29-01-2011, 11:19 AM
(This post was last modified: 29-01-2011, 11:21 AM by Bernice Moore.)
hope this is better David;if it works that is, i read it and my eyes are older than yours...:danceing:b
http://www.acorn.net/jfkplace/07/Daeron/.03-2faq.html
by P.J. Stahl
The REAL FAQ(v2.1) including Parts:
3C: Questions Concerning the Nix and Zapruder Films
3D: Questions Concerning the Rifle(s) Used
ALT.CONSPIRACY.JFK (REAL FAQ v 2.1)
III. C. The Nix and Zapruder Films:
1. What is the difference between Nix and Zapruder films?
The Nix film was filmed by Orville Nix, just on the opposite side
of Elm St. from where Abraham Zapruder filmed his. More precisely, he
was located at the corner of Main and Houston Streets. Both films show
various details of the fatal head shot though, to be sure, the Z-film
(as the Zapruder film has been called) has been the more extensively
studied, and is perhaps the most analyzed film in history (5, ibid.)
A frame from the Nix film(+) may be seen in 7, p32. Best of all, try
to view the entire intact video. The best version I have seen (intact)
is in the Italian made (1976) video 'The Two Kennedys'. One can
clearly see a smoke puff rising from behind the fence of the Grassy
Knoll - just as described by a number of witnesses standing on the
Elm St. Overpass including: Richard Todd, and S.M. Holland (see, cf.
the video 'Rush to Judgment' and segments of interviews with Holland,
Todd, Lee Bowers and others therein.
In the intact Nix film, clearly visible, is the fragment of skull
bone, seen rocketing over the trunk of the car as a direct result
of the head shot. In 'The Two Kennedys', this fragment is ringed for
easy identification throughout its trajectory. There is not the least
doubt in my mind that this is indeed a dislodged bone fragment, and
more than likely the selfsame fragment (occipital) found by William
Harper subsequently, about 25-35' behind where the limo was when
the shot was fired.(Also noted by Mr. Charles Brehm - who was
standing only 30' from the limo at the time, but never called by the
Warren Commission). A missing occipital bone would also
comport with the hole in the head as described, for example,
by Charles Crenshaw at Parkland (10, p86).(See also details
given in previous section of FAQ).
From a purely physics point of view, the motion of the fragment over
the trunk clearly shows the direction of momentum. Its motion is also
perfectly consistent, and matched to the other kinetics visible (i.e. the
head shot, direction of head motion , etc. ) This also indicates
irrefutably, that the shot that produced this backward propulsion of
bone had to have come from the front. (Note Jackie can also be seen
in the film moving over the trunk in an attempt to snatch the flying
fragment (cf. Z-film 7, p38, lower right, p192, bottom) and her own
testimony appearing in transcripts (WC, Vol. V, p. 180) indicates that
is exactly what she was doing. Charles Brehm in an interview ('Rush to
Judgment', 1986) also notes the displacement of what he believed to be
a skull 'particle' to the left and rear of the limo.
Reference has been made to Martin Shackelford commenting that "it seems
like a skull fragment flying through the air would be in more than one
frame" (3, p76, 77) - but it is clear to this observer that what
Shackelford was looking at was *not* the original - intact Nix film, but
rather a doctored substitute that emerged after "the original film was
lost during the HSCA investigations"(3, p78)
Certainly, the version of the Nix film I have (on 'The Two Kennedys')
shows more than 'one frame' and, as I indicated, it is tracked with
the aid of a reference circle (estimated duration: 0.5-0.6s or 8-10
frames). It is evident to me that more than one version of the Nix film
is in circulation, and that there is no assurance that anyone looking at
a copy will see the intact version. ('The Two Kennedys' is dated 1976,
or two years before the HSCA investigations where "original copies were
lost")
Orville Nix himself (interview, 'Rush to Judgment') notes that there
was an original of his film (which went to UPI) and a copy of that -
which went to the federal investigators. When his film was returned to
him (the gov't version) Nix pointedly noted that it was *not* the same
as what he had originally given them. In fact, he observed "a frame here
and there was missing". Assuming that no one knows his film better than
Nix himself, this leads one to suspect that at least three versions of
the Nix film are in circulation:
- The original (UPI) unedited version (also in 'The Two Kennedys')
- The tampered version returned to Nix (frames missing)
- A 2nd tampered version - after a copy 'disappeared' during the HSCA
In his book 'Killing the Truth', Harrison Livingstone notes (2, p77):
"Doug Mizzer reports evidence of forgery with this film, with a frame
having been removed following the headshot. His theory is that the
first frame shows the vapor from the brain shot at the moment of impact
on the front of the head, and the following frame shows a large piece of
skull fragment in the air coming from the back of the head.
This would be conclusive proof that the shot came from the front."
It should also be noted that an original film by Marie Muchmore also
caught the critical instant - and was film facing the Grassy Knoll.
Unfortunately, her film was confiscated, and when returned the key
frame had been mutilated (cf. 7, p37, middle)
Certainly, and remember this is a *conspiracy viewpoint* FAQ, the
cumulative tactical 'hits' on the evidence must set the nerves of
the sincere truth seeker on edge. While critics carp about a mere
'set of coincidences' or 'oversights' and the 'inability of the
government to do anything right or keep secrets' - it is clear that
whoever is behind the pattern of evidentiary compromise has had an
uncanny ability to target the most critical evidence (films, etc.) and
render it near useless or absent. As these instances proliferate, the
'psy ops' theory of Livingstone (see 3A of FAQ) escalates to ever
increasing prominence and credibility.
Fortunately, in the case of Nix's film - not all copies have been
'adjusted'. I have seen at least one version, in the Italian made video
'The Two Kennedys' which shows the flying bone fragment with a reference
circle through its whole trajectory. There is no doubt in my mind that:
a) it is a genuine object - not an artifact (since Jackie is seen
actually reacting to it, pursuing it, and b) there are no frames missing
from the sequence.
Mark Lane also notes, in regard to the Nix film, that it (11, p.57):
"provides graphic evidence that she (Jackie) apparently was reaching for
a portion of the President's skull that seemed to be driven over the
back of the automobile. This possibility is supported by the testimony
of Clinton J. Hill, a Secret Service agent, who ran from the left
running board of the followup car back into the limousine. He told the
Commission that it appeared to him that Mrs. Kennedy was reaching for
something flying over the rear of the car."
By contrast,. the version of the film shown at the beginning of Part 3
of the Nigel Turner series 'The Men Who Killed Kennedy' is decidedly
different. It is shorter (estimated 1/10 sec - 1/20 sec) and the bone
fragment cannot be seen other than in the very initial part of the
sequence, maybe for 1/10 second. Indeed, the fragment shot is so
ephemeral that one could indeed come away with the impression it is an
artifact or 'light trick'. (Though if the blown up view is studied
carefully and re-run, this is dispelled.)
Obviously, however, the perpetrators have not been able to get all
copies replaced, since - as I indicated, mine shows the whole
trajectory. However, their ploy has managed to arouse ambiguity and
obfuscated the identity of the real Nix film. As with every other piece
of evidence that 'seems' to have made it though the covert net of
concealment, the fallback defense is one of neutralization by
counterpoint and spurious information. This has been the ongoing
predicament faced by conspiracy theorists. The psy-ops warriors and
pawns who have deliberately tainted the evidence, have kept the
didactic dynamic in a state such that "anything can be believed" but
"nothing can be known".
2. Was the Zapruder film tampered with? How?
Yes - "the only available print of the Zapruder film at the time
was extensively tampered with. Frames 155 and 156 do not exist". (1,
p185). The film was spliced initially at this location, though
the owner (TIME, Inc.) denied this was the case. (ibid.)
Also, "the Warren Commission only began to print the film starting
with frame 171".(ibid.)
Eventually, the story making the rounds was that a 'junior employee'
- put to work on it in the course of enlarging, 'damaged the key
frames' (op. cit., p186). We will leave the percipient consumer of
information to make of this what they will.
Some personal (e-mail) communications (by persons preferring to remain
anonymous) to me, have also disclosed that various copies of the Z-film
(like the Nix film) appear to have the skull fragment airbrushed out.
(Jackie is seen pursuing it over the trunk - but now it isn't there).
