Decoupling Per-Cycle Momemtum Yields From RPM

[MrVibrating]

Below is basically a standard DC motor, except the 'stator' is a co-rotating '360° pendulum':



Both the 'stator' and rotor have an MoI of 1 kg-m²-rad/s. They share the same axis, and are alternately interconnected by a motor and clutch.

Whatever its speed as it departs 12 o' clock TDC, the motor applies just enough torque to prevent the 'stator' from accelerating under gravity... instead, accelerating the rotor.

At 6 o' clock BDC the motor switches off and the clutch engages, locking both parts together. Since their MoI's are equal, these inellastic collisions halve the per-cycle velocity rise and so burning half the input energy. The system then coasts the 'stator' back up to TDC whereupon the clutch disengages and the cycle repeats.

Hence we have a fairly-ordinary motor, in which all of the counter-momentum is being sunk to gravity.

The motor is controlled for 'acceleration', and a quick'n'dirty feedback loop is applied by metering the green 'stator' weight's acceleration, and feeding it back into the motor's 'acceleration' field, multiplied by the "Inverse Acceleration Multiplier" of "-3". Note the RPM's in the top-left corner - you see the weight's speed is kept more or less constant thru each descent, while the wheel is accelerated by the corresponding counter-torque.

Inevitably, the efficiency tracks ½mV². The reason for this is simply the natural decrease in the "time spent gravitating" each cycle as RPM's increase, and thus the shorter each cycle period gets.

On the one hand, the system is successfully "dragging itself around by its own bootstraps" - no torque is applied to the outside world at the axis, for example (though counter-torques are being earthed via gravity) - it's a mutually self-accelerating system, a rise in momentum in an otherwise closed-system of masses interacting about a common axis.. so seems to come very close to bearing all the hallmarks of an angular N3 violation...

..except it cannot gain energy. So, not a meaningfully 'effective' N3 violation, by the only metric we care about.

Like i say, what's going wrong is the ever-decreasing per-cycle momentum yields. The amount of angular inertia is not changing, hence the amount of work / load applied to the motor is not rising with velocity.. However there's simply less time per cycle for that work to produce momentum, as speed rises.

Thus perhaps the only value in the above simple failure is to highlight and underline this fundamental constraint..

So the burning question becomes, "how do you produce constant momentum per cycle, in spite of rising RPM's?".. because if you can do that, in precisely the same manner as the above sequence of "reactionless accelerations & subsequent inelastic collisions", then the efficiency does not track ½mV²; on the contrary, if we can maintain constant per-cycle input energy and constant per-cycle momentum yield, then we create a divergent inertial frame, and efficiency rises with velocity..

..for instance, the minimum energy that can be paid for 1 kg-m/s or 1 kg-m²-rad/s is half a Joule (0.5 J), so if we can maintain that for say, five cycles, then we'd pay 5 * 0.5 J = 2.5 J total input energy; for a pair of 1 kg inertias now moving at 2.5 m/s, they'd have a KE of 6.25 J, hence we'd have an efficiency of 260%.

If you chew over these points carefully, i believe you too will come to the conclusion they're inherently irreconcilable - we cannot attain mechanical OU if the momentum gain principle is sychronised to external coordinate space!

..it has to be asynchronous to the wheel angle / rotation!

Thus a full 'cycle', from the perspective of the momentum-gain mechanism, is however many degrees it takes to impart that constant momentum, despite rising RPM's!

In short, our 'window of opportunity' for 'doing stuff' inside the wheel - the 'period' of our mechanisms - need not, and probably should not, be inextricably tied to any external aspects of 'angle' such as vertical / horizontal orientation or even limited to 360° - at least, not if it's sourcing our momentum, anyway.

This was my last 'Eureka!' moment, Sunday bath-time.. s'got me all excited again. Finally, the breakthrough i'd been looking for.. The 'stumbling block' is the false constraint of the artifice of Cartesian coordinate space, and our natural N3-based perspective of what constitutes a "cycle"... but in a divergent FoR, such predispositions must go out the window.. a truly 'effective' angular N3 violation means that in the successful system, a "360° cycle" is using more angular displacement than this in our static, external FoR! And considerably moreso, the faster it gets..

So Bessler probably couldn't've been 'milking' momentum from gravity, as i'd been investigating - that's probably an inherently-impractical pursuit, since the gravity vector is static, and can't accelerate around with the system..


I think the breakthrough experiments could be very simple:

W/ gravity off:

• consider a rotor, with two smaller rotors mounted on either side, in balance

• these two smaller ones have equal MoI's

• one of them is a 'variable MoI' - its mass can be pulled into its axial center. It may be comprised of two opposing radially-sliding masses, also mounted on bearings to remain free to rotate about their own axes.

• apply equal torque to each smaller rotor, spinning each in opposite directions, thus cancelling each other's counter-torques, and imparting no 'orbital' counter-momentum back to the central axis.

