MTM5

[MrVibrating]

Just had to correct a wrong output reference in the rotKE meter - only noticed when i started trying to tot things up - so still getting warmed up.. the intended 'completeness' i refer to tho is just the telemetry - end of the day it's just an inertial interaction, so measuring every motion of all inertias is a finite job, and the key to empirically quantifying the gain has to be there in the metrics already, just a matter of unpicking it.

I get what you're saying about loading it up - and in principle all it would require in current form is speed regulation (constant acceleration throughout a cycle is even more efficient than constant speed remember) - i'd envisage assisting a simple GPE interaction for starters, or just driving it uphill against a constant applied torque from another motor, however we're already reading the gain as KE in places so if harnessing this in a sim, we're still dependent upon trusting the input PE meters that we're realistically enjoying the discount its awarding us..

Ultimately however right now i'm not after 'proof' or convincing demos, so much as full comprehension of the disunity - when we can plot it out on the back of an envelope with confidence, then we'll know how best to apply it. All i want to accomplish for now tho is just completing the jigsaw of the gain's development, its manifest causes, nuts'n'bolts stuff. Learning to walk before running.

We know what we're looking for is a momentum anomaly - be it an effective N3 break, N1 or 2, whatevs - the PE discount has to be some form of reactionless acceleration; if there's a PE discount (as implied by a KE gain) then we're talking tangible force over displacement or torque times angle. The irreducible nature of the vis viva relationship directly implies that the same 'inertia' and 'velocity' components embodying the gain will likewise also have a corresponding anomalous momentum product.

These inertia and velocity components must either belong the specific body that is carrying the KE gain, or else whatever accelerated it. It's a simple, small system as you say, now walled-in by telemetry. We got this.

The problem with priming the desired starting velocities by directly entering formulas into body properties (rather than numbers that would all need altering with every run variation) is that any formulas, inputs or outputs used as body properties persist when stopping the sim with the intention of re-starting - such as i'm doing above when discarding the first cycle to let the jitters settle out before taking data - hence you lose all the velocity data from the preceding run. I do use that method for simpler measurements. Priming the kiiking rotor was necessary because it's rotating in the same direction as the wheel - intended to compound, rather than subtract, the absolute velocities of any anomalous momenta - its preference otherwise is to counter-rotate to the wheel.

The fact that the gain is appearing immediately in the first quarter-turn bodes well - you could reasonably extrapolate the possibility of four such interactions per turn, hence "multiplying the effect up as much as four-fold".. - the theoretical gain mechanisms i first began plotting out, years ago now, were usually dependent upon accumulating discount momentum over multiple cycles, driving through a loss phase to accelerate up to gain speeds. Immediate gain in one fell swoop - with the potential for up to four such cycles per rotation for a given wheel width - is obviously much more consistent with what Bessler was demonstrating.

But its good news for getting to grips with the gain principles too, since all we have going on in the first quadrant is an angular acceleration under CF force - not exactly a 'process of elimination' in identifying the gain mechanism then.. Spinning and braking whilst dropping is harvesting a PE discount in the form of a momentum or inertial asymmetry. The only further analysis tools needed are the three laws and the vis viva resolution. It's join the dots. A colouring-in book. Just painting by the numbers baby..

[Fletcher]

LOL .. bon chance ..

[MrVibrating]

OK here's as good a place as any to get a handle on things:

• the preset spin-up speed in our reference run is 12 rad/s relative - so the motor spins up by 12 rad/s, the two discs responding, all else being equal, as a function of their respective inertia differences per N3; the attenuation of these mutual accelerations by the CF force can thus be measured

The kiiking rotor has an MoI of 0.5 kg-m², the weight 0.25 kg-m², so a 1:2 acceleration distribution. If we zero out the wheel and kiiking speeds and control the kiiking motor for acceleration, we can observe the results of spinning it up by 12 rad/s when the axes are free to respond naturally:



..so the weight should get 9 rad/s, the rotor 3 rad/s of the 12 rad/s being dispensed by the kiiking motor.

What's obviously happening in the live run is that CF force is resisting the equitable mutual acceleration of the kiiking rotor, the weight drop forcing it to turn in the opposite direction instead - you can see it does decelerate during the spin-up, but most of the motion being imparted by the kiiking motor is ending up as weight spin.

