Basic OB vs RPM regulation

[MrVibrating]

I've been stuck for a while on the impression that passive OB torque cannot replicate the characteristics of Bessler's wheels, particualrly the load-matching performance and speed-regulation characteristics, epitomised by the slow-but-powerful wheel he claimed was possible but time-consuming to build, and the reports of the Meersburg wheel maintaining the same speed when under positive or negative load as when unloaded.

So instead of weights simply riding the descending side of the wheel down, i'd been looking for something more extravagant such as "the wheel's torque is actually counter-torque from counter-accelerating something else", or maybe the result of inelastic collisions driven by weights falling perhaps linearly / radially or whatevs - anything other than basic OB, wherein you just raise weights radially into overbalance, gaining torque by keeling. One major objection i had was that OB torque on a statorless free axis cannot regulate speeds, since if you move a weight out 90° sideways the wheel will just keel immediately as fast as its angular inertia relative to the weight will allow it. How would that help in the design of a wheel that could rotate arbitrarily-slowly and smoothly, yet with all the more power?

I'd previously even ran simple sims demonstrating this point. But after persistent niggling doubt and re-examination, it turns out i was flat wrong..

Usually i'd go about implementing a simple OB system by making the radial extension and retraction of the weights a straightforward function of the wheel's angle; so the OB system would always be at the same position at a given wheel angle, irrespective of RPM. These systems, unsurprisingly, accelerate freely up to sim-failure (NB. at unity - forget about the whole OU thing for now, i'll come back to the implications there shortly - the point here is simply the practical utility of OB systems in replicating the outwards performance characteristics of B's wheels).

Earlier however the idea came to me to try syncing the radial displacements to a second, 'timing' wheel - ie. use a separate wheel to generate the signal driving the OB wheel, so that the actuators move at their own pace independently of whatever the instantaneous wheel angle, allowing it to swing around and find its feet on its own.. to pick up its own rhythm in response to the speed of its actuators and their GPE lifts. The timing wheel could be driven by a motor, controllable for acceleration and speed.. so you could start with a stationary, keeled OB system just hanging there, then begin moving weights around inside to initiate OB, and sit back to watch and see whether the system accelerated smoothly up to a constant low speed in a controlled manner, or else span around in random spasms alternating directions, or whatever, right?

So this evening i gone done simmed it:


Under positive load



Negative loading


Pretty self-explanatory; the load wheel has an independent motor applying a constant torque preset which can be positive or negative, and has an additional damper to smooth out oscillation whilst simulating some frictional losses. Hence when the load is positive it's trying to perform work against the OB wheel, resisting its overbalancing torque, and when negative tries to over-speed the wheel, driving it in the same direction it's already turning, which it then duly resists with as much vigour as when trying to accelerate..

In short, the wheel doesn't want to accelerate or decelerate, but hold its 'design speed', and will equally perform positive or negative output work in the effort to maintain it.


I honestly expected the result i'd long-assumed inevitable - lumpy output at best, as the system slowly hauled the next weight up and out, then rapidly keeling, perhaps swinging a bit while the next weight again rises.. but no! Smooth, low-speed high-power operation is plausibly accomplished by a passive overbalancing regime (ie. riding the wheel down)!

The system has the following characteristics:

• stable, arbitrarily-low speed

• load-matching reactive power output in both sign and magnitude (!!!)

That is, within the bounds of its OB weight * radius, increasing or decreasing the applied load will not affect its speed - only the output power (in or out) in maintaining that speed!

Yet there's nothing at all remarkable or special about this - the wheel just wants to keel, is all! That's all it's ever trying to do..



Implications:

• per-cycle momentum yield still naturally diminishes as a function of RPM..

• ..either implying that the gain mechanism / exploit is an effective GPE asymmetry..

• ..or else the OB system is tertiary to the exploit and merely a means of capitalising on it

In other words, perhaps there's an asymmetric inertial interaction actually generating the gain, but then spending it on good ol' GPE instead of direct-to-KE.

The preponderance of clues from Bessler himself however would strongly point to the former (eg. the 'quarters' riddle seems to directly invoke an effective GPE asymmetry). Occam too for that matter..



Preliminary conclusions:

I've wasted time looking for explanations to seemingly-exotic performance characteristics that are in fact trivially achieved; there's some kind of effective GPE asymmetry in the frame, and just going back to basic first principles that has to be a divergent inertial frame, ie. discounted height displacement via an effective N3 break.. Somehow, this must be possible..?

[Fletcher]

Yes, fascinating to think B's. wheels might have had a mechanical self-governing attribute. Speed and Power matching on demand.

James Watts governor comes to mind when thinking along these lines.

https://en.wikipedia.org/wiki/Centrifugal_governor

Best -f

[MrVibrating]

I got rid of the damper by adding the inverse of the difference between set and actual speeds to the load motor's torque input, so now it automatically cancels out any oscillations in a lossless way (measuring energy through a damper can be flaky in WM).

