According to Franz Löhner, and his associates, you only need 50 men (per average size stone) to lift and pull it up the 51.5 degree face. His research was extensive.
Here I will add a few additional insights, and facts.
The distance using a spiral ramp system, inside or out, wrapping around the Pyramid would equal approximately 83% of a mile (4,380.89ft.) and/or (1.335k) kilometers. (One mile = 5280ft. or 1.6k) The face of this Pyramid, in surface length, is approximately 612 ft. or .186 kilometers, from bottom to top. 4,380 spiral footage length, div. by 612 ft. face surface length = 7.158. The face length is 14% of the spiral ramp theory. Basically, a little more than 7... (7.143) times as short in distance. This is based on a 5.7 grade degree angle, as proposed by the ramp Spiral enthusiast's.
For fact checkers, here are the measurements of the 22 spiral angle's ascending to the top. I use Sketchup in 3D, (to size) for my results. Those 22 angles measure: 689.03', 591.93',508.49',436.81', 374.72', 321.13', 257.86', 236.98', 192.23', 142.73', 122.61', 105.33', 90.48', 77.72', 57.03', 47.98', 37.88', 24.09', 20.69', 17.78', 15.27', & 13.12'.
The Pyramid face = 51.3 degrees, which is 9 times the spiral angle of 5.7 degrees. In that spiral proposal they use 8 men to transverse upwards. 8 men X 9 ( difference in angle) = 72 men. Franz Löhner calculated only 50 men need to perform one single pull. Additionally, with the ramp concept, if one group stops for any reason, the entire production line would likely grind to a halt.
As there are 22 corners to reach the top, the line grinds to a stop 22 times, lifting and turning each stone, at each end. They are on a time schedule. It's not because they consume 2-5 minutes in this realignment that causes an issue, it's because... this is happening all the time, all at different time intervals. The higher the build, the more frequent the entire line needs to stop, as the tunnels become shorter and shorter, and those ends approach faster and faster. Those on the last run, (short distance) would be stopping those on the first run, (long distance) time and time again. The last turn which happens in 15.27 feet, would be stopping all the men on the first run, 45 times, as they wait for the last 90 degree turn of each stone. Actually, it is worse than that, due to all the variable stoppages.
The stoppage becomes MANIFOLD. Now do you understand why the ramp proposal will not work. 45 times, grinding to a halt, and as we all should know, it is more difficult to get the stone moving, than it is to keep it moving, ie, Newton.
By pulling the stones directly up the Pyramid face, you save on men required, as well as, the time required to reach a working level. Using the straight method, the men could be standing on top utilizing all four sides, and/or, down at the base, where as, the spiral is a single line proposition. By working of top, you have the space, and a multitude of possibilities for moving stones up and on top. The entire project would never come to a halt, as it is multi-faceted. You only need 1/7th the men to accomplish the equivalent work, in 1/7th the amount of time. And, that is based on the Spiral line never stopping... :)
Consider, it only required 100 men, alternately pulling the 2 stones directly up the Pyramids face. A simple track laying on the Pyramid's face, is all that was required. No building and removal of large ramps were necessary. In the illustration below, there is a two track systems, with ascending and descending platforms. There are also two depression in the ground for the platforms, making it possible, to be level with the approaching tracks. Greased tracks would dramatically reduce friction. Both platforms are connected with one or more ropes. Multiple ropes help to reduce friction and strain. As one is pulled to the top, the other descends to the bottom, acting as a counterbalance, to negate the weight of the carriage platforms. When one platform with the two stones reaches the top, that skid is pulled off, while the other skid at the bottom is being reloaded. The illustrations below shows 100 men for two stones at once. An additional increase in production. This requires the rope(s) to make a 180 degree turn, if you want to have a counter balance. There is much debate concerning pulleys or the like. I will address that at the end of this proposal.
Note: the platform is not completely down in the depression, so you can view it.
Simple enough? The building could have been accomplished using only brute force. There are those who feel the ancients were not intelligent.
Everyone agrees they understood the usage of tracks. Continuing those tracts straight up the face of the Pyramid, is not a major leap in thinking. I personally believe they used additional components to aid in their endeavor. That could have been Water, Levers, Cranes, crude Pulleys, a capstan is a vertical-axled rotating machine developed for use on sailing ships to multiply the pulling force of seamen when hauling ropes, or other forms of time saving labor methods and equipment. With men alone, only 1/7th were needed, and would achieve the same result, in 1/7th the amount of time. This works with dry land at the base, or with water contained within the wall, and barges carrying those stones up the Water Funicular Causeway, floating and around the base. I digress...
Only Stone Pullers? Fine, this should work for you, and may be all that was necessary. Did I convince anyone? Please chime in. I welcome your comments. If anyone what's a copy of the Sketchup file(s), I will supply. You can download Sketchup Viewer for free, which enables you to pan in and orbit, enabling different perspectives.
Oh, yes...An Egyptian Pulley?
Keep in mind, a water logged tree/palm would serve to make that 180 turn, while lubrication the rope with wet sap. The log is cheap, and easy to replace, once the ropes wear to deep. Just the same, below is evidence they used rope and made 180degree turnes.
Ref: [www.cheops-pyramide.ch] stone implements, so called bearing stones, found at Giza, that were part of an unknown device to pull or lower three parallel running ropes over an edge. Archaeologists think, that it was put into an oblique shaft or crane and used to lift or lower heavy weights. Franz Löhner, unlike some Egyptologists, doesn't think, that it could have been used in such a way. This shape of stone is not suited for a permanent heavy load. Neither stone nor the ropes could tolerate that kind of strain for long.
The above assumption, would need to be tested. What kind of stone? How long? Amount of heavy load?
Two stones were found. A pair. "This shape of stone is not suited for a permanent heavy load". OK, so they were not used for heavy loads, beyond their working capability. Polished stone and grease reduces friction. The fact that two were found, lead me to this design possibility. You can be the judge, though here is clear evidence, they employed devices, which caused ropes to turn 180 degrees, using more than just one rope. With each additional rope the friction, and stress is cut in half.
You are viewing only 1/2 of a block and tackle system.
Edited 6 time(s). Last edit at 14-Mar-20 00:33 by Steve Clayton.