Decoupling Per-Cycle Momemtum Yields From RPM

[MrVibrating]

[MrVibrating]

..trying to distill these results into a more fundamental - useful - set of conclusions; glean whatever value can be found in the fact that it didn't work..


• from these results, we can project those of different 'target relative speeds':

Asynchronous sequencing was successful, but ineffective; thus many small spin & brake cycles in rapid succession will still only generate 'OU' equal to the net GPE input, as will fewer, longer ones; only the amounts of energy in & out will change, but not their ratios..


..thus, the mechanical decoupling of the inertial interactions from those generating the effective N3 break has no effect upon the base spatio-temporal symmetries.. it's just simple Lorentzian transformations, and ultimately the fact that the true net input energy cost of momentum is still tracking ½mV² means that we cannot harness Noether's theorem to our advantage simply by sinking counter-torque or counter-momentum to gravity!

This in turn implies that the above system is actually 'geo-physically safe' - ie. it's not an 'effective' N3 violation, and hence it does apply equal opposite counter-momentum to Earth, via gravity. Thus the net momentum of Earth-plus-wheel is constant. In short, it doesn't seem possible to render a 'divergent inertial frame' by these means alone..



So an entire class of potential exploits are eliminated there; 'sinking counter-momentum to gravity' as a general principle is not an 'effective' N3 break, by our requisite standards.. it does bear a superficial resemblance, but doesn't deliver the goods in terms of fixing the energy cost of accumulating momentum.

The critical symmetry enforcing energy-unity here is still that identified in the OP; reliance on gravity's vector / external coordinate space, and thus the 'non-inertial' (sic) reference frame of Earth's surface. In other words, the reference frame that needs to be accelerated is that of the source of the effective N3 break itself; we literally need to carry it around with us, on-board the accelerating wheel..




There's only one other 'effective' N3 break (that i can see, anyway); and that's inertial torque - the 'ice skater effect'.

Conveniently, it's also one that carries around with the rotating system.

Like i say, since there doesn't even seem to be any further options, that's very convenient indeed.. if only for concluding the only possible way forwards..


I've previously demonstrated the same reactive feedback techniques in cancelling counter-torque from a motor with inertial torques from controlled MoI changes. It, too, 'worked' perfectly... except for the fact that i was using positive inertial torque, from pulling orbiting mass inwards...

...the result, predictably, was that the KE value of the motor's torque * angle was squarely OU... only, equal to the work done against centrifugal force in rendering the 'N3 break'.

Worse, the requisite condition of reducing the 'stator' MoI whilst holding its RPM's constant was excising its momentum - bleeding it away in the form of MoI reduction, rather than speed loss.. thus, the momentum being imparted to the 'OU' rotor was simply transferring from that of the stator.. for no net change.

Here's the archive footage, for what it's worth:


Torque * angle cost of 1 kg-m²-rad/s = ½ J; KE value = 1.5 J, yesterday


In all these prospective N3-busting interactions we get to glimpse tantalising examples of how the standard KE equations are all the 'magic mechanism' needed for manufacturing mechanical energy.. KE simply squares with velocity, about which we can do nothing.. but we also see how the the value of 'velocity' itself wrests upon N3 and the conservation of momentum; motion's relative, speed is relative and thus so is KE.. with N3 being the lynchpin holding it all together. In a nutshell; the dependence of CoE upon CoM.

Equally though, none of 'em, so far, actually succeed in rendering their N3-bending tricks for less than the resulting KE 'gains'.


I say 'none' - again, they really seem to reduce to just the two examples.. inertial torques, and gravity / OB torques. Both are transietly 'reactionless' from within the rotating FoR.

Yet neither are actually 'effective' as N3 breaks with regards to actually altering the net momentum, or thus generating a 'divergent' / self-accelerating frame of reference.

Neither, in their own right, anyway..

Occam argues against simple multiplication of entities - again, how many prospective N3 breaks should an OU system require? Well that answer's surely still "just one" - but we ain't quite got it yet.

So i can't think of much else to try, but combining 'em..

For example, what might happen if you sink counter-torque to inertial torque whilst in free-fall? So the whole system's accelerating under gravity, and inside that plummeting system, we accelerate a mass against an inertial torque (positive or negative)..

Obviously, if you imagine throwing or shooting a projectile downwards whilst in free-fall, it'll gain more momentum and KE, but you'll lose proportionately equal amounts due to N3...

..now re-run that scenario, only this time, an inertial torque (from a changing MoI) has got your back.. so, undergoing no counter-deceleration:

- the projectile still gets the momentum & KE gains, but no longer at your expense!



What if the same negative inertial torque, from an increasing MoI, is used to cancel BOTH gravity's acceleration AND the counter-torque from a motor, at the same time?

