A search on WIRED's webpage for a link to the article was not successful so I am copying here the essentials of the write-up:
"... while crime scene investigators have always been able to determine the direction spatter comes from, the've never been as good with the height—often key for figuring out how a victim was positioned during an attack. The problem is, blood arcs in a parabola, and different parabolic paths from varied heights can end at the same angle. ... 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 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 would prove a person's position when struck."The equation is given with a list of the variables and their meanings:
Z0 = (τ1 – τ2)·r1 r2 /(2r2 – 2r1)
Z0 height of the blood at the beginning of its parabolic arc, that is, when it left the body
τ1 tangent of the angle at which a particular blood drop hit the ground
τ2 tangent of the angle at which another blood drop hit the ground
r1 horizontal distance the first drop traveled
r2 horizontal distance the other drop traveled
That looked intriguing but also much too simple to account for trajectories described by quadratic equations. Also, how is the angle determined at which a blood drop hits the ground? And secondly, what exactly is meant by the requirement that "enough of the pairs of drops agree"?
The analysis presented here will shed light on the whole procedure and give the conditions for which the equation above can be used.
A) Blood Spot Shapes
B) Drop Trajectories
C) Drop Travel Distance
D) Approximations
E) Use of Equation
