
CHAPTER 4 Comparative Dimensions As it should be expected, the dimensions of an important monument as the Great Pyramid had been measured in numerous occasions, in different ways, and in all epochs. In its surveys had participated engineers, topographers, archeologists, Egyptologists, and many experts in surveying. The dimensions of the pyramid’s structure were reported in the units of measurement preferred by each one of the surveyors. It is known that among the exterior dimensions of the Great Pyramid, the length of the sides of the base is the only one that has been established with enough precision. The measurements of the apothem, and the angle of elevation of the faces, only represent mathematical estimates and projections. The ratio between the height, and half the side length of the pyramid’s base, determines the angle of elevation of the faces. The numerical value between these two numbers represents the function of the tangent (slope angle) of the angle of elevation. This means that knowing the height and the side length, we can calculate the angle of the faces. The other way around, if we know the angle of the faces and the side’s measurements, we can calculate the pyramid’s height. According to the reference books, the face angle of the stone casing blocks found at the center of the north side, varies from 51° 49' to 51° 52'. The measured angle dependents on the casing block measured and the investigator who measured it. To my understanding, the number of casing blocks in that small location is not substantial enough to establish with certainty the elevation angle used by the Egyptians. Particularly, when it is known that over 200 hundred layers of casing blocks were laid in each face of the pyramid and that in each one the face angle was cut. This indicates that the angle of the faces, as well as the pyramid’s height, will be in the obscure side, until the original construction plans of the Great Pyramid are found. In this situation, we have two alternatives. Since we know that the side length is the most precise measurement, we can assume the pyramid’s height and calculate the face angle. Or, on the other hand, we can assume an angle for the faces, and calculate the pyramid’s height. The geometrical configuration used in my theory gives the solution to this problem. The angle of the faces is fixed and is 51° 49' 38", no matter the dimension assumed for the pyramid’s height. Assuming that my angle is correct, and establishing the height of the pyramid as 755.75 feet (more exact 755.7488). My reference, [Ref. #43, Flinders, Petrie, Revised edition by Zahi Hawass) page 11 (indicates = 9,068.8 inches = which could be roundoff to 9,069 inches. = 755.75'),]. The projection of the pyramid’s height will be equivalent to the product of the function of the slope angle and the base length, divided by 2, that is, (1.27201965)(755.7488) / 2 = 480.6637 feet. This pyramid’s height agrees with the traditionally accepted height dimension for the Great Pyramid, and which could be also defined as the product of 153 and (p = 3.1415926) =480.6637 feet. The known Egyptologist, Dr. Mark Lehner, indicates, in his book «The Complete Pyramids», 1997, the height and side measurements of the Monument. According to this reference, [Ref. # 33, Lehner, Mark, page 17, (indicates the height = 146.59 meters = 5,771.19 inches = 480.93 feet), the sides length is 230.33 meters = 9,068 inches = 755.67 feet]. Our calculated height for the pyramid model is equivalent to 480.6637 feet (5,767.96"). It differs by about 3 inches from the value indicated by Dr. Lehner, and the base sides, by less than one inch. Considering the size of the Great Pyramid, and the assumed available construction methods at those times, the differences are more than insignificant. These differences can be attributed to normal measurement errors at the time of erecting such a huge building, due to settlement, deterioration and climatic conditions, and many other factors. We are fair, saying that they are not equal. Anyway, to support my theory, a detailed comparison of all the angles and measurements calculated for the pyramid’s model should be clearly illustrated. This comparison should include the exterior and interior dimensions, corresponding to our pyramid’s model, and those measured in the Great Pyramid. Using such a comparison between the dimensional, and characteristics between the two separate models, it can be established the importance of my theory. As it can be foreseen, many previous theories about celestial alignments, prophesies, Egyptian religion, extraterrestrial participation, and others, will be challenged and possible dismissed. This theory will establish a new engineering interpretation of the art of pyramid’s building in the ancient Egyptian times. With that in mind, a detailed comparison is herein presented. The dimensions for both pyramids are expressed in the English Unit Measurements System. The measurements expressed in other units in our references were converted to the English System for the purpose of this comparison. The