Andrzej Bochnacki
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All Contents on this page are Copyright 2004-2006 by Andrzej
Bochnacki
All Rights Reserved. Reprinted with Permission
On this page:
Introduction | Transport
Theories | O Piramidach Inaczej
(Polish) | Buy the Book
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.
The list of the Seven Wonders of the Ancient World
was originally compiled around the second century BC. The first
reference to the idea is found in History of Herodotus as long ago as
the 5th century BC. Decades later, Greek historians wrote about the
greatest monuments at the time. Callimachus of Cyrene (305BC-240BC),
Chief Librarian of the Alexandria Mouseion, wrote "A Collection of
Wonders around the World". All we know about the collection is its
title, for it was destroyed with the Alexandria Library.
Online Reference:
http://ce.eng.usf.edu/pharos/wonders/list.html
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
lifetime.
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:
- What higher purpose motivated people to continue construction for
periods longer than the lifespan of one generation?
- What motivated the Egyptians to build huge stone pyramids one after
another for over 200 years of the III, IV and V dynasty of pharaohs?
- Why was the trend to build huge pyramids, made with the use of big
stone blocks, so short within 5000 years of Egypt's history?
- Why did the Egyptians, who usually meticulously documented all areas
of their life, fail to describe the construction of the Pyramids?
- Were hundreds of tons of the red granite brought from the quarries
located 1000 kilometres away south in an upper Nile?
- These are questions without good answers, and even more questions
will appear when we start exploring the details of individual pyramids.
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:
- Was a pyramid erected step by step (level by level) or from one side
up?
- Were the stones had come from and how were they transported?
- Could builders work on the south wall of a pyramid in the heat of
the sun shining on it under almost the right angle?
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 Seven Wonders of the World” ("Siedem cudów świata".)
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…
Fig. 2 Enlarged part of the previous drawing.
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
period.
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
Andrzej
Bochnacki. In his book
Different
Story about Pyramids,
he proposes very ingenious technology used to move the pyramid
blocks from the quarries to the construction site.
NOTE: The following quotations from the book
Different
Story about Pyramids are Copyright by Andrzej Bochnacki.
All Rights Reserved. Reprinted with permission of the author.
Copyright 2005-2006 by Andrzej Bochnacki.
"The height of the tunnel was less than 10 m. The tunnel was cut out
on the level that allowed it to be dry when Nile's water was low. When
the water level raised up about 6 m, almost all stone blocks from the
tunnel could be picked up by boats from their spot”.
”Light, made out of papyrus, boats were put on the top of blocks
and tided up with ropes. These transport boats ware waiting for
raising water of the Nile and they could be easily towed to a chosen
destination. The simplest way was to haul them to the west side of
the Nile where water flooded the fields. Here they were left in the
mud to be transported on the land after the flood was over”.
Papyrus boats with the stones tided up underneath,
waiting for high level of the Nile's.
Copyright 2005-2006 by Andrzej Bochnacki.
"The size of the hammering block was chosen to keep a very fast rate of
tunnel building. That is why blocks were as big as possible. Their size
was limited only by available methods of transport. Because they were
transported by water the block weight was about 2,5 tons”.
"How, in ancient times, the difficult problem of boats loading and
unloading process was solved explains the animation and drawing below”.
Animation showing phases of
transporting stones from the tunnel to the ramp.
CLICK ON THE IMAGE TO VIEW ANIMATION
Copyright 2005-2006 by Andrzej Bochnacki.
Websites:
http://www.swbochnacki.com/
http://republika.pl/bochnacki/
Presented with permission.
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:
- the painter took himself a lot of trouble to show just the number of
people in the team.
- one of the four pulling rows of peaple has different dress:as every
second pair has long aprons and first pair has strange head-gears.
- ropes are not attached directly to the sledge, but to the element of
strange shape.
- one of the workers probably pours some liquid in front of the
sledge.
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.
Spatial drawing of statue transport.