In effect, the weight's final spin speed has been boosted by the 'velocity' component denied to the kiiking rotor by CF force.

Thus the first place to look for the emergence of the KE gain is in that lopsided acceleration..

[Fletcher]

Just a reminder to those reading that current doctrine is that Cf is a fictitious force - a pseudo force .. it is the inertia of each and every atom and their distribution in an object forced to translate and rotate at the same time - these atom inertia's are summed into a vector form that we call Cf's -- (Centripetal, Centrifugal, Centrifical force) ..

In a gravity ON environment for a vertical wheel these Cf's (inertias) oppose and reinforce gravity weight-force depending on where the weight is in its travels ..

In MrV's 1/4 and full run cycle the kiiking rotor atoms and the kiiking weight atoms are translating and rotating - thus subject to Cf's, which is reflected in how the motor "equalizer" responds as Load IINM ..

[MrVibrating]

OK so in the live run, the weight spins up by a total of 9.51466567 rad/s. So instead of being accelerated from an initial 3.361 J of rotKE to what would have been a final peak of 25.152 J, we squeezed almost another 2 J out of it, reaching 27.010 J by the end of the spin-up.

The excess we need to make up remember is 6.765 J, so we've already found 1.858 J of that, bringing the outstanding surfeit down to 4.907 J.

The reciprocal place to look for more is obviously the kiiking rotor, which would otherwise have undergone more counter-deceleration, so losing quadratically-more KE, had its reaction not been tempered by the CF force pushing the weight downwards / outwards. If its actual deceleration was less than the 3 rad/s it would have been in a vanilla inertial interaction, then we can again attribute that lack of deceleration to a corresponding KE advantage:

• the rotor deceleration over the run was -2.48914786 rad/s

Summing the two results as a cross-check:

• 9.51466567 + 2.48914786 = 12.00381353 rad/s

..so within a few decimals of the kiiking motor acceleration, a pretty snug fit.

So in KE terms, the rotor would've been slowed down to a final KE of 1.1977 J. Instead, we ended up with 1.8222 J left on it, another 0.6245 J to subtract from our OU tally, which currently thus stands at 4.2825 J.

The next obvious place to check is the work actually done by the kiiking motor, in applying this 12 rad/s relative acceleration.

Again checking in a stationary sim, we find that the motor would have performed a total of 13.5 J of input work, had this been a vanilla inertial interaction. The actual torque times angle plot however only recorded 8.16410627 J of work done, hence a 5.33589373 J input energy discount..

..we only needed another 4.2825 J to account for our KE gain however, so we now have about 1.05 J more potential discount than even needed to qualify the gain..

OK i accept it's not even a 3-sigma result so far - we want precise solutions - but feel free to take a stab at any of the above arguments, or see if you can whittle it down closer yourself - again, everything here is just N1, 2 and 3, there can't be any mysteries or black holes involved..

Bottom line: there's evidently plenty of room to account for the gain internally, and in a causally-consistent manner - there's no errant spikes or dubious fluctuations in the measurements, the gain mechanism responds deterministically, mechanistically (if it didn't get flagged it must be a word) and in a consistently-replicable manner, through multiple scratch-builds and alternative stacking forces, and it's just three moving parts, all rotating, in the same direction. There's no indication of error, and every indication that a plausible gain mechanism is running like clockwork..

I'll prolly give it another day or two to see if we can't nail it down a little tighter before moving on to quadrant 2, but the general form of the solution seems self-evident and quantitatively-sufficient to validate the results..

May try cross-referencing the wheel motor integral with a control case tomorrow - ie. rotating the same weight outwards at the same speed, but without spinning it up, to compare how much work is done on the central motor in resisting the deceleration from the widening MoI. Is the current 5.5 J workload we're seeing there more or less than it would be sans the spin-up? There may be other checks besides that spring to mind - for instance the momentum yield, compared to a passive drop, or anything else anyone can think of..

It's looking more and more watertight with each passing day tho eh..

[MrVibrating]

@Fletch - yup, CF force is 'just' inertia - resistance to acceleration - and thus the reason why angular motion is absolute, whereas linear motion is just relative - is because CF force is either present or absent, because rotation is continual acceleration!

