MOVING AND LIFTING THE CONSTRUCTION BLOCKS OF THE GREAT PYRAMID
Jason Baldridge
Winter 1996
INTRODUCTION.
Located in Giza, Egypt, the Great Pyramid
of Khufu (Cheops) is the oldest of the Seven Wonders of the Ancient World.
It is also the only one still standing. For thousands of years, it has
remained an enigma to the many people who have attempted to discern how
it was made. Although many questions about the Great Pyramid itself have
been sufficiently (though not conclusively) answered, the debate over the
precise manner of its construction has never ceased. Scholars (and non-scholars)
from various disciplines and backgrounds have made countless attempts to
resolve the many different issues involved in the creation of the Great
Pyramid (GP). This paper focuses on the methods of transporting and raising
the blocks of which the GP is made.
The importance of knowing how the GP was
built is readily apparent. The construction of such an imposing building
must reveal a great deal about the labor forces, tools and machinery, technical
knowledge, and people of Egypt 4600 years ago. The sheer size of the structure
alone commands us to reflect upon its builders with a certain degree of
awe. The GP is still the largest building in the world. It stands 450 feet
high (originally 479) and weighs six million tons. Its orientation is within
five arcminutes of true north and the level of its thirteen-acre base varies
by only one inch. The casing stones are so finely jointed that a knife's
edge cannot fit between them. The precision of the workmanship throughout
the rest of the GP is remarkable as well.
Khufu's workers faced several problems
while undertaking the task of building the GP. First, they had to quarry
the limestone blocks which were used to build the GP. After quarrying the
blocks, they had to transport them to the building site and raise them
to their final positions. Raising the blocks to the various levels of the
GP was not a simple task; the limestone blocks weigh up to 15 tons and
the granite monoliths in the interior of the GP weigh up to 70 tons. Indeed,
the questions most often asked about the construction regard the method
of getting these blocks to their final positions in the GP. A wide range
of theories and opinions have been advanced to explain how this was accomplished.
I will dismiss as inconsequential those speculations which attribute the
moving and raising of the blocks to the use of anti-gravity and supernatural
power by the high priests of ancient Egypt. I also will not consider theories
that astronauts from other planets built the GP. The proponents of these
ideas incorrectly assume that ancient Egyptians living in 2600 BC did not
have the ability to do it by themselves--using straightforward, physical
methods and working with the same natural laws we encounter in the present
day. Of course, many scientific theories have been advanced that are less
fanciful and more workable. The various scientific contenders differ substantially
with regards to practicality, engineering feasibility, and the archaeological
record. The purpose of this paper is to lay out and select the most promising
of these.
Before discussing the different ways of
moving and raising the limestone blocks, a contention that the blocks were
never even quarried must be challenged. Polymer chemist Joseph Davidovits
advanced an unconventional theory that the pyramid builders actually made
the blocks by pouring a mixture of disaggregated limestone and a geopolymeric
binder into wooden molds. This mixture then hardened and became almost
indistinguishable from natural limestone. This would have allowed the workers
to have simply passed potfulls of the mixture up the side of the GP, with
no need for ramps or machines. Davidovits says that samples of pyramid
casing stones revealed that they contained as much as thirteen percent
of the binder; however, Michael Tite says that his own analysis of pyramid
stone did not produce the same features (Peterson 1984, p. 327). Geologist
James Harrell, who has done extensive work on the provenance of pyramid
stones, performed an analysis of the very sample that Davidovits used and
concluded that it was natural limestone quarried in the Mokattam Formation
(Harrell 1993). It is quite clear that blocks were quarried, not manufactured.
TRANSPORTING THE BLOCKS.
How the limestone blocks were transported
to the GP is a topic about which engineers have developed many hypotheses.
The generally accepted theory is that the ancient Egyptians dragged the
blocks on sledges over causeways made of either slaked lime or tafla (a
local clay). The remains of causeways constructed of tafla have been found
all over the Giza plateau (Hadingham 1992, p.51). Also, actual sledges
at pyramid sites, and reliefs and paintings in tombs and quarries depicting
the use of sledges have been discovered (Leper 1990, p. 242). A team led
by archaeologist Mark Lehner successfully used the sledge when they constructed
a small, eighteen-foot tall pyramid (Hadingham 1992).
