Decoupling Per-Cycle Momemtum Yields From RPM

[MrVibrating]

..roll with me a sec:

• if these diametric weight levers ARE part of the working mech, then they've gotta activate whilst paired in order to loop over a 180° arc

This would mean that if they WERE responsible for producing the bangs heard on the descending side, why wasn't a corresponding bang heard from the other lever-weight on the rising side?

In other words, if there's any use at all from these long levers, then something happens differently between 180° arcs - ie. when falling on the descending side, versus when rising on the ascending side.. and this difference, whatever it is, must be responsible for rectifying a net momentum gain / and/or sinking counter-momenta to gravity..

But as for what this difference may be, your guess is currently as good as mine..

[MrVibrating]

...just in time for the weekend; i may have found an edge..


- as noted previously, these diametric weight levers, by dint of pivoting, are actually angular inertias

Sure they only move a few inches up and down, a motion which, especially when considered as a pair, seems more substantially linear than angular; nonetheless, angular inertias they are..

- so if one moves 'clockwise' (albeit by the few degrees of rotation available), and the other, anti-clockwise, whilst the whole system is rotating in one or other direction, then this net rotation of the system adds and subtracts to those of the respective diametric weight levers..

- IOW, one of them is accelerated, the other, decelerated..

If the levers were only operated one at a time, individually, then their accelerations / decelerations would be inducing corresponding counter-accelerations of the wheel itself, per N3.. so no momentum advantage would present itself.

However when operated as a pair, their respective counter-torques mutually cancel; so one of them is temporarily gaining momentum, equal to which the other is losing..

..thus, what if the one that is heard landing on the descending side is the accelerated one, and it somehow 'knocks' its momentum gain back into the net system..?

..meanwhile the other lever does not collide (no bangs heard from the ascending side), hence does not commute its loss back to the net system..?


I know, i know - how, though? This doesn't seem a very consistent notion at all, does it? Sure, one briefly gains momentum, the other loses it; but how to rectify / consolidate that into a net gain in system momentum?

The only possible window of opportunity here would have to be opened by gravity..

So, no idea how this will pan out, but i'm gonna do some investigative sims just to see what opportunities might present themselves here.

Christian Wolff seemed certain that the momentum gain principle was inherent to the action of the weights heard landing on the descending side of the wheel.. if those weights were actually these diametric weight levers - and given that they're also likely further accelerated / decelerated by that radial GPE drop connecting via the scissorjack in conjunction with their intrinsic gravitation - then this has to form the core of the momentum gain mechanism, and so this is what i intend to spend some time playing with..

[agor95]

After my initial read you may be correct.

However I generally view things pictorially and with supporting mathematics.

Then supported with a text description to supplement the above.

Regards

[MrVibrating]

Here's the interaction:



..basically identical to my "Mt 40-ish" doodle, except now the weight levers and radial GPE both drop together in the same direction, instead of levering one another in opposite directions.

As you can see it's perfectly useless, as you'd expect. Just dissipates input energy.

And even if it were powered, to maintain energy, it still couldn't gain momentum.

All expected... the question was, and remains, what opportunities might there be here for gaining momentum?

The whole objective is to pay GPE, to buy momentum.

So, either there's some further detail i'm missing, or else there's no way this type of interaction can accomplish that.

Yet if that's the case, then why does so much of MT seem to be reiterating this very interaction..? Either it's all a big red herring, or i'm missing some further little refinement that would turn this into a successful GPE-for-momentum trade..


ETA: i've used that little white lever in place of a scissorjack, same basic function at a fraction of the complexity..

[agor95]

You can always put two of these together at 90 degrees.

[MrVibrating]

Yes sir, you're correct...

MT40 of course does show us that the system (of the above interacting agents) is also subject to a second pair of radially-translating weights at 90°, thus applying over-balance to the net system..

..however we could simply shortcut that, and apply torque directly from a motor; it wouldn't be reactionless, as OB torque is, but for the purposes of trying to identify a momentum gain principle here, i think 'torque is torque'..

I just don't see how momentum gain is possible from these components under any circumstances.

