robin cook wrote:
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> In his diagrams Petrie shows the floors of KC
> south shaft intersecting the casing just below the
> top of course 103, and KC north intersecting at
> the top of course 102. In the text he gives the
> height of the exits as 3248.4" and 3119.1" above
> pavement. (somewhere I read that Goyon gives
> different figures 3157" and 3127"). Gantenbrink
> states on his website - "As we verified in 1992,
> the upper southern shaft emerges on the exterior
> at the 101st layer, the upper northern shaft at
> the 102nd layer".
Gantenbrink is in error. Petrie's analysis is the correct one.
We have enough information to reconstruct the course structure around these exit points to see what is going on. Courses 102, 103 and 104 have thicknesses of 9p, 10p and 9p respectively. Courses 101 and 104 have elevations (at their tops) in whole cubits of 150c and 154c respectively. This makes the elevations of the four courses (tops) as follows:
Course 101 - 150c
Course 102 - 151c 2p
Course 103 - 152c 5p
Course 104 - 154c
In Gantenbrink's scheme, the shafts exit at the same level, at 154c elevation. Gantenbrink's model for the shafts, though simplistic, is very attractive. This creates diagonals for the 154c level and the KCS shaft which express the dual 70:99 and 99:140 geometry of r2. On the other hand, the KCS shaft exits seemingly one course (9 palms) lower. More precisely, the middle of this shaft exits at the top of course 103 (elevation 152c 5p). Why?
If we do the maths, we find that the line at this level is virtually 200 cubits. That must mean something. For a start, it is a measure that has been used in previous pyramids, for the heights of both the Bent and Red pyramids (arguably). It is also used subsequently as the base length of Djedefre's pyramid, maybe Menkaure's pyramid, Neferirkare''s step pyramid, and several pyramids of the Middle Kingdom.
So, in the case of KCS, we have to say it has two exit elevations, the primary design being at the 154c level, which creates a line of length 198 cubits (and diagonal of 280 cubits), and which completes the KCS design of 70-70-99. In practice, however, the shaft seems to target the 152c 5p level, as this creates a line of length 200 cubits, which relates this pyramid to its predecessors the Bent and Red pyramids.
In the case of the KCN shaft, its exit seems to point at the next course below, i.e., the top of course 102, elevation 151c 2p. Yet if we do the maths, we do not find anything interesting regarding the length of its horizontal line, nor the diagonal of this level, so what is going on here? Having a look around, we note that this elevation is very close to 110 cubits above the joint in the floor marking the junction of the AP with the GG (in the same manner as the 154c elevation is very close to 110c above the junction of the ceiling of the AP where it joins the N wall of the GG, at Gantenbrink's so-called "common reference point").
The elevation of this floor joint is precisely 41c 2.5p. If we add 110 cubits on to this, we get 151c 2.5p. This seems to be the elevation targeted by the middle of the KCN shaft, and is consistent with the situation with the KCS shaft, where it is the middle of the shaft that targets the 152c 5p elevation.
To summarise: the middle of the KCS shaft is targeting the elevation which creates a pyramid of base length 200 cubits, while the middle of the KCN shaft is targeting the elevation which is 110 cubits above the junction of the AP and GG.