Validation of the lead‐in method in a practical shooting scenario

The ability to determine bullet trajectories after a shooting incident can allow investigators to reconstruct the locations of individuals and the sequence of events that took place. By using trajectory rods, investigators can be provided with an immediate visual estimate as to what the path of the projectile may have been. In certain instances, the use of the probing method with trajectory rods is not appropriate due to their being a single, thin target material, or no secondary bullet impact site. In these cases, other methods such as the lead‐in or the ellipse method may be useful. Overall, the lead‐in method has not been well studied in the application to practical scenarios, such as those including bullet impacts on vehicle metal surfaces. This study has explored the accuracy of the lead‐in method when a bullet impacts a typical vehicle metal surface using three firearm calibers, three blind participants, and two non‐blind participants. The results of this study have shown that each caliber has its own characteristic error curve. In general, it was found that the lower the impact angle, the less errors were made by the participants. As the impact angle increases, the measurement errors increased, due to the smaller lead‐in area present. The errors were found to have a wide range, with some being as low as 1° and some being as high as 13.9°. Further, it was found there was no significant effect on the errors of blind versus non‐blind participants.


| INTRODUC TI ON
The determination and documentation of bullet trajectories after a shooting incident is crucial as it can allow for a more comprehensive understanding of the nature of events that had occurred and can allow for the reconstruction of the sequence of said events [1,2].This type of analysis provides key information to investigators that can be valuable in the course of an investigation [1,2].This key information can include the path the bullet took, or its trajectory [2,3].When estimating a bullet trajectory, it is broken down into two angles: the vertical angle and the horizontal angle (i.e., azimuth angle) [1,[3][4][5].The vertical angle describes the ascending/descending angle of the bullet when impacting the target material [1,3].It is usually measured relative to gravity [3] but may use another frame of reference.A downward direction of travel is given a negative sign (−), while an upward direction of travel is given a positive sign (+) [3].
The azimuth angle is the compass direction (i.e., North, South, East, and West) of the bullet direction [1][2][3].The azimuth angle is often measured to a reference object, such as a wall, and does not always use the true "north" heading.Different conventions may use angles between ±90°, 0°-180°, or 0°-360°.In all such cases, it is imperative to specify the convention used and the chosen reference direction Figure 1.
The substrate material which a bullet impacts can affect how a bullet defect will look, and thus, the information that can be gained from the defect.When impacting a yielding material, such as sheet metal, the appearance of the damaged location is affected by a multitude of factors, such as the material properties of the bullet itself, the bullet's geometry, substrate properties, and the angle of impact [6].Since vehicles are frequently involved in shooting incidents, it is important to understand how a bullet impacts vehicle sheet metal, and how to interpret information regarding trajectory measurements.One important factor that affects trajectory measurements in sheet metal is the impact angle of the bullet.The impact angle can be defined as the relative angle between the impacted surface, and the trajectory where a bullet strikes that surface.[6].As the bullet's impact angle changes relative to the target surface, the appearance of the bullet defect will change as well [6].When a stable bullet impacts a target surface at 90° (i.e., perpendicular to the target surface), the shape of the bullet hole will appear circular.[7].Generally, angles of incidence from 70° to 90° will appear closer to circular in nature and look very similar to each other [7].As the impact angle decreases from 70°, the shape of the bullet defect becomes more elliptical [4,6].In extreme low angles of incidence, ricocheting can occur [8].Ricocheting is the continued flight of a rebounded projectile and/or major projectile fragments after a low angle impact with a surface or object [8].An elongated ellipse will form at the initial "entry" side of the damaged area, but no perforation will occur [6].
An important characteristic of a bullet defect is the lead-in mark.
A lead-in mark is defined as a thin streak on a bullet defect that is created from the initial contact, or wipe, of a bullet on the target material and is generally found at lower impact angles [8].On sheet metal, the lead-in mark appears at the beginning of the elliptical defect where the bullet first makes contact [6].This can help identify directionality of the bullet path [8].The end of the lead-in area, termed the "lead-in termination," is the edge where the bullet perforates the material [6].The terminology for penetrating bullet holes was defined by Liscio and Park [2021] and is similar to Figure 2 below [6].
