Mathematical Analysis of an Ideal ZED

[MarkE]

Does anyone have an issue with state 1 being a condition where all forces acting on the risers and pod equal zero.

As a matter of fact I do.  But it was a matter of stipulation by Mondrasek.  So, the analysis carries that requirement.

Does anyone have an issue with the end of state 2 having positive forces acting on the pod and risers, this caused by the addition of water into the pod chamber.

The spreadsheet model agrees that pumping in water while the risers are restrained builds excess head in AR7.

Does it not make sense then that the pod and risers will move up as the water columns move back to a lower energy state.

I am glad you mentioned that.  Yes, and yes:  The pod and risers do move in the spreadsheet, and that does cost energy taking the system to a lower energy state.  Thanks for acknowledging the loss.

Does it not make sense that the pod and risers will move until there is no more sum positive force of buoyancy acting on them.

Of course it does.  But how much force and how far depends on the LTI history of the machine.  If you would like to start with a different set of stipulations, such as filling each of the AR pairs to 22mm and then forcing the risers down with the vents open, then you will see a few things:  One of which is that you have to throw away a lot of energy to execute this pre charging step.  The second is that you will have to apply and maintain the restraints at this stage because the bottom of each riser is displacing water.  If you then carry that through State 2 and to State 3, then the equilibrium point occurs around 2.5906mm instead of 1.4688mm.  See: Different constraints yield different answers.  But the character of the answers does not change.  The energy loss going from State 2 to State 3 gets worse increasing from 28.1% to 34.6% of the stored energy at the end of State 2, and losing over 90% of the energy added in State 2.

Does it not make sense that the pod and risers must be restrained while going from state 1 to end of state 2.

The Wayne Travis approved Mondrasek stipulation removed any requirement to restrain at State 1.  Of course pumping in more fluid in State 2 requires restraint.

Does it not make sense that that is an applied force.

Energy gets added to the system and the system is restrained.  That's a good recipe to have some stress or strain show up somewhere.

Does it not make sense that when the pod and risers have stroked until there is no more sum positive force left acting on them that the force to restrain them will drop to zero.

Actually that is a bit backwards.  F=mA.  When the forces come into balance the masses, even the massless ones will stop accelerating.

Does that not make it then 0.5f*ds, which is the energy output from the pod and risers stroking upwards.

Do you still not understand the difference between linear multiplication and an integral?

MarkE has not included this restraining energy in his analysis.

How much energy is required to restrain a motionless object?  Please show your work.

MarkE has stopped the risers and pod lifting while there is still a positive buoyant force acting on them.

Again:  Under the Wayne Travis approved Mondrasek constraint the system reaches equilibrium at 1.4688mm lift.  Remove that constraint and the system comes to equilibrium at 2.5906mm.  Apples and oranges.

The volume that is needed to be added to the system for the continued movement of the risers and pod comes into the system via AR7, and that is air from the atmosphere which is where the fluid volume from AR7 is moved to when the fluid is added into the pod chamber to go from state 1 to end of state 2, ergo this is an allowed event.

It is a fluid model.  The stipulated incompressible fluids freely move within the confinement.

MarkE has not explained what is holding the pod and risers from any further movement even tho there is a positive buoyant force acting on them.

There you go again:  You ignore the Wayne Travis approved Mondrasek stipulation.  Why do you keep doing that when it has been clearly stated many times now? 

[MarkE]

You are ignoring things MarkE.  Force and distance,, buoyant lift and all that, the resistance needed to be applied against the risers,, more things you are ignoring.

Since you have required me to include all such things then I am entitled to require the same from you.

Show what is holding the risers and pod from moving while they still have a positive buoyant force acting on them, you can not!

Kindly answer the question Webby:  When you said this:

The author of the spreadsheet also did not include the energy of restraint needed to hold the risers and the author did not allow for the full lift distance.

What did you mean?  Do you really think the restraints that prevent motion impart energy?

[MarkE]

Webby won't don't you try to wrap your arms around this drawing.  See if you agree that given massless, incompressible "air" and massless risers that the risers will happily just rest right on top of the 22mm water columns.  Then let's see if you agree with the calculations of energy that is stored after, and consumed during the process of forcing the risers into the down position, while venting "air" out from under the risers to the atmosphere.

[TinselKoala]

Here's more mathematical and graphical proof of OU than you will ever see from Wayne Travis.


Not only does the two units of fluid on the right support the entire 13 units on the left, when you remove the two units from the right.... the liquid level only goes down a fraction of that input starting head height. Therefore you have a "net" production that does not reduce the "input" by nearly the same amount.

[mrwayne]

Does anyone have an issue with state 1 being a condition where all forces acting on the risers and pod equal zero.

Does anyone have an issue with the end of state 2 having positive forces acting on the pod and risers, this caused by the addition of water into the pod chamber.

Does it not make sense then that the pod and risers will move up as the water columns move back to a lower energy state.

Does it not make sense that the pod and risers will move until there is no more sum positive force of buoyancy acting on them.

Does it not make sense that the pod and risers must be restrained while going from state 1 to end of state 2.

Does it not make sense that that is an applied force.

Does it not make sense that when the pod and risers have stroked until there is no more sum positive force left acting on them that the force to restrain them will drop to zero.

Does that not make it then 0.5f*ds, which is the energy output from the pod and risers stroking upwards.

MarkE has not included this restraining energy in his analysis.

MarkE has stopped the risers and pod lifting while there is still a positive buoyant force acting on them.

The volume that is needed to be added to the system for the continued movement of the risers and pod comes into the system via AR7, and that is air from the atmosphere which is where the fluid volume from AR7 is moved to when the fluid is added into the pod chamber to go from state 1 to end of state 2, ergo this is an allowed event.

MarkE has not explained what is holding the pod and risers from any further movement even tho there is a positive buoyant force acting on them.

Webby,

LOL I have the spam team on block - so I had to go three pages to find a valid post. Yours.

Do you know the original thread was over 200 pages - after several bashers were removed.

That is going to happen here to (the bashers).

Your making a great point - my opinion - the ignorance is on purpose.

Keep Up the actual "thinking".

Larry shows the state of remaining head in his spread sheets as well.

Onward

Wayne