Projecting the full-cycle results and accumulations would take a friggin' essay, but basically MoI changes influence time-spent-gravitating per 'up' vs 'down' stroke, and thus yields of momentum exchanged with gravity, whilst converting output GPE into 'CF PE' / sprung PE.

Used as 'sinks' for counter-forces in conventional inertial interactions, they cannot cause momentum rises, trading either MoI or velocity in direct proportion to the acceleration of another body.

But combine both dynamics and you have momentum-from-gravity plus torque cancellation invariant to angle or speed..

So it's basically menage a trois time; a tripartite interaction between:

• gravity

• inertial torque

• regular inertial interactions



..really beginning to scrape the bottom of the barrel here tho.. either 'KE gains' / mechanical OU is possible - at a base level - or we've been had..

..as such any 'true believers' should expect guaranteed success can only be all the more imminent.. literally very few permutations left in all of mechanics i think.. it's been a truly exhaustive search through the fundamentals, but if it were there, a 'possible thing', it couldn't hide from such a methodical process of elimination.. input PE reduces to F*d, output KE to ½mV², they're bound by N3, and in terms of fundamental field interactions we have 'gravitational' and 'inertial' - everything else is just variations upon those two elemental exchanges.


So.. ho hum.. let's try cancelling counter-forces in a falling reference frame.

Same objective: constant input PE cost of momentum, for a rising KE value. Or just, any deviation between the input energy cost of an acceleration and its resulting ½mV² value.. any hint of an 'effective' N3 violation / reactionless momentum rise.

After that, i'm done - if it's there i must've missed it, but there won't be anything i haven't actually tried.. so it'll have to be something overlooked in previous results..


Fundamentally, a moving mass only has so much KE, as a function of its mass and velocity; we cannot meaningfully ascribe it any more or less. 'Excess KE' is not a conceptually-consistent thing. An oxymoron. Misnomer. A mass or system can only ever have exactly the right amount of KE for the F*d applied to it.. but this remains true regardless of whether N3 is respected, or not. That clause really is our only hope..

Precipice or brick wall, crunch time's a comin'..

[MrVibrating]

..here's basically what i'm thinking:




• a plain disc 'rotor'

• a weighted, variable MoI as a 'stator'

• extend MoI whilst the OB weight drops, causing a 'reactionless' braking torque..

• ..whilst using the whole thing as a 'stator' to torque the other, balanced rotor against

• cancel half the OB torque with inertial torque from the vMoI, and the other half with counter-torque from the motor

• retract MoI whilst the weight's rising, now braking against the rotor

Rinse, repeat and measure..


Or summink like that, anyway.

Low expectations right now, TBH..

[MrVibrating]

Or summink like that, anyway.

..how many times do i need repeat the same mistake, duh? The system i just described there would STILL produce RPM-dependent momentum yields..

..the base logic still stands - it's gotta be the right ingredients, but the 'recipe' there's a bit random..



So try this instead:


• drop a weight that spools off a vMoI, spinning it up like a ripcord

• use a reactive control loop to perfectly cancel gravity's acceleration with negative inertial torque, from widening MoI

• weight thus drops at constant speed

• this converts all GPE into CF-PE, at any RPM

• once dropped, leave the weight for now - worry about re-lifting it once we have a KE gain

• unload that CF-PE by moving the vMoI masses back inwards, and so now generating positive inertial torque

• again using feedback control, perfectly cancel that positive inertial torque with counter-torque from a motor, spinning up a 2nd rotor


For now, that's the basic interaction i wanna measure. The potential exploit would depend upon the conversion of GPE from its initial form in which its potential momentum yield is inherently RPM-dependent, into one that has no such limitation; thus essentially, that with say ½ a Joule of initial GPE available, we can collect all of it as CF-PE, and then that ½ J of CF-PE will always be sufficient to sink 1 kg-m²-rad/s of counter-momentum from accelerating the 2nd rotor; so the motor will also spend ½ J generating a 1 kg-m²-rad/s momentum increase each cycle.

Basically, using CF-PE to buffer GPE before it's tapped for momentum, type stuff, so freeing the momentum-generating phase from its former dependence upon RPM with respect to gravity's vector, type situation.

I think the testing priority should be that second part - the first part, collecting output GPE in the form of CF-PE instead of KE, i'm confident of (well-tried and tested already IIRC); it all hinges on that next assumption that momentum yields from CF-PE are RPM-invariant, unlike their GPE counterpart.

