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A NEW SLANT ON THE PYRAMIDS
by Andrzej Bochnacki
Over 2000 years ago, a Greek historian Callimachus of Cyrene (305BC-240BC) made a list of wonders around the world which later became known as "the Seven Wonders of the World" and included The Great Pyramid of Giza, The Hanging Gardens of Babylon, The Statue of Zeus at Olympia, The Temple of Artemis at Ephesus, The Mausoleum at Halicarnassus, The Colossus of Rhodes, and The Lighthouse of Alexandria.
Six of them do not exist any more. The Great Pyramid of Giza is the
only one still remaining to this day.
Although we know of them only from written documents, nobody doubts they existed. There is also no question of their purpose and that they were made by human hands.
The approach to the Egyptian pyramids is completely different. They still exist, and their tremendous size is awe inspiring. All attempts to explain the methods used to build them are not convincing. Some writers even suggested that the pyramids were constructed with the help of extraterrestrials.
In many of the publications about the pyramids, there appears an opinion of our “pyramids inferiority complex”. According to it, even today, with our modern methods of planning and construction, it would be very difficult to build the pyramids.
At the same time, we create structures like dams, highways, and huge
tankers that are much bigger than the pyramids. Strangely these modern
structures do not impress us much since we understand their purpose and we
take them for granted.
The "pyramids inferiority complex" is most likely a result of disbelieve that the pyramids were built to serve as tombs for the pharaohs. It is difficult to find proof that a particular pyramid was built for a particular pharaoh and only few clues remain indicating that construction was conducted when a specific pharaoh was the ruler.
The mystery behind the purpose of the Great Pyramid causes people to look for some very special meaning in its dimensions, proportions and design of the chambers. The shape of the pyramid is supposed to have magical powers that would protect a person from harmful cosmic radiation and ensure natural preservation of the mummified corpse.
It is much easier to believe in such fascinating tales than in the idea
that a Pharaoh would start the construction of his tomb immediately after
rising to power, without a likely chance of finishing it during his
Personally, I think that everything created by man had its beginning in
an attempt to meet a practical need. This should also apply to the
pyramids, with the later successive copies possibly being built to fulfil
Pharaohs’ vanity, for religious purposes or for other irrational reasons.
It is rather puzzling that the biggest Egyptian pyramids appeared quite
suddenly. New architectural forms were created by using new construction
methods and material not used before on such a large scale.
Colossal mountains of stones, with chambers inside that were no more than 1% of the size of the volume of the entire structure, started appearing around the year 2650 B.C.. After 2450 B.C. building of such immense structures ended. Pyramids that were built later were not as monumental, and only their shape remained the same as their predecessors. Their construction did not require so much time, material, and effort as before, when pyramids of Cheops and Chefren were built.
The construction cycle required to build the pyramid of Cheops or
Chefren was at least 20 years. Considering that at that time an average
human life span was about 30 years, at least two generations of workers
had to be involved in the construction of each of these pyramids.
All these facts raise few questions:
When twenty years ago I was trying to construct machines that might have been used to build the pyramids, I did not ask such questions.
My only goal was to experiment with construction machines designed like
a human knee which, like everything in nature, ignores discovery of the
wheel turning on its axle.
For my generation, Egyptian pyramids were a perfect example of structure build without the wheel. Using Pyramids as a model, I tried to popularize my machines applying principles of the differential levers, moving pulleys and rope transmission.
My designs have not become popular because hydraulic systems replaced
most of the simple machines and maybe because trying to use the Pyramids
for such plain applications may have angered the spirits of the rulers of
the ancient Egypt. The “Curse of the Pharaohs’ ” followed me for nearly 20
years during which I could not stop thinking about the Pyramids building
and its various intrinsic aspects.
My experiments with models in 1:1 scale of my construction machines
clarified many things for me (they were presented in 1983 on Polish TV in
the Wanda Konarzewska’s show).