• now pull the vMoI masses into their axial center, effectively destroying their share of angular momentum. This action's reactionless, applying no torque back to the central rotor. This results in the vMoI spinning fast, but with negligable MoI, or thus, momentum.

• brake both smaller rotors back to stationary; the vMoI has negligable momentum, so the central rotor and thus whole system is spun up by decelerating the momentum imparted to the other, unmodified small rotor. Thus if each were initially given 1 kg-m²-rad/s, the net system momentum has risen by this much

• we've paid for motor torque * angle. This metric is speed-invariant - the energy cost's the same, regardless of the initial speed of the central rotor.

Spinning up the smaller rotors in opposite directions will always cost the same workload, regardless of how high the 'orbital' rotation speed gets. They always begin stationary relative to the central rotor, and are spun up to the same relative speed each cycle. Thus input torque * angle is constant.

• we've also done work against CF force, destroying half our momentum. Since axial CF is more or less invariant of orbital CF, this cost, too, is more or less constant. It'll start out low, because the vMoI will be the 'counter-rotating' rotor (we're destroying counter-momentum), however as RPM's pick up, it'll initially be counter-rotating relative to the external frame, hence say if orbital speed is 1 rad/s and each smaller rotor's spun up to 1 rad/s in opposing directions, then one of them's at a real speed of 2 rad/s whilst the other's no longer rotating at all, hence its axial CF force is nil.. type stuff..

Point is, that if we can simply keep piling on 1 kg-m²-rad/s each 'cycle' (regardless of how many degrees of rotation that may encompass), and our input energy isn't squaring up with velocity... this should inevitably result in OU.


So even if the energy cost's 1 J of T*a plus 50 J more work done against CF force, that's still a constant input energy of 51 J per cycle... and at some point, past some critical orbital velocity, another 1 kg-m²-rad/s of angular momentum's gonna cause a greater rise in rotational KE than the 51 J it costs to produce..

..this is what i'll be testing next in simulation.

[Johndoe2]

Now that is a Fn genius post Mr vibrating!!
I would rep you if I could!

It's going to take me some time to anakyze and digest everything you said though. From a quick read though excellent post !

[Johndoe2]

After a second read I might have gotten too excited but it's still a great post.
Now from what I think I read angular momentum is based of of the right hand rule. Have you tried using one wheel on the front and one on the back side of the wheel then you could spin them up in the same direction and get a cumulative affect from the torque instead of them canceling each other out?

[MrVibrating]

@johndoe

Yes! Tried it yesterday, after following the same logic (in the bath, as usual) - use TWO vMoI's and make 'em large, with narrow orbiting axes (ie. close to the hub) to optimise the relative orbital / axial MoI's (and thus OU threshold velocity). So placing them on opposite faces of the wheel prevents them interfering with one another.

Then, as you say, simply spin both in the same direction - so applying two 'counter-torques' to these two large orbiting axes, which in turn applies an equal net torque back to the main, orbital, axis itself. Presto, it's already bootstrapped itself into rotation.. then with the vMoI's coasting freely, pull their masses into the centers of rotation, insta-killing all the orbital angular momentum they had, and slam on the rotational dampers (brakes, basically); as expected, all the 'positive' momentum's conserved, all the yucky counter-momentum's destroyed, net system momentum duly rises each cycle..


I was originally over-complicating it! Just generate the main-system torque directly from the counter-momentum you're gonna destroy, duh.

The sim i was using at the w/e is simply the last one i was playing with here - two vMoI's on a central rotor; exactly the same components, just with a different synchronisation of the same actions. As such they're not polished enough to show yet, but you've already perfectly got the idea, evidently..

..besides, i'm still using massless linear actuators.. given that the whole scheme depends upon rendering an effective N3 violation, this is an obvious cause both for contention, and inviting false positives.. more on this in a bit..

[Johndoe2]

Awesome!

[MrVibrating]

..OK, taken a refresher on 'destroying angular momentum' over the weekend, and for it to work, certain criteria have to be met:

• The vMoI masses have to remain free to rotate about their own axes

Thus as they cross the threshold (event horizon? eek!) into the center of rotation there is no means of transference or translation of their orbital angular momentum into axial angular momentum; instead they arrive at dead-center not spinning, and completely stationary... thus whatever orbital angular momentum they had is kaput.

• The vMoI masses have to constitute all of the radially-translating mass

..in other words, the most amount of 'mechanism' or excess, non-radially-translating mass we want, ideally, is a lightweight cord; so pulling the cord yanks 'em into the center, type stuff.

The reason for this is to prevent the angular momentum from being conserved; otherwise, as the vMoI mass is pulled into its center of rotation, its acceleration will also impart momentum to any other non-radially translating mass it's connected to. Equally, this unwanted accelerated mass is dragging back the vMoI masses' speed, so again, limiting the amount of angular momentum they can honey-trap into the center..

