## Simulated blood stains

As one of the students said after the practical work “I’m really glad we are doing practical work in Maths – I could never see the point before”. The simulated blood stain experiment is used to test the theoretical relationship between the semi-major and semi-minor axes of an ellipse fitted to the blood stain and the angle of impact of the blood droplet with a surface. We use simulated blood consisting of a mixture of milk, treacle and a bit of food colouring to improve contrast.

The main part of the write-up is to analyse the quantitative errors on the various measurements of the width and length of the blood stain and the angle of the board that the paper surface was pinned to. The results for a range of angles are plotted as a scatter diagram and the results are quite close in the middle range (20 to 70 degrees) but the errors get serious at very high angles of impact (drop at near 90 degrees to paper – stains almost circular) and for very low angles of impact (drop at 10 degrees to paper – stains very streaky and running down surface). You very quickly realise that the errors in measurement are quite small for moderate angles – around 0.2 degrees if you measure the angle of the board using height and hypotenuse rather than fiddling with protractors.

Qualitative factors such as surface properties come to light. Students control for the height at which the blood drop was allowed to fall on the surface, and we use a range of surfaces (art paper, rough brown paper, I don’t use the paper towels any more as they absorb the mock-blood at different rates against or along the ‘grain’). The error from measurements used to find the W/L ratio for each ellipse is ‘amplified’ at large values of impact angle as a result of the steepening gradient of the sin-1(W/L) graph in that region – see the graph below. This introduces the idea of ‘rate of change’ nicely.

I have had a lot of mileage from this simple experiment (usually takes about 90 minutes to agree method and take results. The mock bloodstains need a few days to dry out enough to measure. I put them in A4 polypockets after a week – they can be scanned through the polypockets).