Mathematical Analysis of an Ideal ZED

[mondrasek]

All, please check the math.  I would appreciate if you can point out any mistakes in the math, assumptions, logic, and conclusions.  Feel free to send your input by PM if you don't want to post in the thread.  It would be nice to know if you check the analysis and agree as much as if you find mistakes.

I preformed this analysis using a CAD model, Excel, and an old Casio calculator.  So precision of the values was carried out to as many as 10 significant digits.  I limited the CAD dimensions to only 7 digits after the decimal so errors are introduced but should still give accurate results if rounded to 6 significant digits or there about.

The model is of an ideal 2-layer (2 risers and 1 pod) ZED.  It was constructed using values intended to simplify the analysis, NOT to optimize expected performance or to show OU.

All dimensions in the CAD drawings are in millimeters.

The model was constructed by first starting with a 20 mm diameter x 60 mm tall pod.  Gaps, ring walls, and risers were all constructed by drawing lines that were offset by 1 mm from that pod and subsequent geometry.  Water (white color) was added to heights that approximate a setup condition that was expected to work for the purpose of analysis, but were otherwise randomly selected.

The remaining black areas under and around the risers are filled with air that is ASSUMED to be an incompressible fluid for the purpose of simplifying the analysis. 

The risers and pod are first ASSUMED to be weightless.  Due to the position of the water in contact with the inside and outside surfaces of both risers, they both would be neutrally buoyant.  The pod would have an initial buoyant force equal to the weight of the water it is displacing.  This calculates to be ~8.168 grams.  Therefor it is assumed that an equal weight of 8.168 grams is applied to the outer riser in order for this setup to maintain an overall neutral buoyant condition.

Please note that the 1 mm gaps between the upper surfaces of the pod and risers are only present to eliminate any confusion about possible stiction between those surfaces.  In reality there would need to be physical spacers to maintain those gaps.  Those spacers are ASSUMED to be in place and are not shown.

With this construction and set up condition we can calculate the pressure at the bottom of the pod chamber due to the 27 mm of water head resting on it as 264.87 Pa.

More to come.

M.

[mondrasek]

Now the ZED is "charged" by adding additional water into the bottom of the pod chamber.  This will require Work/Energy that can be calculated by the Integral of the Pressure of that added water multiplied by the Volume of that added water.

The amount of water added was limited to be that which would cause the water level in the pod chamber to riser to 1 mm less than the total height of the pod when the pod and risers are not allowed to rise.  That volume can be calculated to be ~2.1771 cc.  This will be called Vin.

The positions of the air and water around the risers can also be calculated since their volumes must remain constant.  Once those new positions are found the resultant buoyancy force can be calculated.  For the pod the force now will be able to lift ~18.535 grams.  For the inner riser it is ~31.783 grams.  And for the outer riser it is ~40.440 grams.  The total the ZED can now lift is ~90.758 grams.  Since the setup required the outer riser to weigh ~ 8.168 grams, this needs to be subtracted.  The resultant lift capacity is reduced then to ~82.590 grams.

The Pressure of the water added during this charging cycle must rise from the initial pressure of 264.87 Pa (calculated in first post) due to the increase in the water head in the system.  The total water head in the final charged state is ~151.3463 mm and so the final pressure is ~1484.71 Pa.

If we ASSUME that the Pressure rise of the added water was linear, then the Integral of the Pressure for the added water become the average of the initial pressure before charging and the final pressure after charging.  The average of those two values is ~872.2567 Pa.  This will be called Pin.

The total Work/Energy needed to introduce the additional water to charge the ZED is now calculated as Pin x Vin which works out to ~1.8990 x 10^-3 N.m.

M.

[MarkE]

The first thing that you will want to be very careful with is the assumptions that you make with respect to the amount of work it takes to displace "air" or water in any of the chambers.  A mistake can easily throw energy off by the ratio of area of the cylinder area to the annular ring area of the chamber.  It is tempting to calculate force based on the smaller area in cases where it is actually a function of the much larger area.

[TinselKoala]

And yes - TK a single ZED can be OU - if you simple store the recycled energy and return it on the next stroke, as I said two yeas ago - which you omitted every time you miss applied the context. As I said before - why add the extra effort and time - simply transfer between systems. Get over it - you missed it.

Well, that's a relief. You aren't going to need to complicate things by making dual ZEDs, because we here ONCE AGAIN have Wayne Travis claiming that a single ZED can be OU.... "IF".  Maybe he'll deign to give YOU , mondrasek, the design for the "simple, three layer system that is clearly OU by itself" (his own exact words). Don't hold your breath though.

On another note - my contact information has never changed - to  those that have tried to discredit me and our company all this time - those people never made one call or asked me one single question about their claims against us. Shame on all of you who slander by assumption.

Are you quite sure of that, Travis? How exactly do you KNOW that some of your detractors and scientific critics haven't been there, haven't talked to you and your "engineers" and your lawyers? You shouldn't be so confident, because you DON'T KNOW EVERYTHING that is transpiring around you. Your "contact information" hasn't changed? But your websites certainly have. Name changes, removal of many of the outrageous claims, the Zed animation is gone..... it has been clear for some time that you are scrambling about, reorganizing, shuffling that pea around, flipping the cards in your three-card Monte game. By the way, there is a difference between slander and libel, you should learn what it is.

[MarkE]

Beware of nondescript old pickup trucks.