4. THE TRAJECTORY ANALYSIS*
- A trajectory is the path taken through space by an object such as a missile or bullet. In general, the trajectories of missiles are curved because of factors such as gravity and aerodynamic forces. Nevertheless, in the case of high speed bullets traveling short distances, the curvature is typically slight. (40) In such cases, the effect of aerodynamic forces is small both because the projectile flies almost perfectly nose-on through the air and because any small side-to-side movements tend to cancel one another by virtue of the bullet's spin. (41) The effect of gravity is similarly slight, and can be easily calculated. For a total flight path of 200 feet at 2000 feet per second (the speed of a bullet from a moderate performance rifle), the time in flight is one tenth of a second. During this period, gravity deflects the flight path only two inches.(42) A high performance rifle bullet would be deflected even less because it is traveling faster and its time in flight is shorter. It is, therefore, permissible to characterize the trajectory of each bullet fired at the President as a straight line extending between rifle and victim.
- In connection with the trajectory analysis, the Panel undertook to answer three questions:
* This section was prepared under the direction of Thomas N. Canning, with the assistance of Clyde C. Snow and C.S. McCamy. For the related public hearing testimony of Canning and McCamy, see HSCA-JFK Hearings, 9/12/79, vol. II, pp. 142-203.
- 1. What were the trajectories of the bullets that struck the President?
- 2. Is the trajectory of the bullet that caused the President's back and neck wounds consistent with the single bullet theory?
- 3. Given the trajectories, from where were the bullets fired?
- A straight line trajectory can be constructed once, my two points the missile is known to have passed have been established. In the present study, the inshoot and outshoot wounds inflicted by the bullets that struck President Kennedy and Governor Connally' were used as the two points.
- In order to calculate the trajectory based on these wound pairs, it was necessary to establish the position of each entry and exit point in space at the time it was inflicted. This requires that three determinations be made:
- 1. The location of the wounds relative to recognizable reference features of the victim had to be established. Ideally, this information could be expressed in terms of a measured distance left or right from the midplane of the body along well-defined directions in reference to clear external features such as all ear or elbow.
- 2. It was necessary to determine the angular orientation of the wounded part of the victim relative to his immediate surroundings-that is to say, in what direction he was facing, what his inclination was forward or backward, and to which side he was leaning and by how much.
- 3. It was necessary to know where the victim was located relative to his surroundings, i.e., the location of the victim within the limousine and the location of the limousine relative to known landmarks in Dealey Plaza.
- The requisite information for undertaking this particular trajectory analysis could not be accurately obtained from any single source. Consequently the committee asked its various scientific consultants to provide input from their areas of expertise. The Forensic Pathology Panel was responsible for providing, to the extent possible, the precise locations of the wounds sustained by Kennedy and Connally.* It relied on enhanced postmortem photographs and X-rays of President Kennedy which were produced by the Photographic Evidence Panel. Enhanced photography was further used in the effort to determine the precise orientation of President Kennedy at the time of the assassination. The Photographic Evidence Panel also assisted in the interpretation of motorcade photographs of Kennedy and Connally and in providing photogrammetrically derived measurements of critical aspects of the photographs. Finally, the actual placement of the presidential limousine in the Dealey Plaza area at the time of the shots was established through a photogrammetric analysis conducted by the U.S. Geological Survey (USGS).
* While the Forensic Pathology Panel did provide this information, the actual measurements related to wound locations were determined by the NASA scientist who was responsible for supervising the trajectory project. He was in frequent consultation with members of the Forensic Pathology Panel and with forensic anthropologists from both the FAA's Civil Aeromedical Institute and the Smithsonian Institute.
- All the preceding information was compiled under the supervision of Thomas N. Canning, an engineer from the Space Project Division of NASA, who then was responsible for constructing the actual trajectories. In contrast to the trajectory analysis performed by the Warren Commission, (44) the investigative procedures and analyses in this instance were governed by the hypothesis that there was no other evidence (e.g., the discovery of bullet cartridges and a rifle in the Texas School Book Depository) concerning the source of the shots.
- Although all of the available scientific evidence indicated that President Kennedy and Governor Connally were struck by total of two bullets, one hitting President Kennedy in the back and continuing through to enter Governor Connally after exiting President Kennedy's neck, and the other hitting President Kennedy's head three different trajectories were constructed: One based on the entry and exit wounds to President Kennedy's head, another on President Kennedy's back-neck wounds, the last on the exit wound to President Kennedy's neck and the entry wound to Governor Connally's back. The first two trajectories were constructed for the purpose of determining whether the two shots were fired from the same location and the third to determine whether the relative alignment of President Kennedy and Governor Connally in the limousine was consistent with the single bullet theory.
- Kennedy's head wounds.--The bullet that caused Kennedy's head wounds at Zapruder frame 312 came from a point 29° to the right of true north from the President. The bullet was descending at an angle of 16° below horizontal as it approached him. This trajectory intercepted the plane of the Texas School Book Depository approximately 11 feet west of the southeast corner of the building at a point 15 feet above the sixth floor windowsills.
- Kennedy's back and neck wounds.--The bullet that caused President Kennedy's back and neck wounds came from a point 26 to the right of true north from the President. It was descending at an angle of 21° below horizontal as it approached him. Extending this trajectory from the position President Kennedy occupied at the time of Zapruder frame 190, the trajectory intercepted the plane of the Texas School Book Depository approximately 11 feet west of the southeast corner and 2 feet lower than the sixth floor windowsill.
