MTM5

[Fletcher]

I agree with that approach - 1/4, 1/2, 3/4, 1, 1&1/4, 1&1/2, 1&3/4, 2 X - plot the COP's and refine as needed ..

fwiw I don't think running it at 6 decimals should make any real difference to the trends - but higher accuracy may do for the reason you said i.e. the pause will not stop the sim in exactly the same place each time ..

ETA .. even up the masses of the rotor and K weight by a factor of 10 .. the trends should still be there ..

[nebollinger]

Three points. 1. When I see great ideas the first thing I look for is "bottom heavy" meaning is the CG below the axle.
2. The next thing that can be exploited is match going up and down so there are minimal losses. 3. I have made many machines that exhibit OU but how do you repeat that process with very little work in. I call this the reset and the reset requires "switching" ie. change something back to where it was so it will repeat.

So now go back to point 2. picture 2 balanced seesaws where one goes down and the other up. Now picture two boys on swivel chairs and their feet sticking out horizontally. If one boy rotated his chair toward the pivot and the other away from the pivot what would happen? "those skilled in the arts - not music etc" will understand what this means.

On boy willl have to rotate his feet up and the other down balancing each other out. So if they were tied together the rotation work would be very minimal and the seesaws would go up and down easily by their opposite rotations.

Now if you use that leveraged advantage to lift a mass then that mass could be used to rotate the boys.

I am in the process of measuring this last step.

Norman

[MrVibrating]

Working thru the quarter-turn, i was struck by the realisation that the simplest resolution would be that the kiiking axis is achieving unity not only on a full cycle, but more likely throughout the cycle.. ie. all of the time.

IOW, the simplest implication is that the disunity is arising constantly and progressively on the central motogen axis.

An effective N3 break here - realistic or erroneous - would throw the apparent efficiency of the kiiking action up and down the anomalous V² multiplier, and the resulting rotKE change on the weight will be more or less than the kiiking motor workload. In reality of course it's always running at unity efficiency, but our standard metrics on that view are being skewed by the unaddressed divergent inertial reference frame caused by a directional N3 break on the motogen.

Since the sprung version of the interaction had already shown a directional asymmetry between loss and gain results, i used it to try four different variations of relative angular directions, to see if this would filter out any enlightening trends..

Here's that system, for a recap:


Note that the now-sprung stacking force vector is effectively inverted to the CF vector

Here's the four conditions identified, in no particular order:

If all parts rotate CCW from start, kiiking rotor accelerates, gaining KE, but motogen torque curve asymmetry is inverted, destroying 1.66 J net:

dKE = 13.98139601
kTa = 11.0227353
mTa = 4.622046292
net in = 15.644781592
net out = 13.98139601
diff = -1.663385582
CoP 0.89

If initial weight spin-up is reversed to CW, the other two axes remaining CCW, motogen torque curve reverts, generating 1.66 J, but kiiking rotor is decelerating, losing KE:

dKE = -14.61303529
kTa = -11.38291166
mTa = -4.895167579
net in = 14.61303529
net out = 16.278079239
diff = +1.665043949
CoP 1.14

When weight and kiiking rotor start ACW, motogen CW, both KE and motogen gain, with a 1.66 J excess.

dKE = 8.08092775
kTa = 11.08581429
mTa = -4.668145946
net in = 11.08581429
net out = 12.749073696
diff = +1.663259406
CoP = 1.15

If weight and motogen begin CW, kiiking axis CCW, motogen asymmetry inverts, burning twice the energy it previously pays out; KE goes down and kiiking motor gains 14 J, with a 1.66 J net loss:

dKE = -7.50610709
kTa = -14.32056955
kPt = -14.32187755
mTa = 8.477311485
mPt = 8.477311212

net in = 15.983418575
net out = 14.32056955
diff -1.66
CoP = 0.89


So summarising:

Condition 1; all 3 axes CCW:

• Kikking axis accelerates, gaining KE

• 1.66 J net loss on motogen



Condition 2; weight CW, kiiking and motogen axes CCW:

• kiiking axis decelerates, losing KE

• 1.66 J net gain on motogen



Condition 3; weight and kiiking axis CCW, motogen axis CW:

• kiiking axis accelerates, gaining KE

• 1.66 J net gain on motogen



Condition 4; weight and motogen CW, kiiking axis CCW:

• kiiking axis decelerates, losing KE

• 1.66 J net loss on motogen


Obviously condition 3 here is the gig to be running with, gaining net energy whilst accelerating the kiiking axis.