So a short battery test is in order:

• with gravity off for now, give the vMoI and 2nd rotor equal initial RPM

• spend ½ J on MoI reduction; this would cause a ½ J rise in its rotational KE, but instead, cancel that acceleration with counter-torque from accelerating the 2nd rotor

• see how much momentum can be raised on that 2nd rotor from the same ½ J of input work against CF, across a range of initial RPM


If it's the same each time... get in!

Only reservation at this stage is that gravity's superfluous here - Bessler only ever displayed vertical wheels and insisted there was "nothing for appearances sake only" about them; so either his objective was 'something that looked for all the world like a working gravity wheel' - in which case he's kinda right, insofar as means justifying ends.. or else it was simply PM per se, in which case gravity seems to play only an incidental (near 'ornamental') role; indeed, the whole concept is to stabilise momentum costs in spite of the underlying dependence on gravity.. not because of it! The proposal doesn't depend upon any properties unique to gravity, such as Galileo's principle or its inherent potential as a momentum source / sink, so much as manage them; on the contrary, the objective eschews the very notion of momentum-from-gravity; the brief instead is CF-PE from GPE, and momentum-from-CF-PE..


But whatever, it's intriguing and on-topic so i'm going to try it..

[MrVibrating]

OK just tested a rotor + motor using a vMoI as a 'stator'..


Conditions and results:


• both bodies began with equal MoI of '1' kg-m², at an equal 2 rad/s

• a linear actuator retracted the vMoI masses at a constant slow speed of 0.01 m/s

This would've caused the vMoI to accelerate, conserving its angular momentum, however:

• the motor was programmed to use its counter-torque to perfectly cancel that acceleration, thus accelerating the rotor instead

Thus the vMoI 'stator' remained at constant speed, even whilst its MoI was being reduced.

• Since its speed was constant but its MoI was decreasing, its rotational KE was decreasing.

• The sim was set to pause when the stator's rot KE had been reduced by ½ J.

• The actuator's P*t integral was then taken, and confirmed as ½ J.

• The motor's P*t integral was also taken, coming in at 0.12288085 J.

Net KE had risen by 0.62 J so the system was at unity, as expected; the objective being to check the momentum yield:

•• The rotor's angular momentum increased by 0.5 kg-m²-rad/s.

•• So the energy cost of momentum was 0.62 J per ½ kg-m²-rad/s, or 1.24 J/L

Given that the ½mV² base-rate is just 0.5 J/L, this isn't 'great' news.. but still fine, provided it ain't worsening by the inverse sqrt of RPM..! Dammit, we all know it's gonna, tho, right? :|

Still, gotta go thru the motions eh..

So i did one more run, starting at double the initial velocity:

• initial vel. 4 rad/s

• actuator P*t = 0.5 J

• motor P*t = 0.02945154 J

• rotor's angular momentum rise = 0.24279 kg-m²-rad/s

• yield is thus 0.503 J / 0.24279 kg-m²-rad/s, or 2.07 J/L


Drat.

So evidently, RPM-dependent momentum yields are not an exclusive property of GPE interactions.. converting GPE into CF-PE prior to momentum generation has no effect on the resulting yield potential..

Fundamentally what's happening is that at ever-higher RPM's, a constant "half a Joule" of CF-PE corresponds to a decreasing increment of MoI reduction, and hence period of inertial torque, and thus a diminishing window of opportunity for sinking counter-torque / raising momentum on the rotor.

Thus if a vMoI is to be used as a co-rotating 'stator' to raise reactionless momentum against, the chief requirement would have to be a constant period of inertial torque per cycle, in spite of rising RPM's. Maintaining the inertial torque for longer means further reducing the MoI, doing more work against CF etc., spiralling costs straight back up to ½mV²..

Alternatively, maintaining vMoI velocity in order to stabilise the torque-cancellation periods would mean allowing the rotor speed, and thus motor torque * angle, to diverge from that of the vMoI 'stator', in which case input T*a again tracks ½mV²..


Hmm. Still seem snookered from every angle here.. :|


It's a bit minimal but here's the rig used, with that last run:



"how much momentum can be raised from half a Joule of work against CF force, when both MoI's = '1' and rad/s = 4?"


There's no getting around it; Bessler was buying momentum for less than its KE value. The only possible source or sink of momentum, with no stator and with everything going around together, was gravity. So one way or another, cheap momentum-from-gravity must be possible...

Bessler's wheels did accelerate, and did have top speeds. He did claim their output power increased under load - as would be expected from momentum yields increasing inversely to RPM. So the implication is that there's something we can do that opens a window of opportunity for buying more momentum than would otherwise be possible at a given RPM.

Whatever this trick is, it's of limited effectiveness, only working up to a given RPM, and takes the basic form of 'regulating momentum-from-gravity yields in spite of rising RPM'. 'Mechanical OU' can only mean decoupling momentum costs from KE value. N3 is the arbiter. We're allowed to use inertial interactions, and gravitational interactions.. and that's it.