When a bullet ricochets off sheet metal, it does not always perforate the metal, therefore, there is no lead-in termination edge present [1].Since there is no perforation, it is difficult to determine the end of the lead-in area [1,3,4,6].Further, there is no defined terms in the literature that can help identify the lead-in mark in these instances [1,3,4,6].In a previous study conducted by Liscio and Park [2021], a transition point was introduced to help define ricochet lead-in areas.From the initial point of impact, the lead in area becomes shallower and wider as the bullet deforms and deflects off the metal surface [6].The transition point was introduced and defined as a point where the angle of the lead-in area changes by more than 0.5° [6].With this, the boundary of a lead-in area can be identified [6].The transition point is shown below in Figure 3   Correctly determining the position of the lead-in mark on a metal surface will influence the accuracy of the direction it originated from [4].Correctly determining the depth of the lead-in mark is used to estimate the impact angle (i.e., angle of incidence) [4].When manually performing a lead-in method measurement, a trajectory rod is aligned against a lead-in mark [4].Once the trajectory rod is properly aligned, with a stable setup, the angle of incidence can be measured via various types of instruments such as protractors, inclinometers, plum blobs, or lasers [4,6].The impact angle of the bullet is defined as the total angle from the surface of the plane to the trajectory rod [4].Liscio and Park [2021] defined a set of criteria for utilizing the manual method for primary impact lead-in areas.In addition to the 0.5° transition point for ricochet marks, the authors defined a minimum of a 3 mm length lead-in area [6].Areas smaller than 3 mm do not provide a stable and reliable positioning of the trajectory rod, resulting in greater variation in errors [6].It was also suggested by Mattijssen et al. [2016] that only the first few millimeter of the lead-in mark should be used, as there are possible secondary effects which may be present after the first part [4].Possible secondary effects include deformation, deflection, and structure disruption of the target material [4].Liscio and Park [2021] investigated the accuracy of the manual lead-in method on sheet metal [6].The results of this study found there were characteristic patterns of error across a wide range of impact angles, calibers, and ammunition brands [6].Each combination of caliber and ammunition brand had its own characteristic error curve that appeared to change with the known impact angle [6].
In general, the error increased as the impact angle became more perpendicular to the surface [6].This is because lead-in areas are smaller at larger angles of impact.For the majority of ammunition and impact angle combinations, the errors observed were negative, which indicates the tendency to underestimate the angle of incidence [6].However, for one caliber, the errors observed were positive, indicating a tendency to overestimate the angle of incidence for this caliber [6].These systematic errors and biases of measurement are useful to know when performing a shooting reconstruction.This can lead to the development of correction factors to compensate for these repeatable errors.
In the literature, there has been two other methods that have been described in order to estimate a bullet trajectory.The first method described in the literature is the ellipse method.The ellipse method involves aligning and fitting a manual (physical measurement) or virtual (digital measurement) ellipse on the surface of a bullet impact in order to estimate the impact angle.It is based on trigonometric relationships.In a study conducted by Liscio and Imran [2020], this method was used to determine impact angles of bullet defects on painted sheet metal made by different brands of 9 mm ammunition [9].The results of this study showed there is a characteristic pattern of error across a wide range of known impact angles for the various types of ammunition [9].In general, the smallest amount of error was found at the smallest and largest impact angles [9].The ellipse method may be used for single bullet impacts, like those for the proposed study at hand, however, due to the large F I G U R E 2 Nomenclature of a perforating bullet impact in sheet metal.
error associated with impacts, applicability of this method is limited [9].Therefore, the lead-in method may be better suited for this type of analysis under certain circumstances [9].
The second method is the probing method.The probing method consists of inserting a trajectory rod through two consecutive bullet impacts, creating a visible and defining path between them [3,4,6].This mimics the flight path of the bullet over short distances [3,4,6].Mattijssen et al. [2016] found the probe method to be the most accurate method overall [4].However, at lower incident angles, it was found the lead-in method provides more accurate results [4].
The probe method relies on the spatial relationship between two bullet holes [4].With a high degree of bullet deflection in the secondary impact, the true trajectory of the bullet is not being measured, rather, the deflection path is [4].Since the lead-in method uses features that result from the primary contact of the bullet with the target material, no deflection influence is expected [4].The target material also plays a role in the accuracy of the method.Lead-in areas are most easily identified in yielding materials, such as sheet metals, in angles that are between the critical angle (where ricocheting occurs) to roughly 70° [4].Contrasting this, brittle materials such as drywall or glass, tend to create craters rather than lead-in marks.
Therefore, the probing method is better suited in these situations [4,6].In vehicle shootings, it is very common to see single bullet impacts, where the bullet does not perforate a second surface, or the secondary impact location is not useful.The lead-in method may be a good option for this situation [6].
An example of a high profile case where the lead-in scenario was employed was US v Astarita where between the prosecution and defense, 11 experts testified about the use of the method on a single point bullet perforation through car metal [10].
Overall, there is limited literature on the lead-in method, especially as used in practice.The results from previous research demonstrate the appearance of identifiable patterns or characteristic error for various combinations of target material, caliber, and ammunition brands [8,9,11].This study aims to develop and define a procedure for the manual lead-in method in a practical scenario, provide a sense of its accuracy for various calibers of ammunition, relate the results to past studies, and identify the associated limitations.