And yet, per N2, force is force, accelerating masses, and mass times velocity is momentum. So the idea here is that any force can be applied in conjunction with time, to cause a per-cycle acceleration from an inbound vs outbound force * time asymmetry; that is, the more time you spend under a given constant (or varying) acceleration, the more velocity you're inevitably going to accrue.

This, incidentally, is why falling from higher up hurts more - because you spend more time under gravity's constant acceleration the longer the drop time. So one way of increasing effective G-time is by increasing drop-height. If you want to increase G-time without increasing height, your next best option, i would suggest, is kiiking, by any of the known methods - anything that'll cause you to unilaterally slow down (without external application of force or outside inertial interaction) will likewise mean you spend more 'soak time' under the accelerating force.

So the incentive here was to try gaining momentum or just discount velocity by kiiking against CF force, as opposed to gravity, to see if that improved the options for causing the FoR of the input energy workload to slip from the absolute FoR in which the KE manifests. Switching from the traditional kiiking principle we instinctively use when riding the park swings, to spinning and de-spinning a flywheel was the actual breakthrough however - the former method performs work against CF force, which squares with rising angular velocity, just as KE does, whereas the latter only performs work in the form of accelerating and decelerating angular inertias, which are constant invariant of velocity.

As such, CF force seems incidental to the core effect, which works just as well under gravity or even sprung tension, but CF force also doubles up as a neat way of harnessing the gain, so makes for a kind of mechanical virtuous circle, type situation.. Harnessing this way also seems to eliminate the grounding of stray torques or momenta (at least with idealised frictionless bearings), but everything's still in flux and liable to change tack any moment - whereas it seemed unlikely Bessler was rapidly spinning and de-spinning his weights like this, it now appears there may be simpler, smaller actions that exploit the same principles in redux form, the 146% gain we're currently seeing from the above quarter-turn being prime example.. The other likely-looking opportunity being that big dip in the motor plots as the weight reverse-spins back up and in during quadrant 3. We'll get there before too long, but the ability to disentangle what's going on there begins right here in Q1..

[Fletcher]

Another 'test/check' option is to mount an opposing identical kiiking rotor plus its kiiking weight disk opposite of the main one - have its velocity motor driven values the opposite of but fed by the main ones - I'm a little concerned that in a full 360 degree workup all parts aren't exactly back in their starting positions, and this is maybe effecting the SUM outputs somehow i.e. the blue kiiking weight doesn't end in the same physical position all the time .. may have no bearing at all, let you be the judge ..

[johannesbender]

This, incidentally, is why falling from higher up hurts more - because you spend more time under gravity's constant acceleration the longer the drop time.

Not to be picky I just think this is a common misconception , the final velocity is not determined by the time spend in acceleration , think a slope of 10 degrees and 100 meters long would take a lot of time in gravity's acceleration versus a slope of 45 degrees at 1 meter long , KE = 0.5 * m * v^2 .

eta ..the 45 degrees being higher than the 10 degrees.

[MrVibrating]

Another 'test/check' option is to mount an opposing identical kiiking rotor plus its kiiking weight disk opposite of the main one - have its velocity motor driven values the opposite of but fed by the main ones - I'm a little concerned that in a full 360 degree workup all parts aren't exactly back in their starting positions, and this is maybe effecting the SUM outputs somehow i.e. the blue kiiking weight doesn't end in the same physical position all the time .. may have no bearing at all, let you be the judge ..

'cycles' of the kiiking rotor are clocked in terms of 360° / 2Pi rotations relative to the wheel, and are asynchronous to wheel angle. This is another reason i prefer the internal FoR, as if kiiking under gravity - it makes the kiiking rotor angle visually less ambiguous. As a sanity check tho there's a small meter showing rotor angle in degrees; the precision of the selected cycles or part-cycles (ie. angles) to pause at is always subject to the vagaries of sim freq but are small fractions of a degree here, and besides, no T*a or other data should be 'leaking' or suspect regardless; the efficiency of 1.001 turns or 0.999 turns shouldn't be any different to that of precisely 1 turn, regardless of the microjoule or millijoule absolute difference.

Focusing on the 1st quadrant example, we're spending 14.7 J of empirical T*a or P*t, to cause a 21.5 J KE rise, over the course of 0.7 seconds. It's robust, reproducible, and obviously not attributable to mere imprecision.

