It is a fact that Alvarez omitted the interaction of the incoming bullet with the skull, forcing JFK's head forward.
Not only that, as the fragments of bullet traveled through the brain tissue they eventually encountered the skull a second time - as the fragments exited the skull. This interaction also forced JFK's head forwards and this interaction is completely ignored in both Alvarez's experiments and calculations.
Both of the most significant transfer of momentum interactions are nowhere to be seen in the calculations.
I am not sure why you think he did not take it into account. If the bullet imparted momentum to the skull on exit, it had to have imparted less than its total momentum on entry and while plowing through the head. It doesn't matter when during the interaction of bullet and head when momentum was transferred. His whole point was that the momentum from the explosion can easily exceed the total momentum of the incoming bullet so that the net movement is toward the shooter.
Alvarez states at p. 820 that the target moves toward the shooter if p
j (momentum of the jet) exceeds p
b (momentum of the bullet). He shows how he determined that 10% of the mass ejected at 10% of the bullet speed carries momentum that exceeds the bullet momentum.
Alvarez starts with a 10kg ballistic pendulum into which is fired a 10 gram bullet. From this he concludes that only 0.01% of the kinetic energy of the bullet is converted into mechanical energy upon striking the pendulum. The remaining 99.99% of the incoming kinetic energy is converted into heat.
This is easily calculated because the bullet remains in the wooden block, therefore all of it's kinetic energy is transmitted into the block in one form of energy or another.
What does this have to do with JFK's head-shot?
The answer is - absolutely nothing
Alvarez is using the example where there is no exploding exit wound to show that the momentum of the ballistic pendulum is, initially, in the direction of the bullet. That is how the bullet speed is determined: v
bullet=v
block+bullet x M
block+bullet/m
bullet. The initial speed of the block + bullet is determined by measuring the height reached by the pendulum swing. He then compares that to a situation when the target explodes sending matter forward.
It hardly needs pointing out that JFK's head is not a 10kg block of wood but that is not the real issue. When the bullet strikes JFK's head it breaks up, these fragments pass through the brain and exit the head. The majority of the bullet exits the head and is no longer a part of the head/bullet system. These fragments still have plenty of kinetic energy - one fragment cracks the windshield, one dents the chrome trim and others may have left the limo completely. All of this kinetic energy is lost to the head/bullet system whereas in the pendulum/bullet system all the kinetic energy is kept within the system because the bullet is retained in the block.
The fragments do not carry much kinetic energy. If the bullet exited travelling at 400 fps it would have 1/25th of the original bullet energy, meaning 96% of the bullet energy was transferred to the head.
Alvarez's calculations are meaningless.
Alvarez took this all into account. In fact, he noted that even if you assume only 10% of the incoming kinetic energy is used to propel 10% of the mass of the target, the momentum of the expelled jet is 10
1/2 or over 3 times the momentum of the incoming bullet (p. 820):
"For example, if the bullet weighed 0.1 % of the melon weight, and if 10% of the incoming kinetic energy was used to propel 10% of the mass of the melon forward, then the momentum of the jet expelled forward would be (10)
1/2 times that of the incoming bullet."
The thing is, Alvarez is aware of this discrepancy when he writes:
Ballistic pendulums are designed so that they contain the inelastically dissipated energy. Unfortunately, the human head is not able to contain the major fraction of the energy carried in.by the bullet. This tragic aspect of the assassination is clearly visible in frame 313 of the Zapruder film, and is discussed in detail in the reports of the autopsy surgeons.
However, in the very next sentence he makes it clear he is still applying his meaningless ballistic calculations to JFK's head-shot:
The mechanism of the retrograde recoil turns out to be rather simple, if one remembers that 99.9% of the incoming energy must be accounted for.
It is true Alvarez demonstrated that the momentum of the ejected matter could exceed the momentum of the bullet.
But he then concludes, for no given reason, that this ejected matter "gives the melon an equal and opposite momentum".
It's as though he assumes it is opposite because that is what he has already concluded. He seems to be saying that IF the jet of material provided opposite momentum, it could move JFK's head in the opposite direction to the that of the bullet simply because the momentum of the ejected matter is greater than the momentum of the bullet.
But the ejected matter is not competing with the momentum of the bullet, it is competing with the momentum of JFK's head.
That is a fair point. He is assuming that the ejected matter from the melon or head was in the direction of the incoming bullet. That is how he set up his melons. I agree that the situation with JFK was a bit different. Since the matter explodes out of the right side of his head in many directions, the directions of ejecta and incoming bullet are not quite the same.
Also, he provides no mechanism for why the matter is ejecting in the first place [in the case of any "jet effect" this has nothing to do with the transit of the bullet]. Nor does he allow for any of the ejected matter to be a result of the transit of the bullet.
It doesn't matter what the mechanism is. We can see the exploding exit wound. It is obvious that it is caused by energy imparted to the head by the bullet. All that matters is the direction it is moving, how fast it is moving and its mass. This is about physics, not biology.
His incredibly strained attempts to justify his thought process lead to bizarre statements such as this:
The melon would then recoil backward with about twice the velocity it would have been expected to go forward, assuming it were made of wood.
A melon made of wood??
You are not interpreting it correctly. Instead of "assuming" read "if". He is comparing the movement of the melon after the explosive exit of matter in the direction of the bullet and comparing it to how a wooden object of the same size and mass would move (ie. with no jet of matter being ejected).
In the graphic I posted the main "jet" of ejected matter goes backwards relative to the position of JFK's head, which would force JFK's head forwards and downwards. If it was part of the "jet effect". Which it isn't.
Was JFK exempt from the laws of physics?
We can see the matter exploding from his head. There is a visible piece of matter seen in z313 with a streak from above the head to a point that is at least a metre from the starting point. (Note: the fine spray did not penetrate into the air mass above the car as rapidly. But the initial acceleration and its velocity coming out of the head would have been similar, and it is that velocity immediately on leaving the head that provides the impulse).
Since we can see that streak is at least 1 m long and was created during the exposure of 25 ms. (the frame exposure time determined by Zavada), the jet travelled away from the head at a speed of about 1 m in 25 ms. That is a speed of 40 m/s. And that assumes that the streak is not angled toward or away from the camera.
Only 150 grams of matter at that speed carries the same momentum as the maximum momentum carried by the bullet (and we know that the bullet did not impart all its momentum to the head because the bulk of it exited).
