Decoupling Per-Cycle Momemtum Yields From RPM

[MrVibrating]

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

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

I should've been more specific - it states that the 'common center' is the system's center of mass; that's any freely-rotating system's natural axis..

The TL;DR is that sans some kind of N3-controversy, closed systems of interacting masses can only oscillate, be that a rotation, or wobble.

And the axle must also move

is an evident, important sentence from Bessler.

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

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

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

You've built devices that can change radius / GPE whilst holding constant MoI!? Or rigs that can perfectly cancel inertial torque against gravity, or against counter-torque, or likewise counter-torque against gravity etc. etc., whilst measuring all results and component variables down to 9 decimal places? Cos if i had to build these for real i'd still be stuck on the first one..

Mate, the photos you're posting look like sturdy rigs, whatever their proposed modus oparandi. They're clearly not designed for or capable of isolating their system momentum however so i'm definitely not duplicating your research, sir.

I'm not even going to address the 'points of physics' you raise, there's clearly little point..

If physics / simming pisses you off just ignore the thread mate. But without using computers i wouldn't be able to cover a fraction of the work in the same time. This shit simply wouldn't be getting done. Any one of these rigs, in real life, would be dissertation material, something you spend months on. Programming controllers, hot-gluing Hall sensors etc. - and once built, you'd still need to get all the telemetry / data, still need a spreadsheet to crunch it, notepads and calculators etc. Just more time, money, noise mess and waste, for impoverished second-rate data and results far inferior to a sim..


I'm putting you on ignore for now as i have no time for interpersonals, if you'll excuse me..

[MrVibrating]

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


Yo guys i think Johann might be trying to tell us something..

What's that Johann - "fat", are they? Big, chunky lard-arses? All wadling along, there, huffing and puffing..?

So, not skinny, active horses then; none of that here..

..just hulking great passive ones, apparently.






Why they so lazy?





Why they so 'plump'?





Just what might they be scoffing on their leisurely saunter, one wonders?




Something available 'on the hoof'..




..something fattening..






:|

[MrVibrating]

Re. that previous point about the constancy of the GPE input / output despite the changing MoI - the last run gained 10.4 L of momentum, in 4.2 secs. So here's the same full revolution again, this time with a fixed MoI of '1':


I honestly didn't tweak it for that result, pure coincidence..

So 5.55 L in 2.2 secs is all the output momentum that would normally be associated with this much gravitating mass..

..yet this is easily doubled by an MoI extension - without adding more system mass..

So the same amount of GPE gets turned over either way - same full 360° turn of the wheel - same amount of system mass, but over twice the period, and so undergoing twice the momentum change.

Now put your thinking caps on..

[MrVibrating]

\rant



• Bessler's statorless wheels gained momentum, despite N3.



Having emphatically defined a 'PMM' as 'posessing the potential to perform work' - ie. "energy" gains - he also stresses that this ability is directly contingent upon statorless operation; and by 'statorless operation' the only thing we're talking about is an effective N3 break; that is, an apparently-closed system somehow gaining momentum in one direction purely via the internal expenditure of work..

..so Bessler is clearly stating (as far as he does anything) that this reactionless momentum is inherently amenable to manifesting OU conditions - that the ability to gain KE over input energy is entirely dependent upon gaining momentum without counter-torquing some other inertia in the opposite direction..

..and none of this is in any way arcane or esoteric - just a fact-by-fact account of the conditions actually necessary to render an OU result, the plain truth of the energy efficiency of accumulating reactionless momentum, albeit from half a century before the vis viva disupte was officially resolved..


'KE=½mV²'.

So for 'm' let's choose 1 kg.

For 'V', 1 m/s.

Half of 1 kg times 1 m/s² equals ½ J.

'p=mV'.

1 kg at 1 m/s is 1 kg-m/s of momentum.

So the official base-rate energy cost of momentum is just ½ J per kg-m/s.

Ten of those purchases in series nets us 10 kg-m/s of momentum, for a net input energy of 10 * ½ = 5 J.

That's 1 kg at 10 m/s, for 5 J.

But 'KE=½mV²'..

..and half times 1 kg times 10 m/s² is 50 J, not 5.

This is just the energy efficiency of accumulating reactionless momentum.

There, we just arbitrarily accelerated a lone 1 kg mass, which of course is impossible - forces can only be applied between two or more inertias, so to get a more realistic handle on the maths, we should consider a pair of equal interacting inertias..

..so, two 1 kg masses, in a cyclic reactionless 'accelerate & brake' sequence..

..each cycle, one mass gains 1 kg-m/s as before, then sharing it back with the other in an inelastic collision..

..so for that 5 J of input work, after 10 cycles we'd end up with two 1 kg masses moving at 5 m/s, and per 'KE=½mV²', half times 2 kg times 5 m/s² equals 25 J..