The whole point of the wall-to-wall telemetry is that the gain will be squarely-attributable to a legitimate and empirical exploit. The quarter-turn result here is a microcosm of the fundamental kinematics of mechanical OU, an opportunity to learn, dissect and trawl through the precise causes of the CoE break in vivo as it's happening, backed with simple maths, physics and control examples at every step.

Focus on the quarter-turn results for now - look at it as a chance to analyse and demystify the slow-hand magic trick that it is; the kiiking rotor performs 8.16 J of work spinning up by 12 rad/s relative, yet the rotKE of the weight alone rises by 23.6 J! The whole point of the anal metrology is that this isn't a black box - there's no need for guesswork or handwavium because we have the analytical means to quantitatively substantiate everything that happens and why during those 700 ms. Armed with that knowledge, we can move forwards to optimal design implementations, which may or may not resemble anything like the current system. Trying to second-guess potential applications of the current system basically defeats its whole purpose, squandering the learning opportunity. Adding more rotors will obviously provide various benefits in terms of optimising system design and mitigating stray torques etc., but doubling the part count at this stage is only going to slow and complicate the learning curve.

Our best bet for now is to track how that 8.16 J of work being input to the kiiking motor combines with the 5.54 J of work being input to the wheel motor and the 1 J of output CF-PE to cause this 21.47 J of net KE rise.

For example, as detailed yesterday, the 12 rad/s of relative velocity imparted by the kiiking motor can be squared with the relative acceleration and deceleration between the weight and rotor's velocity deltas, yet finding that this FoR has been accelerated relative to the absolute FoR, transposing the KE's up the V² multiplier, at least part of the gain thus scaling as a function of this net acceleration of the motor's FoR; again, because the load upon it - the angular inertias it's accelerating - are speed invariant (the weight is always 0.25 I and the rotor 0.5 I, regardless of their velocities relative to anything else) - the work done by the motor is the same, even though the KE rise from performing this work in an accelerated FoR is greater; as far as it's concerned, the kiiking motor has performed precisely the right amount of work, according to its pertinent terms and conditions, yet the KE value of that workload is being transposed up the V² multiplier of the absolute velocity rise.

Within the diverging inertial frame, everything still happens at unity, all relevant conservation terms being respected at every step. Indeed, the CoE break arises precisely because of this, the gain or loss dependent upon all conservation laws doing exactly as they're supposed to at all instants, and instead arising in the velocity delta between the diverging and absolute FoR's. An accelerating FoR can only break energy equivalence with all other FoR's if its acceleration is anomalous in terms of inertial interaction or momentum exchange with its environment, so logically, the rotational KE rise on the weight is asymmetric to its input workload, at least in no small part, because the acceleration of the motor was in some practical sense reactionless, the counter-momenta either never produced or else sunk elsewhere, somehow external to the system. Obviously, we're actively sinking the counter-momentum from spinning up the weight to CF force and time, by design, and so this is inevitably how the gain is going to be empirically resolved. Whether that divergence of the onboard FoR is legitimate or not may be a separate issue, but it's already apparent as a causative factor.

I only finished the telemetry last night, so as i say, give it a day or two for stitching together how a + b = c, definitively, at every step..

[MrVibrating]

This, incidentally, is why falling from higher up hurts more - because you spend more time under gravity's constant acceleration the longer the drop time.

Not to be picky I just think this is a common misconception , the final velocity is not determined by the time spend in acceleration , think a slope of 10 degrees and 100 meters long would take a lot of time in gravity's acceleration versus a slope of 45 degrees at 1 meter long , KE = 0.5 * m * v^2 .

eta ..the 45 degrees being higher than the 10 degrees.

Gravity is a uniform acceleration (time rate of change of velocity) - the higher the drop, the longer the drop time and so the greater the net velocity.

Rolling down a slope is an inertial interaction, converting GPE into rotational KE and translational KE - more to the point however is not velocity alone, but momentum - and in your example the weight is physically grounding the momentum it's gaining from gravity.

