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Author Topic: Mathematical Analysis of an Ideal ZED  (Read 414304 times)

Offline mondrasek

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Re: Mathematical Analysis of an Ideal ZED
« Reply #15 on: February 14, 2014, 10:20:42 PM »
New diagrams.

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Re: Mathematical Analysis of an Ideal ZED
« Reply #15 on: February 14, 2014, 10:20:42 PM »

Offline MarkE

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Re: Mathematical Analysis of an Ideal ZED
« Reply #16 on: February 16, 2014, 08:34:21 AM »
I wanted to put all of the dimensions in one place and it is easier for me to see the different pieces by using more colors.  So, here is the initial state drawing.  I would like to know whether we are stipulating that we got to this state, or that we are following some assembly procedure in order to get to this state.


Offline mondrasek

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Re: Mathematical Analysis of an Ideal ZED
« Reply #17 on: February 16, 2014, 02:09:21 PM »
I wanted to put all of the dimensions in one place and it is easier for me to see the different pieces by using more colors.  So, here is the initial state drawing.  I would like to know whether we are stipulating that we got to this state, or that we are following some assembly procedure in order to get to this state.

An assembly procedure would be needed to get to this initial state I think.  It would likely involve vent ports for allowing air to move out (equalize pressure) while the risers and water were assembled.  Those vent ports would then be sealed and not used during the cycle.


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Re: Mathematical Analysis of an Ideal ZED
« Reply #17 on: February 16, 2014, 02:09:21 PM »
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Offline MarkE

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Re: Mathematical Analysis of an Ideal ZED
« Reply #18 on: February 16, 2014, 02:31:55 PM »
OK that works.  For now I will just assume that we can get to the state in the picture.  One other question:  I assume that the pod does not seat.  I used mythical 1um spacers for that.  The idea is that any water pumped into AR1 will freely flow underneath the pod.  Does that work for you?

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Offline mondrasek

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Re: Mathematical Analysis of an Ideal ZED
« Reply #19 on: February 16, 2014, 02:41:21 PM »
Yes, there would have to be that mythical spacer under the pod.  That condition does move this model further from a truly obtainable real world construction but was the only way I could conceive of to start with no water in the pod chamber and still allow for no motion when the water charge is being introduced.  But since the entire model is bound by engineering ideals, we can make that spacer infinitely small.  Assigning it a very small value as you suggest should not cause a noticeable difference I think.

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Re: Mathematical Analysis of an Ideal ZED
« Reply #19 on: February 16, 2014, 02:41:21 PM »
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Offline MarkE

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Re: Mathematical Analysis of an Ideal ZED
« Reply #20 on: February 16, 2014, 02:44:24 PM »
OK so we will treat it that way:  Allowing water admitted to AR1 to flow underneath in a very thin layer without consideration of surface tension, etc.  Are you also OK with the assumption that any water we admit, that we admit through the bottom of AR1?

Offline mondrasek

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Re: Mathematical Analysis of an Ideal ZED
« Reply #21 on: February 16, 2014, 02:50:48 PM »
OK so we will treat it that way:  Allowing water admitted to AR1 to flow underneath in a very thin layer without consideration of surface tension, etc.  Are you also OK with the assumption that any water we admit, that we admit through the bottom of AR1?

Yes, water is to be admitted through the bottom of AR1.

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Re: Mathematical Analysis of an Ideal ZED
« Reply #21 on: February 16, 2014, 02:50:48 PM »
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Offline mondrasek

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Re: Mathematical Analysis of an Ideal ZED
« Reply #22 on: February 20, 2014, 03:52:12 PM »
All, MarkE has not been able to work out his double check of the analysis yet.  Would anyone else like to help?  I am happy to assist in any way possible.  Or if anyone can explain why the method I am using in this analysis is incorrect that would also be helpful.

The reason I am asking is because what my analysis has shown so far is extraordinary.  It appears to show that the ZED is NOT conforming to Boyle's law.  Possibly because it is an open system?  And so PinVin<>PoutVout.  And in the case shown in the analysis, PinVin>PoutVout, so underunity.  But that leads to the following question:  If PinVin<>PoutVout, is there some possible change to the geometry of the ZED model that could lead to PinVin<PoutVout, ie. overunity?

I have already tested the next logical step:  I added the third riser to the current model.  The results of that analysis, by the exact same method outlined in this thread, does result in PinVin<PoutVout, ie. overunity.  So I am anxious to have the analysis duplicated and/or shown to be erroneous.

Thanks,

M.
« Last Edit: February 20, 2014, 08:31:15 PM by mondrasek »

Offline LarryC

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Re: Mathematical Analysis of an Ideal ZED
« Reply #23 on: February 20, 2014, 08:59:14 PM »
Hi M.


First, thanks for the inspiration. I've been looking for an improved way to help other understand the recovery and you gave it to me.


One of the issues is not recovering the stored energy from the previous lift. The attached spreadsheet shows a simple flow analysis between 2 Archimedes and also for a single Archimedes. The efficiency is ~83% with 2 and ~50% with a single. It doesn't have to be a second Archimedes, but some method of recovering the stored energy from the previous rise is required. Only change the parameters in yellow, all others are calculated.


