Let us now calculate a simple sled transport model.
In an experiment I could pull 500 N for a long time with ease, nearly with normal walking speed of about 50 meters per minute. to be on the safe side i grant the Egyptians les than half of the speed, about 20 m per minute.
The transporting distance varies with time. We can seperate it in 3 different sections:
1. The main quarry was, together with the harbor for the Tura marble and the Aswan-granite about 400 m to the south. These 400 m are a fixed distance.
2. The way up the ramp. It varies with the height, for each meter in height the ramp is 12 m long. The ramp runs around the pyramid, how will be discussed later.
3. The last part is the distance from the end of the ramp to the assigned position of the block. The average way is the half diagonal of the current working level, 1/2 sqrt(2) * current level width.
With these informations we can calculate the turn-around-time for a transport group in several layers (and if one has too mouch time he can calculate these times for each and every level). But let's look at some selected levels:
Nothing has to be moved up. The total average transport distance is 400 m from the quarries + half dieagonal of 162 m = 562 m. Each transport group has to go this distance twice. Loaded with 20 m/min, empty with 50 m/min. The whole turn-around-time for one team is 40 minutes.
The ramp way in this height is about (50 x 12) = 600 meters long. The work level has a widthe of 151 meters, so the total distance is 1107 meters. Turn around time: 77 1/2 minutes.
This high already 2/3rd of the pyramid volume are finished. The ramp way is 876 m long, the level width is 115 m, the half diagonal measures 81 m. The total distance is 1360 m, the turn around time is about 95 minutes.
About 99% of the pyramid volume is ready, The last 20 m contain only about 6600 cubic meters or 0.3% of the pyramid volume. The ramp length is about 1440 meters, the diagonal of the level adds only 15 meters. The total turn around time is 129 minutes.
We can derive the different transport volumes in a given height for a team from these numbers. In the first layers 10 blocks per day, or about 10 cubic meters, are possible. Even near the top 2-3 blocks per day were possible.
Although 17 men are enough to pull a sled, let us put 3 additional members to each team - it is easier to calculate with 20, too :-) If we knew now the number of workers used for transport, we could calculate exactly the number of blocks transported per day. Several sources are talking about transport workforces of about 5000-6000 persons.
When we use 5500 workers as basis for our calculations, we get 275 teams with 20 workers each. They had the following transport capacity::
Chufu's pyramid contains about 2.3 million blocks. To build it in about 20 years, 320 blocks each day are necessary. Erich von Daeniken grants the workers a lot of free timeand gets a necessary amount of 420 blocks per day. But even this is only less than a quarter of ther average possible transport volume!
This is an argument, too. With 275 transport groups running around the whole day - 137 to, 137 back - we get a pretty jam on the ramp. On the short way on the base level we would have for example one sled every 4 meters - impossible. But, well, on these low levels no ramps are necessary. Up to a height of 10 meters loose gravel ramps could have been used, allowing access from every point of the plateau.
In a height of 50 meters the total way is bout 1100 meters long, which means one sled every 8 meters (if transporting the theoretical maximum of blocks per day), at half height dhe distance between sleds would have grown to 10 meters.
But as we saw only 1/3 to 1/4 of the total transport volume is needed, therefore we could reduce the necessary number of active teams to 100 or less. this would give us distances between individual teams of 30-40 meters.
Now to the last problem discussed here at the moment: what about transport catastrophies? What happens if a rope breaks, what damage does a block tumbling down the ramp?
Nothing will happen! As you remember I mentioned two friction forces on the ramp-page. As you remember even the sliding friction is about 3 times larger than the sliding force. As long as the sliding force is smaller than the friction, the sled will simply come to rest if anything happens. Tired workers can rest anywhere, just letting the sled go.
Rolling stones too are impossible with a 5° ramp. To let a stone roll you have to flip the stone over the edge, which is equivalent to lifting 1250 kilogramms about 5 centimeters high. This is nothinw what happens incidentally, but even sabotage would be useless: the block would come to a halt after one quarter rotation. The enrgy gained by rolling down is not large enough for a continous movement.
The only possible way for an accident woud be that the whole sled falls sideways from the ramp. But this, too, would be connected with a large effort. Transport disasters are simply impossible with this type of ramp.
Pyramid building