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Desk Study
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Desk Study
2.1 Geometry
The great pyramid was built during the reign of Khufu (Cheops
in Greek), second king of the fourth dynasty ± 2,720-2,560 BC.
It stands on the Giza plateau nearby Cairo and is the biggest
pyramid in Egypt.
The pyramid itself now stands 137 meters high, its original height
of 146.16 meters is indicated by an iron post erected on the apex.
Each side originally measured 230.362 meters or 440 royal cubits
(1 cubit=0.524 metres). At present the side measures 227 meters,
due to the loss of the casing stones. The core masonry consists
of large blocks of local limestone taken from the nearby quarries
and built around and over a rocky knoll. The size of the knoll
cannot be determined, since it is completely covered by the pyramid.
The entrance to the pyramid is in the centre of the northern face.
It is located in the thirteenth course of masonry from the base.
This entrance has a pointed roof formed of massive slabs of local
limestone and opens into a long steeply descending passage. From
there a 36 meters long ascending passage leads to a 35 meters
long horizontal passage that leads to the so called 'Queen's chamber'.
This chamber measures 5.2 by 5.7 meters and the maximum height
of its pointed roof is about 15 meters. The north and south walls
each have a small hole a few centimetres square about 1 meter
from the floor. These lead into narrow channels that originally
opened on the exterior of the pyramid. At the juncture of the
ascending and horizontal passage is an opening of a shaft which
descends to a depth of 60 meters. It opens into the lower part
of the descending passage, close to the unfinished, underground
chamber, and is believed to have been an escape shaft for the
workmen who filed the ascending passage with huge stones after
the king's funeral. From the horizontal passage the Grand Gallery,
which leads to the king's chamber, starts. It is 47 meters long
and 8.5 meters high, and has a corbelled roof. In the centre of
the floor is a sunken ramp about 60 centimetres deep. The Grand
Gallery ends in a horizontal granite passage which serves as an
antechamber. It measures 8.4 meters long and 3.1 meters high,
and has slots for three portcullises. Beyond the antechamber is
the so-called 'King's Chamber' which is lined, roofed and paved
with red granite. It measures 5.2 by 10.8 meters and is 5.8 meters
high. Its flat roof is formed of nine monolithic slabs of granite
The northern and southern walls each have an 'air channel', one
of which is open to the outside. The Pyramid can be seen to have
about two hundred level courses of squared stones. The layers
all have a different thickness ranging between approximately 50
and 145 centimetres. The average block size is about 1 cubic meter.
On the Khufu pyramid all the casing elements were removed in the
14th century. The few casing stones which do remain in the Great
Pyramid all lie in the 1.5 meter thick bottom course and cannot
be representative of the stones which would have been used in
the higher parts of the construction. The only examples of face
work which remains are those on the pyramids at Meidum, Dashur
and Giza (Khafre's).
Figure 1 shows a wire-frame model of the Pyramid. The wall around the pyramid and the temple are not included in this report.
Figure 1, Wire-frame model of the Great Pyramid at
Gizeh
A simplified model of the great pyramid will be used for this
study. The pyramid has a square base measuring 230 meters in length
and the height of the apex will by 146 meters. The foundation
is a level surface on which the first layer can be placed. Any
settlement due to the pressures during or after construction will
be disregarded. The pyramid is solid, without any passages or
chambers. Because the volume of the passages and chambers is only
± 0.07 % of the total volume the passages and chambers can
be omitted. The construction will be done in 200 subsequent layers
of equal thickness being 0.73 meter. The standard element will
be cubical with sides of 1.17 meters. This is a theoretical assumption
since blocks of this size will not be able to balance on the already
placed steps. To be able to estimate to construction time for
the core, the used parameters, such as the number of layers and
the element size, have to be as close as possible to those of
the actual pyramid. During the actual construction the layer thickness
has to be adapted according to the thickness of the strata at
the quarry. The block size will have to be adapted to be able
to balance on the steps. Each layer will have fitting elements
that are slightly smaller or larger than the standard element
size. The core elements will thus form a step pyramid. The size
of the steps is 0.575 meters. The outer layer will consist of
wedge shaped casing elements so the pyramid will have a smooth
surface when completed.
2.2 Materials
The core of the great pyramid consists of solid limestone blocks.
Limestone is a sedimentary rock with a density between 2.5 and
2.7 tonnes per cubic meter. It is quite sensitive to weathering,
therefore the top layer was constructed of a more durable limestone.
The Kings Chamber and the Grand Gallery are constructed of red
granite. Granite, an igneous rock is more dense than limestone
and has better general physical properties and is therefore used
in the upper chambers. The bulk of the limestone was quarried
on the plateau itself. The red granite
had to come from near Aswan about 700 km upstream from Cairo.
The problem of opening and exploiting the quarries needed for
the construction is a very interesting and complex problem but
is not a part of this study. The pyramid for this study is completely
made of limestone, assuming a density of 2,600 kg/m3.
The weight of one element is: 1.17 * 1.17 * 0.73 * 2,600 = 2,598
kg.
2.3 Labour and equipment
The ancient Egyptians built the pyramids with the simplest methods.
Both in quarrying and building workmen used copper chisels, as
well as flint, quartz and diorite pounders. Further they used
wooden crowbars, sledges and rollers to transport the elements.
Figure 2 is a scene showing the transport
of blocks of stone from the quarries in Tura, in which we see
oxen dragging the sledges.
Figure 2, The transportation of stone blocks in a quarry
at Tura
This method works very well for transporting over long distances,
but usually manpower was used to move building elements. Figure
3 shows how 172 men work to drag an alabaster colossus of the
twelfth dynasty monarch, Dhutihotep, from the quarries of Hatnub
in Middle Egypt. This statue measured over 6.5 meters high and
weighed about 60 tonnes.
The scene also shows men carrying levers and others pouring liquid, presumably water, from pots in order to reduce the friction between the statue and the surface. To transport a 2.6 tonnes element in a similar way, 172 / 60 * 2.6 = 7 to 8 people are needed. To transport the elements on the sledges special roads were constructed. They consisted of a base of rock rubble on which wooden planks where embedded at regular intervals in a layer of clay. The friction was reduced by wetting the clay, as can be seen in figure 3.
Figure 3, Transporting a statue from the tomb of Dhutihotep,
El Bersheh
All lifting work will be done by means of levers. With these levers
all elements can be jacked up along the sides of the already constructed
part and put into position. The lifting method will be described
in more detail in the method statement. Levers can also be used
for horizontal transport, but only for short distances or to put
an element at its correct place.
The levers are made of wood and have a length of 2 meters. At
the fulcrum the lever measures 100*100 mm and is tapered to both
ends for easy handling. The maximum lifting force for one lever
is determined by the length of the lever, the place of the fulcrum,
the section of the lever and the type of wood used for the lever.
The section has to be able to resist the bending stresses induced
by the levering action. When assuming that the leverage point
is at 0.1 meters from the end, and the maximum downward force
to be applied by one person is 600 N the upward force on the other
end is 1.9 * 600 / 0.1 = 11,400 N. The actual bending stress in
the lever will be 6.84 N/mm2 which is allowable for
most timber. Three levers would be sufficient to lift a 2.6 tonnes
element, but for reasons of stability four levers have to be used.
Work will be done on 350 days per year, taking into account any
religious or other holiday that may occur. A working day is from
dusk to dawn, since working with artificial light is not possible.
Average daylight per day, measured over a year, is 12 hours. Any
lunch breaks or otherwise will also be accounted for by means
of an efficiency factor of 70%.
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