- Kennedy neck and Connally back wounds.--The bullet which caused President Kennedy's neck wound and Governor Connally's back wound came from a point 27° to the right of true north from the President and was descending at an angle of 25° below horizontal.
* USGS was asked to determine the position of the limousine at times corresponding to Zapruder frames 150, 190, 285, 313, and 413; however, because some of these frames did not provide the required visual. coordinates, the nearest frame with sufficient reference points was used.
No trajectory analysis based solely on the wounds suffered by Connally was attempted because the bullet that struck him in the back hit at least two bones (at oblique angles) and was consequently significantly deflected.
3 Explanatory diagrams supporting these conclusions are set forth in the analysis section of this report.
- Given the position of the two men at the time of Zapruder frame 190, the trajectory intercepted the plane of the Texas School Book Depository 2 feet west of the southeast corner and 9 feet above the sixth floor windowsill. Because this trajectory falls within the trajectory range established when President Kennedy's back-neck wounds are used as the reference points for the trajectory line, the Panel concludes that the relative alignment of President Kennedy and Governor Connally within the limousine is consistent with the single bullet theory. Further, since each of these trajectories intersects the plane of the Texas School Book Depository in the vicinity of the southeast corner of the sixth and seventh floors, it is highly probable that the bullets were fired from a location within this section of the building.*
(1) The head wound case*
- To determine this trajectory, the Panel first had to locate the entrance and exit head wounds as precisely as possible. Figures II-6 and II-7 show where the fatal bullet entered the back of President Kennedy's head at a point 9.0 centimeters above the external occipital protuberance. (45) This distance was measured on postmortem X-rays from point to point, The entry point is 1.8 centimeters to the right of the midplane of his skull. The bullet passed forward through his head and exited at the right coronal suture at a point 11 centimeters forward of the entry wound and 5.5 centimeters to the right of the midplane. This exit point was 1 centimeter lower than the entrance wound, using as the exterior vertical reference a line drawn through the President's brow and upper lip. Thus the bullet was traveling 18.6° to the right relative to his midplane and 5.0° downward relative to his facial axis.
*The above conclusions differ to some extent from the testimony given by Thomas N. Canning before the House Select Committee on Assassinations on Sept. 12, 1978, in each case, the differences reflect new information or analysis resulting from work concluded subsequent to the presentation of preliminary findings at the hearing.
*The interpretation of the head wounds used in defining trajectory reported in testimony on Sept. 12, 1978 differs from this report because the final illustration from the Forensic Pathology Panel showed the exit wound to be 1 centimeter lower than the entrance, rather than level with it as had been concluded earlier. Thus, the resulting trajectory is somewhat steeper.
- Once these wound locations were established, derivation of the bullet's trajectory still required knowledge of the orientation of Kennedy's head relative to Dealey Plaza. Establishing this relationship from the photographs was most easily accomplished in two steps: (1) finding the position of Kennedy's head relative to the line of sight to Zapruder's camera, and (2) accounting for the orientation of that line relative to the entire Dealey Plaza area.
- The Zapruder and Nix films showed the position both of Kennedy's head and of suitable reference structures in the field of view such as walls, street lights, and curbs. Since Kennedy's head is seen exploding in frame 313 of the Zapruder film, frame 312, which was exposed 0.055 seconds earlier, was considered to be the most important photograph available for this aspect of the trajectory analysis. (See JKF exhibit F-254.)
- The key features to be analyzed in frame 312 with respect to determining the orientation of Kennedy's head, were the lateral and vertical position of his right ear relative to the outline of the head and the overall relationship between his ear, nose and eyebrow. Rather than basing the analysis on a purely subjective interpretation, orientation was determined by comparing these features, as they appeared in an enhanced print of Zapruder frame 312 (see fig. II-5, JFK exhibit F-134), with a series of calibration photographs of a replica of Kennedy's head prepared by the Civil Aeromedical Institute of the FAA's Aeronautical Center.* These calibration photographs were taken from many carefully measured aspects (lines of sight), including several which closely approximated the relative location of Zapruder's camera at frame 312. (See fig. II-9, JFK exhibit F-141.)
FIGURE II-9.-- JFK exhibit F-141 -- Calibration photograph corresponding with Zapruder frame 312.
- After studying those photographs most closely approximating the correct aspect, it was possible to determine, by comparing the positions of such. features as Kennedy's ear relative to other parts of his head,-the aspect from which Zapruder's. camera viewed Kennedy. On this basis, it was determined that Kennedy was turned partially away from Zapruder--approximately 25°past the 90°, or profile, direction. His head was tilted away from Zapruder by about 15 ° and he appeared to be nodding forward by about 11 °(clockwise, as viewed by Zapruder).
- In order to obtain a similar set of relationships relative to landmarks in Dealey Plaza, it was necessary to establish the orientation and position of this line of sight. Its direction and the point where it intercepts Kennedy's head were determined by drawing a line on a scaled map of Dealey Plaza between Zapruder, whose position had been derived from other photographs and testimony, and Kennedy at the geographic position on the street corresponding to the Limousine's location at the time that Zapruder frame 312 was exposed. The latter was determined by relying on the photogrammetric analysis of the USGS. (46)* (See fig. II-10, JFK exhibit F-133.) The slope of this line was calculated by considering the relative heights of both the pedestal on which Zapruder was standing and of the street at the point where the limousine was located at frame 312 and then measuring the distance between Zapruder and Kennedy.