Condition 2 gains net energy, but whilst performing negative work, decelerating and recouping the kiiking KE.

Condition 1 successfully accelerates the kiiking axis, but whilst incurring a net loss on the motogen.

Condition 4 decelerates and recoups the kiiking KE, while the motogen again loses net energy.


Conclusions:

There's obviously two different relations being blended here; the first, we're already familiar with:

• the weight's initial spin-up direction is purposed, by design, to vector the resulting counter-torque against the stacking force, thus slowing the drop and speeding the lift; this gains net velocity per cycle equal to the I/O F*t / ±dt/dV asymmetry, as intended.

Conversely, reverse-kiiking scrubs off velocity, shedding it back to the inverse F*t asymmetry. IOW the first pattern of note is just the familiar principles of kiiking - of gaining a little ±velocity delta each cycle from unilaterally speeding up and slowing down between rising and falling strokes.

The other relationship of note however i had not formally recognised until now:

• the motogen creates energy when turning in the opposite direction to the initial weight spin-up, and destroys it when turning in the same direction

This seems to directly imply an effective N3 break across the linkages running between the two motors - the counter-torque from spinning up the weight is performing free work upon the motogen, its sign positive or negative depending on the relative angular directions they're turning..

So the task now it to design tests that specifically target this anomaly, to try establish whether it's physical or not. It'd be a pretty egregious bug if that's what it is - hard to understand why it wouldn't have been picked up before - but then perhaps the same could be said if it's legit.. it's such a simple system, the only detail perhaps verging on the arcane being this kiiking lark..

[MrVibrating]

As i see it there's two possibilities; either:

• WM has a bug that miscalculates or drops counter-torques that should be transmitted across intervening axes

Seems unlikely such a general bug would've made it through beta..

Or else:

• the intervening axes (such as axial vs orbital / translational) are legitimately isolating and rectifying unbalanced torques and counter-torques

IOW that axial-v-orbital moments thing. Note again that N3 is only observed, during the first quarter-cycle spin-up, as balancing between the kiiking rotational axis, versus the weight's translational (ie. orbital) moment, not its spin axis..

Perhaps this conversion of torque from the kiiking axis to the weight's orbital axis isn't reciprocating counter-torques back to the motogen? Something like this must be happening however..

[MrVibrating]

May be hours away from a resolution - dunno if i'll be celebrating or drowning my sorrows but need booze to cheer in the NY regardless, and the off-licences close in another hour..

If it's real though then it's stackable - nested reactionless accelerations presumably amplifying the advantage.

Seems a lot closer to the kind of exploit Bessler might've been applying too - it satisfies the EMGAT principle, it's principally directional, the 'square' vs 'circle' motifs replete throughout MT could thus be the classical allusion to heavenly versus earthly domains, as metaphors for axial versus orbital moments.. and you could easily / lightly lift or swing a heavy weight high if it presented as no load upon whatever was driving it (the effect of an N3 break). It would also presumably be dirty, in its minimal embodiment, but let's wait and see eh..

All that really needs doing now is testing to see how torques and their counter-torques are reciprocated or not, as the case may be, between the axial and orbital moments either end of these kinds of linkage assemblies. One way or another, it's basically pitch'n'put from here..

[Fletcher]

Take a break, get a few drinks in, turn up the music, maybe get together with a few friends or family, and cheer in the NY - you deserve to let your hair down and mind off the job for a few hours ;7) - no one can fault you for dedication to the cause .. it will be what it will be ..

[MrVibrating]

Chears ears and happy NY all!

Here's that interesting trans-dimensional N3 relationship again, highlighted:



..there i've just spun up the kiiking motor in a static system, to clearly show this curious relation that may be at the root of all this..

Could be wrong of course, we'll see, but just shooting form the hip here:

• if N3 is balanced between the rotational moment of the kiiking rotor, versus the translational (ie. orbital) moment of the weight as illustrated above - as opposed to the two spin axes being correlated - then does this imply that the kiiking rotor is likewise subject to non-cancelling counter-momenta from angular accelerations of the weight?

At the very least, it means that any imbalance of axial / spin momenta between the weight and rotor is not actually anomalous; it's just that the interaction is conserving momentum by distributing its counter-component into a different coordinate frame - half of it's angular, the other half translational.. the FoR of the weight motor wouldn't then strictly be divergent if it's not necessarily supposed to be equitably exchanging momentum with the rotor in the first place..