Somehow, these are the implicit ingredients of an 'OU omelette'... so what's the frickin' recipe?



??

[MrVibrating]

There's another potential angle to all this: gaining KE in the form of velocity rise ain't the be-all and end-all; it can be increased by raising MoI instead of RPM...

If it means speeds, and thus momentum yields, can be moderated over successive cycles, perhaps it's the only way forwards?

It would mean a system a bit like what i've previously described as a 'vMoI flywheel' - which is just a variable MoI with springs, converting input energy into sprung PE instead of rotKE, yet still banking ever-more momentum and energy, whilst due to Hooke's law, the springs only stretch out so far, and so converge to a finite radius... basically a flywheel that gets fatter instead of faster.. but only so fat, despite having limitless energy capacity (up to breaking point anyway).

This, too, would kinda fit the load-matching properties Bessler claimed, since trying to slow the system down reduces the CF force holding back the springs, which in turn relax a little, allowing the masses further in, thus causing positive inertial torque that directly counters any external application of negative torque..

This endows a wheel with significantly greater 'stopping power' - an apparent 'momentum' - belying its actual mass and speed. When Bessler describes his assistant being almost lifted off the floor in the effort to stop the wheel, it may well have been positive inertial torque from rapidly-unloading sprung PE he was fighting against.. over and above the wheel's angular momentum and rotational KE as a function of its mass, speed and radial distribution.. and this would appear intuitively peculiar to spectators - almost like a mime artist wrestling an imaginary balloon.. 'excess impetus'..!

It would similarly resist over-speeding; which would cause the sprung masses to stretch further outwards, now producing negative inertial torque, so again resisting the acceleration, whilst gobbling up the additional supplied energy in the form of rising CF-PE, to be spat out again when the applied load switches back to negative..

Basically, swinging masses around on springs would explain the speed-invariance that so piqued some witnesses (the pulley / yard / box of bricks demo) - giving the machine a preferential speed that it'd hold quite doggedly..

It might also go some way towards explaining Wolff's impression of the weights being 'attached', almost quite literally, to radial springs. So, no coincidence there, basically.

If RPM ain't increasing in the first place, 'decoupling momentum yields' is job done, surely..?

..so the question would then become, how in the hell do you raise MoI on the cheap?

Or more specifically, how to raise momentum in the form of rising MoI, as opposed to velocity, on the bloomin' cheap?


Trying to gain the velocity component of momentum on the cheap is where it's all been coming apart - the fundamental 'brick wall'. That's what i'm snookered on. Symmetry-bound at every turn. Maybe it's a mug's game after all, and discount MoI upgrades is where the real bargain's at..?


It'd still need an effective N3 break, and gaining MoI at constant RPM is nonetheless still raising the masses' absolute velocities in the x & y planes (just as the 'edge speed' of a disc at a given RPM is radius-dependent), so it's still essentially a question of 'cut price velocity' - raising MoI at constant RPM is accelerating the masses..

..but it's a shift of focus away from the angular velocity component of AM and rotKE that seems so comprehensively futile.. so maybe it'll inspire dazzling new insights and avenues of investigation into this most pressing of issues, of how to gain momentum, from gravity, on the cheap, like. Maybe not. But what's the worst that can happen eh? (stray torques aside)

An example might be the immediate question of 'if gaining MoI rather than RPM is the key to beating ½mV², that's not inherently directional - so whence the directionality of the one-way wheels?'

This in turn implies that the gain interaction - where MoI is increased, on the cheap, like - is asymmetric with respect to gravity; as in, lifting and dropping in alternate planes / dimensions. Such as radial lifts with angular drops, AKA 'classic OB'.

So, somehow, classic OB offers some kind of opportunity for hustling MoI..

..we already know how to raise GPE independently of MoI..

..so how's about the inverse trick, of raising MoI independently of GPE?

Or perhaps there's other iterations / variations there, too.. mixing in angular and linear accelerations / inelastic collisions etc.. producing inverted-axis, MoI-centric variations on 'staircase' plots..?

Equally, a 'spring-loaded vMoI' also explains the startup characteristics of the bi-directional wheels, too - this could be tuned to trigger at some threshold level of CF force, obviously.. then using stored PE to begin generating OB torque..

..and finally, it's the ideal way to harness rotKE gains without a stator.


So if the base mechanisms are one or more sprung vMoI's, connected to a 'classic OB' GPE interaction, either the 'bangs' are collisions between them (ie. 'inelastic collisions' to consolidate reactionless momentum rises), or else they're simply from the weights being shot outwards radially in the most efficient OB trajectory..

