Mechanics of an Assassination

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Herbert Blenner
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Mechanics of an Assassination Jan 15, 2019 12:51:08 GMT -5

Post by Herbert Blenner on Jan 15, 2019 12:51:08 GMT -5

Debunking the Tumble Theory - I
by Herbert Blenner | Posted June 16, 2001

To tumble or not to tumble was never part of the tumble theory critique. Critics based their objections on the acceleration problem.

The Single Bullet Theory, SBT, says one bullet made a small exit hole in Kennedy's throat, tumbled about one-quarter of a revolution, then made a large entrance wound in Connally's back. We know this explanation of the small exit and large entrance wounds as the tumble theory.

Critics of the tumble theory quickly pointed out that this bullet did not have enough time while going through Kennedy to reach a sufficiently high tumble speed. Opponents of these critics, almost immediately blunted the challenge to the SBT. They proclaimed the critics were wrong and asserted the bullet was tumbling fast enough to make one-quarter of a revolution while traveling between Kennedy and Connally. Ever since this initial debate in 1964, people remember the critics of the tumble theory as those who claim the bullet was not tumbling fast enough.

If we place this dispute in a more familiar setting, we can appreciate what they were saying. Suppose someone said that during a blink of an eye a car went from zero to sixty miles per hour. Nobody would object to the claim that a car reached a speed of sixty miles per hour. However, critics would protest that a blink of the eye does not give the car enough time to reach sixty miles per hour and they would be correct.

Here the critics raised the same objection as the critics of the tumble theory. In both cases they understood and did not explicitly state that acceleration of cars or bullets are limited. This limitation on acceleration restricts the speed that a car or a tumbling bullet can reach in a given time.

We are aware of one limitation on the acceleration of a car. If we try to speed up too rapidly our tires skid and we lose acceleration. Our tires also limit how rapidly we come to a stop. If we apply the brakes too hard, our tires skid and we lose braking force.

Tires are not the only limitation on acceleration and deceleration. Suppose we were traveling at sixty miles per hour when we struck a steel wall. The car will not stop instantaneously. The decelerating force would increase until the car began to crush. This would lengthen the time for the car to stop and limit the deceleration. Ultimately the strength of materials limits acceleration or deceleration.

The single bullet had limited strength. We know the force on this bullet while passing through Kennedy was less than its crushing value. This constraint sets an upper limit on how rapidly the tumble speed of the single bullet increased. Limited acceleration of the single bullet was one factor in the critique of the tumble theory.

Herbert Blenner
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Mechanics of an Assassination Jan 15, 2019 12:51:42 GMT -5

Post by Herbert Blenner on Jan 15, 2019 12:51:42 GMT -5

Debunking the Tumble Theory - II
by Herbert Blenner | Posted July 17, 2001

In 1964, a riddle circulated within the technical community. They asked, "What happens to a fast moving bullet?" Their punch line was, "Very, very little!"

The tumble theory died of a birth defect. Arlene's specter was born without an impulse. (1) According to the initial autopsy information the single bullet passed through Kennedy without striking a bone. Clearly collision between the bullet and homogeneous tissue could not induce any tumbling.

Before they could bury the tumble theory, something astonishing happened. While reviewing an autopsy x-ray, they found the single bullet struck a glancing blow to a bone. This discovery of the missing impulse resuscitated the tumble theory.

A rapid pace made life difficult for the tumble theory. First they demanded the bullet tumble one-quarter of a revolution while traveling between Kennedy and Connally. At 1600 feet per second, the single bullet had less than two-thousandths of a second to tumble. (2)

The single bullet could live while tumbling at more than 1000 radians per second. (3) However, the rapid pace of the single bullet caused complications. An initial symptom was the mere 0.00003 second for the single bullet to accelerate. (4) Shortly afterwards, the tumble theory developed hyperangular acceleration. Preliminary examination showed the tumble theory had a life threatening acceleration count of nearly 37 million radians per second per second. (5) They immediately consulted specialists.

