Prajna

I did add a rather conspicuous wink but thanks for the clarification.

Sorry, I'm not sure of the dynamics yet. The rotor is rotated at whatever angular velocity, the tabs are spaced at 20 deg so the spacing will be varying. At the starting position one or the other side of the device will have a tab/finger centralised between the magnets and the other will have tabs spaced evenly above and below the gap. The magnets are prevented from closing completely on the tabs by a cam groove on the output flywheel. So, at the starting position the magnets with a tab in the gap will be at minimum separation.

In the current design the tabs or fingers are arranged every 20 degrees around the rotor. There are nine tabs and the rotor axle is co-planar with the centre line of the magnets, so when there is a tab central to the gap between the magnets on one side there is a space on the opposite side. The magnets are 10mm x 2mm neodymium (N52?) and the tabs centres are at approximately a 35mm radius. The 'bulb' on the tabs that lies between the magnets is 5mm radius to match the area of the magnets. This may be more or less optimal as far as effectiveness in switching the flux and suffering eddy current drag, I don't know yet. This is somewhat arbitrary and is just my first best guess of what might work. I wish you guys would stop with the perpetual motion slur, I'm rather hoping for over unity!

Sorry, I don't understand. Unless you mean it's a win that I'm belatedly reading about magnetism and you don't need to be involved in analysing the device. By the way, I stumbled back on the article about monopoles, for anyone interested, it was in Popular Mechanics: https://www.popularmechanics.com/science/a60079037/magnetic-monopole-hematite/

It's not so unusual though for magnetic fields to be sharply bent, a keeper on a horseshoe magnet does this when placed across the poles, providing the shortest possible low reluctance path for the field and containing it, effectively neutralising the magnet. By the way, I've just taken a look at the Ferromagnetism page on Wikipedia and am finding it very helpful in understanding magnetism. Soon I may be able to drop my naive model and speak intelligently about it.

That sounds completely reasonable and is just what I was angling for a competent analysis of. I do recall the eddy current demonstration of dropping a magnet down a copper tube, a very impressive demonstration of eddy current drag. Certainly it is my estimation that the fingers will get sucked into the gap and resist being pulled out again but I think (may well be mistaken) that these two forces will cancel each other. However the eddy current drag may be what correlates the input force to the output power. It may be that whatever reconfiguration to reduce the eddy drag will also have an equal impact on the power output, satisfying input >= output. Only my gut tells me that there might be an input < output while my head tells me that cannot be. Thanks for that, @sethoflagos, that is a very useful comparison.

This is exactly the conversation I hoped to have here, @exchemist. Yes, my preliminary experiments showed that with magnets in repulsion a steel sheet, in this case a steel rule, inserted into the gap caused the magnets to be attracted to the rule. My guess at what is happening there is (if you'll indulge my less-than-physically-exact language) the magnets in repulsion, because their competing fields offer a very high reluctance to the other's flux path, try to complete their circuit by adopting (and attracting) the steel rule, a much lower reluctance path, into their circuit. When the rule is removed the magnets again face an unacceptable high reluctance to their circuit and therefore attempt to mitigate it by moving apart.

Thanks, @Mordred, I recently read a headline suggesting that someone has found a magnetic monopole but can't remember where I saw it. I seem to recall reading that Maxwell's equations are not actually Maxwell's, that Maxwell expressed his equations as quaternions but didn't publish them before he died. It was Heaviside who published Maxwell's equations, having converted them all to vectors, so really when we talk about Maxwell's equations we are talking about Heaviside's equations and neglecting Maxwell. But then it might have been some renegade astronomer who wrote that, I can't recall exactly.

Regarding the sliding of a magnet off a sheet of steel, I guess that what is really happening is that you are not feeling the same force you feel when you try to lift it directly, you're not working directly against the magnetic field. Once you get to the edge of the sheet the area of the magnetic contact reduces, and with it the force holding the magnet to the sheet until finally the magnet is clear of the sheet. Triboelectric generation is looking more and more interesting these days. Won't be long before the free energy cranks are baffling themselves with that. Hmm, come to think of it, I've done nothing about adding generation to my device, ... reciprocation, triboelectrics, ... hmm ...

