cladking Wrote:
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> Steve Clayton Wrote:
> --------------------------------------------------
> -----
>
> > The Double Incline Plain science calculator is
> > producing some interesting facts. For pulling
> > stones up from the Harbor, the Funicular would
> > need to carry nearly 3.8 times the weight of
> the
> > other side. On a 5 degree causeway angle, the
> COF
> > (coefficient of friction) would be 0.05 - 0.06.
> > This is the range of becoming in balance, ie.
> > reaching a State of Equilibrium. So basically,
> > whatever the dimensions are of a Pyramid stone,
> > you will need nearly 4 times it's volume in
> water
> > weight, to pull it up the Causeway.
>
> All else being equal the less steep the incline
> and longer the route the less efficient a
> funicular is.  This can be an important
> consideration if water is limited or the ability
> to construct a proper funicular run is limited.
> No matter the source of the water it was seasonal
> and likely limited at least at times if not nearly
> continually.  It seems highly likely that it was
> efficiency and water supply that were the primary
> limitations to just how large they could build.
> Pyramids got larger as efficiencies were learned
> and techniques perfected.  
>
> Needing four times the weight of stone in water is
> no problem, of course, providing they had it and
> such a significant drop in efficiency didn't come
> right off the top.  I doubt more than 3% of all
> supplies arrived by the causeway so water usage
> for this specific funicular would be
> insignificant.  It might have been some of the
> highest tech on site but water needs were limited.
>  
>  
> > A 4 to 1 ratio. Increase the amount of stones
> > needed, you need to build a vessel, 4 times as
> big
> > in volume. 
>
> I picture the ascending "boat" (dndndr-boat) as
> nothing but a sled which would be dwarfed by the
> (henu boat) counterweight.  
>
> > The science calculator also provides the
> Tension
> > involved,...
>
> Cool.  
>
> > ...and the rate of speed it would travel.
>
> Equally cool but remember these were primitive
> materials so acceleration would vary over even
> short distances.  
>
> > The rate of speed, increases as the process
> takes
> > place. It is not a consistent speed.
>
> This acceleration was nominal.   Over a long
> period (a long run) even a small acceleration can
> result in significant speed so it is important but
> hardly concerning to engineers who grew up
> designing and operating these systems.    
>
> > They would
> > need to bail water, to slow it down, and
> thereby
> > maintain control.
>
> This is hardly impossible but very unlikely.  On
> the causeway it wouldn't matter too much if they
> ejected so much water that the system stopped
> short but it mattered a great deal on the pyramid
> because refilling the counterweight would cause
> lengthy delays and would be exceedingly dangerous.
>  The primary danger being overfilling a a system
> not in its proper position resulting in extensive
> equipment damage.   For this reason they would
> have used other means to brake the system.  They
> would use a robust brake operated by the the
> filler (ferryman) and probably partly automatic.
> There are many ways this could be done without
> damaging the ropes.   Once a system was in balance
> they'd never do anything to get it out of balance
> because primitive materials were very unforgiving.
>  
>
> > Doing so may have contributed to
> > the erosion along side the Sphinx?
>
> It would be a small contribution if they operated
> it in this manner.  
>
> > There is also
> > an unexplained ditch, running down alongside
> the
> > Causeway, and into the Sphinx encampment. It
> > starts approximately midway down from the
> Upper
> > Temple. Additionally, the rope tension
> increases
> > the faster the vessels travel.
>
> Really! I can hardly imagine the cause.  Obviously
> there is a slight increase in tension on whichever
> boat is descending but total tension (the force
> pulling against the pulley) should be constant so
> long as the grade is constant, I believe.  
>
> > The Funicular
> > system requires very few men to operate it.
> > Gravity and water do the work.
> >
> > [youtu.be]
> >  
> > geogebra.org/m/ZeZjAfta
> >
> > Working on it... the light could be better.
> >
> > [youtu.be]
>
> Building pyramids was very very easy.  Learning
> how to build pyramids was hard work that took
> three or four centuries to perfect.   Modern
> people just have no idea and don't care that
> Egyptology doesn't really care how they were built
> so they invoke "ramps" and go back to parsing the
> Pyramid Texts in terms of modern abstractions and
> the "book of the dead".  This is what we call
> "science" now days.

Hi Cladking,

Water is essentially infinitely measurable. Providing the ability to fine tune the system.

There are two different scenarios. Pulling up rocks from the Harbor, and pulling rocks up the face of the Pyramid. Both are Incline Plains, and save on water required.

1. Harbor rocks: The would entail a longer travel distance, though you can add Barges in a tandem. The limitation becomes how many ropes and their size. Starting and stopping repeatably is not critical, as the system is in a State of Equilibrium. What the Science calculator reveals, is how much water is necessary to bring both sides out of a static position, and begin moving. Just water and no men pulling. What I still need to solve, is how many men would be required to do this, when the COF is lower. In essence, how many men would be required to overcome a COF of 0.06, or  0.07 and possibly even more? This can be calculated, as we know approx. how many men are required to pull a 2,500lb. stone on a level surface. This becomes more important in the second scenario.

2. A need to be under control. The Causeway is approx. 1,700 feet to the Harbor dock. Khafe's Pyramid is approx. 83% finished, once a height of 50 meters (164 feet) is reached. They would have needed to stop and start 10 times, as they proceeded down the causeway. 1,700 div. by 164' = 10.36  The calculator is based on two stones, (2267kg) 5,000lbs., and a counterweight of (60996kg) 134473.16lbs. If they understood the 2 to 1 lift (pulley which is not required), they could pull up twice the amount of weight, though the length doubles, becoming 5 repeated stops. The advantage is, they would use 1/2 as much water, and time required.

So, all is possible, and can be shown to work. This is a workable scenario, and in my opinion answers how the Pyramids were built. It uses less men, and the assets we all can see, without building something elaborate, ie. Spiral tunnels/ramps and/or other building proposals. Proposals which there is no evidence of... No scarring of the land, or large additional rocks laying about. Nothing of the sort. Though there is a massive Causeway and 4 Walls built, which no one seems to have an answer for.
  
The thought occurred to me, that a Geyser, is more likely in a volcanic location. There is plenty of Basalt rock available in the area. To dismiss it out of hand, is unreasonable. I believe 4,500 years ago there was plenty of water, though not as much during the Summer. They needed to harvest water for the building operation, and even a small stream dumping into the Wall enclosure all night, would be beneficial. As with the Causeway, this is why they expended so much time and energy, in building the Walls. Both were critical. The AE were proficient canal builders, and this is well documented.

Here is a short movie, which shows the two angles, and their relationship to each other. It is a Double Inclined Plane calculator in operation.

The website can be reached at: geogebra.org/m/ZeZjAftaThe website also provides the Tension, ropes would need to handle. You will need to convert from Newtons. It is very difficult to argue with Science.

[youtu.be] 

Occam's razor (or Ockham's razor) is a principle from philosophy. Suppose there exist two explanations for an occurrence. In this case the one that requires the smallest number of assumptions is usually correct. Another way of saying it is that the more assumptions you have to make, the more unlikely an explanation.