Again, fortunately, I have a version of the Z-film which does indeed
show said fragment, comporting fully with what is observed in the Nix
film. (Note - in the Z-film this is in the sequence from about Z-314 -
Z-353. In some Z-film versions, of course, the latter frames may have
been excised - another regrettable turn of events).
Also, there has been speculation, still highly controvesial, that the Z-film
was altered to conflate two separate shots into one, or 'nearly' one.
See 3 (2), below:
3. How do the Zapruder and Nix films disclose the underlying physics
of the head shot?
Each shows clearly the crucial head shot but from opposite sides of the
street. In addition, the fragment of skull is seen dislodged, and flying
over the trunk of the limo - *with Jackie in pursuit.* This shows that
the fragment was not a figment, or 'light effect' - because an
individual *in the film* was reacting to its motion!
The physics can be deduced from this - based on a model in which
a frontal force is exerted on the head, eliciting a displacement.
In what follows I present four different approaches:
Cautionary Points:
(1)The different alternative presentations are provided precisely because
I suspect *one* unique model cannot encompass *all* the elements.
For that reason, it is rather amiss to 'home in' on one, i.e. the torque
model and focus on it to the exlcusion of the complementary approaches.
This is not at all strange in physics, and there are numerous precedents,
for various situations. For example, both the 'liquid drop' and 'shell
model' are needed to describe the atomic nucleus. They perform a
complementary function - each describing particular aspects.
While I am not claiming that bullet shots necessarily approach the
complexity of the atomic nucleus, it is true that complementary
pictures/models may still be needed - say if the evidence of the shot
has been tampered with, or altered. (As appears to be the situation
in the JFK head shot, as Livingston and others note)
(2) At a realistic level, both the free-body (head) and the torque
(torso) models give results at the extremums. (Boundary values)
Thus, the torso model motion would give the lower limit (or
bound) while the free body model gives the upper limit (bound). The
actual result, taking into account all the sundry uncertainties, is
probably somewhere in the middle of these two (extremum) limits.
Again, this discloses why it would be wrong-headed to seize on one
result and neglect the other.
The Approaches:
1) Treatment as a pure inelastic collision (chaotic version):
As Simon notes ('Mechanics', 3rd Ed., Addison-Wesley, 1971) p. 181:
"Collisions of inert macroscopic bodies are always inelastic and
endoergic (Q < 0), the kinetic energy being converted to frictional
forces during impact. The kinetic energy of translation may also be
converted to kinetic energy of rotation and conversely.
Such collisions range from the nearly elastic collisions of hard steel
balls - to the completely inelastic collisions in which the two bodies
stick together after the collision."
In the case of the fatal head shot (Z-313), this is probably somewhere
near the middle of the range cited by Simon, and perhaps much closer to
the inelastic side of the spectrum than the elastic. The primary
difficulty is in quantifying this to a high degree of precision. If - as
I and many others suspect - a 'dum-dum' bullet was used, then the only
likely way to proceed would probably be along the lines of a Liouville
formulation - in a multi-phase space, of particles N and dimension:N x6.
By way of example, if the dum-dum exploded into 540 particles, and the
head into 5 - we would need to work out a density function N of the
form(Phase space dimensions 545 x 6):
N[(X1, X2, ......X545)(V1, V2.......V545(t)] = [d(X1 - X1(t)d(V1-V1(t))
d(X2 - X2(t))(dV2 - V2(t)).... ....x d(X545 - X545(t)(dV545 - V545(t)]
where the 'd' is really a delta - as employed in the Dirac Delta
function.
Because of the inelastic nature and high frictional components - the
density would *not* be conserved and we would expect:
dN/dt <> 0
2)Simple version of above (no jet)
Clearly the complexity entailed in the above would make any
straightforward solution all but impossible.I therefore use the
completely inelastic model of Simon, for which the final head velocity
can be computed from (p. 181):
m(b) v(b) = [m(b) + M] V(h)
where M is the 'head mass' ( estimate 3 kg), m(b) = 0.01 kg (bullet mass
- equal to the 160 grains postulated by a number of authors including
LNutter Posner), v(b) = 545 m/s (metric converted bullet velocity for
Mannlicher-Carcano, 1800 f/s). Then:
V(h) = [ m(b) / (m(b) + M) ] v(b) = [ 0.01/ 3. 01] 545 m/s = 1.81 m/s
which comports with a number of the velocity estimates given - including
by Nutters in this NG (cf. 1.8 m/s or 6 f/s by D. Hixon in 1994).
Note that this is a purely dynamical result - no 'jet' needed to produce
it!
3) More complex version - with jet and fragmentation reckoned in:
In the more complex version, the head is treated as an initially
moving free body (due to the limo's motion). Since the limo
speed was at approx. 11 mph, this would be 4.9 m/s.
Accordingly, as an inelastic collision, we require
(The kinetic energy is not conserved):
total momentum before collision + total momentum after = 0
or (using P for momentum)
P(before) + P(after) = 0
The head (3kg) is moving initially at 4.9 m/s to the RIGHT (vector +)"
-------------------> P (h) = 14. 7 kg m/s
the bullet is directed to the LEFT (c=vector -)
<----------------------------
P(b) = -6 kg m/s
where a bullet speed of 600 m/s is assumed, (The muzzle velocity of
the Mannlicher-Carcano is estimated at 2100 f/s or 636 m/s) and
bullet mass of 0.01 kg. Thus:
Total momentum before collision: = 14.7 kg m/s + (- 6kg m/s)
" " " " " " " " = 8.7 kg m/s
Now, since the sum of the total momenta (before and after collision)
must be zero, this means that we require:
Total mometum After collision = - 8.7 kg m/s
In other words, it is directed toward the LEFT.
Checking:
P(before) + P(after) = 0
[8.7 kg m/s] + [-8.7 kg m /s] = 0
We know that 1.2 kg (approx.) of mass was lost, 1.0 kg of
blood and tissue, and 0.2 kg mass of bone fragment.
An estimate of the fragment's momentum can be found from
the range of the bone fragment. We can calculate the range using:
R = v(o)^2 sin 2(X)/ g
and thence the velocity v(o):
v(o) = SQRT ( R g/ sin 2X)
where v(o) is the initial velocity and X is the 'launch' angle, g the
acceleration of gravity (we use 10 m/s^2 to comport with
the other approximations, estimates).
For the range, we adopt 25 feet, or the estimated distance the
Harper bone fragment landed from the limo just after the head
shot. (cf. 1, p198):
Thus, R = 7.6 m.
then v(o) = SQRT (7.6 m * 10 m/s^2/ sin 90)
where X is estimated at 45 deg.
Thus, v(o) = - 8.7 m/s
(since it is directed leftward)
However, this does not take into account the 'launch' is
from a 'moving platform' (i.e. limo) moving at 4.9 m/s.
Thus, the actual fragment velocity is:
-8.7 m/s - (4.9 m/s) = -13.6 m/s
The momentum of the fragment is therefore:
P(f) = 0.2 kg (-13.6 m/s) = -2.7 kg m/s
This means that - 6.0 kg m/s is left to account for the momenta
of the remnant head (M® = 1.8 kg) and the actual 'jet' (1.0 kg).
(Note: the jet cannot be assumed to have the same speed as
the fragment - since the latter is 'launched on initial *impulse*. Hence,
conservation of total momentum requires consideration of head
and its expelled jet during defined interval del t, but *not*
ejecta dislodged under impulse *before* the commencement
of del t. (cf. Young, 'Fundamentals of Mechanics and Heat,
McGraw-Hill, 1964, p. 160, parag. 3 under Eqn. 7-11).
To separate these two, we note that the *observed* empirical
velocity of M® (see end of next section) is -1.6 m/s. Then,
the momentum is:
P® = M® x 1.6 m/s = 1.8 kg (-1.6 m/s) = -2.9 kg m/s
Thus, the residual momentum, for the expelled 'jet' of tissue,
blood is:
-3.1 kg m/s.
Note this is for a 1.0 kg mass of blood tissue expelled as jet.
Thus, the jet velocity is -3.1 m/s.