Engineer John Cunningham (1988) proposed
that the Egyptians carried the blocks on flexible poles. According to Cunningham,
these poles would have given an incredible mechanical advantage by combining
the weight distributing principle of the suspension bridge with the energy
storing characteristics of the bow. This may be effective for lifting,
but I question whether horizontal progress could be easily made. To keep
the blocks from bouncing erratically, movement would have to be very slow
and cautious. Also, the average limestone block is a cube with sides three
feet long. At best, three poles could fit under one of these, and the onus
of lifting 5000 pounds would be on the six individuals who held the ends
of the poles. Cunningham stated that a load of 2,600 pounds had been lifted
using twelve oak poles (Cunningham 1988). Simple calculations, left to
the reader, will clearly show that Cunningham's proposal could not have
been employed by the builders of the GP.
Engineer John D. Bush (1978) suggested
an alternative method that uses ancient wooden circle segments similar
to those uncovered during excavations (Figure 1a). Egyptologists theorized
that they were used as cradles or rockers. Bush proposed that the pyramid
builders transformed the limestone blocks into cylinders by attaching a
circle segment to each edge of the blocks' square cross sections (Figure
1b). The blocks could then be rolled and moved with ease. Bush has demonstrated
this technique, successfully rolling a 5000-pound block up a ramp with
the help of six other men. However, even though this method is feasible
and workable, it is unlikely that the GP's builders used it. The segments
used by Bush had holes drilled into them to accommodate ropes which held
the segments onto the block, yet none of the ancient segments found have
such holes in them.
Circle
Segments
Figure
1a Figure
1b
How these alternative proposals fail is
most clearly seen by considering the extreme case. Neither theory accounts
for the movement of the fifty-ton granite slabs used in constructing the
internal chambers of the GP. Considering the immense size of these monoliths,
the flexible pole method would be rendered even more awkward. Forward motion
would be extremely tedious--assuming that these monoliths could even be
lifted by this method. Bush's idea would also be problematic. The dimensions
of these slabs are not uniform, so each slab would have needed specialized
circle segments. The largest monolith is about 27' x 4' x 8' at its ends.
Even if larger circle segments were used to create a pseudo-cylinder, the
weight distribution would not be even around the central axis and the size
of the entire ensemble would be quite large and unwieldy (Figure 2a). Ramps
and causeways over 27 feet wide would have been necessary because the slabs
would have moved perpendicular to them instead of parallel. In order to
make these circle segments, the builders would have needed trees with diameters
of at least three feet (perhaps up to five). How easily the Egyptians could
have obtained such trees would have to be checked. Also, some of the slabs
are rough-cut on their tops, which increases their height by one to two
feet in their midsections (Figure 2b). This would cause the midsection
to project beyond the cylinder created by the segment circles (Figure 2a,
top). Consequently, the rolling of one of these blocks would be inordinately
difficult and most likely unmanageable. The most plausible explanation
is the sledge method. It would accommodate even these massive granite slabs,
and it is most consistent with the archaeological record .
Figure
2a Figure
2b
RAISING THE BLOCKS.
The greatest controversy over the GP's
construction regards the manner in which the builders raised the limestone
blocks to the various levels (courses) of the GP. The traditional view
of Egyptologists is that the builders used some sort of ramp to raise the
blocks. Evidence for the use of ramps includes paintings of construction
ramps, a ramp found at an unfinished temple, and the remains of ramps present
at a couple of pyramid sites. Originally, it was thought that a single
ramp extended from one face of the GP. This has been rejected in recent
years because such a ramp would have had a volume up to three times that
of the GP itself. Also, it would have been over a mile long--extending
far beyond the limestone quarries 500 yards away.
Another ramp theory proposes that a series
of switchback ramps zigzagged up one of the faces of the GP. Even more
popular is the idea that a ramp wound around the entire GP. Lehner successfully
used a wrap-around ramp when he constructed his small pyramid. This method
is a strong contender for being the best of the ramp theories, and it may
well have been the one the pyramid builders actually used. Even so, it
has several weaknesses. There is nothing in the archaeological record that
indicates the use of such ramps. The depictions of ramps generally show
straight ones which lead up to a wall. Like the straight ramp, the wrap-around
ramp would be nearly a mile long. Turning corners would have presented
great difficulties, though Lehner's team was able to solve this problem
by planting posts at each corner and pivoting the ropes on the posts as
they pulled a sledge around the corner (Hadingham 1992, p. 51). Even though
Lehner was able to use a wrap-around ramp, I question whether the method
would work for the GP, which is 240 times the size of Lehner's pyramid.
The straight ramp would have also worked well for a pyramid eighteen feet
tall. Also, the wrap-around ramp itself would have been a remarkable feat
of engineering. A large amount of material would have been necessary to
keep it stable, and, according to Zahi Hawass (1990, p.41), the greatest
problem would be that the unfinished faces of the pyramid would not have
supported the weight of the ramp.