Basically, back in my "vanishing point" thread when i first played with this effect, i was simming with massless linear actuators.. but in real-life, they have to have some mass, and however little it is, the vMoI retraction is going to attempt to accelerate it up to whatever speed's required to conserve all of the angular momentum we're trying to destroy..



So this second point's a bit of a head-scratcher, right? At first i was thinking about frayed bits of string and how much momentum they might be able to bleed off to aerodynamic drag.. (ie. if they were rotating really fast, like!) Desperate eh?


Then it hit me:

Per MT43 - follow a spiralling trajectory back in!

The logic's compellingly simple:

- moving orbiting mass inwards generates positive torque - they wanna speed 'emselves up

- if we used a cord to pull the mass into the center (ie. a 'massless' linear actuator), its trajectory will describe a spiral

- pulling it in at constant speed will describe a tightening spiral; it'll be covering more angular distance - and eventually, whole rotations - the closer it gets to the center

- thus pulling it in at an accelerating radial velocity will limit the amount of 'curl' on that spiral.. and so we plot a shorter, faster, shallower curved trajectory into the center

- so in principle, we can identify (calculate and/or measure in simulation) the ideal curve to move inwards at a given ideal radial acceleration rate, for a given ideal RPM.. in other words, design a mehanism that will be optimally efficient (in terms of destroying a maximal amount of counter-momentum) at a specified RPM range


..so instead of moving the vMoI masses inwards on a direct, radial trajectory as i normally would, they will now follow a curved 'rail' into the center, the curvature of which precisely matches the path they would've taken themselves, free of any guidance..

..hence they will not accelerate the wheel - only themselves - and likewise, they won't be slowed down by it either.. thus arriving at dead-center with all of their orbital angular momentum perfectly intact, only to be comprehenseively annihilated a split-second later. Momentum 1: Counter-Momentum: 0

Like i say, this ain't cheap to do either - there doesn't seem to be any getting around the CF workload; we want a high CF load; as high as it needs to be to kill all counter-momentum. Anything reducing the CF load would also necessarily be exchanging momentum, which we want to keep isolated and trapped on its spirally descent into oblivion..

These outstanding points aside.. initial tests are positive; the per-cycle input torque * angle is constant, the per-cycle momentum yield is also constant.. the CF workload has some variation and needs battery testing (ie. pulling integrals from an RPM range) - but in principle this looks like an inherently-OU process.

Another point that came to mind this evening is that, suprisingly, this scheme could in fact be sequenced to external coodinates / angle, and thus a per-rotation basis, since it is not speed-dependent!

Think about it - all we're doing is scooping up unwanted orbital counter-momentum, lugging it back into the central pit and dumping it there... then heading back out to grab more. The bucket size is fixed by the relative speed rise and change in radius, which is constant and not time-dependent... so the same amount of momentum's destroyed each time, regardless of speed, at least, within its designated RPM range.

So we could aim for a wheel that was most-efficiently destroying its own counter-momentum at, say, 1 rad/s - inside, we'd be applying torque to the main axis, against one or more large vMoI's in orbiting axes - having optimised the relative orbital / axial MoI's for a low ratio, and thus minimal cycles to OU. So, motor activates, whole system is torqued one way, vMoI is torqued the other, then the motor's deactivated, and with the vMoI now coasting its masses are pulled inwards.. following a curved slot, the curl of which perfectly compliments their angular & radial acceleration into the center with zero torque applied back to any non-radially-translating mass. Et voila, all counter-momentum for that cycle is destroyed. From there, move them back out in a direct radial path and repeat the cycle: applying torque to the main wheel / central axis by counter-torquing the internal vMoI's, and then killing the counter-momentum and thus conserving the full compliment of its better half, in our otherwise-closed system of masses interacting about a common center..

That's the plan for now, anyway. In simulation i guess the thing to do will be to set a wheel rotating at 1 rad/s, then try tracing or plotting the shape of the spiralling trajectory taken by a 1 kg mass pulled inwards by massless linear actuators, relative to the wheel's frame of reference. Since accelerating into the center seems optimal for reducing the track curvature, but inevitably means KE losses to impacts, there'll need to be a compromise; the CF workload's the same regardless, but radial KE losses obviously square with radial speed.. i guess comparing a 1 m/s constant-radial-speed vs a 1 m/s² radial acceleration would give a good baseline for how radial acceleration affects the curve shape..

Will update as & when this goes anywhere..

[MrVibrating]

..just for a teaser, here's a rough draft from yesterday:



The motors apply 1 Nm until the vMoI's reach 1 rad/s relative velocity - given that orbital to axial MoI's are 2:1 in this example, this accelerates both to 0.5 rad/s in opposite directions..