Consider the only successful principle we've seen thus far that actually does amass a real momentum increase; it depends upon using transiently-reactionless inertial torques (the ice-skater effect) to speed up the time-spent-gravitating during a lift, and / or, equally, to slow down the time-spent-gravitating whilst falling; since gravity is an ambient, constant time rate of change of momentum, shortening or lengthening the period of the 'up' or 'down' stroke of a GPE interaction likewise increases or decreases the time available for exchanging momentum with gravity.

In a nutshell, the working principle (proven and unequivocal) for causing non-zero momenta from closed-loop gravitational interactions is time-variance of the 'up' vs 'down' soak times - the respective period lengths of the strokes, as a function of the quite-arbitrary mechanical speeds of flight of the gravitating mass in either 'up' or 'down' legs of the trajectory, in relation to gravity's constancy of uniform acceleration.

Yet how the flip could that principle be applied here? There just doesn't seem any room for it..


The possible wriggle-room i wanted to investigate this weekend was the fact that, as these diametric lever arms are pivoted, they're actually angular inertias, and pretty hefty ones at that (in relation to the net system MoI, anyway), and hence if activated in opposing angular directions, those angular velocities add and subtract from that of the net rotating system, hence one lever arm undergoes a slight momentum increase, while the other cancels the former's counter-torques that would otherwise be applied back to the wheel, whilst itself undergoing a proportionate decrease of momentum..

..obviously, those two momentum changes are equal and opposite, so no net change was anticipated there, however, note also that in the above configuration that the 'descending' lever arm always lands on the descending side of the wheel; so would seem superficially consistent with the descriptions of where the 'bangs' where sounding from in Bessler's wheels..

..of course though, this is worthless with respect to the balance of momentum; it matters not whereabouts within the wheel the braking torques are applied - instead of landing on the central cross-beam, we could simply brake the lever arms at their pivots instead - it would have exactly the same outcome.

Likewise, the fact that the 'underslung' lever arm does not impact anything, has zero effect on the momentum distributions. It would be naive to expect that the momentum would somehow be 'focused' in the direction of the collision between the upper lever arm and cross-beam; on the contrary, it's not directional at all. Put simply it'd make no difference whatsoever if the 'bangs' were coming from the ascending side, or top or bottom or even dead-center of the wheel..


In summary, there's just nothing here that i can see that can harness the gravity/time differential principle that actually does generate momentum from gravity..

[MrVibrating]

..and yet, in B's wheels, it cannot be entirely incidental that the bangs were indeed emanating from the descending side..!!?

Why would this be, were it not intrinsic to the momentum-gain process?

This was certainly Christian Wolff's interpretation; because it's so pertinent here i'm gonna quote wholesale one of Fletcher's old posts (from this 2016 thread):

http://www.orffyre.com/quotes.html

'...1. To begin with, it would appear to be beyond doubt that Orffyreus' wheel is not moved by any imaginable external force but rather, its movement is due to the internal weights which are applied in a special manner. My reasons for arriving at this conclusion are:

a) I saw, myself, that the wheel began to rotate with speed and uniformity, without any appreciable external thrust or push until it was slowed from outside. Any attempt at fraud from outside was impossible because the wheel bearings were uncovered on both sides and one could see the axle journals turning in their bearings. Upon request, the wheel was moved from its stand and put on another one.

b) Before translocating the wheel, the Inventor who was performing the test for the officially appointed Commissioners, took out the weights and permitted one of them to be touched, wrapped in a handkerchief. He did not allow the weight to be touched on the end, but lengthwise, it felt cylindrical and not very thick. One could hear the weights landing on the overbalanced side, as though they were swinging, from which one can assume that the overbalancing was caused by their impact. Furthermore there is the testimony of the Landgrave of Hesse-Kassel, who is experienced in evaluating mechanical inventions and had seen the internal mechanism of the wheel and ran it for many weeks in a locked room, keeping the keys himself, having personally locked and sealed the doors and windows with his own seal. He testified both verbally and in an officially printed certificate that the movement of the wheel was caused by nothing more than the weights and that it would run continuously unless the internal structure of the wheel was altered.