So the thing to check for first is any hint of cut-price MoI gains from a series of spin & brake cycles between a sprung vMoI and a basic OB system.

Ain't tucked up just yet.. ;)

[Georg Künstler]

Hi MrVibrating,

there are many ways to OU.
But you scratch the surface now.

So if the base mechanisms are one or more sprung vMoI's, connected to a 'classic OB' GPE interaction, either the 'bangs' are collisions between them (ie. 'inelastic collisions' to consolidate reactionless momentum rises), or else they're simply from the weights being shot outwards radially in the most efficient OB trajectory..

The bangs are collisions, impacts ('inelastic collisions') in the Wheel, that I can confirm.
But the collisions are not the Driver of the Wheel.
The collisions are there to arrange the Position of the weights.
This will generate an asymmetric torque, a tilt swing in a positive feedback loop.
It is an uneven variation of acceleration.

And to make it clear, the Besslerwheel does not hurt any Newton law.

[MrVibrating]

This looks like more of the same, but is actually scratch-built with a specific interaction in mind: to maintain momentum-from-gravity yields by growing fatter instead of faster:


Well OK, here it's getting faster.. but it doesn't have to if it doesn't want to!


The previous 'planar-linkage + rotary servo' solution worked great for a constant target MoI, but only has so much travel available if the target MoI becomes variable..

..there were few better options than working out how to do this constant-MoI trick using linear actuators only, and you know what they say about 'necessity'..

..so now, both the OB axis and the weights themselves have independent, dynamically and infinitely adjustable, MoI's.

The interaction of interest will be: progressively raising the MoI of the OB axis in order to produce negative inertial torque (the 'ice-skater effect'), thus limiting gravity's acceleration of the RPM's, and so boosting the 'time-spent-gravitating' per cycle and thus the per-cycle momentum yield, tuning for constancy of yield over some range of RPM, instead of the usual diminishing returns; albeit now making up the difference in the form of its 'MoI' component rather than 'velocity'..

..then the brakes will be activated on the weight axes, locking them to the central axis, and so accelerating their absolute speed, transferring half the gained momentum over to them..

..then retracting the MoI of the OB axis again whilst the brakes remain locked..

..unlock 'em when the OB MoI's reset and repeat the cycle; widening MoI when dropping, then braking the weight axes whilst re-closing the MoI..

..and constantly controlling the net MoI of the weight axes to match that of the OB axis.

This should maintain the step height increments on the momentum 'staircase plot':

• plotted WRT time the steps will lengthen into terraces, but their heights will remain constant

• plotted WRT angle the step lengths will presumably appear equal; not distinguishing momentum by its MoI or velocity components

• the system will also be banking most of the output GPE in the form of CF-PE

..so after some no. of cycles that pent-up CF-PE can be converted back into rotKE of both the OB and weight axes.

Same deal from there; measure efficiency and try suss out whether this nudges us any closer to an effective N3 break / divergent inertial frame / KE gain..


As ever, further variations may include trying to exploit this 'expanded window' per cycle for raising / sinking torque / counter-torque from a motor, too (hopefully at last overcoming previous constraints of rising RPM).


The TL;DR would be - addressing the previous failure of asynchronous inertial vs GPE interactions (rising ratio of latter to former); so now maintaining synchronous inertial / GPE cycles, by 'stretching' their periods together. The inertial interaction's obviously time-invariant, whereas gravity's momentum yield is a function of its acceleration constant, so is time-dependent, and the gig is basically to collect the momentum independently of velocity and KE, siphoning 'em off to be released back into the mix later, once all the momentum's on board, type stuff.

Will hopefully make some progress with it this week..

[MrVibrating]

Hi MrVibrating,

there are many ways to OU.
But you scratch the surface now.

So if the base mechanisms are one or more sprung vMoI's, connected to a 'classic OB' GPE interaction, either the 'bangs' are collisions between them (ie. 'inelastic collisions' to consolidate reactionless momentum rises), or else they're simply from the weights being shot outwards radially in the most efficient OB trajectory..

The bangs are collisions, impacts ('inelastic collisions') in the Wheel, that I can confirm.
But the collisions are not the Driver of the Wheel.
The collisions are there to arrange the Position of the weights.
This will generate an asymmetric torque, a tilt swing in a positive feedback loop.
It is an uneven variation of acceleration.

And to make it clear, the Besslerwheel does not hurt any Newton law.

..who knows mate..

Bangs are a simple solution for the prerequisite of growing a bank of OU momentum - ie. if the form of energy gain is 'KE' then this can only arise from a series of N3-defying reactionless accelerations and inelastic collisions. This 'makes' KE using nothing more exotic than the standard KE equations themselves.. whilst inadvertently altering earth's resting momentum state and yadda yadda oblivion.