..upon reaching that speed the motors immediately disable, and without pause, the actuators kick in, dragging the masses into their centers of rotation..

..upon arrival there, the actuators also disable, and the rotational dampers are activated


So instead of sequencing these actions to the rotation or external coordinate space as i normally might, here the activation / deactivation conditions are all mutually interdependent and so, self-organising, regardless of system angle or RPM... so a 'momentum gain cycle' can run asynchronously of the angle / rotation number relative to the external reference frame.

Other caveats:

- again, this is using notionally-massless linear actuators. See relevant points in previous post; bottom line, for now, is that it's starting out from a presumption of magic.. hopefully spiralling trajectories will obviate the need for massless actuators, but until then, they're unpolished unobtanium..

- the masses aren't currently hitting the 'exact' center; it's a rough draft, so they only land within 0.001 m of dead-center (this precision can be significantly improved) - obviously, if they're even slightly off-center when we hit the brakes then we'll only be annihilating positive momentum with counter-momentum..

- although the torque * angle never increases despite ever-rising RPM, you can already see that the CF workload spikes as the axial RPM's shoot up.. Remember, though, that conservation of momentum is not a matter of energy-dependence! It's supposed to be inviolable no matter how much energy you throw at it.. and with a constant per-cycle momentum yield, there is always some threshold 'unity' velocity above which that next consignment of momentum will cause a greater rise in rotational KE than its cost of production..


-- it's right dirty, if it works; every bit as devastating as any momentum-from-gravity schemes i've considered. We're essentially creating new momentum, from nothing, every time we destroy its associated counter-momentum..

..but what we're 'creating' is the definitive conserved property!!! Where's all this momentum gonna go, then?

So, if this even works, it has to be run in mirrored pairs - only ever creating or destroying equal opposing momenta!

If this DOES work (and frankly when put in these terms it seems so unlikely as to be idiotic) then the moment one of these cycles is run unbalanced, in the real world.. the net momentum of the universe is no longer zero! We'd've imparted a net spin!

So let alone what it might mean for the fate of the Earth, is, once again, that of the entire cosmos. Do we really want to be at the axis of an entirely unprecedented angular acceleration of the whole universe? And more to the point, where's all this momentum coming from and going to, in relation to the Higgs field? Likewise, might not our mechanical energy gain be a conserved loss to the vacuum energy density underwriting the strength of the Higgs interaction? In which case we're back to 'big rip' scenarios, destroying the universe from the bottom up..

Either way, the Christmas flood of 1717 - and its smaller follow-up a fortnight later - still align all too neatly to Bessler's winter 1717 demonstration of his largest, most powerful and longest-continually-running wheel.. which was running alone and unbalanced.. continually generating fresh momentum in a statorless wheel.. and so permanently altering the planet's resting momentum state!

So, yeah.. the mere consideration of such weighty consequences from the sadly deranged act of waving a few masses around should probably predispose one to a certain degree of circumspection, here.. whole thing's crazy talk if you ask me - momentum is so conserved, you can't just selectively 'destroy' it, no way, not allowed. Besides, Wikipedia says it was the maid wot dunnit.

[MrVibrating]

Knocked up a simpler rig in which the central rotor is reduced to a simple beam - one end's pivoted to the wall, the other holds the orbiting rotor. The actuator's now attached to the beam, outside the rotor, and pulls the mass via a cord run through the rotor axis. This eliminates any magic - the actuator can have as much mass as needbe, since it's no longer subject to the angular accelerations it's causing.

Similarly, the 'vMoI' has been reduced to just the weight on the other end of the cord.. so nigh-on all of the radially-translating mass is free to accelerate unhindered, nitro-over-the-cliff-edge.. as angular momentum just kinda flares outa existence..

I misstated the requirements for success previously; it is not that 'all vMoI mass must be radially-translating', but more specifically, that 'all mass that is subject to inertial torque must be radially-translating' - the point being, not to exchange with any other body the momentum we wish to destroy; isolating, trapping and killing it, without allowing it any means to escape, such as by accelerating some other inertia.. basically, if it can't accelerate anything else, and also can't translate itself between orbital and axial axes.. then adios, mr so-called N3-for-rotating-systems..

The following traces are taken from the PoV of the black circle, which is rotating steady at 1 rad/s (but otherwise mechanically inactive, merely something to attach the camera to) - so if you were standing on the system as it spun, these are the paths you'd see the weight take if it was pulled inwards at:


1 m/s constant radial velocity



1 m/s² radial acceleration



10 m/s² rad accel (final rad vel into center = 4.4 m/s)



50 m/s² rad accel (9.8 m/s slam-dunk):


..would be wasting a fair bit in impact energy at those speeds tho.

