We investigated the terminal ballistic properties of different bullet types in ballistic soap as surrogate to animal tissue. To comprehensively characterize a bullet, we performed shots at 4 different speeds, which we measured using light barriers. Our selection of the three lead-free bullets was meant to cover dimensionally stable, partially fragmenting and deforming lead-free bullet types, and the selection of a commonly used lead-based bullet was based on a previous study . We did not consider the ballistic coefficient of the bullets, the type and amount of powder, and the barrel length. All these affect the relationship between shooting distance and bullet speed upon impact. We neglected these aspects because of the high variety of possible combinations and because these combinations essentially reduce to a certain bullet having a certain speed upon impact and well-trained hunters are capable of estimating these numbers for their rifles.
Our analysis of the cavity volume shows that the relationship between deposited energy and cavity volume cannot be described by a simple linear function in general, as has been shown for hand guns and low energies . While for ILS and TAG, a linear fit adequately describes the relationship (Figs. 3, ,4),4), for TSX and NVU a quadratic fit is more appropriate (Figs. 5, ,6).6). There are two explanations for the differences between bullet types tested here. ILS and TAG require no or little energy for deformation because ILS does not deform at all and the deformation of TAG is supported by an aluminum tip. Therefore, less energy is lost for deformation which may be particularly relevant for low energies where ILS and TAG excel at their energy-to-volume conversion. The other reason could lie in the position and shape of the cavity. Since soap is generally incompressible, the soap masses have to get displaced towards the outside of the block, which is visible on the outer surfaces of the block (Fig. 1). Therefore, an initial amount of energy is consumed to accelerate the soap masses which may result an improved conversion rate at higher energies. The delayed expansion of TSX and NVU which results in an energy deposition deeper in the soap block may result in a decreased volume-to-energy ratio at low energies and an increased ratio at high energies. It was reasoned that the cavity volume is a measure for the stretching and tearing of tissue and therefore for the incurred wound damage . Since we show that the cavity volume cannot be predicted from the deposited energy in general, the cavity volume should be measured directly to assess the damaging potential instead of estimating it from the deposited energy. We will include this insight into an ongoing study  where we associate field reports with corresponding soap blocks to assess which features of the cavities correlate with observed effects, such as the flight distance.
The three-dimensional CT acquisition allows visualization of metal fragments and an assessment of their number and position. The lead-containing bullet creates hundreds of small lead fragments (Fig. 7) which remain near the cavity. In this homogeneous soap, the lead-free bullets create much less but sometimes larger fragments which tend to intrude deeper into the tissue surrogate. For the TSX bullet, we found more fragments than expected from a previous study . In that study the Barnes XLC, the predecessor of the Barnes TSX, was used. Furthermore, 2D radiography was used which may have limited sensitivity with respect to small fragments, especially in heterogeneous tissue. We may not be able to detect very small metal fragments or separate closely positioned ones due to the limited CT resolution. To assess the size distribution of the fragments more accurately, we consider imaging of soap pieces in special µCT devices .
Upon impact, a long range hunting bullet needs to expand from its aerodynamic shape into a shape with higher cross-sectional area. The three lead-free bullets rely on different means, i.e. tumbling, expansion based on an aluminum tip, and expansion based on a drilled hole. Consequently, the cavity shape varies between these bullet types resulting in different deviation angles (Fig. 10) and depths of maximum damage (Fig. 9). For hunters it is important that the cavity, i.e. the damage dealt, extends along the line of shooting. Otherwise the shot is not predictable and may result in unnecessary suffering of wounded animals escaping or in collateral damage of other animals in the near range. Still, the angle is around 6° for ILS which should be tolerable for most applications. Full metal jacket bullets, which are rarely used for hunting, are likely to create much higher deviation angles .
The high resolution CT allows non-destructive imaging of the soap block and generation of a detailed model of the cavity. In contrast to the cutting method and previous work using CT to image soap blocks , we performed a voxel-wise segmentation which is more accurate for cavity regions with non-circular cross-sections. Currently, the segmentation of the cavity is created interactively, i.e. the user has to provide some input. In most cases only the start and end of the cavity has to get provided since the other borders of the cavity are confined by the soap. While this only takes a few minutes it could be eliminated completely if an automated segmentation algorithm would be developed . While a strong correlation appears between the volumes determined by cutting and by CT (Fig. 11), there seems to be a systematic error leading to a consistent overestimation of the cutting-based volume compared to the CT-based volumes. Since CT is highly accurate for volume measurements , it is likely that this problem arises during the cutting procedure or the subsequent photographic measurement which involves a perspective transformation which may be difficult to calibrate. We did not assess the volume using water filling because this would have affected subsequent measurement steps by dissolving the soap. Nevertheless, such measurements would allow a better assessment of the accuracy of CT and cutting methods.
In this study we investigated 4 different bullet types at 4 impact speeds, leading to 16 different configurations. Due to differing bullet weights and ballistic coefficients, it is not appropriate to directly compare measurements, e.g. cavity volumes, between bullet types. Instead, we performed parametric curve fitting, e.g. cavity volume as a function of deposited energy, which allows comparison of the parameters between bullet types. While repetitions are not required for the used statistic methods, we repeated all shots under laboratory identical settings to increase the number of measurements. Furthermore, this allowed assessment of the reproducibility of ballistic soap experiments, e.g. by comparing the cavity volumes of first and second shots (Fig. 12). We found that the lead-containing NVU and the lead-free TSX bullets achieved a similarly high reproducibility, while reproducibility was lower for the lead-free ILS and TAG bullets, probably as a consequence of the tumbling behavior and the creation of large fragments, respectively.
The behavior of bullets in ballistic soap is not assumed to be equivalent to the behavior in real inhomogeneous tissue, particularly due to the presence of bones which are often hit when targeting at the heart. Soap has a similar density as muscle, blood and organs such as liver, heart, kidneys, and spleen, while lung tissue is around 60% less dense. Real tissue differs in terms of elasticity, with lung and muscle being considerably less vulnerable to deformation than liver and kidney tissue . Bone fragments and other heterogeneous tissue parts could get embedded into the soap block to generate more realistic structures. This would introduce more variability, however, and more repetitions would be required to robustly characterize the bullets. Furthermore, our results pertain to 7.62 mm ammunition, and extrapolation to other calibers, especially those with lower speeds or different bullet weights, may be inappropriate.
Our study shows that considerable differences exist between lead-free bullets with respect to the energy-to-volume conversion, the number of fragments, and the cavity shape. Interestingly, the lead-free TSX bullet is remarkably similar to the lead-containing NVU bullet in all parameters which we quantified, except for the number of fragments.
While our study mainly addresses questions regarding lead-free bullet development and selection for hunting, the knowledge of the behavior of different bullet types may also be useful for forensic investigations . Furthermore, the 3D rendering of the cavity may be useful to understand terminal ballistic effects and for educational purposes. Therefore, our methods should be useful to support hunters, wildlife managers, manufacturers, policy-makers and scientists in the ongoing transition towards lead-free hunting ammunition.