Kiiking however means leveraging an input vs output force * time asymmetry that gains momentum from the I/O period difference times whatever the acceleration constant, without external inertial intervention. So your per-cycle momentum yield is a direction function of the ±G-time asymmetry, the difference between the I/O F*t asymmetry (the force being constant, only the time period changing).

When kiiking by spinning up the weight, we're thus producing counter-torques that brake against the down-swing acceleration, preventing the natural acceleration by the force, and so actually yielding less velocity rise, in the first instance; however something is still accelerating, even if forcefully - the weight spin - and thus the system is still gaining momentum from the force's acceleration constant.

Obviously, when the weight is then de-spun, returning to stationary relative to the wheel upon reaching BDC, all of the angular momentum it gained is transferred over, from the weight's own axis, to the kiiking axis. Thus compared to a passive drop of the same inertially-closed system, we've gained momentum - specifically in its 'velocity' component - by prolonging the period of what was, essentially, a free-fall - resisted purely by the production of forces internally to the system, without any support from the ground or direct application of torque at the kiiking axis as from a stator. The same weight has fallen over the same height against the same force, yet by unilaterally modulating its drop speed relative to the force (read: 'acceleration') constant, arbitrarily-greater momentum yields are possible. Needless to say that applying the same torques and counter-torques without the stacking force present would invariably result in zero momentum change, per N3 and N1, so the momentum source / sink is categorically the I/O F*t / ±dp/dt, and more time under a force's acceleration means more momentum, including its velocity component.

To put it another way the default correlation of dp/dt yield to a given GMH distribution is incidental and entirely arbitrary - the pendulum swing only conserves momentum because its upswing and downswing strokes are time-symmetric in relation to gravity's constancy, and the kid on the park swing only gains or loses momentum equal to the asymmetry of the accelerating vs decelerating periods, the per-cycle yield equal to the non-cancelled ±dp/dt remainder.

As far as i'm aware these kinds of autonomous decelerations and accelerations are only possible in angular systems - there's no analogous effect that could be exploited in an elastically-bouncing ball for example, since the system center of mass is always subject to the uniform acceleration - however if i'm wrong about that then it would likewise be possible to gain linear momentum from any applied force in precisely the same manner.

For angular systems however, this open-ended flexibility of momentum yields in relation to drop height and force constant is the make-or-break concession allowing us to subvert the usual conservation laws to harness effectively-reactionless accelerations. To put it another way, if we don't spin up the weight as it drops, instead just letting it swing down passively, then the system resolves to unity; we only get an energy gain off the back of an anomalous momentum or velocity gain.. and the 'anomalous' aspect being specifically the reactionless / unilateral nature of that acceleration.

[MrVibrating]

OK so in the live run, the weight spins up by a total of 9.51466567 rad/s. So instead of being accelerated from an initial 3.361 J of rotKE to what would have been a final peak of 25.152 J, we squeezed almost another 2 J out of it, reaching 27.010 J by the end of the spin-up.

The excess we need to make up remember is 6.765 J, so we've already found 1.858 J of that, bringing the outstanding surfeit down to 4.907 J.

The reciprocal place to look for more is obviously the kiiking rotor..

Snap! - rotor net dKE = -4.90905693 J!

The KE lost by the decelerating rotor was transferred to the weight. That's basically bingo to 0.002 J. I'm literally rounding these 8-figure numbers down to three decimals in the above calcs, so probably dropped 2 mJ in the process.

So the gain appears squarely attributable to the 0.514 rad/s acceleration of the kiiking motor's FoR relative to the ground / absolute frame, and the angular deceleration of the rotor in response to the spin-up counter-torque.

Retaking those numbers with eight sigfigs:

weight iKE = 3.36069388 J at 5.18512787 rad/s

Without interference from a stacking force the 12 rad/s relative acceleration imparts 9 rad/s to the 0.25 I weight and 3 rad/s to the 0.5 I rotor, remember:

5.18512787 + 9 = 14.18512787 rad/s = 25.15223159 J - what we would've got in a vanilla inertial interaction

5.18512787 + 9.51466567 = 14.69979354 rad/s = 27.01049126 J - what we actually got, boosted by the acceleration from CF force

27.01049126 - 25.15223159 = +1.85825967 J

6.765296924 J net gain minus 1.85825967 J - 4.90905693 J = -0.002019676 J. Three zeros still..

Given that the current sim frequency this is taken at is low enough to accommodate the full cycle, we could try getting a few more zeros in there by spanning the quarter-cycle across all 32,765 frames. Since this is the closest attempt at a resolution thus far i'll try this next, as the correlation seems logically causative rather than just random coincidence..

