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If people can lift
water with a counter weight, why not use the same
principle to lift stones, huge stones, like the
ones used to build the pyramids? Back in ancient
Egypt, a device called a shadoof was commonly used
to move water. A shadoof is a long pole, weighted
at one end, perhaps with a stone, and a vessel on
the other end, used for raising water to irrigate
the land. They pulled down the vessel, filled it
under the water, and then easily lifted it by the
counter weight. These water lifting machines showed
that the Egyptians knew something about weights,
fulcrum, and balance long before they built the
pyramids .
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This method of lifting heavy stones with
a counter weight is an idea that I am sure
Historians may have thought of in the past, but
dismissed because there is no evidence that it was
ever done with huge stones.
So, how did they
lift a five-ton block of stone to build the
pyramids? We know that at the time of the first
pyramid the Egyptian culture was well developed and
they were knowledgeable in some methods of building
and construction. To get the blocks so close and in
such perfect order would be extremely difficult
using just man power. It would be impossible to
assemble enough men around a 9,000 pound stone that
is perhaps three and a half feet by three and a
half feet, by five feet long to move it. To lift
this stone onto a barge and off a barge, and then
to maneuver it in place on the pyramid would take
ten men, three on each side and two at each end.
This placement means that each man, if all lifted
equally, would be lifting 900-pounds. Obviously
such a miraculous display of strength not only
seems impracticable, but impossible.
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The most
commonly held solution for moving these large
blocks is to slide skids under the blocks so that
many men would pull the skid along the ground and
up ramps built around the pyramid to the level
required. Pictured is a hieroglyphic panel showing
the use of skids. Getting the block off the skid
would be laborious enough, but moving the 5-ton
block and placing it in its proper position in the
pyramid by pushing and shoving seems
inconceivable.
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Perhaps the
Egyptians rolled the stones by placing them on
platforms and used round logs under the platform to
push the stones along. However, the same difficulty
of getting the 5-ton block off and on the platform
exists.
At the time of the
first pyramid, basic devices to pull heavy stones
such as the windlass were very much in use. The
windlass is a wheel and axle machine where the axle
is fasten to the wheel. On both sides of the axle
are large wheels, poles, or bars much larger than
the axle. Let us say that the diameter of the wheel
is ten feet and the diameter of the axle is one
foot. By winding a rope around the axle and turning
the wheel a mechanical advantage equal to the ratio
of the diameter of the wheel to that of the axle is
realized. Therefore, in this case the ratio would
be one to ten. With a windlass ratio of 1:10, and
considering the bearings as frictionless, a 2000-lb
load could be lifted by applying a 200-lb force.
With suitable bearings, bedding, and geometry, even
a smaller force would be required to slide the
load. Thus, it would require 900-pounds of force to
pull a 9,000-pound stone, or six men applying a
force of 150-pounds each. By putting the stone on a
skid and using the windlass, 6 men could move the
stone across the surface much easier. Also, by
putting the windlass on the level of the pyramid
they are working on, the 6 men could hoist stone up
the side of the pyramid on a narrow ramp. However,
they would still face the challenge of placing the
stones on and off a skid or barge, and lifting them
into place.
Although the use of
skids or rolling platforms may have been the method
to get the stones to the barges, the Egyptians must
have had a better method for putting them on the
barges. Also, they must have had a method of
lifting the blocks off the barges onto the
platforms at the pyramid site. They recorded
nothing about how they lifted the stones to the
level they wanted them once the stones were
delivered to the pyramid.
To lift a five-ton
stone using a shadoof, the counter weight would
have to weigh almost as much as the stone to be
lifted. So how could the workers produce a counter
weight to lift the stone almost the same way the
shadoof lifts the water?
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When I started to
seriously think about how the Egyptians could
accomplish the counter weight problem I came up
with a method the Egyptians could have used to lift
a five-ton stone. Why not use a material that they
had plenty of - SAND?
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| The first thing would be to build as many as
four towers with four legs each out of heavy timbers and ropes, with
all the legs meeting near the top. They would be approximately ten
to twenty feet high, with perhaps a stone spool at the top. The base
would be a solid platform of logs to give it stability.
