Mathematical Analysis of an Ideal ZED

[MarkE]

care to elaborate a little

The value immediately preceding is the change in riser GPE going from ST2 to ST3.

This is why I am asking.

If the risers are at a higher energy state, then will they not return to a lower state if allowed?

They are at a higher GPE in ST3.  They do fall back to the lower GPE returning to ST1.  It is an internal energy loss.  It does affect the amount of energy that comes out during the ST3 => ST1 transition.  Hint:  The force acting on the water in the pod chamber is not just the weight of that water column.

ST1=>ST2 takes the same input but ST2=>ST3 is over a shorter distance,, make the riser walls thinner and that force goes down,, make them 0 and it goes away.

By "that force" I believe you mean the weight that Mondrasek intentionally added to counter the buoyant up force in ST1 of the submerged portion of the risers.  Yes, if the riser walls had no volume they would not displace water and there would be no buoyant up force to compensate.  The flip side is that the volumes and forces would change as well.

[minnie]

    Yes Mark,
                  I think a bucket of slippery water would perform nearer the 100%
    than the stupid Ideal ZED.
         Is there anyone out there who could foresee any possible use for a
   ZED, other than an amusing conversation piece.
        minnie is my wife's name by way, I didn't realise how the thing worked
   when I joined up many years ago, never bothered to change it. Don't
   see why an ideal user name should be gender specific anyway.
                     John

[MarkE]

    Yes Mark,
                  I think a bucket of slippery water would perform nearer the 100%
    than the stupid Ideal ZED.
         Is there anyone out there who could foresee any possible use for a
   ZED, other than an amusing conversation piece.
        minnie is my wife's name by way, I didn't realise how the thing worked
   when I joined up many years ago, never bothered to change it. Don't
   see why an ideal user name should be gender specific anyway.
                     John

Ha!  I wasn't thinking of you when I said:  a woman named John?  It is a line from an old movie.

Like you, I do not see the least bit of utility in Wayne's contraptions.  Their efficiency gets better and better the less that they do.  Ultimately they are surpassed in utility by a brick. 

[MarkE]

I was running under the impression that it is the total reflected weight in the pod chamber.

That then would include the riser weight.

That is correct and it affects the energy dumped out the pod chamber drain.

That is what I used to "test" if my calculations were working to provide a net zero condition,, I made the thickness 0 and the final two calculations were still the same value as each other.

Zeroing the riser wall widths tells you if the up lift calculations on the undersides of the walls are reasonable.  In terms of inergy in and out, one still has to put the same amount of energy in to go from ST1 to ST2 as before.  What changes is the additional energy that comes out going from ST3 to ST1.  You sort of had the right idea that you needed to account for the energy that goes into the R3 GPE.  But where you subtracted it in two places to cancel out, you should have added in two other places instead.

So I was thinking then that if the energy is balanced and accounted for, then I can look at the forces, which are not energy and do not need to be conserved.

For God's sake why look at forces which are not conserved when trying to see if a machine conserves energy or not?  What is force alone going to tell you that is of any use at all?

I was also thinking that I could just take the difference between the spillway output and the ideal output and keep track of that so that the totals are still a net zero,, just trying to account for all the energy so that none is missed or doubled up.

If you want to try zeroing out then set the spillway movement time to some huge number like 1E30 seconds.  You will run Excel out of significant digits forcing the ST2 => ST3 efficiency to 100% to Excel's precision limit.

[mondrasek]

Well, maybe you have a different idea of what it is that you would like to try and obtain from this analysis exercise than I think you do.  Please state clearly and succinctly what you are trying to determine from this exercise.

What I am trying to determine from this exercise is if an Ideal ZED acts analogous to a simple (or compound) hydraulic cylinder as has been contended as the basis for previous "proofs" of the impossibility of the actual functionality of the "dual ZED" devices demonstrated by Wayne Travis to Mark Dansie.

I maintain that if you are trying to determine what level of efficiency is "ideally" possible, then the mechanisms do need to be specified, or else the exercise is rather pointless.  It is pretty simple to state that as the throughput power approaches zero the energy efficiency approaches, but never reaches 100%.  If you are content with that conclusion, then we are back to the device being more or less a complicated way to emulate a spring, actually two springs, where one more or less falls out in the ST3 to ST1 transition.

I appreciate our mutual understanding of the "Ideal" Analysis.  And I also agree that by the definition of an Ideal Analysis, any real world device must display efficiencies below that of the ideal device.

If you have not been picking up the hints, the change in R3 GPE is negative in the ST3 => ST1 transition as is the internal energy change in the water columns.  In your spreadsheet you did not account for the R3 GPE.  If you did then your 88.3% number under the assumptions you state would come up to close to but less than 100%.  The device remains fundamentally lossy.  The whole question of whether something like this could be OU was answered by Powercat or Minnie back at like page 3 of the thread:  Using accepted First Principles, a properly constructed math model cannot show over unity as First Principles do not allow for it.

And this is my favorite part so far!  And I thank you for teaching again.

I did pick up on the hints (I believe) and understood them to mean that the Energy that could be extracted from the difference in the Energy between State 3 and State 1 would be 1/2 that total (and not the 100% I used to calculate the 88.3% efficiency).  But I had not considered that this could make the efficiency greater.  I also do not fully understand how?

BTW, my water heater has blown and I am now stuck at home for tomorrow.  I hope to be able to mentally digest all the logic changes due to the interesting negative GPE revelations.  But for now I may be preoccupied with if I can comfortably wash my face in the morning.  So please grant me a short hiatus.

Once again, I do greatly appreciate when you teach.

M.