FEMM shows interesting OU effect, the airgap is everything.

[Verpies]

It's just an example value to keep the math simple. 

You misunderstood.  I was not asking about the particular numeric value of the current.  I was asking why the current was the same.

Let me rewrite your mathematical statement in a proper symbolic manner so there are no misunderstandings:

So say input i₁*Φ₁/2=W₁ vs 2*(i₂*0.7*Φ₂/2)=W₂

Why i₂ = i₁ ?

2) While maintaining a constant current on it you bring the other coil to the same current

and how do you propose to maintain that current in your 1-2-3 plan ? 

1) You energize one coil
2) While maintaining a constant current on it you bring the other coil to the same current
3) Then you deenergize both coils simultaneously back down

You can assume an ideal coil when answering this question because non-ideal coils only complicate the analysis and don't bring anything beneficial to the table...

[broli]

You misunderstood.  I was not asking about the particular numeric value of the current.  I was asking why the current was the same.

Let me rewrite your mathematical statement in a proper symbolic manner so there are no misunderstandings:

So say input i₁*Φ₁/2=W₁ vs 2*(i₂*0.7*Φ₂/2)=W₂

Why i₁ = i₂ ?

In the coming days I will make a better illustration of the different steps and their math. Granted I have made some mathematical mistakes so far but all of it should be ironed out now. The solid state run was an important aspect to this as it cleared out the mistakes and finally made clear why there IS a fundamental difference between it and the mechanical design using a moving permanent magnet. I finally have a good explanation of why and where the extra energy comes from.  I believe Smudge has written a paper on this; a permanent magnet is essentially a constant current source that can be exploited.

[Verpies]

The solid state run was an important aspect to this as it cleared out the mistakes and finally made clear why there IS a fundamental difference between it and the mechanical design using a moving permanent magnet.

So you are going to revert to the mechanical design.

When you do, keep the answer to the following question in your mind:
Q: What happens to the current flowing in an ideal coil when a p. magnet is mechanically removed from it ?

  A permanent magnet removed
  from an ideal shorted coil.

Note that the speed of the magnet's motion DOES NOT have any influence on the final current flowing in such coil.

[Magluvin]

I'm always seeing the 'ideal' examples...  Neat to think on a bit, but it is beyond the real world.

The question would be, can you even remove the magnet from the shorted 'ideal' coil?

mags

[Verpies]

I'm always seeing the 'ideal' examples...  Neat to think on a bit,

That's for the reason stated below:

You can assume an ideal coil when answering this question because non-ideal coils only complicate the analysis and don't bring anything beneficial to the table...

, but it is beyond the real world.

Superconductive coils really exist even if they exceed your budget.
Poor-man's alternative to S.C. is a short time scale relative to the L/R time constant.

The question would be, can you even remove the magnet from the shorted 'ideal' coil?

Yes, but the closer the coil hugs the magnet, the more force is required to remove that magnet. The mechanical energy needed for removal to infinity stays the same, though.

[F6FLT]

... a permanent magnet is essentially a constant current source that can be exploited.

A permanent magnet can probably be exploited, but only as an accessory, not in its true nature.
The laws of nature are such that translations or rotations that are invariant over time require no energy to be sustained.
Whether it be electron spin or the current in a superconducting coil, as no energy is required for the motion, we cannot extract this hypothetical energy that would sustain the motion – it does not exist. Energy is only required to set something in motion, or to bring it to a halt. We can only recover the energy from the cessation of motion.
That said, slowing down or stopping electron spin is a grand undertaking; we would surely recover energy, but from where – really, at no cost? And I suspect that some version of Murphy's Law will prevent us from doing so.

[broli]

Attached the concept. I hope some critical minds can find the flaw with it. Key things I want to stress is the anisotropic behavior of the core and the distance between each core as to avoid them mechanically interacting with each other. I perhaps didn't do a good job illustrating the latter but was too tired to put even more work into it.

But the two main issues is the mechanical energy and the condition that the cores are far enough apart as to not interact with each other but a bigger distance changes the area of each coil too. But if they are literally meshed into each other you are essentially going in exchange interaction theory.

EDIT: After some pondering I don't even think the last remark should be an issue. All you need to do is change the relative permeability to 3 of the cores and all the numbers of this toy model should remain the same essentially. Attached an 3d example model for this.

[Verpies]

2. While rotating and maintaining constant current:
    1. electrical input from source: 2*1A*2Wb= -4J
    2. Mechanical work gained: +4J

Please justify this.

[Smudge]

A permanent magnet can probably be exploited, but only as an accessory, not in its true nature.
The laws of nature are such that translations or rotations that are invariant over time require no energy to be sustained.
Whether it be electron spin or the current in a superconducting coil, as no energy is required for the motion, we cannot extract this hypothetical energy that would sustain the motion – it does not exist. Energy is only required to set something in motion, or to bring it to a halt. We can only recover the energy from the cessation of motion.
That said, slowing down or stopping electron spin is a grand undertaking; we would surely recover energy, but from where – really, at no cost? And I suspect that some version of Murphy's Law will prevent us from doing so.