Also replaced the text box for the load torque input with a slider - so now it can be varied whilst the sim's running, demonstrating that it always settles back to the design speed even when the sign of the load flips.

Finally, added the actuators' P*t to that of the load motor, making a 'net P*t' meter which duly plots out a flat line at 0 W (obviates needing to take integrals to prove unity):



..for me, this basically settles the question of how momentum from G*t was applied - it was classic OB all along (ie. i was wrong in a long-held assumption).

The really cool part however is simply that this property that so impressed and perplexed Wolff is accomplished so trivially. A statorless wheel 'should', under any other circumstances, run at a higher speed under negative load, and lower under positive, than unloaded. Instead however an OB system simply switches, seamlessly, between sourcing momentum and energy, or sinking them, but either way in the effort to match the pace of its GPE system.

Another issue it clears up regards the question of power output estimates - at its design speed a Bessler wheel is making minimal energy - just enough to balance its rolling losses - but it only really starts putting its shoulder into it when encountering a load. Thus any estimates based on the likely MoI and speed ranges can only tell us how much KE the system might've had once up to speed and settled close to its keel position, but not its max power. If we also knew the spin-up speed then we could also estimate power and energy, but again this would be different depending on any applied load. Thus, within the range of the available OB torque, the answer to the question of how much power his or 'a' wheel might output is partly a question of how much load is placed upon it..!

Additionally it answers the more-trivial question of why an OU system doesn't simply accelerate to failure.

Finally however it confirms more about the nature of the exploit; ie. that it must somehow involve an effective GPE asymmetry - a discount on one or other of the components of input GMH..

[WaltzCee]

Thus, within the range of the available OB torque, the answer to the question of how much power his or 'a' wheel might output is partly a question of how much load is placed upon it..!

to some limit, the greater the load, the less rpm's, the less c.f.

The less c.f. , the more able things are to hold their structure and the more able they are to move & do the work they were intelligently designed to do.

That is given they were intelligently designed in the first place.

Infatuation with some mechanism isn't a sound course if you ask me. Not saying you're doing that yet some do.

I know I was guilty of that.

[MrVibrating]

The most load this 'un will handle (with ½ kg weights at 1 m radius) is a little over ±2 N-m - so yes, anything more than that and rotation will completely lose sync with the GPE system. Within those limits however, the only wobble is from perturbations when changing the load; we could conceivably switch out the load wheel & motor for a box of bricks being lowered or raised to any height via a pulley, and provided it didn't exceed max torque it would pretty much replicate what Wolff et al reported seeing at Meresburg.. Minus the OU of course.

Re. CF, now that i'm more confident on what the GPE system needs to do (or rather, how little it needs to do!), i'm considering a 'cross piece' comprising two scissorjacks at 90° to each other, handles facing outwards and thrusting weights in and out as above, with their handles interconnected such that the ones rotating in the same direction are working together, but then also driven by inertial torques via the ice-skater effect.

My strong hunch is that the "thresher and scholar" are alternate strokes of a scissorjack action (the 'flail'), but driven by MoI variations (ice skater effect). So one mass moving in will generate positive inertial torque, torquing one handle of each jack in the same direction as the wheel, whilst another moving out produces negative torque, turning the other two handles the other way, ie. a CW and CCW action simultaneously extending one OB jack whilst retracting the other.

What's potentially interesting here is that the FoR of the inertial torques working the jacks and thus lifting the weights is rotating with the wheel, whereas usually we only raise GPE from the FoR of the ground.. and obviously the ability to drag your inertial FoR along with you is a central requirement for any chance of breaking PE:KE symmetry..

..or to put it another way, one pound can trivially cause the raising of more than one pound, if applied to cause inertial torque rather than mere gravitational weight..

Furthermore a handle being turned by positive inertial torque - from a mass moving inwards - represents an input of energy, whereas the other handle being operated by negative inertial torque - mass moving outwards - is an output of energy from system KE to GPE. Thus each lift is partly powered by further input energy, but also partly from any rotKE the system already had.. IOW each lift would be accomplished by both an input and output of work, which seems a potentially-novel form of exchange..

A final thought for consideration is that the Gera wheel exposed a control screw on the axle by which the wheel's equilibrium speed could be freely adjusted; it stands to reason, then, that this was varying the speed of the GPE system, somehow and for some reason.. So just a thought, but maybe that screw varied the change in radius / MoI and thus speed of the inertial torques lifting the weights? Inertial torque / angular forces generally are obvs also strongly alluded to on the Toys page by the text added alongside the upturned whistling top, ie. the 'game' that might be applied in a different way to extraordinary results..