In other words, the effiency of ten consecutive helpings of this source of momentum is simply the square of its input energy cost - it costs 5 J, but it's actually worth 25 J. It just is 25 J of bona fide KE, regardless of its provenance or cost.

Input 10 J and you get 100 back out.

Give it 100 and you get a kilojoule.

Both that cost and value - and thus the gain margin - are set by the same KE equation. Accelerating 1 kg to 1 m/s really does only cost ½ J. For the first serving, anyway.

Maintaining that ½ J/L input energy cost of momentum is the demarcation line between CoE and OU.

That line is drawn by N3, and the implicit need for reaction mass, and thus the inevitability of counter-momentum and CoM / CoE.

Bessler's simple decleration of 'EMGAT' is the smoking gun - proof that he understood the nature of mechanical OU in terms of the energy efficiency of the momentum accumulations it depends upon..

..IOW, that he'd solved the vis viva dispute long before anyone else... and gone so much further..

..yet that 'solution' - dependent upon distinguishing not just the conserved product of inertia and velocity in a closed system from the 'potential to perform work' in terms of the conserved product of force and displacement, but also the squaring nature of the KE equation and its dependence upon CoM and N3 - was also his IP, and the secret of his wheels!

If anyone thinks i'm reaching, check those facts once more: 'EMGAT' and the whole statorless thing; it's open and shut. Not simply 'for appearance's sake only'. Not concealing a stator inside. But explicitly depending upon the accumulation of momentum not raised against a counter-inertia.. and he further generalises that to any 'true PMM' - mechanical OU per se...

..as noted earlier, it's true of classical physics per se; even a magnet motor would involve an effective N3 violation at some level - if not Lenz's law at macroscopic scales, then deeper down (at a fundamental level it'd be an asymmetric inertial interaction with the quantum vacuum, mediated by 'virtual photons' exchanging signed momenta in units of h-bar)..

..hence he definitively understood the PE / KE relationship and the dependence of CoE upon momentum symmetry. He unequivocally understood pretty much everything i do, here, now, three centuries hence.. standing on the shoulders of teh interwebz.

I'm beginning to conclude it almost takes a degree of intellectual laziness to deny Bessler had explicitly and comprehensively resolved the vis viva dispute not merely long before anyone else, but to have realised it in such depth and clarity as to have seen the implicit possibility of OU, thus taking a giant leap beyond simply deducing the KE equation, conserved products of F*d and m*V, and ploughing on to recognising the dependency of work/energy symmetry upon momentum symmetry, and the implicit possibility of exploiting gravity to skew momentum distributions from on-board (ie. co-rotating) inertial interactions.. thus fixing the energy cost of momentum to a speed-invariant value across some RPM range. That's just the implicit '2 + 2'; and basically wilful ignorance to ignore..

For genuine mechanical OU... EMGAT. To know this - to be able to state it so confidently and conclusively - means you fully grasp how PE-to-KE symmetry is enforced by N3. That momentum scales linearly, while KE and F*d / T*a / 'input work' generally, all square with velocity. That products of 'inertia' and 'velocity' are conserved, in a scale-invariant law..

That's what's implicit in 'EMGAT'. Black and white.


..but his solution is also his IP! Shaggy dog story or what, eh? He can't be credited with his breakthrough because he went too damned far with it.. ended up snookering himself..

Had he succeeded in the sale, both Newton and Leibniz would be playing second fiddle in the development of classical physics. 's Gravesande etc. too - he eclipsed them all. Enlightenment physics would've grown up alongside mechanical OU, and likely, quantum-classical resolution as a result..

..provided of course the risk of perpetually grounding stray momenta was addressed; this, too, i think Bessler cannot deny awareness of, since it's also implicit in the predicates underlying the EMGAT principle; success depends upon recognising and wilfully manipulating distributions of this fundamentally-conserved property. That momentum added to Earth is literally perpetual, and will never simply dissipate back to former equilibria.. only steadily accumulating, over time..



And so back to the here & now, tackling that same bull by the nads, of simply maintaining an input-energy-cost-of-momentum that we're totally entitled to per the KE equation, if we can just overcome the practical constraints normally limiting such repeat purchases - specifically, buying the same amount of momentum, for the same energy cost, over multiple cycles..

..and critically, gaining it in the form of speed rather than inertia..


..which is the exact opposite of what i'm doing here..

..but that's because gaining speed inevitably, inextricably, means reducing cycle periods, and so diminishing momentum-from-gravity yields..

..so gaining the 'speed' component of momentum alone is, by definition, insufficient..

..topping up per-cycle velocity rises with MoI rises is therefore the only possible way to compensate per-cycle momentum yield losses from rising RPM!

So 'success' - doing this usefully, to make energy - by sheer elimination, must hinge upon decoupling the energy cost of transforming the 'MoI' component of this MoI-boosted per-cycle momentum yield, into its 'velocity' counterpart..

..obviously, the 'ice-skater effect', converting inertia into speed, costs input energy / work done against CF force, and equal to the resulting rotational KE rise..

..we have some stored CF-PE on board, that came from output GPE that didn't convert into KE..

..if we spend it pulling the MoI back in, the net result will be a system that has the same amount of KE, equal to the net GPE input, as it would from a fixed-MoI run of identical length; just with more MoI and less speed. Same energy either way..

..but it would also have more momentum. It's still at energy-unity, though..

So how to cross the CoE barrier?

Juggling momentum gains between the OB and weight axes seems to be about the only option..


..plus there's now an additional free axis there since each 'weight' has become a set of four.. if one extra axis wasn't enough..

So, how to grow an OU quantity of momentum, using only OB torque, MoI changes and angular collisions / brakes?

Ideally i want to be able to map out a clear mathematical route to OU, like the hypothetical examples above.

The key example there used two 1 kg inertias, with 1 m/s reactionless accelerations and so a 1 kg-m/s per-cycle momentum yield.

Here, we have the angular equivalents ready to roll; two 1 kg-m² inertias, reactionless torque across arbitrary angle, and arbitrary per-cycle momentum yields; 1 kg-m²-rad/s constant yield per-cycle is no problem.

So we have the same real-life components as the hypothetical 'ideal' system - the means to physically manifest the 'maths of OU'; this is the de facto 'parts list' for an OU system.. we should have the complete kit, part-for-part, here..

..one that Bessler would instantly recognise..

..we've got the ingredients, and the recipe..


..so i need to think carefully about designing the details of the following interaction - each stage has to have been thought through with the clear end-objective of bootstrapping the reference frame of an input workload, such that its absolute velocity and thus KE rise is decoupled from its relative velocity rise and cost of acceleration; and CF-PE / inertial torque remains velocity-dependent, so in previous similar attempts, the energy gain has always been equal to the input GPE plus work done against CF force..

So the key to gaining OU efficiency from CF-PE is going to have to involve collisions, somehow.. since that's all that's left to really mix things up..

Really want to be able to plan out a gain, before trying to achieve it.. but whereas that's normally my starting point, here i'm just ticking boxes off an ever-shortening list of remaining possibilities.. automatic deduction over much inspiration..

So.. drop, expand, brake, retract, unbrake and repeat... summink like dat? How might that pan out, energy-wise? Waste of time? Is there a more promising interaction here i'm missing?

/rant

[MrVibrating]

OK i'm measuring a PE gain.


Probably a false positive, but i haven't identified an error yet...

Strange thing is, the amount of gain in Joules is the same number as the OB torque, and angular acceleration value, and thus momentum change rate.. and thus gravitation rate.

MoI begins at '1', and F=mA / T=I*rad/s², which is why 'acceleration' and 'torque' share the same initial output number - if MoI had any other value besides '1', the 'torque' and 'accel' figures would no longer be equal..

..that could help with debugging (ie. change initial 'target MoI' to something other than '1', and see which quantity the 'gain' now mirrors - accel or torque?)

..similarly, since angular momentum is angular velocity times MoI, when the MoI is set at '1', the angular momentum has the same number as the angular velocity - and likewise the acceleration constant of 2.45 rad/s² is the same number as the system time-rate of change of momentum (AKA 'gravity')... which, as you can see from the 'momentum' plot, is completely unfazed by the sudden change from 'faster' to 'fatter' momentum gain modes..

So the pattern reduces to this:

• OB torque = 2.45 N-m constant

• momentum change rate constant = 2.45 kg-m²-rad/s² (= the gravitational constant of the OB axis)

• anomalous PE gain = 2.45 J




Only reason i even bothered reporting it at this stage is that as far as i'm aware, the sim in question is supposed to be really accurate..

..like, spent a week setting it up, meticulously optimising everything - it can run stably at 200 Hz / 1 integration step per frame, but obviously for data acquisition i used an over-nighter, 6.2kHz @ 1,000 steps/frame..


I'll post the sim below, but each of the two identical mechanisms (90° out of phase) work like this:

• one actuator controls the distance between each pair of radially-opposed weights, adjusting on-the-fly to maintain a constant MoI

• another actuator controls the radial displacement of the above 'MoI actuator', and thus causing the OB / GPE cycle

So each mech is one 'MoI actuator', being moved radially across the central axis by an 'OB/GPE actuator'. Identical masses are mounted on the opposite ends of each MoI actuator...

..and that's basically it, aside from one further addition:

• tensioning springs are added to keep each pair of masses centered either side of the keyed-slot carriage moved by the OB actuator

This is because the MoI actuator only connects between each pair of masses, not to the central carriage between them - so without a strong elastic restoring force relative to it, the instantaneous OB torque value could wobble, even though the MoI tracking was working perfectly.. (ie. one mass could sag in or out too far, yet the MoI actuator would just move the opposite mass too far out or in to compensate, resulting in perfect MoI control but variable OB torque).

So the end result is a system that gains momentum, from gravity, by selectively getting faster and/or fatter,

It's a 'classic OB' system - radial lifts, angular drops - plus a 'vMoI'; OB-while-getting-fatter. Very simple concept.

To be absolutely clear, tho, this is not an anticipated result. The rig was not 'complete' for its intended task - which was entirely speculative - of transferring OB momentum to a second internal axis with equal MoI. All it's missing for those tests are the brakes, and metering / driving code..

But i got it to a sufficient state where it was ready for a dry run - so, no prospective 'gain interaction' was being tested, but all metering was in place to be able to accurately solve to unity.. so it seemed a good time to take the baseline integrals..


And this is where the gain's cropped up..



Far as i can tell, it appears to be 2.45 J of OU PE in the springs...


At these 'HQ'-levels of accuracy the system should solve down to fractions of a millijoule. The gain is thus well-above noise, and curiously, or perhaps indicatively, precisely equal to the OB / gravitational acceleration, and thus time-rate-of-change of system momentum.


So, if it's error, then how so..?

..and if it's not error, then.. how so?

[MrVibrating]

OK started chipping away at it..

Gonna begin by seeing how the anomaly changes at higher precision settings.

Obviously, if this just shaves a few more sig figs off the result - ie. it's converging to ~2.45 J - then it's potentially interesting.

If OTOH it significantly reduces the anomaly, then it's obviously an artifact - integration error, somehow, that can be remedied with better maths..

I've already completed one run at lower precision: 3 kHz @ 10 integration steps / frame (so half the freq and 10x fewer integrations compared to the original anomalous result); this reduced the excess down to 1.94 J.

Can't read too much into that first bite, but that's still 2 J clear from 'pretty good' precision settings, so seems consistent with it not being an accumulating integration error - ie., suggesting that higher-precision tests will indeed only shave a few more decimal places off a converging 2.45 J excess. It'd still provisionally be an 'error', but would have to be arising elsewhere..

The original sim was an over-nighter - 6.2 kHz at 1,000 is/f.

So i'm currently running another in the background here, at 32765 frames / 5.27565 secs and 10,000 is/f..

..this is the maximum-possible precision, without breaking the interaction up into smaller sims (which is totally do-able BTW - instead of a full 360° rotation, any smaller angle could likewise be spread over all available memory, so 180° at a time or 90° or whatevs)..

..but it's gonna take time to run.

Debugging this thing with sims that need 14 hrs to run is gonna take forever - if the results from the present run do indeed converge to ~2.45 J, then i'll accept lower-quality, faster-running sims as proxies to work with in the meantime, only using higher-precision runs when their results are expected to be more worthwhile.

Again, this was supposed to be a baseline test-run of a simple unity interaction, with a view to moving on to a series of 'spin & brake' cycles, which would first gain momentum from gravity on the OB axis, before 'colliding' it into the 4 internal axial axes, repeating a series of these 'accelerate & brake' cycles and measuring the resulting energy evolution...

...so this was supposed to be a 'test-fire', not a study subject in and of itself...

..so while it's almost certainly error at this stage.. it's unplanned and unanticipated, and so i don't wanna risk chucking the baby out with the bathwater - we know a gain's possible, and if gaining momentum's 'velocity' component is indeed a dead-end then going for its 'MoI' component instead is the only remaining option - so we're standing right on the 'X', and thus digging in the right place (ie. trying to gain OU PE instead of KE).. and you can't second-guess serendipity..

So i'm gonna be patient for now, sit back and wait for the current max-quality run to complete.

With an order of magnitude more integrations, either the 'gain' will reduce significantly, say, down to 1.5 J or less, in which case it's more likely just error, or it'll converge to ~2.45 J, in which case we may yet have snagged something..

Will report back with results whenever the current sim's complete..

[MrVibrating]

..also just begun a second, parallel run using exactly the same original settings, but with the addition of a second elastic PE meter using an alternative measure:

• original sim calculated 'spring length' as the distance between the two bodies each spring connects between (a mass at one end, and the carriage-in-a-slot moved by the OB actuator at the other)

• a second meter now meters each spring length directly, using that as the basis for the EPE calcs instead

So any deviation between the two metrics must be the error source.

The reason i didn't use the direct spring lengths originally is because the equations are longer that way, ie:

(0.5*input[219]*(length(27,4)-0.998+input[232])^2)

..is slightly shorter than..

(0.5*input[219]*(Constraint[63].dp.x-0.998+input[232])^2)

..which can make all the difference since there's four of these than need adding together and equation lengths for any one meter can only be finite length; too long and it won't fit (the cursor stops responding), and just before that stage the file save gets corrupted..

If it turns out to produce a different figure however then it's obviously an optimisation too far..

While this still needs i think 6-8 hours run time, it'll still finish before the other one so i'll report back the results as they come in..


ETA: obvioushly, the '0.998 + input232' being deducted is the initial starting length of each spring, minus any preload set.

This is to 'zero' the displacement being metered:

• if preload's set to '0' then the preset tension in each spring is zero, and thus PE in each is also zero - PE only increases with displacement

• if preload's positive then so is tension and thus initial PE is ½kd²

..or to put it another way we don't want to include preset PE as 'work done' during the interaction, since it wasn't.. it was already there before the action commenced.

[MrVibrating]

..just realised a third way of metering the EPE - spring power * time!

More the merrier..

If all three still insist there's 2.45 J excess PE, then it gets interesting..

[MrVibrating]

OK that second sim started this afternoon has finished:

(This duplicates the settings of the original, just adding more meters)

Damper = -14.80192818

Acts = 1861.99888

Elastic PE = 1896.66425

Alt. EPE = 1896.66425

Net spring P*t = -1840.773642

EPE preload = 54.35834

KE rise = 7.34439


..so taking the input energy as the actuator integral, and the output energy as the KE rise plus summed net damper and net spring P*t integrals, we get:

• input energy = 1861.99888 J

• output energy = 7.34439 + 1840.773642 + 14.80192818 = 1862.91996018 J

..so the excess has reduced to 0.92108018 J.

Re-checking the 'Hooke's law' metric:

• 1896.66425 - 54.35834 = 1842.30591

..so that's

• 1842.30591 - 1840.773642 = 1.532268 J

..more than the P*t integral.

We were 2.45 J over, so that's just killed 1.5 J of it... with 0.9 J left standing.


So.. this means its similarity to the torque / accel figures was probably coincidental after all - the anomally has two sources, not one..


So i'll leave the other sim running, however long it takes, since 0.9 J is still way above usual noise levels (with 0.92108018 J of KE, a 1 kg mass would be moving at precisely 1.35726208228183 m/s - an unacceptable error margin given the entire rig only weighs ½ kg.. total KE's only 7.3 J!)..



So this remains interesting, for now...

Specifically, it appears that the standard derivation of elastic PE from Hooke's law predicts a significant PE rise (1.5 J = 1 kg @ 1.73205080756888 m/s)...


..yet, the integral of power times time (taking 'power' as force times velocity) also calculates a non-trivial PE rise (again, 0.92108018 J = 1 kg at 1.35726208228183 m/s - if that hit you in the head, you wouldn't consider it 'trivial').

If it's error then it still needs eliminating before i can move on to the intended 'spin & brake' tests.

..again, if i could only see some way to plot out a PE gain from an N3 break the same way you can with KE gains, it'd be a conceptual step forwards... without that framework it's kinda 'suck it and see'..

..but brainstorming revolutionary 'breakthroughs' when it's just yet another error is so lame, let's not go there just yet..

Could the actuator integral be at fault? Ie. could they be supplying more F*V than it's acurately recording, if that's possible?

Maybe the 'gain' will change with the FFB multiplier setting? The multiplier takes the difference between the actual and target MoI's, multiplies it by the selected value and feeds the result back to the MoI-control-actuators as 'velocity' data - so they're stationary (radial velocity is zero) when the actual MoI matches the target value, or have positive or negative radial velocity inversely to the change in MoI, thus accurately tracking it. Too low a multiplier (relative to the accuracy settings) and the actual MoI lags the target value, too high and you get judder as it starts needing to over-correct excessive radial accelerations... but generally (with all FFB applications), you want the multiplier as high as it'll go without causing jitter, to keep the action as 'tight' as possible..

..so i'm thinking, maybe there's some kind of 'micro-jitter' going on down below the noise floor that's accumulating to significance?

If so, then the '0.9 J' figure would be sensitive to small changes in the FFB multiplier..


..too late to try tonight, but tomorrow..

The 'mental-quality' run began earlier has so far reached 1.36 seconds.. will have to leave it overnight.. if not all day tomorrow too...

[MrVibrating]

Well here's a day's worth of results, using the original 'gain' settings whilst progressively raising the FFB multiplier over three consecutive runs:


FFB = 1,000
-----------

freq = 32765 frames / 5.27565 secs

i-s/f = 10

dampers P*t = -14.80180791 J (integral)

KE rise = 7.34439 J (scalar)

acts P*t = 1862.58371 J (integral)

preload EPE (per Hookes, scalar) - 54.35834 J

final EPE per Hooke's (scalar) = 1896.66464 J

final Hooke's minus preload = 1842.3063 J

springs net P*t (integral) = -1840.763481 J

diff = 1.542819 J




springs net P*t + KE rise + losses:

1840.763481 + 7.34439 + 14.80180791 = 1862.90967891 J

minus acts = 0.32596891 J gain


Hooke's EPE rise + KE rise + losses:

1842.3063 + 7.34439 + 14.80180791 = 1864.45249791

minus acts = 1.86878791 J gain


diff = 1.542819 J


..so both derivations of EPE show anomalies - 0.325 J excess from P*t, and a whole 1.542 J more from Hooke's EPE, at 1.868 J excess.



Now repeating the run, with the FFB multiplier raised by a factor of ten:



FFB = 10,000
------------

freq = 32765 / 5.281

i-s/f = 10

dampers = -14.80763058 J

KE rise = 7.34932 J

net spring P*t = -1843.231724 J

EPE per Hooke's = 1899.25152 J

preload per Hooke's = 54.35843 J

EPE minus preload = 1844.89309 J

acts = 1872.750899 J



springs net P*t + KE rise + losses:

1843.231724 + 7.34932 + 14.80763058 = 1865.38867458 J

minus acts = -7.36222442 J loss


Hooke's EPE rise + KE rise + losses:

1844.89309 + 7.34932 + 14.80763058 = 1867.05004058 J

minus acts = -5.70085842 J loss


..so, still a difference between the two sprung PE metrics, and now it's a loss..



Repeating one more time, raising FFB multi by another order:



FFB = 1e5
---------

freq = 32765 / 5.2815

i-s/f = 10

dampers = -14.79743993 J

KE rise = 7.34973 J

net spring P*t = -1842.69575 J

Hooke's EPE = 1899.50182 J

preload = 54.35834 J

EPE minus preload = 1845.14348 J

acts = 1939.070007 J



springs net P*t + KE rise + losses:

1842.69575 + 7.34973 + 14.79743993 = 1864.84291993 J

minus acts = -74.22708707 J under



Hooke's EPE rise + KE rise + losses:

1845.14348 + 7.34973 + 14.79743993 = 1867.29064993 J

minus acts = -71.77935707 J under


Conflict between the two EPE metrics: 1845.14348 - 842.69575 = 2.44773 J




So again, EPE from Hooke's law (½kd²) seems to be consistently calculating excess PE compared to the force * velocity * time integral.

Plus the actuator integral appears to be showing increasing losses as the feedback strength - and thus the radial accelerations controlling the MoI - are cranked up over each successive run.

Further, raising the FFB by an order of magnitude has likewise raised the loss, from 7 J up to 70.

Yet at the same time, with the FFB multiplier set at 1e5, the MoI control is perfect - locked to exactly '1' on both axes right up until the mode switch, and then perfectly tracking the target value all the way out. At all previously-lower settings, the MoI control was noticeably sloppier..


So bit of a bizarre mix of results thus far.. the FFB multiplier seems to be having an effect on the actuators' P*t integral, and then there's this persistent discrepancy between the sprung PE metrics...

I've used the standard EPE equation in the past, solving to unity, so can't understand why it's failing now. Of the two, though, the P*t integral seems the more accurate..

Debugging this is gonna require more work..

[MrVibrating]

..minor update:

• nothing in the sim has changed - like i say, it was designed with precision - all the main meters are using all the same equations, and all i've done in debugging is copy/blow up one of the MoI-controlling actuator P*t integrals, alongside an added F*d integral for the same workload; then tuning freq / integration steps per frame and the FFB strength, until the error between those two sample metrics is minimal.

Making a combined F*d integral for all actuators would seem dodgy, since they all have potentially different lengths and excursions, and taking 20 different F*d integrals - one for each actuator, at 32k data points per pop - is so much work as to begin defeating the purpose of simming in the first place.. So nailing the combined P*t integrals to within an acceptable error margin is the practical solution.

Results so far (still using the previous 'max freq / HQ' sim) look like this:

i-s/f = 10

FFB = 1e5

F*d = 933.1995241 J

P*t = 932.7370251 J

diff = -0.462499 J



i-s/f = 1

FFB = 1e4

F*d = 915.9918219 J

P*t = 915.1067633 J

diff = 0.8850586 J



i-s/f = 1,000

FFB = 2.5e5

F*d = 946.9764142 J

P*t = 946.7414876 J

diff = 0.2349266 J


i-s/f = 10,000

FFB = 2.5e5

F*d = 950.5879602 J

P*t = 950.3541813 J

diff = 0.2337789 J



..so it looks like v. high i-s/f's are redundant - gonna settle at a value of 100 since there's little difference between 10 and 10,000; cranking the FFB multi as high as it'll go without spazzing out seems to minimise the error, and ultimately we only need to know reliably whatever the error margin is - be it 2 mJ or whatever - to proceed with some degree of confidence..


.. i say 'proceed' - still ain't seen any gain potential yet tho, so all i have in mind is speculative 'spin & brake' regimes (ie. lock the weight axes as they descend, then unlock 'em when rising, or whatevs) and just measure the energies looking out for anything interesting..

..and yet in all this time spent debugging i've pretty much already run those tests in me head, and like i say, not seen anything interesting - obviously, it can't get wider forever, and even 1 full turn is way too much, so the actuators need to reverse at some point, and there needs to be a collision in between... uh.. but how to plot out a KE gain from an N3 break that way? Or a PE gain?


So while chewing over that central question, i've come back to a thought experiment that's just a slight variation on a previous rig i keep mentioning in all these threads, wherein counter-torque from a motor is cancelled by inertial torque from a vMoI:





I just figured another way of looking at this interaction.

It's the same general concept Fletch was playing with a few years back, namely, converting (somehow) a given quantity of momentum into a higher-energy distribution of mass and velocity, for (somehow) less than the resulting KE gain..

..the point is this:

• a 'rotor' and 'stator' begin in equal co-rotation; so, stationary with respect to each other, and at equal speed relative to the observer FoR

• a motor placed between them is activated, thus attempting to further accelerate the rotor, whilst decelerating the 'stator' to absolute stationary

• this would conserve the net momentum, simply migrating the initial momentum on the 'stator' over to the rotor

• however, the stator is also a 'vMoI' - as the motor fires, the stator mass is pulled inwards, generating a positive inertial torque that counteracts the motor's counter-torque, perfectly matching it..

• ..as a result, the momentum gained by the rotor has still come at the expense of that of the 'stator', only, it has donated it in the form of MoI rather than velocity

So you see there the connection to the current line of thought - specifically, manipulating the 'MoI' component of momentum rather than 'velocity'..


..the new question i'm asking now is this: would it be possible to repeat that interaction with unmatched MoI's instead of equal ones, such that the 'donor' MoI loses say 1 kg-m²-rad/s with a KE value of say ½ J (its optimal value per KE=½mV²), while the boosted MoI gains 1 kg-m²-rad/s for ½ J of torque * angle from the motor, yet having a KE value in the observer FoR transposed up by whatever the initial system velocity..?


IOW, exactly the same interaction as above - equal momentum in as out - but decoupling the KE loss and gain ratio. For example, instead of pulling the masses all the way in on a matched vMoI, why not pull them partially in on a much larger vMoI - so instead of starting with 1 kg-m² of MoI turning at 1 rad/s and donating ALL of that MoI, why not begin with say 10 kg-m² of vMoI at 1 rad/s so 10 kg-m²-rad/s of momentum, then reduce it by the same 1 kg-m²-rad/s, so leaving 9 kg-m²-rad/s remaining, and whilst accelerating say a ½ kg-m² 'primary' MoI against that 1 kg-m²-rad/s of 'destroyed' momentum on the vMoI?

The TL;DR would be:

• reduce 10 kg-m²-rad/s on a 10 kg-m² MoI by 1 kg-m²-rad/s

• note KE destroyed in order to sustain that 1 kg-m²-rad/s deceleration

• note KE generated as a function of the differing MoI/V distributions


..so, primary and variable MoI's begin in equal co-rotation..

..vMoI is then reduced, while maintaining velocity by:

..torquing the primary..

..thus vMoI sheds 1 kg-m²-rad/s and x J..

..while primary gains 1 kg-m²-rad/s for y J of work, but WORTH z J of KE. Type stuff.

Maybe?

[MrVibrating]

..some quick back-of-fag-packet calcs before work, to show what i'm on about:



donor / decelerated MoI


10 kg-m² @ 1 rad/s = 5 J

...minus 1 kg-m²-rad/s:

9 kg-m² @ 1 rad/s = 4.5 J




Primary / accelerated MoI

0.5 kg-m² @ 4 rad/s = 4 J

...plus 1 kg-m²-rad/s:

0.5 kg-m² @ 6 rad/s = 9 J



..IOW, any given change in momentum in one direction presents a window of opportunity for balancing a matching change in momentum in the opposite direction...

...but the distributions of 'inertia' and 'velocity' in those two discrete momentum changes needn't be the same - one could be caused by a change in MoI whilst being forced to maintain constant velocity, whilst the other could be due to a change in velocity at constant MoI; net change in momentum is zero, but change in I/O energy symmetry is positive - unlike the simmed result above when the initial 'MoI' and 'velocity' distributions were equal..


I could probably dig out that old sim and try these variations..

[MrVibrating]

..that last example was a bit random; here it is again with a bit more finesse (maybe):


• begin with two unequal MoI's co-rotating at equal speed; call it 10 kg-m², versus ½ kg-m², and 1 rad/s

• the large one's a vMoI, the small one's just a plain disc

• they're connected via a motor

• pull 1 kg-m²-rad/s off the vMoI, taking it from 10 kg-m²-rad/s, down to 9, by moving its mass inwards, whilst:

• ..keeping its speed constant, by absorbing the counter-torque from accelerating the plain rotor with the motor..

• ..thus the vMoI speed remains constant, whilst the plain rotor is accelerated

• so the vMoI donates momentum in the form of MoI reduction but not speed, whilst simultaneously, the plain rotor gains momentum in the form of speed; hence, in a nutshell, we're:

• ..transforming the 'MoI' component of one rotor's momentum into the 'velocity' component of another's - thus 'changing it up' for higher-energy

• if this works (it's not going to work) then the momentum's a zero-sum (so no 'wandering Earth'), whilst still bagging a KE gain from an effective N3 break (via the mutual cancellation of counter-torque with inertial torque)



So there's no need to even sim this for now - it's just the standard momentum and KE equations:

• 10 kg-m² at 1 rad/s has 5 J

• ½ kg-m² at 1 rad/s has 0.25 J

So we begin with 5.25 J invested.

Pulling 1 kg-m²-rad/s off the vMoI whilst holding its speed constant costs ½ J of work against CF force; however there's no need to take the CF work integral to verify that, since we can prove it simply by calculating its change in KE; 9 kg-m² at 1 rad/s has 4.5 J - so half a Joule less than 10 kg-m² at 1 rad/s. Thus logically, we've performed half a Joule of negative work against CF force, spending ½ J to reduce the vMoI's KE by ½ J.


Raising the ½ kg-m² plain rotor's momentum by 1 kg-m²-rad/s costs a minimum of 1 J; again, we can simply shortcut this by noting that to carry that much momentum it must be rotating at 2 rad/s, and applying the KE equation. If it costs 1 J from a standing start, that's how much it'll cost with an effective N3 break in operation.

So the interaction begins with 5.25 J, then inputs another 1.5 J - half a Joule of CF work, and 1 J of torque * angle.

So let's look at the energy outcome:

• the vMoI loses half a Joule, going from its initial 5 J, down to 4.5 J

• the plain rotor begins with 0.25 J at 1 rad/s, and is then accelerated up to 3 rad/s, whereupon it has 2.25 J; so, a 2 J rise

So in the end, we spent 1.5 J, to cause a 2 J KE rise...

..but also a 0.5 J KE loss.

Hence unity.

Well at least that saved a few hours animating the damned thing.

If an arbitrary 20:1 ratio pans out to unity, so will any other. It could never be so easy eh..

Or safe, i guess.. actual momentum gains must be a necessity, and the only possible source is a gravity / time differential. Bessler wheels are terraforming machines.



So OK, where we got to: we can freely gain or lose momentum from or to gravity. This is cool, and obviously integral to success.

Furthermore we can maintain momentum yields across an RPM range. This would cause OU, but only if the 'velocity' component of that momentum yield was constant; instead, it's still decreasing with RPM, but now being compensated with an 'MoI' contribution..

..and so we're only bagging 'lower quality' momentum, the fatter we get to absorb it. We're also bagging CF-PE that can be converted back to KE any time, however i can't yet see any way to calculate a non-unity outcome...

Obvioushly, CF work is inherently conservative; the KE change is equal to the CF-force * radial displacement.. so, changing up that CF-PE for KE isn't going to invoke any magic.. all the PE has been collected from input GPE..


Maybe i should just sim this part, to double-check exactly what happens? The current sim seems good for it.. i just can't see any point tho - the end result will be more momentum but less velocity so less KE, surely..?


Is there some other way of maintaining momentum yields besides raising MoI? No; only MoI changes can produce reactionless torques, thus manipulating gravity / time momentum symmetry. Simply no other game in town.


So the default conclusion must be that there's some kind of 'OU trajectory' possible here; ie. some way of changing up low-grade momentum for higher-grade, faster stuff.. but on the cheap, using a cyclic MoI variation, somehow..

The perennial 'sticky spot' eh..


So here's an idea - run that last sim for 1 turn as before, converting input GPE into mostly CF-PE plus a little KE..

..then calculate exactly how much CF-PE there is, and move the masses back inwards until precisely that much PE has been returned.

I could try returning the PE under a variety of conditions, such as regards locking / unlocking the weight axes and/or using only the 'OB' or 'weights' axes (ie. via either the pink and/or green actuators)..

Like i say, no expectation of any anomaly, but maybe it'll highlight the way forwards..

[MrVibrating]

OK so here's a basic test run to analyse:




Note how the 'target MoI' condition causes the speed to converge to 1 rad/s..




..a max-freq run using 100 i-s/f should only take a couple of hours or so, and be accurate to within a couple of millijoules.

Then, however much energy's there, i'll run it back in under a variety of conditions and see how this affects the resulting momentum and KE distributions, as compared to the same 1 turn at constant MoI..

[MrVibrating]

..LOL, the absolute BASTARD in that little MoI-juggling sideline was that a total of 1.5 J of input energy actually performs 2.5 J of work... only, half a Joule of it was 'negative' work, undoing momentum and thus its associated KE.

So ultimately 1.5 J out for 1.5 J in. That's N3 for ya.. total git huh? We can do 2.5 J of work with just 1.5 J of energy, no problem... but even then CoE defies us!

The take-home i guess is that 'counter-torque versus inertial torque' alone cannot gain momentum.. which can only be obtained by adding gravity and time into the mix..