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Analysis
of Relieving Chambers in Khufu's Pyramid
Anthony
Sakovich
Abstract: 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
The Grand Gallery sits right outside of the King's Chamber. From a bird's
eye view, it is situated something like this:
Plan
View of the Burial Chamber and the Grand Gallery
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)
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
Author's
note:
It
has come to the author's attention that this is almost precisely the same
construction explanation offered by Dr. Rainer Stadelmann. In light of
this, none of this work is now intended as original, nor should it be
construed as an attempt to declare it as such.
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
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