Gunshot-wound dynamics model for John F. Kennedy assassination

Abstract

U.S. President John F. Kennedy was assassinated while riding in an open motorcade by a sniper in Dallas, Texas on 22 November 1963. A civilian bystander, Mr. Abraham Zapruder, filmed the motorcade with a 8-mm home movie camera as it drove through Dealey Plaza, inadvertently recording an ≈8 second sequence of events that included a fatal gunshot wound to the President in the head. The accompanying backward motion of the President's head after impact appeared to support later "conspiracy theories" because it was claimed that this was proof of a shot from the front (in addition to one from behind). In this paper, simple one-dimensional dynamical models are uniquely applied to study in detail the fatal shot and the motion of the President's head observed in the film. Using known parameters from the crime scene, explicit force calculations are carried out for determining the projectile's retardation during tissue passage along with the resulting transfer of momentum and kinetic energy (KE). The computed instantaneous KE transfer within the soft tissue is found to be consistent with the formation of a temporary cavity associated with the observed explosion of the head, and subsequent quantitative examination of this phenomenon reveals two delayed forces at play in the backward motion of the President following impact. It is therefore found that the observed motions of President Kennedy in the film are physically consistent with a high-speed projectile impact from the rear of the motorcade, these resulting from an instantaneous forward impulse force, followed by delayed rearward recoil and neuromuscular forces.

Keywords: Mechanics; Physics.

Figure 1

Kennedy assassination crime scene in Dealey Plaza, Dallas, Texas. Shown is the location of cameraman Abraham Zapruder along with the trajectory of the third and fatal shot that killed President Kennedy (blue line) from the Texas School Book Depository (TSBD). The map is oriented with true north pointing toward the top of the page; non-permanent geographic features (e.g., tree canopies, parking lot, road signs, cars, etc.) are contemporary with year 2017 and not as they were in 1963, and the solar shadows are not valid for the historical date and time. Google Earth Pro © map data: Google, SIO, NOAA, U.S. Navy, NSA, GEBCO.

Figure 2

Un-enhanced high-resolution digital copies of Zapruder Film Frames 312 and 313 (Z312 and Z313) showing the high-powered rifle gunshot that fatally wounded President Kennedy. Frame 312 has been horizontally adjusted to correct for tracking error between the two frames. The annotated red line segments demarcate features relevant to the kinematical discussion in the text: dashed line O is flush with the back of Kennedy's head in Z312; lines a and e are stable limo features (viz., the Secret Service hand grip and chrome window frame, respectively); line b is Kennedy's back; line c is Mrs. Kennedy's hat and hair; line d is Governor and Mrs. Connally; and line f is the Secret Service agents. Zapruder Film © 1967 (Renewed 1995) The Sixth Floor Museum At Dealey Plaza.

Figure 3

Finite-difference layer drag force computations for deforming (half-parabolic growth) spherical projectile passage through visco-elastic soft tissue (i.e., brain tissue): (a) Eq. (15) (Sturdivan Model), and (b) Eq. (16) (Peters Model). The different colored lines correspond to different effective exit wound diameters, d_e, spanning the range described in the Autopsy Report.

Figure 4

Modeled effects of collision of a deforming, high-speed spherical projectile (i.e., impact speed v₁ = 55,700 cm/s) with a human head: (a) computed impulse forces, Eq. (11) and Eq. (24), (b) projectile velocity retardation, Eq. (10) and Eq. (18), and (c) projectile KE loss through soft tissue (brain) layers, |ΔK_L|. The different colored lines correspond to different effective exit wound diameters, d_e, spanning the range described in the Autopsy Report.

Figure 5

Cropped high-resolution digital Zapruder Film Frames 313–316 showing initial “backward lurch” of President Kennedy along with the distribution of ejected material in the wake of the projectile passage. Frames Z314–Z316 have been adjusted to remove jiggle caused by camera tracking errors of the cameraman. Solid particles (i.e., skull fragments) discussed in the text are annotated with the arrows directed counter to the direction of the particles' trajectories. Note that the bullet was already long gone by the time the shutter opened at Z313 [50, p. 173]. Zapruder Film © 1967 (Renewed 1995) The Sixth Floor Museum At Dealey Plaza.

Figure 6

Graphs of the approximate locations of solid particles observed in the Zapruder Film: (a) particle locations by frame indicated by different colored circles, and (b) multi-frame locations of 3 individual particles (distinguished by color), with the approximate “origins” indicated in red circles, and dashed gray lines indicating approximate ballistic trajectories (neglecting air resistance) for the estimated angles and particle speeds.

Figure 7

Calculated recoil displacements ΔX_r (inches per Zapruder frame) using Equation (27) for assumed exhaust jet (or “spray”) velocities, v_s: (a) 3000 cm/s, (b) 3200 cm/s, (c) 3400 cm/s, and (d) 3600 cm/s. The abscissa and ordinate of each plot are the assumed mean elevation angles and mass of the spray, θ and δm, respectively. To obtain the actual change in position of the President's head from Z313 to Z314, these values must be superimposed upon the observed speed of the forward head-snap between Z312 and Z313, namely ≈2.0–2.5 inches per Zapruder frame.

Figure 8

Motion of President Kennedy's head relative to the rear of the seat of the limousine determined from the Zapruder Film by Kennedy assassination author Josiah Thompson: (a) position of the President's head relative to the rear seat as originally published by Thompson [9, p. 91], with red data points showing impulse and recoil model-predicted values from a hypothesized frontal shot assuming the same weapon (as discussed elsewhere in the text), (b) first-order change in position calculated as Δx_i+1 = x_i+1 − x_i, where i is the frame number, and (c) second-order change of position calculated as Δ(Δx_i+2)=Δx_i+2 − Δx_i+1 (plotted at the midpoints between frames i + 1 and i + 2). Error bars denote uncertainty estimates based on those shown in [9, p. 91] (a), and propagated through the first- (b) and second order differences (c). The rightmost y-axis shows approximate elapsed time in seconds, and the top x-axis shows distances in centimeters. Data points are linearly connected by dotted lines in (b) and (c) to assist with pattern recognition, but do not accurately represent non-linear high-speed changes between data points, especially the impulse and recoil spikes. Note that there was no data point at Z318 due to blurring of the frame from camera jiggle.