Still, the idea would be, either pull the mass inwards thru a hole in the axis as above, thus always allowing it to find its own route into the center whatever the RPM, or else, construct some kind of rail or slot with one of these exact curves tuned to a given combination of angular and radial velocities, thus engineering a 'sweet spot' RPM range for optimal destruction of counter-momentum.

Outside that optimum RPM range, the inbound mass will be applying some torque back to the rotor via the slot joint, but at its ideal RPM the mass will come all the way in without any angular interaction at all with the rotor; crucially, not accelerating it, or thus, being decelerated by it either.. thus achieving peak efficiency at a desired RPM, and a coasting speed well above that.. which would be consistent with Bessler's claim that "attaching loads improves performance".

Similarly, we might suppose that if such a system's peak efficiency arose at, say, 26 RPM, yet it also needed to produce some energy in order to get up to those speeds from a standing-start or light push, then the upper end of that envelope would lie in the ~58 RPM range, even though it was creating or destroying no more momentum at that speed than it did at 1 RPM..

This peculiar claim of 'reactive efficiency' has always struck me as potentially telling of the nature of the exploit, and an 'optimum momentum-killing RPM' would seem a neat fit..

I guess the thing to try next is testing an actual slot mechanism - however it's obviously not going to be able to replicate the intricacies of the tighter end of the spiral, which will presumably be where momenta get exchanged anyway - maybe the radial velocity can be fine-tuned to help mitigate that..

Can't say i'm too hopeful at this stage, but if we can even take out a little counter-momentum this way - and so create a corresponding amount - in the real-world, we'll have a fixed-rate energy cost of momentum, and thus beyond some threshold speed, a coupon for discount KE..

Also wanna take a refresh on what happens when the process is reversed and masses are dropped outa the axle, because if that likewise increased momentum..(!)

[MrVibrating]

I took a closer look at this so-called 'vanishing point' - the supposed threshold radius below which an orbiting mass was effectively stationary at the exact orbital center.. and found that there is none. Instead, if no loss mechanisms are present, then it is effectively impossible to pull an orbiting mass into its exact orbital center whilst it remains free to rotate about its own axis!


The most you can do is reduce the radius to an infinitesimal degree, thus raising orbital velocity - and KE - to infinity. Even at this stage however you'd still have exactly the same amount of orbital angular momentum you began with.

If however loss mechanisms are present, then we ultimately only seem to have two options - friction between the rotation and the environment (the air and / or the earth, basically), or else, friction between the rotation and the cord being pulled through the axis to pull the mass inwards. In short, if the system is able to shed momentum or energy somehow, then CF force, and thus input energy, needn't go to infinity.. IOW, there would be some threshold radius below which the mass had meaningfully moved into the exact center, and thus ceased to possess orbital angular momentum..

..obviously however, if it was due to friction between the axial and orbital axes, then momentum's gonna be conserved (as we all know, friction can't violate N3).

Which leaves friction between the axial rotor and the environment. I suspect even then, that atmospheric drag, for example, won't violate N3; any negative torque it applied to the axial rotation would still induce a corresponding counter-torque at the orbital axis, thus shedding equal momentum of both signs.

Being able to preferentially shed momentum of one sign only to some kind of entropic / dissipative loss mechanism could yet be promising... i can't think of one yet tho.


For now, here's a short graphic of a system in which the orbital radius has been reduced all the way down to microscopic scales:



This began with 1 kg at 1 m radius and 1 rad/s, so 1 kg-m²-rad/s of momentum at 0.5 J RotKE. The orbital radius was then reduced at 1 m/s radial velocity, progressively pausing the sim and raising the sim frequency whenever the momentum meter began to waver..

..so what you see there is the 1 kg weight orbiting the end of the blue pole at up to:

• Orbital Radius = 41 microns

• Orbital Velocity = 56 trillion RPM

• Orbital RotKE = 293 megajoules

• Sim Frequency = 100 megahertz

• Orbital Angular Momentum = 1 fucking kilogram per meter^2-rad/s

..mug's game, eh - the radius is already down to phonon wavelengths; in R/L this thing would be buzzing with X-rays.. damn momentum ain't going nowhere..

So, there is no 'threshold' radius below which RPM can no longer compensate reductions in MoI - orbital angular momentum is fully conserved as far down as we care to accurately measure. In R/L, the cord would snap, or else friction would square up with velocity and prevent CF forces from ever getting so high in the first place; maybe the mass would slide neatly into the exact center, using finite input energy... but friction would ultimately mean that inertias in the axial and orbital planes were exchanging momentum equally in each direction..

I'd love to see it actually tried in the real-world, provided the rig was even in with a chance at the outset - so just using a strong-but-light cord to pull an orbiting mass into the exact center whilst leaving it free to rotate about its own axis.. i'm skeptical it'd ever deliver clear repeatable momentum yields tho..

Killing counter-momentum remains a potentially killer exploit, of course.. i'm just not sure anymore that this method can actually do it, as-is..