At first the specialists were optimistic. The single bullet was small and had a minuscule moment of inertia. They hoped the tumble theory could survive a torque of 24 lb ft. (6) Their hope turned to despair as they realized the small bullet had a moment arm of one-fortieth of a foot. Grimly they calculated an accelerating force of more than 900 pounds (7) and a reaction force of nearly 1300 pounds (8) from the struck bone. As the specialists advised them to make arrangements, alarms on life monitors sounded. The vital signs of the tumble theory ebbed to dangerous levels.

Experts placed the tumble theory on life support. They performed a radical numerallectomy and the tumble theory lived happily ever after. Well almost happily, those damning numbers kept growing back.

Last Edit: Jan 15, 2019 12:52:50 GMT -5 by Herbert Blenner

Herbert Blenner
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Mechanics of an Assassination Jan 15, 2019 12:52:23 GMT -5

Post by Herbert Blenner on Jan 15, 2019 12:52:23 GMT -5

Notes
(1) Newton equated change in motion to the impulse.

(2) Given:
Distance between Connally and Kennedy = 2.33 ft.
Speed of bullet = 1600 ft/sec
Calculate time of travel:
2.33 ft/1600 ft/sec = 0.0014 sec

(3) Given:
Bullet rotated ninety degrees (pi/2 radian)
Calculate angular speed:
1.57 radian/0.0014 sec = 1078 radian/sec

(4) Given:
Length of bullet = 0.1 ft
Speed of bullet during collision = 1700 ft/sec
Calculate duration of collision
.05 ft/1700 ft/sec = 0.000029 sec
Note: The half length of the bullet is the most favorable length to induce net rotational acceleration.

(5) Given:
Change in angular speed = 1078 radian/sec
Duration of collision = 0.000029 sec
Calculate angular acceleration
(1078 radian/sec)/(0.000029 sec) = 36,600,000 radian/sec2

(6) Given:
Moment of inertia of bullet = 0.000000651 slug ft2
Calculate accelerating torque:
(0.000000651 slug ft2)(36,600,000 radian/sec2) = 23.83 lb ft

(7) Given:
Average moment arm = 0.025 ft
Note: The moment arm varies linearly from zero to the half length of the bullet. This gives an average moment arm length of one-quarter the length of the bullet
Calculate accelerating force:
(23.83 lb ft)/(0.025 ft) = 953 lb

(8) The most favorable circumstance to induce angular acceleration occurs when the reaction force acts at a 45-degree angle to the moment arm.
Under the best conditions the reaction force becomes 1,348 lb.

by Herbert Blenner | Posted July 17, 2001

Herbert Blenner
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Mechanics of an Assassination Feb 13, 2019 20:38:26 GMT -5

Post by Herbert Blenner on Feb 13, 2019 20:38:26 GMT -5

Reflections on Deflection

by Herbert Blenner | Posted March 2, 2003

An analysis of the deflection of a bullet by an obstacle has produced the following results. This analysis, which is discussed later, assumes the obstacle can provide sufficient deflecting force and the bullet deflects without fragmentation.

In particular the base of an acute triangle, OB represents the incoming momentum of the bullet. A line segment, CB represents the deflecting momentum. The line segment, OC, corresponds to the outgoing momentum of the bullet.

Details of the collision between the bullet and the obstacle determine the angle of the deflecting momentum, OBC. This complication at first appears to render solution of this problem impractical. However the deflecting momentum must be equal or less than the incoming momentum of the bullet and vanish when angle OBC is ninety degrees. This suggests the deflecting momentum equals the impulse from the obstacle times the cosine of angle OBC.

Calculations show that as the angle of deflecting momentum increases from zero, the deflection angle of the bullet increases, reaches a maximum then decreases. This result is not surprising since the magnitude of the deflecting momentum decreases with its increasing angle. The idea of a maximum deflection angle of the bullet permits solution without knowledge of orientation of the bullet or shape of the obstacle.