You have seen my older spreadsheet with recursive iterations performing millions of calculations to get the water levels in the risers correct during the rise, due to interconnection of air compression/decompression. I don't know how to do this it any other way, so I can not help with your calculations. My recent spreadsheets analyze the latest design Zed flows the same as the attached Archimedes and they all show efficiency's much greater than 100%. But, as you know, I can not post them here due to my NDA.


Good work and please let me know if you or anyone find any errors in the spreadsheet, should be easy as there is no VBA.


Larry

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Re: Mathematical Analysis of an Ideal ZED
« Reply #23 on: February 20, 2014, 08:59:14 PM »
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Offline TinselKoala

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Re: Mathematical Analysis of an Ideal ZED
« Reply #24 on: February 20, 2014, 09:38:18 PM »
And of course your NDA is preventing you from producing any kind of real system that shows the same degree of OU as your spreadsheet. But what's preventing Travis from using your information to get himself out of his hole? I know the answer to that one... and so do you.

Meanwhile, here's proof that a simple U-tube is overunity.



Offline mondrasek

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Re: Mathematical Analysis of an Ideal ZED
« Reply #25 on: February 20, 2014, 09:38:46 PM »
You have seen my older spreadsheet with recursive iterations performing millions of calculations to get the water levels in the risers correct during the rise, due to interconnection of air compression/decompression. I don't know how to do this it any other way, so I can not help with your calculations.

Hi LarryC!

Oh yeah, I remember the spreadsheets and the iterative nature of those calcs!  I even did some by hand a few times but found that too frustratingly tedious.  I would have had to ask someone to write a program just like you did in your spreadsheet if I was to continue that way!  Hopefully MarkE can show us the proper way to simply set up and solve the Integrals instead.

In this "ideal" analysis the air is assumed to be incompressible.  So no iterations needed.  I just solve for all the needed values on a calculator and keep track of them in a spreadsheet and by drawing the results and measuring new results and relationships in CAD.  CAD is not even necessary but saves me some time.  It is all very straight forward math now.  I also use the spreadsheet to do some quick volume checks at each step to double check my work.  If you don't catch a mistake in one fluid interface adjustment it throws off all the subsequent ones!  A complete analysis of the model presented in this thread only takes me about two hours now, including those double checks.

M.

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Re: Mathematical Analysis of an Ideal ZED
« Reply #25 on: February 20, 2014, 09:38:46 PM »
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Offline mrwayne

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Re: Mathematical Analysis of an Ideal ZED
« Reply #26 on: February 21, 2014, 03:49:48 PM »
Great collaboration! I am logging out till needed.

Looks Like you Men have a great handle on the ZED system.

Wayne

Offline mondrasek

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Re: Mathematical Analysis of an Ideal ZED
« Reply #27 on: February 21, 2014, 09:58:25 PM »
I was hoping to have someone check my math and process of analyzing the 2-layer system before ever posting the 3-layer.  That has not happened and so here is the next model if anyone is interested.  It utilizes the exact same 2-layer model and adds an additional third riser on the outside.  That way the same calculations for the 2-layer portion to find the water levels after introducing the Vin volume "charge" could be re-used.

The PinVin I calculate now rises to ~2.103 mJ.  If PoutVout is to be equal to that per Boyle's law, then the system should stroke ~1.9094 mm.  That is drawn on the right hand side and analyzed to see if it is neutrally buoyant.  It is not, and actually is still pushing upward with ~31.8276 grams of force.  So the ZED would stroke further than shown until it could come to rest again with neutral buoyancy.  And that would require that PouVout would be greater than the PinVin of ~2.103 mJ.

M.

Offline mondrasek

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Re: Mathematical Analysis of an Ideal ZED
« Reply #28 on: February 22, 2014, 12:37:17 PM »
All joking aside, the system to be analyzed is surrounded by the red box.  Everything that occurred previous to these steps are "manufacturing" or "setup" costs/conditions for the process to be analyzed and do not need to be considered.

There are exactly two "units" (blue box) crossing into the system on the right.  That is equal to the two "units" that are exiting the system on the left.  Both are crossing into or out of the system at the same height and both are moving the same vertical distance.

Offline TinselKoala

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Re: Mathematical Analysis of an Ideal ZED
« Reply #29 on: February 22, 2014, 02:24:38 PM »
And your nested system is significantly different.... how?

1. You are confusing yourself with "Boyle's Law" pressure/volume calculations, because Travis and Red Sunset and Webby have all said that the air can be replaced with incompressible fluid. All chambers in your system should be filled with fluid that doesn't change in volume when it's under pressure.

1b. Air -- wet air -- is not an ideal gas and you will find that it deviates from strict Boyle-Charles law behaviour. How much? Enough to account for your numerical result? I don't know. Do you?

2. You should be able to demonstrate some actual gain in something, somewhere, using just three layers. Travis has told us so!

3. What, exactly, is the real "output" of your system? Is it a lifted weight? If you are counting pressing against a stop as "output work", that's not kosher!


 

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