Copyright 2005-2006 by Andrzej Bochnacki.
It appears that when people try to keep running away rope in their hand,
the situation changes diametrically. Rope tension is not a trouble any
more, legs stand still, only hands change the place of grasp. Besides, a
man catching running rope does not do any work, meaning power multiplied
by movement, he is able to keep much more than pull.
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.
Animation showing the method of increasing the pulling power.
CLICK ON THE IMAGE TO VIEW ANIMATION
Copyright 2005-2006 by Andrzej Bochnacki.
Websites:
http://www.swbochnacki.com/
http://republika.pl/bochnacki/
Presented with permission.
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.
View of the loading platform
Copyright 2005-2006 by Andrzej Bochnacki.
"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”.(....)
CLICK ON THE IMAGE TO VIEW ANIMATION
Copyright 2005-2006 by Andrzej Bochnacki.
Websites:
http://www.swbochnacki.com/
http://republika.pl/bochnacki/
Presented with permission.
“Stones coming closer and away, like rings of a huge worn, could
look from a distance like legendary walking stones”.
Copyright 2005-2006 by Andrzej Bochnacki.
Walking stones on the ramp.
This kind of transport will be always less energy absorbing than classical
team of men pulling heavy sledge and using 90% of platform surface to
transport themselves.
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."
Lifting the stones from one step to another, from the book
by Andrzej Bochnacki "Different Story About Pyramids"
Copyright 2005-2006 by Andrzej Bochnacki.
"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
Copyright 2005 by Andrzej Bochnacki.
Website:
http://www.swbochnacki.com/
Presented with permission.
NOTE: The quotations above came from the book
Different
Story about Pyramids and are Copyright by Andrzej Bochnacki. All
Rights Reserved.
Reprinted with permission of the author.
Fragmenty ksiazki Andrzeja Bochnackiego
"O Piramidach Inaczej"
Kiedy mówimy "piramidy", to myślimy przede wszystkim o piramidzie Cheopsa.
Jest największa i najbardziej tajemnicza. To właśnie ona zaliczana jest do
słynnych siedmiu cudów świata. Jako najbardziej wyróżniająca się ze
wszystkich piramid egipskich była głównym przedmiotem badań i dociekań na
temat genezy jej powstania. Najbardziej rozpowszechniona teoria
nawiązująca do trzech komnat znajdujących się w jej wnętrzu głosi, że
każda komnata była związana z kolejnymi zmianami początkowego projektu.
Teoria ta w zasadzie wyjaśnia fakt istnienia trzech komór "grobowych" ale,
co tu dużo ukrywać, niezbyt przekonywująco. Natomiast brak w niej
jakiejkolwiek odpowiedzi na cisnące się pytania związane z innymi
szczegółami tej budowli. Zaczynając od cech zewnętrznych piramidy, pytania
te brzmią:
- Dlaczego tak dokładnie według stron świata ustawiona jest
podstawa piramidy?
- Dlaczego kąt nachylenia wynosi akurat 51°52’?
- Czy dziełem przypadku jest fakt, że połowa obwodu piramidy
podzielona przez jej wysokość daje w wyniku liczbę zbliżoną do”π„?
- Dlaczego jedyny ślad powiązania piramidy z faraonem Cheopsem to
znak kamieniarski na kamieniach, z których konstruowano puste
przestrzenie nad Komorą Króla?
- Czy Komora Króla odsunięta jest od osi piramidy z powodów
organizacyjnych prowadzenia budowy, czy na skutek błędu budowniczych?
- Dlaczego kanał uznawany za wentylacyjny usytuowany jest w
najmniej właściwym dla tego typu kanałów miejscu, bo w bocznej ścianie
komory i na dodatek 1 m nad podłogą?
- Jaki sens miała nisza wykuta we wschodniej ścianie środkowej
komory nazywanej Komorą Królowej?