I became convinced that such machines could have existed and do the
job. These machines did not consume a lot of wood and fit roughly the
description presented by Herodotus:
“The pyramid was built in steps, battlement-wise, as it is called,
or, according to others, altar-wise. After laying the stones for the base,
they raised the remaining stones to their places by means of machines
formed of short wooden planks. The first machine raised them from the
ground to the top of the first step. On this there was another machine,
which received the stone upon its arrival, and conveyed it to the second
step, whence a third machine advanced it still higher. Either they had as
many machines as there were steps in the pyramid, or possibly they had but
a single machine, which, being easily moved, was transferred from tier to
tier as the stone rose - both accounts are given, and therefore I mention
both. The upper portion of the pyramid was finished first, then the
middle, and finally the part which was lowest and nearest the ground.”
There are many possible solutions based on mechanics of the knee joint
that could have been used in making lifting machines(I have described them
in my article "How the Pyramids were built" published in magazine "Problemy"
No 8, 1986) and in the end, it became less important to me how the stones
were really lifted.
My attention began to shift in a different direction and new questions became more important:
Human imagination has no limits. Recently a new theory was proposed suggesting that pyramid stone blocks were made of some kind of concrete.
I have nothing against such theories since they stimulate thinking and
experimentation with new materials. Also they do no harm since they are
addressed to adults who can be sceptical about such revelations.
I would not rush to publish my theory about the Pyramids (my plan was to wait with it until my retirement) if it was not for the recent new circumstances.
Every once in a while the subject of the pyramids comes back to life
and different hypothesis are being published. Within the last few years,
among other books, two beautifully edited books for children and teens
came out (as part of the series “How People Lived”: “The time of Ancient
Egyptians" published by Wydawnictwo DolnoSlaskie, Wroclaw 1990, and "Seven
Wonders of the Ancient World” published by BWG, Warszawa 1990.)
Authors of these books are trying to convince children that the pyramids were build by pulling stones on wooden rollers logs up the ramps as shown on the picture below.
Looking at such pictures children may draw conclusion that building
pyramids wasn't difficult as long as there were enough people to pull the
ropes. They may think that Egyptians were rather primitive people who
built their pyramids by using only slave labour of thousands of workers.
Fig. 1 Construction of a pyramid according to the
author of the book
The reader can easily miss the fact that this drawing is in conflict with the laws of physics.
A closer look at the enlarged part of the previous drawing shows that
when the ropes, which are turning under 90o angle, get fully tensioned,
some of the pulling them slaves will be hanging over the edge…
In another part, where the ramp is changing from an inclined section
into a flat surface, a stretched rope would have to press down on the
edge. Let’s hope that slaves would not get hurt by the rope pressing their
hands against the rough surface of the ramps edge.
Writing a book for children does not give one a license to spread naive ideas about methods of transportation of 2.5t stone blocks. Not only pulling such a long rope that is turning on the ramp is impossible, but the idea of transportation based on just few such ramps attached to the sides of a pyramid is illogical.
The pyramids exist, the stone blocks used to make them are counted, and
the time to build them is well estimated in tens of books. The rate of
construction, 120 thousands of stone blocks per year, is fairly well
documented. We can accept it as highly probable, that such was the
construction rate throughout the whole 200 years of pyramid building
Assuming (for simplicity of calculations) 10-hours of work per day and
300 days of work per year, it is easy to calculate that the construction
rate would be equal 40 stone blocks per hour. During this hour the stone
blocks had to be elevated to appropriate height and precisely positioned
in the right places. The groups of pulling workers would have to move with
a speed of at least 2km/hour. Moving at such speed on an inclined ramp
requires a lot of effort in itself and on top of it the rope would have to
be pulled with a force of at least 20kG. Using this method of
transportation people working in the heated by the sun wall of a pyramid
would have to generate power close to 1 Horse Power, which is not
possible. The authors of the mentioned above books for children cannot
expect that choosing such methods of transportation would allow building a
pyramid in just 30 years.
When dealing with ancient events, the accuracy is measured in years,
however in physics the time frame is much more critical. The laws of
physics were true 5000 years ago the same way they are true today. It is
important to understand that the accomplishment of any work (labor) is
limited not only by the force but also by the time the force is applied.
