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* Analysis of Relieving Chambers in Khufu's Pyramid * 

The so-called "Relieving Chambers" over the King's burial chamber in the
pyramid of Khufu have generated much discussion, and in many ways, have
been seriously misunderstood over the years. The following diagrams and
notes are provided to convey a clear understanding of the simple dynamics
of the relieving chambers, how "relieving chamber" is actually a misnomer,
and show how the support structure actually relates to the pyramid
interior surrounding it. First and foremost, this is not a simple concept
to understand, because it is a three-dimensional puzzle, that interlocks,
as I've suggested, in all three dimensions. 

I will do my best to diagram
it in two dimensions, so bear with me. To begin, here is an excellent
picture of the chambers, as taken from "The Pyramids of Egypt", by Alberto
Siliotti. Excellent book, great pictures. Buy it if you get a chance. We
can see that the chambers are merely stacks of stones, going up higher and
higher, until they reach the "peaked" roof stones at the top. It is
important to understand what role the peaked roof (or gable) plays in the
structure. Here's a simple diagram. It shows a pair of blocks, just like
the peaked roof of the chambers: The black block is the "weight" being
placed above the chamber. The gray blocks are the slabs in the peak. The
orange blocks are the recipients of the force being transferred by the
gables, and the red blocks are the core masonry. The green and blue blocks
are the structure under the gable, that protects our "precious cargo"
underneath. 

Now... so long as you have something VERY solid near the
bottom (orange transfer blocks) of the two angled slabs (in gray), you
can, most effectively, remove the green/blue blocks, and the structure
stays put. In effect, this is the precise design we see at the very top of
the 5 relieving chambers: two angled slabs, and a "detached" set of
spacers underneath. These spacers are there solely to take up the space
between the north wall and the south wall, and keep the 15 meters of walls
from caving inward. To test this theory, simply look at the structure, and
ask, "Can this structure exist without any of the surrounding pyramid
blocks?" In other words, could this structure still stand up, independent
of the surrounding core masonry? 

The answer is "yes"... until you get to
the angled slabs at the top. These blocks appear to be independent of the
rest of the structure... but wholey reliant upon the core masonry for
their support. In actuality, we are looking at two completely different
structures over Khufu's burial chamber, not one. But why do those angled
slabs need to be 10 meters up in the air? The structure over the Queen's
chamber does just fine, with the peaked roof right on top of the room.
/Photo by Jon Bodsworth, Gizaview.com home.freeuk.net/gizaview/Home.html>/
The Grand Gallery sits right outside of the King's Chamber. From a bird's
eye view, it is situated something like this: So... it becomes necessary
to raise the angled slabs well above the top of the Grand Gallery. The
force MUST be transferred down the slope of the pyramid. If they tried to
transfer the force into the wall immediately adjacent to the southernmost
wall of the Grand Gallery, it would most certainly push right through...
as shown here... The blue arrows show the force as it is transferred down.

The right angled slab has now pushed through the wall of the Grand
Gallery, and has allowed the force over the King's Chamber to be fully
absorbed by the roof. No longer is the structure independent... the entire
weight of the pyramid above has been thrust onto the flat roofbeams.
Evidence of the stress/pressure involved was noted by Gantenbrink when he
ran his robot into the southern shaft of the Queen's chamber. As
Gantenbrink states in a caption on his autocard drawings (reproduced VERY
poorly below) 

*"The thrust created by the roof-beams of the Queen's-Chamber is reflected
horizontally"* 

(Link to Gantenbrink's Site www.cheops.org/>) This evidence
shows that the transfer is, mostly horizontal, rather than vertical. It is
obviously mandatory that we raise the angled roof slabs above the
Gallery... far above the gallery. To test this theory of construction, we
need to make sure that the walls of the "relieving chambers" (as I said,
it is a misnomer... they are actually just "spacing chambers") are: 1.
directly connected and supported by the walls of the King's Chamber; and
2. NOT in direct contact with the angled slabs on top. 

In Siliotti's
drawing, notice the tiny space at the very top of the "walls" of the
relieving chambers -- the red arrows point to the spaces: This area of
"non-contact" is precisely what we need to show that the force is being
totally and completely transferred away from the roof of the King's burial
chamber... and also right over the top of the Grand Gallery. We also find
this is somewhat corroborated by Petrie: "/"All these chambers over the
King's Chamber are floored with horizontal beams of granite, rough dressed
on the under sides which form the ceilings, but wholly unwrought above.
These successive floors are blocked apart along the N. and S. sides, by
blocks of granite in the lower, and of limestone in the upper chambers,
the blocks being two or three feet high, and forming the N. and S. sides
of the chambers. On the E. and W. are two immense limestone walls wholly
outside of; and independent of; all the granite floors and supporting
blocks. Between these great walls all the chambers stand, unbonded, and
capable of yielding freely to settlement. 

