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BUILDING THE GREAT PYRAMID(Published in a Special Issue of New Dawn Magazine 2013, Vol 7 No 1)
Machines formed of short wooden planks.- Herodotus (484-425 BCE) on pyramid construction -
By Henk J. Koens
jan 2013
We have all wondered how the ancient Egyptians
managed to transport the 2.5 million individual limestone
blocks needed to build the Great Pyramid of Giza. The
handling of such an enormous quantity of stone blocks,with each block weighing an average of 2.5 metric
tonnes (t), constituted a gigantic operation, even by
todays standards.
The general idea in the existing literature is that the
Egyptians transported the stone blocks on wooden sledges,
which were dragged forward by a team of human workers.
However, the efficiency of a transportation by sledgesis extremely low. It would have required an enormous
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effort and so many human workers that the working area
and the road to the pyramid would have been
overcrowded. Sledges were probably used in special
situations, but it is difficult to believe that this was thecase for the great majority of transportation.
There must have been a more efficient transportation
system to meet the required building and time conditions.
IS THERE AN ALTERNATIVE?
In the late 1990s, Cambridge University engineer DickParry and, separately, researchers Roumen J. Mladjov and
Ian R. Mladjov, came up with a revolutionary idea: stone
blocks were transported by rolling . The use of a vehicle
on wheels was not an option because the wheel was not
known to the Egyptians and above all not solid enough
for such heavy loads. The authors failed to give us a
satisfying and practical solution. However, their idea was
not new. Already in 1977 an english engineer suggested
this method and it was earlier described by Vitruvius, the
ancient Roman architect and engineer, in his celebrated
treatiseDe Architectura (On Architecture).
Was there a simple and practical solution? We know
that the use of rollers for the transportation of heavy loads
was an every day technique in ancient Egypt.
Therefore, upscaling this proces for large items is a logicalthought.
The Eyptians did their work with ropes and levers.
The only materials available to them were copper, stone
(dolerite) and wood and probably also bronze, a
material 2 to 3 times as hard and strong as copper. (A
tool made of bronze was found in the pyramid.)
Simplicity had to be the key.
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A realistic alternative might have been the rolling
stone carrier. This hypothetical device consists of two
wooden discs, with a stone block placed in-between,
firmly tied together with a rope a practical solution forthe transportation of stone blocks weighing 2.5 t.
A disc could be made of a number of similar-shaped
wooden circle segments. If copper nails were not
available, wedges, wooden pins or a rope could be used toconnect the parts.
Stone block
TWO WOODENDISCS WITH A
STONE BLOCK
IN-BETWEEN
THE ROLLING STONE CARRIER
THE BASIC PRINCIPLE :
CONNECTED AND
FIXED
WITH A ROPE
A practical solution
for a load of 2.5 t.
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A carrier for the transport and temporary storage of
heavy stone blocks up to 15 t, used in the lowest layers of
the pyramid, is showed in the next design. The stone block
is supportedby four wooden bars and fastened by wedges.
HOW DID IT WORK?
The discs and stone as a whole is a rolling element.
With a pair of shafts and holes in the center of the discs
the carrier could be pushed and pulled forward by humanpower or by an animal. Long shafts would make it easy to
Carrier for stone blocs
up to 15 t.
With padding blocks it was
possible to use it fordiferent seizes.
1.7 m
to
2.5m
circle segment
A disc made of 8 identical
wooden circle segments and a
rope laced through the holes
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round sharp bends. As the force of the heavy load is
directly transferred to the bottom through the discs, the
centre holes would serve only as input for the light pulling
force, rather than suffer the heavy load. But even withoutthe shafts, the workers would be able to roll the stone
block by pushing upward on both discs.
On a firm, plain surface (wood, stone or bricks) such a
system with wooden discs has a friction factor against
rolling of about 0.025. This value can be determined by
experiments involving models. Furthermore, it is known tocertain transportation companies that large wooden cable
reels start rolling down at a slope of slightly more than
2.5 % (1:40), which means that the friction factor is equal
to the value of that slope, or 0.025.
Therefore the transport of a stone block with a weight of
2.5 t (2,500kg) on a plain surface requires a pulling force of
0.025 x 2,500 = 63 kilogram-force (kgf). So a team of6 human workers can easily pull this stone block forward.
In contrast, a wooden sledge with this load has a friction
factor of 0.2 to 0.4 and requires a pulling force of at least
0.2 x 2,500 = 500 kgf !
To reach the construction platform of the pyramid,
there existed a ramp or a spiral road around the pyramid
with a slope of about 5% (1:20).