information and dimensions written in bold types correspond to the dimensions calculated for our pyramid’s model, while those shown clear and in Italics, correspond to those actually measured in the Great Pyramid. Ref. # 13, I. E. S. Edwards, "The Pyramids of Egypt", Penguin Books, 1993 Ref. # 43 Petrie Flinders, W. M. The Pyramids and Temples of Gizeh, with and Update by Zahi Hawass, 1990. Ref. # 44, Pochán, André, "El Enigma de la Gran Pirámide", Plaza & Janes, 1974 Ref. # 47, Smyth, Piazzi, "The Great Pyramid" Reprint 1880 ed. Bell 1978 EXTERNAL STRUCTURE DIMENSIONS (see figure 82) Pyramid’s height 480.66 feet Ref. # 13, page 118 481.4 feet Ref. # 43 (from 480.75 to 481.91 feet) Ref. # 44, page 40 480.45' Ref. # 47, page 95 484.90 feet Side’s length 755.75 feet Ref. # 13, page 118 Side’ length average 755.79 feet Ref. # 43 755.75 feet Ref. # 44, page 40 Side’s length 755.41 feet Ref. # 47, page 39 761.59 feet Face’s angle 51° 49' 14" Ref. # 13, page 118 51° 52' Ref. # 43 51° 51' 30" Ref. # 44, page 40 51° 51' (more or less 1 minute) Ref. # 47, page 49 51° 51' 14" Original Entrance  Vertical distance (distance from point m to point n) (See figures 82 and 83) 54.17 feet Ref. # 13, page 119 55 feet more or less Ref. # 43 55.68 feet Ref. # 44, page 42 55.70 feet Ref. # 47, page 221 49 feet more or less
Figure 82 & Figure 83 INTERNAL STRUCTURE DIMENSIONS (see figure 84) DESCENDING PASSAGE Inclination angle  26° 33' 54" Ref. # 13, page 120  26° 31’23" Ref. # 43  26° 33' 54" Ref. # 44, page 42  26° 33' 54" Ref. # 47, page 222  26° 8' Inclined length (from point m to s) 344.91 feet Ref. # 13, page 120 close to 345 feet Ref. # 43 345.25 feet Ref. # 44, page 52 345.3 feet Ref. # 47, page 221 340.34 feet Descending passage  horizontal section (point s to point y) 26.79 feet Ref. # 13, page 120 29 feet Ref. # 43  Ref. # 44, page 52 29 feet Ref. # 47, page 221 27 feet Subterranean Chamber’s width 26.79 feet Ref. # 13, page 120 27.1 feet Ref. # 43 Ref. # 44, page 52 27 feet Ref. # 47, page 222 27.11 feet
Figure 84 DEADEND CORRIDOR 53.57 feet Ref. # 43 Ref. # 44, page 52 53.83 feet Ref. # 47, page 222 52.80 feet ASCENDING PASSAGE Angle of elevation + 26° 33' 54" Ref. # 13, page 121 + 26° 2' 30" Ref. # 43 + 26° 33' 54" Ref. # 44, page 47 + 26° 33' 54" Ref. # 47, page 222 + 26° 17' Length to the Grand Gallery (point I to point p) 129.90 feet Ref. # 13, page 121 129 feet Ref. # 43 128.90 feet Ref. # 44, page 52 128.8 feet Ref. # 47, page 222 128.66 feet CORRIDOR TO THE QUEEN CHAMBER Horizontal length 126.25 feet (From point p, to the entrance to the Queen’s Chamber) Ref. # 13,   Ref. # 43 128.9 feet Ref. # 44, page 52 128.90 feet Ref. # 47, page 223 126.74 feet GRAND GALLERY Inclined distance from north to south wall 156.81 feet Ref. # 13, page 124 153 feet (ceiling) Ref. # 43 Ref. # 44, From the N. wall to the great step 151.08 feet Ref. # 47, page 544 156.94 feet Great Step (height) 32.52 inches Ref. # 13,   Ref. # 43 32.50 inches Ref. # 44, page 61 35.41 inches Ref. # 47, page 222 36 inches Note: It can be noticed, at the Great Step site, that a large section of the step was reconstructed, something that could have changed its height. Reference # 43 took in account that the top elevation of the Great Step, at its sides, was raised. He measured its original elevation at the South wall of the Grand Gallery and found it as 32.50 inches, equal to the calculated in the pyramid's model. VENTILATION SHAFTS  QUEEN’S CHAMBER
Figure 85 Angle Total length Horizontal section North’s Side Shaft 38° 10' 21.8" 244.90 feet 6.98 feet Ref. # 13, page 123 Aprox. 30° (No exit at faces) (6.5 feet horizontal section) (Note: In our case, with 222.95 feet height, the exit will be located at layer 86. Ref. # 43 Ref. # 44, page 53, 56,  37° 28' (Exit estimated perpendicular to the faces 226.38 feet) Ref. # 47, page 428 (dimensions taken by W. Dixon, discoverer of the shafts) the openings are 9 inches width and 8 inches height. It extends for 7 feet horizontally, then, inclined at an angle of approximately of 32°. (The elevation of 32º given here is too far from being correct). South’s Side Shaft 38° 10' 21.8" 244.90 feet 6.98 feet Ref. # 13, page 123 Apron. 30° (No exit at faces) (6.5 feet horizontal section) (Note: In our case, with 222.95 feet height, the exit will be located at layer 86. Ref. # 43 Ref. # 44, page 53,56, 38° 28' (Exit estimated perpendicular to the face) 226.38 feet Ref. # 47, page 428 (dimensions taken by W. Dixon, discoverer of the shafts). The openings are 9 inches width and 8 inches height. It extends for 7 feet horizontally, then, inclined at an angle of approximately of 32°. (The elevation of 32º given here is too far from being correct). VENTILATION SHAFTS  KING’S CHAMBER