Considering remnant head and jet together, their tota; momentum:
-6 kg m/s = 1.8 kg (v + dv) + dm(v - u)
or:
-6 kg m/s = 1.8 kg (v + dv) + (-3.1 kg m/s)
-2.9 kg m/s = 1.8 kg (v + dv)
-1.61 m/s = v + dv
But we know (from empirical data, v = -1.6 m/s) so:
-1.61 m/s = -1.60 m/s + dv
or dv = -0.01 m/s
This enables us to obtain the jet speed relative to the head (u):
We assume here the jet is as shown in the Z-frames, acting
from Z-312 - Z-321 or approx. 0.55s. Then the average acceleration
is:
del v del m [ u + del v]
----- = ------ x ------------
del t del t m
or:
-0.01m/s/ 0.55s = 1.0 kg/ 0.55s [u + (-0.l m/s)]/ 3.0 kg
-.0.18 m/s^2 = 1.81 kg/s [u - 0.01 m/s]/ 3.0 kg
-0.054 kg m/s^2 / 1.81 kg/s = u - 0.01 m/s
-0.029 m/s = u - 0.01 m/s
or : u = -0/029 m/s + 0.01 m/s = - 0.019 m/s
i.e. the jet speed relative to the head is minuscule compared
to the dynamically observed motion.
What about the jet 'back reaction force on the head?
F(J) = m(J) a(J) = 1.0 kg (-0.018 m/s^2) = - 0.018N
So that, from Newton's 3rd law, the force on the head
(acting toward the limo front) is: 0.018N
And the accelerated motion of the 'remnant head' in this direction is:
a® = m(J) a(J)/ M® = 0.018N/ 1.8 kg = 0.01 m/s^2
or again, minuscule in comparison with the dynamic action in the
opposite direction. (The velocity on the order of millimeters per
second).
4) Head shot treatment by external torque acting off -center.
In this treatment I want to compare the results with those above -
particularly for the head final velocity.
(rev 3/98)
Torque Model of the Head Shot:
This is a revision of my original torque model, following certain
errors having been pointed out to me by an alert Stanford physicist.
The primary error was the failure to distinguish impulse action
time from post-impulse (or 'coasting') time. Also, following his
suggestion, I displace the pivot point to the contact point of the torso
with the seat - rather than midway up the torso.
I must point out that this is a *generalized* model. No claim is
made to precisely replicate a *known* shot. There are a number
of reasons for this:
i) It is not yet unambiguously ascertained where, exactly, the
frontal shot originated from.
ii) There are other models based on torque possible (see, e.g.
Lifton's proposal in 'Best Evidence', pp. 51-52)
iii) It is possible - some would say very probable - a 2nd
shot was made just before the kill shot.
Livingstone ('Killing Kennedy', Carroll & Graf, 1995, p. 143)
has brought up the very real possibility that two distinctly
separate shots (which would have clearly betrayed a conspiracy)
were ambiguated by tampering with the Z-film. This cannot be
automatically ruled out - since if these (black ops technical
pros) could alter autopsy film, or x-rays, they could alter any
other to suit their fancy or agenda. The real tragedy in this case
is that *no one* is in a position to 100%, absolutely exclude the
possibility of tampering with *any* evidence presented. Since any-
thing available may only be what psy-ops *want* people to see,
not what actually exists in and of itself. As Livingstone notes:
"..they (forgers) had a film showing *two* major and separate
shots to the head almost a second apart from different directions
and had to eliminate one of them. ....
The fact is that a shot came from behind and drove the head
violently forward, and either before or afterward another shot
came from the left front and drove it violently backward. The forgers
compressed the two shots into one.
"The forgers eliminated most of the evidence of the first head
shot except for the two and a half inch forward movement which
they evidently did not notice in their haste, and compressed the
action, aligning the bottom half of each frame with new and
stretched frames showing the car moving along the street and
grass and people going by in the background."
If Livingstone's conjecture is true, and there is much ongoing dispute
about this (as well as a recent book entitled 'Assassination Science' which
presents an even more radical proposition, i.e. that every other frame was
removed), it means that no physics model is really possible - since the
situation reflected in the film is totally *unphysical*! That is - it is an
artificial creation that does not comport with known physical laws.
This expedient would enable psy ops to 'shoot down' anyone attempting
an analysis based on physics.
Nonetheless, by excluding the 'residuals' from the presumed
first (forward) motion shot (which - if Livingstone is correct,
are corrupted anyway) I believe some basic principles can
still be shown - in terms of how a frontal shot can at least
result in a backward head motion. (Again, since this is a
very generalized model, I do not get into the precise comportment
of the physics with the bullet entry-exit wound positions in
the head).
Now - to the revised torque model.
(Note: the bullet velocity values used here are as
suggested by Posner - e.g. see the special issue of U.S.
News & World Report, Aug 30-Sept 6, 1993, p. 94). It
should be understood that most conspiracy advocates
regard these as far too low - and hence the resultant
answers will be underestimated significantly. Despite that,
I intend to show that a definite backward motion - is still
feasible.)
I use a torque or moment about the center of gravity, acting
perpendicular to moment arm as shown below:
H 0 <------ bullet (e.g. from GK)-produces force F on H
!
!R
!
!
x CG
In the above, H denotes head, and CG is the center of gravity of the
body (near point of contact with limo seat). R is the 'moment arm'
(R = XO) and we assume a shot is placed at O and let R = 0.6m
for ex.(The 'torso' can actually be modeled as a solid, uniform mass,
cylinder 'block' centered at x and symmetrical about both sides of
the axis XO. )
For ex. for a bullet of mass 0.01 kg, traveling at 545 m/s (see above)
initially and decelerated to 445 m/s in 0.0004 s, we have a force of F =
dp/dt = m(dv/dt) = 0.01 kg( 545 m/s - 445 m/s)/ 0.0004 s = 2500 N
force exerted at O.
(Comment on time interval:
Assume the very reasonable estimate of 20 cm (about 8 inches) for
the bullet path thru the head. At the velocities noted, this
implies an average of 495 m/s for which the 'head transit' time
is:
dt = 0.20 m/ 495 m/s = 0.0004 s
This would produce a torque (couple)T = F x R about 1500 N-m
at O. Thus a shot from the front (depicted) would produce a torque
of 1500 N-m that would displace the head O toward H by some angular
amount.
To find it we need the moment of inertia (I) of the 'torso' and from the
cylindrical model we find: I = M/12[3r^2 + l^2] where M is the cylinder
mass (say 50 kg), r is the cylinder radius (shoulder to center of torso
dist. = 0.25 m), l =R,the cyl.length, say 0.6 m). Now, the force of the
bullet F impacting at moment arm distance R from CG exerts an external
torque on the torso such that:
T = F x R = dL/dt = I(@)
where dL/dt is the rate of change of the angular momentum of the
body, I is as defined above, and @ is the angular acceleration
@ = dw/dt or rate of change of angular speed). On substitution
(say using the above reasonable values) we can solve for @:
@ = T/I = 1500 N-m/ (2.281 kg-m^2) = 657.6 rad/s^2
This is the angular acceleration *under impulse*. From this the
angular velocity (arising in same time) can be obtained as:
and w = @t = 657.6 rad/s^2 (0.0004s) = 0.263 rad/s
Ft
_
! !
! !<----Impulse
! !
--! !_______________
uniform motion!
!------------------------
The sort of physical situation we have can be depicted above.
The foregoing treatment basically took care of the very brief
(0.0004s) impulse part of the motion. There is still a uniform
part left to reckon (torso motion under uniform deceleration).
(N.B. The Dirac Delta function and Laplace transforms are usually
used for impulse computations, but that is omitted here so as
not to overly complicate the solution).
Under conditions of uniform deceleration, we have:
@(u) = (w(f) - w(i))/ t
where t is the elapsed time over Z-frames 314-321, with a mean
film advance rate of 18 frames per second. (t = 0.44s). The
initial angular velocity is known from the impulse calculations
(0.263 rad/s) and the final angular velocity w(f) = 0.
@(u) = (0 - 0.263 rad/s)/ 0.44s = - 0.598 rad/s
Again, under conditions of uniform motion we have:
w^2 = w(i)^2 + 2@ (theta)
whence:
theta = [w^2 - w(i)^2]/ 2@
theta = [0 - 0.263^2]/ 2(-0.598 rad/s)
= 0.05783 rad
This must now be added to the angle made under impulse:
theta (total) = theta (impulse) + theta (uniform)
= 0.0001 rad + 0.05783 rad = 0.05793 rad
theta (deg) = 0.05793 rad (57.3 deg/rad) = 3.3 degrees
This is an extremely minute angular displacement which the
entire torso makes relative to its 'pivot'. This can be translated
into linear dimensions by using the fundamental definition of arc length:
theta = s/ R so s = theta x ® = 0.05793 rad (0.6m) = 0.0347 m
or 3.47 cm (1.37 inches)
Clearly, this is too small(see below) - but this does not mean the model
is necessarily wrong. For example, the *entire* mass of the torso is
taken into account, as opposed to just the head mass (as in Approach
#3). This again suggests the best interpretation may be that of a lower
bound on the dynamics, as opposed to a *unique* solution.
