Blood From Stone

[MrVibrating]

Ahh i think i got it:

• the lift is only partly radial..

• ..and partly angular!

Duh..!

So 7.7 J is just the radial portion of that total lift effort.

• 9.80665 - 7.7 = 2.10665 J of that workload must've been done by OB torque!

The radial work subsidy is precisely equal to the angular work contribution.

Thus, gaming this relationship would mean exploiting differences in their respective units and dimensions - ie., differences between how they evolve with respect to velocity / time etc.. or maybe, their respective N3 constraints..

So, the 9.81 J of output OB GPE converted into 7.7 J of rotKE, plus 2.10665 J of input GPE..

..IOW, of the conserved GPE quantity..

..the more we distribute to rotKE..

..the less we have left to subsidise input radial work..

Thus it is this relationship that must be manipulated, somehow, in order to effect an advantage..

[MrVibrating]

Well for the Bessler wheel to be a fact, there has to be some kind of mechanical paradox or else it could never run. That's the key to the whole thing is capitalizing on some kind of paradox to make it rotate. The Bessler wheel did output some torque, but not a whole heck of a lot in proportion to it's size - especially if you were to have a steam engine or petrol engine of equivalent size. Still, some amount of slight over unity that self-propels an item is a pretty cool thing and if you could even do a little extra work beyond that - even cooler. I still believe you are discovering key elements which were part of Bessler's wheel someway somehow.

silent

Thanks mate, we'll get there.

Ultimately, the disunity has to be between abnormally accelerating reference frames - that's what 'excess KE' is, in terms of its literal units and dimensions, and mechanical OU can have no other corporeal form - so you can't have "excess" or "OU" PE for example, since its dimensions are time-invariant - it's usually just F*d. Only excess KE is even a self-consistent concept. But it means the value of the "V" term has diverged from the non-inertial (ie. stationary) reference frame! The body of mass / inertia that 'V' is relative to from the internal, mutually co-rotating reference frame of the work actually being done - to wit, the 'stator' - is by definition rotating with the mass / inertia being accelerated.

Like B. 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."

We already have the implicit instructions on what works and why...

..but it's like staring at one o' them 1980's 'magic eye' stereograms... i never could see anything in 'em! You gotta look through the image, defocus, somehow..

[MrVibrating]

..so it would seem the most interesting thing we can try now is to finally start raising the MoI using the red masses.

How this affects the distribution of rotKE to input GPE will be of particular interest.. should help further eliminate or elucidate the possibilities for an effective asymmetry anyway..

[MrVibrating]

So, how to apply the red masses?

Options:

• Move 'em out at constant speed. Try a range of such speeds, note the trends.

• Or else try something more adventurous - what about using adaptive feedback control - ie. move them out (or in) at whatever speed results in the RPM's being held constant, or else, accelerating / decelerating by a controlled amount?

So, using their 'inertial torque' to counter the angular accelerations / decelerations caused by the angular / radial GPE interaction?

If RPM's are thus held constant, does this hold the per-cycle momentum yield constant?

Presumably the widening red MoI will also be significantly affecting the resulting momentum distributions, so the actual relationship may not be so simple - and might even be non-linear.. with diminishing or negative returns beyond certain bounds..

Similarly, we could try a form of adaptive feedback based upon the changing momentum - so the red actuators could be programmed to use their inertial torque to try and maintain the p/c momentum yield, regardless of RPM's per se..

So decisions have to be made about what exactly the testing objectives are - is there a potential exploit we can attempt right now, or else, what outstanding questions could we attempt to answer..?

The exploit i think we could take a shot at is this:

• constant per-cycle momentum rise, for constant per-cycle input energy, across some RPM range

IOW, an input energy-cost-of-momentum that doesn't square with RPM - and thus, a step closer to de facto 'excess KE'.

Will give it a bit more thought, but that looks like the most obvious place to start digging..