Ah, ok, you were talking with regard to the device and I was (at that time) talking with regard to the thought experiment. Cross purposes, sorry for the misunderstanding. Yes, I'm sure that at some point I will need to consider distortion in the fingers/tabs but engineers often just over-engineer things, add s fudge factor, rather than fuss about such details. This particular design is just a proof of concept and the objective was to make it easy for people to grasp the principal of operation. The rotor is designed so that the number and geometry of the tabs can be changed easily in order to test different configurations. That provokes images of some structure bowing down to hoist a tiny metal sheet up into the air. Sure, to some barely detectable extent a solid structure will distort due to the forces involved in the thought experiment I described but really, is it really fair to say in this situation that the structure is doing all the work and the magnet is doing none? That is a very strange way to describe the situation in my view.

Ok, the situation in the device though is that the magnets are not moved closer nor separated by the operator, rather the magnets move under the effect of their changing state of repulsion or attraction governed by whether there is a finger or no finger between them. So, in my view, energy is being exchanged between the magnetic fields on one side of the device and the fields on the other. Is this a reasonable description? The operator is not moving the magnets, not even by poking them with a stick, he is merely turning the rotor that determines which side of the device has a finger in the gap and which doesn't. Maybe I should rename my 'fingers' to 'tabs' to avoid the idea that there is any poking of the magnets going on. I don't see where there is any direct link between the work or energy or effort required to turn the rotor and the work or energy or effort produced by the switch state of the magnets, unless there is some reason to suggest that the eddy current drag is directly related to the output. The drag will certainly depend on the strength of the magnetic field on the side of the device that the finger/tab is passing through and the speed of the finger/tab through that field and, I guess, on the area of the tab that's in the field, perhaps even other things I have yet to consider.

Chatham: yes, there was a nuclear submarine port there, I believe. Sailing on the Medway is very interesting too, that sub being one fascination. Good, we're getting closer now. I think @swansont is still confused in thinking I'm talking about lifting something by attaching it to a magnet and lifting the magnet whereas I'm talking about the magnet being fixed and the object being lifted by the magnetic field. There's some ambiguity somewhere and I am not sure if it is in what I described or in @swansont's understanding of what I describe. No matter. I hope he can agree that in the thought experiment I described the magnet appears to be doing work as in W = fD. Certainly it looks like work is being done. Once we get this thought experiment done and dusted then maybe we can examine my proposed device and see how we correlate what is happening in it with thermodynamic laws. Maybe we can even discuss it in general terms without having to divert into obscure formulae. Can we say then, in this thought experiment with a fixed magnet attracting to itself, that work is being done by the magnet? Can we say also that the strength of the magnet is not depleted in the process of that? In that example some work must be done to remove the steel sheet from the magnet, if it is a permanent magnet, or the current must be interrupted to let the sheet fall if it is an electromagnet. So we can include that work and so on and develop the experiment further to include the mechanics of removing the sheet again etc. but let's leave that there and move back to the SMT. In the SMT the magnets are fixed at the end of rockers (levers really, on an axle at their centre). When a metal finger is rotated into the space between the magnets then the magnets will switch from repelling each other to being attracted to the finger. Obviously some work will be required in order to rotate the finger into the space. That work will be reduced, maybe even to some extent overtaken by the finger being attracted into the field in the gap between the magnets. Obviously the reverse will be true as the finger exits the gap since the field is still attracting the finger back into the gap and this will add to the work required to rotate the finger out of the gap. So these two effects should balance or cancel each other out. This is what I mean by 'symmetrical and why I disregard this effect since overall it neither adds to or reduces the force required to turn the rotor. There will be some eddy current drag on the finger as it passes through the magnetic gap, since any ferromagnetic material passing though a magnetic field acquires an induced magnetic field opposite to the magnetic field inducing it. How much drag will that be? Probably it will be proportional to the strength of the magnetic field that gives rise to it, that's logical and I'm happy yo accept that being the case. The magnets, in attraction to the finger on one side of the rockers and repelling each other on the other side, will cause movement, work in fact, on the rockers, causing them to rotate in a reciprocating manner as each magnetic gap encounters either a finger or a space. The force involved in that movement will depend on the strength of the magnetic fields which will vary dependant on the distance the opposed magnets are from each other - when the magnets are close they will exert more force, either in attraction or repulsion, and the converse; according to the inverse square rule. It may be that whatever the power of the magnets the eddy current drag will always be equal to the forces generated by the magnets in switching from attraction (to the finger) and repulsion (on the side that has a space rather than a finger.) Or maybe the eddy current can be reduced, perhaps by making the fingers small enough that they only just switch the magnets, perhaps by redesigning them to use some form of lamination such is done in transformers to reduce eddy currents. I'm not sure if you have noticed but when a magnet is stuck to a sheet of metal the force required to remove it can be much reduced by sliding it transverse to its field. In the SMT the fingers pass transverse to the field rather than in line with it and, like sliding a magnet off a sheet of steel, there may be less work required than if something was moving in line with the field. Thanks for further constructive comments, @exchemist Did I say the area of the plate was greater than the magnet? You're again talking about attaching something to a magnet and then lifting the magnet. I'm not. I'm talking about a SMALL plate of metal being ATTRACTED to a magnet that is in a fixed position. Do your stress tensors and Hookes laws and elastic distortions really contribute to what I'm discussing? Thanks for your interest but I really don't think what you've offered is contributing to illuminating what I was discussing.