* The construction of the replica and the taking of the calibration photographs are described in addendum A, at par. 169-176 infra.
- The pedestal on which Zapruder stood was 12 feet above the point on Elm Street occupied by Kennedy at the time of Zapruder frame 312. When both the, height at which the camera was held and the height of Kennedy's head above the street were considered (about 5 feet and 4 feet, respectively), the camera was determined to have been about 13 feet higher than Kennedy. The distance between Kennedy and Zapruder was about 70 feet at the time of the fatal shot. (See fig. II-10, JFK exhibit F-133.) Given this, height difference and the distance between the two men, a line of sight downward from Zapruder to Kennedy was computed to be at an angle of 10°.
Figure II-10 -- JFK exhibit F-133.
- Once these factors had been established, the geometric relationship between the line of sight from Zapruder's camera and the trajectory line defined by the inshoot and outshoot wounds in Kennedy's head was determined.
- A physical reconstruction, consisting of a wooden mockup based on the photographic analysis of Zapruder frame 312, was used. In the mockup, the camera line of sight was represented by a straight dowel. The midplane of Kennedy's head was represented by a flat piece of wood to which the line-of-sight dowel was affixed in a manner reflecting its relative slope and direction. A second straight dowel was installed vertically at the front of the midplane to represent the external facial axis defined by the forehead and upper lip. Finally, to simulate the location of the entry and exit wounds, two short posts were fastened to the midplane 11 centimeters apart and extending 1.8 and 5.5 centimeters outward on the same side as the line-of-sight rod. These posts were fitted with circular tips--one open and the other solid--to serve as sighting points. The positions of the posts relative to the facial axis and line-of-sight rods duplicated the positions of the wounds as located by the Forensic Pathology Panel.
*Because Zapruder frame 313 provided better reference points, the USGS used that frame to determine the location of the limousine. Based on the limousine's estimated average speed, an adjustment of 1 foot was made to locate the vehicle at frame 312.
- This assembly was then supported on a photographer's tripod in a laboratory so as to duplicate the slope of the line of sight of Zapruder's Camera and the inclination of the facial axis simultaneously. The direction of the line of sight in the laboratory was registered by mounting two plumb bobs on the line-of-sight rod and marking their positions on the level floor. The direction of the bullet trajectory in the-laboratory was similarly registered by mounting two plumb bobs on separate, movable supports that were positioned to correspond with the circular posts representing the wounds. The resulting (angle) between these two lines established the angle between the direction of the camera's line of sight and the direction of the bullet's trajectory.
- The slope of the bullet's trajectory was deduced by placing markers on the two plumb bobs Mined with the two posts (wounds). The difference in height of these two .markers above the laboratory floor and the distance between the two plumb bobs were used to calculate the slope of the trajectory.
- The direction and slope determined in the laboratory were then related to the real case by incorporating the same data on scale drawings developed from a topographic map of Dealey Plaza. First, the limousine and Kennedy's head were positioned in the drawing. Then the line of sight was drawn between Zapruder and Kennedy's head. Next, the direction angle derived from the laboratory replication was duplicated in order to arrive at the trajectory direction line on the Dealey Plaza map. This line was then extended rearward until it intercepted the face of the first building it encountered--a point approximately 11 feet west of the southeast corner of the Texas School Book Depository. (See fig. II-11.)
LINE OF SIGHT FROM ZAPRUDER CAMERA TO JFK DIRECTION OF BULLET CAUSING HEAD WOUND
FIGURE II-11.--This diagram depicts the line of sight from Zapruder's camera to President Kennedy and the trajectory direction of the bullet that caused the fatal head wound. Note that the limousine shown at the right is an enlargement of the one drawn in the middle of the diagram.
- In order to show the slope of the trajectory without distortion, it was necessary to develop an oblique elevation view shown in fig. II-12. This view is an orthogonal projection onto a vertical plane parallel to the bullet's trajectory. In this view, the resulting trajectory slope of 16° is shown to intersect the Texas School Book Depository at a point approximately 11 feet west of the southeast corner of the building and 15 feet above the sixth floor windowsills.*
* The revision in relative heights of the inshoot and outshoot wounds in Kennedy's head resulted in most of the difference in this trajectory from that presented in testimony before the House Select Committee on Assassinations on September 12, 1978. The remaining revisions resulted from the availability of a superior enhanced reproduction of Zapruder frame 312 for comparison with the calibration photographs.
LINE OF SIGHT FROM ZAPRUDER CAMERA TO JFK/SLOPE OF BULLET CAUSING HEAD WOUND
- A circle with a radius of 23 feet has been drawn around the intersect point in figure II-19 represents the estimated minimum reasonable margin of error for this trajectory analysis.* To derive this estimate of the margin of error, each step in the analysis was checked for possible errors. Factors such as the position of Zapruder and Kennedy and the height of the pedestal on which Zapruder stood were not considered significant sources of error. The major uncertainties related to the wound positions and the orientation of Kennedy's head relative to Zapruder.
