Category: Non classé

11-02 Hydraulic reading of the Red Pyramid

On By khufuliteIn Non classéLeave a comment

The external dimensions of this pyramid were different: the base is between 418 and 420 cubits, the height between 209 and 210 cubits, and the faces’ angle in relation to the horizontal ranges from 43°20 to 44°36°; a volume of 1.688 MM3; and a protection sphere with a radius of 44 m (144.35 ft.). The funerary complex is at a height of 44 m (144.35 ft.).

Builders did not use degrees to measure slope like we do today, but the SKD or 7 times our current cotangent, by counting the heights in cubits and the lengths in palms (one palm = 1/7 of one cubit). One can assume they took a value as simple as possible, limiting the SKD to 7, meaning either a base of 418 palms for a height of 209 cubits, or a base of 420 for 210 high, 45 degrees for the faces’ slope. The “Entrance” is at 31 m (107.7 ft.). The design of this pyramid is very similar to that of Meidum.

I recommend reading the article on the Meidum Pyramid before going further.

The protection sphere of the red pyramid is 10 m (38.8 ft.) larger than that of the latter, but is smaller than the Rhomboidal pyramid. This suggests that the Red Pyramid was built second in time and the Rhomboidal Pyramid third.

The red pyramid has three internal volumes, one of which, the southernmost, has been identified as a funerary chamber by the accepted consensus, while the other two antechambers, which are practically identical in size to the chamber. The internal layout of the pyramid is very close to that of Meidum.

A descending corridor of 1.05 x 1.21 m (3.44 x 3.96 ft) in cross-section, whose entry is at a height of +31 m (101.7 ft), and extended by a horizontal corridor, whose bottom is at level zero, gives on an antechamber of 3.67 x 8.38 m (12.04 x 27.4 ft) and 12.3 m (40.35 ft) high on the right, and on a second one on the left. A chimney closes it, and opens on a last chamber of 4.2 x 8.38 m (13.7 x 27.4 ft) with a vertical wall of 3.7 m (12.1 ft.), whose original floor (the masonry is destroyed) is at a height of +8 m (26.2 ft.).
The Meidum pyramid hides two of its vertical well shafts behind lintels; in this pyramid, the antechamber is highlighted.

As in the previous pyramid, the chambers’ and antechambers’ volumes are the elevator floats of second-generation remains that had been doctored, and which were used to build a portion of the pyramid. However, even though the lifting height of each well shaft was about 20 m, they couldn’t be used to hoist the stones up the summit at 105 m (344.48 ft.). And following the model of all the great pyramids, starting from a certain height, courses were filled by hoisting the stones along the faces already erected. To understand the method used, you can read the chapter devoted to the last floors of the great pyramid.

The first antechamber whose floor is at level zero could have been the loading room for the blocks coming into the pyramid via an access gallery probably opening onto the east face, its floor would have been dug up to the next level 22 or 23 m the length of the hull of the float, which depended on the weight of the stones, a weight which to this day is unknown. Subsequently this well would have been filled.

The blocks could have been raised up to 17 m to be passed to the loading path of the second floor

A second well could have been placed in the second antechamber which would then have been the bottom, taking at level +17 m the blocks hoisted by the first floor to take them up to level + 34 from where they would then have been passed to the third floor whose well started from “the king’s bedroom”

At that time the connections between rooms and antechambers were blocked.

As in all pyramids from Meïdum onwards, the central cages and wells would have been closed from above.

At the end all the floats had been dismantled, the stones to block the wells and cages, then finally the access chimney to the mortuary complex would have been hoisted along the side of the pyramid, hoisted both by the stones which descended into the cages and well and/or by ballast which attached to a rope attached to the stone which rises, passing over a rope return and allowing itself to be lowered on the opposite face. (But the use of a seat winch could have obtained the same result)

03 – 05 Stones issue

On By khufuliteIn Non classéLeave a comment

Granite for the upper chamber, refined limestone for the siding, or coarse limestone for the filling—no matter its aspect, stones are the primary resource for the pyramid.

Granite:

The upper chamber masonry is made of granite extracted from the Aswan quarries, 900 km to the south, and precisely cut. I did not go to the extent of explaining the extraction and manufacture processes of these blocks, sometimes gigantic, but I gave more details about their handling from Aswan to their final position in a chapter dedicated to the megaliths.

Casing:

The siding blocks were extracted from Turah quarries, 20 km to the south of the construction site. I don’t mention their extraction either; however, the extraordinary “Merer’s journal” unearthed by P. Tallet provides us with significant information about the fluvial transportation of the blocks.

Filling:

The filling blocks are made of nummulites limestone; they represent 96 % of the total volume of the pyramid. The entire operational problem of the stone treatment is about this material.

Calcaire nummulite

For all that, is it well known?

To my regret, despite the considerable number of measures taken on these pyramids, I failed in finding hardness, density, or compressive force measures for these stones.

This lack of information about the physical characteristics of the stones reveals how little effort was made by the authors of the different studies to really understand the work involved in building these monuments.

In addition, we found many geological studies about the constitution and composition of stones but very few measures about their physical characteristics.

Lacking anything better, I fell back on a nummulites limestone that can be found in stores in France, whose density varies from 2.1 to 2.5 T/M3 and compressive force between 30,000 and 60,000 Kn/M2.

For my calculation, I arbitrarily retained the following values: 2.4 T/M3 and 40,000 Kn/M2.

To dig furrows into the rock, there was no other way but to use a tool with a cutting edge at its end to exert a pressure that exceeded the compressive force of the rock to break it and smash it to dust.

Therefore, to break the stone with a cutting edge, a pressure must be exerted on it that equals the rock’s compressive force multiplied by the contact surface of the tool.

It breaks the rock down bit by bit.

The energy consumed by the cutting is the result of the movement of the tool, and the volume of broken rock is the result of the contact surface of the cutting edge.

Therefore, the cutting movement of one meter on a 1M2 surface breaks 1M3 of the rock down and meets a 40,000 kN resistance and consumes an energy of 40,000 KJ, or 11.1 kWh.

To realize this work in an hour, it requires a power of 11.1 kW.

Whether it is made in one big cut or in smaller cuts, it still has a power of 11.1 kW.

Needless to say, the cutting edge has to be harder than the nummulites limestones to obtain this result, so it doesn’t warp.

This requirement disqualifies the metals available at that time, including copper because its hardness is the same as limestone’s.

This means that the cutting edge must be either a gemstone like corundum, quartz or diamond, either amorphous stones like basalt, flint or obsidian or compound stones such as granite or diorite.

In all these cases, these hard stones will disintegrate quickly with repeated, hard shocks.

A solid tool is efficient since there is no wasted time replacing it.

Therefore, the stone must be gradually cut without inflicting shocks on the cutting edge.

Extracting blocks