The Power is restricted strictly by the minutes and seconds. The magnitude
of the physical force can be increased easily with the help of the simple
machines, however the time we cannot control. Ironically, Herodotus’
description of the pyramid construction agrees much better with the laws
of physics than many of our modern publications. The concept of moving
stone blocks from step up to another (tire to tire) provides a great
advantage – it allows for a very wide construction area (front). It makes
possible having, at the same time, many workers on the pyramid walls
performing construction tasks at a slower rate.
Let’s leave for now the details of building the pyramids, since we do not know for sure where the pyramid’s stone blocks came from, how were they produced and delivered to the construction site and, finally, why were the pyramids built at all.
Recently, a sensational statement by American writer Zecharia Sitchin was published, in which he claims that a marking (a cartouche) on the stone in the ceiling of one of the chambers in the Cheops pyramid, so far the only link between the pyramid and the pharaoh's name, is simply a forgery.
It is not obvious at all that pyramids were built in order to serve as
Pharaohs’ tombs. There is no question that they were used as tombs,
however we cannot be sure that this was the main reason for building them.
The pyramids give impression that they exists independently from
surrounding them buildings of the burial complex. Without any inscriptions
on the outside and on the inside they are so impressive only due to their
shear size. There is also no certainty that all the pyramids had smooth
casing on their walls.
A pyramid without the outer layer of casing stones is far less elegant
than surrounding buildings and it reveals that the pyramid is nothing else
but a heap of stones put one on the top of the other. In modern times
applying our criteria we would assume that stock of stones like that is
rather a "pile" of stored materials for construction work, than structure
itself. Or it could be good for nothing waste from some construction area.
Fig. 3 Placement of the pyramids
Approximately 70 Pyramids were discovered in Egypt, however 10 largest,
with the combined volume of 10 million cubic meters, are located in the 50
km long area along the Nile. If we add to it all support ramps and
buildings from the same area, like mastabas, small satellite pyramids,
temples, walls surrounding burial areas and tombs, considering the
quarrying methods, the pit left by the stones removed to build the above
structures within previously mentioned period of 200 years of the Old
Kingdom would have volume of 20 to 25 millions m3. The work of this
magnitude should live much more noticeable mark than quarry in Tura.
This raises a question: what is a bigger accomplishment, pyramids or
the pit left after the removal of the stones needed to build them?
If we consider the amount of work needed to achieve the task, then
excavation of 25 millions m3 blocks of rock would take many times more
energy than transport and pilling them up into the pyramids.
If the stones for the pyramid building were cut out from one place, the
pit created as the result would deserve more than the pyramids to be
called The Seventh Wonder of the World.
To explain this problem we have to go back in time to the III Dynasty of Pharaohs, to the year approximately 2650 BC when according to the majority of sources the pyramids did not exist yet. Let's try to imagine what could have been a priority for the rulers of Egypt at that time.
One of the most elegant pyramid building theories has been
suggested by Polish engineer and inventor
Bochnacki. In his book
Story about Pyramids,
Animation showing phases of
transporting stones from the tunnel to the ramp.
Editor's Note in support of the theory that Nile at flood stage was used to transport stone blocks to the pyramids' construction sites
This computer generated image shows probable course of Nile in Old Kingdom (the left channel). Note that Nile at flood stage pushed very close to the feet of major pyramid sites. This would make transportation of huge stone blocks from the quarries to the construction sites much easier.
This image is based on information from David Jeffreys, Institute of Archeology, University College, London; Oriental Institute Computer Laboratory, University of Chicago and Archeological Graphic Services. NOTE: Vertical scale exaggerated to show ancient Nile river channel (on the left).
TRANSPORT of Large Stone Blocks on Land
Transport of the 60-ton statue.
If we presumed that the painter tried to show the real scene of statue
transport as precisely as he could, we should notice:
Because it is physically impossible for 166 people to pull ropes with
power of about 9 tons (probably it is sufficient power to pull 60 ton on
the sledge), they had to find some equipment which would enable them to
transfer the power and find any support to have possibility for increasing
the pulling power. Only the trial of finding the reason, why the pulling
row is different than other ones, helped to find most likely
interpretation of the drawing shown below.