The above can be compared to an independent result obtained
by close examination of the key Z-film images (cf. TKOAP, p35)
and a knowledge of the film timing, and geometry. Thus:
The frame Z-312 establishes a good initial position for the
head (lined up against the limo door on the other side - just 1/18 sec
before the shot. Remember the Z-film moves at 18.3 frames/sec so this
would be just into Z-313 for the beginning of the reaction time. )The
other frame on the page (Z-321) shows the most rearward position.
From the best estimates I've been able to make -along with some others,
the distance traveled *across*- the CG of the head along the arc from
Z-312->321 is ~ one foot. However, the head is moving clearly in
3-dimensions here - not only front to back but *also* to the other
(left) side of limo. I estimate the leftward deflection distance at
anywhere from 1.5 to 2'.
Thus we have the (simplified situation where I am even ignoring the
third dimension - for downward tilt of head - though I compensate
somewhat by using the upper bound of R-L displacement 2'):
y
!
!1.5' - 2'
!
!
!-----------x
1'
What we want as the head displacement d is therefore the diagonal
displacement d = (xy) = SQRT[2^2 + 1] = SQRT(5) (taking the upper limit
of leftward distance) d = 2.24 f. The frame separation is 321 - 313 = 8
or (in time) 8/18.3 = 0.43 sec. The velocity from this works out to: v =
2.24 f/ 0.43s = 5.2 f/s = 1.6 m/s (approx.), or within the possible
error of a value cited by many observers, including D. Hixon (a
'lnutter')in 1994.
This (empirically) obtained value, discloses that one or more
inputs were underestimated in the torque model.
3a. So, a jet effect such as some have proposed would not create this+
No - not from detailed analyses I have done, as well as reconstructions
and simulations of Alvarez' methods. The magnitude of the 'jet' is
simply nowhere near as large as the pure, first order dynamical
effects. (See also treatment 1(b) above)
3b. But certainly, isn't it true that if the head is driven back a
certain amount - say one foot, the shooter should be driven back the
same amount, and maybe lose balance and fall over?
The movement of JFK's (or anyone's) body/head is not exclusively the
result of transfer of momentum. Complete treatment of a system requires
energy in addition. Energy (KE) varies as the *square* of the velocity.
Energy transferred, e.g. from bullet to body - would therefore also
depend on this.
The shooter's upper body is *not* required to move back a comparable
distance for three reasons:
1) The force and therefore impulse produced (I =Ft) will not be as great
for a recoiling rifle as for a bullet impacting a head. The Force (and
impulse)depend on the *rate* the velocity changes which is more
important for the bullet than for the recoiling rifle.
2) The pressure exerted by a bullet on impact with a body part (p = F/A)
is greater than for a recoiling rifle - since the force F(b) in the former
case is distributed over vastly less area (A) - essentially the
cross-section area of the bullet. The force F® in the latter case is
vastly diminished by being distributed over a much *larger* area
(the area of the base of the rifle stock).
3) The energy (kinetic) transferred from bullet to body is much larger
than the energy transferred from recoiling rifle to body - since the
velocity of the bullet is so much larger than recoiling rifle (and KE
varies as *square* of velocity)
The above explains why the common objection that - 'a 180 lb. man
shooting would be knocked backwards' is totally spurious.
3a. Is there a new version of the Zapruder film now available?
Yes, it is produced by MPI Video and is entitled 'Image of an Assassination'.
According to press reports (cf. The Baltimore Sun, July 16, 1998, p. 1E)
"it went on sale for $16.99at video outlets."
3b How is it different from the version shown before on newsreels,
documentaries?
As noted in a recent Baltimore Sun article ('History Comes toYour VCR;,
July 16, 1998, p. 1E, by Bob Hiassen):
"Besides a lengthy behind the scenes look at the restoration, the
documentary ends with a flurry of new versions of the famous sequence
- including slow motion and zoom versions, where technology keeps
President Kennedy front and center in each frame. Even the rectangles
of blank film caused by the sprockets of Zapruder's camera have been
restored to reveal, if nothing else, additional scenery."
4. Can the actual shot timing be deduced from either film?
Yes - a dispassionate analysis of the film - taking into account
facial reactions (using jiggle analysis), and the reactions of both
JFK and Connally(7, p20-37). We must also reckon in the
missing frames (155-56), otherwise the firing begins erroneously
late. (1, p185-191). The results are estimated as follows (there
remains some disagreement, because one or more other frames
appear to have been removed from the Z-film, cf : 12, pp. 70-72).
Shot 1 (miss) at Z150-52: Shows crowd reactions at missing frames
(155-56), JFK too.
Shot 2 (throat shot): at Z-207; JFK reacts by Z220.
Shot 3 Connally shot(1st time), at 236-7, note his rotation motion,
dropping of right shoulder. However, he still holds his Stetson so his
wrist still not hit.
Shot 4 (fatal head shot), at Z312-13
Shot 5 Connally shot(2nd time) in wrist and thigh, at Z328 (approx.)
Shot 6? Tague sprayed with pavement (could be simultaneous with #5)
Interestingly, this matches the results of the acoustic analyses
performed by the Weiss group, which found "at least four shots that
were scientifically provable, and at least two more impulses with
an extremely high probability of being additional shots." (1, p224).
An additional point, is that the neck shot and Connally's shot are
separated by barely 29 frames, or about 1.6 seconds. This means that
two rifles would have been needed. (The Mannlicher-Caracano's bolt
action limited it to one shot every 2.25 secs.)
The Ramsey Panel analysis (see previous section) is alleged to have
'refuted' the original study, but in fact only showed that the Weiss group
had omitted some considerations. The Ramsey analysis certainly does
not 'nullify' the Weiss/Barger analysis since up to now it has not been
reproduced, so cannot be accepted as a bona fide scientific conclusion
(I place it in roughly the same category as the 'cold fusion' claims of Pons
and Fleischmann regarding some years ago - for which reproducible results
were never forthcoming). Bear in mind also, that the Ramsey Panel was
not comprised of actual acoustic scientists (personal communication, A.
Marsh). This dilutes the value of their re-test even further.
4a But why can there be no agreement on the shot timing?
You have touched on a matter with explosive political and other
implications, as well as uncertainties (i.e. human reaction times).
Given these factors, there is bound to be significant disagreement
in interpreting when the shots occurred. Even then, these may be merely
confused with the times that *reaction* took place. Interpretation is
also contingent upon the filters through which one views the Zapruder
and Nix films. For example, if one adopts a 'lone nut' filter, which
limits the shot total to 3, then clearly there must be a massive
'compression' of shots (massive expansion of shot-to-wounds ratio) -
with two or more condensed to one, and one producing 7 wounds (as the
magic bullet theory requires). But - as we already saw, with the
anatomical error in wound placement ('base of neck' instead of in upper
back) and neutron activation analysis - that 'compressed'
bullet/shot scenario is no longer viable. Hence, at the very *minimum*
there must be at least four shots, and more likely five. Where
exactly these occur - in the respective running of the films, is what
must now be resolved.
Sources: Referenced as in previous 2 sections -
1 'High Treason', 1989: Groden, R.J. and Livingstone, H.E.
3 'Killing the Truth', 1993: Livingstone, H.E.
5 'The Assassination of John F. Kennedy', 1992, Duffy, J.P. & Ricci,
V.L.
7 'The Killing of a President', 1994: Groden, R.J.
10 'JFK: Conspiracy of Silence', Crenshaw, Charles A.
11 'Rush to Judgment': 1964, Lane, Mark
12 'Killing Kennedy - and the Hoax of the Century', 1995,
Livingstone, H.E., Carroll & Graf.
Also:
Video: 'The Plot to Kill JFK: Rush to Judgment' (A film by Emile
de Antonio and Mark Lane), MPI Home Video, 1986.
Video: 'The Two Kennedys', (A Ben Barry & Associates Release),
1976, Overseas Cinema Resource Establishment (A film by
Gianni Bisiach).