[johannesbender]

we only get an energy gain off the back of an anomalous momentum or velocity gain.. and the 'anomalous' aspect being specifically the reactionless / unilateral nature of that acceleration.

Reactionless would be nice.

[MrVibrating]

..it's still angular rather than linear, but yeah, from an energy-efficiency point of view it's handy..

[MrVibrating]

OK so here's the digits on a max-freq run of that quarter-cycle:


dKE = +21.47507952

CF-PE = -0.999984585

kPt = 8.163851907
kTa = 8.164080707

wPt = 5.545329283
WTa = 5.545329355

net in = 8.164080707 + 5.545329355 + 0.999984585 = 14.709394647
net out = 21.47507952
diff = +6.765684873
CoP = 1.46

rotor dRKE = -4.90908801
weight dRKE = 23.64971278

weight dRV = 9.51464265
rotor dRV = -2.48917088

9.51464265 + 2.48917088 = 12.00381353 rad/s - note that the catch condition for pausing is upon meeting or exceeding the specified angle ("dø >= inputX") hence will always be a little over, and it is this slight overlap that i think is getting calculated into the 2 mJ remainder in the mooted resolution; it will probably thus get smaller here from the shorter overlap at higher-frequency settings, but won't disappear unless the quarter-cycle's caught at precisely 90° in..

weight iRV = 5.18512787

5.18512787 + 9 = 14.18512787 rad/s - hypothetical final weight speed if N3 had been observed during spin-up

0.5 * 0.25 * 14.18512787^2 = 25.1522315860313421125 J - the final rotKE the weight would've had if N3 had been observed

weight fRKE = 27.01040666 J - actual final rotKE of weight

27.01040666 - 25.15223159 = 1.85817507 J - the additional energy the N3 break contributed to the weight rotKE

6.765684873 - 4.90908801 - 1.85817507 = -0.001578207 J - the rotKE transferred from the rotor, plus the rotKE from the N3 break, equals the gain to within 1.5 millijoules.. this remainder, as noted, likely attributable to the slight over-run of the kiiking cycle due to the finite size of integration steps between frames - since it's statistically unlikely the final frame will coincide precisely with the selected pause angle, some overlap is inevitable.

If this was a unity result i'd consider it put to bed here - the only thing happening during this 90° of interaction is a spin-up, whilst dropping under CF force: if we do the drop without the spin-up, we get unity; if we do the spin-up without the drop, we get unity. But if we do them together at the same time we get OU, manifestly caused by the CF interaction accelerating the spin-up interaction. We can see and quantify that biasing of the spin-up to eight sigfigs (it's 0.51464265 rad/s), and thus resolve the gain down to ~0.001 J.

So we know where the gain's manifesting, how it's materialising; counter-momentum from spinning up the blue disc wants to decelerate the green one, but centrifugal force and time are impeding that counter-deceleration, basically absorbing counter-momentum. The weight inherits the KE the rotor is divested of by decelerating, plus the half-square of the anomalous 'velocity' component times its MoI. That wraps it three zeros into the noise floor.. It's plausibly, consistently OU to at least the same certainty i usually accept for closure on conservative outcomes..

[MrVibrating]

Hmm, tried that same quarter-cycle solution with a spin-up of 24 rad/s and got a CoP of 1.76, yet the gain is significantly more than the rotor KE loss plus the weight KE gain from the CF acceleration.

Besides, even if the previous solution was valid, it doesn't explain why the energy gain isn't presenting as a load on the wheel motor..

More work's required evidently.. A 24 rad/s spin-up is pretty extreme to be fair - the kiiking rotor almost grinds to a halt, taking forever to get pulled down the full 90°. I should probably keep trying with a more sensible range of spin-ups - try halving to 6 rad/s for instance instead of doubling, see if the resolution still fits.. change in small increments to see where results start to differ from predictions, etc.

I think my analysis has to be in the right ballpark, since there's little else going on over the quarter-cycle.. but it's obviously not the full story, yet..