2. Since it is impossible, according to mathematical proof, for a machine to run continuously by its own force, some matter from outside must contribute to its motion. That matter can not be perceived by any of the senses but could be made use of by people who know nature better. I suggest, therefore, that the weights on the wheel's periphery are attached by rods in such a way that when at rest on the lighter side of the wheel, they can be lifted, but when they start to fall, after the wheel has turned, they deliver a force on impact, acquired during the fall, onto a piece of wood which is fixed to the periphery. In this way, the wheel is put into rotation by the impact of the weights, which can be heard. But the force which drives the weights, does not come from the machine itself, rather it comes from some fluid, invisible matter by which the movement of the falling weights becomes faster and faster. Orffyreus' whole invention consists of an artful arrangement of weights, in such a way that they are lifted when at rest and acquire force during their fall, and in my opinion it is this that he keeps secret. This is also consistent with what Orffyreus says, that anyone could easily understand his invention, as soon as he is allowed to look into the wheel.

3. It is possible therefore, that when the internal structure of the wheel has been revealed, some mathematicians may decide that it is not a perpetual motion machine as there is an additional force involved, namely the unknown substance which applies continuous pressure to heavy bodies when they fall, and which adds to the force of their impact...'

- letter from Christian Wolff to Johann Daniel Schumacher, 3rd July, 1722.

Wolff assumes things because he saw short boards at right angles to the rim. He also says in an earlier letter that other circumstantial evidence supported the idea of weights attached to moveable or elastic arms on the periphery of the wheel. He heard impact sounds.

I conclude, not only from this but also from other circumstantial evidence, that the weights are attached to some moveable or elastic arms on the periphery of the wheel. During rotation, one can clearly hear the weights hitting against the wooden boards. I was able to observe these through a slit.

Under the circumstances his assumptions would be normal. But this was not a normal impact OOB wheel.

We know this because Bessler wasn't overly concerned about recovering wasted energy of sound etc. He even used felt covering in some attempts to quite the noise, but then gave that up. His later two-way wheels were much quieter. When you have low elasticity impacts (less than 100%) then always some energy is lost to structural deformation and heat etc. At 100% efficiency and elasticity it is at very best a Zero Sum Game.

So he gained extra impetus and momentum from some primary action internally, and impact of weights on rim boards was a bi-product of the mechanical processes and a secondary action IMO.

Guys and gals; read that, then read it again!!!


It's not simply the cogency of thought, but its sheer prescience in relation to our modern understandings of CoM and CoE - remember, this is from 1722, before the vis viva dispute had been universally accepted as solved (Bessler's own unfortunately-secret solution notwithstanding)..

..a less erudite mind would interpret such revelations as proof of a CoE violation - the evidence of one's own eyes! Yet Christian Wolff does not leap off that precipice; instead - and most astutely - recognising that "absence of evidence is not evidence of absence"; and thus rendering what must be the earliest-ever description of what we now term "vacuum energy" or ZPE... 300 years before Bohr, Heisenberg, de Broglie and Dirac et al had laid its modern foundations..!

Where any lesser mind would've perceived 'creation ex nihilo', Christian Wolff saw evidence of an energy source 'beyond the senses' - thus implying a substrate more fundamental than the material world we're able to perceive. . to borrow from David Bohm, three centuries hence, evidence of an implicate order lying beneath, and foundational to, the explicate order of the material realm.

Such circumspect rationale is certainly attributable to the philospohy of Leibniz, who likewise concluded that apparent evidence of a CoE violation was, more properly, to be interpreted as evidence direct of an unidentified source..

..in modern parlance, that 'OU' implies not a gain in energy in a closed system, but rather an unexpectedly open thermodynamic system; ie. one that would be anticipated to be closed, but which, obviously, is somehow not..


The symmetry break in Bessler's wheels is, quite patently, the aforementioned momentum / time / gravity differential. This is why "in a true PMM, everything must go around together" (EMGAT) - ie. why his systems were - and had to be - statorless. It wasn't 'pro forma' (for appearance's sake only) - ie. to maintain the mere guise of the mythical 'gravity wheel', but actually a substantive, integral step in the momentum gain process, along with the bangs and other noises (scratching sounds) heard.

Not least, because a CoM violation - the production and accumulation of momentum sans counter-momentum - is the only legit way of making KE from first principles; of using / abusing the rest of the laws of CoM and CoE into actually substantiating the terms of an actual KE gain, per KE=½mV².. Of goading the standard, conservative laws of physics into actually making mechanical energy, directly, from its natural component terms.

