Using Geometry to Become a CSI
8:40 am- A call comes in to 911 from a concerned citizen. There were some strange noises coming from next door about 11:30 pm last night. She was too afraid to go out and check on the noise late last night, but she is worried so she called it in this morning. You are a first year CSI and you are assigned to go with the police to check out the house. When you enter you find that several areas in the living room have blood spattered on the floor. There is a remote control next to a chair, but no television and the drawers in the desk are not fully shut. It is your job to find out as much as you can about the incident that caused the blood stains.
Part 1: Determine the type of weapon that caused the splatter.
As a drop of blood flies through the air, the surface tension pulls the drop into a spherical shape. When the blood strikes the surface, the angle at which it hits determines the shape of the stain. The drop will have a smooth front edge and the side farthest from the source will have ragged edges called spines. In some impacts the force is sufficient to overcome the surface tension and it allows satellite spatters to break off from the parent.
To identify the type of weapon used, you need to measure the width of the parent blood drops. The drops generally have the shape of an ellipse with the width of the drop being the minor axis of the ellipse.
width
A relationship has been found between the velocity of the weapon and the width of the drops. Use the blood stain pattern that you found to determine the most common width. Record your results in the table below.
Width of the drop / Number of drops / Proportion(# of drops/total drops measured) / Percent of Total Blood Spatter
0.1 mm – 1 mm
1 mm – 1cm
Over 1cm
Total drops
Experts agree that low impact velocity generally produce stains that are at least 1 cm in size, medium impact velocity weapons produce drops that are 1mm to 1cm in size, and high impact velocity weapons produce drops that are 0.1 to 1 mm in size.
Examples of each velocity range are:
Low velocity is the result of blood dripping from a wound
Medium velocity is the result of swinging fists, clubs, knives, etc
High velocity is the result of gunshots, explosions, etc.
According to this information, what category of weapon caused the wound that you are examining? Explain your reasoning.
What are some possible weapons that would fit into this category?
Write a brief explanation of what you think occurred in the living room.
Part 2 Determine how the wound was caused
Now that you know what caused the blood splatter, you will continue to investigate to find out how it happened. The victim was admitted to the local hospital where a member of your team measured and found out that the wound is exactly 5 ft from the ground. Use what you know about trigonometry to find out how far away the victim was from the blood stains you found.
Using the width and the length of the blood spatter, we can determine the angle of elevation of where the victim was hit.
Sin (angle of elevation) =
Measure the width and length of 4 blood drops from the category with the highest frequency and use the equation above to find the angle of elevation of each.
Blood Spot # / Width (mm) / Length (mm) / Angle of Elevation1
2
3
4
Show work for angle of elevation here:
Drop 1 / Drop 2 / Drop 3 / Drop 4What is the average angle of elevation for these 4 drops? ______
Using the information that you are given and the fact that the wound is at 5 feet from the ground, calculate how far the victim was from the blood when the incident occurred Hint: Draw a triangle to help you.
Distance from spatter ______
Using the information you have calculated, determine where you think the victim was when the injury occurred that caused your group’s blood spatter. Mark their location with an X.
Scale 1cm = 1 foot
Now that you have more information, write a detailed explanation of what you think occurred in the living room.