[MrVibrating]

Just for closure, here's the second 90°, completing the cycle:



Weight 2 Actuator F*V(*t) = -0.241286314 J

Weight 2 CF/CP Work Done = 7.952391446 J

Weight 2 Actuator F*d = 0.204735352 J

Note however that the F*d meter doesn't quite finish returning to zero - the sim has paused a fraction of a millisecond too early.. so the actual integral is probably closer to the 0.241 J F*V*t result, and not worth hours more work re-running the sim for an extra 0.00001 seconds..


So again, the direct force-sensing metrics include the CF work integral, so subtracting it:

7.952391446 - 0.241286314 = 7.711105132 J was, again, the work done against gravity, for the second half of the interaction, as the first.

The only difference being, in the first half, the CF work was only 0.6 J, whereas in the second, it's left a much bigger exit hole, accounting for 7.7 J of the lift energy, and only topped up by another 0.25 J drawn by the actuator.. coincidentally, the same amount of energy as the kickstart KE..

But in conclusion, it looks like a fairly straightforward conversion of GPE into 'CF PE', then back into GPE - fully conservative, with no obvious advantage with regards to input energy cost of momentum or GPE symmetry, at least under the current test conditions..

Time to wheel out the vMoI..

[MrVibrating]

Just spent a few hours poring over Fletch's "spring shifter" concept - it's good to step outside one problem and into another for a little while - dunno which thread it's from so i'll just give my conclusions here:


What's happening:

Driver bob falls - in the process, briefly underbalancing the right side and introducing a corresponding CCW torque.

Because this lever dispacement is caused by gravity, it applies no instantaneous counter-torque back to the wheel, hence the rotation of the lever and wheel are both in the same CCW direction.

As the spring goes taut and the driver weight lever reaches maximum angle, its CCW motion is thus arrested..

..however this effective counter-torque is being applied against the inertia of the wheel body, hence inducing a CW counter-momentum.

Thus the desired CW moment is only applied to the wheel in response to that braking of the lever's CCW AM.

The lever's return to position is also effectively using the wheel base as a 'stator' to push against - the latches release, the spring now has advantage over the lever's gravitational torque * angle, and in the process of returning EPE back to GPE is applying a CW torque to the lever, and a corresponding CCW torque back to the wheel base..

The remaining net momentum after that restore stroke is the CCW 'under-balancing' momentum from the initial 'reactionless' downwards displacement of the lever under gravity..

The central issue, as i see it, is that the concept is predicated on a kind of dualistic anticipation - commonly arising in OB schemes - of a GPE performing or converting to more than one output workload:

• we could convert a GPE into sprung PE, or rotKE - but divide it into both and there's less of each..

• if most of the GPE is efficiently conserved as EPE, then a negligible amount has converted into KE, and vice-versa

Since the desired outcome is a rise in AM per cycle, and a rise in momentum is contingent upon a rise in KE (since both terms refer to the same mass and velocity components), success would hinge upon an effective N3 break at some point in the process - the energy gain would then be the KE component of the net momentum rise - ie. equal to half its value, squared..

It's a brilliant construction throughout though - very clean, using advanced, clever techniques..

..but just further demonstrates that the key obstacle to a break in energy symmetry is, first and foremost, momentum symmetry!

In order for momentum to rise, it has to be paid for, and in order to get 'OU' efficiency, we have to pay less than the ½mV² value for it! That price point is set and enforced by momentum symmetry / CoAM / a la N3 in whatever guise..

If the return stroke of the lever weight applied no counter-torque back to the system, inducing no counter-momentum back to it, the system would work splendidly.. gaining five momentum inputs per rotation. Since the 'input energy' paid for that momentum would ultimatley be GPE, which is time-invariant and thus speed-invariant, the input energy cost of that momentum rise would be constant, and the system would thus be OU by the 2nd or 3rd impulse.

Fundamentally, whatever approach we take to a prospective mechanical energy asymmetry, all our efforts will be futile unless the system - even inadvertently - somehow defies N3.