---------------------------------------
3D. The Rifle(s) used:
[color=white][FONT=Couri...
http://www.acorn.net/jfkplace/07/Daeron/.03-2faq.html
by P.J. Stahl
The REAL FAQ(v2.1) including Parts:
3C: Questions Concerning the Nix and Zapruder Films
3D: Questions Concerning the Rifle(s) Used
ALT.CONSPIRACY.JFK (REAL FAQ v 2.1)
III. C. The Nix and Zapruder Films:
1. What is the difference between Nix and Zapruder films?
The Nix film was filmed by Orville Nix, just on the opposite side
of Elm St. from where Abraham Zapruder filmed his. More precisely, he
was located at the corner of Main and Houston Streets. Both films show
various details of the fatal head shot though, to be sure, the Z-film
(as the Zapruder film has been called) has been the more extensively
studied, and is perhaps the most analyzed film in history (5, ibid.)
A frame from the Nix film(+) may be seen in 7, p32. Best of all, try
to view the entire intact video. The best version I have seen (intact)
is in the Italian made (1976) video 'The Two Kennedys'. One can
clearly see a smoke puff rising from behind the fence of the Grassy
Knoll - just as described by a number of witnesses standing on the
Elm St. Overpass including: Richard Todd, and S.M. Holland (see, cf.
the video 'Rush to Judgment' and segments of interviews with Holland,
Todd, Lee Bowers and others therein.
In the intact Nix film, clearly visible, is the fragment of skull
bone, seen rocketing over the trunk of the car as a direct result
of the head shot. In 'The Two Kennedys', this fragment is ringed for
easy identification throughout its trajectory. There is not the least
doubt in my mind that this is indeed a dislodged bone fragment, and
more than likely the selfsame fragment (occipital) found by William
Harper subsequently, about 25-35' behind where the limo was when
the shot was fired.(Also noted by Mr. Charles Brehm - who was
standing only 30' from the limo at the time, but never called by the
Warren Commission). A missing occipital bone would also
comport with the hole in the head as described, for example,
by Charles Crenshaw at Parkland (10, p86).(See also details
given in previous section of FAQ).
From a purely physics point of view, the motion of the fragment over
the trunk clearly shows the direction of momentum. Its motion is also
perfectly consistent, and matched to the other kinetics visible (i.e. the
head shot, direction of head motion , etc. ) This also indicates
irrefutably, that the shot that produced this backward propulsion of
bone had to have come from the front. (Note Jackie can also be seen
in the film moving over the trunk in an attempt to snatch the flying
fragment (cf. Z-film 7, p38, lower right, p192, bottom) and her own
testimony appearing in transcripts (WC, Vol. V, p. 180) indicates that
is exactly what she was doing. Charles Brehm in an interview ('Rush to
Judgment', 1986) also notes the displacement of what he believed to be
a skull 'particle' to the left and rear of the limo.
Reference has been made to Martin Shackelford commenting that "it seems
like a skull fragment flying through the air would be in more than one
frame" (3, p76, 77) - but it is clear to this observer that what
Shackelford was looking at was *not* the original - intact Nix film, but
rather a doctored substitute that emerged after "the original film was
lost during the HSCA investigations"(3, p78)
Certainly, the version of the Nix film I have (on 'The Two Kennedys')
shows more than 'one frame' and, as I indicated, it is tracked with
the aid of a reference circle (estimated duration: 0.5-0.6s or 8-10
frames). It is evident to me that more than one version of the Nix film
is in circulation, and that there is no assurance that anyone looking at
a copy will see the intact version. ('The Two Kennedys' is dated 1976,
or two years before the HSCA investigations where "original copies were
lost")
Orville Nix himself (interview, 'Rush to Judgment') notes that there
was an original of his film (which went to UPI) and a copy of that -
which went to the federal investigators. When his film was returned to
him (the gov't version) Nix pointedly noted that it was *not* the same
as what he had originally given them. In fact, he observed "a frame here
and there was missing". Assuming that no one knows his film better than
Nix himself, this leads one to suspect that at least three versions of
the Nix film are in circulation:
- The original (UPI) unedited version (also in 'The Two Kennedys')
- The tampered version returned to Nix (frames missing)
- A 2nd tampered version - after a copy 'disappeared' during the HSCA
In his book 'Killing the Truth', Harrison Livingstone notes (2, p77):
"Doug Mizzer reports evidence of forgery with this film, with a frame
having been removed following the headshot. His theory is that the
first frame shows the vapor from the brain shot at the moment of impact
on the front of the head, and the following frame shows a large piece of
skull fragment in the air coming from the back of the head.
This would be conclusive proof that the shot came from the front."
It should also be noted that an original film by Marie Muchmore also
caught the critical instant - and was film facing the Grassy Knoll.
Unfortunately, her film was confiscated, and when returned the key
frame had been mutilated (cf. 7, p37, middle)
Certainly, and remember this is a *conspiracy viewpoint* FAQ, the
cumulative tactical 'hits' on the evidence must set the nerves of
the sincere truth seeker on edge. While critics carp about a mere
'set of coincidences' or 'oversights' and the 'inability of the
government to do anything right or keep secrets' - it is clear that
whoever is behind the pattern of evidentiary compromise has had an
uncanny ability to target the most critical evidence (films, etc.) and
render it near useless or absent. As these instances proliferate, the
'psy ops' theory of Livingstone (see 3A of FAQ) escalates to ever
increasing prominence and credibility.
Fortunately, in the case of Nix's film - not all copies have been
'adjusted'. I have seen at least one version, in the Italian made video
'The Two Kennedys' which shows the flying bone fragment with a reference
circle through its whole trajectory. There is no doubt in my mind that:
a) it is a genuine object - not an artifact (since Jackie is seen
actually reacting to it, pursuing it, and b) there are no frames missing
from the sequence.
Mark Lane also notes, in regard to the Nix film, that it (11, p.57):
"provides graphic evidence that she (Jackie) apparently was reaching for
a portion of the President's skull that seemed to be driven over the
back of the automobile. This possibility is supported by the testimony
of Clinton J. Hill, a Secret Service agent, who ran from the left
running board of the followup car back into the limousine. He told the
Commission that it appeared to him that Mrs. Kennedy was reaching for
something flying over the rear of the car."
By contrast,. the version of the film shown at the beginning of Part 3
of the Nigel Turner series 'The Men Who Killed Kennedy' is decidedly
different. It is shorter (estimated 1/10 sec - 1/20 sec) and the bone
fragment cannot be seen other than in the very initial part of the
sequence, maybe for 1/10 second. Indeed, the fragment shot is so
ephemeral that one could indeed come away with the impression it is an
artifact or 'light trick'. (Though if the blown up view is studied
carefully and re-run, this is dispelled.)
Obviously, however, the perpetrators have not been able to get all
copies replaced, since - as I indicated, mine shows the whole
trajectory. However, their ploy has managed to arouse ambiguity and
obfuscated the identity of the real Nix film. As with every other piece
of evidence that 'seems' to have made it though the covert net of
concealment, the fallback defense is one of neutralization by
counterpoint and spurious information. This has been the ongoing
predicament faced by conspiracy theorists. The psy-ops warriors and
pawns who have deliberately tainted the evidence, have kept the
didactic dynamic in a state such that "anything can be believed" but
"nothing can be known".
2. Was the Zapruder film tampered with? How?
Yes - "the only available print of the Zapruder film at the time
was extensively tampered with. Frames 155 and 156 do not exist". (1,
p185). The film was spliced initially at this location, though
the owner (TIME, Inc.) denied this was the case. (ibid.)
Also, "the Warren Commission only began to print the film starting
with frame 171".(ibid.)
Eventually, the story making the rounds was that a 'junior employee'
- put to work on it in the course of enlarging, 'damaged the key
frames' (op. cit., p186). We will leave the percipient consumer of
information to make of this what they will.
Some personal (e-mail) communications (by persons preferring to remain
anonymous) to me, have also disclosed that various copies of the Z-film
(like the Nix film) appear to have the skull fragment airbrushed out.
(Jackie is seen pursuing it over the trunk - but now it isn't there).
Again, fortunately, I have a version of the Z-film which does indeed
show said fragment, comporting fully with what is observed in the Nix
film. (Note - in the Z-film this is in the sequence from about Z-314 -
Z-353. In some Z-film versions, of course, the latter frames may have
been excised - another regrettable turn of events).
