2018-08-02 17:34:35 UTC
30 Apr 2018 - Volume 4, Issue 4 Mechanics, Engineering, Physics
Gunshot-wound dynamics model for John F. Kennedy assassination
Nicholas R. ***@imsg.com
Cite as: Heliyon 4 (2018) e00603
Gunshot-wound dynamics model for John F. Kennedy assassination
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.
U.S. President John F. Kennedy was assassinated while riding in an open limousine within a motorcade through the city of Dallas, Texas on Friday, 22 November 1963. President Kennedy had appeared in countless such motorcades routinely during his presidency. The Dallas motorcade had proceeded without incident up until the end of the route when the President was suddenly shot twice by a sniper. Prior to the arrival of the motorcade, a local civilian named Abraham Zapruder had positioned himself on a 4 foot concrete abutment in the green space known as Dealey Plaza with his state-of-the-art Bell & Howell 8-mm “Zoomatic” color home-movie camera to film the President from a perfect elevated vantage point [1, p. 11]. Shortly after he began filming, he was startled to hear a gunshot, and seeing the President raise his arms, he first thought that the President was morbidly play-acting being shot [2, p. 571]. Mr. Zapruder kept filming while another shot rang out, this one fatally wounding the President in the head. Zapruder would thus both inadvertently and fortuitously record the entire ≈8 second sequence of tragic events on film.
The film was initially withheld from the public (given the disturbing graphic violent content), but it was utilized as evidence by the U.S. Federal Bureau of Investigation (FBI) as well as a Presidential Commission established by Executive Order by President Lyndon B. Johnson and headed up by Supreme Court Chief Justice Earl Warren (thus informally known as the “Warren Commission”). The bipartisan Warren Commission (or WC for short) was necessitated after the primary (and only) suspect in the crime, a local man named Lee Oswald, was himself murdered two days later by a local vigilante named Jack Ruby. Based on its investigation, the WC would determine in 1964 from the available evidence that Lee Harvey Oswald was the lone assassin, firing three shots from the sixth-floor southeast (SE) window of the Texas School Book Depository (TSBD) building. The Commission considered the question of a conspiracy, but ultimately found no compelling evidence of one [3, p. 374]. Three additional independent U.S. federal government investigations would affirm the WC's basic findings [4, pp. 369–381], [5, pp. 50–58], along with other non-government investigations. In spite of the overwhelming physical and circumstantial evidence presented in these investigations,1 conspiracy conjectures have proliferated in the decades since [6, 4, 5], some out of genuine inquiry concerning a plethora of apparent irregularities in the investigation  and “oddities” in the Commission's findings.
Among these oddities were counterintuitive behaviors and anomalies perceived by WC “skeptics” within the now-famous “Zapruder Film.” However, it was not until a bootleg copy of the film was aired on national television (ABC's Goodnight America, hosted by Geraldo Rivera) in March 1975, that a stir was created among the mainstream American public [4, p. 371], [1, pp. 69, 261]. The stir it created is not surprising, given the sequence of events depicted in it, namely the graphic violence, especially the depiction of a fatal wound to the head caused by a high-powered military rifle bullet, something that ordinary citizens would not have had an inkling about in that era. But in particular, the hosts of the program (including Rivera) were adamant about bringing attention to the President's “back and to the left” movement immediately after being shot, making an unjustified claim that this was “consistent with a shot from the front” (which echoed the assertions of early WC skeptics [8, 9]), in defiance of the other far more definitive evidence that had been made available to the public in the WC Report. Responding to such claims, the illustrious Nobel-prize winning physicist Luis W. Alvarez would shortly thereafter publish his own analysis of the Zapruder Film . Prof. Alvarez examined a number of different questions being posed at the time, including the number of shots (based on jiggle analysis), the shutter speed of the camera, and the President's reaction to the fatal shot. On the latter question, he concluded that the puzzling backward lurch was the result of a recoil effect (commonly referred to as “the jet effect”); this conclusion has been backed up by subsequent independent experimental studies [11, 12, 13].