A new approach is needed, i think... been trying to come up with some use for dropping masses outa the axis instead.. all it seems able to accomplish tho is raising the amount of inertia a given momentum's divided into, thus reducing the velocity and KE accordingly.. IE. big loss with no apparent benefit.. might yet try the 'spiral track' idea - maybe it could still produce tantalising results, who knows.. just being able to reliably kill some counter-momentum would still be a winner.. ain't gotta be full cancellation..

[MrVibrating]

..OK consider a large rotor with two vMoI's attached, as before:

• begin with the vMoI's locked to the central rotor, which is rotating at 1 rad/s; thus all three are at 1 rad/s absolute, and stationary relative to one another

• program the motors and actuators such that whatever the current RPM, when the vMoI's are stationary relative to the central axis and their masses are fully extended, counter-spin them back down to zero absolute RPM: this transfers their AM over to the central axis..

• ..at 0 RPM abs., retract the vMoI masses into their centers, against zero CF force - so essentially, for free..

• ..now drop the clutches / rotational dampers etc. - et voila, we've completed an asymmetric inertial interaction and gained unidirectional AM..

• ..with the vMoI's now stationary relative to the central axis and everything rotating together at equal RPM, re-extend the vMoI masses and let the cycle repeat..


This seems much more practical - circumnavigating the need to do any work against CF at all (let alone infinitely-rising CF) - as RPM's build up, the motors will have to do ever-more work to fully de-spin the vMoI's in the opposite direction, however the torque * angle always restarts from relative stasis between the two inertias, hence we keep resetting our 'V²' multiplier on the input energy cost of accumulating momentum (per rotKE=½MoI*RPM²); so, the first kg-m²-rad/s of each and every power stroke only costs ½ J, and the second only costs 2 J, 4.5 J for the third etc. etc. following the standard formula. Hence this should still mean we're paying significantly less for our AM than its resulting RPM² value.

Will give it a shot later..

[MrVibrating]

..quick recap on the basic logic of mechanical OU:

• a momenta's given distribution of inertia and velocity determines the only KE value it can have, by definition of the term; there's no such thing as 'excess KE', it's an inherently contradictory, oxymoronic concept

• hence the only physical embodiment of mechanical 'OU' possible is actually an under-unity input-energy-cost-of-momentum; ie., paying less than its KE=½mV² value.. even tho the resulting momentum, by definition, still holds that standard KE value


• what the KE equation says is that for a given magnitude of inertia, momentum gets more expensive the more you buy, and hence the faster you go

• Q: "..but if motion's relative, and speed is also relative, then who's to say how fast a given inertia's moving, or thus how much KE it has, or equally, how much energy/work it costs to accelerate?"

• A: Newton's 3rd law, which ensures the net momentum of the universe remains constant (presumably zero) by tempering every change in momentum in one direction with an equal opposite change in the other; this enforces the equivalence of KE from any given reference frame..

• ..thus to buy cheap momentum, we need to cause an effective violation of N3.. gaining momentum in a closed system of masses interacting about a common axis, without torquing the system against the outside world (as by a stator), since our speed's going to rise relative to it, and with it, the energy cost of buying more momentum that way..

In short, the source for our momentum has to rotate with the system - like Bessler said, "in a true PMM everything must, of necessity, go around together - there can be nothing involved in it that remains stationary upon the axle!" - so each 'asymmetric inertial interaction' we're aiming to gain momentum from has to start and end at 'stationary' relative speed to the central axis, the whole system accelerating itself by its own bootstraps..

To be successful doesn't necessarily require a completely speed-invariant energy-cost-of-momentum or yield; the efficiency can deteriorate with speed, so long as it doesn't quite track ½mV².. any margin will do..

[MrVibrating]

OK last idea was stupid, basically reducing to - "pay input energy to transfer axial momenta to orbital axis, then share it back with a collision; net change in system momentum = zero, all input energy wasted", ie. 'a heater', duh.

Change of tack; here's a basic demonstration (back from Dec '15) of gravity being used to invert the sign of counter-momentum:



• so we have two equal angular inertias, one of which is subject to gravity, whilst the other is not

• a brief torque's applied between them, imparting equal opposite momenta

• however the gravitating one gets reversed by gravity - it gets up about so high, stops, then heads back down the way it came..

• ..upon its return to 6 o' clock BDC, both momentas are now at equal sign, magnitude and location

So this end state is identical to the result of an effective N3 violation - momentum and counter-momentum are in the same place at the same time with the same speed and direction. With them in relative stasis like this, we could apply a second impulse, again starting from the bottom of the 'V²' multiplier in the KE=½mV² equation, thus paying only ½ J per kg-m/s of momentum - the minimum price - in spite of our previous purchase at that same rate..