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The legs
would extend a foot or more below the platform to
allow for uneven terrain. The platform would also
serve to hold bags of sand if needed for additional
steadiness. The tower can be constructed as a
system of multi-connected tetrahedrons if internal
bracing is provided. Such a structure would be
rigid, or stable, and could support significant
loads with appropriate dimensions, timber, and
foundation. |
Tetrahedron
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The spool would resemble
a spool of thread, except the area where the
thread is wrapped around would be cut deeper to guide
the ropes. A hole through the center of the spool
as in a spool of thread would allow it to turn
freely as the ropes move. A large substantial log
would be placed through the hole at the center of
the spool and tied firmly on top and between the legs
of the tower. These towers would be set at each
corner of the pyramid or one tower at one corner
at the level being worked. A rope would be tied
around the stone block on the ground and brought
up to the level on which the men are working.
Then the rope was swung above the tower and
tied on the other end to a basket at the center height
of the tower. The basket was filled with sand
until the basket's weight was equal to
or more than the weight of the stone. Once the
basket was full, it was moved down the side of the
pyramid, thus lifting the stone easily up the
adjacent side. The purpose of hanging the basket
five or ten feet up from the base of the tower was
to insure that the stone clears the edge of the
level to which it was lifted. The spool would be
set at an angle so that the ropes would fall on the
adjacent sides. If the spool was not used then the
workmen could have greased a groove in the log at
the top and swung the rope over it. The pyramid was
built so there would be a substantial size landing
on every block level. As the pyramid rose stepping
stones were placed on each landing so the sand
carriers could bring sand to the tower level, fill
the baskets, and return for more sand.
Several men would push
the basket with sand over the side of the pyramid
and then pull on the ropes to lift the stone from
the ground, using the counter weight of the basket
to help them. Other men would be stationed all the
way down on each of the landings with long poles to
keep the basket from hitting the sides of the
pyramid and insure a smooth ride to the ground.
Additional men would be on the adjacent side with
poles to keep the stone blocks from hitting the
pyramid on the way up.
When the stone was on the
level of the tower and was placed on a skid or
platform, the ropes around the stone were untied
and the sand in the basket on the ground was
emptied. The empty basket could then be pulled back
up to the tower with the other end of the rope
going to the ground, and the process started again.
Once the stone was on the level desired, it than
could be rolled to its location. A smaller tower
would be used to lift the stone into place using
the same method. This method could also have been
used to put the stones on or off the barges. The
Obelisk can be lifted and put into place by lifting
it at the center to balance it and turn it to a
vertical position.
One cubic foot of sand
weighs approximately one hundred ten pounds. A
9,000-pound block of stone would require eighty-two
cubic feet to equal or exceed the weight of the
stone. A basket just 4½ feet by 4½ feet by 4½ feet
high would do it. A fifteen-ton stone block would
require two hundred seventy-three cubic feet of
sand to equal or exceed the weight of the stone, or
a basket 6½ feet by 6½ feet by 6½ feet high. It
would take actually on site conditions to
accurately determine how many men they would need
to carry the sand and pour it into the basket, how
long it would take to lift the stone, and the time
to repeat the process. While the stone was being
untied the workmen would pull up the empty basket,
and other workers would wait to pour their sand
into it. To do the same job in the same time by
building ramps and rolling the stones up the sides
of the pyramid would take many more thousands of
people to accomplish the same results.
Why are the measurements
of Khufuís Great Pyramid such odd figures
like 432 cubits for each base? The cubit, about 21
inches long, was the standard measure of the
Egyptians. It seems reasonable that the architect
would have used an even number like 400, 450, or
500 cubits for the bases. Imagine Khufu asking his
architects to build a pyramid 300 cubits high or
525 feet, so it would be the greatest monument ever
built. (I doubt that he would have said,
ìBuild the pyramid 275.43 cubits
high.î) The architects would then need to
know two things: the angle of the pyramid and the
length of each of the four sides of the base. The
most manageable size block of stone at the time was
about two cubits by two cubits, so the pyramid
would be 150 stones high to equal 300
cubits.
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| The Egyptian architects would draw a number of
pyramids on paper as the most likely design. By laying out blocks on
paper and starting with the top block, the designers concluded that
there are three most natural methods of building the triangular
shape. The building blocks were of approximately equal size and
square, 2 cubits high by 2 cubits wide by 3± cubits long. Using the
squared side as the face of the pyramid, the first block would be
placed on half of each of the blocks in the row below. See figure 1
below.
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Pyramid
Figure 1
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The next layer down would
be placed the same way forming a brick pattern.
Note that the second row down would contain two
blocks, the third row down would contain three
blocks, and so on, until 150 blocks high would
equal 150 blocks for the base, or 300 cubits high
by each base at 300 cubits long. This would form an
equilateral triangular shape that would have been
considered too steep, perhaps from the experience
of the Bent Pyramid, or the landings would be too
small for the sand carriers or the stone masons to
do their work.
