## 4 Discussion and Conclusions  
In this study, impact tests were conducted to identify glass damage patterns caused by slingshots and establish a comprehensive database. The experiments involved launching 8 and 10 mm steel balls at various velocities using a test setup simulating a slingshot, targeting 5 mm thick low-emissivity (low-e) glass. Subsequent analysis focused on the cone cracks and perforated holes generated in the glass upon impact. The damage limit velocities for 8 and 10 mm steel balls were determined to be 40 and 21 m/s, respectively. For the 8 mm steel ball, a probabilistic damage limit velocity range of 25-39 m/s was identified, with damage occurring at approximately 40% probability within this range. The 10 mm steel ball exhibited a probabilistic damage limit velocity range of 15-20 m/s, with damage occurring at approximately 22% probability. Analysis of damage patterns involved dividing the maximum and minimum diameters of cone cracks and perforated holes by kinetic energy. The relationship between \(CE_{avg}\) and kinetic energy revealed similar exponential functions for both 8 and 10 mm steel ball collisions. However, the relationship between \(PE_{avg}\) and kinetic energy demonstrated distinct exponential functions, with the 8 mm steel ball exhibiting a relatively larger exponent, resulting in a flatter curve. The study revealed significant differences in perforated hole damage patterns between 8 and 10 mm steel balls, while cone crack patterns showed minimal variation. The magnitude of damage caused by kinetic energy varied considerably, likely due to the brittle nature of glass. The distinct relationship between \(PE_{avg}\) and kinetic energy for different steel ball diameters suggests that impact velocity can be estimated based on perforated hole size measured at accident scenes. However, distinguishing between 8 and 10 mm steel balls remains challenging based solely on perforation or cone crack diameters within the simulated slingshot power range. The reason for the relatively consistent size of cone cracks is attributed to the interplay between the steel ball diameter and the glass plate's thickness and material properties. In all damaged specimens, cone cracks manifested at the rear of the impact point. According to scabbing theory, the rear face failure is induced by tension-controlled shear stress resulting from the impact force ([PERSON] and [PERSON] [13]; Society of Material Science of Japan [14]). Given constant glass thickness and material composition, the impact force required to initiate rear face damage--specifically, cone crack formation in this study--shows relatively low variation. It is hypothesized that a portion of the steel ball's kinetic energy is initially consumed in the scabbing process, with the surplus energy contributing to glass penetration. Figure 11: Relation of \(PE_{avg}\) and kinetic energy. As a result, it is considered that the size of the perforated hole exhibits a tendency to increase with rising impact velocity, while cone crack dimensions show relatively minimal variation. From a forensic science perspective, our experimental results can be utilized to narrow down the velocity range of projectiles. When investigating property damage caused by slingshots to identify suspects, determining the firing location is crucial for tracking the perpetrator. The majority of cases investigated by the National Forensic Service of Korea have involved 8 mm and 10 mm steel balls. If steel balls are retrieved from the crime scene, their diameter and the resulting fracture pattern can be used to estimate the collision velocity, which in turn helps identify the firing location. In cases where no steel balls are retrieved, collision velocities can be estimated based on the assumption of 8 mm and 10 mm steel balls being used. We believe that the findings of this study can significantly contribute to predicting firing locations based on these estimated velocities, thereby enhancing the efficacy of forensic investigations.