What you seem to be describing sounds dangerously close to an effective GPE asymmetry, so cannot 'make' energy since there is no 'gain' gradient there, what with G, M and H all being time-invariant..

KE gains using pr0per maffs aren't magic - but require the opening up of a differential; that is, some kind of 'slip' between the dimensions of our respective 'input' and 'output' work /energy fields.. and an N3 break does this, by repeatedly snaking back down the 'V²' ladder of the KE=½mV² equation following each reactionless acceleration, thus constantly resetting the energy cost of accumulating momentum to its baseline value of ½ J/L, while the KE value of that same '1 L' remains a function of the net system velocity relative to the external FoR; at 2 m/s it could be worth 2 J, or 4.5 J at 3 m/s, frickin' 50 J at 10 m/s and so on. That's using a series of reactionless accels, speed-equalising collisions, and the standard KE formulas. Nu'in else.

This is the only way - regardless of how it may be manifested; fundamentally, symmetry of input PE to output KE is enforced by N3.

This is a general solution, applying across classical physics - so the same principles and maths apply equally to Lenz's law with respect to mechanical magnetic F*d or induced B and EMF's etc. That is, a working magnet motor would also be an effective N3 break - that's the only way thermodynamically that any energy gain is possible, across the board, from magnet motors to 'gravity wheels' and harmonic oscillators etc. etc.

Fundamentally, energy symmetry / CoE is bound to momentum symmetry / CoM. One shudders at the wasted lifetimes that've failed to heed this simple self-evident maxim, but i'm damned if i'll be one of them!

[Georg Künstler]

Hi MrVibrating,
you wrote:

KE gains using pr0per maffs aren't magic - but require the opening up of a differential; that is, some kind of 'slip' between the dimensions of our respective 'input' and 'output' work /energy fields.. and an N3 break does this, by repeatedly snaking back down the 'V²' ladder of the KE=½mV² equation following each reactionless acceleration, thus constantly resetting the energy cost of accumulating momentum to its baseline value of ½ J/L, while the KE value of that same '1 L' remains a function of the net system velocity relative to the external FoR; at 2 m/s it could be worth 2 J, or 4.5 J at 3 m/s, frickin' 50 J at 10 m/s and so on. That's using a series of reactionless accels, speed-equalising collisions, and the standard KE formulas. Nu'in else.

I think you don't know how close you are with your insights.

You write.

some kind of 'slip' between

So what is this slip function? It is an overlay like a consdense, or is it like a expand ?

In my view it is an overlay with an saw shape oscillation.
A folding function
Only an Impact can cause a saw shape sprung function. A tilt swing in the gravity Wheel, documented with 8 impacts on the down going side of the Besslerwheel.

[MrVibrating]

The previous example held a fixed MoI, but also displayed a "Target MoI" value; unused there, but which was being calculated as simply the initial MoI of '1', plus the rise in speed in rad/s..

..so in the following example, that 'Target MoI' is now being put to use, with this, slightly more refined, function:

Code: Select all

if &#40;output&#91;74&#93;.y1 < 2, 1, output&#91;74&#93;.y1 - 1&#41;

'Output 74' is the 'angular momentum' calc, so the instruction is simply:

"maintain an MoI of '1' until AM reaches '2', then begin increasing it in direct linear proportion"


So the system starts out accelerating under OB torque - gaining speed - then, after collecting 2 kg-m²-rad/s of momentum, it begins getting fatter instead:



Notice how the time rate of change of momentum is completely unfazed by the switchover - Galileo's principle in action; you'd never know from that plot alone whether the speed or inertia was rising..


So that's the means by which i'm proposing to gain a constant, fixed amount of momentum per cycle, over some contiguous sequence of cycles; basically 'RPM be damned' - i'm decoupling the rotation rate itself from the interaction period. Each cycle will be 'complete' when - and only when - a consistent target rise in momentum has been reached.



The next step in each cycle then is the 'inelastic collision' - braking the weight axes against that central axis, so sharing the gained momentum back with them.

Obviously, if the brakes were engaged as-is, with the central MoI much larger than the weight's axial MoI's, the resulting momentum distribution would be unequal, transferring little across..

..so first i need to set those axial MoI's expanding in-step with the central MoI, so they're equal whenever the brakes engage.


So what'll happen is, both the pink and green actuators will widen together, keeping 'net axial' MoI equal to orbital / overbalancing MoI, all the while gaining momentum on the latter..

..then, having reached a target rise in momentum, the brakes will bite, braking the OB axis against the axial angular inertia of the weights themselves; speeding them up, whilst slowing itself down.. with equal MoI's, the resulting momentum distributions will also thus be equal..