In the current paper, the physics surrounding the shot that struck President Kennedy in the head (near-instantly killing him) will be examined in considerably more detail. Figure 1 shows an overview of the Dealey Plaza crime scene (using Google Earth Pro), including the locations of Mr. Zapruder, the Presidential Limousine (or limo), the sniper's nest, and the trajectory of the shot, which was fired at an approximate distance of ≈81 m (266 feet). The weapon purportedly used was an Italian military Carcano Fucile di Fanteria (infantry rifle), Modello 91/38 (Model 1891/1938), manufactured in 1940 at the Royal Arms Factory in Terni, Italy.2 This weapon fires ≈10.5 g supersonic projectiles with a muzzle speed of 658 m/s
that remain highly stable in flight through air. The effect produced by such high-energy projectiles [14, 15] upon collision with a human head is catastrophic as has been characterized through ballistics experiments [12, 16]. In examining this, three separate dynamical phenomena will be considered in Section 2 that explain behaviors observed in the Zapruder Film, namely (1) the initial effect of the forces directly imparted to the target (head) by the projectile (discussed in Section 2.1), followed by (2) the secondary effect of the directional release of explosive energy escaping the skull cavity (discussed in Section 2.2.1), and finally (3) the nervous system reaction to a massive wound to the brain (discussed in Section 2.2.2).
Direct impulse effect of projectile-target collision
In the Zapruder Film President Kennedy is seen to react to three separate gunshots, the first missing him and the limo [6, 16, 4, 17], the next two hitting him with increasing accuracy. Further discussion of the first two shots is beyond the scope of this paper other than to note that all three gunshots had associated 1–2 frame anomalous movements, and a outward impulse is observed on the jacket lapel of Texas Governor John Connally (who had accompanied President and Mrs. Kennedy in the motorcade and was collaterally wounded in chest) at the same time the President begins showing signs of being injured [12, 6, 7], but no other discernable impulses are otherwise seen on either of the two men (prior to the third shot).
Figure 2 shows the two Zapruder Film frames that captured the fatal shot, namely Z312 (the moment just before impact) and Z313 (the moment just following impact). In Z313 the catastrophic effect of the energy deposit from a supersonic projectile passing through a human head is clearly evident. However, while it is not immediately noticeable at this scale (and not detectable while viewed in motion at normal speed), a careful comparison between the two frames also reveals that President Kennedy's head snaps forward from Z312 to Z313 [9, pp. 87–89], as referenced to the red dashed line labeled O. There is nothing new in this observation—early researchers with access to the still frames first noticed this in the mid-to-late 1960s. Notable among these is author Josiah Thompson, who estimated the position of the President's head relative to two fixed objects on the rear of the limousine, the results of which are plotted in his book Six Seconds in Dallas (1967) [9, p. 91] that will be returned to in Section 2.2. However, for the moment it should be noted that this motion amounts to an anomalous forward impulse on the order of several centimeters over the time interval of one Zapruder frame (≈0.055 s) at the moment of impact (an impulse comparable to Connally's “lapel flap”). It is also crucial to note that this anomalous forward impulse at Z313 is only observed on Kennedy's head—it is not observed on any of the other limo occupants (with reference to dotted lines c, d and f), nor is it even observed on Kennedy's own torso (line b), wherein lies his body's center-of-mass (CM). This implies that an isolated real force acted directly (and solely) upon the President's head just prior to Z313; the only plausible source for this instantaneous, isolated forcing mechanism is manifestly and unequivocally the projectile impact. Therefore, what follows in Sections 2.1.1–2.1.4 is an examination of the relevant dynamics involved in the direct interaction  of a high-speed projectile with a human head.