F
Weight
The stone block moves forward
when F is greater than:
friction factor x Weight
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To overcome the gravity component of the load, an
additional pulling force was necessary of 5% of 2.5 t, or
0.05 x 2,500 = 125 kgf, which makes the total effort 63 +
125 = 188 kgf.In order to obtain the required extra power, ten workers
with a rope were added at the foot of the Pyramid. With an
effort of 188 / 16, or about 12 kgf per worker, a team of in
total of 16 human workers could transport the load uphill.
Most researchers believe the Egyptians had to quarry
and transport daily 40 stone blocks per hour to meet the
required construction period of 20 years.
This means a delivery to the construction platform of one
stone block every 1.5 minutes. In this time, with anassumed speed of 1.5 km per hour, a transport team could
cover a distance of 1.5 / 60 x 1,500 = 37.5 metres. With
this system, it would have been possible to create a
continuous flow of stone blocks to the construction
platform, with a distance of 37.5 metres between two
successive transport teams.
Rope
Slope 5%
Stone block
Transportation of a 2.5 t stone block
- 6 workers for a horizontal transportation
- 16 workers for an uphill transportation
b
a
Slope = tan( ) = a/b
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It would have taken roughly one hour to transport a
stone block over a road (slope 5%) with a length of 1,400
metres from the foot of the pyramid to an altitude of 70
metres (halfway to the top).
Since the distance from the pyramid to the nearby
quarries was about 700 metres, the total length of the
transport line from the quarry to a construction platformhalfway to the top was 1,400 + 700 = 2,100 metres. With
an average distance of 37.5 m between two transport
teams, the number of carriers on the road was 2,100 / 37.5
= 56. This means that, together with the same number of
returning carriers, a total of 112 were in use daily.
The uphill transportations to a construction platform
halfway to the top, required 1,400 / 37.5 or 37 teams of 16
workers and the horizontal transportations 700 / 37.5 or 19
teams of 6 workers. This gives a total of 37 x 16 + 19 x 6
= 706 workers. The same number of workers was always
on the way back. The returning workers had time enough
to do additional jobs on the construction platform and in
the quarries. We can therefore conclude that roughly
706 x 2 = 1,412 workers were on the road daily.
Transport teams of 16
workers with each a
2.5 t stone block
Slope
5% 1:20
V = 1.5 km/h
28 m37.5 m
A continuous flow of stoneblocks to the
construction platform
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When the quarry workers with their stone or bronze
tools had finished removing the material on both sides of
the stone block and underneath it, two beams and rollers
were placed under the stone block. Then they carved agroove on the upper side of the stone block and placed
wedges to split it. Once split, the stone block rested on the
rollers and could be rolled away from the stone wall. In
this position, it was possible to give the stone block its
final size in accordance with the dimensions of the
rectangular area inside the carrier. Both sides of the stone
block were accessible now for mounting the discs.
A 1997 NOVA (television episode) pyramid building
experiment showed us that, allowing for the tools used by
the ancient Egyptians, it would have taken two workers
two days to carve a single stone block. (It therefore would
have taken four workers one day to carve a single stone
block). The production of 40 stoneblocks per hour, or 320
per day, required a daily manpower of 320 x 4 = 1,280
workers.
QUARRY
Loading of a 2.5 t stone block ( 0.7 x 1.1 x 1.3 m)
( thickness x width x length)
A rectangular
framework
attached to
the disc with
ropes and
wooden pins
Holes for rope
RollerBeam
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To prevent differences in height in a layer of stone
blocks, it was very important that each stone block
comprising that layer had the same thickness. Considering
that the thickness of each stone block was dictated by thedimensions of the centre area of the carrier, this
requirement was always met when the same-sized carrier
was used.
Unloading the stone blocks took place with rollers and
slanted beams. Afterwards the empty discs were returned
to the quarry to be used for the next load of blocks. If
necessary, adjustments could be made to the stone blocks.When possible, large fragments of stone were transformed
into usable building elements rather then discarded. Debris
was used as filling material. The final positioning of the
stone block took place with a heavy ram.
Positioning the stone block on the
platform with a 700 kg rolling ram
Cylindrical
stone
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GENERAL CONCLUSIONS
The rolling stone carrier was a simple design and
made of local available materials.
This tool made it possible to transport heavy stone
blocks in an efficient way and with human power.
The carrier was very compact, easy to handle and it
could easily round sharp corners. The activities in the quarry can be fully explained
with this device.
The carrier made it possible to deliver stone blocks
with a constant thickness.