Also, there has been speculation, still highly controvesial, that the Z-film
was altered to conflate two separate shots into one, or 'nearly' one.
See 3 (2), below:
3. How do the Zapruder and Nix films disclose the underlying physics
of the head shot?
Each shows clearly the crucial head shot but from opposite sides of the
street. In addition, the fragment of skull is seen dislodged, and flying
over the trunk of the limo - *with Jackie in pursuit.* This shows that
the fragment was not a figment, or 'light effect' - because an
individual *in the film* was reacting to its motion!
The physics can be deduced from this - based on a model in which
a frontal force is exerted on the head, eliciting a displacement.
In what follows I present four different approaches:
Cautionary Points:
(1)The different alternative presentations are provided precisely because
I suspect *one* unique model cannot encompass *all* the elements.
For that reason, it is rather amiss to 'home in' on one, i.e. the torque
model and focus on it to the exlcusion of the complementary approaches.
This is not at all strange in physics, and there are numerous precedents,
for various situations. For example, both the 'liquid drop' and 'shell
model' are needed to describe the atomic nucleus. They perform a
complementary function - each describing particular aspects.
While I am not claiming that bullet shots necessarily approach the
complexity of the atomic nucleus, it is true that complementary
pictures/models may still be needed - say if the evidence of the shot
has been tampered with, or altered. (As appears to be the situation
in the JFK head shot, as Livingston and others note)
(2) At a realistic level, both the free-body (head) and the torque
(torso) models give results at the extremums. (Boundary values)
Thus, the torso model motion would give the lower limit (or
bound) while the free body model gives the upper limit (bound). The
actual result, taking into account all the sundry uncertainties, is
probably somewhere in the middle of these two (extremum) limits.
Again, this discloses why it would be wrong-headed to seize on one
result and neglect the other.
The Approaches:
1) Treatment as a pure inelastic collision (chaotic version):
As Simon notes ('Mechanics', 3rd Ed., Addison-Wesley, 1971) p. 181:
"Collisions of inert macroscopic bodies are always inelastic and
endoergic (Q < 0), the kinetic energy being converted to frictional
forces during impact. The kinetic energy of translation may also be
converted to kinetic energy of rotation and conversely.
Such collisions range from the nearly elastic collisions of hard steel
balls - to the completely inelastic collisions in which the two bodies
stick together after the collision."
In the case of the fatal head shot (Z-313), this is probably somewhere
near the middle of the range cited by Simon, and perhaps much closer to
the inelastic side of the spectrum than the elastic. The primary
difficulty is in quantifying this to a high degree of precision. If - as
I and many others suspect - a 'dum-dum' bullet was used, then the only
likely way to proceed would probably be along the lines of a Liouville
formulation - in a multi-phase space, of particles N and dimension:N x6.
By way of example, if the dum-dum exploded into 540 particles, and the
head into 5 - we would need to work out a density function N of the
form(Phase space dimensions 545 x 6):
N[(X1, X2, ......X545)(V1, V2.......V545(t)] = [d(X1 - X1(t)d(V1-V1(t))
d(X2 - X2(t))(dV2 - V2(t)).... ....x d(X545 - X545(t)(dV545 - V545(t)]
where the 'd' is really a delta - as employed in the Dirac Delta
function.
Because of the inelastic nature and high frictional components - the
density would *not* be conserved and we would expect:
dN/dt <> 0
2)Simple version of above (no jet)
Clearly the complexity entailed in the above would make any
straightforward solution all but impossible.I therefore use the
completely inelastic model of Simon, for which the final head velocity
can be computed from (p. 181):
m(b) v(b) = [m(b) + M] V(h)
where M is the 'head mass' ( estimate 3 kg), m(b) = 0.01 kg (bullet mass
- equal to the 160 grains postulated by a number of authors including
LNutter Posner), v(b) = 545 m/s (metric converted bullet velocity for
Mannlicher-Carcano, 1800 f/s). Then:
V(h) = [ m(b) / (m(b) + M) ] v(b) = [ 0.01/ 3. 01] 545 m/s = 1.81 m/s
which comports with a number of the velocity estimates given - including
by Nutters in this NG (cf. 1.8 m/s or 6 f/s by D. Hixon in 1994).
Note that this is a purely dynamical result - no 'jet' needed to produce
it!
3) More complex version - with jet and fragmentation reckoned in:
In the more complex version, the head is treated as an initially
moving free body (due to the limo's motion). Since the limo
speed was at approx. 11 mph, this would be 4.9 m/s.
Accordingly, as an inelastic collision, we require
(The kinetic energy is not conserved):
total momentum before collision + total momentum after = 0
or (using P for momentum)
P(before) + P(after) = 0
The head (3kg) is moving initially at 4.9 m/s to the RIGHT (vector +)"
-------------------> P (h) = 14. 7 kg m/s
the bullet is directed to the LEFT (c=vector -)
<----------------------------
P(b) = -6 kg m/s
where a bullet speed of 600 m/s is assumed, (The muzzle velocity of
the Mannlicher-Carcano is estimated at 2100 f/s or 636 m/s) and
bullet mass of 0.01 kg. Thus:
Total momentum before collision: = 14.7 kg m/s + (- 6kg m/s)
" " " " " " " " = 8.7 kg m/s
Now, since the sum of the total momenta (before and after collision)
must be zero, this means that we require:
Total mometum After collision = - 8.7 kg m/s
In other words, it is directed toward the LEFT.
Checking:
P(before) + P(after) = 0
[8.7 kg m/s] + [-8.7 kg m /s] = 0
We know that 1.2 kg (approx.) of mass was lost, 1.0 kg of
blood and tissue, and 0.2 kg mass of bone fragment.
An estimate of the fragment's momentum can be found from
the range of the bone fragment. We can calculate the range using:
R = v(o)^2 sin 2(X)/ g
and thence the velocity v(o):
v(o) = SQRT ( R g/ sin 2X)
where v(o) is the initial velocity and X is the 'launch' angle, g the
acceleration of gravity (we use 10 m/s^2 to comport with
the other approximations, estimates).
For the range, we adopt 25 feet, or the estimated distance the
Harper bone fragment landed from the limo just after the head
shot. (cf. 1, p198):
Thus, R = 7.6 m.
then v(o) = SQRT (7.6 m * 10 m/s^2/ sin 90)
where X is estimated at 45 deg.
Thus, v(o) = - 8.7 m/s
(since it is directed leftward)
However, this does not take into account the 'launch' is
from a 'moving platform' (i.e. limo) moving at 4.9 m/s.
Thus, the actual fragment velocity is:
-8.7 m/s - (4.9 m/s) = -13.6 m/s
The momentum of the fragment is therefore:
P(f) = 0.2 kg (-13.6 m/s) = -2.7 kg m/s
This means that - 6.0 kg m/s is left to account for the momenta
of the remnant head (M® = 1.8 kg) and the actual 'jet' (1.0 kg).
(Note: the jet cannot be assumed to have the same speed as
the fragment - since the latter is 'launched on initial *impulse*. Hence,
conservation of total momentum requires consideration of head
and its expelled jet during defined interval del t, but *not*
ejecta dislodged under impulse *before* the commencement
of del t. (cf. Young, 'Fundamentals of Mechanics and Heat,
McGraw-Hill, 1964, p. 160, parag. 3 under Eqn. 7-11).
To separate these two, we note that the *observed* empirical
velocity of M® (see end of next section) is -1.6 m/s. Then,
the momentum is:
P® = M® x 1.6 m/s = 1.8 kg (-1.6 m/s) = -2.9 kg m/s
Thus, the residual momentum, for the expelled 'jet' of tissue,
blood is:
-3.1 kg m/s.
Note this is for a 1.0 kg mass of blood tissue expelled as jet.
Thus, the jet velocity is -3.1 m/s.