- Po co zbudowano nad górną komorą puste przestrzenie, nazywane
niezbyt trafnie komorami odciążającymi, skoro zastosowane i wcześniej
sprawdzone sklepienie namiotowe i tak wystarczająco zabezpieczałoby
płaskie płyty sufitowe komory, tworząc co najwyżej pojedynczą pustą
przestrzeń?
- Do czego służył lub miał służyć największy i najtrudniejszy pod
względem konstrukcyjnym chodnik nazywany Wielką Galerią?
- Dlaczego część poziomego chodnika prowadzącego do Komory Królowej
jest wykuta w istniejącym już wcześniej rdzeniu piramidy a nie murowana
jak inne jego fragmenty?
- Skąd wziął się dość absurdalny (szczególnie przy założeniu
warstwowej metody budowy piramidy) układ chodników, z którego wynika, że
odgałęzienie skierowane do góry zaczęto w momencie, kiedy dwie górne
komory jeszcze nie istniały?
- Jakie kryteria decydowały o miejscu rozpoczęcia chodnika i
skierowania go do góry pod takim a nie innym kątem?
- Jakie to wyższe cele pozwalały kontynuować budowę dłużej niż
świadome lata życia budowniczych?
- Jakie cele kazały Egipcjanom budować jedna za drugą duże kamienne
piramidy przez 200 lat panowania III, IV i V dynastii faraonów?
- Dlaczego moda na duże kamienne piramidy była tak krótkotrwała w
5000- letniej historii starożytnego Egiptu?
- Dlaczego Egipcjanie opisywali wszystko oprócz budowy piramid?
- Czy setki ton czerwonego granitu sprowadzano z kamieniołomów
leżących 1000 km na południe, w górnym biegu Nilu?
- Jaką metodą piętrzono bryłę piramidy, stopień po stopniu, czy
inaczej?
Kliknij na obrazek aby zobaczyc animacje.
Copyright 2005 by Andrzej Bochnacki.
http://www.swbochnacki.com/
- Skąd brano i jak transportowano kamienie?
- Czy człowiek może pracować na południowej ścianie piramidy,
nagrzanej prostopadle padającymi promieniami słonecznymi ?
- Powstaje pytanie, co jest większym dziełem, pojedyncze piramidy,
czy olbrzymie wyrobisko po kamieniach zużytych na ich budowę?
Metoda powstawania piramid,
przedstawiona przez Andrzeja Bochnackiego w ksiazce "O Piramidach Inaczej"
przynosi revelacyjne i możliwe do zaakceptowania odpowiedzi na
powyzsze pytania. Na tej stronie prezentujemy kilka fragmentow z tej
ksiazki.
Ksiazka ta jest niedostepna w druku (jej maly naklad zostal wysprzedany
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Fragment ksiazki Andrzeja Bochnackiego "O Piramidach Inaczej"
[...]
Zacznijmy więc od szukania śladów metod transportu, jakie Egipcjanie
zostawili po sobie. Zanim skorzystamy z legend o chodzących kamieniach,
spróbujmy przeanalizować jeden z nielicznych rysunków obrazujący transport
olbrzymiego posągu pochodzący z czasów XII dynastii czyli około 800 lat po
piramidach.
Właśnie ten rysunek narobił najwięcej szkody w wyjaśnieniu metod
transportu. Jego zbyt pobieżna analiza prowadzi do fałszywych wniosków.
Jeżeli przyjmiemy jako główne założenie, że rysownik starał się jak
najdokładniej przedstawić rzeczywistą scenę transportu posągu, to
analizując treść rysunku powinniśmy znaleźć wyjaśnienie co najmniej
czterech jego cech charakterystycznych nie spotykanych gdzie indziej. Po
pierwsze, rysownik zadał sobie bardzo dużo trudu, aby przedstawić właśnie
tyle osób w zaprzęgu.