All these absolutely-key points are fully consistent with one another. Anyone - particularly any physicist - who would attempt to deny or whitewash the Bessler case, would not be able to negotiate their way out of the above points, because it's all-but conclusive that they must be so, and taken together, support the claim in all but an actual working model..

..you can extract and accumulate angular momentum from gravity (proven eight ways from Sunday already, right here in these threads)..

..this momentum gain is reactionless - applying no counter-torque, or thus incurring no counter-momenta, at the axis of rotation..

..and, just by way of example, ten discrete 0.5 m/s reactionless accelerations of two 1 kg masses at say 1 J each will cost us 10 J of input energy, even though 2 kg at the resulting 5 m/s has 25 J, not 10 J!

All this is unequivocal. KE gains aren't simply possible - it is all but impossible not to 'create' KE when accumulating momentum sans counter-momentum! Upon achieving an effective N3 violation, you literally cannot move without creating KE, 'from nothing', besides that resulting momentum itself!

To put this in the context of Christian Wolff's (and not least, Leibniz's) conclusions, what this means in practical terms is that the weights heard landing on the descending side of the wheel had been sped up by a reactionless acceleration, prior to their impacts; an incredibly simple mechanical principle, at its core; they were somehow accelerated, without applying counter-forces back to the wheel itself.

That's it. That's all you need accomplish to replicate Bessler's wheels. Accelerate some internal mass without counter-accelerating (or decelerating) the rest of the system in direct opposing proportion, crash it into the rest of the system, rinse and repeat.. and et voila, you're making KE!

It would all be so simple - trivial, even - but for the non-triviality of CoM...

..which in turn is found to be immutable and inviolable, due to mass constancy, and the speed of light (ie. 1 kg is always 1 kg, and mechanical forces are commuted instantaneously and reciprocally, without time-variance).



In closing this little CoE soiree, why, again, would Bessler's wheels always emit their characteristic 'bangs' from the descending side of the wheel?

Surely, either because their fall was reactionless (release a mass from your grip; it falls without applying counter-forces back to Mr Hand), or else because some additional reactionless force was applied to their fall, such as from inertial torques (the ice-skater effect, also reactionless).

And as noted above, i can't currently see how those diametric lever arms can assist much in that endeavor..

..but also as noted previously, we might interpret MT 134's radial lever arms as some kind of functional development over MT 133's diametric ones; perhaps they do offer some kind of reactionless-acceleration opportunities withheld or precluded by their diametric forerunners..?

Purely speculative, again, at this stage - this is the infuriating thing, knowing conclusively what the physical processes that cause mechanical OU are, yet being so pathetically impotent in being able to actualise them in manifest form using basic moving masses.. of simply arranging a system of basic interactions that actually does what the maths do.. and what they do so elegantly and unambiguously...

Just look at the maths:

• KE=½mV², so accelerating 1 kg definitely costs ½ J!

• Crashing that 1 kg, inelastically, into another, static 1 kg definitely dissipates half that energy..

• ..and likewise, definitely leaves us with 2 kg moving at ½ m/s, with ¼ J of net KE left..

• A second such cycle definitely takes us to 2 kg moving at 1 m/s, so having 1 J of KE, which is the same amount we've spent (ie. reaching unity efficiency)..

• A third, brings us to two * 1 kg mass, moving at 1.5 m/s, so possessing 2.25 J of KE, yet only having invested 1.5 J in their net acceleration!

• 2.25 J out, divided by 1.5 J in, definitively equals 1.5; ie. an efficiency of 150% of unity!!!


The impossible magic, right before our eyes, yet completely demystified... no more exotic than the base KE equation enumerating it, nor the momentum term (m*V) substantiating it!

The only extravagance - the singular indulgence making the 'impossible', incontrovertible - is that reactionless acceleration beginning each cycle!


If this is capturing your imagination, so it damn-well should! Because for all the gassing, i'm obviously an idiot. It's all laid out before me - has been for years - and i still can't wrap it up in actual moving masses..