Last Edit: Jun 23, 2019 21:29:48 GMT -5 by ADMIN

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Mechanics of an Assassination Feb 13, 2019 20:45:39 GMT -5

Post by Herbert Blenner on Feb 13, 2019 20:45:39 GMT -5

Energy Crisis
by Herbert Blenner | Posted October 16, 2006 -Revised October 27, 2007

Scientists at the Edgewood arsenal fired bullets from the MC rifle directly into obstacles simulating the neck of President Kennedy and Governor Connally's chest and wrist. Their experiments provide data to test the yaw explanation of the size of Connally's back wound.

The Edgewood tests showed that the simulation of Kennedy's back deformed test bullets to an extent comparable with CE 399 and the simulations of Connally's back and wrist deformed the test bullets to a greater extent than CE 399. From these results, they concluded that the bullet, which inflicted wounds on Connally had slowed considerably before striking.

The experimenters had no way of predicting the details of bullet impact upon the bones. So they placed their velocity screens along a straight line extending from the shooter through the target. As a result they failed to obtain data on bullets, which deflected through larger angles during a prolonged grazing collision with a bone.

Source: Warren Commission testimony of Dr. Alfred G. Olivier
Mr. SPECTER. What was the velocity of the missile at the time it struck the wrist depicted in 854 and 855?
Dr. OLIVIER. The average striking velocity was 1,858 feet per second.

Mr. SPECTER. Do you have the precise striking velocity of that one?
Dr. OLIVIER. No; I don't. We could not put velocity screen in front of the individual shots because it would have interfered with the gunner's view. So we took five shots and got an average striking velocity.

Mr. SPECTER. When you say five shots with an average striking velocity, those were at the delineated distance without striking anything on those particular shots?
Dr. OLIVIER. Right, and after establishing that velocity, then we went on to shoot the various arms.

Mr. SPECTER. And what was the exit velocity?
Dr. OLIVIER. On this particular one?

Mr. SPECTER. If you have it?
Dr. OLIVIER. Yes. Well, I don't know if I have that or not. We didn't get them in all because some of these things deflect. No, I have no exit velocity on this particular one.

Mr. SPECTER. What exit velocity did you get on the average?
Dr. OLIVIER. Average exit velocity was 1,776 feet per second. This was for an average of seven. We did 10. We obtained velocity on seven.

Mr. SPECTER. Would the average reduction be approximately the same, in your professional opinion,
as to the bullet exiting from the wrist depicted in 854 and 855?

Dr. OLIVIER. Somewhat. Let me give you the extremes of our velocities. The highest one was 1,866 and the lowest was 1,664, so there was a 202-feet-per-second difference in the thing. Some of the cases bone was missed, in other cases glancing blows. But I would say it is a close approximation to what the exit velocity was on that particular one.

A penetrating collision produces negligible deflection of the bullet. Here the penetrating bullet alters the shape of the impacted obstacle so that the direction of the force from the obstacle is opposite the direction of the bullet. So penetration slows the bullet without changing its direction of motion.

During a grazing collision the force from the obstacle upon the bullet is perpendicular to the surface of the obstacle at the point of impact. The direction of this force differs from the bullet's direction of motion. As a result the direction of the bullet changes throughout the duration of the grazing collision. They measure the net change in direction by the deflection angle.

This consideration explains how a bone may deflect a bullet without leaving radiological evidence.

Although the force upon the bullet from a grazing collision is less than the force from a penetrating collision, these forces act over widely varying distances. So the change in kinetic energy of the bullet from a grazing collision maybe larger than for a penetrating collision.

Deflection changes the yaw of a bullet without necessarily inducing yawing. When the action of a force from a grazing collision is asymmetrically distributed about the center of gravity of the bullet, the tangential component of this force produces yawing in addition to deflection. For this reason any obstacle that causes yawing also deflects the bullet. However, the converse of the preceding statement is not always true. An obstacle can deflect a bullet and change its yaw without inducing yawing. In this later case the action of the force is symmetrically distributed about the center of gravity.