The problem fundamentally reduces to gaming ½mV², and its dependence upon N3! All other artifices are subordinate to that central conceit.

[Fletcher]

My comments in reply inside MrV's quote in blue.

Just spent a few hours poring over Fletch's "spring shifter" concept - it's good to step outside one problem and into another for a little while - dunno which thread it's from so i'll just give my conclusions here:


What's happening:

Driver bob falls - in the process, briefly underbalancing the right side and introducing a corresponding CCW torque. Yes. Anytime a lever and/or weight of mass falls it goes MIA in terms of the wheel on that same side. It's an inertial effect where the lever weight (lw) and the wheel proper move towards each other as a compromise, rather like how the earth moves towards a mass dropped in a gravity field.

Because this lever displacement is caused by gravity, it applies no instantaneous counter-torque back to the wheel, hence the rotation of the lever and wheel are both in the same CCW direction. Yes.

As the spring goes taut and the driver weight lever reaches maximum (opening) angle, its (the Diver Lever and bob) CCW motion is thus arrested. Yes. It is no longer MIA in terms of what the wheel 'feels' but the Driver weight is now in a new position.

..however this effective counter-torque is being applied against the inertia of the wheel body, hence inducing a CW counter-momentum. This 'new' position is outwards at a greater radius than start position and downwards. Thus the wheel CoM has shifted outwards and downwards giving CW torque to the wheel as a whole. It now gathers pace CW.

Thus the desired CW moment is only applied to the wheel in response to that braking of the lever's CCW AM. Yes. The CW torque comes from the now displaced (right shifted) wheel CoM. This is the end of the first weight transition stage.

The lever's return to position is also effectively using the wheel base as a 'stator' to push against - the latches release, the spring now has advantage over the lever's gravitational torque * angle, and in the process of returning EPE back to GPE is applying a CW torque to the lever, and a corresponding CCW torque back to the wheel base. Anytime a Lever weight (lw) is pulled downwards (gravity) or upwards (spring) it has an effect on the wheel proper. This is proportional to the two inertias in play. Pulled upwards you might say the whole-of-wheel attempts to move toward the lw, same as the downfalling scenario. These two temporary torque effects on the whole-of-wheel are dependent on the path the lw falls and rises. IOW's if in the lws transitioning to new positions it advances or retards, or both in the same movement, relative to wheel orientation then the wheel proper moves the other way to meet it.

The remaining net momentum after that restore stroke is the CCW 'under-balancing' momentum from the initial 'reactionless' downwards displacement of the lever under gravity.

The central issue, as i see it, is that the concept is predicated on a kind of dualistic anticipation - commonly arising in OB schemes - of a GPE performing or converting to more than one output workload:

Comment - This is IMO the fundamental issue with this type of construct. First point - for simplicity sake we can forget about CW and CCW induced wheel torques of Driver lws falling and rising, since there is no extra power available to raise the lw far faster than it does under spring release (linear springs). Second point - the CW rotation of the wheel is fundamentally due to the imbalance of the fully deployed Driver lw which favourably right shifted the wheel CoM. Very good. Third point - the EPE stored in the linear spring is proportional to the GPE lost by the Driver lw, consequentially the spring can not give more kinetic energy of transition to the Driver lw as it transitions back to position than it got as GPE stored as EPE. If the latch is released too early (is time operated in sim but could be degs of rotation) then the 'angle' between start bob position and end bob position is too steep i.e. the wheel has rotated a little, it has greater height loss to recover than start conditions gave it, therefore the spring can not manage a full restitution of GPE (leading to negative torque contribution problems) ... Release the latch too late and the steepness is less than start conditions so there is less height to recover, and the spring does this quickly and with with ease. BUT .. when the recovery slope is less (which seems ideal) the spring will indeed enact a quick and full transition BUT the whole-of-wheel CoM has been on the ascending side for a period of time (negative torque contribution) slowing the rpm to that point of release. Last point - the latch timing of catch and release can be varied mechanically, but the interplay of CoM displacement after catch and release each side of the vertical below axle and lws and wheel inertias in transition always balance out to a zero sum game, IMO.

