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

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.

Figure 1

(a) Reconstruction of the trajectories associated with four bloodstains using straight trajectories versus ballistic trajectories and the geometry (locations of the stains, of the victim, and the impact angles). Panel (a) is reproduced from teaching material graciously provided by H. McDonell. Drop size is assumed to be 3 mm, implying velocities in the 5.3–7.5 m/s range. (b) Definition of the angle of drop impact α and directional (sideways) angle γ, which is equal to the angle between the vertical plane containing the drop trajectory and another vertical plane containing the bullet trajectory and the target.

Figure 2

(a) Geometry of a 0.40 caliber hollow-point bullet. (b) Sketch of the experimental setup with the horizontal paper substrate used to collect back-spatter blood drops. The $Y$ axis directed into the figure and the coordinate trihedron XYZ is located on the floor under the center of the sponge target, approximately at the location of the bullet impact.

Figure 3

(a) Origin of trajectory families of blood drops in back spatter. Only two trajectory families corresponding to $\mathrm{\Phi }=\pi /2$ (the uppermost trajectory family) and $\mathrm{\Phi }=3\pi /2$ (the lowermost trajectory family) are shown. (b) Normal cross section of the conical tip with the azimuthal angle Φ.

Figure 4

Strips used for the processing of the experimental data. The strips were chosen to minimize uncertainty by being as small as possible, yet not too small to become meaningless. It was found that 5-cm strips (in the $X$ direction) are the optimal size.

Figure 5

(a) Experimental bloodstains in back spatter formed on a vertical paper sheet. (b) Horizontal paper sheet. Note that the elongated shape of some stains in (a) is mostly due to the angle of impact, rather than due to the drop sliding down the surface after impact.

Figure 6

Numerical predictions versus experimental data set H-a0-D300 corresponding to the bullet impact angle $\delta =0^{\circ }$. The light blue squares represent experimental trial H-a0-D300-#1, orange triangles represent experimental trial H-a0-D300-#2, and red circles depict the numerical results. The dark blue diamonds represent the average of the two trials.

Figure 7

Numerical predictions versus experimental data set H-a60-D150 corresponding to the bullet impact angle $\delta ={60}^{\circ }$. The light blue squares represent experimental trial H-a60-D150-#1, orange triangles represent experimental trial H-a60-D150-#2, and red circles depict the numerical results. The dark blue diamonds represent the average of the two trials.

Figure 8

Cumulative percentage for the number of stains and cumulative percentage for the impact angle. (a) and (c) Comparison of the predictions with the data sets H-a0-D300-#1 and H-a0-D300-#2. (b) and (d) Comparison of the predictions with the data sets H-a60-D150-#1 and H-a60-D150-#2. The colored symbols have the same meaning as in Figs. 6 and 7, i.e., the blue squares are for trial 1, orange triangles are for trial 2, and large red circles are for the theoretical predictions.

Figure 9

Predicted impact Weber number for (a) H-a0-D300 and (b) H-a60-D150.

Figure 10

Top views of predicted drop locations on the floor. (a) Predictions for the case H-a0-D300. (b) Predictions for the case H-a60-D150. The projection of the bullet path on the floor corresponds to $Y=0$. The colored symbols have the same meaning as in Figs. 6, 7, 8, 9, i.e., the blue squares are for trial 1, orange triangles are for trial 2, and large red circles are for the theoretical predictions.