| ME THODOLOGY
In this study, three different caliber handguns were used, with one type of ammunition for each (Table 1).Each handgun was fired repeatedly, 10 times at 10 known angles, not exceeding roughly 65°.
Angles above 70° were not attempted in this study, as it was found by Liscio and Park [2021] that bullet impacts above this angle do not provide accurate and reliable lead-in areas [6].In total, there were TA B L E 1 Summary of firearms and ammunition used in this study.10 sample shots for each caliber, totaling 30 shots for the study.The handguns were fired at a 2002 Honda Civic vehicle.

| The vehicle
The make and model of the car used in this study was a 2002 Honda Civic, which can be seen in Figure S1, with an approximate metal body thickness of 0.85 mm.Ten shots from each caliber were fired at either the driver side or passenger side of the vehicle at 10 different angles.The muzzle of the handgun was placed between 2 and 4 m away from the vehicle.The distance from the muzzle to the target vehicle varied depending on the angle of incidence; however, the distance remained less than 4 m so that there was a negligible effect of parabolic bullet trajectories, which can occur over larger distances [4].Before firing, the vehicle was prepped by wiping the surface with Windex© and paper towel to remove any dirt and debris from the surface.

| Initial setup
A Colt Official Police, 0.22 Long Rifle caliber revolver handgun was placed into a Ransom Rest (gun mount) with appropriate rubber grips so that it was securely held.The Ransom Rest provided a stable and repeatable setup for each handgun to be fired from.After several test fires, the gun was verified to be stable in the grips so that negligible movement was detected.The distance from the muzzle to the vehicle side was checked with a Bosch GLM 40 Laser Measure, with a manufacturer stated accuracy of ±1.5 mm.
In order to determine the ground truth of the impact angles, the handgun in the Ransom Rest was laser scanned using a Faro Focus S350+ terrestrial laser scanner.To measure the trajectory of the shot, a 3D-printed plastic adapter with a trajectory rod attached was inserted into the barrel of the gun (Figure S2).Attached to the trajectory rod were two trajectory spheres.Since the center of each sphere is concentric with the central axis of the trajectory rod, this helps to identify the center of the bore of the gun in the Faro Zone 3D software [2].The entire scene, including the vehicle and the gun with the trajectory rod and trajectory spheres, was then scanned using the Faro Focus S350+ terrestrial laser scanner with 1/5 resolution and 3X quality settings which results in a point spacing of 7.7 mm at 10 m.Higher quality settings provide more accurate data but take more time to scan.The 3X setting provided sufficient quality for this examination and mimics setting often used in forensic casework.The set up of the car, Ransom Rest, and Faro Focus S350+ terrestrial laser scanner can be seen in Figure 4.
Once laser scanning of the firearm position was completed, the handgun was then loaded using a 0.22 Long Rifle caliber rimfire cartridge with a weight of 38 grains, produced by Federal.Each bullet was taken from the same ammunition package.This was done to ensure the consistency of the grain weight of the gunpowder and therefore velocity should be consistent with each fired shot.After being loaded, the distance from the muzzle of the handgun to the car was measured using the digital laser measure and the result was recorded.The shot was then fired.