• we could convert a GPE into sprung PE, or rotKE - but divide it into both and there's less of each..

• if most of the GPE is efficiently conserved as EPE, then a negligible amount has converted into KE, and vice-versa

Since the desired outcome is a rise in AM per cycle, and a rise in momentum is contingent upon a rise in KE (since both terms refer to the same mass and velocity components), success would hinge upon an effective N3 break at some point in the process - the energy gain would then be the KE component of the net momentum rise - ie. equal to half its value, squared.

It's a brilliant construction throughout though - very clean, using advanced, clever techniques.

..but just further demonstrates that the key obstacle to a break in energy symmetry is, first and foremost, momentum symmetry!

In order for momentum to rise, it has to be paid for, and in order to get 'OU' efficiency, we have to pay less than the ½mV² value for it! That price point is set and enforced by momentum symmetry / CoAM / a la N3 in whatever guise..

If the return stroke of the lever weight applied no counter-torque back to the system, inducing no counter-momentum back to it, the system would work splendidly.. gaining five momentum inputs per rotation. Since the 'input energy' paid for that momentum would ultimatley be GPE, which is time-invariant and thus speed-invariant, the input energy cost of that momentum rise would be constant, and the system would thus be OU by the 2nd or 3rd impulse.

Fundamentally, whatever approach we take to a prospective mechanical energy asymmetry, all our efforts will be futile unless the system - even inadvertently - somehow defies N3.

The problem fundamentally reduces to gaming ½mV², and its dependence upon N3! All other artifices are subordinate to that central conceit.

[MrVibrating]

You've given me pause to go back over DT and pay a bit more attention to this passage:

p191

these weights are
themselves the PM device, the ‘essential constituent parts’
which must of necessity continue to exercise their motive force
(derived from the PM principle) indefinitely – so long as they
keep away from the centre of gravity. To this end they are
enclosed (page 21) in a structure or framework, and co-
ordinated in such a way that not only are they prevented from
attaining their desired equilibrium or ‘point of rest’, but they must
for ever seek it, thereby developing an impressive velocity which
is proportional to their mass and to the dimensions of their
housing. This velocity is sufficient for the moving and raising of
loads applied to the axis of rotation.

(MS / JC)


Never really paid much attention to these clues before, but there must be good capital in analysing these words in respect of a prospective momentum asymmetry.

Straight away (without even giving it any thought yet) - that final sentence would imply that he considers the gain in terms of "sufficient velocity" - that's his "potential to perform work", or to close-loop... the causative principle appears, to him, to be velocity-dependent.

Furthermore, it may be implied that the very process of seeking certain equilibria - "thereby developing an impressive velocity" - is the same action constituting the effective N3 break..

..IOW, this 'frustrated flight to equilibrium' is a form of reactionless acceleration, and since the only fundamental forces involved are inertial and gravitational, it can only be an acceleration by CF, or else gravity. If the latter, then this 'denied equilibrium' is a lower CoG, if the former, then it's a wider MoI.

Just because of the general futility of gravitational asymmetries, the attention is drawn to that former possibility - either the reactionless acceleration is centrifugal, or is initiated by / culminates in an effective N3 break...

"keeping away from the CoG" has to be equally telling.. the weights themselves are obviously part of the system's CoG, so the CoG he is referring to must be between some other masses.

The CoG is what actually gravitates in a gravity wheel - the aspect that wants to get lower in the gravity field - yet if the weights remain outside that CoG, then they're not necessarily getting lower along with it.

The CoG cannot refer to that of the weights themselves, since they're already, always, at the periphery of their respective CoG, which by definition lies betwixt 'em.

If the wheel body / supporting frame is itself balanced, then its CoG is always at its axial center, so the "CoG" in question cannot be between it and some other mass - IOW, both masses bookending / defining this "CoG" must be gravitating.

Could it perhaps refer to a CoG between points of application / suspension / articulation of weights, rather than the masses themselves?

