Here’s an interesting problem. Imagine a crime scene in which blood has spattered across a floor. Is it possible to use the spatter pattern to determine the position of the source in three dimensions?

This may come as a surprise to anybody who has watched CSI: Crime Scene Investigates but according to conventional forensic analysis, the answer is no. And a quick look at the diagram above shows why.

Any droplet that hits the ground at an angle leaves an elliptical mark. It’s straightforward to measure the shape of these ellipses and then extrapolate along their semimajor axes to see where they cross. This gives you the location of the vertical axis of the source.

But try determining the height of the source and you’ll soon run into trouble. The eccentricity of the ellipse tells the angle of impact but trace this back to the vertical axis and you’ll find that there can usually be more than one possible source height.

Forensic scientists have always had to rely on other clues to help them work out what the true height must have been.

Now Christopher Varney and Fred Gittes at Washington State University have found a way to solve this problem using elementary trigonometry. First, they derived a simple expression that links the launch height and angle of the droplet with its horizontal flight distance and angle of impact.

They then realised that although the launch height of a single droplet cannot be uniquely determined, it ought to be possible with data from many droplets released with the same launch angle and height but different velocities. In that case plotting a certain relationship between the angle of impacts and horizontal flight distances of all the droplets should produce a straight line.

But here’s the clever part. The technique only works if the droplets all have the same launch angle. If they have different launch angles it fails. But in this case, the plot produces a scatter rather than a straight line and so can be picked out as a null result rather than giving an erroneous measure of height.

That’s important in forensics. A “fail safe” technique is crucial for evidence that can be used to obtain a conviction.

Varney and Gittes have even tested the method using a “clapper” mechanism to spread droplets of “blood” across their lab. (In fact, their blood was 2-3 parts Ashanti Chicken Wing Sauce with 1 part Ivory Dish Soap to aid clean up and a dash of food colouring.)

There’s another application. Varney and Gittes are currently using the technique to estimate the height from which spattered lava must have spewed from ancient volcanoes, which will give an idea of the size of the volcano at that time. Clever!

Ref: arxiv.org/abs/1102.5134: Locating The Source Of Projectile Fluid Droplets