Mathematical Analysis of an Ideal ZED

[TinselKoala]

Those four blue LEDs are in _series_ and that is one AG-3/LR41 battery lighting them up.

[minnie]

   What have we learned?


    1, You've got to be pretty smart to do a meaningful mathematical analysis
         of even the simplest of things.
     2, Even experts can drop the odd clanger.
     3, With a passive device, consider the answer should be predictable.
     4, Simplify things by removing anything superfluous.
     5, Beware of traps like Archimedes paradox
              John

[MarkE]

Magluvin does seem to claim that there is no boost.  But it is quite possible that Magluvin is mistaken.  It is possible that the circuit is a booster, and Magluvin did not recognize it. It is also possible that MileHigh made a mistake.  We will have to see what Magluvin comes up with for history.

Meanwhile back in Zydro-land Mondrasek came up with a fairly clever scheme to try and harvest as much of the energy as possible going from State 2 to State 3.  Let's apply that to the three riser "ideal ZED":

From the spreadsheet:
ST2UPTOTALUPF   1.195618   N   Total uplift force at the end of State 2
ST2_3KFORCE   -0.479825   N/mm   Total Rate of Force Change / mm
ST3_UPLIFT   2.491781   mm   Up Lift Distance

From these we can calculate the size of the water pan necessary:
Water_pan_area =-ST2_3KFORCE/(G0*pWater*(m_per_mm³)) = 49,107 mm²
Water_pan_diameter = 249.8mm
Water_pan_depth = ST3_UPLIFT = 2.49178mm

Energy imparted pushing water up over the spillway:
=0.5*-ST2_3KFORCE/m_per_mm*((ST3_UPLIFT*m_per_mm)²) = 1.490mJ  That's right a quarter meter diameter pan to deliver ~1.5mJ

The energy that will be required to return to State 2, is the same as the internal loss going from State 2 to State 3:  1.903mJ.
The idealized efficiency of the State 2 <=> State 3 cycle is therefore:  1.490mJ / 1.903mJ = 78.3%.  This is better than the single riser case.  But still way short of what we can do with an electric motor directly moving the payload.

Since the single riser and triple riser examples demonstrate different idealized efficiencies, is there some configuration of the idiotic ZED that can at least theoretically compete with a brick?  Or is there an upper limit on the idealized efficiency that can be realized that is well below the idealized 100% of a brick?

Looking at comments in the old thread there was talk by the HER/Zydro proponents of: "capturing" 15in³ hydraulic fluid at 640psi pressure 3.7 times a minute.  There was also some talk talk of 30in³.  If we take the larger number it means that there is 15W power being expended.  Given the tiny energies we see in the "ideal ZED" it is not surprising that the real ZEDs have very low power density, seeing how they slowly raise and lower weights.  And there is no sign of any surplus energy from those machines at all.

[MarkE]

   What have we learned?


    1, You've got to be pretty smart to do a meaningful mathematical analysis
         of even the simplest of things.
     2, Even experts can drop the odd clanger.
     3, With a passive device, consider the answer should be predictable.
     4, Simplify things by removing anything superfluous.
     5, Beware of traps like Archimedes paradox
              John

I think that what it takes to do a good analysis is primarily patience and good book keeping skills.  Smart people make mistakes all the time.  Careful book keeping reduces the chances that the mistakes will get through or stay out in the wild for very long.

This particular contraption screws with intuition because it employs several mechanisms such as buoyancy  that are easily misinterpreted.  Pile on little complexities like the effects of: the annular rings each having unique areas, pressure effects of nesting, combining buoyancy with hydraulics, and the necessity to do things like integral calculus to get some of the values, and there are lots of opportunities for mistakes.  What I find interesting is that looking through the old hydro differential thread I can see that Kan Shi laid things out almost two years ago.  It's just amazing to me that people were still struggling to perform a decent numerical analysis so long after Kan Shi really showed what needed to be done.  Her posts really helped me double check my work, and fix my miscalculation of the ending lift height.

I also don't think it helps when the promoters of an idea go out of their way to misrepresent standard physics as we have seen in the five videos and countless posts that talk about comparisons of quantities that are not conserved in the context of a free energy claim:  force, power, volume, etc have all been tossed around, when if they were serious, HER/Zydro should have been talking about energy:  How they measure what goes in, how they measure what goes out, and how third parties can verify their claimed measurements.  In the old thread I see that MileHigh repeated asked for those simple and fair parameters.  I did not find anywhere that the parameters were supplied.  I saw a lot of the dodging and distraction that has gone on in this thread.

So, here we are with the "ideal ZED" emulating a ~$1. spring, except that to do so it needs over 1000 times the volume, and substantial complexity.  And despite the fact that the spring emulating "ideal ZED" is a passive thing, and passive things don't produce energy, the HER/Zydro promoters continue to pretend that they have some miracle hiding behind some curtain.

[minnie]

   Thanks for mentioning KanShi, very interesting,
                            John.