Mathematical Analysis of an Ideal ZED

[MarkE]

Once we start talking about anything other than the Mathematical "Ideal" model, I agree completely.  There are obviously losses during all of the dynamic interactions in a Real World ZED Cycle.  Those loses would need to be incorporated properly into any complete simulation of a real world system.

So if an "Ideal ZED" system acts only as "Ideal" (IE efficiency of 100%), then real world losses would necessitate that it be less that 100% efficient.

BTW, this gives rise to one of my concerns about the claims that the "pre-charge" causes the dual ZED system to be able to cycle for the length of time as shown in Mark Dansie's video:  In my experience, the losses built into the entire dual ZED system would consume any excess Energy due to a "pre-charge" in only ONE or at best TWO cycles.  I contend that a precharged dual ZED system could not oscillate like a teeter-totter for several cycles, let alone the minutes shown in those videos.

My opinion is that something must be DRIVING the dual ZED system behavior that was video taped by Mark Dansie.  But that is only my opinion.

M.

As has been shown many times already, even the "ideal ZED" is fundamentally lossy.  The risers will not lift going from State 2 to State 3 if the payload identically equals the force versus position transfer function.  The payload must have a lower energy transfer function and that difference is irrecoverable loss.

What drives the contraption that Mark Dansie filmed is energy obtained from the outside used to overcome the internal losses of Wayne Travis' useless prop.

[MarkE]

Then could you tell me exactly where the formulas are for the total amount of displaced water volume.

I see riser volume for air and water, but not how much is creating a buoyant lift,, in other words I am NOT seeing where you have the displaced volume calculated and shown.

This is what I have done with my add-ons.

You have demonstrated that you have added erroneous calculations with your add ons.
All you have to do to see that they are the same is perform some algebra on the formulas that are in the spreadsheet.

[MarkE]

No. 

The VOLUME of any object submersed in a body of water will displace an equal VOLUME of water.

True and the basis of the paradox is that is so even if a like volume of water was not first there to displace.

However, the weight (mass) of the object must not equal the weight (mass) of the displaced volume of water.

There is no such requirement.  If the SGs are equal then the submerged object is neutrally buoyant.

But the VOLUME of any object submersed in a body of water will displace an equal VOLUME of water.

Again this is true, even if the original volume of water was far smaller than the volume of the submerged object.

Archimedes "paradox" (not Principle) does not apply at all in this case.

It absolutely applies.   Note that the total up lift force in State 2 is 1.471N which is equal to the force exerted by 150,277mm³ displaced water.  However the total volume of water in the device is 24,212mm³.   5/6ths of the "displaced water" is not water at all.

[MarkE]

Yes.  And Archimedes' "paradox" (or the "hydrostatic paradox") is concerning a specific case.  That 'case'  states that an object can float in a quantity of water that has less volume than the object itself, if its average density is less than that of water.

Please show me where we have anything in the Ideal ZED model that has an average density less than water?

M.

The volume occupied by each riser and the "air" trapped underneath has an SG of 0, as does the pod.  The last time I checked:  1 is always greater than 0, even for very large values of 0.

[MarkE]

One of the things I have observed is that the buoyant lift can be greater than the pressure lift, but it has a shorter distance of lift.

This can also go the other way depending on the dimensions and there relationships.

I just had one that was about -110%,, very lossy,, but I am having the ~2.5% over when using the "stock" settings.

The net buoyant lift force on any riser is the same as the sum of the pressure based up forces and down forces on the same riser.  The same is true for the pod.
As long as you keep basing your results on formulas that do not represent the actual physics of the thing that you are trying to model, you will continue to get invalid results.