8- PHYSICS ON THE CASE

How Newtonian mechanics and fluid dynamics are transforming criminal investigations.

On average, there are 250,000 cases of gun-related deaths reported across the globe every year [1]. One of the challenges facing crime investigators is finding evidence to convict the perpetrators, and in the period 2018- 2019, 83% of crime in England and Wales was unsolved or encountered problems with evidence. A common technique used in firearm-related criminal investigations is Blood Pattern Analysis (BPA); this is the process of analysing blood spatters to gain an understanding of how the crime unfolded [2]. However, existing methods of BPA encounter criticism for their lack of scientific accuracy, and so inspectors are turning to physicists for help. 

In 1985 Joe Bryan, a high school principal from Texas, was convicted of murdering his wife. BPA was performed on Bryan’s torch and found substantial evidence that he was near to his wife at the time of her murder; whilst Bryan claimed to have an alibi and continues to maintain his innocence till this day. In 2018, 33 years after Bryan’s conviction, the BPA evidence used in Bryan’s case was found to be inaccurate and not scientifically supported. It is Bryan’s story, amongst others, which have been the root of speculation over BPA and its value in obtaining a just sentence in court.

Figure 1 - Diagram showing how the length and width of an elliptical bloodstain contain the information of the angle of impact of the original blood droplet [3].

At the time of Bryan’s trial, BPA was carried out by investigators with limited knowledge of the physical behaviour of the blood droplets. The technique involved analysing the elliptical bloodstains to estimate the angle of incidence of the blood droplet. The major axis (L in Figure 1) and the minor axis (W) of the stain would have been measured and related by elementary trigonometry to the angle of incidence (α) of the droplet [3].  After multiple strains were analysed, the different angles could be extrapolated to find the point where all the angles intersected. This intersection point was used to estimate the height of the origin of the blood source, illustrated in red dashed lines in Figure 2. The issue with this technique is its lack of scientific accuracy since the horizontal lines are unrealistic approximations for the path of the blood droplets. This is reflected by the considerable errors in the values of height produced which average at 40%.

 

Figure 2 - Diagram showing the inaccuracy of straight trajectories (red dashed lines) in comparison to trajectories accounting for gravity (blue dashed lines) and trajectories accounting for gravity and drag (solid black lines) [4].

In 2011 Fred Gittes and Christopher R Varney, from Washington University, decided to conduct further research into BPA methods to help improve its accuracy. They designed an experiment to test whether a model which incorporated the effects of gravity on the blood droplets could improve the results obtained by BPA. They spattered a fake blood sample with a machine which could send the fluid out at different heights and angles to create experimental stains [4]. They collected data on the width and length of the stains to determine the angle of impact (θI) and angle of projection (θ0).  They also measured the horizontal distance (rI) from the stain to the blood source so that an experimental value for the height of the origin (zo) could be obtained. The experimental variables are illustrated in Figure 3. 

Figure 3 -  Diagram defining the experimental variables in Gittes and Varney’s experiments [5].   

Gittes and Varney approximated the droplets to tiny, spherically symmetric, solid projectiles. To analyse their data they incorporated the equation of motion: z = zo ((v+vO)/2), where zo was the height of the fake blood source they wanted to determine. Since the final velocity of the blood was unknown, they manipulated the original equation to be dependent on the angle of impact (θI) and angle of projection (θ0) exclusively.  

Their experiments produced accurate results for the estimation of the height of the origin z, with an average error of 8% on these values. One of their best estimates calculated a height of (95.0 ± 2.2) cm for a launch angle of (−5.8 ± 2.4) o. This is a promising result since an error in the order of a few cms is almost insignificant in the context of confirming whether a victim was sitting or standing, for example, which could potentially allow for corroboration of a suspects’ recount [5]. 

In 2019, Alexander Yarin, Patrick Comiskey and Daniel Attinger, mechanical engineers and fluid dynamicists from University of Illinois and Iowa State modelled blood droplets to include fluid dynamics. They created a model which accounted for the interaction between the blood droplets and the air, which could act on a pre-existing data set to reconstruct the most probable trajectory of a given blood droplet. Their advanced, realistic model also removed the approximation of the blood droplets to symmetric solid spheres and considered in more detail the collision of the droplets with a surface. Despite providing a more detailed model, the statistical uncertainties associated with their experimental variables have limited the model to the same accuracy achieved by Gittes and Varney [6]. 

Whilst traditional methods of BPA are still widely used, the creation of tested, and scientifically supported models by experts has increasing relevance in the modern world. As Figure 2 emphasises, realistic models of the physical behaviour of blood droplets can drastically improve the accuracy of results obtained by BPA. Whilst there is still more work to be done, including improving the existing models and delivering training to professionals on their use, the gap between science and BPA is steadily being reduced. The hope is to see physics assisting our police and crime investigators, and providing more reliable evidence in criminal cases soon. 

References 

Inspired by ‘The Physics of Blood Spatter’, source 4. Cover image sourced on https://unsplash.com/. 

Further content sourced from: 

[1] https://www.bbc.co.uk/news/uk-49986849  - 

[2] https://pressbooks.bccampus.ca/criminalinvestigation/chapter/chapter-10-forensic-sciences/  

[3] Forensic Science International 206 (2011), pages 22–28, Ursula Buck, Beat Kneubuehl, Silvio Nather, Nicola Albertini, Lars Schmidt, Michael Thali.

[4] The Physics of Blood Spatter, Physics World, Volume 32, 10/08/19, pages 43- 46  

[5] https://news.wsu.edu/2011/05/24/physicists-improve-crime-investigation-method/ - 

[6] https://arxiv.org/pdf/1102.5134.pdf 

[7] https://pubmed.ncbi.nlm.nih.gov/30974388/