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| Jon |
 Posted: Thu Aug 30, 2007 12:46 am Post subject: Construction Technique for the Great Pyramid (stone lifting) |
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Joined: 27 Jul 2006
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Location: Minnesota, U.S.
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I was looking through a book about the standing stone megaliths of Great Britain, when I saw a picture of a group of guys trying to lift a particular megalith with a lever system. I started to wonder, why do they pull down so hard, when they can ultimately only lift their weight in stone because the lever will cause the men fall back once the stone lifts too high on the other end.
This got me thinking about the pyramids.
I was going to have this post shaped up nice and bright, but I don't have time for to do those sort of things any more. Here it is then, plain and simple.
I think the easiest and most efficient method for lifting stones onto the pyramid would be to tie ropes around the stone at the bottom of the pyramid, run them up to the top of the other end, and then tie the rope/ropes around multitudes of people, who would essentially just use their own weight to pull the stone from the other end. Any number of methods could be employed to ease the movement of the stone up the pyramid.
The average weight of each stone is roughly 2.5 tons, which translates into 5000 lbs. At about 200 lbs. per man, that means that it would take only 25 people to equal the weight of the average block. Throw in a bunch extra, say 200 more, and you could easily have enough to counter the weight of the block and lift it just by the weight of the people tied to the other end. I'm wondering if there is anyone who would want to figure out just how much extra weight would be required to overcome the frictional forces of the moving stone and its initial inertia. I'm no physicist, nor an engineer, so I have little in the way to offer any puzzle like this, other than to throw out this slightly baked idea.
Regards,
Rv. Jon
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| Doddy |
| Posted: Fri Aug 31, 2007 4:38 am Post subject: I'm a scientist - I'll do it, Jon |
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Joined: 31 Aug 2007
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First, I shall convert all your measurements to the language of physics - metric.
I'll let the mass of the block be 2300kg. I shall also assume an Egyptian is 60kg in mass (they didn't eat enough to be 200lbs). Assuming an incline of 51o on both sides. Let's give gravity the value of 10ms-2 just to be easy.
The tension in the rope just holding that block will be:
T=2300kg x 10ms-2 x sin51o
T=18000N (rounded up to err on the side of caution)
And the force the pyramid exerts to hold up the block will be:
FN=2300kg x 10ms-2 x cos51o
FN=14500N (approx.)
If I assume that the coefficient of kinetic friction (μk) is 0.3 (they're using boards or something under the blocks, ok), then the force required to keep the blocks moving up the gradient is:
fk=μk x FN
fk=0.3 x 14500N = 4400N
The same trig I used to work out the tension in the rope could be applied to the 'falling' workers (mass of workers = mw) pulling the block. So,
T=mw x 10ms-2 x sin51o
We know we need a combined tension of 18000N (to hold the block) + 4400N (to keep it moving up). So,
T=22400N=mw x 10ms-2 x sin51o
mw = 22400N /(10ms-2 x sin51o)
mw = 2900kg
Remember that an Egyptian is 60kg, so that equates to 49 people. And that's just if the people are 'falling' rather than actively pulling on the rope. |
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| Jon |
| Posted: Fri Aug 31, 2007 4:46 am Post subject: |
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Thank you so very much for your hard work, Doddy. I very much appreciate what you've done to help me out with this.
Thank you greatly!
Jon
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| Lucifer |
| Posted: Sat Sep 01, 2007 3:34 am Post subject: |
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You know pyramids weren't built as continuous slopes, do you? They where built as tight-pitched step pyramids, then the stony steps were filled in to form a slope, then it was coated with plaques of white limestone which where polished in place.
The problem of puting in place the blocks still would be the same while building the step pyramid...
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| Jon |
| Posted: Sat Sep 01, 2007 4:00 am Post subject: |
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| Lucifer wrote: |
You know pyramids weren't built as continuous slopes, do you? They where built as tight-pitched step pyramids, then the stony steps were filled in to form a slope, then it was coated with plaques of white limestone which where polished in place.
The problem of puting in place the blocks still would be the same while building the step pyramid... |
There are two ways to look at this:
1) What you have said is the commonly-held belief about how the pyramids were constructed, and is somehow incorrect, as it is also possible that the pyramids' finishing layers could be applied during its upward construction as part of each level, instead of being put on like a casing.
2) Wooden beams could be used to slide the stones over the jagged steps.
Personally, I'm somewhat fond of (1), since it makes more sense in all ways. See, why build the pyramid all the way, climbing each level as you go, and then come back and redo it all again on the outside. That's how framed construction is done, but I'd argue that it's an entire different story for stack-and-pile construction, and that the Egyptians probably saw the casing as so essential that it was not a ‘finishing touch’ but rather a core part of the pyramid's construction.
Regards,
Rv. Jon
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| Lucifer |
| Posted: Tue Sep 04, 2007 7:42 am Post subject: |
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| Jon wrote: |
| Lucifer wrote: |
You know pyramids weren't built as continuous slopes, do you? They where built as tight-pitched step pyramids, then the stony steps were filled in to form a slope, then it was coated with plaques of white limestone which where polished in place.
The problem of puting in place the blocks still would be the same while building the step pyramid... |
There are two ways to look at this:
1) What you have said is the commonly-held belief about how the pyramids were constructed, and is somehow incorrect, as it is also possible that the pyramids' finishing layers could be applied during its upward construction as part of each level, instead of being put on like a casing.
2) Wooden beams could be used to slide the stones over the jagged steps.
Personally, I'm somewhat fond of (1), since it makes more sense in all ways. See, why build the pyramid all the way, climbing each level as you go, and then come back and redo it all again on the outside. That's how framed construction is done, but I'd argue that it's an entire different story for stack-and-pile construction, and that the Egyptians probably saw the casing as so essential that it was not a ‘finishing touch’ but rather a core part of the pyramid's construction.
Regards,
Rv. Jon |
As per 1), I never said they bult the whole pyramid first and coated it later. The point was that the slope was made of limestone, which is not the sort of stuff they (nor anyone else) would use to drag anything on it. Limestone is too soft and frangible to be used that way.
And as for dragging things up a 51º slope... I'm not physicist, but I can tell you that the horizontal vector is going to be really big, they will be pushing the block against the slope as they try to lift it. This additional friction will be larger than if they just stand on top of the construction.
Also should be considered the length of the ropes...
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