..then with the brakes still engaged, the OB MoI will be reduced back to to its initial value of '1' again, tranferring across exactly 50% of the remaining momentum gain, hitherto stored as MoI increase / CF-PE..

..and so ending each cycle with an equal net rise in system momentum and velocity.


If the system still can't break unity, despite gaining constant momentum per cycle, then it's back to sussing out why, and thus what else to try..

So the next iteration will feature:

• expanding weight MoI's, their net sum matching that of the rising OB MoI

• brakes / rotary dampers, set to trigger once a target momentum yield is met

• retraction of the MoI's


Regarding that last point, the MoI's could be reset to the same initial value each cycle... thus inputting more work against CF given the ever-rising speed, or else, only reset back as far as is possible using just the CF-PE stored from the output GPE that didn't convert to KE. The latter option seems more interesting to try first i think..

With linear actuators being the sole form of input work, all of them can be combined into a single 'net F*d' integral. The only other integral will be that of the brakes - again, 'net T*a' - so it's a pretty simple system, thermodynamically.. should solve precisely and unambiguously, one way or the other..

[MrVibrating]

..quick plot showing how the mode change affects the KE evolution in relation to the rising MoI:




..so the main effect is a switch from the exponential (squaring) rise in KE we'd normally see from such a 'free-fall' acceleration, to a linear one; the arc of whitespace between where the green trace was initially headed, and where it ends up instead, represents the output GPE now stored as CF-PE.

So basically what i'm hoping is that the torque * angle value of that CF-PE (which i'll soon be metering directly), will end up buying angular momentum at a rate of ½ J/L in terms of accelerating the weight axes, but resulting in a KE value, from the external reference frame, transposed up by the net rise in system momentum / velocity about the central axis.. so with say a 1 rad/s leg-up, half a joule T*a in becomes 2 J of KE out, or 4.5 J @ 3 rad/s etc. etc.

For instance, the CF-PE could be loading up a spring, angular or linear, which could then torque the weights against the wheel base..

..since the interacting inertias begin each new cycle stationary relative to one another, the T*a cost of momentum is constantly reset to its ½ J/L base rate. With all counter-torque / counter-momentum sunk to gravity, a half Joule of work does cause a 2 J rise in KE at 1 rad/s, 4.5 J @ 2 rad/s, 8 J @ 3 rad/s etc. - that's not even controversial - so as ever, it'll all boil down to how meaningfully 'effective' our prospective N3 break here, is.. will the KE 'gain' + dissipated heat again be equal to the net input work by the actuators..?

[MrVibrating]

You write.

some kind of 'slip' between

So what is this slip function? It is an overlay like a consdense, or is it like a expand ?

In my view it is an overlay with an saw shape oscillation.
A folding function
Only an Impact can cause a saw shape sprung function. A tilt swing in the gravity Wheel, documented with 8 impacts on the down going side of the Besslerwheel.

I'm talking about an inequality between how two different forms of energy scale up with respect to spatiotemporal changes in whatever system properties they're each a function of; to wit, breaking input-PE to output-KE energy symmetry, which itself hinges upon N3 and the conservation of momentum. Within the available breadth of scope of classical mechanics, this is, unfortunately, the only possible path to a solution for mechanical OU. This is because our objective energy gain is kinetic energy, which is stone-cast as ½mV², and we cannot meaningfully just change the metric (or else i could just as easily run a hundred meters in 3 secs)..

..similarly, 'input work / energy' reduces to "force times displacement".

These formulations are basically encoded into the universe and they're the inflexible 'elements' of mechanical input and output energy that we have to work with.

So the only way to open up a disunity between them is to manipulate the effective value of 'velocity'; since motion's relative, so is speed, and thus KE. And that's simply just another way of saying that 'mechanical OU is only possible from an effective N3 break.'

So knowing nothing else about Bessler's wheel, we're already off to a flying start, just from basic deductions..

..however of course, when you look at the evidence, it is not simply expressly consistent with an effective N3 violation, but exclusively so, by warrant of direct confirmation IN PRINT from the man himself: "in a true PMM everything must, of necessity, go around together; there can be nothing involved in it that remains stationary upon the axle", further attested by all witness testimonies that the wheel and axle turned together as one piece, without needing to apply torque via a stator..

If you think about it, if any 'other' forms of classical symmetry break were possible and relevant here, such as the mythical GPE asymmetry ('pick it up when it's light, drop it when it's heavy'), none of those hypothetical gain principles would be categorically disabled simply by being used in conjunction with a stator..

..apart from an effective N3 break, which WOULD be outrightly precluded by use of a stator.

