Equation: Blood Spatter a Math Matter

The forensics of blood spatters: A new formula using high school trig and introductory physics helps investigators determine whether a victim took a blow standing up.
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A new formula helps CSIs determine whether a victim took a blow standing up.
Photo: by Jonathon Kambouris

Dexter makes deciphering blood spatter look so easy. But the fact is, while crime scene investigators have always been able to determine the direction spatter comes from, they've never been as good with the height—often key for figuring out how a victim was positioned during the attack. The problem is, blood arcs in a parabola, and different parabolic paths from varied heights can end at the same angle. Math to the rescue! A new equation uses simple high school trigonometry and introductory physics to reverse-calculate height by finding an elevation consistent with two blood drops. If enough of the pairs of drops approximately agree (indicating that they flew off the victim at a similar angle), then the investigator can say definitively how high the blood was when it exited the body—which could prove a person's position when struck. Cue music over a montage of sexy forensic investigators ... solving this math problem.

1// Height of the blood at the beginning of its parabolic arc, that is, when it left the body.

2// Tangent of the angle at which the first blood drop hit the ground.

3// Tangent of the angle at which the second drop hit the ground.

4// Horizontal distance the first drop traveled.

5// Horizontal distance the second drop traveled.

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