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Secondly, by placing the
top block on top of the block directly below, with
two blocks placed on either side, the second layer
would have three full blocks on that row. See
figure 2 below. The third layer down would have
five full blocks in that row, and the forth row
would have seven full blocks. Carrying this down to
the 150 blocks level, there would be 290 blocks at
each base, or 580 cubits, or 1,015 feet for each
base of the pyramid. This isosceles triangle
appears to be too flat, and this area of 1,015 feet
by 1,015 feet is much too large for the area and
would require many more stones.
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Pyramid Figure 2
The third and seemingly
best design would be to put the top stone one and a
half cubits in from the face of the stones on the
second level. See figure 3 below. The second row
would have two and one half stones, the third row
would have four full stones, the fourth row would
have five and one half stones, and so on. Carrying
it down to the 150 block level, there would be 225
blocks at the base, or 450 cubits. This measurement
would be 787.5 feet at each base of the pyramid,
making the pyramid 300 cubits high and 450 cubits
at each base. These are numbers I can
understand.
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Pyramid
Figure 3
Each step of the pyramid
would measure three and one half feet with a
landing of 31½ inches. The sand carriers and
stonemasons would have room to easily climb up and
down the pyramid and to do their work. Assuming the
architects used this design, the Great Pyramid
would have originally been 31½ feet wider at each
base and 43 feet higher than the present figures
indicate. The vandals and looters may have taken
more stones to build Cairo than previously
thought.
To build the landings,
the angle, and the smooth exterior surface of the
pyramid, the foundation was first laid out and the
size of the base determined (as noted above, this
would have been 450 cubits). They set the corners
at right angles from the first line and measured
the distance of the line so all sides would be of
an equal length. Pegs were inserted at each corner
and a rope with knots tied every cubit and a half
(31½ inches) were wrapped around the pegs. After
wrapping the rope, the first block would be placed
into position at the edge of the rope. All the
corners would be positioned first and with a block
that was cut approximately three and a half feet
high, three and a half feet wide, and three to six
feet long. This measurement would be equal to a
block measuring two cubits by two cubits by three
cubits. Then the perimeter would be filled from
corner to corner with blocks cut to the same
measurement and adjusted as they reached the
center. The bottom of each block was carefully
placed along the rope line. This was important as
it determined the angle of the entire pyramid. When
the perimeter was complete, the center of the level
was filled in with various blocks to an approximate
height of the top of the outer core of blocks or to
the top level of the perimeter blocks.
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After the first course or foundation was laid
and one and a half cubits were deducted from each side, pegs were
inserted at the top of corners of the first course and wrapped with
the knotted rope. The number of knots on the rope should be equal on
all four sides. A line could have been drawn exactly one and a half
cubit in from the top of the stone, but the planners still needed to
be sure all sides were equal.
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This method
would make the second course one and a half cubits
shorter than the one below it on each side. By
using a cubit and a half instead of one cubit, the
stones were laid in order to give the workmen a 31½
inch platform to work on. It gave the sand carriers
and workmen easy access, using stepping stones, to
the level on which they were working. Cutting the
outer stones from base to base also gave the
pyramid a satisfactory angle to rise from the
ground to the top.
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Figure 1. For detail of circled item see figure 2
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As in the first course
they would lay the outer most stones, made of
limestone, starting at the corners and laying the
base of each stone on the rope or line. Again they
would fill in the center to the height of the outer
stones. They were building a pyramid with steps,
three and half feet high and thirty-one and half
inches wide. They would repeat this until they
reached almost to the top of the
pyramid.
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The artist rendering show sand and stone ramps
used to roll or pull the platforms or skids with the stones on them
up the sides of the pyramids, but I do not believe that the
Egyptians ever built any ramps. It is my opinion that the men
climbed the side of the pyramid to deposit their sand in the
basket.They could have made this climb easier by placing stepping
stones on top of each of the large blocks creating a crude stairway.
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Figure 2
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Two stones would be
placed on each 31½ foot landing, one 14 inches
high, the other 28 inches high. The length and
width could vary. Thus, every landing would have
three steps to the top of the next level, each step
no more than fourteen inches high.
