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pyramid problem


idk12
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It took 20 years to construct the great pyramid of Khufu at Gizeh in Egypt. This pyramid is 500 feet high and has a square base with edge length 750 feet. Suppose also that the pyramid is made of rock with density ρ = 120 lb/cubic foot. Finally suppose that each laborer did 160 ft/lb/hour of work in lifting rocks from ground level to their final position in the pyramid and worked 12 hours daily for 330 day/year. How many laborers would have been required to construct the pyramid? I have attached my work here. Thanks for helping.

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Edited by idk12
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  • 4 weeks later...

Well, I guess I'm the resident expert here now. ;)

 

First off your numbers are terrible. The pyramid is a five step pyramid with each step 81' 3" (http://hdbui.blogspot.com/) except the construction atop the top step is slightly shorter to allow for the combined thicknesses of the rows of stones that cladded the tops of the steps. This makes the pyramid approximately 481' 1" as it was probably completed. The density of the stones was actually 2.69 or about 172 lbs/ ft ^ 3. The slope was about 52 degrees. There is a hill under the pyramid which probably has an average height of about 12'. Of course this barely affects the answer since stones at this height would require very little lifting. The bulk density of the pyramid can be inferred from the gravimetric scan but it's not known if the exterior conditions prevail throughout. There are more closely packed stones near the exterior cladding (now missing) called "backing stones". For bulk density your numbers might not be too bad. The center of gravity of a pyramid is at 1/ 4th the height (~120').

 

Building likely occurred only about 7 months per year in 10 hour days with every tenth day down (for maintenance) and interspersed with numerous holidays.

 

The difficulty with your question is that no one knows what means was used to lift the stones. The orthodox assumption that ramps are the only possible method has been disproven, or at the very least, debunked. In any case the efficiency of method used to lift the stones is key to computing the amount of "Horse Power" necessary (1 HP = ~11.5 ancient man power = 550 ft lb/ sec). With a remarkably inefficient means like ramps you'd be lucky to achieve 5% efficiency meaning you'd have to multiply the result by twenty (reciprocal of .05) to reflect needed manpower.

 

I'd be happy to help further if you get stuck but I believe the tradition here is to just help and not provide the answer. This is only my second post.

 

By the by, the builders actually said that the Gods built the pyramids and went on to define the Gods such that the statement can be true. In other words men didn't actually do any lifting of the stones. I believe they were correct and am here to seek help in proving it.

Edited by cladking
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Well, I guess I'm the resident expert here now. ;)

 

First off your numbers are terrible. The pyramid is a five step pyramid with each step 81' 3" (http://hdbui.blogspot.com/) except the construction atop the top step is slightly shorter to allow for the combined thicknesses of the rows of stones that cladded the tops of the steps. This makes the pyramid approximately 481' 1" as it was probably completed. The density of the stones was actually 2.69 or about 172 lbs/ ft ^ 3. The slope was about 52 degrees. There is a hill under the pyramid which probably has an average height of about 12'. Of course this barely affects the answer since stones at this height would require very little lifting. The bulk density of the pyramid can be inferred from the gravimetric scan but it's not known if the exterior conditions prevail throughout. There are more closely packed stones near the exterior cladding (now missing) called "backing stones". For bulk density your numbers might not be too bad. The center of gravity of a pyramid is at 1/ 4th the height (~120').

 

Building likely occurred only about 7 months per year in 10 hour days with every tenth day down (for maintenance) and interspersed with numerous holidays.

 

The difficulty with your question is that no one knows what means was used to lift the stones. The orthodox assumption that ramps are the only possible method has been disproven, or at the very least, debunked. In any case the efficiency of method used to lift the stones is key to computing the amount of "Horse Power" necessary (1 HP = ~11.5 ancient man power = 550 ft lb/ sec). With a remarkably inefficient means like ramps you'd be lucky to achieve 5% efficiency meaning you'd have to multiply the result by twenty (reciprocal of .05) to reflect needed manpower.