The Coler/Unruh Stromerzeuger discussed in another bench broke Murphy's Law as verified by some Professors some 100 years ago, but fearful for their reputations thay forbade publication of their findings.  The unusual feature was current flowing within the ferromagnetic cores, and that brings us into the relatively new science of Spintronics that was unknown to those Professors.  It is now known that electrons have, in addition to their electric charge and their mass, two other linked features, angular-momentum and magnetic dipole-moment, now under the name Spin.  A rotating mass that occupies volume will have angular-momentum, and a rotating charge that occupies volume will have a magnetic dipole-moment, so using Spin to describe these two features is not unreasonable.  The Law of conservation of angular-momentum applies to any system where momenta are mixed and that leads to the conservation of energy.  I ask the question, is there a similar Law of conservation of magnetic-dipole moment that would apply to any system?

Smudge

[Allcanadian]

A permanent magnet can probably be exploited, but only as an accessory, not in its true nature.
The laws of nature are such that translations or rotations that are invariant over time require no energy to be sustained.
Whether it be electron spin or the current in a superconducting coil, as no energy is required for the motion, we cannot extract this hypothetical energy that would sustain the motion – it does not exist. Energy is only required to set something in motion, or to bring it to a halt. We can only recover the energy from the cessation of motion.
That said, slowing down or stopping electron spin is a grand undertaking; we would surely recover energy, but from where – really, at no cost? And I suspect that some version of Murphy's Law will prevent us from doing so.

I agree for the most part but make an important distinction. If we read the literature and prior art of many of these FE inventors we find a divergence in their perspective from others. We find they are less concerned with science and more concerned with the result. They build weird stuff to see what happens.

For example, when someone says "permanent magnet" I suspect we both see a picture of a classic PM in our mind. The PM is rectangular with a red north pole on one end and a blue south pole on the other end just like our textbooks. This bias was programmed into us at an early age in school which is why we can all relate to the subject. As well we almost always take the purists view due to our bias and tend to reject anything different. I'm no different and when someone say's PM I see the same thing. However it took me about 40 years to understand I am biased and try to work around it.

For example, I heard a guy named Howard Johnson was doing a lot of stuff with magnets and magnet motors about 30 years ago but he seemed like a bit of a quack. On the surface this seems to be the case until we look deeper. So I did the research and found Johnson was doing something most of us cannot even imagine. Johnson was making his own permanent magnets which are nothing like the ones you and I presume to be normal.

Here is the AI version of how to make a PM,
"Permanent magnets are made through a process called Powder Metallurgy, which involves melting raw materials, compacting them into a fine powder, and then aligning the particles to create a magnetic field. After compaction, the magnets are heated in a vacuum to densify and then finished to achieve the desired shape and strength."

However what Johnson was doing was very different and some areas of the magnetic powder(s) were compressed to a higher density than others at a lower density. As well he used different materials in different areas which may have been diamagnetic. As such our purists view of what a magnet should look like and act is not accurate. Do you know what happens if we were to dope any area of a permanent magnet with a variable transition of material(magnetic/diamagnetic) and density?. I don't, I have no freaking idea because the complexity of the possible number of variations compound on one another. So the field could act normally as expected until it meets some threshold then it could be opposed, could turn, could expand, it could do any number of unexpected things.

It could be as simple as, if we always make our magnets the same way we get the same results. If we make them unlike anything else the results may differ...

[broli]

And digging we keep on doing. The previous designs all lead to unity but it opened new insights and better understanding. Here is the latest design in trying to exploit the electron spin.

Say you had a coil which you could stretch out to make longer. What would happen? Well to keep things simple lets consider a coil made out of two layers so we can translate one layer of it to essentially double its length. Additionally lets say you hold the current constant during translation.



When you do this you will experience a force against said translation which requires you to do mechanical work to essentially stretch out the coil. Magnetically this would roughly lead to halving of the flux in the coil since we didn't change the current or # of windings only its length. Also since we keep the current constant during translation this would lead to pumping electrical energy back into the source. However the full round trip energy bookkeeping will conclude that the electrical energy gained will be exactly compensated by the mechanical work required to lengthen the coil. So perfect unity.

However what if we added a ferromagnetic material to this system. Consider this core material to be made out of long individual strips rather than one solid core. Again we magnetize the coil which will now also magnetize the core. And again we pull out the coil and this time we also pull out half of the core strips with it. What will happen now? You might naively state that this is exactly the same situation as before since all we did was change the relative permeability of the system so everything just multiples by said factor and the energy book keeping will ultimately lead to the same balance.



However there is one major flaw with that reasoning. Yes the coil-on-coil interaction remains the same. But the cores don't mechanically act like coils. In fact they do opposite thing. Their forces actually point in the direction of motion and thus assist the translation!



So now we have this uncomfortable situation where during the separation the flux is dropping so we are pumping energy back to the source just like we did before with the coreless coil. However mechanically we have a different story as we are now gaining mechanical energy because the core pieces are essentially pushing each other out rather than wanting to remain stuck to their neighbors.

If you are not convinced by that here is a quick FEMM simulation showing an array of magnets that are all aligned in the same direction but half of them have been translated. As you can see their force is pointing in the positive x direction.



This of course does not represent the described system but at least hints at an interesting behavior. I also came to this conclusion from a completely different design but I wanted to lay the groundwork and use the simplest possible design to explain it.