This is exactly the construction
of the Pyramid of Pepi at Sakkara, where the end walls E. and W. of the
sepulchral chamber are wholly clear of the sides, and also clear of the
sloping roof-beams, which are laid three layers thick; *thus these end
walls extend with smooth surfaces far beyond the chamber, and even beyond
all the walls and roofing of it, into the general masonry of the
Pyramid.*/" (emphasis added) Pyramids and Temples of Gizeh, 1883 Although
Petrie is specifically describing the east and west end walls of Davison's
chamber, it is not unreasonable to assume this also applies to the north
and south supporting blocks of the granite spacers underneath, especially
in light of his unambiguous statement that: / "Between these great walls
all the chambers stand, unbonded, and capable of yielding freely to
settlement." / This assessment is in complete agreement with the diagrams
we have from both Sillioti and Gantenbrink.

In
"The Complete Pyramids" (1997), Lehner shows the top row of lintels extend
into the core masonry, and it is the second row that begins the
independent structure. /From Mark Lehner's, "The Complete Pyramids", p.51/
The Grand Gallery is only about 2 meters wide at the base. Given this
relative narrowness, Hemiunu did NOT have to raise the roof for the entire
20 cubit length of the King's chamber... he could have lowered the roof
above the chamber immediately after the end of western end of the Grand
Gallery. It seems unreasonable to assume that he was going to take a
chance with a split level roof system. It's only 20 cubits long... he
might as well do the whole thing the right way. 

*The Question of Cantilevers* 

There has also been conjecture that the gabled blocks act as a cantilever,
and actually force the entire weight of the pyramid above the chamber down
onto the exterior walls. This theory is contingent upon the two gabled
slabs acting independently from each other, and not forcing themselves
against each other in the middle. Naturally, they do lean against each
other in the middle. As we can see from the diagrams above, there is no
fulcrum present under the gabled slabs, so they in no way can /act/ as a
cantilever. In fact, unlike peaked roofs of houses, these roofs actually
transfer /more/ weight horizontally as you lower the slope. This is why
the slope of the roof in Davison's chamber is only slightly more than 30
degrees (based on Gantenbrink's autocad drawings). It is this precise
principle that allows martial arts experts to do things like this: The
harder you push down on the martial artist's head in this example, the
harder his legs push out against the walls. No force is being transferred
to the ground below, obviously... except through the walls at his feet.  
In the same way, the gables transfer the weight of the blocks above the
chamber to the core masonry on each side. Without a fulcrum, the limestone
blocks are merely being compressed... not stressed.

The final area I want
to address is the depiction of the double gables over Davison's chamber.
These double gables are drawn for two reasons, as far as I can determine:
1. The main entrance to the pyramid has double gables (see below); and 2.
The pyramids after Khufu are shown to have double and triple gables over
the burial chambers. Based on these pieces of evidence, it does seem
reasonable to place double gables over the spacing chambers above Khufu's
burial vault. Based on this overall understanding, the form and function
of the Spacing Chambers over Khufu's Burial Vault should be reasonably
well explained. (c)Copyright 2002, Anthony Sakovich. All rights reserved.

*Bibliography* ___________________________ 

*Arnold, Dieter*; /Building in
Egypt: Pharaonic Stone Masonry/; Oxford University Press, New York, 1991

*Arnold, Dieter*; "/Temples of Ancient Egypt/"; Cornell University Press,
New York, 1997 

*Petrie, Sir William Flinders*; "/The Pyramids and
Monuments of Gizeh: 1883/";
http://www.users.net2000.com.au/~fmetrol/petrie/ 

*Lehner, Mark*; "/The
Complete Pyramids/"; The American University in Cairo Press, 1997

*Siliotti, Alberto*; "/Guide to the Pyramids of Egypt/"; Barnes & Noble
Books, New York, 1997 Field Research conducted in December, 2001 /It has
come to the author's attention that this is almost precisely the same
construction explanation offered by Dr. Rainer Stadelmann. None of this
work is intended as original, nor should it be construed as an attempt to
declare it as such./ // // * *//