Prediction of blood back spatter from a gunshot in bloodstain pattern analysis

Abstract

A theoretical model for predicting and interpreting blood-spatter patterns resulting from a gunshot wound is proposed. The physical process generating a backward spatter of blood is linked to the Rayleigh-Taylor instability of blood accelerated toward the surrounding air, allowing the determination of the initial distribution of drop sizes and velocities. Then the motion of many drops in air is considered with governing equations accounting for gravity and air drag. Based on these equations, a numerical solution is obtained. It predicts the atomization process, the trajectories of the back-spatter drops of blood from the wound to the ground, the impact angle, and the impact Weber number on the ground, as well as the distribution and location of bloodstains and their shape and sizes. A parametric study is undertaken to predict patterns of backward blood spatter under realistic conditions corresponding to the experiments conducted in the present work. The results of the model are compared to the experimental data on back spatter generated by a gunshot impacting a blood-impregnated sponge. A theoretical model for predicting and interpreting blood-spatter patterns resulting from a gunshot wound is proposed. The physical process generating a backward spatter of blood is linked to the Rayleigh-Taylor instability of blood accelerated toward the surrounding air, allowing the determination of the initial distribution of drop sizes and velocities. Then the motion of many drops in air is considered with governing equations accounting for gravity and air drag. Based on these equations, a numerical solution is obtained. It predicts the atomization process, the trajectories of the back-spatter drops of blood from the wound to the ground, the impact angle, and the impact Weber number on the ground, as well as the distribution and location of bloodstains and their shape and sizes. A parametric study is undertaken to predict patterns of backward blood spatter under realistic conditions corresponding to the experiments conducted in the present work. The results of the model are compared to the experimental data on back spatter generated by a gunshot impacting a blood-impregnated sponge.

Hydrodynamics of back spatter by blunt bullet gunshot with a link to bloodstain pattern analysis

“…In a dense spray, like those in blood spatter, air entrainment is dominated by the fastest moving droplets "leading" the spray (the two-phase jet), whereas the other droplets are moving in the aerodynamic wake of the leading ones and experience either no aerodynamic drag, or a significantly diminished drag, as was previously shown for sprinkler jets and diesel sprays [7,8] and implemented in the predictions of backward spatter in [4]. The effect of the aerodynamic wake of the preceding droplets can be so severe that the trailing droplets can be even accelerated due to it, as it was recently shown in the analysis of high-speed video observations of backward spatter caused by gunshots [19].…”

“…These bins were considered as interpenetrating continua with air which was entrained into motion by viscous suction due to the eddy viscosity. Individual blood droplets from bin i experience air drag expressed using the drag coefficient correlation already used for the forensic applications in [2,4], namely, …”

“…In some situations, this assumption gives rise to large uncertainties [2,3] in the determination of the region of origin of a blood spatter, and of the relative positions of the persons involved, as in the famous trials of music producer Spector and physician Shepard [2]. Also, a sound physical theory describing the fluid mechanics of the blood pattern formation is not yet available to BPA practitioners [4]. Thus, a lot of the quantitative information from the crime scene such as the number of stains, their spatial distribution, and their area are left out of current crime scene reconstruction.…”

“…This information should not be neglected because it could help to differentiate between spatter types, for example, blood patterns produced in forward spatter and backward, or blunt-force versus shooting spatters [5]. It is therefore imperative to develop hydrodynamic models of blood spatter [2], as for example [4] where the formation of blood drops was attributed to the Rayleigh-Taylor instability. That instability necessarily occurs when denser blood is accelerated towards lighter air [6], which is the case when blood deforms following a bullet impact.…”

“…The recent theory of the back spatter of blood was developed specifically for slender bullets [4], e.g., full metal jacket bullets. Here we propose the fluid mechanical theory of blood back spatter from blunt bullets.…”