- For example, of critical importance in comparing calibration photographs with Zapruder frame 312 was the apparent position of Kennedy's right ear in relation to his nose, brow and back of head. An error of 1.0°(equal to about 0.16 centimeter), in positioning the ear on the replica of the head would yield approximately 1.0° error in the deduced trajectory ** if not offset by other factors in interpreting the photographs or elsewhere. Similarly, establishing the relationship of those elements critical in determining the degree to which Kennedy's head was nodding forward (for example, the line from his brow to his upper lip relative to the slope of the street) also required careful and repetitious measurements to minimize errors. All measurements were made repeatedly, using as many independent image clues as could be found. The redundancy of the clues selected and the repetition of the studies, coupled with the probable random direction of any errors introduced, allows the Panel to conclude that a liberal estimate for the margin of error is about 5°(that is. a 23-foot radius around the intersect point at the Texas School Book Depository).
(2) The back-neck case
- According to the autopsy photographs, the first bullet to strike Kennedy entered his back slightly about his shoulder blade and slightly to the right of his backbone. (See fig. II-13.) This bullet passed through soft tissue hitting no bone, and exited at the front of his neck. (47) Independent determinations by the Photographic Evidence Panel showed the entrance wound to be from 4 to 5 centimeters from Kennedy's center plane and the exit wound to be on the center plane or as much as 0.5 centimeters to its left. When seen in the autopsy position, the outshoot wound was described as being at about the same height (or slightly higher) relative to the inshoot wound, The distance between the wounds was determined to be 14 centimeters.
*That is to say that the margin of error could be greater.
**A 1-degree error results in a movement of about 4 feet at a range of 250 feet.
FIGURE II-13 -- J.F.K. Wound locations Note: Distance between inshoot and outshoot wounds = 14 cm.
- Based on the acoustics results (48), the camera blur study (49) and the visual observations made by the Photographic Evidence Panel., (50) it was determined that Kennedy was struck by this bullet at a time corresponding approximately to Zapruder frame 190. Accordingly, to determine Kennedy's orientation at that point, frame 190 and adjoining frames were closely scrutinized. (51) (See JFK exhibits JFK F-225-227.)
- The best record of Kennedy's posture, torso inclination, and shoulder "bunching" is a photograph taken by Robert Croft at about the time of Zapruder frame 161. (52) (See fig. II-14, JFK exhibit F-135.) This correlation was established by the Photographic Evidence Panel by examining features in the Croft photograph and studying Croft's movements as recorded in the Zapruder film.
- In Croft's picture, Kennedy and other persons in the limousine are seen from a perspective that permits a reasonable determination of their posture and orientation. Kennedy's upper torso/neck region was inferred from this photograph to have been inclined forward at an approximate angle of 11°to 18° relative to a line drawn upward from and .perpendicular to the road surface. The range of this angle is well within a much larger range derived from studies of many other photographs taken during the motorcade. Although the Croft photograph corresponds to Zapruder frame 161, there is no indication in the Zapruder movie that Kennedy changed his inclination substantially before he was hit in the back. (53) (See JFK exhibits F-226-242.)
FIGURE II-14-- JFK exhibit F-135.
- The Croft photograph also shows Kennedy's torso facing nearly straight forward. At Zapruder frame 190, however, he is seen to turn his head about 60° to his right (see JFK exhibit F 226), and it is reasonable to expect that he also would have rotated his shoulders a small amount in the same direction. Most probably, this rotation was only 5°or less, as judged by the absence of obvious large shifts in body position in the Zapruder movie. Thus, it was assumed that, except for turning his head by about 60° and his torso perhaps by 5°, Kennedy made no major changes in posture after frame 161. This assumption is supported by a photograph taken by Phillip Willis at about the time of Zapruder frame 202.* (See fig. II-15, JFK exhibit F-155.)
*Establishing when the Willis photograph was exposed in reference to the Zapruder film was done by the Photographic Evidence Panel by studying the Zapruder film and determining when Willis could actually be seen snapping his picture. In the study of the back/neck wounds trajectory, calibration photographs of the anthropometric dummy were taken but not used (that is, for measurement analysis) because, unlike the head, the torso is quite mobile, and consequently there is no stable relationship between the various body parts. It was decided that to rely on the calibration-photograph technique in this instance would have given a false sense of accuracy to the analysis.
FIGURE II-15 -- JFK exhibit F-155.
- The Panel then had to adjust slightly the wound locations that been provided based on the autopsy photographs and X-rays because of their difference in body position from that at the time of the shooting. During the autopsy, Kennedy was in an anatomical position with his face tilted as if looking upward about 35°, a posture and conformation significantly different from those at the time of the assassination.
- Appropriate adjustments were made under the direction of Dr. Clyde Snow, a forensic anthropologist at the Civil Aeromedical Institute of the FAA's Aeronautical Center. It was determined that returning Kennedy's head to a normal position relative to his body would, according to laboratory tests on men of similar build, adjust his neck wound down about 1.0 centimeter toward his breastbone. Returning Kennedy's head to the position it was in at the time he was first wounded--about 60° to the right of straight ahead of his torso-caused only a slight change in the position (approximately 0.1 centimeter to the right of its observed position in the autopsy photographs). (54)
- Because the Zapruder film showed that Kennedy had raised his right shoulder slightly so as to place his elbow on the side of the limousine, the resulting movement of skin at the inshoot location was also assessed. It was found that the wound was approximately 0.1 centimeter higher and 0.2 centimeter closer to his midplane than the post mortem photographic observations by themselves indicated. (55) While only the vertical position of the neck wound was substantially altered by these changes in conformation, all the adjustments were included in the analysis of trajectory.
