Does the Bent Pyramid have Sky Shafts ?

Shafts have currently not yet been found in the upper chamber of the Bent Pyramid, but there is some evidence that they might exist.
If there were shafts, the exits into the chamber would not be visible anyway for reasons which I will explain - and some pictures.

Before getting to the shafts there is need to study Petrie's survey notes for the correct dimensions of the pyramid. Up to now it seems that researchers (like Legon) have failed to understand what Petrie wrote and measured. In some analyses the base is assumed to be 360c and in others 361.7 (or 362) cubits. Which is correct ?

The answer is both ! There were two bases. One was the foundation or true base on which the pyramid was built. It had sockets for the corner stones. A picture of this base with an embedded corner stone is below. Petrie refers to it also as 'the socket base' which is the level in the picture.



The second base is one which Petrie called 'the apparent base' or pavement level. This was a pavement constructed above the foundation base using paving stones and mortared to the pyramid after the casing stones were put on. Petrie sketched a diagram of one corner here :



The question is - what is the height of the apparent base over the actual base ? Petrie give us two measurements only, because most of this pavement has disappeared and in some cases only a mortar line is left. These were 11 and 34 inches.

Now we need to remember that there was slippage of the corner stones, especially on the SW corner in a downward direction. It took place before the apparent base was constructed. The damage was then patched up. Maragioglo and Rinaldi reported a dislodgement of the descending passage in the region of 10 inches.

The slippage explains the different levels of the pavement above the base. So an assumption needs to be made here in order to continue. The average of the two 11 inches and 34 inches is 1.09 cubits. It will thus be assumed that the original intended height of the apparent base above the socket base was 1 cubit all round.

This can be put on the diagram :



We can now proceed with Petrie's other surveyed dimensions.

The upper part of the pyramid Petrie concluded had a height of 110 cubits.

The slope of the upper part was actually slightly convex so Petrie gave two sets of angles. The average of the angles is 43 deg 11 mins. This gives the horizontal part a length of 117.1 cubits, or 117 cubits to the nearest whole number. (Greater accuracy that this cannot be expected with average slopes, and also the slippage of one or two corners will slightly have affected the slopes.)

Petrie triangulated a corner to the bend to get that dimension and found it to be 63 cubits.
He wrote that the height of the lower section of the pyramid was measured as 90 cubits above the apparent base : "In height the change of slope occurs at 1857 inches (90.0) from the pavement." and "The base of this part will be 63 cubits for the 90 cubits vertical". This is abundantly clear !

Putting these measurements in the diagram :



So the width of the apparent base is 63 + 117 + 117 + 63 which equals 360 cubits. No doubt about this.
The 90 cubits and the 360 cubits go together.

Petrie measured the angle of the lower edge and found that it too was convex with 55 deg 1 min in the lower part and 54 deg 31 min in the upper part. Using the lower down angle and the base platform at 91 cubits below the bend, the length of the sloping part horizontally along the ground is 63.7 cubits (instead of 63c)

The foundation base length is thus 63.7 + 117+117 + 63.7 which equals 361.4 cubits.
This equals one of Petrie's physical measurements. The other two being higher at 361.8 and 361.9. The variation may be due to the inevitable moving apart of the base corners after the slippage.

The Great Pyramid Sky Shafts

In the Great Pyramid N-S cross section there was a geometric rectangle (shown in red) that created the shaft angles.
It had dimensions 77 x 198 cubits. This is in the ratio 7:18.
How the shafts (in green) relate to the chamber is shown here.



The red rectangle was created by the two KC shafts which had angles overall of 45 degrees to the south and slope 7 on 11 to the north. The lines of the shafts intersected 5 cubits below the Kings Chamber. This virtual intersection was 22 cubits from the central axis.

(In fact the blue rectangle has the same dimensions, so there was one rectangle directly stacked on another.)

The shaft exits divide the height of 280c into 154 and 126 cubits, which is in the ratio of 11 to 9.

These rectangles were probably the starting point for the GP design and shape.


The Bent Pyramid Rectangle

In the Bent Pyramid cross-section there is a similarly proportioned rectangle using the true base and the bend corners.



It has dimensions 91 x 234 cubits which is in the same ratio 7:18 as the GP and thus also creates the same shaft angles of 45 degrees and 7 over 11. This cannot be a co-incidence as it is too specific and both pyramids have the same architects.

There was clearly some connections between the Bent Pyramid and the Great Pyramid. The common rectangle of proportions 7 : 18 contained the shafts angles. It influenced the shapes and sizes of both. It suggests that the inclusion of shafts into the designs was of primary importance for both.

In the case of the Bent Pyramid, the vertical height was split by the rectangle into two parts of ratio 11:9 and in the case of the Great Pyramid the shaft exits split the height in the ratio of 9:11.

The base of the Bent Pyramid was 360 and the Great pyramid was 440 and the ratio of these two is 9:11.

We might well expect the sky shafts to be first tested in the Bent Pyramid as were other features that were also used in the Great Pyramid.


The Shafts Exit Points

While all the Bent Pyramid data used above is based on Petrie's survey, the following diagram uses unconfirmed measurements, pending my review of other surveys of the Bent Pyramid.

The exact relation of the upper chamber in the Bent Pyramid to the shafts is shown in the diagram below (it is very similar to the same diagram for the GP) :



The lines of the shafts shown intersect on the base at 5c below the chamber.
This virtual intersection was 26 cubits from the central axis.

The shafts, if they exist, are shown in the diagram exiting into the upper chamber as in the Great Pyramid : 2 cubits above the floor and mid-way along the north and south walls.

Both these exit points were covered with structures added to the chamber after the slippages to support the chamber cavity and prevent compaction. The north end had what is called a 'massif' which has been largely cleared away there except for cedar beams enclosed in a plaster wall. The black things are small bats !



The southern wall has a short wall that is about 4 cubits high and 2 cubits wide. It is used to support the current ladder. The man in the photo is standing on the short wall that blocks where the shaft exit might be. This wall is less valuable and could possibly be removed to check for the shaft.



If there were shafts, a question remains. Why would the builders block up the exits into the chamber ?
One answer is that the shafts were already disjointed and blocked along their length by the slippage of the base.

Summary

The pyramid used two bases - a foundation base and an apparent base separated by 1 cubit. This was probably done to create the following pairs of numbers.

The apparent base created the pair :
90 and 110 - for the 9 to 11 ratio

The true base created the pair :
91 and 324 which are the 7:18 dimensions for the shafts' rectangle.

Probably the whole pyramid was designed at the outset to achieve these numbers.

There is good evidence to believe that the Bent Pyramid was designed with sky shafts similar to those in the upper chamber of the GP.




Edited 1 time(s). Last edit at 12/29/2014 08:28PM by GChase.