Again, you're getting into marginally relevant details. Rather than go there, why not address in general and simple terms the exchange of potential energy? Anyway, I'm sure the upward force is not a point source at the centre of the sheet but is distributed in some way across the sheet.

Thanks. I'll look it up. Ok, "The Cauchy stress tensor is used for stress analysis of material bodies experiencing small deformations: it is a central concept in the linear theory of elasticity. For large deformations, also called finite deformations, other measures of stress are required, such as the Piola–Kirchhoff stress tensor, the Biot stress tensor, and the Kirchhoff stress tensor." I'm not interested in "small deformations" in this example. I think I have clearly stated what I am considering and "small deformations" is an aside to that conversation. What's happening in terms of changes in potential energy and how can that be simply and clearly described?

Ah, I think you misunderstand what I was referring to. I was describing an experiment where there is a table top, 30mm above the table is a magnet fixed to a support. Small sheets of steel are on the table. Pushing a steel sheet across the table top until it is situated under the magnet, the magnet will attract the steel sheet upwards til it sticks to the magnet. In this experiment I describe what is happening is that the magnetic field attracts the sheet so that it rises against gravity and, in the process, the gravitational potential energy in the sheet has increased. I'm not getting bogged down in deformation (which may, indeed, occur to some extent in this situation but is not a major factor in what is happening), simply I am looking at the exchange of energy and how that can be described. @swansont insists it can't be described as the magnet 'doing work' and that magnets 'don't do work'. Ok, then how do we describe it and if a magnet appears to be causing something to move via some force over some distance, if that is distinct from other forms ofwork then how and why?

Thanks @Mordred, I'm aware of the polarity shift, referred to as the Right Hand Rule, iirc, if you wrap your hand around a wire with your index finger pointing along the wire, that indicates the current direction, then we have the magnetic field and electric field perpendicular to the current, indicated by the middle finger and thumb. If that's the same thing you're talking about. But anyway, in the above example I am only discussing the change in energy of a steel sheet as it is attracted by a magnet situated above it. I don't think that in general terms we need to consider polarity shifts. I think I am getting closer to a reasonable understanding in the discussion with @exchemist.

This is a much more reasonable response, @exchemist, thank you. At least you understand what I'm talking about. So what is happening is that there is a movement of energy into and out of the magnetic field, much like storing energy in an inductor, I guess. That's what I was referring to as 'work', perhaps inaccurately. We might consider that the steel sheet is 'falling upwards' towards the magnet in its magnetic field, that when the steel sheet is on the table and the magnet is fixed 30mm above it there is a potential energy imposed by the magnetic field and when the steel is attracted up to the magnet then that magnetically induced potential energy is converted to kinetic energy until the steel sticks to the magnet. Now the magnetic potential energy has been converted to gravitational potential energy. Then if the magnet is an electromagnet and we cut the current to it the steel falls to the table, a conversion of gravitational potential energy to kinetic energy until the steel rests on the table again. Have I understood correctly? As an aside, I used to live in Chatham, Chattenden and Maidstone when I was at RSME and serving in the Royal Engineers. I spent a good deal of time at the Historic Dockyard in Chatham, where I drove steam cranes on the docks at the weekends. So I'm quite familiar with the area. That place is very interesting too. If you get a chance to visit the Officer's Mess at the dockyard you can see the vaulted ceiling that was built by ship's carpenters and is really the upside-down hull of a ship.

Ah, so there's no simple answer to my question, only answers that demand a couple of semesters studying physics and you guys are exercising your right of pedantry and hubris to dodge the question, or, as a layman might put it, you don't know the answer. No problem. So much for "Trust the science". @exchemist, thanks for the civil and helpful replies. The rest of you, meh.