- Using the average locations and adjustments, the back wound was located at a point 4.4 centimeters to the right of and 1.1 centimeters above Kennedy's neck wound at the time of the shot. The bullet was moving from right to left by 18° and downward by 4.0° relative to Kennedy if he were sitting erect (not inclined forward or aft). Since Kennedy was believed to have been turned about 5° to his right relative to the fore-and-aft line of the limousine, it is concluded that the bullet was moving from right to left by. 13° relative to the midline of the limousine. By a similar analysis, since Kennedy was inclined slightly forward by approximately 11° to 18° (from true vertical), the downward slope of the trajectory, taking into account the 3 slope of the street, was established at between 18°and 25° (4° plus 11° plus 3°). The Panel decided to use an angle of 21° for its analysis.
- The analysis by the USGS of the limousine's motion through Dealey Plaza provided both the location and angular orientation of the limousine at a time corresponding to Zapruder frame 193; (56) adjustments were then made with reference to Zapruder frame 190. (See fig. II-10, JFK exhibit F-133)
- The direction of the trajectory was then determined by drawing a line on a scaled diagram of Dealey Plaza at a 13°(that is, 18° minus 5°) angle relative to the car and extending it to the rear until it intercepted the first building that it encountered. Assuming frame 190 as the moment of impact, the trajectory line intercepts the Texas School Book Depository approximately 14 feet west of its southeast corner. (See fig. II-16). Using an angle of 21°, the slope of the trajectory was then drawn onto a similarly scaled diagram and found to intersect the Texas School Book Depository at a point almost level with the sixth floor windowsill. (See fig. II-17.)
- A circle with a radius of 13 feet has been drawn about the intercept point of the trajectory in figure II-16, reflecting the margin of error. It represents the estimated minimum reasonable margin of error that can be ascribed to this analysis.
- The same kinds of considerations as were discussed for the head wounds case were applicable in assessing the accuracy of the trajectory based on the President's torso wounds. Here the most critical issue was Kennedy's upper torso attitude rather than the orientation of his head. Consequently, different types of problems were encountered.
- The Croft photograph, while quite illustrative of Kennedy's posture, lacked two features noted in Zapruder frame 312. Since the torso is flexible, no clear stable relationship could be established between the photographed exterior and the unseen interior. Further, this picture was taken at least 1.5 seconds before Kennedy was wounded. During this interval, he had turned his head about 60° to his right and may have shifted his torso slightly. Thus, errors of 5° may easily be present in this interpretation. Finally, an accurate determination of his back and neck wound locations was impeded both by the extremely inappropriate lighting and composition of the autopsy photographs and by the distortions resulting from the tracheostomy performed at Parkland Memorial Hospital. These latter problems probably contributed little to the uncertainty in trajectory location as compared with the more serious difficulties arising from the poor photographic definition of his posture and position.*
(3) The single-bullet theory trajectory
- In order to examine the hypothesis that the bullet responsible for Kennedy's back and neck wounds was also responsible for Connally's wounds, a trajectory was constructed based on Kennedy's exit neck wound and the entrance wound in Connally's back. The hypothesis was to be evaluated by determining whether this trajectory lay close enough to the back-neck trajectory to make it reasonable to conclude that both are consistent with the trajectory of one bullet. Necessarily; the margin of error radius for the Kennedy-Connally trajectory would have to intersect the depository at a point within the 13-foot-radius circle of probable accuracy for the back-neck wound trajectory established earlier. Ideally, of course, the two trajectories would line up precisely, but this standard was considered unrealistically high, because, as with Kennedy, Connally's position at the time of this shot could not be precisely established; moreover, each trajectory was subject to its own sources of error.
*The 5° margin of error resulted in a smaller margin-of-error radius than the head wound trajectory because in this case the limousine was substantially closer to the Texas School Book Depository. (See fig. II-10, JFK exhibit F-133.)
- In addition to the information that already had been analyzed concerning Kennedy's neck wound, derivation of this trajectory required placement of the location of Connally's entry wound to the back. At the committee's request, Connally agreed to have the position of his back wound redetermined by the Forensic Pathology Panel. His inshoot wound was described as being immediately above his right armpit. This description is essentially consistent with figure II-18. (JFK exhibit F-377.) (57)
FIGURE II-18 -- JFK exhibit F-377.
- In contrast to the analyses involving Kennedy's wound pairs, the two-man wound combination required focusing on the positions of the two men relative to each other and to their surroundings in Dealey Plaza, rather than just on individual details of posture and orientation. This analysis was accomplished by reviewing Zapruder frames 180-207, the Croft photograph, and photographs taken by Hugh Betzner and Phillip Willis, two witnesses who were bath standing behind and to the left of the Presidential limousine.
- Two independent determinations of the lateral relationship between the two men were made. The first consisted of a photogrammetric analysis of several pairs of pictures taken from the Zapruder movie between frames 182 and 200. These pairs were viewed together in a stereoscopic viewer so that together the pairs would project a single, three-dimensional image that could be evaluated for the relative depths of the objects that they portrayed.* The stereo pairs clearly showed that Kennedy was seated close to the right-hand, inside surface of the car, with his arm resting atop the side of the car and his elbow extending, at times, beyond the body of the car. Connally, On the other hand, was seated well within the car on the jump seat ahead of Kennedy; a gap of slightly less than 15 centimeters separated this seat from the car door. (See fig. II-19.) (58)
*A similar stereophotogrammetric analysis, performed by the Itek Corp. and verified by the photographic evidence panel, indicated that in several stereo pairs Connally was sitting 10.2 to 20.3 centimeters to the left of a line extending straight forward from Kennedy. (See John Kennedy Assassination Film Analysis, Itek Corp. (1976), pp.