Remember, this is the key to mechanical OU: breaking N3 to game KE=½mV² - specifically the 'V²' multiplier - by scamming the special introductory base rate of ½ J per kg-m/s. That's why "in a true PMM, everything must go around together". Statorless or bust. No such thing as "excess KE", just ½mV²; the real trick is under-unity input energy. Buying momentum for less work than its resulting KE value.


Follow it through, though, and you see the above penduwheel's only good for one cycle - it can't accumulate momentum this way, without the relative speeds - and thus KE's and input energies - between the two inertias rising over succesive cycles, or else the momentum yield decreasing with RPM as per the first rig in the opening post..


And there's the rub - it's only an 'effective' N3 break if it can be cycled without breaking the results; ie. if it has speed-invariance. "Everything must go around together" = a constant energy cost of momentum across some useful RPM range.. so assuming a 75% loss per cycle (as indicated by the Toys Page), 2 J / kg-m²-rad/s, if only at some limited RPM.. basically any deviation between the input energy cost of momentum and its resulting KE value will do, but to get there, we don't want relative speeds to increase between the two interacting inertias. "EMGAT".

So how might we try applying this principle - of using gravity to reverse the sign of counter-momentum - whilst satisfying the EMGAT condition?

Perhaps we could add some other axis, to which we could apply the momentum gains?

So for example a cycle might look something like:

• spend some energy to generate equal opposing momenta

• employ gravity to reverse the sign of one

• knock the combined pair into a net acceleration of some other, shared axis

• repeat, plotting rising KE about the shared axis in relation to internal work done..


My initial approach, of trying to destroy orbital counter-momentum, would've obviated gravity... yet Bessler only ever showed vertical wheels. Ergo, he must've been using gravity to cause an effective N3 violation..

Gravity's speed-invariant - there's no 'terminal velocity', it's a uniform acceleration regardless of speed. However RPM does limit time-spent-gravitating per cycle, as seen in the first rig in post #1; obviously, it's the energy cost of momentum that matters more than the per-cycle momentum yield, and Bessler's wheels were speed-limited, so decreasing yield with rising RPM may simply be an inevitability and incidental to the efficiency in the sweet-spot RPM range..

In short, asynchronous momentum yields aren't the be-all; the objective remains the same, of beating ½mV² on the input energy cost of momentum, by any means possible..

Will see what i can come up with..

[MrVibrating]

New idea: Whereas previously i'd tried variations on paying CF work to buy momentum from gravity via an up vs down time/height differential - finding that, predictably, the rising cost of the CF work with increasing RPM caused the efficiency to track ½mV² - how about flipping it around, and instead, using that time/height differential to sink counter-momentum to gravity?

So, as before, apply a motor between two angular inertias, torquing each in opposite directions. Then, whichever's designated the 'counter-momentum', upon that rotor we increase its MoI whilst a weight is rising; raising MoI applies a negative reactionless torque, slowing down the ascent, and so increasing the 'time-spent-gravitating' - and thus momentum shed to gravity - by the rising weight. Alternatively, or additionally, we could in turn decrease MoI again, whilst the weight's now descending; applying a positive reactionless acceleration that speeds up the weight's descent, and so decreasing its time-spent-gravitating - and so momentum gained from gravity on the way down..

..the net result is that rather than sourcing reactionless momentum from gravity, we're now sinking counter-momentum to gravity..

..as before, this effectively creates an excess of 'positive' momentum, by eliminating a corresponding negative quantity..

..except, whereas before, we had to pay work done against CF force to buy momentum-from-gravity, now the 'negative KE' of this counter-momentum does work for us, against CF force, in destroying itself along with its corresponding momentum; the way i'm looking at it, we could spend say 1 Joule generating two lots of ½ J of RotKE in opposite directions, then with one of them, we can use output CF work to spend that half-joule, burning it off to gravity along with its momentum, leaving us with the other half-joule of positive momentum, which can in turn be shared back between both rotors via a collision / clutch / rotational damper etc., eliminating a further 50% of the remaining input energy..

By my reckoning, this basically destroys 75% our input energy per cycle, which should put us on-track for the 5-cycs-to-OU regime the Toys page alludes to..

Momentum yields will still inevitably drop in line with rising RPM, but what really matters is that the energy cost of the momentum being gained doesn't increase in step with ½mV²..

This is what i'll be testing out next..

[MrVibrating]

"..the weights themselves are the PPM.."

"..a motive force they must continue to exercise so long as they remain outside the center of gravity.."

Never previously resolved that last clue, until now; he's referring to the OB / GPE system, which exploits speed variations to rinse unidirectional momentum from gravity.

That is, fast rise, slow drop causes the weight to 'soak up' more momentum from gravity on its descent than it sheds back when rising again, extracting a net gain in momentum, which is the very stuff of his 'motive force' / 'excess impetus'..

The 'weights themselves are the PMM' since they embody the momentum gains - it's their mass * velocity that substantiates it.