Considering remnant head and jet together, their tota; momentum:
-6 kg m/s = 1.8 kg (v + dv) + dm(v - u)
or:
-6 kg m/s = 1.8 kg (v + dv) + (-3.1 kg m/s)
-2.9 kg m/s = 1.8 kg (v + dv)
-1.61 m/s = v + dv
But we know (from empirical data, v = -1.6 m/s) so:
-1.61 m/s = -1.60 m/s + dv
or dv = -0.01 m/s
This enables us to obtain the jet speed relative to the head (u):
We assume here the jet is as shown in the Z-frames, acting
from Z-312 - Z-321 or approx. 0.55s. Then the average acceleration
is:
del v del m [ u + del v]
----- = ------ x ------------
del t del t m
or:
-0.01m/s/ 0.55s = 1.0 kg/ 0.55s [u + (-0.l m/s)]/ 3.0 kg
-.0.18 m/s^2 = 1.81 kg/s [u - 0.01 m/s]/ 3.0 kg
-0.054 kg m/s^2 / 1.81 kg/s = u - 0.01 m/s
-0.029 m/s = u - 0.01 m/s
or : u = -0/029 m/s + 0.01 m/s = - 0.019 m/s
i.e. the jet speed relative to the head is minuscule compared
to the dynamically observed motion.
What about the jet 'back reaction force on the head?
F(J) = m(J) a(J) = 1.0 kg (-0.018 m/s^2) = - 0.018N
So that, from Newton's 3rd law, the force on the head
(acting toward the limo front) is: 0.018N
And the accelerated motion of the 'remnant head' in this direction is:
a® = m(J) a(J)/ M® = 0.018N/ 1.8 kg = 0.01 m/s^2
or again, minuscule in comparison with the dynamic action in the
opposite direction. (The velocity on the order of millimeters per
second).
4) Head shot treatment by external torque acting off -center.
In this treatment I want to compare the results with those above -
particularly for the head final velocity.
(rev 3/98)
Torque Model of the Head Shot:
This is a revision of my original torque model, following certain
errors having been pointed out to me by an alert Stanford physicist.
The primary error was the failure to distinguish impulse action
time from post-impulse (or 'coasting') time. Also, following his
suggestion, I displace the pivot point to the contact point of the torso
with the seat - rather than midway up the torso.
I must point out that this is a *generalized* model. No claim is
made to precisely replicate a *known* shot. There are a number
of reasons for this:
i) It is not yet unambiguously ascertained where, exactly, the
frontal shot originated from.
ii) There are other models based on torque possible (see, e.g.
Lifton's proposal in 'Best Evidence', pp. 51-52)
iii) It is possible - some would say very probable - a 2nd
shot was made just before the kill shot.
Livingstone ('Killing Kennedy', Carroll & Graf, 1995, p. 143)
has brought up the very real possibility that two distinctly
separate shots (which would have clearly betrayed a conspiracy)
were ambiguated by tampering with the Z-film. This cannot be
automatically ruled out - since if these (black ops technical
pros) could alter autopsy film, or x-rays, they could alter any
other to suit their fancy or agenda. The real tragedy in this case
is that *no one* is in a position to 100%, absolutely exclude the
possibility of tampering with *any* evidence presented. Since any-
thing available may only be what psy-ops *want* people to see,
not what actually exists in and of itself. As Livingstone notes:
"..they (forgers) had a film showing *two* major and separate
shots to the head almost a second apart from different directions
and had to eliminate one of them. ....
The fact is that a shot came from behind and drove the head
violently forward, and either before or afterward another shot
came from the left front and drove it violently backward. The forgers
compressed the two shots into one.
"The forgers eliminated most of the evidence of the first head
shot except for the two and a half inch forward movement which
they evidently did not notice in their haste, and compressed the
action, aligning the bottom half of each frame with new and
stretched frames showing the car moving along the street and
grass and people going by in the background."
If Livingstone's conjecture is true, and there is much ongoing dispute
about this (as well as a recent book entitled 'Assassination Science' which
presents an even more radical proposition, i.e. that every other frame was
removed), it means that no physics model is really possible - since the
situation reflected in the film is totally *unphysical*! That is - it is an
artificial creation that does not comport with known physical laws.
This expedient would enable psy ops to 'shoot down' anyone attempting
an analysis based on physics.
Nonetheless, by excluding the 'residuals' from the presumed
first (forward) motion shot (which - if Livingstone is correct,
are corrupted anyway) I believe some basic principles can
still be shown - in terms of how a frontal shot can at least
result in a backward head motion. (Again, since this is a
very generalized model, I do not get into the precise comportment
of the physics with the bullet entry-exit wound positions in
the head).
Now - to the revised torque model.
(Note: the bullet velocity values used here are as
suggested by Posner - e.g. see the special issue of U.S.
News & World Report, Aug 30-Sept 6, 1993, p. 94). It
should be understood that most conspiracy advocates
regard these as far too low - and hence the resultant
answers will be underestimated significantly. Despite that,
I intend to show that a definite backward motion - is still
feasible.)
I use a torque or moment about the center of gravity, acting
perpendicular to moment arm as shown below:
H 0 <------ bullet (e.g. from GK)-produces force F on H
!
!R
!
!
x CG
In the above, H denotes head, and CG is the center of gravity of the
body (near point of contact with limo seat). R is the 'moment arm'
(R = XO) and we assume a shot is placed at O and let R = 0.6m
for ex.(The 'torso' can actually be modeled as a solid, uniform mass,
cylinder 'block' centered at x and symmetrical about both sides of
the axis XO. )
For ex. for a bullet of mass 0.01 kg, traveling at 545 m/s (see above)
initially and decelerated to 445 m/s in 0.0004 s, we have a force of F =
dp/dt = m(dv/dt) = 0.01 kg( 545 m/s - 445 m/s)/ 0.0004 s = 2500 N
force exerted at O.
(Comment on time interval:
Assume the very reasonable estimate of 20 cm (about 8 inches) for
the bullet path thru the head. At the velocities noted, this
implies an average of 495 m/s for which the 'head transit' time
is:
dt = 0.20 m/ 495 m/s = 0.0004 s
This would produce a torque (couple)T = F x R about 1500 N-m
at O. Thus a shot from the front (depicted) would produce a torque
of 1500 N-m that would displace the head O toward H by some angular
amount.
To find it we need the moment of inertia (I) of the 'torso' and from the
cylindrical model we find: I = M/12[3r^2 + l^2] where M is the cylinder
mass (say 50 kg), r is the cylinder radius (shoulder to center of torso
dist. = 0.25 m), l =R,the cyl.length, say 0.6 m). Now, the force of the
bullet F impacting at moment arm distance R from CG exerts an external
torque on the torso such that:
T = F x R = dL/dt = I(@)
where dL/dt is the rate of change of the angular momentum of the
body, I is as defined above, and @ is the angular acceleration
@ = dw/dt or rate of change of angular speed). On substitution
(say using the above reasonable values) we can solve for @:
@ = T/I = 1500 N-m/ (2.281 kg-m^2) = 657.6 rad/s^2
This is the angular acceleration *under impulse*. From this the
angular velocity (arising in same time) can be obtained as:
and w = @t = 657.6 rad/s^2 (0.0004s) = 0.263 rad/s
Ft
_
! !
! !<----Impulse
! !
--! !_______________
uniform motion!
!------------------------
The sort of physical situation we have can be depicted above.
The foregoing treatment basically took care of the very brief
(0.0004s) impulse part of the motion. There is still a uniform
part left to reckon (torso motion under uniform deceleration).
(N.B. The Dirac Delta function and Laplace transforms are usually
used for impulse computations, but that is omitted here so as
not to overly complicate the solution).
Under conditions of uniform deceleration, we have:
@(u) = (w(f) - w(i))/ t
where t is the elapsed time over Z-frames 314-321, with a mean
film advance rate of 18 frames per second. (t = 0.44s). The
initial angular velocity is known from the impulse calculations
(0.263 rad/s) and the final angular velocity w(f) = 0.
@(u) = (0 - 0.263 rad/s)/ 0.44s = - 0.598 rad/s
Again, under conditions of uniform motion we have:
w^2 = w(i)^2 + 2@ (theta)
whence:
theta = [w^2 - w(i)^2]/ 2@
theta = [0 - 0.263^2]/ 2(-0.598 rad/s)
= 0.05783 rad
This must now be added to the angle made under impulse:
theta (total) = theta (impulse) + theta (uniform)
= 0.0001 rad + 0.05783 rad = 0.05793 rad
theta (deg) = 0.05793 rad (57.3 deg/rad) = 3.3 degrees
This is an extremely minute angular displacement which the
entire torso makes relative to its 'pivot'. This can be translated
into linear dimensions by using the fundamental definition of arc length:
theta = s/ R so s = theta x ® = 0.05793 rad (0.6m) = 0.0347 m
or 3.47 cm (1.37 inches)
Clearly, this is too small(see below) - but this does not mean the model
is necessarily wrong. For example, the *entire* mass of the torso is
taken into account, as opposed to just the head mass (as in Approach
#3). This again suggests the best interpretation may be that of a lower
bound on the dynamics, as opposed to a *unique* solution.