I think the next thing i'll be looking at is the vagaries of using the ice-skater effect to raise GPE.. Hopefully i'll have thought of a simple experiment to try by the W/E..

[MrVibrating]

..hmm just had an interesting idea:

• consider a pair of scissorjacks aligned radially and 180° apart, pointing inwards, with a weight on the end of each

• so you have two pairs of handles out by the rim, one of each turning CW, the other two CCW

• align the system vertically so that as the weights drop, one jack's collapsing whilst the other's extending

• cross-connect a CW and CCW handle from each jack - buffering with a spring or differential if necessary..

..are the weights now effectively counter-balanced? Or maybe the jacks are just locked and the weights no longer moveable?

Something to try perhaps..

[WaltzCee]

..hmm just had an interesting idea:

• consider a pair of scissorjacks aligned radially and 180° apart, pointing inwards, with a weight on the end of each

made me think of this, only backward



Thank you Bill

[MrVibrating]

What i was actually considering was a seeming impossibility - two radially-oriented vertically-aligned jacks - say at 12 o' clock and 6 o' clock - with a weight mounted to each one, yet somehow (paradoxically) counter-balanced such that both weights could move up or down freely..

..IOW, idly daydreaming about being able to lift weights for free.

But it#s a dumb idea of course, because counter-balancing obviously only works when the weights move in opposite directions. Not the same direction. So if one moves up, the other has to move down. They can't both move up or down without inputting or outputting the corresponding GMH.

Yet consider MT 143 - "A demonstration: pounds in equilibrium", showing two different methods for counter-balancing; although the net system is overbalanced, if allowed to keel the weight levers would need re-lifting, hence neither the Roberval or contra-rotating weight levers appear useful principles for us.. but for serving to illustrate that there was evidently some lesson to be learned about counter-balancing per se.

I mean it goes without saying that one pound can cause the raising of more than one pound if the latter were effectively weightless..

One particular detail perhaps worth reiterating in this respect is that once the wheel speed has caught up with the finite speed of the OB system, G-time goes to zero; that is, at startup G-time is positive, reducing to zero at whatever the design speed, and then flipping to negative if the wheel is over-sped. In practical terms all this means is that once the wheel is up to speed, the center of mass of the weights is keeled, hanging straight down below the axle. When initially accelerating, it is raised on the descending side, and when over-sped, it is instead biased over on the ascending side, like this:

Positive Load



Negative load



Unloaded


..in that latter case, note that the load motor is contributing nothing at all to the P*t meter (it's off), which is thus solely receiving any actual inputs from the actuators driving the OB system.. yet these two actuator workloads are nonetheless summing to zero.. IOW the actuators are each lifting and lowering weights at the same time, inputting and outputting equal GMH..

..IOW, upon reaching its design speed, the weights are counter-balanced against one another! One is lifted whilst the other is lowered in equal measure..

Thus we may surmise that the weights in a working wheel are in fact counter-balanced in a similar way - yet with this additional element of speed-dependence:

• when wheel speed is slower that that of the OB system (ie. at startup or when under load), there is some advantage to angular drops over radial lifts

• upon attaining equal speed to the OB system, there is no advantage or energy difference between angular and radial I/O

• if wheel speed is forced to overtake that of the OB system, the 'angular > radial' advantage persists, but the sign inverts - there's always more work being done on the angular axis rather than the radial plane if RPM <> OB speed, but it can be positive - gaining momentum and energy - or negative, sinking them.. Only when RPM = OB speed does the asymmetry go to zero.

The 'quarters riddle' obviously has context here:

"He will be called a great craftsman, who can easily/lightly throw a heavy thing high, and if one pound falls a quarter, it shoots four pounds four quarters high."

Or else for an alternative via translation engines:

"This nota bene add:
He will be called a great artist
Who can throw a heavy thing up easily,
And when a pound falls a quarter
It jumps four pounds to four quarters. x
Who can speculate on this,
Will soon perpetuate the course;
But if you don't know this yet,
All industry is in vain"

My initial solution to this was that one unit of GPE can be broken up into four equal sub-units, each used to accelerate four times the mass, four times in succession, if using reactionless accelerations.. So for example suppose we had 1 J of GPE via a 1 kg weight * 102 mm of height, we could break that up into four portions of 0.250 J each, and if we burn 250 mJ to unilaterally accelerate 4 kg then we raise its velocity by 0.3535 m/s each time, four times in succession thus burning the whole 1 J and bringing the 4 kg up to a final velocity of 1.414 m/s (square root of two!), hence applying the KE equation ½mV² we find that ½ * 4 kg * sqrt(2)² = 4 J, a 400% gain over the 1 J we began with.