An alternative method of raising the blocks
is suggested by a comment the Greek historian Herodotus made in the fifth-century
BC. When Egyptian priests were showing him the GP, they told him that the
stones had been lifted with levers made of short timbers. Some theorists
feel that this clue may offer a better solution than the ramps. The largest
and heaviest blocks lie on the first course, and the blocks become smaller
on each higher course. J.P. Lepré (1990) says that a ramp would
be feasible only up to the fifth course, and that a different method would
be necessary for the next 196 courses. He proposes that a machine which
uses levers and counterweights could have effectively lifted the blocks.
A line of such machines would have extended up one of the faces of the
GP, each machine passing the blocks up to the next. Though I agree that
machines were possibly used by the builders, the particular machine which
Lepré devised seems much more complex than the builders actually
needed, and it would have been too large to fit on the stepped sides of
the GP. I am also uncomfortable with Lepré's machine because his
knowledge of physics seems questionable; he depicts a 1-ton block that
is 15 feet from a fulcrum as being in balance with a 10-ton block that
is 5 feet from the fulcrum (p. 256). The 1-ton block would actually need
a lever arm of 50 feet to balance the 10-ton block at 5 feet.
Sculptor and pyramid researcher Martin
Isler felt that a simple levering process was employed (Boxer 1987, p.
8). According to Isler, a block could be elevated by alternately lifting
each side of the block with a lever and placing a board underneath it.
However, when this method was attempted during the construction of Lehner's
pyramid, it failed miserably. After getting a 3-ton block two feet high,
the whole setup became very wobbly and tricky to manage. It was also very
time consuming.
Some theorists suggest that a simple machine
using levers and counterweights was used to elevate the blocks. Such a
machine, called a shadoof, has existed in Egypt for millennia and is still
used to elevate pots full of water from the Nile River to the irrigation
canals. Though a shadoof itself could never lift a 2.5-ton block, engineer
Olaf Tellefsen (1970) observed three men using a similar machine to lift
very large stones while he was riding up the Nile. Even so, a few considerations
must be met before one can propose a machine that could be used on the
GP. First, it must fit and be capable of operation on the pyramid's stepped
face. Second, it must be manageable and controllable so that damage would
not be done to the blocks being lifted and so that workers would face a
minimal risk of falling or being knocked off the edge. Third, it should
be simple so as to align as closely as possible with the scant archaeological
record that such machines can claim. Finally, it must be capable of lifting
at least 5000-6000 pounds.
I suggest that such a machine system could
have been successfully employed by the pyramid builders. Having raised
the first five or six courses of the GP (where the heaviest stones lie)
with a straight ramp, the builders would have added a one-block extension
to a twenty foot section up the entire face of one side of the GP (see
Figure 3). They also would have not installed certain blocks so as to allow
room for levers to operate. Stone blocks with special grooves would be
installed on the extension as fulcrums over which long wooden tree trunks
would be placed. These timbers would have diameters of one-half to one
foot and would be 20 to 25 feet in length. The short arm of a timber would
be attached to a block, while the longer arm would have a net-basket attached
to it. Weights would be incrementally added to this end, thus raising the
block (Figure 4). For example, about 2100 pounds 14 feet from the fulcrum
would raise a 5000-pound block that is 6 feet from the fulcrum. Including
the weight of the timber, the weight required would actually be less than
2100 pounds.
Figure 3a. Isometric view of pyramid-face extension
with fulcrums and levers in place.
Some blocks have not been installed
so that the lever and basket may move unobstructed.
Figure 3b. Plan view. Shading denotes altitude.
The blocks are approximately 3' x 3'.
Figure 4. Block lifted after weights have been
added in increments.
Workers would use their weight to
manipulate the machine once the two ends gained equilibrium.
Once the height of the next course was
cleared, the operators would use their own weight to maneuver the block
onto the next course (Figure 5). The weights would be removed and the pole
would be positioned on the next highest fulcrum and the process would begin
again (Figure 6). In this way, each block would traverse a linear path
up to the course it finally rested upon. When the pyramid was nearly finished,
the machine staircase would have been completed from the top down, with
the blocks from the extension being used to fill in the omitted areas.
The fulcrums would have been shattered and sent down the pyramid with the
machine weights. Alternatively, depending on their original dimensions,
they could have been cut and finished and used as construction blocks.
More than one such fulcrum-and-lever staircase could have been used, as
needed. A lot of fine tuning would be necessary to make such a system perfectly
workable, but as such it is quite simple and feasible. It must be noted
that whether this particular system was the precise one used is not the
main issue. My primary interest is in demonstrating that pyramid blocks
could have been raised without ramps.