In between each shot, the impact site was labeled on the vehicle in permanent marker with the sample shot number (i.e., T1S1, T1S2, etc.).Each time the Ransom Rest was moved to a new firing position, the azimuth and vertical angles were changed with enough clearance between impact sites to ensure the newly fired shot would not have any significant influence on the adjacent bullet defect.Once the 10 shots were fired from one caliber, the Ransom Rest was prepared for the next caliber handgun.An example of an impact from each caliber can be seen in Figures S4-S6.
In this study, the impact angle is the angle between bullet's path direction to the target surface (the immediate surface around the bullet impact site).Specific reference markers were placed in multiple locations on the vehicle so that participants could measure from a reproducible position on the car body when using the FARO Zone 3D software.The reference markers can be seen highlighted in Figure S3.This reference plane was also used for the ground truth values and thus, should limit the influence of participants using very different reference planes.Also, the inclination angle was held between 88° and 91° for safety reasons, and thus, the azimuth angle had the greatest contribution to the overall impact angle since all fired shots did not deviate much in the vertical angle.
Following criterion outlined in Liscio and Park [2021], impact sites were eliminated from the sample if there was no lead-in area for the bullet defect or the lead-in area was less than 3 mm [6].This criterion was followed as the lead-in method can only be used when there is a sufficient lead-in area.If an impact site was determined to not have a sufficient lead-in area, the Ransom Rest was moved to a slightly different angle and a new shot was fired.

| The lead-in method
For measuring the trajectory of the impact, specially designed trajectory rod adapters were used to mount standard trajectory rods to the vehicle.Quarter inch trajectory rods were held in place by a flex arm, with a specially designed 3D-printed adapter that was attached to either a magnet or a suction cup, in order to secure it to the vehicle.On the trajectory rod, there were 55 mm trajectory spheres Figure 5.
The proposed lead-in procedure that was outlined in Liscio and Park [2021] were followed for this experiment, with minor changes to the methodology [6].

| Proposed lead-in method
1. Inspect the damaged location and determine if an obvious lead-in area exists.If not, the lead-in method is not suitable to be used for analysis.An appropriate lead-in area is normally found at angles lower than approximately 60°.
2. If the lead-in area is suitable for analysis, attach the suction cup or magnet to the vehicle adjacent to the impact damage, and place the trajectory rod on the lead-in area and apply light pressure with fingers to secure the trajectory rod in place.
3. The trajectory rod must be aligned parallel to the bullet's path of travel.This should be checked for "play" using a "side to side" motion of the rod relative to the lead-in area.
4. The trajectory rod resting position on the lead-in area is often subjective and should be checked by moving the rod toward and away from the surface of the panel.This is often useful in finding and limiting the range of possible resting positions of the trajectory rod.Once the trajectory rod is properly aligned, tighten the arm of the suction cup to ensure the trajectory rod stays in place.
A piece of tape may be used to hold the trajectory rod in place to prevent any movement or "sagging" from the trajectory rod.