The above considerations show that the Edgewood data on relatively undeflected bullets transited and exited the simulations with negligible yaw. This result enables testing the yaw explanation of the sizes of Connally's wounds.

Source: Warren Commission Appendix X, Tests Simulating President Kennedy's Neck Wound
After reviewing the autopsy report on President Kennedy, the Edgewood scientists simulated the portion of the President's neck through which the bullet passed. It was determined that the bullet traveled through 13.5 to 14 centimeters of tissue in the President's neck. That substance was simulated by constructing three blocks: one with a 20-percent gelatin composition, a second from one animal meat and a third from another animal meat. Those substances duplicated as closely as possible the portion of the President's neck through which the bullet passed. At the time the tests were conducted, it was estimated that the President, was struck at a range of approximately 180 feet, and the onsite tests which were conducted later at Dallas established that the President was shot through the neck at a range of 174. 9 feet to 190. 8 feet. At a range of 180 feet, the Western bullets were fired from the assassination weapon, which has a muzzle velocity of approximately 2,160 feet per second, through those substances which were placed beside a break-type screen for measuring velocity. The average entrance velocity at 180 feet was 1,904 feet per second.

To reconstruct the assassination situation as closely as possible both sides of the substances were covered with material and clipped animal skin to duplicate human skin. The average exit velocity was 1,779 feet from the gelatin, 1,798 feet from the first animal meat and 1,772 feet from the second animal meat.

Using the measured entrance and exit speeds with the revised mass, 7.27 X 10-4 slug, of a MC bullet permits calculation of the kinetic energy lost during transit of the simulated target.

The loss of kinetic energy by the bullet equals the length of the wound track multiplied by the mean force. Since the mean force equals the mean yield stress of the target multiplied by the striking area, the loss of kinetic energy by the bullet is proportional to striking area of the bullet. So when the yaw angle increases the striking area by a factor k, the loss of kinetic energy increases by the same factor. This consideration enables calculation of the largest striking area for the bullet to exit the simulated chest.

The bullet at the striking speed of 1929 fps has a kinetic energy of 1352 ft-lb. For a striking area of 0.049 sq-in the bullet lost a kinetic energy of 346 ft-lb. So the loss of kinetic energy by an exiting bullet can increase by a factor k = 1352 ft-lb / 346 ft-lb or 3.91. Taking the striking area of the yawed bullet, 0.049k, as a rectangle gives a wound whose width is 2r or 0.25 inch and length is 0.049k / (2r) or 0.77 inch.

Combining results from Kennedy's simulated back and neck wounds with Connally's simulated back and chest wounds produce a more realistic description. The test bullet exited the simulated neck with a speed of 1743 fps, lost 3 fps while traveling between targets and struck Connally's simulated back with a speed of 1740 fps. Now the available kinetic energy becomes 1100 ft-lb and reduces k to 3.18. So the dimensions of the rectangular wound become 0.25 inch by 0.62 inch.

The medical evidence documents the longest dimension of Connally's back wound as 0.6 inch. So without the additional burdens of transiting the wrist and penetrating the thigh, attributing the length of Connally's back wound to yaw is marginally feasible.

Source: Warren Commission Appendix X, Tests Simulating Governor Connally's Wrist Wounds
Following procedures identical to those employed in simulating the chest wound, the wound ballistics experts from Edgewood Arsenal reproduced, as closely as possible, the Governor's wrist wound. Again the scientists examined the reports and X-rays from Parkland Hospital and discussed the Governor's wrist wound with the attending orthopedic surgeon, Dr. Charles F. Gregory. Bone structures were then shot with Western bullets fired from the assassination weapon at a distance of 210 feet. The most similar bone-structure shot was analyzed in testimony before the Commission. An X-ray designated as Commission Exhibit No. 854 and a photograph of that X-ray which appears as Commission Exhibit No. 855 show a fracture at a location which is very similar to the Governor's wrist wound depicted in X-rays marked as Commission Exhibits Nos. 690 and 691.