 

I'd be happy to help further if you get stuck but I believe the tradition here is to just help and not provide the answer. This is only my second post.

 

By the by, the builders actually said that the Gods built the pyramids and went on to define the Gods such that the statement can be true. In other words men didn't actually do any lifting of the stones. I believe they were correct and am here to seek help in proving it.

bolded mine

Very interesting post.

 

Where did you find the information about the hill under the pyramid?

And where did you find that the ramp theory has been debunked?

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Where did you find the information about the hill under the pyramid?

 

Multiple sources. The western corners are actually carved of bedrock as is most of the western side to about 22'. The descending passage near the eastern side has about a 15' elevation where it passes through solid stone. The grotto a little west of this is at 22'. The entire structure sits on a water collection device that channeled water to the cliff face where it was apparently used in cliff face counterweights. The builders referred to the cw run as the "ladder of Set" and Set was the God of the water which puddled after falling naturally from altitude. There were three cliff face cw's with the primary being in the center of this picture;

 

http://www.wikimapia.org/#lat=29.9805733&lon=31.1365682&z=18&l=0&m=s

 

The builders referred to the canals feeding them as the "knsti-canals" which means "desert's edge".

 

And where did you find that the ramp theory has been debunked?

 

I debunked it;

 

Proof that ramps weren't used must wait for the powers that be to use 1970's technology to prove beyond doubt the route of the stones and mode of lifting. They are currently not seeking such information but a virtually air tight case can be made against ramps by observation and logic alone. While innumerable signs point away from ramps I'll try to limit the discussion to only the major points.

 

Historical accounts say that the stones moved to the pyramid 300' at a time after a priest attached a piece of paper to them. This is inconsistent with ramps. Indeed, there are no historical accounts until more recent times that involve ramps. Herodotus' description almost precisely matches the usage of counterweights. (they were shaped like the dorsal carapace of a grasshopper and composed of "short pieces of wood".) They were built in "battlements" (steps) and the lifting devices could be moved between them.

 

The culture has no word for "ramps" as applied to lifting objects. There is no such record for the use of this term. While they, no doubt, physically used ramps to lift objects the lack of the word is glaring omission. There is no "god of ramps" and not a single drawing of a ramp from the great pyramid building age.

 

Far more importantly is there is no overseer of ramp builders, ramp architects, or ramp dismantlers buried anywhere in Egypt. There are no overseers of basket makers, no overseers of harness makers or salve makers. There is not even a single stone dragger or his overseer in evidence. The pyramid town had equal numbers of men and women and was a tiny fraction of the size that would be required to drag stones and build ramps. The town is hardly large enough to supply such a large army with water and supplies far less do all the work themselves. It is little larger than a couple soccer fields. Indeed the builders' town was a mere 300' by 700'. By today's standards this would accomodate only 933 people in an office building. People need far more space where they live. Only about 40% of the population was men so there wouldn't even be nearly enough labor to supply food and water to the thousands necessary to build ramps and drag stones up them. You say ancient people didn't mind being cramped up. Modern sanitation and processes are more efficient than they were in 2750 BC but let's say they were willing to be jammed in cheek to jowel. This only increases occupancy to about 2800 men which is still grossly insufficient. With so many people in close contact disease would spread like wildfire. Since there were storage and production fascilities in the town as well it's highly improbable that there were numbers even approaching these levels.

 

Logic says that on a gargantuan project that a highly efficient means must be used. Ramps not only are hugely inefficient due to the high friction and high cost of building and dismantling ramps but also because the weight of the team dragging stones to the pyramid top is simply wasted as they walk back down on already constricted and overused ramps. Getting the manpower necessary to build this requires massive ramps because 55 HP being done by men at extraordinarily low efficiency requires vast numbers of men. They couldn't even see the pyramid to build it under the amount of ramping that would be needed to project so much power. Logic says it would be far easier to just drag stones up the side from the top. Friction is reduced to almost nothing since the route of the stones can be greased. The men don't have to lift their own weight and can pull much more effectively from a level surface. The concept that they must have used ramps is absurd when there are numerous better evidenced and easier means.

