Date: April 01, 2020 10:30PM
Steve Clayton Wrote:
> >they have to hold three times their weight in
> How do you arrive at that fact, 3 to 1.
> There are water displacement formula's &
> Calculator online:
The weight of air and water cancel out and the density is the determinant of the volume of a boat needed. Limestone's density is 2.7 so you need a boat with 2.7 times the volume of the stone you want to carry. Figure 3 times to support superstructure and keep the load above the water line.
By the same token in order to balance the stones on the other side of the funicular they have to hold three times the weight of the fully loaded barge coming up the causeway.
I don't doubt they could design such a contraption; I doubt they'd need or use anything so complex.
I am still having problems understanding your 3 to 1 ratio. If you wish, plug that into this calculator, so I can better understand. What is complex?
So, here is a calculator everyone can use, to help establish bouncy on water, as well as, other fluids. In my illustrations, the barges are basically 30' x 10'. Using Sketchup calculates volume. In the example below the volume is 1551.136 cubic feet. Using the Omni calculator, the weight of displaced fluid (water) = 96,846lbs. As I understand it, this calculator establishes the point of Equilibrium. It is neither sinking nor floating.
What establishes how much the object floats, is based on a percentage. Lessen the weight, the more the barge will raise. Buoyancy is: Density = mass/over volume.
As the average weight of a stone was 2,500lbs., the barge in my example will be in equilibrium at (96,846 div. by 2,500 = 38,738) 38 stone capability. As you can see, that is allot of stones. The question then becomes, if the barge was out of water, would it be able to support 38 stones. I would say no, it could not. So, then it becomes an issue of how much, the wooden structure can support, when weight is placed atop it. Strong internal bracing would be a "prerequisite". (a thing that is required as a prior condition for something else to happen or exist.)
As for balancing stones, that is accomplished when placing the stones on a floating barge. The water line being even around the circumference of the boat. When the barge(s) are on the Funicular, they are already in balance. The returning empty barges are also in balance, as water is self leveling.
Why I like the Funicular approach, is that it can be tailored to fit the build ratio required. No other proposal is capable, of achieving this with less material and (labor) men.
When using this calculator, the Bouyant force B = Weight of displaced fluid. They are the same number. 430,793 newtons = 96,846lbs.
There are 24 stones on this example. I have been proposing 10 or 12 stones.