4. Wound ballistics and physics

      Like most people, I came to the Kennedy assassination thinking that a bullet explodes a head as it passes through it, presumably by compressing brain tissue ahead of the bullet. In actuality, the opposite happens. The bullet bores a relatively small tubelike hole through the tissue as it speeds through, but deposits so much kinetic energy to the sides of the tube (as a consequence of slowing down) that the void ultimately expands into a larger "temporary cavity." The degree of expansion depends strongly on the velocity of the bullet, with high-speed bullets producing much larger cavities than slower bullets. Cavities from high-speed bullets may ultimately reach 30 times the diameter of the bullet.
Relative to understanding the Kennedy assassination, the critical aspect of this phenomenon is that the time needed for the cavity to form and die is much longer than the transit time of the bullet. The cavity grows, undulates a few times, and contracts to a final intermediate size in about 5–10 milliseconds. Even before this process begins, the bullet is long gone. Thus the cavity forms behind the bullet, not ahead of it, and only after the bullet has left the head.
To be specific, consider how long it took the Mannlicher-Carcano bullet to pass through Kennedy’s head. Josiah Thompson claimed it required 2–3 milliseconds (p. 90), but it is easy to show that this figure is too high. If the bullet decelerated at a constant rate through the head, its average speed in the head would just be the average of the initial and final speeds. Assuming the bullet entered the head moving at 1800 feet per second, as proposed by the Warren Commission (page __), and exited with sufficient speed to dent the inside of the limousine’s windshield and the chrome strip above it, its final speed might still have been hundreds of feet per second. For purposes of illustration, assume the final speed to be 400 feet per second. The average speed through the head would then be (1800 + 400)/2, or 1100 feet per second. The slowest possible average speed would be the final speed of 400 feet per second, under the unreasonable assumption that the bullet decelerated completely at the instant it entered the skull and not at all as it passed through the brain or when it left (even though it blasted a big hole at the point of exit). This scenario can be immediately eliminated. If the bullet traveled six inches through the President’s skull (a maximum distance), the most reasonable time required would be 0.5 ft/1100 ft per sec, or about 0.5 milliseconds.
    But the bullet obviously didn't decelerate smoothly as it passed through the head. It would have decelerated abruptly as it broke through the rear of the skull on entering and abruptly again as it broke the other side to exit. In between, it would have decelerated smoothly and slowly. Curiously, however, the second scenario gives the same time of transit as the first scenario, as can be seen by a simple example. Imagine that the bullet instantaneously decelerates by 300 ft s-1 each time it penetrated the cranium. It would then impact at 1800 ft s-1 and reduce immediately to 1500 ft s-1. It would then impact the other cranium wall at 700 ft s-1 and immediately decelerate to 400 ft s-1. Its average speed through the head would then be (1500 + 700)/2, or the same 1100 ft s-1 found for the original scenario. A little thought will convince the reader that no matter how much the bullet decelerates while entering and exiting, its average speed will be 1100 ft s-1. Thus the transit time of 0.5 ms is an invariant number. 
The half-millisecond transit time is 10–20 times shorter than the 5–10 milliseconds required for the cavity to form and collapse behind it. This means that the head retained its basic shape and integrity while the bullet was passing through it, at least relative to its devastation by the later explosion. In terms used by physicists, the first phase of the interaction of a bullet and a head is a simple two-body collision. The bullet transfers part of its momentum and kinetic energy to the head, but little more happens.
How does the head move in response to the bullet during this first phase? Overall, it snaps in the direction of the bullet, because the bullet transfers some of its momentum to the head. Two-body collisions are really simple like that. The head will suddenly move in the same direction the bullet was moving in. It will be a very quick acceleration, for the bullet can only transfer momentum during the brief period it is in contact with the head (less than one millisecond according to the calculation above). The quick acceleration can be viewed in two ways, however, corresponding to the two patterns of deceleration discussed above. The simple pattern of constant deceleration of the bullet will produce a constant acceleration of the head, which means a steady increase in its velocity forward (a quick, smooth acceleration). The complex pattern of three decelerations will produce a correspondingly complex  pattern of three accelerations of the head, in which the head first snaps quickly, then snaps more slowly for a "longer" time, and lastly snaps quickly again. Both patterns will give the same final velocity of the head, however.
      Independent of pattern and detail, the direction of the forward snap
determines unambiguously the direction the head is hit from. The bullet approached from the same direction as the head snapped. In this case, the forward snap proves that the head was hit by a forward-moving bullet, i.e., a bullet from the rear.
Now consider the second phase of the collision. During the first 5–10 milliseconds after the bullet leaves the head, the kinetic energy left behind by the bullet expands the cavity rapidly to its maximum extent, after which it oscillates a few times and contracts to its final size. High-speed bullets can expand the cavity so greatly that pressures of 100–200 atmospheres may be developed (1500–3000 lb per sq. in.!). It is these later pressures that explode the head, long after the bullet has left it.
Note that the pressure builds up isotropically (equally in all directions) inside the head, because the pressure is no longer linked directly to the movement of the bullet. Thus it is not usually possible to predict which part of the head will give way first, other than to note that the weakest parts of the head will generally be the front (the vicinity of the eye sockets) and wherever the bullet left the head. The latter effect is caused by the bullet blasting a larger hole where it leaves than where it enters (because by the time it leaves, the bullet is tumbling and so presents a greater cross-section to the point of exit than to the point of entrance). In the special case where the head is hit from behind, both the exit hole and the weakest parts of the skull will lie at the front of the skull, and it can be reasonably expected that the bulk of the fragments will be expelled frontward.
This second phase of the collision imparts a second movement to the head. If fragments are ejected in a preferential direction, they will cause the head to recoil in the opposite direction. The remainder of this monograph shows that these forces of recoil were significant in JFK's case. Because the direction of the fragments cannot be predicted reliably, the second movement of the head (in recoil) also cannot be predicted. But if the motions of the fragments can be observed and quantified (as is the case here), the recoil of the head can be calculated from them, for the two are bound together by strict physical laws.
In summary, then, a high-speed bullet striking a head produces two separate motions, an immediate snap in the same direction as the bullet, and a subsequent motion 5–10 milliseconds later, in a direction not predictable but calculable after the fact from the aggregate motions of the fragments ejected by the exploding head.

Ahead to 5-Variables and Values
Back to 3--Physics of Colliding Bodies

Back to Physics of the Head Shot