The above can be compared to an independent result obtained
by close examination of the key Z-film images (cf. TKOAP, p35)
and a knowledge of the film timing, and geometry. Thus:
The frame Z-312 establishes a good initial position for the
head (lined up against the limo door on the other side - just 1/18 sec
before the shot. Remember the Z-film moves at 18.3 frames/sec so this
would be just into Z-313 for the beginning of the reaction time. )The
other frame on the page (Z-321) shows the most rearward position.
From the best estimates I've been able to make -along with some others,
the distance traveled *across*- the CG of the head along the arc from
Z-312->321 is ~ one foot. However, the head is moving clearly in
3-dimensions here - not only front to back but *also* to the other
(left) side of limo. I estimate the leftward deflection distance at
anywhere from 1.5 to 2'.
Thus we have the (simplified situation where I am even ignoring the
third dimension - for downward tilt of head - though I compensate
somewhat by using the upper bound of R-L displacement 2'):
y
!
!1.5' - 2'
!
!
!-----------x
1'
What we want as the head displacement d is therefore the diagonal
displacement d = (xy) = SQRT[2^2 + 1] = SQRT(5) (taking the upper limit
of leftward distance) d = 2.24 f. The frame separation is 321 - 313 = 8
or (in time) 8/18.3 = 0.43 sec. The velocity from this works out to: v =
2.24 f/ 0.43s = 5.2 f/s = 1.6 m/s (approx.), or within the possible
error of a value cited by many observers, including D. Hixon (a
'lnutter')in 1994.
This (empirically) obtained value, discloses that one or more
inputs were underestimated in the torque model.
3a. So, a jet effect such as some have proposed would not create this+
No - not from detailed analyses I have done, as well as reconstructions
and simulations of Alvarez' methods. The magnitude of the 'jet' is
simply nowhere near as large as the pure, first order dynamical
effects. (See also treatment 1(b) above)
3b. But certainly, isn't it true that if the head is driven back a
certain amount - say one foot, the shooter should be driven back the
same amount, and maybe lose balance and fall over?
The movement of JFK's (or anyone's) body/head is not exclusively the
result of transfer of momentum. Complete treatment of a system requires
energy in addition. Energy (KE) varies as the *square* of the velocity.
Energy transferred, e.g. from bullet to body - would therefore also
depend on this.
The shooter's upper body is *not* required to move back a comparable
distance for three reasons:
1) The force and therefore impulse produced (I =Ft) will not be as great
for a recoiling rifle as for a bullet impacting a head. The Force (and
impulse)depend on the *rate* the velocity changes which is more
important for the bullet than for the recoiling rifle.
2) The pressure exerted by a bullet on impact with a body part (p = F/A)
is greater than for a recoiling rifle - since the force F(b) in the former
case is distributed over vastly less area (A) - essentially the
cross-section area of the bullet. The force F® in the latter case is
vastly diminished by being distributed over a much *larger* area
(the area of the base of the rifle stock).
3) The energy (kinetic) transferred from bullet to body is much larger
than the energy transferred from recoiling rifle to body - since the
velocity of the bullet is so much larger than recoiling rifle (and KE
varies as *square* of velocity)
The above explains why the common objection that - 'a 180 lb. man
shooting would be knocked backwards' is totally spurious.
3a. Is there a new version of the Zapruder film now available?
Yes, it is produced by MPI Video and is entitled 'Image of an Assassination'.
According to press reports (cf. The Baltimore Sun, July 16, 1998, p. 1E)
"it went on sale for $16.99at video outlets."
3b How is it different from the version shown before on newsreels,
documentaries?
As noted in a recent Baltimore Sun article ('History Comes toYour VCR;,
July 16, 1998, p. 1E, by Bob Hiassen):
"Besides a lengthy behind the scenes look at the restoration, the
documentary ends with a flurry of new versions of the famous sequence
- including slow motion and zoom versions, where technology keeps
President Kennedy front and center in each frame. Even the rectangles
of blank film caused by the sprockets of Zapruder's camera have been
restored to reveal, if nothing else, additional scenery."
4. Can the actual shot timing be deduced from either film?
Yes - a dispassionate analysis of the film - taking into account
facial reactions (using jiggle analysis), and the reactions of both
JFK and Connally(7, p20-37). We must also reckon in the
missing frames (155-56), otherwise the firing begins erroneously
late. (1, p185-191). The results are estimated as follows (there
remains some disagreement, because one or more other frames
appear to have been removed from the Z-film, cf : 12, pp. 70-72).
Shot 1 (miss) at Z150-52: Shows crowd reactions at missing frames
(155-56), JFK too.
Shot 2 (throat shot): at Z-207; JFK reacts by Z220.
Shot 3 Connally shot(1st time), at 236-7, note his rotation motion,
dropping of right shoulder. However, he still holds his Stetson so his
wrist still not hit.
Shot 4 (fatal head shot), at Z312-13
Shot 5 Connally shot(2nd time) in wrist and thigh, at Z328 (approx.)
Shot 6? Tague sprayed with pavement (could be simultaneous with #5)
Interestingly, this matches the results of the acoustic analyses
performed by the Weiss group, which found "at least four shots that
were scientifically provable, and at least two more impulses with
an extremely high probability of being additional shots." (1, p224).
An additional point, is that the neck shot and Connally's shot are
separated by barely 29 frames, or about 1.6 seconds. This means that
two rifles would have been needed. (The Mannlicher-Caracano's bolt
action limited it to one shot every 2.25 secs.)
The Ramsey Panel analysis (see previous section) is alleged to have
'refuted' the original study, but in fact only showed that the Weiss group
had omitted some considerations. The Ramsey analysis certainly does
not 'nullify' the Weiss/Barger analysis since up to now it has not been
reproduced, so cannot be accepted as a bona fide scientific conclusion
(I place it in roughly the same category as the 'cold fusion' claims of Pons
and Fleischmann regarding some years ago - for which reproducible results
were never forthcoming). Bear in mind also, that the Ramsey Panel was
not comprised of actual acoustic scientists (personal communication, A.
Marsh). This dilutes the value of their re-test even further.
4a But why can there be no agreement on the shot timing?
You have touched on a matter with explosive political and other
implications, as well as uncertainties (i.e. human reaction times).
Given these factors, there is bound to be significant disagreement
in interpreting when the shots occurred. Even then, these may be merely
confused with the times that *reaction* took place. Interpretation is
also contingent upon the filters through which one views the Zapruder
and Nix films. For example, if one adopts a 'lone nut' filter, which
limits the shot total to 3, then clearly there must be a massive
'compression' of shots (massive expansion of shot-to-wounds ratio) -
with two or more condensed to one, and one producing 7 wounds (as the
magic bullet theory requires). But - as we already saw, with the
anatomical error in wound placement ('base of neck' instead of in upper
back) and neutron activation analysis - that 'compressed'
bullet/shot scenario is no longer viable. Hence, at the very *minimum*
there must be at least four shots, and more likely five. Where
exactly these occur - in the respective running of the films, is what
must now be resolved.
Sources: Referenced as in previous 2 sections -
1 'High Treason', 1989: Groden, R.J. and Livingstone, H.E.
3 'Killing the Truth', 1993: Livingstone, H.E.
5 'The Assassination of John F. Kennedy', 1992, Duffy, J.P. & Ricci,
V.L.
7 'The Killing of a President', 1994: Groden, R.J.
10 'JFK: Conspiracy of Silence', Crenshaw, Charles A.
11 'Rush to Judgment': 1964, Lane, Mark
12 'Killing Kennedy - and the Hoax of the Century', 1995,
Livingstone, H.E., Carroll & Graf.
Also:
Video: 'The Plot to Kill JFK: Rush to Judgment' (A film by Emile
de Antonio and Mark Lane), MPI Home Video, 1986.
Video: 'The Two Kennedys', (A Ben Barry & Associates Release),
1976, Overseas Cinema Resource Establishment (A film by
Gianni Bisiach).
---------------------------------------
3D. The Rifle(s) used:
[color=white][FONT=Couri...