Or perhaps this is attempting to read too much into a translation / transliteration of technically-antiquated / naive concepts? Perhaps "center of mass" or "rotation" was what he was actually referring to? Which points us back to CF workloads?

Yet there was a gravitating component, and furthermore the outwards operation of the machines gave every impression of being an effective GPE asymmetry - static torque in a statorless wheel implying weights are "dropped when heavy, lifted when light" despite the impossibility of that being the case..

So, something along the lines of "a CF workload corresponding to a GPE output that lowers a CoG, rather than the weights themselves" would seem to be implied.. suffice to say, as far as i've been able to determine, work can only be done by an output GPE when the weights themselves are able to get lower in the gravity field.

I've tried causing points of application / suspension of weights to gravitate instead of the weights themselves, and it seems inherently futile - unless a mass itself descends, no output work can be performed by its weight.

However, i haven't explicitly tried applying this to CoG's / CoM's, rather than actual weights as point masses.. since a CoM / CoG is itself massless, this would seem a great launching-off point for an effective N3 break..?

Dunno, lots to think about there...

Meantime i need to finish what i've started here - in my head, there's this persistent notion that moving the red masses outwards in a controlled way will limit the RPM rise and so maintain the per-cycle momentum yield (the size of each step on the momentum 'staircase' plot). If per-cycle input energy also remains constant (as it is so far) then that's de facto OU..

I now suspect what'll actually happen is that the current speed-invariance of the p/c input energy is dependent upon the RPM's rising during the interaction - IOW the angular acceleration between input and output halves of the CF workload is what's keeping the net input work constant p/c - hence restricting the RPM's by extending the red masses will likewise restrict the output CF workload by the green weights, causing input energy to rise in proportion to the now-constant momentum rise per cycle.. and the gradient of that input energy increase will perfectly match ½mV²!

Still, gotta model it to be sure, that's the whole point. We only need to hold the input energy cost of momentum constant over a few cycles to generate an energy gain.. a 'complete' interaction, as i see it, would involve moving the red masses out over a few cycles, then finishing by moving them back in again. Net energy / momentum at that point is presumably going to be unity.. but at least it's another dead-end eliminated.

[silent]

.

[MrVibrating]

Finally finishing up on this rig:

Here's 1 full rotation, comprising 2 full cycles:


Lo-Fi version for speed of demonstration - Hi-Fi data source version below.

The red actuators are now programmed to move their masses outwards - thus generating negative inertial torque - at whatever speed keeps the RPM's constant; so, precisely cancelling gravity's accelerations.

Looking at the momentum plot, it appears to be having the desired effect - net angular momentum rises by 31 kg-m²-rad/s on both the first and second cycles.

Likewise, input energy to the green actuators performing the GPE interaction also appears to be equal each cycle.

In short, per-cycle input energy certainly hasn't quadrupled, even though net momentum has doubled over the two cycles, and likewise, the per-cycle momentum yield hasn't decreased by the inverse square of input energy, even though input energy has remained constant across two cycles. So on face value, we appear to have overcome the constraints of the previous green-only interaction... if not quite defeated ½mV² yet!

Obviously it ain't gonna be OU - that would surely be too easy - so the interesting lesson, as ever, will be the manner in which CoE has been enforced, despite having met conditions that 'should' break it..!

Where exactly, does the plan fall short..?

So let's look at the integrals.

First up, the CF work done by the green actuators; since RPM's are held constant, net input / output CF work by the green actuators should be a fat zero:

• Green Acts CF/CP Work Done = -0.00005201 J

Close enough. Let's see how much work they did lifting the weights radially against gravity:

• Green actuators F*V(*t) = 30.80827024 J

..divide that by two for the two cycles (could take 'em individually but they look identical enough) = 15.40413512 J per radial lift.

Since we know each lift raised 19.6133 J of GPE:

• 19.6133 - 15.40413512 = 4.20916488 J must be the output 'OB GPE'

We could measure the OB GPE directly, as the change in height of the center of mass between the two green weights, however that seems unnecessary for now..