..but maybe you can..? If you can follow the above maths, you're ahead of the curve, my friend. Ahead of all the physicist and armchair experts who believe (in the truest, most irrational sense of that word) that it is 'impossible', that Bessler was a fraud, that Leibniz was a mug. You've got the jump on all of 'em..

Any one of you could be the sonofabitch that picks up this ball and runs with it..

So don't sleep well tonight, you sonsofbitches.. i mean it, unreservedly. This or any other night. Boil this broth til the wee hours. 'Cos you can crack this. It's simpler than we're making out. Simpler than any naysayers could ever dream of. Karl said so. Bessler himself. It's no more complex than the very features Christian Wolff perceived, and recollects, so pragmatically. Accelerate... but without counter-acceleration / deceleration. Collide, but don't bounce. Repeat. Accumulate. Job done. OU maths, embodied. Maybe my part here isn't to solve this, after all. Maybe it's merely to set the problem out, to light the path, for others to see the goal line..

For my part, i'm moving on to mulling over radial lever-weights, per MT 134. Again, with the singular objective of somehow harnessing the gravity / time / momentum differential, to achieve an equal reactionless acceleration, for equal cost per cycle, invariant of RPM, over some useful range of RPM. Just lining 'em up, and knocking 'em down, one step at a time..

..nothing at all to stop anyone else comprehending this from leaping ahead!

[Fletcher]

..but maybe you can..? If you can follow the above maths, you're ahead of the curve, my friend. Ahead of all the physicist and armchair experts who believe (in the truest, most irrational sense of that word) that it is 'impossible', that Bessler was a fraud, that Leibniz was a mug. You've got the jump on all of 'em..

Any one of you could be the sonofabitch that picks up this ball and runs with it..

So don't sleep well tonight, you sonsofbitches.. i mean it, unreservedly. This or any other night. Boil this broth til the wee hours. 'Cos you can crack this. It's simpler than we're making out. Simpler than any naysayers could ever dream of. Karl said so. Bessler himself. It's no more complex than the very features Christian Wolff perceived, and recollects, so pragmatically. Accelerate... but without counter-acceleration / deceleration. Collide, but don't bounce. Repeat. Accumulate. Job done. OU maths, embodied. Maybe my part here isn't to solve this, after all. Maybe it's merely to set the problem out, to light the path, for others to see the goal line..

LOL .. sleeping like a baby Mr V .. never were truer words spoken by you or anyone else to this matter ! .. working on it, as you do, mate ;7)

[agor95]

May I suggest you allow the mass weight to drop when reaching the top and us that P.E. is used too push the horizontal section to the left.

When the mass is passed horizontal it slides back to the end when it rotates around.

Thus hitting the leading side of the wheel.

[silent]

.

[Fletcher]

FWIW .. Wolff and Liebniz, and sGravesande, Wagner et al, i.e. Bessler contemporaries, could not then or now (should they be alive today) have fathomed, from now known and generally accepted mathematical principles, Bessler's 'Principle of Perpetual Motion'.

Newton, who published his Laws of Motion Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy) in 1687 refused to engage with Bessler and his machines. Bessler must have been aware of Newton's Laws of Motion and recognised the state of incongruity his Principle created with the more famous and respected Englishman's treatise. Bessler perhaps went so far as to call his the "Principle of Perpetual Motion' as an addendum to Newton's Laws of Motion as a nod and wink to Newton and the others ?!

It was not that they were incapable of following the math and physics, but simply that even Newton's Laws (gaining popularity and acceptance) did not adequately describe the physical conditions of Perpetual Motion as Bessler knew it. Those that allowed a machine of pure physical applications to accelerate, accumulate momentum, and self sustain rotation whilst EMGAT, solely in the presence of conservative gravity force and nothing else.

I would guess that they like us would rationalize Besslers' machines behaviour as a violation of Newton's Third etc, if they were convinced they were genuine and knew Newtons' Laws. But beyond that they would be a stumped for a mathematical explanation just as much as any of us today. The coherent Laws just don't distill any further. Indeed as Bessler was also stumped, IMO. Bessler could predict his machines behaviour from observational results and further calculation but could not explain the math behind it any more successfully or conveniently than we can today, IMO.