Maybe the only reactionless acceleration / N3 break required is that of the OB / GPE system, then? This applies no counter-torque back to the axis, it's unidirectional momentum, and we only need one such example in the loop.

This would mean the second part of the mechanism deals with harnessing the KE gains to power the radial lifts causing that OB torque.

In principle, such KE gains could be harvested using a CF workload of some kind.. that is, an angular momentum gain has an associated rotational KE gain which can be harnessed via a corresponding gain in CF force over a given radius.

The main design specification is simply the input energy / 'work done' cost of momentum gains, versus their resulting KE value in the external reference frame; engineering a disunity between PE=F*d versus KE=½mV².

[MrVibrating]

dichotomy:

Either:

A) the time/height momentum asymmetry is applied to source momentum from gravity, or else

B) it is applied to sink counter-momentum to gravity

..for example, lifting weights by rotating them upwards, whilst dropping them radially, sinks momentum to gravity, so instead of using your basic OB scheme to create angular momentum, we could try applying it to destroy counter-momentum caused by some other basic inertial interaction (such as from motor torque or whatever).


Furthermore, either:

1) the momentum is being raised against some other internal inertia that nonetheless co-rotates coaxially with the system, hence the requirement for collisions

OR

2) the thing rotating with the system against which momentum is being raised is some kind of active counter-momentum-sinking process such as the ones mooted above - so a weighted vMoI or reversed OB system, type stuff, in an orbital axis about the main axis

..so in other words, either we're dragging our stator around with us in a 'friction-motor' type action - launching off from it without displacing it and then colliding with it to share back the momentum gain..

..or else we're using an orbiting, spinning system to actively 'destroy' counter-momentum as we go around.



Interesting alternatives to fathom out. Again, the objective remains buying momentum at an energy cost cheaper than its resulting KE value, so maybe one or other of these options will offer the better prospects..



Also been thinking a bit more about inertial frames - crucial as they are to analysis of B's wheels; thus far i've been describing the internal reference frame of the wheel as a 'divergent inertial frame'..

..the rationale being that gaming ½mV² - ie., repeatedly paying just ½ J per kg-m²-rad/s in spite of RPM's - means effectively accelerating the 'rest' frame of whatever forms the 'stator' against which the momentum's being applied. So mechanical OU pivots upon a 'pseudo-rest frame'; one that acts like it's at rest, and effectively is at rest relative to the rotating system, yet nonetheless is accelerating with it.


However i suspect that by further refining and clarifying these issues in terms of the implicit respective FoR's, a better, more useful understanding's possible..

For example, going back to the large rotor with two smaller ones attached, and spun up/down by motors:


• from the FoR of the orbiting motors, the torque * angle is invariant of the RPM, therefore they're in an inertial frame; on an OU wheel they'd be in a divergent inertial frame

• however, if we make those small rotors vMoI's, then from their linear actuators' FoR, there is axial CF force, therefore they're in a non-inertial frame

• since the orbital CF force mutually-cancels / sums to zero over complete cycles of both axes, it is effectively also an inertial frame, and divergent in an OU wheel


So we've got a non-inertial frame, sandwiched between two inertial frames..

The key hurdle, thus far, has been the CF workload's rising energy cost of buying this unidirectional momentum from gravity, as RPM's increase. It doggedly tracks ½mV². Frustrating, since we're ticking all the other 'right' boxes for success..

But viewed in the above terms, you can surely see what i'm seeing? We need to somehow fix or substitute the CF workloads such that they're effectively also in the diverging inertial frame..

..another instance where spiralling radial trajectories, rather than direct ones, might be useful; in making radial translations without incurring work against CF in the first place..

..i've already tested examples of 'changing GPE without changing MoI', thus demonstrating the viability of harvesting momentum from gravity without performing any work against CF at all (can post examples if anyone's interested); the per-cycle momentum yield still drops off inversely to RPM of course, enforcing ½mV², but in terms of FoR analysis these systems are also effectively inertial and thus able to diverge along with the main system FoR..

So: an orbiting 'vMoI', against which the main system axis is torqued, absorbing the counter-momentum and then dumping it to gravity by using a reverse-OB cycle that changes GPE without changing MoI, or, thus, incurring any work done against CF force. All three FoR's there are inertial (two angular, one linear), so should diverge together; input energy is torque * angle on the orbiting axes plus GPE, output energy is rotKE on the central axis. I've already simmed all the parts individually so it's just a matter of combining them into a single system.

As noted, the momentum yield's still inevitably going to decline as rising RPM's on the central axis squeeze the time available for offloading counter-momentum to gravity each cycle, however the energy cost of that momentum is all that matters, and here, its input dimensions are in inertial FoR's, so do not escalate with rising RPM like CF forces do..


Will give it some more thought, but this seems like conceptual progress at least..