Blood left at a crime scene can tell you a lot about the events. To rewind the clock and look back in time, you just need a ruler and some trigonometry.

## You will need

- Red food dye
- Chocolate topping (or corn syrup)
- Water
- Measuring cup
- Mixing bowl
- Spoon
- Drinking straw
- Old clothes
- A large sheet of paper (5 x A4 sheets also works well)
- Ruler
- Scientific calculator
- Protractor

### Make fake blood

- Put on old clothes to avoid staining anything nice.
- Measure 3 parts chocolate sauce or corn syrup into a mixing bowl.
- Add 1 part water.
- Add a few drops of red food dye.
- Stir the mixture with a spoon.

### Create a crime

- Lay a large sheet of paper on the ground in a place which can get messy (such as outside).
- Alternatively, lay 5 sheets of A4 paper end to end on the ground to make a long strip.
- Dip the drinking straw into your fake blood mix, and place your thumb over the end to trap a few drops.
- Hold the straw over the paper and let a few drops fall straight down.
- Refill the straw.
- Swing your arm in an arc to cast a few drops down the length of the paper. It might take a few goes to get it right.

### Calling Detective Trig

- Look at the shapes of the different bloodstains. Some have tails, some are round.
- Find a stain towards the end of the paper.
- Measure its width and its length.
- Divide the width by the length.
- Use your scientific calculator to find the ‘sin-1’ of this number. This number should be the angle the droplet hit the paper.
- Look up the angle on your calculator on your protractor. Put the protractor on the drop – does the angle look right?
- Repeat steps 3-6 for another drop closer to your standing place.

## What’s happening?

As drops of liquid fall through the air, they form a shape that is a little like a slightly squished sphere.

Blood is no different, which means a drop that hits the ground from straight up will form a fairly neat circle.

If the blood is coming in from a distance, however, it could hit a surface at an angle. The drop’s inertia then forces it into a longer bloodstain, resulting in a round end and a pointy ‘tail’ that points away from the blood drop’s source. This gives detectives one useful hint about the events.

A second useful hint is the angle the drop hits the surface. A smaller angle would show it came from further away than a wider angle.

To find it, we imagine a blood drop moving down and across as it hits the paper. The length of the smear depends on the angle the drop travels, as well as the size of the blood drop.

A mathematical function called sine can be used to work out the size of the drop based on the length of the stain and the angle it travelled.

We can also estimate the size of the drop by measuring the width of the stain. Working backwards, the inverse of sine – which is sin-1 on your calculator – can be used with the length and width of the stain to give the angle.

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