Discussion and conclusions
This paper has presented a unique quantitative scientific analysis of gunshot wound dynamics observed in the Zapruder Film of the Kennedy Assassination. Based on known parameters of the crime scene, theoretical model calculations were performed for an idealized high-energy spherical projectile possessing the mass and speed (assuming air resistance over the 81 m distance between the muzzle and target; cf. Figure 1 and 2.1.2) of a Carcano military rifle bullet. The model projectile collides with and passes through a target that takes into account the cumulative resistances presented by skull (cortical bone) and soft tissue (brain). The projectile deforms during target passage (initiated by the rigid skull collision), then deposits the majority of its KE to the target, a part of which is consumed toward imparting an instantaneous impulse force that propels the target forward by ≈2 inches (≈5 cm) during the course of one shutter cycle (i.e., with a speed of ≈+2 in/frame), the exact magnitude depending upon uncertainties in parameters such as the projectile deformation and impact time. The remainder of the KE goes toward “heating” (i.e., deforming and disrupting) the target soft tissue. The actual transfer of energy is known to occur through temporary cavitation, which increases the interaction region via a separated flow field, outward propagating pressure wave and restoring force undulations. In the Zapruder Film, the skull is observed to rupture (as a result of the temporary cavitation pressure) with a significant quantity of mass being propelled forward and upward from a single large opening on the mid-front right of the President's head. The observed wound location roughly lags the computed location of maximum KE transfer, and a theoretical explosive “jet” exhaust speed was found to be of the same magnitude as that observed in the film. The delayed observed forward momentum of this jet (or spray) of material, occurring well after the projectile had passed, was then quantitatively shown to be associated with a short-lived recoil effect that imparted a backward change in velocity (i.e., deceleration) on the President's head from the initial ≈+2 in/frame forward head snap to ≈0 to −3 in/frame (≈0 to −8 cm/frame) over the following shutter cycle (again depending upon uncertainties in parameters). Finally, it was shown that a second delayed backward acceleration (delayed relative to the impulse and recoil, but still rapid by everyday experience) is detectable in data published previously by , and this acceleration occurs on the President's entire upper body (not just his head). The most plausible forcing mechanism for this second distinct backward acceleration (i.e., one that would act on the body's CM and is consistent with the observed time scale) would be a nervous system reaction to massive brain injury as proposed by earlier investigators . This neuromuscular effect causes the large torso muscles to undergo a delayed involuntary contraction, straightening the torso and thus torquing the entire upper body backward from its seated posture. From the foregoing modeling calculations and observations of the Zapruder Film it was thus quantitatively shown that the President's reactions just after the projectile impact were physically consistent with a gunshot wound caused by a high-energy Carcano military rifle bullet fired from the vicinity of the TSBD.
In criminal homicide cases, establishment of facts is critical to establish causes, reconstruct the crime and properly assign guilt (or innocence). In the case of the “Crime of the Twentieth Century,” such a task is obviously of even greater importance given the historical dimension and relevance. Noted homicide prosecutor and Kennedy assassination expert Vincent Bugliosi had suggested that the conclusions of the WC would be wholly deducible had the Zapruder Film never existed (i.e., from the autopsy and other forensic evidence), and thus he cautioned his readers not to make too much out of it [4, pp. 450–451, 464–466]. While he may indeed have been correct that the film was not necessary to solve the crime (and get a guilty verdict), it nevertheless is the case that the film provides remotely sensed optical data amenable to gunshot wound ballistic analysis. Although the “large-defect” wound location and forward expulsion of mass seen in Z313 are suggestive of a through-and-through trajectory from the rear, the recoil and neuromuscular effects in and of themselves do not identify the origin of the shot—the recoil was the result of the observed explosion in the wake of the projectile and the neuromuscular reaction could occur from any brain injury of that magnitude regardless of the projectile's origin. However, these are indirect effects of the projectile-target interaction that quantitatively explain the delayed “back and to the left” motion observed in the Zapruder Film. On the other hand, the implications of the instantaneous impulse brought on by the high-speed projectile collision and passage through the target may be logically summarized as follows. If P denotes “collision impulse in ±x direction” (i.e., cause) and Q denotes “instantaneous change in target momentum in ±x direction” (i.e., effect), where the “target” here is President Kennedy's head, then from physical reasoning the following logical statement holds
P ⇒ Q . (33)
Q is observed to be true in the Zapruder Film for the +x (left to right down Elm Street) direction, which is consistent with statement (33) for the observed forward impulse. But if an equivalent statement is attempted for the hypothetical case occurring in the opposite −x direction (i.e., originating from a shot to the front of the limousine), from the Zapruder Film Q is false for reasons explained in Section 2.2. Thus, from the tautological expression
(P⇒Q) ⟺ (¬Q⇒¬P) , (34)
a frontal impact at Z313 is physically ruled out. Of course, the validity of statement (34) does not rule out conjectured missed shots (although no physical evidence was ever recovered for any such shots), nor does it pinpoint the exact origin of the shot that hit (e.g., the TSBD as opposed to another nearby building). But the modeling study (and underlying dynamics and conservation laws) presented in this paper, in corroboration of the autopsy findings , do imply that President Kennedy was not hit by a hypothesized gunshot from the front. The conclusion is an important one given that the hypothesized existence of a shooter in front of the limousine (viz., on the Grassy Knoll) has been the primary physical foundation for virtually all conspiracy conjectures to date on the topic.
13 As a parting note, while the simple one-dimensional physical models presented in this paper were derived for application to a special case study (viz., the Kennedy Assassination), the underlying physical principles provide an approximate quantitative description of the interaction between a high-speed projectile (slowed by an intervening atmosphere) and a heterogenous body comprised of bone and visco-elastic tissue (viz., the human head), and may also form a basic conceptual basis for understanding the wounding mechanisms involved in such interactions.