Mathematical Analysis of an Ideal ZED

[minnie]

I'll tell you where we are, we want water to flow uphill.
                                       John.

[mondrasek]

I'm sorry Minnie.  I would like to continue but MarkE must be working on something else at the moment.

I hope MarkE will rejoin our conversations soon.

M.

[TinselKoala]

Wait, wait. We seem to be close to a full "timing cycle" description of how the contraption is alleged to work.

Start with the thing level, the accumulators charged and whatever water-air precharge the Zeds need. Call this the Start position. (not with one down and one up).

OK, now to get the thing started we are allowed one "Flow assist" from outside, as I understand it. This causes the bidirectional Flow Assist Ram FAR to push on the framework in the direction that forces down on one bag and start the Teeter-Totter rocking down on one side and up on the other. The side going down, say the left side, that bag pushes water into the left zed LZ and creates the LZL left zed lift that pushes UP on the Left Production Ram LPR forcing hydraulic fluid HF out and into the Accumulator. Meanwhile the side of the Teeter-Totter going up pulls water out of the RZ and into its bag, allowing the RZ internal parts to sink, pulling its Production Ram RPR in, drawing HF at low pressure from the Reservoir. Some of the high pressure fluid from the LPR stored in the Accumulator is diverted to drive the FAR the other way and rock the Teeter-Totter back, at the right time. As the FAR cycles, it too pumps fluid from the Accumulator, as fluid is pushed in on the powered side, fluid flows out from the unpowered side into the low pressure Reservoir.

Right so far? So the Teeter Totter has rocked all the way to one side, the LZ is fully up and the RZ is fully down and the first 1/4 cycle is complete.

Now what makes it go past this point, so that the LZ begins to rise and the RZ to sink? It must sink partway on its own because Travis has told us, I believe, that the Flow Assist to the sinking side is applied once partial sink has occurred.

There is one other thing that I'm worried about. In the "ideal" system that you have been analyzing quantitatively, the upward travel is rather... er.... minuscule. Yet the Zeds, the true and holy Zeds in the diagram, must be able to push those Production Ram pistons into and out of those looonng cylinders with considerable force all the way up that power stroke. A thousand times more distance than you are figuring, from the looks of it.

[mondrasek]

Anytime we can bring back "MarkE" we can move forward with the Mathematical Analysis of an Ideal ZED, AFAICS.

[MarkE]

MarkE, I have never solved for the correct final State 3 lift height.  I have solved for a State 3 calculated from an Energy balance (drawings are on page 2 IIRC) that still showed a positive total buoyant Force.  Due to the presence of this Force I concluded that the ZED could not stop in this state, must lift further, and therefore was breaking the law of COE in favor of OU.  It is very similar to how you initially solved for a State 3 based on a V_in = V_out relationship and also learned that it resulted in a condition where the ZED must also lift further due to the remaining sum positive buoyant Force.

I have openly stated on several occasions that I did not know how to calculate for the correct final State 3 lift height, and that I believed that would require iterations or calculus that I was not prepared to delve into.  But I will make a correction:  It does not require iterations or calculus.  That was a mistake on my part and came from my previous attempts (two years ago) to do this type of analysis without the assumption of the air being incompressible.  So yes, it can be done algebraically.  But I have not done that, nor do I intend to do it this weekend.  I would gladly start by accepting that you have done that, and done it correctly.  If so, you can publish the numbers for the water heights in each annulus, and the lift height, and I would be happy to work from there.  If not, I will show the results of my false State 3 calculations next week.  Or if you insist, I can work them up from the diagrams I posted on page 2.  But please be clear that my State 3 is not, and has never been said to be, a correct final State where the sum of the buoyant forces is zero.

In your OP you stated that you want people to check your "math, assumptions, logic, and conclusions."  Well, just show them.  Where is your math?  If for some odd reason the computer that you use to write internet messages lacks the capability of a calculator, don't solve the calculations you rely upon.  Just show them without the results.  It is absurd that you continue to insist upon a claim without showing how you supposedly get to it.

All, please check the math.  I would appreciate if you can point out any mistakes in the math, assumptions, logic, and conclusions.  Feel free to send your input by PM if you don't want to post in the thread.  It would be nice to know if you check the analysis and agree as much as if you find mistakes.

I preformed this analysis using a CAD model, Excel, and an old Casio calculator.  So precision of the values was carried out to as many as 10 significant digits.  I limited the CAD dimensions to only 7 digits after the decimal so errors are introduced but should still give accurate results if rounded to 6 significant digits or there about.
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