Rys. 21 Transport 60-tonowego posągu
Po drugie, jeden z czterech rzędów ciągnących zdecydowanie wyróżnia się
strojem: co druga para ciągnących ma długie fartuszki, a pierwsza para
posiada dziwaczne nakrycia głowy. Po trzecie, liny nie są zaczepione
bezpośrednio do sań, lecz do elementu o nietypowym kształcie, który jednym
końcem opiera się o płozy. Po czwarte, jeden z pracujących
najprawdopodobniej wylewa jakąś ciecz z przodu sań. Ponieważ jest rzeczą
fizycznie niemożliwą aby 166 ludzi było w stanie ciągnąć liny z siłą co
najmniej rzędu 9 ton, należało szukać rozwiązania w zastosowaniu jakiegoś
urządzenia umożliwiającego przełożenie sił i oczywiście znaleźć punkt
oparcia umożliwiający zwiększenie siły. O ile nie jest rzeczą trudną
znalezienie odpowiedniej maszyny prostej umożliwiającej zwiększenie siły,
o tyle trudno było znaleźć na rysunku interpretację punktu oparcia.
Dopiero próba znalezienia przyczyny, dla której jeden szereg ciągnących
różni się od innych, pomogła znaleźć wielce prawdopodobną interpretację
rysunku przedstawioną na szkicu poniżej.
Rys. 22. Przestrzenny rysunek transportu posągu.
Egipcjanie nie rozważali problemów ciągnięcia ciężkich głazów i posągów
teoretycznie, oni to po prostu realizowali w praktyce. Sprawdzili, że
nawet 300-tu czy 400-tu ludzi nie dałoby rady ciągnąć z siłą
przekraczającą 9 ton. Liny z włókien oprócz szeregu zalet, mają jedną
uciążliwą wadę, rozciągają się. Wydłużenia liny zależą oczywiście od
wielkości siły rozciągającej, rodzaju splotu i długości liny.
Gdyby kilkudziesięcioosobowy szereg ludzi usiłował ciągnąć za pomocą
jednej liny, to ostatni w szeregu musiałby zrobić o kilka kroków więcej od
pierwszego zanim lina uzyskałaby właściwe naprężenie. Każdorazowe
zwolnienie napięcia zmuszałoby do wykonania ponownej pracy naprężania (niebagatelnej),
a znajdowanie coraz nowych punktów oparcia dla nóg i zachowanie
równoczesności działania wszystkich 50 ludzi jest mocno wątpliwe. Ludzie
ci mogliby co najwyżej szarpać liną i byłoby to zajęcie bardzo mało
efektywne.
Egipcjanie znaleźli genialne rozwiązanie. Okazuje się, że kiedy ludzie
starają się utrzymać uciekającą z rąk linę, sytuacja diametralnie się
zmienia. Rozciągliwość liny przestaje przeszkadzać, nogi pozostają w
miejscu, najwyżej ręce zmienią miejsce chwytu. Oprócz tego, człowiek
trzymając uciekającą linę nie wykonuje pracy, w rozumieniu siła razy
przesunięcie, jest w stanie utrzymać znacznie więcej niż ciągnąć.
Egipcjanie stworzyli coś w rodzaju ruchomego punktu podparcia składającego
się z trzech rzędów ciągnących, którzy byli w stanie stawić chwilowo opór
rzędu 65 kG każdy, co dało w sumie siłę oporu równą około 8 ton. Dopiero
czwarty rząd, właśnie ten wyróżniający się ubiorem, najważniejszy, bo
wymagający równoczesności pracy, był tym rzędem ciągnących, który
wykonywał właściwą pracę przeciągania posągu. 43 ludzi ciągnęło z siłą 25
kG każdy, co dawało w sumie ponad 1 tonę.
Przy zastosowaniu bardzo ciekawego elementu, w postaci belki drewnianej
o niezwykłym kształcie, umożliwiającego przełożenie około 1: 9, mogli oni
wywierać na sanie z przymocowanym do nich posągiem, siłę 9 ton. Była to
siła wystarczająca do ciągnięcia posągu, tym bardziej, że obie strony,
ciągnąca i dająca oparcie, dysponowały pewnym zapasem.
