About Egyptian Pyramids
by Jimmy Dunn writing as Alan Winston
Before the physical orientation and layout of a new pyramid took place, considerable planning was needed under the direction of a "royal master builder". Ultimately, the responsibility fell on the vizier, who was typically the head of all royal works. The first step in the process was taken by specialists who would draw up plans for the pyramid on papyrus. After the construction began, plans and sketches were drawn on papyri or flat slabs of limestone. Planners even made models of their projects, as evidenced by a limestone model of a substructure found in the Pyramid of Amenemhet III at Dahshur. After the planning stage, each step of pyramid building was initiated with foundation rituals.
Pyramids, unlike many other types of religious structures, required strict orientation to the cardinal points. Pyramid alignment may have been carried out through a number of different means, including some methods we have probably never thought of. The primary theory of how the ancient Egyptians oriented most any building that had to conform to true primary coordinates has been by stellar measurements. This involved building a small, circular wall of perhaps mudbrick that had to be perfectly level at the top. Within the circle, a man would stand and through a straight pole with a forked top called a bay, sight a circumpolar star as it rises. A second man at the perimeter of the small circular wall would then "spot" the wall where the star rose. Using a type of plumb line, or merkhet, he would also spot the mark at the bottom of the wall. When the star set, the process would be repeated. Measuring between the two spots would then provide true north from the center sighting pole.
Recently several other theories have been raised, all of which involve some sort of astronomical measurements. A British scholar named K. Spence believes that the Egyptians used two circumpolar stars (Delta Ursae Majoris and Beta Urae Minoris or Epsilon Usae Majoris and Gamma Urae Minors) Another theory set out by a Slovak Egyptologist, D. Magdolen, believes that the ancient Egyptians oriented their monuments using the sun, by means of wooden stakes and ropes. There is in fact a reference in ancient text referring to "the shadow" and the "stride of Ra".
The sun rises and sets in equal but opposite angles to true north. Using a plumb line, a pole would have been set as vertically as possible. Then, about three hours before noon, its shadow would be measured. This length then becomes the radius of a circle. As the sun rises higher, the shadow shrinks back from the line and then becomes longer in the afternoon. When it reaches the circle again it forms an angle with the morning's line. The bisection of the angle is true north. However, this method would be less accurate than the stellar method, but could be fairly accurate during the solstices.
Creating the Ground Plan
After the primary coordinates were determined, the ground plan would be marked out. Some of the methods used to do so varied from pyramid to pyramid. Here, we examine the means by which the ground plan of the Great Pyramid of Khufu at Giza was determined.
Initially, a reference line along true north was constructed from the orientation process. The next step would be to create a true square with precise right angles. Within Khufu's pyramid, there is actually a massif of natural rock jutting up that was used as part of the pyramid's core. Therefore, measuring the diagonals of the square to check for accuracy was impossible.
We believe that the ancient builders could have achieved a precise right angle in any of three ways. The first method would have involved the use of an A-shaped set square. The set square would have been placed along the established orientation line and the perpendicular taken from the other leg of the square. The set square would then be flipped and the measurements repeated. The exact 90 degree angle would then be taken by taking into account the small error of the angle between the two measurements.
The problem with this method is that no set squares large enough to give a precise angle for the distances have been found in ancient Egypt. The perpendicular measurement it provides would be very short considering that the line would have to be extended some 230 meters (754 ft) in the case of Khufu's pyramid.
A second method would have employed the use of a sacred or Pythagorean triangle. The triangles seem to be present in the design of the Old Kingdom pyramids, but there is no real conclusive evidence of their use. Basically, this triangle uses three equal units on one side, four on the next, and five on the hypotenuse to give a true right angle. At Khufu's pyramid a series of holes along the orientation line are dug at seven cubit (3.675 meters or about 12 ft) intervals, so the triangle probably used these positions in the measurement. In other words, the triangle would have been measured as 21 cubits by 28 cubits with a 35 cubit hypotenuse. This would have resulted in a much longer measurement for the perpendicular line then with the use of a set square. If the unites used were any greater, the measurement would have been interrupted by the rock outcrop.
A third method possibly available to the early Egyptians would have been through the use of intersecting arcs. In this method, two circles would have been sketched by rotating a cord around two points on the orientation line. The intersection of the two circles would then provide a right angle. Some doubt this method was used because the elasticity of the string or rope used to sketch the circles would lead to inaccuracies. However, at Khufu's pyramid, there are a number of post holes dug that might have been used to draw such circles, so the method cannot be ruled out. Furthermore, the Egyptian may have used a rod or other device rather than rope or string to draw the circle, eliminating elasticity.
An orientation reference line was set up in a larger square by measuring off the established square ground plan. This was done by digging post holes at measured distances from the inner square in the bedrock and inserting small posts through which a rope or string ran. These holes were dug at about 10 cubit intervals. This outer reference line was needed because the original orientation lines would be erased by building work. Various segments of the reference line could be removed so that building material could be moved into place. Then measurements were taken from the guide line as the material for the platform were put in place so that the the platform was in accord with the initial floor plan.
The platform of Khufu's pyramid was made of fine white Turah quality limestone slabs with occasion backing stones of local limestone for leveling. Today, we know that the platform was one of the most important elements to a pyramid's survival over great lengths of time. It also appears that the builders of Khufu's pyramid were well aware of this, but such knowledge seems to have been almost forgotten from time to time. Some later pyramids platforms were not built upon solid bedrock, or the platform was poorly built and those pyramids built atop these poorly constructed platforms did not survive for long.
Not only was the platform required to be laid in a perfect square, but it was also required to be very level. In Khufu's pyramid, the platform is level to within about 2.1 cm (one inch). There were several means that this too could be accomplished. Traditional though, apparently originally conceived by Edwards, suggests the use of water to level the platform. He thought that the ancient Egyptians might have built a mud enclosure around the platform that was then filled with water. A grid of trenches would have been cut at a uniform depth below the water. However, modern Egyptologists believe this method would have been cumbersome at best. The platform would have had to have been chiseled beneath the water. Perhaps a more accepted theory involves channels being cut to form a grid within the platform, which was then filled with water. At the top of the water's surface, the level would be marked along the sides of the channels, and then the platform cut accordingly.
However, Lehner, who must be taken very seriously in any discussion of Giza pyramids, does not believe that water was used to level Khufu's pyramid. In fact, he doubts any water related theories of leveling, mostly because evaporation might cause considerable variations in the measurements. Specifically though, Khufu's pyramid is built on a sloping base, and here, it is the platform itself that is leveled and not the bedrock beneath the platform. In fact, the ancient builders were required to cut down the northwest corner of the platform, while actually building up the opposite, southeast corner.
Another leveling method might have utilized the posts used to build the reference line of the pyramid. These posts could have been made of equal heights, or marked to provide a reference level. Apparently the leveling techniques used in pyramid construction are not well understood at this time.
However, what is understood is that when the Egyptians, such as those who built Khufu's pyramid, were at the top of their skills, the monuments they built could indeed last virtually forever.
Last Updated: June 20th, 2011