# Tandem bullets: case report and ballistic analysis – Egyptian Journal of Forensic Sciences

#### ByPierluigi Passalacqua, Margherita Pallocci, Lucilla De Luca, Claudia Zanovello, Giulio Sacchetti and Michele Treglia

Sep 22, 2022

Historically, the evenience of “tandem bullets” is determined by insufficient propulsion of the cartridges inside the barrel with retention of the same. The subsequent explosion of a second shot determines the impact on the held ball and the expulsion of both bullets from the barrel (Spitz 2006).

Although in most cases the phenomenon involves two bullets, there are cases in the literature of three bullets shot together (Simmons 1997) and others in which the projectile is ejected in tandem with foreign bodies (Mihailovic et al. 2007).

Crucial to understanding the analysis of cases of tandem bullets is the discovery of the weapon from which the shots are fired. The analysis of the compatibility between the caliber of the cartridge and the weapon is important, as stated by Ersoy et al. (2012), since a smaller cartridge allows gunpowder and deflagration gases to pass into the space between the bullet and the barrel, preventing it from being ejected.

Another relevant data in the ballistic analysis of the phenomenon is the firing distance, as it affects the penetration capacity of the bullet, as a result of the sudden drop in speed that occurs in such cases. In fact, assuming that the two bullets follow the linear moment principle, it is likely that an inelastic impact between the two bullets occurs inside the barrel, resulting in a speed at the exit of the barrel that can be calculated as:

$$V_t=frac{m_p}{m_p+m_c}cdot V_p$$

where Mp and Mc stand for the masses of the two projectiles, Vp for the speed of the tail bullet, and Vt for the total speed which, in our case, can be assimilated to the speed of impact with the subject’s body (equal to 130.196 m/s) because of the minimum distance at which the shot occurred. It is therefore likely to theorize that the increase in the mass of the exploded shot, resulting from the sum of the two fused bullets, almost halves the speed with which they exit from the barrel (Rabl et al. 1998; Kneubuehl 1994). It is then possible to calculate the penetrating capacity of the tandem bullets inside the skin, according to the Sellier formula, based on the speed limit (Vlim) for its penetration, which can also be calculated as follows:

$${V}_{mathrm{lim}}=125frac{G}{S}+22$$

where G stands for the total mass of the tandem bullets, S for the section of the same, expressed in cm2. From this, it can be deduced that the speed limit to penetrate the naked skin for the tandem bullets of our case would have been 61.75 m/s. Furthermore, the penetration of projectiles into the tissues of the body can always be defined according to the Sellier formula:

$$P=2,3frac{G}{S}ast ln frac{V_t-{V}_{mathrm{lim}}}{50}$$

In our case, the analysis of the tandem bullets showed a total mass of 20.525 g and a section of 64.535 cm2 from which, according to the formulas above, it is possible to obtain a penetrating capacity of the bullet of 3.19 mm, compatible with the reported injury in the emergency room.

The rarity of our case also lies in the unjacketing of the front bullet, which represents a unique occurrence, never reported in the literature. As it is known, the bullet jacket was introduced following the Hague Conferences of 1899 and 1907 in order to regulate war conflicts. In fact, the use of easily deformable bullets inside the human body was prohibited, as they were characterized by an easier tendency to fragmentation and therefore capable of causing greater damage to the internal tissues. In addition, full metal jacket bullets, compared with bare lead bullets, have a greater range, better shelf life, and resistance to deformation. These characteristics make them suitable for use in automatic weapons (such as submachine guns), while at the same time, they preserve the weapon from possible jams and leave no trace of lead deposits on the barrel rifling, which would progressively deteriorate the accuracy of the weapon itself.

For the tandem bullets found in our case, the partial unjacketing of the first bullet did not allow the lead core to deform or fragment, also because of the low injury potential given by the large mass of the two bullets fused together. However, we believe that in the case of smaller caliber bullets, with a resulting mass lower than one reported by us, a complete unjacketing of the anterior bullet could cause greater damage than the ones described in the literature by “tandem bullets.”