- The second photographic analysis, which was based primarily on the Betzner and Croft photographs, confirmed these observations. The Betzner photograph (see fig. II-20) was determined by the panel to have been taken at the time Zapruder frame 186 was exposed.*
*A first generation print of a photograph taken by Hugh Betzner, very close in time and from a similar vantage point as the Willis No. 5 photograph, was examined by the panel; no enhancement processing was performed as the original negative was never located. The Betzner photograph was correlated to the corresponding Zapruder frame by establishing when a Secret Service agent riding in the car behind Kennedy could be seen in both Zapruder's find Betzner's immediate line of sight.
Scrutiny of enlarged portions of the area surrounding Kennedy showed the direction in which an extension of the line of sight would travel from Betzner's lens. It goes by the upper right corner of the Secret Service handhold on the left side of the limousine trunk lid, then passes by the extreme tip of Kennedy's left shoulder, and then by the edge of the limousine's rollbar center post (to which the wind-wing window is attached) just ahead of the right rear door at Connally's right.** This line establishes a boundary to the left of which no part of Kennedy can be seen. Nor are there visible signs of Connally's right shoulder or arm slightly to the left of this boundary (the line of sight is limited by the spectator's arm in the foreground). Therefore, Connally must be seated to the left of this line of sight.
FIGURE II-21 -- JFK exhibit F-136.
- With these two observations and some supportive evidence drawn from the remaining pictorial evidence, it was possible to outline Kennedy as he would have been seen from directly above. The key additional features used were his posture and inclination, which were derived from the Croft picture (see fig. II-14), and the slight indication of torso rotation to his right, derived from the Zapruder film. Next, a similar outline was drawn for Connally, with his shoulders against the backrest of the jump seat as far to the right as can be justified in view of the Betzner photograph, and turned to his right.
- The direction in which Connally's torso was facing has been determined on the basis of viewing the Zapruder movie and by careful study of a particularly clear stereo pair taken from the movie. The estimates of the angle of his twist vary from 30° to slightly over. The two outlines show the positions of the men relative to one another. (See fig. II-23.) Connally cannot have been sitting very far to the left of this position in view of his location in Zapruder frame 190. (See JFK exhibit F-226.)
**Fig. II-21 (JFK exhibit F-136) demonstrates the Betzner photograph line-of-sight analysis. The rollbar center post has a diagonal appearance in the Betzner photograph because it is inclined inward from the side of the car toward the rollbar. See fig. II-22 for a clearer view of the rollbar post, as seen from a similar angle in a photograph taken by James Altgens on Houston St. less than a minute earlier.
RELATIVE POSITIONS OF PRESIDENT KENNEDY AND GOVERNOR CONNALLY AS DEDUCED FROM PHOTOGRAPHIC EVIDENCE
- The point-to-point distance between Kennedy's neck and the part of Connally's back that was wounded was determined photogrammetrically in the Croft photograph to be approximately 60 centimeters. The height differential between the two was determined in a similar manner to be 8 centimeters.*
- Using the lateral and longitudinal relationships, given the limousine as the frame of reference (see fig. II-23), the direction in which the bullet was found to have been moving from the rear was 19.7°from right to left relative to the midplane of the car. The direction of the trajectory was thereby determined by drawing a line at a 12.7° angle relative to the car and extending it to the rear until it intersected the first building that it encountered--the Book Depository, at a point approximately 2 feet to the west of the southeast corner of the building, using Zapruder frame 190 for the moment of impact. (See fig. II-24.)
*The appearance of an even greater height difference between the two men, as depicted in the Croft photograph, resulted from the more inward position of Connally in the car and the slightly downward line of sight from Croft's camera.
- In deriving the slope of the trajectory, the difference in height between the two wounds, the 60-centimeter distance between them, and the inclination of Elm Street, were taken into account. Kennedy's neck wound was 1.1 centimeters below his first thoracic vertebra; his forward inclination lowered the wound an additional 2.4 centimeters. Connally's inshoot wound was 18 centimeters below his first thoracic vertebra. Thus, if the men had been sitting so that the tops of their heads were at equal heights, Kennedy's wound would have been 14.5 centimeters higher than Connally's.* Then, taking into account that Kennedy was seated approximately 8 centimeters higher than Connally (as observed in the Croft photograph), Kennedy's wound is found to have been 22.5 centimeters higher (14.5 plus 8 centimeters) than Connally's relative to the car. This height difference over a distance of 60 centimeters (point-to-point, distance between the wounds) yields a downward slope of about 22° from Kennedy's wound to Connally's. Finally, accounting for the 3° slope of the street, the slope of the trajectory is found to be 25°.
- This means that the bullet was traveling at an angle of 25° below true horizontal as it passed forward from Kennedy's neck to Connally's back.** Using the position of the men at the time of Zapruder
*This analysis makes the assumption that the distance in each man from the top of his head to his first thoracic vertebra is approximately the same.
**This slope is 2° steeper than described in testimony before the committee on September 12, 1978, because the former was based on a 6-centimeter height difference instead of 8 centimeters, as presently interpreted.