Figure 86 Angle Length Elevation over base North’s Side Shaft 31° 41' 3" 233.77 feet 261.13 feet Ref. # 13, page 126 31° Exits at face (openings at 3 feet over floor) Ref. # 43 Sir W. Flinders Petrie in his book The Pyramids and Temples of Gizeh, 1883, indicates that the exit of the north air channel is located between layers 102 and 103. Note: The elevation over the base, for layer 102 is 260.10 feet; and for layer 103, is 262.60 feet. The elevation over the base calculated for our pyramid’s model is 261.08 feet, then, the exit of the shaft would be also between layers 102 and 103. Ref. # 44, page 57 31° 33' 232.88 feet  Ref. # 47, page 223  233.23 feet  South’s Side Shaft 45° 175.74 feet 262.83 feet Ref. # 13, page 126 45° Exit at face (openings at 3 feet over floor) Ref. # 43 Sir W. Flinders Petrie in his book The Pyramids and Temples of Gizeh, 1883, indicates that the exit of the south air channel is located between layers 103 and 104. (Note: The elevation over the base, for layer 103 is 262.60 feet; and for 104, is 264.93 feet. The exit elevation for the model pyramid shaft is 263.34 feet. So, the shaft will exit between layers 103 and 104. Ref. # 44, page 57 45° 14' 173.84 feet  Ref. # 47, page 223  174.42 feet  New Information about the Ventilation Shafts In 1993, Rudolf Gantenbrink, a German engineer, brought the World’s attention to the Great Pyramid. As part of a project in the ventilation shafts in the Queen’s and King’s Chamber, he designed and used a small mechanical robot vehicle for that purpose. His robot was equipped with light and a video camera to transmit its route images inside the shafts to his recorder and television set inside the chambers. The robot has a front mounted laserrod to measure the height and width of the shafts. These shafts, commonly called ventilationshafts, have almost a square section of about 8 inches. As we know, these dimensions do not permit human entrance into the shafts. The robot was used to explore the King’s Chamber shafts. These shafts have their openings at the chamber’s north and south walls, with exit at the pyramid’s north and south faces. The shafts in the Queen’s Chamber were also explored. The investigation of the north Queen’s shaft had to be suspended since the robot could not negotiate a sharp corner inside the shafts, without the hazard of getting stuck inside the shaft. To the surprise of Rudolf Gantenbrink, and to the whole World, the robot, in its exploration journey inside the south shaft, about 195 feet from the shaft entrance opening, found itself in front a smoothly polished stone that closed its way through the shaft. According to the recorded images, the closure stone seems to be a small limestone slab, (see figure 87). It shows two slightly conical fittings (probable made of copper or bronze) protruding from two holes drilled in the stone’s face. These two fittings appear to be two small metal handles. The left fitting is partially broken off. Its fragment could be seen on the shaft’s floor. The closure stone slab, at its base, has its right corner edge broken, showing a triangular gap. Apparently, the closure stone was held in place by grooves at the shaft walls, without the use of mortar. It is assumed that the slab stone could be movable. Gantenbrink opinion was that he could redesign his robot to explore and find what is located behind this slab stone. Rudolf Gantenbrink finally proposed to redesign his robot to make it capable of introducing an optic fiber, equipped with a camera’s lens, through the small triangular gap and find what is behind the closure stone. However, several years have elapsed with no action on this respect from the Egyptian authorities. In his report, The UPUAT PROJECT, displayed in the Internet web site http://www.cheops.org, Rudolf Gantenbrink showed a summary of his report. Early in the year 2000 the Egyptian Government announced that they have no intention, at least for this year, of doing any investigational work to determine what exists behind the closure stone. Therefore, the UPUAT PROJECT was dismissed officially until a future time. Rudolf Gantenbrink was also dismissed from conducting this research work, or any other for the Egyptian authorities. He decided to write his own book about his work.
Figure 87 Comparison of the airshafts dimensions taken by R. Gantenbrink in his survey and those calculated in my pyramid’s model. R. Gantenbrink Measurements Pyramid’s model King’s Chamber  north shaft Shaft Length = 71.50 m = 234.52' 233.77' Height above ground = 257.31' at 102 layer 261.13' (to the face) King’s Chamber  south shaft Shaft Length = 53.56 m = 175.72' 175.74' Height above ground = 77.55 m( 254.42') exit at 101 layer 263.27' (to the face) Queen’s Chamber  north shaft Shaft Projection Length (not found yet) 244.90' (projection) Height projection above ground level (not found yet) 222.90' (projection) Queen’s Chamber  south shaft Inclined length to the closure stone 59.5 m = 195' 222.89' Height projection above ground level (not found yet) (projection) Length projection to the Pyramid’s face = 74.89 m = 245.7' 244.90' (to the face) Note: The fact that in R. Gantenbrink report, the length projection for this shaft up to the face of the pyramid, is equivalent to the model pyramid shaft projection, also to the face of the pyramid, shows that the geometry of the Great Pyramid, as set up in his drawing, agrees with my pyramid’s model geometry.