 

Maitaining this level of efficient power with muscles alone would require massive ramps and a means for the workers to get back down. Then there is the impossibility of cladding the structure with any possibly evidenced ramping system. Anything that required cladding stones as they went would leave nothing for ramps to adhere to and any other means would require the ramps to be rebuilt to apply the cladding.

 

Then comes the physical evidence which just puts a nail into the heart of the ramp ideas. Perhaps most glaringly is the utter lack of any evidence whatsoever for ramps on the pyramid. This wouldn’t be such a glaring void if not for the existence of numerous vertical lines visible in the pyramids. These lines tend to appear in pairs with one on opposite sides. This is consistent with counterweight operations where one line marks the counterweight and the opposite the route of the stones. It is most highly inconsistent with any ramping ideas. Simply stated ramps wouldn’t leave such lines no matter how they were configured except for ones that can be ruled out by logic such as integral ramps. The grooves on the Great Pyramid are also these routes of the stones that the builders called the “ladders of the Gods”.

 

Giza%20pyramids%20Egypt_20090218143916.jpg

 

Simply stated you can see the routes of the stones right up the middles and in two places above the boat museum. You can also see that these pyramids are five step (battlement) pyramids on some pictures but especially in the gravimetric scan half way down the page here;

 

http://hdbui.blogspot.com/

 

I have a truly beautiful depiction of these five steps drawn on the scan but can't get permission to use it. But this is still conclusive proof that it's a five step pyramid which is more than adequate to debunk ramps. They would not have used steps unless it was necessary and the only reason steps might be necessary is that they could lift the stones only 81' 3" at a time.

 

Each of the great pyramids after Djoser’s were five step pyramids. There is simply no reason to build these as step pyramids unless the height of each step defined the height they were able to lift stones. In order to lift stones to the top they must have needed to be relayed the greatest distance they could lift. Of course this could be as simple as the length of the ropes by which they lifted them up the side. No matter the actual reason it simply isn’t consistent with ramps. It is highly consistent with counterweights and using water for ballast since the geyser sprayed 80’ and this is the height of the steps. It might be consistent with locks that lifted 81' 3" at a time or any water or ballast lifting system limited by natural laws or infrastruture/ materiel concerns. It is not consistent with ramps.

 

Ramps can’t explain the various infrastructure all around and within the pyramid. They are inconsistent with the history, culture, logic, physical evidence, and the evidence left by the actual on-site builders.

 

Perhaps the greatest inconsistency is the cultural evidence right on site. In the pyramid builders cemetery is the “Overseer of the Boats of Neith”. This would be the loader on the south side in all probability but it could have nothing to do with ramps. There are canal overseers, overseers of metal shops, director of draftsmen, inspector of craftsmen, controller of a boat crew, controller of the side of the pyramid, inspector of metal workers and a host of other jobs that reflect a sophisticated and intelligent culture. Most tellingly is that there is a “Weigher/ Reckoner”. This job would be critical on a device that was said to be sensitive enough to tell the difference in weight of a “heavy heart” from a feather. They found a standard weight in the queens “air siphon” and a hook.

 

In point of fact there simply isn’t anything consistent with ramps. While the evidence isn’t deep it is very broad that counterweights were used and the vertical lines on the great pyramids are simply sufficient to say ramps are debunked. This scale is tipped so much you’d think there’s nothing on the ascender at all. There were no ramps. They are debunked.

 

 

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Well, I guess I'm the resident expert here now. ;)

Thanks. A nice piece of logical work, especially on debunking the ramps.

 

Could you explain a bit more what you mean by "geysers" and "ascenders".

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Thanks. A nice piece of logical work, especially on debunking the ramps.

 

Could you explain a bit more what you mean by "geysers" and "ascenders".

 

 

Just to be clear nobody actually considers me an expert in Egyptology (especially myself). I am however very well versed in the facts and the physical data that are known about the great pyramids. Nobody in the world has a better understanding of the literal meaning of the Pyramid Texts as derived from context than I, but no one else believes that this literal meaning has any relevance and it's this which I hope to be able to establish here. (I'm thinking on the computer forum).