Figure 5a. Block and lever rotated so that block
rests on next level.
Figure 5b. Plan view. Note: the true length of
the lever is given in these two figures.
Figure 6. The levers are shifted onto the next
highest fulcrum and the process continues.
One issue that has been left unexplained
by theorists was raised by F.M. Barber (in Tompkins 1971). He questioned
that the monolithic granite slabs used in the construction of the internal
chambers of the GP could have been lifted by wooden machines. Barber felt
that steel cranes or derricks would have been necessary to elevate them.
Because the pyramid builders did not have such machinery, Barber concluded
that ramps were the only way for them to raise the monoliths, some of which
weigh 50 to 70 tons. Actually, the wrap-around ramps would also be strained
to accommodate the inordinate weight and dimensions of the granite slabs.
However, I feel that it was entirely possible for the builders to raise
these massive slabs without the use of huge ramps or machines. All they
needed to do was store them on the top construction level of the GP as
it grew course by course. Once a course was completed, work would begin
on the next. After the new course was partially built, a small ramp would
be constructed and the slabs would be pulled up to the new course. The
builders would have continued this process until the slabs were placed
in their final positions. Though there are a large number of these slabs
in the building, the builders would not have been lacking space to store
them, since the area of the base of the GP is about 13 acres. None of the
slabs is located more than halfway up the GP, where there would still be
over four acres to work with.
One common objection to machine theories
is that the ancient Egyptians would not have had access to the wood necessary
for them. The trees that grow in Egypt are either too valuable as sources
of food or they are not long and straight enough, nor are they sufficiently
strong. However, the hieroglyphic Palermo Stone text states that the Pharaoh
Sneferu (Khufu's father) had sent 40 ships to Lebanon to bring back timbers
of cedar (Meiggs 1982, p.63). Cedar trees are quite straight, and they
commonly reach up to eighty feet in height (sometimes 120). Other kinds
of wood sufficient for machine purposes were available in the Mediterranean
area, and there were plenty of trading networks through which the ancient
Egyptians could obtain timbers (Meiggs, pp. 54-66). Some of Sneferu's pyramids
contained cedar beams and timbers. A ship made of cedar wood was found
in a pit near the south side of Khufu's pyramid. Clearly, the pharaoh who
was responsible for raising the largest building in the world could have
acquired the timbers necessary for machines easily enough.
Machine theories are also criticized because
machines are not found explicitly in the archaeological record. I do not
find this surprising. Wood, though available, was not in abundance in Egypt,
so once the machines had lost their usefulness, they were probably disassembled
and used for building other things or, at the very least, burned as firewood.
The long timbers used in my method could easily have been utilized for
other purposes. Thus, these machines disappeared from the archaeological
record. It should be noted that the record does show that the pyramid builders
were well aware of the principles of the simple lever, though it does not
explicitly reveal any particular machinery. Also, some researchers, such
as Tellefsen, consider Herodotus' statements about machines to be a part
of the archaeological record, despite the opinion of many scholars that
Herodotus is not a credible source.
CONCLUSION
Ramps were not the only means available
to the pyramid builders. Making them and removing them would have been
an enormously laborious process. Also, dragging the blocks up a lengthy
ramp would have taken far more effort than using levers to move them straight
up the face of the GP. The levers are feasible--they can lift loads
like the limestone blocks. And though there is currently no explicit, physical
archaeological evidence of them, clues from Herodotus and the ancient use
of the shadoof hint that they were not unlikely. Also, the GP itself
is unusually void of hieroglyphics or decoration, suggesting that the builders
may not have left such evidence.
Why create huge, long ramps and pull heavy
blocks thousands of feet when a lever can lift them much more easily and
avoid extra work caused by friction? Lepré does not feel that designing
and building these machines would be beyond the abilities of the pyramid
builders:
Surely, the architect of the first built
and last remaining of the Seven Wonders of the Ancient World was capable
of devising a more sophisticated system than we give him credit for [the
ramp theory] -- one where heavy stone and minimal manpower is used to lift
other, heavier stone. For an architect whose stamp of genius is so artfully
contrived in the dimensions and symmetry of the Grand Gallery and King's
Chamber complex, it would all be in the balance, rather than in the struggle."
(1990, p. 254)
The theory that the ancient Egyptians used
some sort of simple machine in the construction of the GP is a strong contender.
Of course, it is entirely possible that a combination of different methods,
including ramps and machines, were used by the builders of the GP. However,
as one commentator put it when discussing pyramid construction methods,
the only certain thing we know is that the Great Pyramid most definitely
was built.
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