So total input energy thus far is 30.80827024 J, of which we have 15.7768 J of net KE, therefore the CF PE we've loaded into the red actuators must be equal to:

• 30.80827024 - 15.7768 = 15.03147024 J

..and, taking their integral:

• Red Acts CF/CP Work Done = 15.4220323 J

So the difference between the expected and actual red CF PE is:

• 15.4220323 - 15.03147024 = 0.39056206 J

So within 0.4 J of unity so far..

Net energy, the sum of CF PE and net KE, is:

• 15.7768 + 15.4220323 = 31.1988323 J

So if our net input energy is only 30.80827024 J, we have:

• 30.80827024 - 31.1988323 = -0.39056206 J

..again, 0.4 J difference... and this must be the initial input energy applied by the red actuators as the red masses are pushed out from the center, before CF grabs 'em and starts performing 'output CF work' against them.

So unity, basically..

The final step, of pulling the red masses back in to the center, seems unnecessary - it'll obviously just conserve net momentum whilst converting that CF PE back into rotKE, and it makes no difference whether the final net energy is all KE or part-PE..

So what went wrong? The design objectives - of constant input energy and momentum per cycle - appear to have been successful.. so, why doesn't this result in gain?

The intended exploit - of buying momentum on the cheap, for less PE than its KE value - has failed, and the actual efficiency conforms perfectly to ½mV².. for both input and output workloads.

And yet, we succeeded in holding the momentum yield and input energy constant for two cycles!

So this is what needs puzzling out:

• buy 1 kg-m/s of momentum for ½ a Joule

• this is the min price for 1 kg at 1 m/s, per ½mV²

• now do it again

• you've just spent 1 J for 2 kg-m/s of momentum

• but 1 kg @ 2 m/s has 2 J.. not 1 J! 200% OU!

Yet in the above sim we've just bought equal quantities of momentum for equal input energy over two cycles...

...so what critical detail has been overlooked!?

What is it that the hypothetical example does, that the experiment does not?

It must be some kind of confusion regarding necessary conditions, versus sufficient conditions..

..we've ostensibly met the 'gain' criteria...

..yet have somehow missed the mark..

Hmmm..








Here's the max-frequency version the data's from, @ 1,000 integration steps * 32,765 frames:




Somehow, this experiment is invalidating what should be a winning ticket..

..but if we can identify whatever's been missed in the small-print, we can tackle it head-on and avoid making the same mistakes in future..

[MrVibrating]

All I can say is if they have such velocity they could do work, they must have really been moving at a good speed. It almost sounds like some kind of variable gyroscope/flywheel combination.

I also try to think what in the heck could he have made with 1700s technology that we can't seem to figure out today? He wasn't just going down to NAPA to get timken roller bearings, belts, and pulleys.

Amazing stuff and evidently some kind of an arrangement with some kind of a well-hidden and unknown mechanism.

Thanks for the write-ups - I always enjoy reading them.

silent

Thanks mate. The causative principle has gotta be simplicity itself - 'KE' is relative, because so is motion itself. Thus an 'OU' motor is simply any normal motor in which the 'stator' - against which the torque is somehow being leveraged - is nonetheless rotating around with the rotor. The resulting wheel always has precisely the right amount of KE for its RPM and momentum, but the internal energy cost of that momentum is less than its external KE value.

This much is simply an axiomatic reduction from first principles.

But B. also repeatedly infers that construction is long and complex. When he says "were God to grant me enough time, i could build a wheel that turned very slowly, yet with great force, while emitting a steady chatter", he's directly intimating that it is the sheer number of repeated mechanisms - of individual cycles per rotation - that is the main time-consuming factor. Each individual complete mechanism could thus be mechanically quite complicated.

Yet we can also make certain deductions - static torque in a statorless wheel can only be caused by an OB weight resting against the descending side of the wheel, such that only rotation allows it to get lower.