As the workmen built up the various levels,
moving the towers up was necessary as they went. When they
filled in the levels to the height of the perimeter stones, in order
to
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fill in the area under the tower they
tilted the tower over on its side onto logs, and
rolled it a cubit or so away. They filled in the
tower area with blocks of stone previously brought
up, rolled the tower back, and lifted the tower to
its upright position. When the top was reached, it
was time to install the cap stone. The cap stone
would also be two cubits high, but it was cut into
a small pyramid one and a half cubit short on all
four sides of the base on which it was placed. The
pyramid would be built up to this level. As the
pyramid got smaller as they approached the top,
they would remove the log platform of the tower
they were using and wedge the four legs onto the
top of the pyramid. Then they would hoist the
balance of the stones and the cap up. After the cap
was in place, the tower would be discarded. Now it
would be time for the stone masons to start the
work of cutting the stone into a smooth finish.
They would start at the base of the cap on top of
the pyramid and cut down to the outer base of the
next row of blocks. It would be a rough cut at
first, but as they got nearer to the proper angle
they would use a straight edge or straight piece of
wood as a guide. When the surface from the base of
the cap to the outer base of the lower stone was
smooth, the masons would step down to the next
level, standing on the thirty-one and a half inch
ledge, that is on every level. They used this ledge
and the step stones where necessary as a scaffold
while cutting the stones. As they came down, they
would discard the stones making up the crude
stairways used by the sand carriers. The masons
would then start to cut the limestone from the base
of the stone just completed at the level above to
the outer base of the next row of stones below.
When the stonemasons finished chiseling away a row
of stones then they would grind and polish the
surface to a smooth finish, probably using a
granite stone the size of the palm of their hand.
If they laid the stones exactly one and a half
cubit from the edges, then the cutting and
smoothing of the surface would automatically give
the pyramid its approximately 53°±
angles.
There is no real mystery
as to why and how the shape of the pyramid was used
for the tombs of the pharaohs. The purpose was to
build a monument that would last forever, be at a
great height for all to see, serve as the burial
place of the pharaoh, be relatively easy to build,
secretly hide the burial chamber, keep visitors
out, and discourage robbers from desecrating the
tomb.
If you ever watched a
child playing with blocks, you noticed that the
child quickly realizes that a structure built by
placing one block on top of another becomes very
unstable the higher the structure goes until it
falls. However, the child notices that when
building the blocks in a triangular shape, the
structure becomes very stable. Obviously, the
architects of the day must have arrived at the
conclusion that the monument to be very stable
should have a pyramid shape. This shape was easier
to build than one straight up on all sides and
allowed for the sand carriers to bring their sand
up to fill the baskets, and enabled the stonemasons
to work from the top down to give the structure a
smooth finish. Given enough stones and workmen, a
pyramid could be built to almost any height the
Pharaoh wished by changing the size of the base and
the angle of its sides. It could be built with
secret passage ways and tombs within the structure.
The architects would have the sides cut smooth
finish to keep people from walking on the structure
and damaging it, and it would discourage robbers
from climbing around looking for the entrance. The
shape of a pyramid was the most logical one to
use.
I think that this method
of building the pyramid worked for the first few
hundred years until the weakest areas, the filled
in entrance, may have begun to show wear and reveal
itself.
These are my theories as
to how the Egyptians could lift the stones, how
they laid the stones, how they determined the size
and angles, and how the exterior was finished to a
smooth surface. I believe these methods are much
more feasible than building a ramp almost as large
as the pyramid itself.
There is a good reason
why there is no evidence that the shadoof method
was used. After they built the pyramid, there was
no reason to keep the towers. They consisted of
wood and rope and in time would totally disappear.
Historians, seldom, if ever, record how a picture
is painted, how a building is built, or how a
tradesman did his work. It appears that only the
results count. This picture was painted by . . .
This is the work of . . . I have been looking, but
I have yet to find a picture of a pyramid in any
ancient Egyptian art.
These pyramids built by
the Egyptians 4,000 to 4,500 years ago are one of
the seven wonders of the world. If there were any
references to any machines used in building the
pyramids they may have burned in the fires of the
Alexandrian Library. I believe I have given
Egyptologists and Historians completely new ideas
to think about. Considering the vast amount of
information still available, perhaps the scholars
really did not know what to look for. Perhaps the
scholars will now revise their thinking on how the
Egyptians built the pyramids.
Richard
Koslow
5950 Pelican Bay Plaza, # 1102
Gulfport, Florida 33707-3961
Phone: 1-727-347-3327
E-mail:
rkoslow@tampabay.rr.com
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©Richard Koslow. All
rights reserved. The use or republication of this article is
forbidden
without the written consent of the
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