And one only need look a little further to see that gravity is not only ideal for rendering 'reactionless' momentum rises... but that it's also trivially easy - 'kid's stuff' that we all sussed as kids down the park. :|

N1 = "the net momentum of a mass or system of masses interacting about a common center is constant with respect to time"

Or to put it another way:

"the net momentum of a closed system cannot be altered by the internal expenditure of work".

This should be Sellotaped to every park swing across the land..

It's gotta be easier than we've been making out, is all. As ever, don't do what you gotta do to get a 'unity' outcome, and you won't.. the implicit instructions for creating energy are written between the terms of its conservation.

The only 'secret' is knowing it's possible!

[Georg Künstler]

MrVibrating wrote:

N1 = "the net momentum of a mass or system of masses interacting about a common center is constant with respect to time"

True, but a loose axle has no common center, it is wobbling.

And the axle must also move

is an evident, important sentence from Bessler.

A moveing axle is a moving of the Center of Mass in any direction, up,down,left,right.

In your Simulation, tryings, you turn the masses around a fix point.
All the swingings, rotations are going therefor in a perfect circle.
You can increase the Speed, but there are still going in a circle path.

I have build such devices which you are running in your simulations in real,
and learned my lessons.

[MrVibrating]

The MoI-matching's done, so now it just needs brakes, and it'll be ready to start investigating energy results:



"A great fat herd of fat, lazy, plump horses wanders aimlessly."


Also started filtering the feedback signal to make things a bit less explodey - the multiplier alone is only good for tuning to a given MoI, but not when it's constantly changing..

This introduces a lag between the 'Target MoI' and the rig's current value, preventing instability from accidental overshoots and the resulting paroxysms of counter-corrections and counter-counter-corrections..


Note that the expanding weight MoI's (in green) have no effect as yet - the OB system is oblivious to whether they're expanding or not, since it's still the same weight, at the same radius..

..the sole purpose of raising the weight MoI's like this is to equalise the momentum distributions when their brakes engage, thus accelerating the net system by half the per-cycle momentum rise, resulting in the shortest possible route up the ½mV² escalator.. provided we have anything interesting going on N3-wise, anyway..

So next up, brakes..





ETA: another point perhaps worth highlighting is that the momentum is constant in part because of Galileo's principle - gravity's a uniform time-rate-of-change of momentum, rather than a 'force' per se (or per a trivial application of N2 anyway) - but also in part because the balance of the system is not changing, despite inflating..

..what's happening is, the GPE output / radial lifts are programmed into a 'base' pair of actuators, one for each plane in the x and y, which each move a carriage-in-a-slot between opposing 1 meter radii across the center of the wheel. The actual wheel radius is 2 meters however, so a second level of linear actuators are added; one extending 1 m out from the central carriage to move a weight to the rim, the other extending 1 m inwards to park its weight at the center. Those two actuators only control the MoI, while the base actuator of each pair controls the OB / lifts... and hence why the GPE and thus momentum gain is constant, in spite of the MoI wandering off to find its fortune..

The way the paired MoI actuators work is also maybe worth a mention - ideally i'd control them for 'length', as an exact function of the desired mass radius / angle required for the otherwise-delicate feat of changing GPE independently of MoI..

..however all my attempts to derive what is obviously a simple geometric function, so far, have produced less-than-ideal results..

..hence why i've stuck with using reactive feedback, and just refined it..

It's a bit like using GA or cellular automata for problem-solving; i've only a sketchy idea as to how it's arriving at the solution.. but it does, so i don't really need to know, so long as the results integrate cleanly..

So rather than controlling them to track a definite trajectory or radius / angle, they're simply set to 'velocity' control..

..so get this; all each pair of MoI actuators know about is their independent velocities - how fast they're moving in or out - and the resulting MoI between each opposed pair of masses.

What i've done is to calculate each MoI pair independently on the fly, and then set that calculation itself - not its solution - as the 'velocity' input to the MoI actuators... with the 'Target MoI' subtracted from it!

So this produces a number in the MoI actuator's 'velocity' field... and that number reaches zero when actual MoI - being calculated instantaneously every frame - matches the 'Target MoI' value..

In other words, if that number's zero then the target MoI has been reached and so radial speed between each opposed pair of masses goes to zero. Likewise, if it is over or under target then the 'velocity' field will be receiving a signal of proportionate sign and magnitude, auto-adjusting accordingly.

So these small incremental deltas between 'actual' vs 'target' MoI get magnified through the 'Feedback Multiplier' into changes in radial velocity, which is what causes the sensitivity to the much larger increments involved in a changing MoI, hence necessitating the filter / cap function.

Boooring, i know... but just as well to record techniques i'm likely to forget later..

Also while i'm back 'ere, sim attached: