Success..?

[MrVibrating]

Applied the axial spin'n'brake cycles from the 'chicken run' mockup, to the 'perfect OB torque' rig.

So now, instead of sinking axial counter-momenta to a hidden wall-mounted motor, they're sunk to OB torque.

It appears you can apply inelastic collisions to modify the resulting net KE change in relation to the corresponding GPE change..


..Thus the 'OU efficiency' of the spin'n'brake cycles is no longer necessarily equal to the input GPE..



• Constant per-cycle momentum yields, invariant of RPM.

• Constant input energy cost of that momentum.

• Forcibly accelerating an OB system inevitably increases the number of GPE interactions per unit time, however GPE in/out is always a zero-sum; the additional rotKE gain rides on top of this GPE float.

• Longer spin'n'brake cycles lose net energy, non-dissipatively (ie. more than braking losses alone).

• Shorter ones gain it.


..again, shorter S&B cycles can consolidate more KE, post-inelastic collisions, than the corresponding change in GPE responsible for sinking their counter-momenta.


Example attached.

[MrVibrating]

...so, this was the original 'chicken run':



The two blue rotors are spun up and then braked, whilst a hidden motor locks the 'acceleration' value of the system axis to 'zero', but only when the rotors are accelerated - not when they're braked.

This spoofs the results of an effective N3 break - the 'orbital' axis is only responding to the braking torque of the rotors, but isn't allowed to respond to their acceleration, so we're seeing an accumulation of counter-angular momentum over successive cycles.

It is gake, and fay, but gives a visual reference to something that can only otherwise be represented in terms of maths; that with N3 effectively 'under manners', the input energy cost of momentum remains constant, not squaring with velocity like it usually does... even though its resulting KE value still does so.


So last weekend, after the latest round of failures, i went back to this old doodle, and got to thinking.. "what else might be used to sink counter-torque, besides a sneaky motor?"



And that's when i thought of this:





It's just a basic over-balancing system - angular drops with radial lifts, via linear actuators - with one slight embellishment; in-between each weight pair is a 'rotary solenoid' that constantly adjusts the distance between each weight, to lock their combined moment of inertia to a selected value: this eliminates any 'inertial torques' from the otherwise-varying MoI, resulting in a smooth and constant overbalancing torque. 'Distilled' OB torque, if you will..


..perfect, then, for sinking counter-angular momenta from asynchronous spin & brake cycles, right?


The acceleration constant of the OB system (2.45 rad/s²) is equal to gravity /4.


So now i'm spinning and braking the latter weights, tuning the combined axial MoI of the weights and their acceleration to produce a counter-acceleration equal to G/4.

This means that from a standing start, the system is in a classic 'overbalancing' position with weights extended on one side, yet it is not over-balancing, since it is perfectly counter-balanced by the net axial counter-torques. Instead, the rotors spin up to the selected speed, relative to the main axis (ie. subtracting the latter from the former), and are then braked against it; only then can the weights actually start getting lower..

..the system's only ever actually gaining any rotKE from its input GPE during those brief instants of braking..

..once in motion, successive spin'n'brake cycles simply repeat this process; there's minimal conversion of output GPE to rotKE (to three zeros, anyway), almost all of which is instead imparted by braking the weight axes.


So, the question arises: does the amount of rotKE that can be so imparted have to equal the 'sacrificed' GPE?

I mean, for instance, we could reduce the MoI of the weights, such that we'd have to accelerate them that much harder in order to still counter-balance the OB axis with their counter-momenta, meaning more rotKE input, relative to a given change in GPE.. which, if correct, would seem to suggest some degree of flexibility may be available..?


Furthermore, the actual amount of rotKE generated per unit of forsaken GPE is partly a function of the KE lost to the inelastic collision / braking phase, for each full 'spin & brake' cycle.

That, in turn, is also a function of the net axial vs orbital MoI ratio, and also the bias provided by the OB torque..


For the first few runs i'd begun with a 'target relative speed' of 1 rad/s. These runs consistently lost - pretty much exactly - 1 J. "Lost" as in, "not dissipated by the brakes".

Given the inevitably high GPE float as RPM's pick up, 1 J here or there mightn't seem worth worrying about, however the error margin was down in the 2 mJ range, relative to which 1 J is a shit-load of kapow.. just mechanically speaking..


So i tried varying various variables, still consistently getting that -1 J result... until i hit on shortening the spin-up cycles, down to 0.1 rad/s relative... then the loss inverted to this apparent gain..



So, fuck-up on my part? Near-certainty.

Fuck up by the software? Less likely, but not unprecedented..

Chance of actual success? "False positive" implies an actual working theory behind the result, which just complicates shit - confirmation bias, selective evidence, all that bollocks... none of which should sway a robust analysis tho..

It's an anomaly, at this stage, that seems to follow a basic causative principle re. loss / gain margins in relation to the respective energy * time integrals of the counterposed inertial and gravitational interactions; the next step is to trawl through it one S&B cycle at a time - spreading each one over all available memory and taking the integrals before going on to the next, and plotting up those results..

Per usual, if it's a sim error then results will vary when we zoom in like this; if it's 'real' then they'll refine the value, shaving more zeros off it..

Here's an anim, anyway (only got the gain result 2 am last night, and had no time this morning):




..just a quarter-turn of the system, already at quite-high resolution:


Acts = 35.48449126 J

Motors = 1.3387548 J

Brakes = -0.599897032 J

Sols = -1.474369706 J

Total = 34.748979322 J

KE Rise = 36.381989 J

36.381989 - 34.748979322 = 1.633009678 J gain, on the 1.3 J motor workload, not on the efficiency of the GPE interaction, which can only ever be a zero-sum!


So GPE in = GPE out, but the efficiency of the motor's work appears to be OU, at least, from the terrestrial / GPE reference frame; the correct amount of work has been done on the weight axes, for the correct input energy, relative to the FoR of the central / OB axis, in terms of torque * angle and their respective MoI's (each weight has an axial MoI of '1', here, so a net axial MoI of '4', relative to the orbital / central axis MoI of '8'), with the correct amount of KE dissipated by the brakes etc.. that's the working theory anyway. TL;DR - we're getting more momtom from gravitah than would be possible via over-balance alone.

Either that, or else it's yet another fuck-up, again.


Usual drill; will run higher-res sims and post spreadsheets for the integrals if the gain persists..

[Robinhood46]

This i like.
I asked on another post for other attempts where the weights are " not going around in circles".
At first glance i thought this was an example, i was wrong, the weights are "going around in circles".
90° of rotation is a whole cycle of the wheel. The configuration of all the composants is exactly identical every 1/4 of a turn. As with simone stevin's explaination nothing has changed. If the balls were painted different colours then you would see clearly that something has changed but the difference of the change would be equal to zero. Considering the paint of different colours to be of the same weight.
If the weights once they reach the center went back to the rim on a different path then they would not be "going around in circles" they would be evolving with regard the wheel. Their path would be a "V"
Point 1 on the rim - centre - point 2 on the rim - center - point 3 on the rim - centre, etc. etc.
This would not be "going around in circles". it would be evolving with regard the wheel.

[MrVibrating]

This i like.
I asked on another post for other attempts where the weights are " not going around in circles".
At first glance i thought this was an example, i was wrong, the weights are "going around in circles".
90° of rotation is a whole cycle of the wheel. The configuration of all the composants is exactly identical every 1/4 of a turn. As with simone stevin's explaination nothing has changed. If the balls were painted different colours then you would see clearly that something has changed but the difference of the change would be equal to zero. Considering the paint of different colours to be of the same weight.
If the weights once they reach the center went back to the rim on a different path then they would not be "going around in circles" they would be evolving with regard the wheel. Their path would be a "V"
Point 1 on the rim - centre - point 2 on the rim - center - point 3 on the rim - centre, etc. etc.
This would not be "going around in circles". it would be evolving with regard the wheel.

Yeah you're looking at two different reference frames - the static, external frame of the ground / earth, relative to which the KE is being measured, plus the rotating internal frame of the wheel, relative to which the momentum is being input, and its cost measured. Different energies as a function of velocity / time, type deal.




Attached is a slightly updated version, now controlling the motors for 'torque' instead of 'acceleration'; originally i was using reactive feedback, setting the counter-acceleration of the rotors as an inverse function of that of the central axis, however since the OB torque's constant that's kinda redundant, and so can be substituted with that simple torque constant instead.



I've also reduced the sim frequency just to make it quicker to get to grips with; obviously, it should be maxed out for the sim duration when actually taking data.

It's currently set to a loss configuration, just because it's clearer to see what's going on when higher target relative speeds are set; under current 'gain' conditions the S&B cycs are so short, the 'braking' animation frames get dropped.. obviously, tho, the interaction looks the same either way, so unless you're taking those four integrals you'd have no idea what the efficiency was..

[MrVibrating]

Just in from work; gonna use that last sim to re-run the original gain config - 0.1 rad/s spin-ups, -100 N-m brakes, one-quarter turn.

If the outcome remains the same, we'll at least have eliminated any error that might've been particular to controlling motors for 'acceleration'.

Plus, applying a constant torque also obviates the former reactive feedback loop, eliminating another potential error source.


I know about reigning in my expectations and all that, and from previous misfires i'm almost inured to feeling any excitement (just angst, really), but just check out this tantalising detail..


"4 cycs to unity, 5 to 125%" - ie., evidence of a 25% per-cycle efficiency accumulator, just as i've been predicting all these years?


..as the system starts up you see that for the first application of the brakes, the net KE drops significantly. On the second however, it dips slightly less. Still less on the third, and from the fourth onward, no more net KE drop when braking!

..i've added the velocity plot alongside to highlight that the per-cycle momentum yield is not apparently decreasing, yet - so are we finally witnessing the 'maths of OU' in action?

Gonna have some dinner, then pull dem integrals, see if the gain still arises when the motor control mode's changed..

If so, maybe we only need to analyse 5 S&B cycs in a series, which'll be handy..

[MrVibrating]

LOL even without poring over the data tho, you can already ask some interesting questions; not least of which:

• if the overbalancing torque's being cancelled 99% of the time by the internal counter-torque, yet the system IS rotating, and with it, more and more GPE being lifted per unit time... Then where the hell is the output GPE going? The weights are mostly not 'falling' back down, and the central axis lowering them is not accelerated from doing so - the whole 'overbalancing' gig is adding negligible momentum-from-OB per cycle..

I mean just suppose the energy result's in error and the system's actually at perfect unity; that means GKE out = GPE in, right? Yet how is that 'GKE' expressed if not by the over-balance causing acceleration?

The central axis is overbalancing when the brakes are applied..

..plus it's also being accelerated by the braking counter-torque..

..hence in order to arrive at a unity result, that GKE has to be found in the work done by the motors; in the rotKE of the rotors, right? Yet the actual work done by the motors is only a fraction the energy of the GPE!

Thus the only possible explanation is that just in order to render a unity result, the motor's PE to KE symmetry must already be broken! Ie. ~1.3 J of torque * angle is generating ~30 J of rotKE, thus compensating the output GKE 'sacrificed' by cancelling its OB torque..


I've demonstrated these types of unity interactions elsewhere - yeah it's unity, but the manner in which it is manifested is the point of interest: it's already trivial to yield OU work coefficients, however currently the energy cost of generating the effective N3 break is equal to the 'OU efficiency' of the accelerated workload. But you still get to witness a little bit of magic in action there.. so for an actual energy asymmetry, all we're talking about is moving the margins, not even turning a whole page..

Still, that's me tea nearly done, better get some bacon and eggs on..

[MrVibrating]

OK so that last result's in:

• freq = 32765 frames / 1.396037 secs

• acts = 35.92143626

• motors = 1.315770692

• brakes = -0.849141604

• sols = -1.456879722

• Total = 34.931185626 J

• KE Rise = 36.382467 J

• PE Discount ('KE gain') = 1.451281374 J


Sim and sheets in the attached zip.



So, not an artifact of the motor control mode, then.

Was thinking earlier, may as well start on analysing a loss scenario as much a gain, since it's the same asymmetry either way..

But whatevs - spreading each s&b cycle over 32,765 frames and then solving each one at a time is, unfortunately, hours of work, and i've a dentists appointment in the morning.. hopefully will get a couple of cycs in tomorrow evening, maybe a couple more Sat night.. but still no days off on the horizon so unless anyone else wants to start contributing to the data acquisition, we'll all have to be a bit patient here..

[MrVibrating]

..just realised - i don't think i ever bothered checking the actual efficiency of the original chicken run..

..as it was half-joking, i never thought to actually take the integral from the hidden motor..

..but if GPE-GKE is a zero sum here, then maybe gravity adds nothing more than that directional bias..?

Will check it out later...

[WaltzCee]

. . .
Hello MV

Are you saying that there is more energy in the rotational path of the blue arrow then is
required to push it up through the middle along the translational energy path of the red
arrow?

In other words, are you saying that gravity isn't a conservative Force?

[MrVibrating]

Hiya mate!

Yes and no; the gravitational interaction's a zero-sum (yet to be definitively measured but hey, pretty much foregone conclusion, right?), however the work done by the motors IS measuring as over or under-unity, depending on the 'target relative speed' value.

It appears this excess rotational kinetic energy is at least partly converting to a net negative centrifugal workload on the rotary solenoids; so the energy required to lift the weights - by the actuators - is still at unity, but the work involved in varying the distance between the weights in order to maintain a constant MoI is negative..


This is what the current numbers appear to be saying anyway, as we look closer things should become clearer..


The general theme of the work though is that gravity's conservative with regards to energy, but that gravity * time is NOT conservative WRT momentum (per kiiking etc.), and further that the energy cost of accumulating this momentum does not necessarily square with velocity.. so, 'discount angular momentum from gravity' is basically the name of the game.


Just back from the dentists; can't talk, drink tea or smoke a ciggy but i can still measure shit, so i'm polishing up the initial 'chicken run' - only ever intended as a joke - to produce actual high-quality data. I'll do a run using the same spin'n'brake parameters as the OB_chikenrun, and sum the integrals..

..what's bugging me tho is that maybe gravity isn't required - if it's just earthing counter-momentum, then why not do that directly with a simple ratchet-type mechanism on the main axis? So i'll take the integral from the motor earthing the counter-torque and just check it's equal to the 'spoofed' KE gains... Seems crazy to be checking something so simple and obvious, but if the gain persists, joke's on me eh.. Could've had it last year...

[Robinhood46]

I agree that time plays a role in the solution.
Momentum is moving energy through time. Gravity is constant.
Once you have movement you have gravity + the energy brought forwrd through time = more than gravity at any moment.

[MrVibrating]

It works like this:

• the KE equation is ½mV² for linear, ½Iw² for angular, but same deal either way; half the inertia times the velocity squared

• motion is relative, thus speed is relative, thus KE is relative; specifically, to the 'zero momentum frame'

• accelerating the ZMF allows us to transpose the value of our input work up and down the 'V²' multiplier in the KE equation; basically, 'spoofing' a lower-than-actual velocity on the input energy cost of accumulating angular momentum from gravity

• we accelerate the ZMF by sinking counter-momenta to gravity in an otherwise closed system of masses interacting about a common axis, and accumulating the resulting per-cycle momentum rise over successive cycles; violating N1 by violating N3

• thus we might legitimately purchase, say, 10 rad/s on a 1 kg-m² wheel in ten discrete 1 rad/s accelerations costing half a Joule each, per the ½Iw² equation; net cost = 5 J... however we'd then have a 1 kg-m² system at 10 rad/s, so 50 J of KE, per the same ½Iw² equation..

So basically, just playing the game, by the rules set down by CoE and CoM.

If you follow that logic, it becomes clear that really, CoE doesn't exist as a fundamental law; it's actually an epiphenomenon that falls out of the confluence of the three laws, which themselves are only anchored by mass constancy... whereas MoI is of course variable.. which in turn causes reactionless torques, caused by CoAM, which in turn cause asymmetric inertial interactions with gravity, which can accumulate momentum-from-gravity over time, and yadda yadda...

sorry i just dribble this shit these days, even without the dentists.. just study the KE equation, ask yourself why energy squares with velocity instead of just rising linearly, what factors does PE-to-KE symmetry depend on; start doing throwaway calcs for fun, just using the KE equation, momentum and gravity * time or any notional N3 break, because the thing you want to see, to understand, IS a mathematical entity in the first instance, since 'KE' and 'momentum' are differentiated by their respective terms of conservation during inertial interactions of varying elasticity; so you HAVE to grasp the 'vis viva debate' insofar as understanding the basics of energy and momentum, force, mass and motion etc.; woolly mechanical descriptions are just handwavy approximations of the real meat and potatoes..


Just finished high-precision measurement of the original chicken run; unity to multiple zeros. Phew! That's almost a relief..

..it seems to mean gravity's a factor tho.. i still think i got it pretty much right in the first post - the system's decoupling rotKE from GPE, in error or otherwise..

[MrVibrating]

Right, just doubled the efficiency by making an obvious improvement:

• Remembering that the shortest route to OU - and the greatest efficiencies - is a 1:1 ratio between the interacting inertias in the accelerate-and-brake cycle, i've increased the MoI of the weights to 2 kg-m² each; there's four of them so that raises their net MoI to '8', matching their orbital MoI around the central axis.

Repeating that same quarter-turn of the system, one full GPE interaction, i get the following results:

• Acts = 34.70492906

• Motors = 1.526070247

• Brakes = -0.760699544

• Sols = -3.172371112

• Total = 32.297928651 J

• KE Rise = 35.494368 J

• PE Discount = 3.196439349 J


Suffice to say this behaviour is consistent with the result being legit...

I've also delineated the KE plot into its respective components, revealing further encouraging details, such as this:


39 steps, * 0.04 J impulses = ~1.56 J of work

Note the way that the green staircase plot - the OB axis - is taking progressively taller steps, for the constant step-size of the momentum rises? 'Velocity' being the stand-in for a momentum plot here (since MoI's constant the 'momentum' trace would follow exactly the same plot anyway, hence little point metering it)..

This is of course exactly what you'd expect to see - KE squares with velocity, after all - however note also that the motor's input workload is not increasing with each s&b cycle - it's the same size 'blip' each time in the sawtooth plot:



..with the same area under the 'curve' each cycle..

Evidently, the same input work per cycle is buying the same rise in momentum per cycle, at escalating KE value...


"But ah!" you're thinking "You said yourself it's trivial to get 'OU' work efficiencies via these methods, however the energy cost of actually rendering the effective N3 break ultimately equals the KE 'gains', right?" and yes, that's always been true, perhaps, until now..

..but is the rate of GPE interactions actually increasing during this run? Are we accomplishing more GPE interactions per unit time, and thus lifting more and more weights as those KE steps get ever-taller..?

Well, no: it's one-quarter turn of the wheel; a single, full GPE interaction, lifting and dropping equal distance from start to finish.

As a baseline for comparison, here's the results of a 'passive' OB drop of the same weight over the same angle:



30.832204 J of rotKE is likewise all the GPE that's been input; it's the value of the GPE interaction.

Let's double-check it anyway by taking those integrals:

• acts = 38.53388135 J

• sols = -0.107862049 J

• total = 38.426019301 J

..from which we need to subtract the final radial KE:

• radKE = 7.719195 J

• 38.426019301 - 7.719195 = 30.706824301 J

..so within a millijoule of the output GKE - note that this was just a low-res example with 11,000 frames; going up to 32k would probably shave a few more zeros off that..

So we know the GPE value to within a mJ. We can thus factor this into the results of the 'live' run:

• the total input work was 32.297928651 J

• of that, we know how much was GPE, hence:

• 32.297928651 - 30.706824301 = 1.59110435 J

..is all the additional input work that wasn't GPE, and this has yielded the net 3.19 J of gain - basically 200%.

Is that right? Everyone's invited to play around with the figures - it's late, and i'm pretty burnt out here..


As ever, i want to maintain expectations here - it's a rig designed for measuring an interaction, not a machine design; everything about its design is optimised solely for taking useful data under controlled conditions. If this IS a valid result, a machine harnessing it, and the motions involved, will likely look very different; active MoI-control isn't necessary, the exploit is simply sinking counter-momenta to earth via gravity and accumulating the resulting momentum rise at fixed unit energy cost for rising KE value. That's your basic 'Bessler wheel'.

Also, consider for a moment that as the OB axis is inertially-suspended, not being accelerated back down, the Earth is still mutually gravitating upwards towards that weight, with nothing to arrest that small, but non-trivial acceleration..

A system with non-constant energy and/or momentum is evidently not closed... and we can see precisely where it's open - we're intentionally earthing counter-momentum via gravity * time!

On the plus side, a spacecraft has mass, hence a weak gravity field.. but if it can harness and vector momentum from that gravity field then it also has inertia.. and remember what gravity is equivalent to?

Would this result still stand if gravity were replaced by actual mechanical acceleration of the 'ground' FoR? Imagine a spaceship powered by its own inertia, gravity and time? Both for onboard systems and propulsion...

OK getting a bit ahead, with our poxy 3 J 'gain' here, but still; would counter-posed systems spinning in opposite directions cancel out the stray acceleration of the planet... or just leave a net 'upwards', purely radial acceleration?

We have to be thinking about how to deal with this inadvertent-warp-drive risk in parallel to every step of the system's development..

We already know the successful system reduces to something easily replicable, and there'll be many more folks out there smart enough to take themselves off-grid, than those able to grasp - or care about - the inevitable consequences..

But here i am getting all ranty about another rounding error.. i know, one step at a time.. and it has to be this way, on the BWF, cuz that's what it's here for.. all in the fates. Just along for the ride..

[MrVibrating]

OK just in from work - my 7 days slog delivering all the precious things is officially done, so at 10 pm on a Sunday night, my weekend starts NOW! Allowing ~4 hours kip before i have to get up and do it all over again, might just have time to slot in a measurement or two..

So let's have a look at a loss, just for side-by-side comparison.

As mentioned, to make a non-dissipative loss we need to decrease the ratio of rotKE being consolidated from the s&b cycles, relative to the GPE lifted. That simple.

There's obviously two ways of attempting this - we could increase the spin-up speed of the weights; since the counter-torque is balancing the OB torque, we don't want to increase the torque itself (that'd make the system rotate backwards), so we'd have to apply the same amount of torque, only for longer, in order to accelerate the weights to a higher axial speed... thus, necessarily increasing the period of the s&b cycles, and so fitting fewer into the 90° rotation / single GPE interaction.

The other approach would be to decrease the braking torque, so that more time is spent braking before another acceleration phase can begin; this, too, will reduce the number of s&b cycles per GPE cycle, so should also produce a loss.

So what i'll try next - just for a little symmetry - is to change the braking torque to match the value of the OB torque; thus the s&b cycles should produce perfect sawtooth plots, but taking up that much more time for each cycle to complete.

I'll keep the spin-up speed to 0.10 rad/s for now, just for comparison to the previous gain config.

Beer first, results when i got 'em.

[MrVibrating]

OK wow, surprise:

• as expected, this reduced the number of s&b cycs over that 90° to around 30 - down from 39

• unexpectedly, this has had negligible effect on efficiency:

Acts = 34.64441551 J

Motors = 1.199973029 J

Brakes = -0.393136357 J

Sols = -3.182225927 J

Total = 32.269026255 J

KE Rise = 35.454976 J

PE Discount = 3.185949745 J


..compare that to the previous run:

Acts = 34.70492906

Motors = 1.526070247

Brakes = -0.760699544

Sols = -3.172371112

Total = 32.297928651 J

KE Rise = 35.494368 J

PE Discount = 3.196439349 J

..when braking torque was -100 N-m

So that's interesting - the obvious question being, how low can the ratio of s&b to gravity cycles go before that efficiency starts to change significantly?

This might be tested by making the braking torque really low, so that one or two s&b cycles take most of the 90° rotation to complete..


..but for now, i wanted a loss to examine, and this ain't it... so let's try restoring the braking torque back to -100 N-m, and try raising the spin-up speed instead.

Again, the original anomaly was a loss, which seemed to correspond to a spin-up speed of 1 rad/s, so let's try that again now, with the revised rig..

Give it an hour and i'll have some more results..