Mathematical Analysis of an Ideal ZED

[TinselKoala]

Let me help you TK - you can't rove our system is anything less than we claim....

End of story.

Good Day - I have a meeting.

Heh... guess what, I don't have to "rove" or prove anything at all! YOU ARE THE ONE MAKING CLAIMS, it is up to you to "rove" them. But you cannot, all you can do is point to LarryC's apparently two dimensional spreadsheet numbers. Where is the self-running system you have claimed to have? Nowhere, that's where. Go ahead, prove me wrong. You cannot !

[LarryC]

Thanks for checking the math, any confusion that is perceive helps me to improve the example.   


The water head in the Pod is equal to water in the pod chamber annular ring heights, however the water head for the riser is equal to the Outermost annular ring (O1) - Next inner annular ring (O2).


Thus the 95 represents 100 in O1 - 5 in O2. Then during equalization the water dropped 15 in the Pod to 35. When this occurs, the water in O2 follows up and rises 15 to 20 and the water in O1 follows down and lowers to 85. So now the water head is 65 which represents 85 in O1 - 20 in O2. That is why I brought up earlier that 1X changes in the Pod Water causes 2X change in riser water head as Wayne stated early is his thread.

You can see this effect in the drawings.

Larry

Got hung up on explaining water head and forgot to mention about your volume point. In actual practice the gaps are adjusted to maintain water head at a desired performance level in each Riser. These kind of calculations are done in my complex spreadsheet, but I was trying to keep this simple for easy understanding. I can add if that small difference is your hangup.

[mondrasek]

No, I don't think that is right. I considered this issue before when the "incompressible fluid" was replacing the air in the trapped chambers. The outer ringwall and the outermost layer of trapped whatever seals the rest of the system from contact with the outside air, and even in spite of that, there is nothing happening, or that can happen, in any Zed system that can change the pressure of the _outside air_.

TK, here the "red box" has been drawn around the ZED system.  The charge water is not shown in the diagram on the left, but is assumed to cross that barrier and enter the system into the pod chamber to result in the state of the center diagram.  When doing so, air in the outer annulus (shown in yellow) is also pushed across that barrier.  Then when the system is allowed to stroke, the Outer Riser (and the volume within it's borders) crosses the barrier at the top.  When doing so, the initial volume of air in the outer annulus crosses back into the system, and is followed by even more air.  Therefore the system is open to the atmosphere, right?  Am I misunderstanding what you presented?

[LarryC]

Got hung up on explaining water head and forgot to mention about your volume point. In actual practice the gaps are adjusted to maintain water head at a desired performance level in each Riser. These kind of calculations are done in my complex spreadsheet, but I was trying to keep this simple for easy understanding. I can add if that small difference is your hangup.

Went ahead and added a riser gap that would give it the same SI as the pod gap. Wanted to see how big a difference it would make in the efficiency. Darn, it went from 153.94% to 153.56%.
Larry

[MarkE]

Got hung up on explaining water head and forgot to mention about your volume point. In actual practice the gaps are adjusted to maintain water head at a desired performance level in each Riser. These kind of calculations are done in my complex spreadsheet, but I was trying to keep this simple for easy understanding. I can add if that small difference is your hangup.

Larry, it is not my hang up.  It is that the math does not represent the model represented.  It's like estimating pi as 3.  Whether or not that is close enough depends on the circumstances.  In order to determine the magnitude of the error, one has to reverse engineer your spreadsheet, guess your intent, then substitute the correct relationships and evaluate the differences.  That is a big PITA and rather unreasonable.  It would be very helpful for you to state your assumptions, and for you to perform sanity tests on your own as to the validity of those assumptions.  Introducing ~16% error terms is a recipe for trouble.  I don't care if you fix the ring dimensions for constant area or keep them on a 0.5" grid as long as your calculations represent the model faithfully.

Let me make a suggestion that will make it easier to keep simple numbers on the spreadsheet:  Assign a constant to pi/4.  Then you can represent all your circular areas in integer units multiplied by the constant.  This should make it easier for you to audit your calculations.  The other thing that can be an immense help is to use named fields.  That saves a lot of chasing around.  Instead of a formula looking like: = $H$2*F19*E12 it would look like:  = riser_diameter*riser_length.  My last suggestion you may or may not like:  Using MKS units generally makes it easier to avoid mistakes between mass and force.  I can work in whatever units you are comfortable using.