Bullet trajectory analysis using photographs
Written by Edward E. Hueske   

Bullet trajectory analysis is dependent upon a number of variables that include bullet design, velocity (initial and terminal), angle of departure, angle of impact, distance of travel, target composition, temperature, relative humidity, and altitude.

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The trajectory specified for a given bullet impact is actually an approximation of the flight path of the incoming bullet. It is only an approximation due to the inherent yawing, nutation, and precession of a bullet in motion (see diagrams that follow). Although spin stabilization (imparted by the rifling within the bore of the barrel of a firearm) is working to counter the inherent destabilization characteristics of yaw, precession, and nutation, that job is only accomplished to a somewhat limited degree. Thus, a bullet seldom impacts a target at precisely the same orientation each time, requiring the labeling “approximate” to any trajectory specified for a fired bullet.

Once a bullet penetrates a substrate (i.e. strikes a target of some sort), it is generally subjected to deflection, distortion, and possibly fragmentation. If the bullet exits (i.e. perforates the substrate), spin stabilization has been reduced or lost, and unpredictable, erratic exit trajectories are frequently encountered. Obviously, the representation of bullet paths through objects as straight lines is for convenience only and in no way truly representative of actual trajectories.

The accepted margin of error for bullet trajectory determination within the shooting reconstruction community is plus or minus 5 degrees, both vertically and horizontally, for the typical shooting scene. That is correctly represented three dimensionally as a conical zone of possibility (+ 5 degrees and – 5 degrees, both along the x axis and along the y axis (Figure 1).


Figure 1

In order to be able to provide a reasonable approximation of the trajectory of an incoming bullet, it is necessary to be able to measure and utilize the two angular coordinates that are required to specify a trajectory relative to a vertically oriented target (Figure 2).


Figure 2

Once these two angular coordinates are known, scale diagrams (either three dimensional or two dimensional) may be created to illustrate trajectory approximations for shots fired (Figures 3 & 4).

Figure 3 (left)—2D drawing of shots fired into a vehicle based upon Y trajectory coordinates. This allows shooter position to be approximated using shooter height and gun position.

Figure 4 (right)—2D drawing of shots fired into a vehicle based upon X trajectory coordinates. Shooter position cannot be specified on the basis of these alone (nor is the insertion of any “triangle of possibility” appropriate).

Analysis

In the absence of any trajectory coordinate data, it is impossible for anyone to reliably establish possible shooter positions. Very general directionalities (X coordinates) for shots into various substrates (vehicle panels, walls, doors, windows, etc.) may sometimes be determined from photographs based upon bullet entry or impact site appearances, but it is not possible to ascertain anything concerning the requisite information (Y coordinates) for establishing shooter positions from photographs having no trajectory rods in place. Even for the shots that have exit holes, nothing can be reliably determined from photographs as to the vertical (Y) trajectory coordinates without being able to positively eliminate internal deflection (see Hueske, E.E., “The Need for Bullet Deflection Training for Field Investigators”, Forensic Science Policy and Management: An International Journal, 2010).

An example of the unreliability of attempting to use scene photographs of bullet holes in a vehicle door is provided by the apparent shots to the driver door shown below. It is obvious from the shapes of the holes in the photograph (Figure 5) that the camera was not positioned directly above and held with the focal line at 90 degrees as required for any accurate assessment. But other questions must be asked:

1. Are both of those actually bullet holes?

2. If they are bullet holes, how was it determined that one or both resulted from this incident (it is not uncommon that vehicles, buildings, etc. in high-crime areas have non-contemporaneous bullet strikes)?

3. If they are contemporaneous with this incident and other shots with obviously different trajectories are present, why are their apparent trajectories so drastically different than for any of the other shots?


Figure 5—Photograph of the bottom area of driver’s door of the vehicle.


Figure 6—Photograph of the inside area of the driver’s door of the vehicle.

The image in Figure 5, in and of itself, cannot be used to provide any meaningful information as to possible shooter position. The photograph in Figure 6 purports to show exit holes in the inside area of the driver door.

Once again, the photograph in Figure 6 was taken with the camera not directly above the holes (focal line was not at 90 degrees). Neither photograph was taken with a scale (ruler) present, making them inappropriate for any sort of evaluation based upon measurement. As for attempting to use the combination of the two photographs to arrive at some sort of trajectory, it cannot be done for the following reasons:

1. There is no way to positively conclude which exit hole is associated with which entry hole due to the possibility of internal ricochet off cross bracing and/or the power window mechanism (the upper hole above exhibits an oval shape indicative of traveling sideways at impact with the inside door section).

2. As for the question as to whether these were shots contemporaneous to the incident, where are the responsible bullets that passed through?

The locations of fired cartridge cases at a scene do provide some potential means of general horizontal positioning of persons within the scene, but when no cartridge case ejection testing has been carried out (using the involved weapons, similar ammunition, similar terrain, and firing from similar positions), no quantitative assessment of the cartridge case locations is possible. The only meaningful horizontal limitations present are buildings and other structures.

Conclusion

Without having any reliable horizontal (X) trajectory coordinates and no vertical (Y) trajectory coordinates, it is impossible to propose scientifically reliable shooter positions for any of the shots fired into vehicles and other target media using photographs alone.


About the Author

This e-mail address is being protected from spam bots, you need JavaScript enabled to view it has spent 40 years as a practicing forensic scientist, including 23 years with government crime labs in Texas, Oklahoma, and Arizona (retiring in 1996), and 14 years as a full-time faculty member in the department of criminal justice at the University of North Texas (retiring in 2012). He currently consults with prosecution, defense, and police agencies in civil/criminal matters and provides training to police agencies in shooting incident reconstruction. He is a Consulting Forensic Scientist Fellow of the American Academy of Forensic Sciences, Emeritus Member of the American Society of Crime Laboratory Directors, Emeritus Member of The Southwestern Association of Forensic Scientists, and Distinguished Member of the Association of Firearm & Tool Mark Examiners.

 
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