And if the form of the energy gain is rotational KE (ie. the exploit being cut-price angular momentum), then in a statorless system, this gain in rotKE can only be harvested by raising weights, or else, a CF/CP workload.

Yet the one-directional wheels were under static torque when tied-off stationary.. hence their excess energy under that condition must be in the form of PE, not KE; hence some kind of PE-management system is unequivocally implied.

This must involve the harvesting of rotKE into PE - either via springs, or GPE's - in order for the one-way wheels to remain in an OB state once stopped.

More fundamentally, we simply have to have an internal PE store that can rotate with the system, since this is both a practical requirement of an effective N3 break, as well as 'OU efficiency' as a general concept, ie. more energy out than in..



But, much more than this, is where things start getting more speculative.. hence the current attempt to deduce the explicit gain conditions we know must exist.

Really, it won't be until we've nailed a gain cycle, and reduced it to a minimal demonstration, that we can start to speculate on how Bessler might've arrived there - happy accident, or brute-force ingenuity? He says he reached some kind of elucidation or enlightenment, possibly dream-inspired, when everything just fell into context..

..but whatever that foresight was, mechanics is pretty simple - force, mass, motion, CoM and CoE, so with the benefits of modern science we really ought to be able to methodically follow from first principles and a process of elimination - the exploit can only be an effective N3 / N1 violation - in other words an asymmetric inertial interaction - somehow contingent upon vertical rotation / gravity..

Once we've nailed that - and it's an inevitability, if not quite yet a fait accompli - we'll have a better idea of what a minimal embodiment might look like..

[MrVibrating]

Right, a HQ soak in the bath (@ ~120 secs / minute) would seem to suggest i've made the same kind of mistake before - on that occasion i was maintaining velocity at the expense of MoI, hence no net gain in momentum or KE. This time, the momentum gain's real enough, only i've increased it by raising its inertia component, rather than the velocity component that a KE gain would depend upon! Duh..

Gaining momentum for its own sake is no more useful than velocity for its own sake. It is specifically the velocity component of rising momentum that must manifest OU... getting wider instead of faster is pointless in this regard - we want 'excess energy', not 'excess radius'..

__________________


Regarding further the direct clues from Bessler, it's perhaps worth bearing in mind that the Toys Page is specifically pointing to the number 5 as preeminent.

Items A + B (the 'staff and chain') represent a series of 5 asymmetric angular accelerations about a common axis, culminating in 'something extraordinary' (obviously, KE gain).

This particular gain trajectory corresponds not to a passive acceleration as by gravity, but rather an active acceleration which is applied preferentially to one inertia against that of another, initially non-accelerated, inertia. The two inertias then collide, equalising their velocity difference via an inelastic collision, dissipating 75% of the input energy, but holding on to - and progressively building upon - the 25% remaining KE and its corresponding momentum rise each cycle.

Two such cycles in succession yield a 50% net loss. Three, 25%. Four resolves to unity, and five, 125% of input energy.

The key causative ingredient that is accumulating is velocity (not inertia, duh)...


So, what i'm gonna try next is a more direct interpretation of that '5 cycs to OU' maths:


• suppose we have a uniform disc rotor, and also a pendulum bob / weight hanging from the same axis

• give them equal MoI, such that with gravity off, a motor applied between them will accelerate each to equal RPM in opposite directions

- so basically, two equal MoI's, one of which is also subject to gravity.


•• with gravity on, control the motor like this:

• as the weight rotates downwards from TDC to BDC, apply precisely enough torque between it and the disc to prevent the weight's acceleration by gravity...

• ...instead, accelerating the disc

• when the weight reaches BDC, lock the motor, thus 'inelastically colliding' the two bodies as per a standard clutch

• the disc's momentum rise is thus shared back to the bob/weight, the motor remaining locked as they coast the weight back upwards to TDC - shedding back most of gravity's momentum contribution, but keeping most of that which was input via the motor

• repeat * 5


Logic: per-cycle input energy is GPE and angular inertia, both of which are speed-invariant...