 

I believe the aquifer at Giza was carbonated. Indeed, I believe it was highly carbonated. There are hot springs in the area even today and the aquifer here is lightly carbonated apparently. This water was so highly carbonated that it sprayed out of the ground like a shaken soda and was named "Osiris". We call these cold water geysers today and they are quite rare.

 

 

I should probably avoid the term "ascender" as this was a term invented by Egyptians from much later in history but the specific name for this device doesn't appear in the PT and the general term is used only a single time. The counterweight was known as the "[]nw-boat". Later in Egyptian history it was known as the "henu boat" and had characteristics of the ascender and the counterweight. The boat that was laden with stone was on the opposite side of the pyramid and for now I'll just call it the ascender.

 

1375c. Neit is behind him; Śrḳt-ḥtw is before him.

1376a. The ropes are knotted; the boats of N. are tied together

 

Neit is the Goddess of the (S) ascender and Serket the (N) counterweight.

 

1742b. The ropes are tied, the boats are assembled,

 

620b. Horus has set thee up, in his name of "[]nw-boat"

620c. he carries thee, in thy name of "Seker."

 

The language was like computer code and this is why it has been misunderstood for so long.

 

http://www.sacred-texts.com/egy/pyt/

 

It looks like you have the qualifications.

I'll take some time to read throughly your wonderful post, and your blog.

I run out of time right now.

Anyway:

Welcome.

 

Thank you very much.

 

I would be interested in any opinions you might have about it.

Edited by cladking
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Just to be clear nobody actually considers me an expert in Egyptology (especially myself). I am however very well versed in the facts and the physical data that are known about the great pyramids. Nobody in the world has a better understanding of the literal meaning of the Pyramid Texts as derived from context than I, but no one else believes that this literal meaning has any relevance and it's this which I hope to be able to establish here. (I'm thinking on the computer forum).

 

I believe the aquifer at Giza was carbonated. Indeed, I believe it was highly carbonated. There are hot springs in the area even today and the aquifer here is lightly carbonated apparently. This water was so highly carbonated that it sprayed out of the ground like a shaken soda and was named "Osiris". We call these cold water geysers today and they are quite rare.

 

 

I should probably avoid the term "ascender" as this was a term invented by Egyptians from much later in history but the specific name for this device doesn't appear in the PT and the general term is used only a single time. The counterweight was known as the "[]nw-boat". Later in Egyptian history it was known as the "henu boat" and had characteristics of the ascender and the counterweight. The boat that was laden with stone was on the opposite side of the pyramid and for now I'll just call it the ascender.

 

1375c. Neit is behind him; Śrḳt-ḥtw is before him.

1376a. The ropes are knotted; the boats of N. are tied together

 

Neit is the Goddess of the (S) ascender and Serket the (N) counterweight.

 

1742b. The ropes are tied, the boats are assembled,

 

620b. Horus has set thee up, in his name of "[]nw-boat"

620c. he carries thee, in thy name of "Seker."

 

The language was like computer code and this is why it has been misunderstood for so long.

 

http://www.sacred-texts.com/egy/pyt/

 

 

 

Thank you very much.

 

I would be interested in any opinions you might have about it.

(bolded mine)

with all my respect, that is quite a bold statement.

Maybe you should present yourself, the "who's talking" is important to me.

 

My opinion:

_In short, I agree, there were no ramps.

 

_in long:

I am architect. I have on my bookshelf a very interesting architectural book on the subject, with details, methods of construction, etc.

The book is a french edition in black & white, from the 80's. External ramps are described and proposed as the way the pyramid were build.

They should have been huge, representing more than 1/3 of the pyramid.

I always disagrred with external ramps, considering that it would be insane to build something (pyramid + ramp) and then demolish 1/3 of the construction in order to obtain the pyramid. I strongly suspect that ancient egyptians had the same considerations than today about economy of means, rentability, etc. and were certainly not insane.