5.
Once the trajectory rod is secured, it will be scanned using the Faro Focus S350+ terrestrial laser.This resulting scan will allow for the vertical and azimuth angles to be determined in the Faro Zone 3D Software.
The method being applied by a participant can be seen in Figure S7.Measurements were taken by three blind participants and two non-blind participants.All five participants did not know the exact ground truth of the incidence angles since these were laser scanned and only known after processing.However, since two researchers were present during the firing of the shots, they are considered as non-blind participants.Prior to measuring the angles, participants were instructed on how to use the manual lead-in method with the flex arm and suction cup/magnet.Five flex arms were available for testing; thus, each participant would establish five bullet paths and that set was scanned using the FARO Focus S350+ laser scanner.Once the scan was acquired, the five flex arms were taken off and reused for the next five impact locations.This process was repeated until all 30 impact sites were laser scanned for each participant Figure 6.
For perforated sites, the trajectory rod could be inserted deeper into the impact site while still holding the trajectory rod stable for an accurate measurement.For ricochet marks without a lead-in termination to indicate the end of the lead-in area, the The Ransom Rest with the Colt Official Police 0.22 long rifle revolver secured in place with the trajectory rod and spheres secured.The Faro Focus S350+ Laser Scanner is attached to a tripod to scan the scene.

F I G U R E 5
A close-up the flex arm of the trajectory rod attached to the car with a suction cup and trajectory spheres on the trajectory rods.

F I G U R E 6
A closer view of the trajectory rods attached to the car.
participant was instructed to identify a transition point, which is prior to the bend of the impact mark.Previous studies have shown that the transition point may be identified with as little as a 0.5° change from the starting position [6].The transition point can be identified by resting the trajectory rod on the forward portion of the lead-in area.As the tip of the rod is moved further into the transition zone, a small gap will appear between the rod and the bullet impact site.It is important to ensure there is maximum contact between the trajectory rod and the surface of the lead-in area.This is because the measured angle can provide a better estimate of the true slope of the lead-in area [6].

| RE SULTS
A total of five participants were instructed on how to perform the manual lead-in method and were then asked to setup and align a trajectory rod on each of 30 impact sites.One non-blind participant could not complete measurements for the 0.45 caliber due to time constraints.The measured impact angles were then compared to the known impact angles to determine the error across all measurements taken for the blind participants.The actual errors and absolute errors of the azimuth angles were graphed based on the ammunition caliber.This allows visualization of the general trends of the errors.The actual errors can be defined as values that were positive or negative, thus indicating the direction of error (i.e., overestimation vs underestimation).The absolute values can be defined as the overall magnitude of error.The blind participant errors versus the non-blind participant errors were then graphed together and a polynomial trend-line was added.The ground truth data of the 10 shots from each caliber can be found in Table S1.

| DISCUSS ION
The azimuth angles demonstrate a general definable trend where at smaller impact angles, the errors were closer to the ground truth.For all ammunition calibers used in this study, the errors were generally underestimated.As the azimuth angle of impact increases (i.e., near 50° and 60°), the errors show greater variability.This was also found by Liscio and Park [6].This is due to the smaller lead-in area that is present on impacts with higher angles of incidence.The smaller lead-in area provides less stability for the trajectory rod to be placed, therefore, leading to higher errors.
For the 0.22 LR caliber results, shown in Figures 7 and 8, the azimuth angle demonstrated a spread of errors that is minimal in smaller angles and gradually increases as the azimuth angle increases.The smallest deviation in the true value was in the range of 20° to 35°, as shown in Figure 8.There were four angles within this range; 20.8°, 25.0°, 25.3°, and 33.4°.The absolute average error measurement for these angles, respectively, were as follows 3.4°, 0.3°, 1.8°, and 2.0°.
In contrast, the largest error was observed between 56° and 58°, with an absolute average error measurement of 11.3° and 13.9°.
For the 9 mm Luger caliber results, shown in Figures 10 and 11, the spread of the errors show there is minimal error when the incident angle was at 6.0°, with an average absolute measurement error of 0.7°.As the angle of impact climbed over 15°, the margin of error also increased.The largest deviation from the true measurement was upward from 40°.There were three recorded angles above 40°; This study has identified errors that appear to correlate with varying impact angles, calibers, and bullet design.Following in line with previous studies, the results here show a predictable trend of smaller errors made at lower impact angles and larger errors made at larger impact angles [6,9,11].For all calibers used in this study, there was a tendency for the participants to underestimate the azimuth angle, meaning the observed errors were generally negative.smaller lead-in area at higher impact angles.Due to the small lead in area, there is not much stability for the trajectory rod to reliably be positioned.Therefore, this can lead to greater variation observed in the errors.
In this study, only incident angles from 5° to 65° were attempted, as impact angles above 65° do not provide a suitable lead-in area for this method.The 0.22 LR caliber showed the most variability among the errors, with the errors being more spread aside from each other as compared to the other two calibers.In Figure 7, the errors begin to deviate from each other upward of 30°, and further spread aside as the incident angle increases.This finding was consistent with Liscio and Park [2021], where it was hypothesized that the smaller lead in area may lead to an inability of the trajectory rod to be properly positioned [6].Due to the smaller caliber, the lead-in area was smaller compared to the 9 mm Luger and the 0.45 ACP calibers.Therefore, the trajectory rod may not have been properly aligned against the lead-in area, leading to larger errors.This was also confirmed as the 0.45 ACP caliber ammunition had the smallest margin of error across all angles of incidence, even at higher angles.
When comparing the blind and non-blind participants, there appears to be minimal bias.The averages are relatively close together for the blind versus non-blind participants.Further, both averages follow the trend that greater errors occur at larger incident angles.
This trend can be visualized in