...whereas output rotational KE is speed-dependent!


Gravity is, first and foremost, an ambient rate of change of momentum, hence perhaps it can be simply decoupled from a GPE's corresponding KE value, as a function of the ever-rising angular velocity of the 'stator' against which its own angular momentum is being generated..?

Per-cycle momentum yields will still inevitably decrease with rising RPM, since less time's spent gravitating each cycle, however since the per-cycle input energy is also a function of the p/c time-spent-gravitating (ie. the motor's 'duty cycle'), if it, too, decreases in direct proportion then we nonetheless have a constant energy-cost-of-momentum across some rising range of RPM's..

We can monitor our ongoing success (or lack thereof) as a function of this ideal 75% dissipative loss per cycle - if we can get it to drop to 50% loss on the second cycle, then we should be on-course for a 25% loss at the third, unity at the fourth and 125% at the fifth...

It's basically a no-frills, literal interpretation of the OU maths - essentially a 'standard' motor, albeit with a mutually co-rotating stator..

Plan.

[MrVibrating]

So here's an overview of the next system:







What it is
__________


A motor, in which the 'stator' is a co-rotating gravitating weight.


The weight is attached to a central hub via two radial rods.


The weight's hub is attached to the wheel via a motor.


The motor only applies torque when the weight's descending.

The equation needs refining, but ideally, the motor torque should perfectly cancel the weight's downwards acceleration by gravity - instead, accelerating the wheel.

When the weight's not descending (ie. from BDC back up to TDC), a clutch activates, locking the weight's hub to the rotor.

Both components have an MoI of 1 kg-m²-rad/s.





Why?
____


It's essentially a literal interpretation of the basic KE-gain-from-N3-break principle - a series of reactionless accelerations followed by inelastic collisions.

At least, that's the intention.


It's all but inevitable that the per-cycle momentum yield of these types of systems must decrease with RPM's, since less time is spent gravitating p/c the faster they rotate.

However, provided we can simply maintain a constant input energy cost of momentum, we should still be able to claw our way ahead - since the KE value of that momentum still squares with its velocity in the external, stationary reference frame.

Internally however, the work being done by the motor is simply against angular inertia, and gravity, both of which are speed-invariant.

The motor knows nothing about gravity - with gravity disabled, the motor will accelerate stator and rotor to equal RPM's in opposite directions. But with gravity enabled, the motor will still be performing the same amount of work, accelerating the same amount of inertia by the same relative velocity... Gravity simply skews the resulting distribution of momentum and counter-momentum! So instead of spinning up each inertia in opposing directions, gravity causes the motor to apply most (ideally, all) of its acceleration to only the wheel, whilst the weight rotates downwards at (ideally) constant speed.. effectively cancelling all counter-momentum..

..then, at BDC, this positive momentum preferentially loaded into the wheel is collided back with the weight's hub via the clutch, locking 'em together for the rest of the cycle back up to TDC..

Basically it's a standard motor, albeit one that's alternately tugging its own stator around with the rotor, hence accelerating its own reference frame.

In short, this should prevent the input energy cost of momentum from squaring up with RPM, thus defeating ½mV² (or more specifically ½Iw²) - input energy's just inertial acceleration, plus GPE - both time-invariant - whereas output KE squares with the rising net speed.

No prizes for guessing that it (once again) won't work...

..but much kudos to anyone who can predict exactly why..

So in the coming days i'm gonna be plastering this thing with meters, and trying to refine that algorithm to keep the weight's speed of descent rock-steady.

It's a piss-easy measurement to take, for once - simply torque * angle of the motor, vs net KE.

This is the simplest, most direct embodiment of the 'OU maths' i can think of - it's basically just a series or reactionless linear accelerations + collisions, looped back on itself in a circular trajectory.. noo imagination whatsoever..

[silent]

.

[TheVisitorV]

Mr Vibrating can you help me with a simulation?
or some calculations?