So I always disagrred with external ramps.

 

There are some theories about internal ramp, but I don't think they are correct. these theories require some difficult gymnastic to make the ramps coincide with the final scheme of a pyramid.

 

Also, I believe we are looking at the pyramids in a wrong way today. We have those grandious monuments surrounded by desert and think that the builders had only sand, stones and ropes as building material.

If we had a look at the pyramids 5.000 b.c., maybe (maybe) we'd look at monument surrounded by gardens, trees, maybe forest, instead of desert. IOW they had wood also as building material. Still today, wood is one the most basic material for construction. Wood was the only technical material for ages, remember all invention of Leonardo Da Vinci, all in wood. With wood you make cranes, chariots, ships, etc. So to me the slope of the pyramid is a function of the technical means of the times, it is the height at which one could elevate a stone with a kind of crane or other mean (with counterweight, no doubt)

 

To be continued.

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(bolded mine)

with all my respect, that is quite a bold statement.

Maybe you should present yourself, the "who's talking" is important to me.

 

Sad to say that it is not in the least a bold statement. Indeed, I've been the world's leading expert on the literal meaning of the Pyramid Texts almost from the day I began studying them. The simple fact is that almost no researchers at all have ever even considered that this work might have a literal meaning. It's just like they found the world's first book and never even bothered to read it.

 

It wasn't found until long after the language was translated and the finder (Masperro) was familiar with a later book that is derived from it. This is the book of the dead and it is obviously a book of magic and obviously derived from it so it wasn't noticed that the PT was distinct, it is ritual and it is not magic nor religion. It simply is written in an older form of the language where meaning is determined by context like computer code.

 

There are two or three other people who take the PT literally and I've studied their work. While some is quite insightful and all of them are very scientific, I personally don't believe the meaning they found actually exists as they interpret it. Their interpretations are mostly wrong. This isn't so much to say that I discount their conclusions so much that I find them unsupportable linguistically, scientifically, and (probably) culturally. No one to my knowledge claims to basically understand most author intent other than myself. Egyptologists consider this work something akin to gobblety gook that can't be understood but still use it to try to understand the people. These people come off looking like bumpkins because you can't ascribe a deep seated belief in illogical and contradictory religious beliefs as well as superstitious beliefs in magic and incantation in anyone and have them look sophisticated.

 

The PT does have a consistent and literal meaning and it was I who found it. I have used this meaning to uncover the physical facts and the physical facts to aid in understanding the PT. The work is actually quite simple or I'd have never cracked it. The bulk of the real work to solve this was really done by google.

 

I understand that most people are very concerned with "credentials" and the like. Suffice to say I normally describe myself as a disabled ditch digger. Of course, like everything, it's more complicated than this. I personally don't believe it matters where ideas come from; they are either supportable or they are not. I've always considered myself a "generalist". There is another term for what I mean that actually pre-dates my term and this is "nexialist" that I've discovered only very recently (with a little help from a friend);

 

http://www.nexial.org/nexialism.htm

 

This is similar to what I mean by "generalism". I believe that widespread specialization is one of the greatest threats to the human race.

 

http://www.sciencefo.../page__st__2680

 

Also, I believe we are looking at the pyramids in a wrong way today. We have those grandious monuments surrounded by desert and think that the builders had only sand, stones and ropes as building material.

 

These would have been spectacular in their day. This site is probably the most disturbed by man site on the face of the planet and has been disturbed for at least 6000 years probably. There was water and in a desert water is life. In all probability their word for "life" was a representation of the geyser we call an "ankh".

 

Most people don't realize that the builders invented the calender and that these structures are oriented perfectly N/ S so that they will work as a timepiece and a calender. Each side is indented a few inches so on the equinox the light will flash across the side as the sun sets. On the solstice the shadows of the corners of the three Giza pyramids form a wide straight line at sunset.

 

http://www.catchpenny.org/concave.html

 

Bronze was of critical importance to their ability to construct these.

Edited by cladking
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