190, if this line is extended toward the rear, it intercepts the depository building about 9 feet above the sixth floor windowsill.* (See fig. II-25.)
SLOPE OF "SINGLE BULLET THEORY" TRAJECTORY
- In figure II-25, a circle of 7 feet radius, representing the estimated minimum reasonable margin of error, has been drawn around the intercept point. It is smaller than those of the other two trajectories simply because the distance between the two wounds (60 centimeters) is more than four times as great as that for the back/neck case (14 centimeters) and five times that for the fatal bullet (11 centimeters). This longer baseline distance admits greater error in wound location and body position, while yielding superior accuracy. The eastern border of the error circle is somewhat better fixed than the western because the right-most position of Connally was better defined than the left-most.
- The consistency of the single-bullet theory trajectory with the back/neck shot trajectory described earlier is illustrated by their similar direction and slope. Note that the intercept point of the single bullet theory trajectory at the Texas School Book Depository lies very close to the margin of error circle established for the back* neck case. Indeed, the two error circles overlap substantially. (See figs. II-17 and II-25.) Clearly, this analysis supports the single-bullet theory. The reliability of this trajectory in indicating the position of the gunman would be less if it could be shown that the bullet had been deflected as it passed through Kennedy's tissue. Nevertheless, the evidence indicates that the bullet passed near, but did not strike, the right lateral processes of the seventh cervical and first thoracic vertebrae (nor any other bony matter). (59) Consequently, the deflection, was probably negligible.
*This result differs somewhat from the testimony given before the committee on September 12, 1978, because the adjustment in the height differential between the two men affected the ultimate determination of trajectory slope.
CALIBRATION PHOTOGRAPHS OF THE REPLICA OF PRESIDENT KENNEDY'S HEAD
- Photographs of Kennedy taken immediately before each shot provide invaluable, albeit imperfect, records of his position and orientation at the time of the assassination. The quantitative interpretation of these photographs was facilitated through detailed comparisons with calibration photographs taken of a full-scale replica of Kennedy's head, upper torso, and arms.
- Calibration photographs may be defined as photographs of a replica that is geometrically and texturally representative of a subject; they are taken under controlled conditions and are used to facilitate quantitative interpretation of photographs of the real subject that were taken under uncontrolled circumstances. Requirements for a good calibration photograph include: accuracy of the replica, photographic distortion similar to that in the real-life photograph under study; comparable positions for the camera and replica; and comparable lighting distribution. The calibration pictures should have somewhat superior photographic qualities in terms of spatial resolution and contrast so that error will not be introduced into the interpretation.
- To maximize the accuracy of the replica, the Aeromedical Research Institute of the FAA's Aeronautical Center worked with a group of high-quality photographs from the National Archives. Using dimensions obtained from well characterized X-rays of Kennedy's head taken shortly before the assassination, the size and proportions of his skull and the thickness of overlying tissue (front and rear) were established. Modeling clay was applied to a standard plaster skull until the form of his head was duplicated in many aspects. To achieve improved photographic realism, artificial eyes and a wig were added. The head was then mounted on the neck of a standard FAA anthropometric dummy.
Simulation of lighting and environment
- A single studio light was used to simulate the Sun, with two small studio flood lamps to augment the illumination by the studio skylight of the figure and the neutral background. At the time of the first shot, Kennedy had been facing west. The spotlight was accordingly positioned to the model's left. It was placed about 36° above horizontal from the head, a position comparable to that of the midday November Sun Similar lighting was arranged for the head-wound shot. In this case the elevation of the spotlight (Sun) was about 56°, compensating the erect placement of the head on the dummy, and it was placed nearly straight in front because Kennedy had been facing south.
- Camera stations--the various points from which the dummy would be photographed--were marked out on the studio floor in an arc 25 feet from the bridge of the model's nose. Two plumb bobs were suspended beside the figure to provide a precise vertical and angular reference respectively. Beads were installed on each plumb line at a point level with the bridge of the dummy's nose. The elevation of the camera was varied to achieve the desired angles of elevation relative to the dummy. (This caused the actual distance between the camera and the dummy to change slightly.)
- Once the camera stations were established, a series of photographs was taken at varying elevations from each station, with the location of each photograph recorded. The pictures were then compared with an enhanced photograph of Zapruder 312. (See fig. II-8.) The goal was to determine the angular orientation of Kennedy's head relative to his surroundings in Dealey Plaza. Since the positions of the Zapruder and Nix cameras, with which the best pictures had been taken, were known, only the position angles relative to each camera's line of sight and to vertical references visible in the respective pictures had to be found.
- The relative positions of the features of Kennedy's head varied with the viewing aspect. In Zapruder frame 312, part of Kennedy's nose was obscured by his right cheek because his head was turned slightly away from the camera. His right ear appears slightly forward where it would have been had he not, been facing slightly away. His cheekbone and ear appear slightly elevated in Zapruder frame 312 as the camera was, in effect, viewing the President from slightly "below" the inclination of his head to the left.
- All these relationships among features were accounted for simultaneously during comparison with the calibration photographs. Serious impediments to accurate interpretation of the photograph were occasioned by the extremely complicated background to the President's face resulting from Mrs. Kennedy's pink suit and dark blue blouse and by the interior surface of the left side of the limousine. These problems were overcome in part by the use of a computer-enhanced version of Zapruder frame 312. (See fig. II-8.)