Ah, I hadn't seen this, perhaps it was edited in after I read your post. Thanks for the correction on Ed's name, I should really have looked it up. Yes, fascinating guy. He did some seemingly miraculous things and free-energy-cranks have been arguing over his book(s) for years, suggesting they were written in cipher, maybe they were. I rather thought that if anyone would be considered a crank then Ed would be right up there. Nice to be disabused regarding that. Your curious fact is indeed curious, or certainly interesting. Whether I have enough interest to wade deep into relativity and QM to see it is another matter. If you can point me to general info about it that doesn't involve glazing over with esoteric formulae then I would certainly like to read it. I explained exactly that the magnet is fixed. Maybe it's been there for years. Did I suggest, insinuate or even hint that it's floating? Eddy currents? What does that have to do with my question? I want to know what, in the circumstances I described, causes the increase in the potential energy in the steel sheet that is attracted to a magnet positioned above it. Just that. Answer that. Simply and clearly and without diversion, obfuscation or irrelevance. Can you do that?

Ok, so it takes some work to lift and fix the magnet into place. But that has nothing to do with what I asked: what is lifting the sheet of steel I slide into position under the magnet? I don't lift it. Sliding it horizontally into position under the (fixed) magnet is a little work but it adds no potential energy to the sheet of steel. The magnet lifts the steel from its position below the magnet by magnetic attraction,which you insist is not work. The potential energy in the steel has increased since it has been lifted against gravity by the magnet; not by me, not by the (rigid and fixed) support but by the magnet. Something somewhere did some work and it wasn't anything but the magnet! When I slide another sheet of steel under the magnet (it's raised above where the sheets are slid under it, doesn't move, is fixed in place, so I really have to spell all this out?) You are speaking as if someone or something is lifting the magnet. In this example assume the magnet is fixed in place 30mm, say, above a table. I have a handful of small steel sheets on the table top, not directly under the magnet. I slide a sheet under the magnet, a horizontal move, and let go. What happens? Well in my world the sheet is attracted to the magnet and physically lifted off the table by the force of the magnet so that it sticks to the magnet. Say it was an electromagnet rather than a permanent magnet (didn't want to bring in electromagnets and let you guys complicate things further but necessary now in the explanation) and at this point in the experiment the electromagnet is switched off. What happens? In my world the sheet drops back to the table, its acquired potential energy converting to kinetic energy in the process. If you think the magnet did no work in that situation then I need a better explanation of how that can be since anything else adding potential energy to a system is doing work. Or am I wrong?

Are you saying that in fixing the magnet to its support work was done but when the magnet lifts a small sheet of steel,say, that is placed under it that no work is done? Are you saying that the support is doing work? In placing the sheet under the magnet then work is done, no problem with that, but that work, unless the sheet is lifted into position, has not increased the potential energy of the sheet, whereas when the magnet lifts the sheet the potential energy in the sheet has increased. What caused that increase in potential energy?

That still doesn't compute here, @swansont, maybe it's just me being thick. The object is lifted, seemingly by the magnet, and thus its potential energy has increased and surely some work must have been done to achieve that, n'est-ce pas? What did the work? Surely you understand what I mean and I hope you are not being pedantic with regard to terms. In this example (to remove ambiguity, I'm referring to a permanent magnet fixed to some structure above the object, say a small sheet of metal).

How does this relate to my response to @swansont above? Is it an attempt to answer that? My example refers to a permanent magnet rather than an electromagnet. It seems to me that the magnet is doing work rather than redirecting force. Or are you saying the magnet is redirecting the force I am using to hold the magnet up? What if the magnet is affixed to something? Interesting but off topic, I believe, @KJW

Absolutely it will stop with no input, I expect nothing else. If I hold a magnet above a ferromagnetic object the object (if it's not too heavy) will be attracted to the magnet. That has increased the potential energy in the object, so work has been done, has it not?

Turning the rotor merely provides switching for the magnets. Unless I'm mistaken, the torque required to do so will be determined by friction in the rotor bearing (and some trivial air resistance) and eddy drag on the finger that is in the magnetic field (and, balanced out, attraction into the magnetic gap on entry and exit from the gap). The output torque on the flywheel will be determined by the magnetic field strength of the magnets (and some friction, da dah, da dah). Where am I falling down on my understanding? The rotor doesn't determine the output except in terms of how quickly it effects the magnetic switching. Or is there some other principle at work?