Calculations concerning transportation capacity and
the use of manpower lead to reasonable values.
The device could be used for temporary storage
purposes, and was an optimal solution for long distance
transportation by ship.
Althought the wheel wasnt known to the ancient
Egyptians, the rolling of heavy objects and the use of
rollers were every day techniques in those days. So far, no
single system has been excavated other than some tools
with wooden circle segments found by the Britisharchaeologist Sir Flinders Petrie.
Wood was a valuable material for building and fuel, so
it is understandable that not much of this material can
nowadays be found. Nevertheless, we know that the
Egyptians built ships and were good craftsmen. Therefore,
use of the rolling stone carrier is a realistic possibility.
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OTHER MYSTERIES
Use of the rolling stone carrier applies to the bulk -
though not the entirety - of the building materials used to
construct the Pyramid. Left unanswered the question of
how the Egyptians managed to transport the extremely
heavy granite blocks needed for the construction of the
Kings Chamber and how they lifted them to a height ofabout 60 metres. About 50 such blocks were used, each
with a weight of between 50 to 70 t. Furthermore, much
speculation surrounds the type of ramp or upward road
used by the Egyptians.
How were stone blocks of 50 tons and more raised to
a high level? The answer is simple. At the beginning of
construction of the Pyramid, these heavy objects were
placed on one of the first levels of the working platform.
After the completion of each layer, blocks were lifted to
the next level of the platform, until the required height
was reached. There was space enough on the platform for
special tools and extra workers.
How were these stone blocks transported? Theseenormous granite stone blocks arrived by ship from
Aswan, located approximately 800 km south of Giza. If
additional transportation took place with a wooden sledge,
at least 400 workers would have been required. Even
with lubrication and a very low friction factor of 0.2 , the
pulling force was already as high as 0.2 x 50,000 =
10,000kgf. A better solution, of course, would have been a
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How were these heavy stone blocks placed in the
transport discs? This process required a special wooden
tool, consisting of two circle segments connected by
wooden bars. The moment the stone block in the quarry
had been removed, it rested on this tool. Using levers andropes, the workers then moved the block away from the
stone wall, allowing them to mount the discs on both ends
of the stone block.
A special tool for
large stone blocks
Lifting and
floating bylowering the
water level in the
ponton
A 60 ton
stone block in
transport discs
Canal tothe Nile
Ponton
system,filled with
water
Transport over the Nile(BoatmodelFranz Lhner, adapted for a ponton system)
Roll-on, roll-off
facility
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What type of ramp was used? The step-by-step method
described earlier of lifting heavy stone blocks on the
working platform of the Pyramid had a great advantage.
That construction of the Pyramid began at low height
would have eliminated the need for a large capacity ramp.
Only a short ramp would have been needed to place these
enormous stone blocks on the first layers of the Pyramid.
A spiral road for the bulk of transportation. A
transportation team with a rolling stone carrier was usually
no wider than 1.5 metres and the great majority of loads
were no heavier than 2.5 to 3 t. These values are such that
a normal road with a width of 5 metres would have been
adequate, providing enough space for the upgoing and
downgoing transportations. Therefore, from a logistical
point of view, an ascending spiral road along the periphery
of the pyramid would have been the most appropriate
solution.
A special tool for mounting the discs on a
60 t granite stone block ( 1.5 x 2 x 8 m)
The stone block was
rolled away after
splitting
The discs were
mounted on both ends
of the stone block
4m
Transport
QUARRY
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An ascending road along the Corner and serviceperiphery of the pyramid area (10 x 10m).
( 5m width).
Top view of the pyramid at a height of 40m and
64% of its final volume. Estimated building time
up to this phase is about 13 years.
Centre of the working
platform is the spot for
the construction of the
Kings Chamber.
Lined up material for
the Kings Chamber.
Ascending road,
slope 5%, for thetransportation of
stone blocks and
other material.
232m
164m
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LAST WORDS
Described above are some possible solutions to
unanswered questions or so called mysteries thatcontinue to circulate about the construction of the Great
Pyramid. Many of these mysteries can be realistically
addressed by considering the proper use of locally
available materials, simple engineering techniques,
skilled craftsmen and human labour and, above all, high
quality management. All of these suggestions can be
supported by simple calculations. Not all thesesuggestions are new, but they are now placed in a
context that gives us possible answers concerning how
this incredible structure was built!
FOOTNOTES
1. John D. Bush, The Rolling Stones, October 1977.
2. Vitruvius,De Architectura, Vol. X, chapter 2