So whichever way you cut it, we are looking for a machine of physical applications that is fit to demonstrate Bessler "Principle of Perpetual Motion". Tho we will never from within the current paradigm be able to mathematically describe it's aforementioned behaviour, also imo.

Possibly the best we can do is say that some Law of Newton's is violated in certain physical conditions and this leads to asymmetric torque or 'torque prejudice' within his wheels. We might describe the Effect, but not the Cause, with any certainty. The Cause might need a rethink of Newtonian Physics and perhaps Einsteinian and Quantum Physics as well in due course ?!

Bessler might not have known the math behind his own machines but he would have known the observational Physics i.e. the physical reasons it behaved the way they did (they were simple and unambiguous, once known, no doubt). And he tells us it starts with his Principle of 'Zusammen Gehängten' ('Together Hung', also interpreted as Connectedness in some quarters) which must be diligently appreciated and applied. It is the first and most important clue in MT appearing at MT9 followed by other physical clues thru to MT38 where correct application of Storks' Bills get a special mention, imo. Not to mention the Toy's Page substitution/addition near the end of MT which wraps them altogether in one location.

Bessler was a canny individual so don't be surprised if there are deliberate plays on words and double meanings in his friendly guidance thru MT. MT11 ( MT i i ) comes to mind, coming so close after MT9. The 'Connectedness/Together Hung' Principle might equally well apply to the Prime Mover and also to the Secondary Mechanical System, for example !? One Principle with duality applying to both the Primary and Secondary Physical Systems in play, perhaps ! Covers all bases !

However you unravel the physical metaphors contained in MT, and AP-DT-GB, you must deduce a physical embodiment of interacting parts that do justice to Bessler's self titled 'Principle of Perpetual Motion'. One that simply (say it quickly) accumulates Momentum from contrived imbalance conditions,, IMO.

Sleep on it ;7)

[MrVibrating]

..thinking more on this at work today:

- i think it's too early to be giving up on the diametric weight levers.

Reasons:

• Christian Wolff's apparently strong impressions that the weights were attached at the rim; not the hub / axle..

• I've long suspected that certain translations may be leading us astray - did Bessler really mean that his "axle contained many 'compartments', as anyone who felt inside the wheel would notice" (paraphrasing); that is, are 'compartments' really what he was talking about?

To me, 'compartment' evokes imagery something akin to 'breadbins' around the axle - little cubbyholes, or 'pockets' / excavations, but maintaining an overall cylindrical profile to the axle..

But maybe we should be thinking more in terms of the axle being 'compartmentalised' into sections...

In another passage, (sorry i forget exactly where) he responds to the question of whether his axle is broken up, internally, into sections connected by pins - to which he responds that there are many such items; which would have to be the case if the weight levers were indeed diametric (extending from the opposite rim) rather than radial (extending from the hub / axle); in other words, indicating that the internally-concealed part of the axle was basically like what we would call a crank-shaft; the gaps being required to allow the diametric lever arms to pass through the axle, and also affording them enough room to move up and down..

• And again, a persuasive argument in favour of diametric levers is in maximising their MoI, relative to that of the net system, which we know from the maths is a really pivotal determinant of the OU gain margin - specifically, the per-cycle efficiency accumulator..

We know from the maths that the shortest possible route to OU is equal interacting MoI's / masses, achieving unity at two reactionless-accelerate-and-brake cycles, and 150% at the third. Whereas, if they're in a 2:1 ratio, it takes three cycles to reach unity and four to hit 133%. But the Toys page seems to implicate a 3:1 ratio, hitting unity at four cycles and 125% at the fifth.

Yet achieving that ratio using radial lever weights would seem unlikely, since if they came as a pair, and only one is impacting at any one time, then the MoI ratio would be 1:1, hence 2 strikes to unity and three to OU. A 3:1 ratio would mean each complete 'minimum mechanism' (as presumably indicated by the Toys page) would comprise 4 radial lever arms, one impacting against the net MoI of the other three at any one time. So four lever arms per set. Not two.

Whereas, using diametric lever weights, we double their effective radius relative to that of the wheel / net system, and since MoI squares with radius, a single diametric lever weight has four times greater MoI than its MoI about the central system axis!

