Establishing the Royal Cubit Length
For centuries, Egyptologists have attempted to establish an official length for the Royal cubit (Rc). Many samples of this ancient measure have been recovered from various archeological sites and are presently on full display in several museums throughout the world and it is these samples that present the problem…they all vary in length!
Although the difference is minute the question remains…what was the standard of measure implemented by the ancients for constructing the monuments at Giza?
It may appear to be an insignificant issue, but once a measure can be confirmed as absolute then accurate scaling of all measures on site may direct us toward greater understanding and reasoning for the ancient’s structural and architectural designs.
Numerous sites indicate they were constructed specifically for astronomical study throughout the seasons. We have also learned and understand that ratios of length were fashioned into the stonework of other sites. Once the principle reasons for these designs are understood then it is realized that the measures are actually basic in nature…most important…they were limited in their use !
It was demonstrated in Topic 3 how the three pyramids form a 191.5 degrees angle. This implies the builders having gained full understanding of planet motion. By the greatest of coincidence, the most hospitable planet closest to Earth is Mars and it orbits 191.4 degrees average in one Earth year…the identical angle as indicated at Giza (Ill. 1).
Illustration 1. Mars orbits 191.4 degrees average in one Earth year. The three Giza pyramids are set out and demonstrate the identical angle.
Four thousand years had passed before the discovery of a simple mathematical fact relating to the center pyramid of Khafre (P2) and Petrie confirmed the measure true.
The remaining granite casing stones surrounding the base of P2 have a smooth angular face and are carved on a precise 4:3 ratio, or the equivalent of the 3-4-5 right-angle triangle. This angle has prompted many to believe that the ancients may have understood the right-angle theory before the pyramids were constructed, but it must be understood that a single and basic ratio cannot be used to substantiate a theory. Scholars realize that a 3-4-5 ratio can also be illustrated on a grid without any knowledge of the right-angle formula. The angle selected may have been for geometric symmetry, architectural splendor, or convenient for construction practicality (Ill. 2).
Illustration 2. The granite casing stones at the base of Khafre’s pyramid demonstrate the 3-4-5 right-angle triangle, a geometric format illustrated on a simple grid.
Modern studies of the Giza site have recently promoted the use of the King’s Chamber in Khufu’s pyramid (P1) as a reference measure. The chamber’s dimensions are established as 20.0 Rc long by 10.0 Rc wide. Using the measures recorded by F. W. Petrie then the average/mean length of the Royal cubit is 20.63 inches or 52.40 cm.
Applying this information to the three large pyramids on site then the individual base measures calculate as follows:
P1 (Khufu)…440.00 Rc
P2 (Khafre)…410.80 Rc
P3 (Menkaure)…201.25 Rc
The first stage is now established…implementing a measure to be used as a possible standard…the King’s Chamber.
The second segment of this design analysis is the compiling of information from the three pyramid bases and it is here where a second phenomenal discovery is made:
The total length of the three pyramid sides is equal to (440.00 + 410.80 + 201.25) = 1052.05 Rc.
Presented above was the 191.5 angle separation of the three pyramids, it is factual and corresponds to the orbital distance Mars travels in one Earth year. What we also know of these two planets is their individual orbital period: Earth orbits the Sun in 365.26 days compared to Mars of 686.98 days. The total days for both planets to orbit the Sun is (365.26 + 686.98) = 1052.24 days and this numerical value equals the total length of the three pyramids (Ill. 3) !
Illustration 3. The numerical sum of the three large pyramid widths in Royal cubits is equal to the sum of the orbital periods of Earth and Mars.
For the first time we begin to realize that more than simple geometry and mathematics is involved at Giza. The designers demonstrated their gained knowledge using numerical values of Royal cubits to represent Earth days; it enabled them to confirm their understanding of Mars and Earth orbiting the Sun…planet motion !
There is no evidence indicating any mathematical ratio between the three large pyramids, are we being prompted to question why the designers built P2 on a simplified 3-4-5 right-angle triangle with a base measure of 410.8 Rc? Why did they not build a base of even length e.g. 400, 405, or 410 Rc? Nothing is to be overlooked.
From questioning these small discrepancies in measure we discover another piece of information locked within this monument.
Using the same technique, the formed 3-4-5 right-angle triangle measures of P2 are compared to Earth days.
Petrie’s base measure of P2 converts to 410.8 Rc forming two side of 342.34 Rc each, therefore the perimeter of the formed triangle is (2 x 342.34 + 410.8) Rc = 1095.48 Rc…a mathematical fact.
