### Abstract:

Expert witnesses employ bloodstain pattern analysis (BPA), to provide objective analysis of bloodstain evidence in criminal cases. This thesis added to the scientific understanding of BPA by generating and analysing a large data set of 785 horse blood experiments. The experiments produced impact velocities, u0, of 2:89ms-1 to 6:54ms-1, with impact angles, [theta]f , 90°, 72°, 54°, 36°, and 18°. Different surface roughnesses were investigated: conditioned and unconditioned paper, smooth steel, and three roughened steel substrates with roughness values, Ra, 1:6x10-6 m, 3:2x10-6m, and 6:3x10-6 m. To analyse the data, two computational tools were developed. The first tool extracted the diameter and velocity of a droplet from high-speed videos. The second tool measured stain properties and counted spines of stains resulting from 90° and 72°.
The results of these experiments are investigated, extracting relationships between impact properties of droplets to stain properties. Each of the stain properties were related to some combination of a non-dimensional number (Bond number, Bo, Froude number, Fr, or Reynolds number, Re) and impact angle. It was found that the stain area and stain perimeter are proportional to Bo(sin[theta]f )-1. The numberof spines and/or tails on a stain is dependent on Fr(sin[theta]f )2. The major diameter is proportional to Re(sin[theta]f )2 and conversely the minor diameter is proportional to Re(sin[theta]f)2. The full length of the stain is proportional to Bo(sin[theta]f)-2. The results showed that increased surface roughness, promotes increased variability in the bloodstains, up to a limit of Ra = 6:3x10-6m. The roughest steel is statistically the same as paper in almost all stain properties.
The results proved a need to account for surface roughness in modelling the spreading of a droplet on a substrate. Starting from the laws of conservation of energy, a new model for predicting spread factor was derived which accounts for the impact angle and substrate roughness. This model uses a coefficient based on properties from the stain and is able to predict the experimental spread factors in this thesis more accurately than the spread factor models in literature. Two new equations were derived that calculate the impact velocity and droplet diameter using only stain properties, not experimental fitting constants, making the expressions more robust.