The average striking velocity of the shots was 1,858 feet per second. The average exit velocity was 1,786 feet per second for the 7 out of 10 shots from bone structures which could be measured. These tests demonstrated that Governor Connally's wrist was not struck by a pristine bullet, which is a missile that strikes an object before hitting anything else. This conclusion was based on the following factors: (1) Greater damage was inflicted on the bone structure than that which was suffered by the Governor's wrist; and (2) the bone structure had a smaller entry wound and a larger exit wound which is characteristic of a pristine bullet as distinguished from the Governor's wrist which had a larger wound of entry indicating a bullet which was tumbling with substantial reduction in velocity. In addition, if the bullet found on the Governor's stretcher (Commission Exhibit No. 399) inflicted the wound on the Governor's wrist, then it could not have passed through the Governor's wrist had it been a pristine bullet, for the nose would have been considerably flattened, as was the bullet which struck the bone structure, identified as Commission Exhibit No. 856.

In a composite situation with the bullet striking a simulation of Kennedy with a speed of 1904 fps, acquiring a yaw, transiting the simulations of Connally's chest and wrist to emerge with negligible speed requires the factor k to be 1100 ft-lb / ( 346 ft-lb + 95.3 ft-lb ) or 2.49. Allowing an additional loss of 20 ft-lb for the bullet to penetrate a simulated thigh gives the bottom line for the yaw explanation of a single bullet event. The factor k becomes 1100 ft-lb / ( 346 ft-lb + 95.3 ft-lb + 20 ft-lb ) or 2.39. The longest dimension of the rectangular wound is 0.47 inch and discredits the yaw explanation of Connally's back wound.

Source: Warren Commission Appendix X, Conclusions From Simulating the Neck, Chest, and Wrist Wounds
Thus, the Governor's wrist wound indicated that the bullet passed through the President's neck, began to yaw in the air between the President and the Governor, and then lost substantially more velocity than 400 feet per second in passing through the Governor's chest. A bullet which was yawing on entering into the Governor's back would lose substantially more velocity in passing through his body than a pristine bullet. In addition, the greater flattening of the bullet that struck the animal's rib (Commission Exhibit No. 853) than the bullet which presumably struck the Governor's rib (Commission Exhibit No. 399) indicates that the animal bullet was traveling at a greater velocity. That suggests that the bullet which entered the Governor's chest had already lost velocity by passing through the President's neck. Moreover, the large wound on the Governor's back would be explained by a bullet which was yawing although that type of wound might also be accounted for by a tangential striking.

Clearly the above analysis shows the impossibility of attributing the dimensions of Connally's back and wrist wounds to a single bullet with yaw inflicting seven wounds on two victims.

An accounting of kinetic energy shows the infeasibility of wounding by a pristine bullet. The loss of kinetic energy by a pristine bullet in producing the neck, chest, wrist and thigh wounds would be 213 ft-lb + 346 ft-lb + 95.3 ft-lb + 20 ft-lb. These wounds diminish the initial kinetic energy of 1317 ft-lb by 674 ft-lb. So a single bullet event requires means to consume an additional kinetic energy of 643 ft-lb. Although the earlier considerations show that the yaw angle of a bullet can consume far more than 643 ft-lb, the experimental design excluded grazing collisions that consume considerable kinetic energy while deflecting and yawing the bullet. Without doubt attributing the consumption of 643 ft-lb to yaw is unsupportable, especially when the shapes and positions of Kennedy's back and neck wounds require a considerable deflection of the transiting bullet.

Last Edit: Feb 12, 2020 22:18:11 GMT -5 by ADMIN