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
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