Or perhaps more likely is that N3's applying alternately between both angular-angular and angular-translational interactions, depending on whether the kiiking motor is torquing against the motogen, or vice-versa - since this is one of the practical effects of constant velocity or acceleration on the motogen, sometimes resisting acceleration, sometimes deceleration, in response to the varying counter-torques coming off the kiiking motor. Hence if this to-and-fro of alternating torques and counter-torques is also alternating between angular-angular and angular-translational interactions, then N3 itself may end up being subverted to rectify non-cancelling momenta between the two different coordinate spaces.. The principle would thus be legit, albeit still amazing no one's noticed its potential before..

I guess i can see the next, perhaps final (?) round of sims coming up - two motors either side of an axial-translational interaction, linked by a free axis, then checking for N3 symmetry between axial-axial vs axial-orbital exchanges in opposite directions, again plotting out the finite permutations of each motor either torquing or being torqued by the other, and alternating between acceleration vs deceleration in both directions - so another four interactions in total (axial-axial in each direction and axial-orbital in each direction), noting which observe N3 and when..

Unless i think of anything better to try first, that looks like the best lead for now..

[MrVibrating]

Hmm can't help thinking - the translational moment of the weight is actually part and parcel of the angular moment of the rotor, no?

I mean, if modelling the system from the bottom-up i'd calculate the mr² of the blue disc relative to the green axis, adding it to the green disc's moment: it's 1 kg at 0.5 m radius from the green axis so mr² = 0.125, plus the green disc's 0.5 moment makes 0.625, and multiplying this by the green angular velocity gives its angular momentum (and half that squared its rotKE)..

Point is, if the blue translational axis is really just the green axial axis, then momentum and counter-momentum are actually born on the same moment and thus already cancel out to zero.. leaving the 2.250 L of axial momentum on the weight unbalanced..

In effect, the top-down model i ended up implementing - just summing WM's metrics for discrete angular momenta and rotKE's - may be misrepresenting the system somewhat - arguably in a mathematically-equivalent way, but still over-complicating the picture of what is, in essence, just an unbalanced remnant momenta from an otherwise mutually-cancelling interaction.

The reason i threw in the towel on sorting the bottom-up model i was originally working on was because of the epicycle as the weight alternates between orbiting in the same direction as the rotation around the outside part of its loop, but then travelling in retrograde motion back the other way when passing around the inside leg. This means adding and subtracting translational and rotational velocities depending on their constantly-alternating relative directions..

A problem any 18th century-educated kid could probably solve on the back of an envelope, i could only tackle using kludgey operator logic. Getting the maths right for stationary and rotating in either direction is painstaking - i could presumably have looked up some leaner solution, but then i realised that simply summing all discrete momenta was numerically equivalent, and wanted to get the sim usable ASAP..

But the same point obviously applies to the transKE's as well - the tKE of the rotor for example is really part of the rotKE of the wheel.. Still adds up the same way, but the presentation's somewhat misleading, requiring this recognition that it's simpler than it's making out..

[MrVibrating]

Not sure that isn't another false start:



..spinning and then braking shows no remnant.

Still curious as to why a remnant is implied in the figures in the first place.. is that not weird?

Might just try assigning equal MoI's to all axes, axial and orbital, to see if that simplifies the results..

May also try adding the translational values to their respective axial moments to remove their extraneous plots from the presentation..

[MrVibrating]

I've added the translational KE's of the two mounted discs to the rotational KE's of the discs they're mounted to, and then inverted that KE sum by the angular velocities of the respective discs to derive their MoI's, multiplying back by the velocities to plot the momenta.

As far as i can see this has to be arithmetically accurate.

In the calibration version of the sim, below, the wheel motor is held stationary whilst acceleration is applied to the kiiking motor:



Pay attention to the momenta - noting that N3 symmetry is observed between axial and orbital momenta of the weight and rotor.

If the wheel axis were unlocked and free to rotate, i would expect that all momenta would still cancel, yet this is not what is observed:


Ignore the spike, it's non-mechanical & caused by infinitesimal division as the green rotor speed inverts momentarily

It's weird - if i then lock the kiiking motor at any point on that wave, there's a small but persistent residual. The k-motor is only set to accelerate to the target spin-up speed then coast, which you can see it's doing correctly in the velocity plots.

Here's a simplified example:


Only the smallest disc is motorised, accelerating for one second from stationary, then coasting.

Upon coasting, CoE is observed, but not CoM, at least as-formulated by the KE-derived momenta - and the KE sums match kinetic(), as well as basic logic..

