actually are. Another factor could be the device which was used to measure the bullet hole. For example, lasers are more accurate than dowel rods and string.

Introduction

One bullet hole can help solve a crime! Determine the height of a suspect based upon the bullet trajectory.

Concepts

• Forensics
• Ballistics
• Bullet trajectory

Background

Case Background

Marty Higgins had just come back to her Riverland Terrace, SC, home from a late night grocery run. She had family coming to stay with her the next day and with her busy work schedule hadn’t found any other time to go the store. When she entered her house from the garage she heard strange noises coming from the back bedroom. She set the groceries down in the kitchen and called out “hello?”, thinking maybe someone from her family had arrived sooner than she planned. There was no answer and suddenly the noise stopped. Convinced she had heard something in the back bedroom she proceeded to open the door. She saw a person dressed in all black with a black ski mask quickly turn around. When Marty opened the door the intruder shot a bullet in Marty’s direction. After the shot was fired the intruder jumped out of the bedroom window of Marty’s ranch home. She immediately ran and called 9-1-1 from her bedroom phone. The police came and removed the section of drywall for bullet trajectory analysis. Ms. Higgins was advised this was most likely a random home burglary since the house looked like nobody was home and they had reports of other break-ins in the area over the past few weeks.

Technical Background

Bullet analysis or ballistics is an integral component of forensic science. Forensic scientists are able to use ballistics to determine many key components about a crime. For example, a bullet hole in a wall, ceiling, furniture, etc. allows scientists to determine what kind of gun was used, the distance the shooter was from the bullet hole as well as the height of the shooter. Often we think of bullet holes as round but this very rarely occurs. The only way for a bullet hole to be perfectly round is if the gun is held straight out from the shooter’s shoulders to the wall and shot into the wall at a 90° angle. Most of the time the gun is shot from an angle, no matter how small, producing an ellipse-shaped hole. Elliptical bullet holes allow investigators to calculate the location of the gun when the bullet was shot.

Basic geometry is required to determine impact angles, distance of the shooter and height of the shooter. Remember the acronym SOH-CAH-TOA. See the following for a review of each function.

Sin = opposite/hypotenuse
Cos = adjacent/hypotenuse
Tan = opposite/adjacent

In order to determine the location of the shot fired, the impact angle must be calculated. This can be done by inserting a dowel rod, which is the same diameter as the bullet hole into the bullet hole and measure the angle between the dowel rod and the surface. The problem with this method is that insertion of the dowel rod can destroy other forms of evidence useful in solving the crime. Investigators now often use lasers to determine the impact angle. However, there is a simpler and more cost effective means to do so—with trigonometry. As mentioned previously, the only way a round bullet hole will be produced is if the gun is directly against the target at a 90° angle, otherwise, the hole will be an ellipse. The ellipse in Figure 1 represents a bullet hole on the surface of the wall. The vertical line represents the major axis and the horizontal line represents the minor axis. The angle of impact can be determined using the sine function given the lengths of the major and minor axes. For example, if the minor axis is 13 mm long and the major axis is 19 mm long (see Figure 2), what is the angle of impact?

Sin (i) = length of minor axis/length of major axis
Sin (i) = 13/19
i = sin^–1(13/19)
i = 43.17° or 43° (to the nearest degree)

The impact angle provided from the above calculations is not the most accurate means of determining the location of the shooter compared to more modern laser methods. However, it is important to realize that the greater the difference between the major and minor axis the greater the accuracy of determining the bullet’s origination location. Therefore an ellipse with a minor axis of 19 mm and a major axis of 20 mm will not produce as accurate of an angle as an ellipse with an 11 mm minor axis and a 20 mm major axis.

Now that the impact angle has been calculated, the location of the shooter can be determined by using the properties of right triangles. The three interior angles of a triangle must always add up to 180°. One of the angles will be 90°, representing the angle between the floor and the wall. Therefore, if the second angle (the impact angle) is determined from the elliptical bullet hole left in the wall the third angle can be calculated. Using the impact angle calculation above, angle A is 43° and angle B is 90°, which is the angle between the wall and the floor. Since all three interior angles must add up to 180° the unknown angle can be calculated, 180 – 90 – 43 = 47°. Angle C is known as the angle of elevation or angle of depression. If the bullet hole is higher than the shooter’s shoulder it would be an angle of elevation, if it is lower it is known as an angle of depression. In this case, the bullet hole is in the wall at 93" above the floor. The height of the suspect is 6'3" (75") assuming the suspect’s head is 8" tall the shoulder height of the suspect would be 5'7" (67"). Since the bullet hole is above the shooter’s shoulder, the angle from the shooter would be considered an angle of elevation. With this information we can determine the distance the shooter was from the wall when the bullet was fired. The length of side a would be calculated by subtracting the height of the suspect’s shoulder from the height of the bullet: 93" – 67" = 26". The length of segment a is 26" and the angle of elevation is 43°. The tangent function can now be used to determine the length of b. Tan = opposite/adjacent (see Figure 4). See the following equation.

Tan (47) = 26/b
b = 26 / tan(47)
b = 24.25"

This information is clearly useful in that it can determine if it is possible for a given suspect to have been the shooter. For example if the distance of b had been calculated to be 102" and the room was only 8' wide, it is not possible for someone who is 6'3" to have been the shooter.

Experiment Overview

The police received an anonymous call from someone who said they heard shots being fired in an abandoned warehouse outside of town. They said it seemed like the shooters were conducting target practice. Police arrived and the shooters had left. However, there was evidence left behind. There were footprints in the dirty floor and bullet holes in the wall. Police found three different footprints and the crime scene has been reconstructed for each of the three suspects. Calculate the height of the suspects based upon the reconstruction of the crime scene.

Materials

Prelab Questions

1. Calculate the angle of elevation in the triangle below if the impact angle is 42°.
2. Determine the shoulder height of a shooter based on the sketch below. The bullet hole is 85" from the ground. The shooter’s footprints are 92" from the wall and the impact angle is 77°.
   {12493_PreLab_Figure_5}
3. Based on the information calculated in Question 2, what is the overall height of the shooter assuming the head is the height provided in the Background section?

Safety Precautions

This laboratory activity is considered nonhazardous. Please follow all laboratory safety guidelines.

Procedure

1. Measure the distance from the ground to the center of bullet hole 1, in inches. Record this value in the Bullet Height column of the worksheet.
2. Measure the length of the minor axis of bullet hole 1, in mm. Record this value in the Minor Axis column of the worksheet.
3. Measure the length of the major axis of bullet hole 1, in mm. Record this value in the Major Axis column of the worksheet.
4. Measure the distance from the wall to the tip of footprint 1, in inches. Record this value in the Footprint Distance column of the worksheet.
5. Draw a triangle sketch of each crime scene on the Flinn Forensic Files—Ballistics Worksheet and label each element as it is determined to help visualize the crime scene. Note: Based on tests with dowel rods and lasers done by the investigator’s bullets 1 and 2 are angles of elevation (above the shooter’s shoulders) and bullet 3 is an angle of depression (bullet hole below the shooter’s shoulders).
6. Repeat steps 1–5 with the bullet holes 2 and 3.

Student Worksheet PDF

12493_Student1.pdf