CORRELATING TRAJECTORY TO THE ACOUSTICS RESULTS: TRAJECTORY OF HEAD-SHOT WOUNDS BASED ON ZAPRUDER FRAME 327
- The acoustics analysis indicates that four shots were fired at the Presidential limousine with the first, second, and fourth shots coming from the Texas School Book Depository, and the third from the grassy knoll. (60) Given these findings, as well as the timing of the shots, approximately 1.6, 6, and 0.7 seconds apart, Zapruder frame 312, which immediately precedes the frame that shows the fatal head shot, theoretically could be the time of impact of either the third or fourth shot of this sequence. (471) * If it was the fourth shot, the third shot would have had to impact (if it had hit) approximately at Zapruder frame 296; (62) if it was the third, then the fourth shot would have had to impact (if it had hit) approximately at Zapruder frame 327. (63)** (See illustration 33a, fig. II 26.)
*The first two shots are spaced only 1.6 seconds apart. Consequently neither of these shots could have caused Kennedy's fatal head wound, since it is apparent that at least by Zapruder frame 224, Kennedy and Connally are already reacting to their earlier wounds.
**The correlation between the acoustics tape and the Zapruder film indicate that this shot would have occurred approximately at Zapruder frames 328-329. See pars. 108-109 supra.
- The acoustics, medical, ballistics, and neutron activation analyses, taken together, establish that a shot from the Texas School Book Depository struck the President's head. (64) The head shot trajectory analysis based on Kennedy's orientation and location at Zapruder frame 312 assuming this to be the fourth shot fired is consistent with this. Nevertheless, the committee decided to examine the possibility that the fourth shot fired from the Texas School Book Depository impacted at Zapruder frame 327 and that the third shot, fired from the grassy knoll, was therefore responsible for destroying Kennedy's head hit frames 312-313.
- A trajectory analysis was undertaken based on Kennedy's orientation and location at Zapruder frame 327.* If the trajectory were found to go back to the alleged sniper's window in the Texas School Book Depository, it would not necessarily resolve, the question. On the other hand, if it did not go back to that location, the conclusion could be drawn that frame 312 was, in fact, the fatal fourth shot which struck Kennedy's head. This conclusion would have to be drawn because the medical, ballistics, and neutron activation analyses, taken together, indicate that the bullet which struck Kennedy's head was fired from the Texas School Book Depository. If the trajectory analysis indicates that this particular bullet could not have, impacted at Zapruder frame 327, then the shot must have occurred at Zapruder frame 310, as the trajectory analysis for that frame (described above) does point in the vicinity of the sixth floor window.
*At the time that this trajectory analysis was undertaken, the preliminary correlation of the fourth shot (based on a third shot at approximately frame 312) was at Zapruder frame 327. Frame 327 was exposed less than 1/18 of a second before frame 328. Kennedy's position did not change noticeably during this interval. Therefore, any difference in resulting trajectory would not be significant.
- While precisely the same analytic techniques were employed as those used earlier for the head wounds at Zapruder frame 312, various factors made the results here less precise. Even though the key photograph, Zapruder frame 327, was unenhanced, it nevertheless had good color rendition. The aspect from which Kennedy's head was viewed in this frame, however, did not permit as accurate a determination by comparison with calibration photographs as was the case with Zapruder frame 312.
- Little of Kennedy's face was visible, and his right ear was not distinct. In addition, the angle between the direction in which Kennedy's head was "looking" and the line between him and Zapruder's camera could, at best, only be defined plus or minus 5°. The apparent height of the camera relative to Kennedy's facial axis reference was even more poorly defined because of the absence of good visual reference points.
- Best estimates of these two angles, as well as an educated judgment of the degree to which Kennedy's facial axis appeared to be tilted left or right relative to level in the Zapruder frame, were achieved after careful study and comparison of calibration photographs approximating Zapruder frame 327. These angular relationships, plus the position estimated for the limousine at Zapruder frame 327 (based on an extrapolation of data on its earlier position) were then used to orient Kennedy's head relative to the surroundings in Dealey Plaza. Completing the analysis required construction of the line through the wound locations as before and extending the line toward the rear. When plotted, the line intercepts the face of the Texas School Book Depository about three-fourths of the building's length to the west of the southeast corner. (See fig. II 27.) When the slope of the line is derived as before, the line then intercepts the building's vertical plane just above the roof of the building. (See fig. II-28.)
- A. step-by-step examination of potential errors suggests that this trajectory is subject to approximately twice the error estimated for the head shot trajectory for Zapruder frame 312 because the photographic aspect was so much more difficult and the photographic quality slightly inferior in frame 327.
- Despite the problems, this analysis was sufficiently precise to establish that the firing point for a Zapruder frame 327 head shot trajectory is highly inconsistent with either that of the Kennedy back-neck or the single bullet theory trajectories. The latter two are quite consistent with an origin in the southeast sixth floor window of the Texas School Book Depository, whereas, even with a 46-foot estimated minimum reasonable margin of error radius, the head trajectory for Zapruder frame 327 does not take in the alleged sniper's window. For this reason, it is highly unlikely that the head wounds were inflicted by firing a bullet from the southeast window that impacted at the time of Zapruder frame 327.
- Once Zapruder frame 327 has been eliminated as a possible fourth shot fired from this window, the conclusion must be made that this fourth shot must have occurred at Zapruder frame 312.
5. PHOTOGRAPHIC EVIDENCE OF DEALEY PLAZA
[See pars. 241-346 infra.]