Steve Clayton Wrote:
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> 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.