| CON CLUS ION
Overall, the lead-in method demonstrated a predictable trend over different impact angles and over different calibers.This conclusion was also found in Liscio and Park [2021] where the trend demonstrates an indication that the formation of the lead-in area may be dependent on how different bullets and calibers interact with sheet metal, such as those seen in practical scenarios [6].By identifying predictable trends of error for different calibers, it supports the development of correction factors or behavioral curves.This can be expanded to include correction factors for different types of bullets and brands.With the understanding of the behavior of different calibers and how they interact with sheet metal, this knowledge can be applied by forensic investigators to estimate the true impact angle, and therefore, increase the accuracy when using the lead-in [6].The clear definement and standardization terminology for the landmarks of the lead-in area is important to the field of forensic firearms as these F I G U R E 1 Depiction of the vertical and azimuth conventions.
landmarks are crucial in correctly identifying the trajectory path of the projectile.

F I G U R E 7
A 0.22 LR azimuth angle actual error for blind participants.41.6°, 45.4°, and 48.5°.The average absolute measurement errors associated with these angles were 9.8°, 9.9°, and 6.7°.Lastly, for the 0.45 ACP caliber, the results followed this predictable trend shown in the previous two calibers.For angles lower than 35°, the errors are close to the ground truth, meaning there is minimal error and smaller range of errors.Following the pattern of results from the other two calibers, the smallest error was seen at the lowest incident angle.The smallest impact angles for this caliber were 4.2° and 4.6°.There was an average absolute error of 1.8° and 1.2°.The largest spread of error seen with this caliber was at angles F I G U R E 1 0 A 9 mm Luger azimuth angle actual error for blind participants.F I G U R E 8 A 0.22 LR azimuth angle absolute error for blind participants.F I G U R E 9 A 0.22 LR blind versus nonblind participant average measurements.over 45°.Three impacts were recorded above 45°; 49.0°, 49.3°, and 49.5°.The average absolute error of these angles was 4.2°, 7.2°, and 2.8°.

For
the absolute error, the values generally increased as the azimuth angle increased for all calibers.This trend of actual error and absolute error was observed in Mattijssen et al. [2016] and also observed in Liscio and Park [2021] [4, 6].This is thought to be because of the F I G U R E 11 A 9 mm Luger azimuth angle absolute error for blind participants.F I G U R E 1 2 A 9 mm Luger blind versus non-blind participant average measurements.F I G U R E 1 3 0.45 ACP azimuth angle actual error for blind participants.
Figures 9, 12, and 15.All values are relatively close together, and show no signs of obvious bias.

F I G U R E 1 4
0.45 ACP azimuth angle absolute error for blind participants.F I G U R E 1 5 0.45 ACP blind versus non-blind participant average measurements.