If the riddle is instead alluding to an effective GPE asymmetry then it must have some other, more according solution - the underlying principles and math may pan out similarly, but the 'reactionless acceleration' is obviously an OB moment, the actual exploit taking the form of an angular vs linear / radial asymmetry. Thermodynamically it still has to be a divergent inertial frame, gaining momentum from G*t and energy from inertia, but we're apparently looking principally for some kind of angular > radial advantage that intrinsically involves relative speeds.

On the one hand, the verbs 'to shoot / jump / throw' imply weights are thrown upwards in singular impulses - these thus presenting potential opportunities to apply effective N3 breaks - yet on the other this would seem incompatible with the practicality of arbitrarily-slow operation, which the above demonstrations reveal to be constrained by the lift speed of the rising weights. This would leave gradual, piecemeal displacements as more likely, proceeding in turn as a function of wheel angle (the children with heavy hammers perhaps?) - though obviously, these can't be mere GPE outputs themselves as this alone breaks no symmetries. But we know also that CF workloads must be applied somehow in order to harvest rotational KE gain back into internal GPE - and remember also item 5 on the Toys page - the upturned whistling top; allegedly a principle with extraordinary potential if applied in another way.. Yet this too breaks no symmetries that i can see, simply converting RotKE back into GPE.. i obvs need to think more on this..

Ultimately one or other component of GPE - G, M or H - has to enjoy some kind of advantage between angular vs radial dimensions, but only when RPM < OB speed, going to zero when at speed, and inverting when over-sped. If any of my deductions here are off, please correct me, but this is the current status quo as i see it..

[WaltzCee]

Sounds like science fiction.

Has science and mathematicians painted perpetual motion into a corner? I don't think so.

Pseudo motion/energy might be an imaginary current, a physical model of reactive currents.

Pseudo accelerations. Balance out unnecessary or unwanted variables. Warp time.

The answer might seem science fiction until it's understood. Who knows when that will be?

There have been claims

[Sam Peppiatt]

Mr. Vibrating,
-----"idly daydreaming about being able to lift weights for free". It's not a dream. You can lift weights for free, with the ring and roller concept. It seams impossible but it isn't. Don't you just suppose that Bessler must have made the same discovery? I mean how else could he have done it? It's not science fiction.

It's a minor miracle; a here to for unknown phonumonum. It seams like no one can figure it out----------------Sam

[MrVibrating]

I'm unfamiliar with the 'ring & roller' concept.. please elucidate?

[Sam Peppiatt]

I stumbled onto it quite by accident. Reference mryy drawing, page 29, zeroing in on Bessler's wheel---------------Sam

[MrVibrating]

I don't see any advantage indicated there, i'm afraid (and if i were making such a claim i'd be posting data clearly measuring input and output energies)..

The problem i did try tackling last w/e was the one previously outlined - i made two jacks with a weight on the tips, one pointing up, the other down, then tried interconnecting their CW vs CCW handles, finding that (obviously, in retrospect) it's impossible to raise both together whilst counter-balancing each other; the jacks effectively locked. Only when one can descend can the other rise.

The idle daydream was that there might be some simple planar folding linkage or other principle of suspension that would allow a pair of weights to be raised whilst mutually counter-balancing, hence the 'lift' would only be an inertial interaction, which could be accomplished by an arbitrarily-smaller GPE output for a nice easy gain.

Bessler is strongly intimating that there is some means of lifting on the cheap available, but i'm not seeing it yet. What he cautions against of course is the notion of perpetual OB merely by trying to make the descending side always heavier; rather, the real focus of attention should be the problem of engineering an effective GPE asymmetry - ie. lifting weight without inputting the full corresponding compliment of G*m*h. To "lightly raise a heavy thing high". Crack that and we're free to OB all day, but horse before cart..

[Sam Peppiatt]

Mr. Viberating, You're certainly not alone. It's the same response I get from just about every one. It's like so what? what's it good for. I think you mentioned 'data', that I don't understand. All I can confirm is that it is perfectly balanced.

You did mention counter-balancing; that's exactly what it does. Don't you see? It counter-balances the weights and, lifts them back up to the top of the wheel. It's just as you said, to "lightly raise a heavy thing high". I did crack it! To take it to the next step, you can trick it into being OOB on the down side-----------------------Sam

[MrVibrating]

LOL what am i missing - as one weight rises another gets lower, no? To see if the net system energy has changed i'd measure the mass * height (*G) change on each side, up vs down, before & after the interaction, summing all PE and KE.. and then IF it panned out i'd lead with those numbers, reducing and simplifying it down to how much we could expect back out for each Joule in for a given config, dividing that output by the input to state a net efficiency or CoP. Others could then replicate (or not), development thus progressing (or not), but one way or another i'd want to see the issue resolved as quickly as possible so i could move on to other, potentially more-productive enquiries if it was indeed yet another zero sum..