Prater’s Theory concludes twenty-six and fifty-two degrees are fantastic inclines for millions of small 2.5-tonne blocks, moving them quickly up from the pyramids’ large perimeter.
These ramp inclines could keep pace with a 25-year project deadline. Many ramps with steep gradients could fit around the perimeter of the pyramid. The 26-degree, moving some of the small blocks and the 52-degree, moving millions.
26 & 52 – Degree Ramps
26- Degree Ramps
The base length of a 26.6-degree pitch is twice the distance as the height. Blocks seem to move into it as they climb up this ramp gradient.
In the small model test, dropping a weight of 7.25 drew 13 up the slope. The weight theoretically moving 13 tonnes up the 26-degree ramp. If each man exerted 150 kg of force, a 13-tonne block would equal 49 men, and 10 to 14 men for a 2.5-tonne block, based on the small-scale test.
The weight alone of a large spool travelling down the slope would bring up a 2.5-tonne block, such as the one in the image below, inserted between the blocks forming the grand gallery. The 10 to 14 men would increase the load, brought up the slope, to 5-tonnes. And this is also enough men to get the large spool back to its starting position, as tested on a small model. But what is wrong with ten 2.5-tonne blocks on a 2-degree ramp, 25-tonne moved within 5 minutes?
Another way, would be a few ramps, side by side, each moving 2.5-tonne at a time easily. Doing it easy, you would soon get into the rhythm. I suppose using the grand gallery spool would take fewer men.
The one thing I am not keen on, is the fact the 26-degree ramp eventually cuts through the building, giving complexity to the construction process.
Building the pyramid as shown in the image, would be a nightmare, with the casing stones sitting on different levels. Again, placing the casing stones after the internal structure is better.
If the foot of the central 26-degree ramp started 15-metres out from the base of the pyramid, the void above the grand gallery could be utilised.
Yes, it all starts to get messy and complicated, but the speed at which the 2.5-tonne blocks could go up to form more than half of the pyramid, is tempting. And the tonnage could be increased, by inserting a spool, into the side of the pyramid. Even more so, using the axle to draw the blocks. The number of men on the ramp, could also be increased, as well.
There are around 800 men shown on the three central 26-degree ramps. If each man produced a pulling force of 0.100 kg / 0.1 tonnes, that would be 80 tonnes of pulling force/power.
The ramp ratio from the test was R1.79. So 143 tonnes for 800 men, based on the small-scale model. Introduce a wall spool, men on the scaffold, ground rigs, cows and the figures start getting crazy.
O’, and maybe a small circumference or two.
The great pyramid sides slope inwards at an angle of around 52 degrees. If the 52-degree had a base length of 1, the height would be 1.279.94, and the slope length would be 1.624.27, which is decimally close to the golden ratio.
Anyway, we’re getting near to vertical now, and even with the spool’s guide ropes fixed to the pyramid’s structure, bringing the casings up the 52-degree slope would put immense pressure on the equipment.
It would take the tension off the guide ropes if the men pulled the rope above the load, using the smaller circumference to draw the limestone blocks up.
Small blocks in the 2.5-tonne range would not be an issue, with both of the spool’s guide ropes taking the weight
An example of what is possible at the pyramid 72-metre mark.
There would be 9.18 million 2.5 tonne blocks, 22.96 million tonnes, in 25-years using one side of the pyramid if it stayed at this level.
Blocks and tonnage, 72m Level
|Roller sets 28||Blocks||Tonnage|
|Rig cycle time||10 min||2.5|
|9 hr day||1,512||3,780|
|243 days pa.||367,416||91,850|
A large contingency, could be given to all the figures above.
Men on the 72m level
- Each rig, 30 men
- Number of rigs 28
- Working hour per day 840
- Shift workers + Maintenance 860
- Men placing blocks 840
- Total men on work area – 1,700
- 72m level – area – 3,446 m2
- Minus 1/3 rig space – 1,149m2
- Space for men – 2,297m2
“Though it’s difficult to see”, the men are pulling the block straight up the side in the image above. The spool is rotating up the rig and away from the load, which takes more effort. The men are now lifting the block weight, less the ramp ratio, which is the reverse of using a lattice rig.
In tests, the lattice rig vertically lifted 13 for 10.25, a 21% gain, and now a 21% loss. After deducting the ramp ratio, 2.5 tonnes becomes around 3-tonnes. Worth providing the extra men to get the blocks up quickly. Each man exerting a force of 0.100 kg.
The above was an example. Utilising the rig’s spool correctly and having the men elevated, pulling the ropes perpendicular to it would be better. Seven rigs could be placed on each corner, at different elevations. The blocks would then move 90-degrees, which feed and merge into three 7.5-degree spiral ramps, side by side, each capable of moving four blocks at once. That’s 336 blocks or 840-tonnes.
The Casing Stones
The casing stones that once covered the great pyramid weighed between 10 and 25 tonnes. Hauling them up the side of the pyramid wouldn’t be my choice, but knowledge and other tests show that this is possible. A 2 or 7.5-degree spiraling up on the casings stones, cutting the casings back flush afterwards, would be easier for the heavier blocks.
If the internal structure is set in place first, the procedure for the casing stones would be similar for any external ramp. Once the ramp is built to the intended level, the casings travel along the flat to the point of placement and then get filled with blocks between the structure, forming the next level.
Builders then prepare for extending the ramp, whilst others place blocks to the far corner, working back towards the ramp. On the next course, the last block placed is bonded into the perimeter.
If the rigs and rollers were placed centrally, on the four sides of the pyramid, then it would seem as though it would be just a case of working from the corners, back to the ramp, before moving up to another level, afterwards attaching a guide roller to the roller ladder. But there would be difficulties in squeezing a central block between the casings before filling in behind from above and replicating this four times around the perimeter. For this reason, it would be better to have all four set-ups, working back from one corner, leaving the last 52-degree set-up on that level to finish the course.
Having each set-up taking it intern placing the casings, providing better bonding in the face of the pyramid. But this does not leave the other set-ups idle because as soon as the casings are in place and filled behind, by the set-up working on that level, they are back repeating the same thing, every time, getting better at doing it.
Bedroom Model Test – Using A-frame
Before carrying out the test, I knew only a slight difference would exist between the amount of weight moved up the 52-degree ramp and the weight dropped.
The great pyramids’ sides are steep, so the test was an important one, giving some indication of what the builders may experience.
Dropping a weight of 12 drew 13 up the 52-degree slope. If 12-tonnes became 23.15-tonnes, this would theoretically haul 25 tonnes up the outside of the pyramid, involving 154 men.
In the early stages of the project, A-frames could be useful, but as the pyramid progresses, there would be difficulties in using them.
- Lifting the blocks up the sides of the pyramid, using the A-frame requires a large amount of space to put the equipment.
- Heavy casing stones require lots of men, which also need space on or within the same area as the equipment.
- The higher the pyramid gets, A-frames would become less useful and more of a hindrance.
It’s all about space, and 12-tonnes for 13-tonnes wasn’t great at the time. Something had to change, so I came up with the lattice rig, which provides plenty of room for quite a few men, within the pyramid works area, on the side of it, and it also can be used on the ground.