Taking that point a step further, if we add a second diametric lever weight (since they presumably come as pairs, as indicated in MT 40 et al, with an impulse every 180° per individual set), then the ratio of one, single active diametric lever weight, in relation to that of the net system about the central axis and comprising that same lever arm plus one more, inactive (upside-down) one, is 3:1, by my reckoning..

Hence two diametric lever weights, as depicted above, could reasonably have a net system MoI about the central axis that is still three times lower than that of either single lever arm about its rim pivot. This is the sweet-spot ratio for a 4-cycs-to-unity, five-to-125% efficiency envelope..

I'll try confirm this tomorrow with a simple sim, but if it checks out, then diametric lever weights are still odds-on favourites over their radial, hub-mounted counterparts.


Obviously, another central problem of allowing any such lever arm to fall under gravity is the underbalancing moment this necessarily applies; the instant a weight is dropped from say the left side of a wheel, that left side becomes under-balanced, resulting in negative gravitational torque applied to the net system.

Obviously, you'd think we'd need the descending side of the wheel to remain over-balanced. It seems a bit much to ask for the descending side to remain overbalanced whilst a weight is also being dropped on that same side, so this too needs particular focus and study - how do diametric lever weights fare in this regard, compared to radial ones?

And finally, we still have the actual issue of the thread topic to consider; that of per-cycle momentum yields decreasing with RPM. Again, this is manageable, if and only if the energy cost of that momentum doesn't increase - in other words, if it costs equal energy per cycle but the momentum yield's decreasing, then the actual energy cost of momentum is rising. Not good.

What we want is an interaction wherein the energy cost of momentum is a function of unit time, hence if per-cycle momentum yields decrease with RPM, then the per-cycle input energy needs to drop off in proportion, thus maintaining a constant (or near-as-poss) unit energy cost of momentum.

So i'll come back to this tomorrow, with some more tests on these diametric lever arms. Specifically, checking the ratio of their individual MoI's, relative to that of the net system (comprising a pair of them) about the central axis. If that does indeed fall into a 3:1 ratio, then that would seem good confirmation they're the right way forwards.. (ie. consistent with the Toys page).

Just dead-simple test rigs, is all it should need; simple circular weights, attached via (massless) rigid rods to the opposite rim. Obviously we can all do the MoI formula in our heads, but seeing it actually confirmed will eliminate any doubts.

[WaltzCee]

Fletcher sure will make you think. If you don't like thinking don't read what he says.

[MrVibrating]

May I suggest you allow the mass weight to drop when reaching the top and us that P.E. is used too push the horizontal section to the left.

When the mass is passed horizontal it slides back to the end when it rotates around.

Thus hitting the leading side of the wheel.

Hmm if i follow correctly then i don't see the benefit there - we already know asymmetric GPE interactions are impossible, and likewise, as noted last night, the location of the impacts is incidental to the resulting momentum distributions; the only way to introduce more momentum to the system is via this gravity / time differential, which the rig currently cannot access.

Again, the objective has to be paying output GPE to purchase momentum from gravity - so the workload we need from that GPE has to somehow cause (some) weight to spend more time falling than rising.

We've seen various methods of achieving that end - such as by using inertial torques via the 'ice skater effect' - but also, 'classic OB', wherein a mass is raised in the radial plane (ie. pulled upwards and inwards from 6 o' clock BDC), and dropped in the angular plane (rotating around from say 12 0' clock TDC back down). Maybe there's other ways yet to be found. But in the configurations i've tried so far, this MT40-ish lark is doing neither - it only loses momentum to gravity (the proportion of the system mass that is gravitating spends more time rising than falling).

These are the terms we need to get used to thinking in - momentum in / out as a function of time-spent-gravitating as weight rises, as compared to when falling.. and furthermore, paying GPE as the input currency for achieving that gain..

So an input of GPE has to cause some gravitating mass to spend more time per cycle falling, than rising.

It's hard to snap out of the allure of "perpetual OB", but we know it's an intrinsic dead-end... Momentum-from-gravity via time manipulations is the only de facto path to a solution!

[ovyyus]

However you unravel the physical metaphors contained in MT, and AP-DT-GB, you must deduce a physical embodiment of interacting parts...

you'll soon find, you splendid mechanics, that this is a nut you can't crack!

If not mechanics, then which discipline can crack the nut?