|
The differential pulley (3 Wheel Device)
- The tension on the rope never exceeds half the load. - Both ends of the rope are loose. They can be tied up together to make a loop. - The energy needed for somebody to carry a load to the top of a pyramid is the energy necessary to move the load plus the energy to move his own weight. This system saves the energy of moving bodies up and down the pyramid. - This device would allow the Egyptians to use a steep incline. Ramps can be made on the face of the pyramid. - Temporary material can be used to make a smooth surface for the ramps.
Could the differential pulley be the "machine" that Herodotus was told about when he visited Egypt in 450BC? He is not the most reliable source of information but that does not mean that he is always wrong.
The rope problem:
There is no limitation to the amplification of the force produced by the system. Could that break the rope? If each one of the 50 men pulls with a force of 20 Kg the rope will be submitted to 1000Kg. The strength of the rope is a limitation. The weight of the stone is equally divided between the two sides of the pulley. The rope will never have to pull more than half the weight of the stone. By using two of the devices, the weight of the load can be divided equally by 4. Using two devices to lift a 2000Kg stone would require ropes of 500Kg. Today a Manila rope of 4cm diameter has a strength of 10000Kg. We assume that their ropes could hold 500Kg
....whatever they were made of.
- While you are building the first layers of the pyramid there is space for many teams around the base. As the pyramid goes up the number of teams will be reduced and the number of people per team can be increased.
- The differential pulley can be used to move the stones horizontally or to lift it vertically, or move the stone along a ramp at any angle. - Several differential pulley can work in parallel. There is no need to mount them in series when the differential pulley can give you any amplification required. - The building of the pyramid is not limited to building successive horizontal layers. It is possible to start with one small pyramid and add successive layers on any one of the 4 faces. - The differential pulley can be used to press several blocs against each other. A rope (or several ropes) can be placed around all the blocs and the differential pulley will pull the two ends of the rope together.
Why a pyramid? Why not a cube? If you want your edifice to be made of large blocs, sooner or later you will need many men pulling on the same rope. The shape of the pyramid gives you an opportunity to have many men standing on different steps above each other and pulling on the same rope. Their work is used only to lift the bloc. They don't waste energy lifting also their own weight.
Compatibility with other theories: Building many ramps on the face of the pyramid is obviously not compatible with the idea of an external spiral but the differential pulley could coexist with an internal spiral. The small incline of an internal spiral could be used to bring draft animals to the working level. They are easier to feed than people and do not expect to be paid. When the fields are flooded oxen are available as much as the peasants.
The missing proof: The differential pulley is based on the use of two pulleys turning together on the same axis. A chariot turned upside down could have given the Egyptians the idea of using a wheel as a pulley. If they could carve big stones they could also carve two pulleys together out of the same bloc of wood or stone. Please let us know if you ever find such pulley.
The philosophy corner: The poet says that man destroys what he loves. By cutting a flower he makes it wither. The differential pulley works by lowering in one side and lifting on the other. To make a parallel with the two sides of the rope may be far fetched by worth considering.
Could we take it one step further? The pyramid was made by using a simple idea that we were not conscious of. There could be many other ideas around us that we are not conscious of. The differential pulley moves only stones. It amplifies the force of the human body. It is human thinking applied to matter. Is there something else in humans that can be developed further?
We cannot make the difference between a cat asleep on a sofa and a stuffed animal. We need to see it move or hear it purr to make the difference between what is alive and what is not. We are not directly conscious of life. We become conscious of it through its consequences. The same idea applies to heat. It is everywhere in us and around us but we need its consequences to become conscious of it.
After applying human thinking to matter, the next step may be to develop its application to levels above matter. We could look at plants and animals like we look at pyramids. We could see in them the implementation of beautiful ideas that we still have to discover. The next level could lead to a better way for people to look at each other.
The pyramids are pointing to the sky. That could mean that we still have a long way to go.
MAKE YOUR OWN PYRAMID http://spreadsheets.google.com/ccc?key=0AifYd02zwjM5dDRpbXAxVExaeGlCSFRpQWJjWTllS3c&hl=en
Is it practical to use the differential pulley to build a pyramid?.... How many blocs could you lift per day? .... What amplification would you need from the 3WD?
We made the following assumptions: - All the stones are lifted at the height of the center of gravity of the pyramid. - The weight of each stone is 2000Kg - A man can pull a rope vertically with a force of 10Kg at a speed of .2m/sec. - People work 8 hours a day. - We introduced a coefficient of efficiency of 70% for the losses by friction and to give them some time to rest before lifting the next stone. - We divided the workers into teams. One differential pulley and one rope per team.
Work necessary to lift one stone: 2000Kg x height of center of gravity Work that one man can produce: 10Kg x .2m/sec = 2 Kg.m/sec
The amplification 2D/(D-d) is the ratio of length of rope pulled by the team divided the height where the stone has been lifted. The numbers above are averages over the period of construction of the pyramid. The number of stones lifted per day will be higher at the beginning of the construction. The total number of men does not include those necessary to cut the stones, bring them to the site......
Size of the double pulley necessary to get the amplification ratio
The missing proof is the double pulleys. If you ever find one (or part of it) in a museum or near a pyramid, PLEASE let us know
USING OXEN
Building a pyramid would be much easier if most of the work could be done by oxen. To speed up the construction there is also a need to move the stones along several paths in parallel.
PHASE 1: The first layers at the base of the pyramid. Many ramps of dirt are made penpendicular to the side of the pyramid. Oxen are pulling the stones up the ramp.
PHASE 2: The stone elevators Many stone elevators are built on the other 3 sides of the pyramid. Oxen are pulling up the stones from the top level of the pyramid. A differential pulley can be used to amplify the force of the oxen.
The problem is "How to get oxen up and down the pyramid?" The dirt that was used to make the ramps in phase 1 is now used to make a path for the oxen (and the people) on one side of the pyramid. This path is built as the work progresses. One elevator is used to lift the dirt to further build the top of the path. This elevator is on another face of the pyramid.  This path should be as steep as possible as long as an ox can climb it and come back down.
A tunnel inside the pyramid would avoid the need for the external path of dirt.
PHASE 3: Man power at the top.
Oxen cannot be used to lift the stones all the way to the top. Men and the differential pulley could be the last resort. The number of elevators will be reduced gradually as we get closer to the top. People standing on the steps on one face of the pyramid could lift a stone on the opposite face.
The Egyptians must have used simple ideas
but simple ideas are the most difficult to find.
We welcome your comments. They will be posted on the spreadsheet below
|
