Mysteries :
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Let's do Math Steve. I agree. There clearly was a word for ramp in the Old Kingdom but this doesn't necessarily mean a ramp was used to build the top levels of the pyramids. Let's keep an open mind for now and not take anything off the table.

In order to identify the method used and the solution to this enigma, we should first define the problem: The number and size of blocks in the top half of the Great Pyramid. I found a good photo I took of the summit to do some old-fashioned Math: Counting blocks. It turns out the block number is near the course number counting down from the summit. It's just a coincidence which simplifies the math.

You can get a rough idea from a sample of course counts as you can see and I have indicated the numbers on the left and the squares of the right. The squares are the estimated block numbers for a given course. Roughly, as you go down one course you add one block. It's just an estimate to get an idea of the magnitude of the problem.

To get the sum of the blocks you compute the sum of the squares and I show the formula. In other words 9x9 +10x10....42x42

For example, assuming one block added per course down from current summit to course 160 is

42x(42+1)x(84+1)/6= 25,585 blocks.

Technically, we have to subtract the top 10 courses, about 200 blocks, but it doesn't matter. Let's even call it 26,000.

How big and how heavy was the average block in the top half of the Great Pyramid?

Size:

From Petrie, we know that most of the top 100 courses are on average less than 30 inch and more than 20 inch thick. The average course is thus about 8 palms thick (0.6 m), between 16 and 24 palms wide (av 20 p; 1.5 m) and 16-24 palms deep (~1.5 m) judging from the summit (I am looking at Yukinori Kawae, Nagoya University,

Thus, the average block volume is: 1.4 m

Weight:

The Mokattam Formation is in the Middle Eocene. Density range: 2.1-2.4 ton/m

So, the average block in the top 100 courses of the Great Pyramid weighed 3.0 tons.

ERGO: The current top 42 courses of circa 26,000 blocks weighed a total of 78,000 tons.

Assume you have enough room up there to set 100 blocks per day. Then, you have a construction time of 260 days for these 42 courses. If you only count the four months of inundation then the timing stretches to 2 seasons and change. Less than 15 minutes per block, but this is of course done with multiple blocks set simultaneously. At lower courses, there is more room and so you have to assume more blocks per day were laid by this elusive method.

Conclusion: You need a method which can haul 100 3 ton stones per day which are 8 x 20 x 20 palms in size.

Update:

Course Numbers by the notch at half-way up. Course 105/210 is in the notch; 140 cubits is within course #94.

I count 68 blocks at course #118.

The more accurate block#/course# gradient: In the upper segment it is ~8 blocks added per 10 courses and in the lower segment to the midway point it is ~5 blocks added per 9 courses. The overall ratio averaged is something like 3 blocks per 4 courses.

EDIT: Corrected Course Numbers on Petrie Plate 8 right pane

EDIT: Added further count to course 154

Edited 8 time(s). Last edit at 07-Apr-20 17:31 by Manu.

In order to identify the method used and the solution to this enigma, we should first define the problem: The number and size of blocks in the top half of the Great Pyramid. I found a good photo I took of the summit to do some old-fashioned Math: Counting blocks. It turns out the block number is near the course number counting down from the summit. It's just a coincidence which simplifies the math.

You can get a rough idea from a sample of course counts as you can see and I have indicated the numbers on the left and the squares of the right. The squares are the estimated block numbers for a given course. Roughly, as you go down one course you add one block. It's just an estimate to get an idea of the magnitude of the problem.

To get the sum of the blocks you compute the sum of the squares and I show the formula. In other words 9x9 +10x10....42x42

For example, assuming one block added per course down from current summit to course 160 is

42x(42+1)x(84+1)/6= 25,585 blocks.

Technically, we have to subtract the top 10 courses, about 200 blocks, but it doesn't matter. Let's even call it 26,000.

How big and how heavy was the average block in the top half of the Great Pyramid?

Size:

From Petrie, we know that most of the top 100 courses are on average less than 30 inch and more than 20 inch thick. The average course is thus about 8 palms thick (0.6 m), between 16 and 24 palms wide (av 20 p; 1.5 m) and 16-24 palms deep (~1.5 m) judging from the summit (I am looking at Yukinori Kawae, Nagoya University,

*Construction Methods for the Top of the Great Pyramid at Giza*)Thus, the average block volume is: 1.4 m

^{3}Weight:

The Mokattam Formation is in the Middle Eocene. Density range: 2.1-2.4 ton/m

^{3}So, the average block in the top 100 courses of the Great Pyramid weighed 3.0 tons.

ERGO: The current top 42 courses of circa 26,000 blocks weighed a total of 78,000 tons.

Assume you have enough room up there to set 100 blocks per day. Then, you have a construction time of 260 days for these 42 courses. If you only count the four months of inundation then the timing stretches to 2 seasons and change. Less than 15 minutes per block, but this is of course done with multiple blocks set simultaneously. At lower courses, there is more room and so you have to assume more blocks per day were laid by this elusive method.

Conclusion: You need a method which can haul 100 3 ton stones per day which are 8 x 20 x 20 palms in size.

Update:

Course Numbers by the notch at half-way up. Course 105/210 is in the notch; 140 cubits is within course #94.

I count 68 blocks at course #118.

The more accurate block#/course# gradient: In the upper segment it is ~8 blocks added per 10 courses and in the lower segment to the midway point it is ~5 blocks added per 9 courses. The overall ratio averaged is something like 3 blocks per 4 courses.

EDIT: Corrected Course Numbers on Petrie Plate 8 right pane

EDIT: Added further count to course 154

Manu

Edited 8 time(s). Last edit at 07-Apr-20 17:31 by Manu.

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