I have put a LOT of work into trying to simulate a single layer single ZED.  I finally felt that I had all the equations worked out describing the relationships of volumes and forces between the different internal structures.  I put everything into the sim yesterday and hit the go button.  It spit out an answer that was self consistent, but it was not the answer I was expecting.  I have spent a day going over it in my mind and can not find anything wrong with the result, so I am going to throw it out here for comment.  I have attached a screenshot of my simulator input/output result.

The simulation is based on applying an input force to the piston at the bottom, then finding the riser position that balances the internal heads and pressures.  The input force is stepped from 0 to 2 pounds in 108 steps to generate a transfer function curve.

The interesting thing is what happens to the air pressure as the Pod moves up. 

1. Initially, the Pod head and air pressure increase linearly (increasing the lift), until the total lift is more than the 1 pound output load. 

2.  When the Pod starts to move up a little, it increases the air chamber volume.  This drops the air pressure.  The piston and Pod head have to move up to balance the input force.  However, the increase of the Pod head, increases the buoyancy force.  This places less importance on the air PSI as a lift force, so the air PSI decreases as the Pod head increases.  This can be seen in the 10x Air PSI curve in the graph.  If the stroke is long enough, the air PSI can actually reverse from being a lifting force, to being a sink force to keep everything in balance.  This is also evident when the Exit Head is lower than the Middle Head.

3.  Once the upper stop has been hit, then any increase in input force once again results in increasing the air pressure.

I never expected to have the internal air pressure in a situation where it was hurting rather than helping lift the output weight.

If anyone has a clear single layer ZED already built, it would be easy to check to see if this is what is actually happening.  Slowly feed the water into the Pod chamber and observe if the outer head increases until the pod starts to move up, then decreases until it gets to the top. 

If the outer head keeps going up the whole time, then I have some more head scratching on the simulation formulas.

Can anyone help with this, or do I have to cobble something together to make this observation?

Dennis .. debugging & checking suggestions.

You could try simplifying your sim to check to check basic hydraulic facts - then add back complexity later.

Make a copy of your sim & simplify it by making air non compressible & give the riser the same mass density as the fluid so there is no buoyancy force.

Check that the sim follows well known hydraulic rules based on Pascal's Laws - i.e. that pressure is transmitted undiminished in a fluid in an enclosed system - this means the head must not change & only the riser rises i.e. treating it as a hydraulic ram.

In your case your Input Force is applied to raising the piston - that Force will raise the riser with a force proportional to the areas.

i.e. hydraulic leverage is a force multiplier but Work Done In & Out energy remains the same - that is, hydraulics is a form of leverage of trading force & distance & pressure is linear.

N.B. the hydrostatic paradox will show internal pressures consistent with pgh from the top of the piston to fluid height - this does not effect the force multiplication effects of area ratio's.

Once this is working as it should then add back complexity to the sim - first by adding buoyancy force by making the riser less dense than the fluid - let the head rise again & become an open system.

Next make air compressible again.

Optional extras - adding viscosity drag to add some frictional loses.

Check against real build results & tweak as you are doing.

@All,

Wildew has pointed out an error in my spreadsheets that have the Channel SI Calculation section at the bottom, this was taken from part of a shop floor spreadsheet. Checked with Wayne and he passed me the Swiss Eng's spreadsheet and he had it corrected. The error correction will make hydraulic looks even worst, not happy news for the closed minded skeptics, so I'll just be correcting and sending updates later.

In my short review, I find the Swiss Eng's spreadsheet extremely impressive. Those who have made fun of his existence should be very careful. History will be recording what you are stating and I guarantee, that you will be the ones made fun of later.

Regards, Larry

@mondrasek: Looks good to me, man! ..... better than I expected, better than I could have done. I'd have a mess of fingerprints and tear-drop cross sections. I'm amazed that the lap joints came out so well. Could you detail for us, please, your gluing method and materials? (I know you told me already but maybe the rest of the readers might like to know too.)
Have you done any pressure testing? I'm worried that the open ends of the tubes won't hold their shapes without a reinforcing ring at the open end (a half-inch ring of the same material?, doubling the wall thickness and with the lap join 180 degrees opposite the tube's lap seam). Also, what is your inter-tube spacing, and have you been able to test for the self-centering phenomenon yet? I have a feeling this effect, if it happens, depends on capillary action and will happen mostly with small interwall spacings relative to the system's characteristic length. I am hoping to be surprised here, though, because it would make things a lot easier from a builder's standpoint.

@see3d: I think, if I am understanding you correctly, that I have actually experienced the effect you describe in the single-layer Zed I have in my PerPump v.2.2. The pumping pressure seems to me to behave like you have described, when I have the starting water levels in the Zed chamber just right (apparently just enough to allow the riser to make a gastight seal between the ringwall and the outer chamber, a 1/4 inch or so.) Even in my crude system, I think I'm seeing both the enhanced pressure and the negative pressure effects, due to the volume changes as things move around. I don't have a way to lock my riser/pod combo except by varying its weight (buoyancy at a given displacement) to make it heavier so it stays down longer, and my range of motion is limited to under an inch, but even so, I see the effects on the water output that correspond to what you are seeing in the sim, if I am understanding your description. I interpret this in my PerPump as a force multiplier, like a hydraulic lever, that trades off increased pressure for shorter pumping time... in other words, less volume pumped at a greater pressure. I reported this effect and demonstrated it in a couple of videos last week sometime, but nobody around here seems to pay much attention to Koalas any more -- even if one of them does have a self-powered table top waterpump demonstrating the active Zed principle in action by pumping 13 1/2 inches of water head above its outlet fountain.

Quote from: fletcher on September 02, 2012, 06:23:08 PM
Dennis .. debugging & checking suggestions.

You could try simplifying your sim to check to check basic hydraulic facts - then add back complexity later...

fletcher,  Thanks for all your suggestions.  That is the route I travelled to get to my current point.  When redoing my sim, I went back to just a zero layer system.  That gave me some new insights that I could carry forward one step at a time to the one layer system (although without the complexity of the friction).  I don't ever expect to take the sim that far, because it is not needed for my purposes of defining an optimal static design.  Building a working model would be easier... LOL

I added one formula at a time and substituted it for an alternate form to see that the sim gave identical results before moving on to the next relationship.  I did the sim starting from the Pod Head going forward, then from the output head differential working backwards.  I was not satisfied until things works the same with either set of formulas and that some other formulas just used as consistency checks were happy.

As far as the incompressible air, I did look at that.  In other words, using light oil instead of air, and giving it zero weight, or alternatively upping the density of the water to compensate.  I would just use the same formulas that describe the action of the water pockets again.  However, it was not really needed for my model.  As far as the final result goes, the air PSI changes so little and so does the corresponding volume, that it might as well be a liquid.  THe PSI changes by +/- 2% and so does the volume.  To me, it just means that Wayne is right, and a water/mercury ZED would be like a air/water ZED in a practical operation.