Przyjmując proporcje wymiarowe rysunku możemy w przybliżeniu ocenić
wielkość przesunięcia posągu w jednym cyklu pracy. Jeśli przyjmiemy za
możliwy 60° obrót belki w specjalnym gnieździe
na końcu płóz, to przesunięcie sań mogło wynosić około 6 cm, w tym czasie
szereg ciągnących przesunąłby się o 54 cm, następnie ciągnący cofnęliby
się o 48 cm, szeregi stawiających opór przesunęłyby się do przodu o 6 cm (nie
wykonując żadnej pracy) i cykl mógłby się powtórzyć. Najbardziej
obciążonym elementem byłoby gniazdo obrotu belki w zakończeniu płóz.
Naciski występujące w tym miejscu z całą pewnością wymagały polewania wodą.
Rys. 23. Sposób zamocowania belki do sań na wzór
stawu kolanowego.
Rys. 23 a. Wyjaśnienie sposobu zwiększenia siły
ciągnącej.
Czyżby więc Egipcjanie potrafili wykorzystywać zjawisko względności
ruchu i stosować nieznane nam współczesnym maszyny proste. Prawdopodobnie
byli jedynie doskonałymi obserwatorami przyrody. Jeżeli uważnie przyjrzymy
się pracy konia lub wołu podczas wykonywania ciężkich prac np. orki, to
nietrudno zauważyć, że koń ciągnie pług wbijając się trzema kopytami w
ziemię. Te trzy kopyta, podobnie jak trzy szeregi napinających liny
robotników na rysunku, to punkt oparcia dający możliwość wykonania pracy
przesuwania posągu lub wyorania skiby ziemi. Czwarta noga podobnie jak
czwarty szereg robotników wykonuje znacznie większy krok do przodu niż
przesunięcie pługa. Różnice wynikać będą jedynie z różnych sposobów
wywierania siły oraz z faktu, że nogi końskie naprzemian zmieniają swoje
funkcje, a szeregi ciągnących mają funkcje przypisane na stale.
Jeżeli przyjrzymy się kolejnemu rysunkowi przedstawiającemu ten
tajemniczy element, do którego przymocowane są liny ciągnących posąg i
obok przekrój przez staw kolanowy konia, to nie będziemy się dziwić w jaki
sposób Egipcjanie wynaleźli nietypową maszynę prostą umożliwiającą
zwiększenie wywieranej siły.
Nawet jeżeli przezorni Egipcjanie wyłożyli powierzchnię gniazda blachą
miedzianą, belka na pewno z czasem zużywała się i trzeba było ją od czasu
do czasu wymieniać, dlatego na rysunku widzimy ludzi niosących zapasową.
Taka interpretacja rysunku dość jednoznacznie wyjaśnia znaczenie
wszystkich nietypowych elementów widocznych na nim, pozwala przypuszczać,
że Egipcjanie zdawali sobie sprawę, że bez zastosowania przełożenia siły
nie ma mowy o optymalnym wykorzystaniu mocy człowieka.
Człowiek nie lubi pracować ani bardzo wolno, ani bardzo szybko. Dzięki
podobnym zaprzęgom budowniczowie piramid mogli znacznie zwiększyć gęstość
strumienia kamieni na rampie poprzez znaczne, bo 3 lub 4-krotne
zmniejszenie liczby ludzi ciągnących głazy. Gęściej ustawione na rampie
sanie mogły poruszać się wolniej przy zachowaniu tej samej liczby kamieni
transportowanych w ciągu jednego dnia.
Nie odmawiajmy jednak Egipcjanom inteligencji. To co dobre w transporcie
jednostkowym wyjątkowo ciężkich elementów, nie musi być optymalne przy
transporcie niemal astronomicznych ilości typowych elementów. Mogli
wykorzystać zasadę nie powielając bezmyślnie sposobu.
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