By calculation, this pyramid forms a triangle of perimeter 1095.48 Rc…and we know that a triangle has three sides. Therefore the average length of each side is (1095.48/3) or 365.16 Rc…the number of days to an Earth year !
The perimeter of P2 in Royal cubits is numerically equal to three Earth years of 365.256 days (Ill. 4) !!
Illustration 4. The total numerical value of the perimeter is equal to the days required for Earth to orbit the Sun three times (1095.77 days).
If we assume the designers understanding the exact length of an Earth year being 365.26 days then calculating in reverse…
Three complete orbits of Earth equaling 1095.78 days set into a 3-4-5 triangle having a base measured length of 8475 inches (average length by Petrie) will produce a Royal cubit base length equaling 8475/(1095.78 x 6/16) = 20.63 inches.
“….Probably the base of the chamber was the part most carefully adjusted and set out; and hence the original cubit used can be most accurately recovered from that part. The four sides there yield a mean value of 20.632 this is certainly the best determination of the cubit that we can hope for from the Great Pyramid…”
Petrie’s value of 20.632 +/- 0.004 inches extracted from the King’s Chamber compared to the 20.63 from a simple calculation using Earth days confirms his measure correct and verifies the designers understanding the length of one Earth year.
The measures are most precise and impressive, but we are not to stop here. There are other significant dimensions indicating a slight discrepancy…a discrepancy that Petrie was obviously eager to overlook.
A journey to the Queen’s Chamber and additional measures from Petrie:
The Pyramids and Temples of Gizeh… Chapter 9, section 41, pg. 67
“…The size of the chamber (after allowing suitably in each part for the incrustation of salt) is on an average 205.85 wide, and
226.47 long, 184.47 high on N. and S. walls…”
Using the calculated 20.63 inch standard from the King’s Chamber, then the Queen’s Chamber would measure 9.98 x 10.98 x 8.94 Rc and this chamber is situated forty cubits below the King’s Chamber…it was constructed first !
Since it was built first then it is obvious that the intended size of the Queen’s Chamber was 10.00 x 11.00 x 9.00 Rc…indicating a smaller cubit length of 20.59 inches. It now appears that a transition of the cubit measure was made between the times of constructing the two chambers.
The Queen’s Chamber was accessible while building the King’s Chamber…it always provided an accurate standard or reference for the Royal cubit. Leaving us with an additional issue to resolve. If the standard was available why did the builders elect to alter the cubit length…and was it intentional?
From illustration 4 it was shown how the total length of the triangle formed by P2 equals the number of days in three Earth years…it also displays each side measures 342.34 Rc. The sum of these two sides equals 684.68 and it is realized that Mars orbits the Sun in 686.98 days…the difference in value is 2.30 days. Were the designers attempting to use P2 to indicate the orbital period of Earth and that of Mars? It is impossible to accomplish unless there is a slight change…adjust the Royal cubit to a shorter length !
Using the cubit measure from the Queen’s Chamber as a reference then the calculated lengths for both sides of P2 equal (1/2 x 8475 x 5/3)/20.59 = 343 Rc; the total length for both sides now equals 686 Rc…and the error reduced to ½ Rc on each side, or a total error of one day/Rc (Ill. 5).
Illustration 5. Using the Queen’s Chamber as a standard, the two sides of P2 measure 686.00 Rc representing one orbit of Mars (686.98 days).
Assume the designers understanding the orbital period of Mars equaling 686.98 days then calculating in reverse…
One orbit of Mars equaling 686.98 days set into a 3-4-5 triangle having a base measured length of 8475 inches (average length by Petrie) will produce a Royal cubit base length equaling (8475 x 5/3)/686.98 = 20.56 inches…
The Queen’s Chamber indicates an average length of 20.59 inches…an error of 0.03 inches.
The designers deliberately used two separate measures for the Royal cubit within the chambers of Khufu (P1). They had full intentions of building Khafre’s pyramid (P2) on a 3-4-5 right-angle triangle to express the two specific orbital characteristics for the planets: Earth and Mars.
The ancients concealed the pyramid passages from view hoping for the inquisitive to discover their existence. Having traveled their course over time they have directing us to the chambers above and now we are at an age capable of accepting the next challenge.
There is much to uncover…but not a stone to be removed. We are to read…with all our senses…the messages left within.
The Pyramids and Temples of Gizeh…..1882……………Sir W. M. Flinders Petrie
“1o6” The Dawn of Man………………………….1999 sb……….C. Ross
Larousse Astronomy………………………..….1987……………Philippe de la Cotardiere
459689 1997…C. Ross “1o6” The Dawn of