The Egyptians did not consider the problem of pulling heavy stones and statues theoretically, they solved it practically. They even checked that 300 or 400 people could not pull with power over 9 tones. Ropes made of fiber besides many advantages have one heavy disadvantage- they stretch up. Extension depends on the stretching power a kind of angle and length of the rope. If row of peoples would try to pull with one rope , the last people in the row had to made a few steps more than the first. Every slowing down the tension would make people to do new (great) effort of tension. And it is very doubtful that 50 people could find new supports for theirs feet and act synchronously. The Egyptians found brilliant solution.
Egyptians created something like moving fulcrum, combined with the rows
of pulling people, able to give a momentary resistance with 65 kG each,
which gave in summary 8 tons. Only the fourth row distinguished by dress
pulled and did the proper work of pulling the statue. 43 people pulled
with power of 25 kG each, which gave in summary over 1 ton. Using very
interesting element, the strange shaped wooden beam, which enabled
transfer 1:9, workers could pressure the sledge and the statue with power
of 9 tons. This power was enough to pull the statue and both sides
resisting and pulling had some reserve. If we accept the dimensional
proportion from the drawing, we can approximate movement of the statue in
one round of work. If the beam spanned by 60 degrees in special nest at
the end of runners, the movement of the sledge was about 6 cm. At that
time pulling row moved forward within 54 cm, and then moved 48 cm
backwards . Rows of resisting people moved 6 cm forward (but without doing
any work) and a round might start again.
TRANSPORTING BLOCKS ALONG THE RAMP
“We can push away the sixth stone from five stones connected together. Five or more stones always stay still, because the friction of a few stones is always bigger than the friction of one stone. So joining the stone in-groups we can move stone one by one. Simple wooden levers and wedges or only wedges will be completely suitable tools for blocks transport along the ramp. And we do not have to worry about friction, because stone platform coated thinly with sand, would be not only the transport road but also the tool smoothing the surface of stone block. It should be noticed that this method of transport did not need any special tools; it is the ability, which disappears in time, when this way of transport was not needed any more.
"At the end of February the work was stopped because the raising sun hit also the northern wall. Then the stones were left on the platform just where they were placed. So when the next year work started people did not need to waste time for starting. "Sleeping" stones became "alive" and at the first hour after starting the pyramid was already rising".
Stones placed densely in two or three rows will slowly move up,
securing proper transport efficiency. Very important advantage of such
transport is that people stay in one place. They do not have to transport
themselves along the platform and it is big energy saving”.(....)
“Stones coming closer and away, like rings of a huge worn, could look from a distance like legendary walking stones”.
Walking stones on the ramp.
THE BLOCK HOISTING MACHINE
"Necessary power to pull the 2,5 ton stone along the wooden beam inclined about 30 degrees, was about 1600 KG. Using the lever with leverage 1 to 10, six people could successfully do this job, moving with small steps, let's say 4 or 5 centimeters. After 30 moves the block was one pyramid step higher and it was possible to do this work in time no longer than half an hour. Stones traveled on the northern wall of the pyramid, and finally were put in the right place."
"Special care was needed for outside stones, on which there were put
precisely fit and smoothed face bricks. The gradient of the outside walls
had to be very precise and they also had to hold the gradient of northern
wall to enable the workers work for 100 days in shadow, when stones did
not burn their feet and the air was not so hot that it made breathing
impossible. Every day 100 blocks were put in a place of their destination
and every day 100 blocks had to be dug out of the mud and delivered to the
bottom of the ramp.
CLICK ON THE IMAGE TO VIEW ANIMATION
NOTE: The quotations above came from the book
Story about Pyramids and are Copyright by Andrzej Bochnacki. All
O Piramidach Inaczej
Fragmenty ksiazki Andrzeja Bochnackiego
Metoda powstawania piramid,
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