If we then drop the anchors on the middle disc too, everything, mercifully, freezes - there's no net energy or momentum left about the central free axis.

Logically there's no net momentum at any instant when performing the acceleration whilst orbiting the free axis, yet if that is the case, how to formulate it correctly? Are the KE-derived momentum formulas consistently valid? How can we observe N3 symmetry unfolding - as it demonstrably must be - like we do with the wheel axis locked?

You can see the dilemma - i want to monitor N3 symmetry throughout an interaction, yet if i can't even do that in a control case when it obviously isn't compromised, how am i supposed to formulate any anomaly that might develop in a live run?

[Fletcher]

I think I have run into this head-scratcher previously MrV - on cross-checking a sim or two in years gone by .. basically metering Momentum outputs that the sim calculates then cross-checking by striping out the individualized components and separately metering them, them summing them as the cross-check against total generating outputs ..

IIRC I think I concluded at the time that the sim package is a program running on our screens - so when we lock things (pin) in free-flow that momentum must go somewhere - in real-world it goes to earth - the thought at the time was the screen is effectively the earth for all intents and purposes, but it doesn't physically move about thru N3 when we lock something - IOW's some momentum disappears etc ..

Now this was a long time ago, and I haven't thought about it since, so my memory is not entirely reliable on that .. but I recognise the process and logic you are going thru to get to the bottom of anomalies and irregularities and come up with a plausible explanation .. actually I'm enjoying watching your workups, refining the theory, and your conclusions ..

[MrVibrating]

Yes you're right of course, any net momentum we measure must be balanced by a cancelling counter-component even if grounded & unmetered. Usually, based on the iron-clad assumption of N3 & N1 it'd be safe to simply infer its presence - even in the case of a floating base; if it contains parts with a net dp of '1' then all else being equal we could confidently just write down its counter-dp as '-1'.

If there were anything contentious to be demonstrated OTOH, it obvs needs calculating too..

We know that in a control case, when the k-motor's simply accelerated with the wheel axis unlocked, the net system momentum remains a constant zero - proven by locking the two orbiting axes at any point.

So until i can come up with a meter that displays this fact, it's going to be impossible to characterise the exploit empirically. If it's real, e/p is the blood in its veins, the stuff of the energy gain / loss.

I could just side-step the issue and proceed purely on the basis of energy results in the hope of coming up with a plausible physical experiment, but even if it works it'll be impossible to write down the maths of why without invoking a miracle. Proceeding to builds before eliminating the possibility of error is likely a waste of time and resources - cargo-cult reverse-engineering - whereas we want to be able to write down the underlying theory and test its specific predictions. So frustrating as the cliffhanger is, logging momentum is the main mission not a side-quest..

My Calibration version currently has umpteen different panels calculating everything in slightly different ways - top-down and bottom-up - ie. subtracting bottom-up calcs of MoI * Vel from kinetic()-derived momenta should leave a value matching the summed transKE-derived momenta as well as WM's body[x].mass * body[x].v values - but i still can't figure out how to recombine these into a constantly self-cancelling running total when the central axis is free..

If it takes another week or more, it obviously has a logical solution so it's just a matter of puzzling it out. I tried popping the question on Stack Exchange but anything resembling the 3-body problem is unlikely to get a bite (even though this is a bounded linear system, not chaotic)..

If i have a hunch, it's that since the MoI values derived from the rotKE or transKE values are constant not varying, simply multiplying them by the correct angular velocities should suffice. The fact that this doesn't currently work can only imply that relative velocities need factoring in. The cognitive dissonance i have there however is that the rot and trans KE values are based upon the absolute not relative velocities, hence logically the inverse operation to derive the MoI must be I = 2*(KE / w²) where the latter term means abs(w²) (KE being scalar), so does this also mean the resulting MoI's must be re-multiplied back by the abs vels to give valid momenta, or is it legit to then subtract 'base' vels from ' mounted' ones? I'm wary of invoking 'relative momentum' before i have a handle on the absolute variety, but maybe this is the real conceptual hurdle here..

[MrVibrating]

..on further reflection i think that might be the solution.. will try it later. Bashically whereas the net KE sums the instantaneous component KE's, i need to be tracking the internal changes in L, which should produce a net zero. If that makes sense.

Once the momentum's accurately calibrated, we can apply N2 using the correct MoI's and relative accels to derive the torques acting between these inertias..

..and then compare that to the torques actually being applied on the wheel motor / moto-gen. This should reveal any torques sans counter-torques, which in turn can be correlated with any anomalous momentum or velocity delta that develops, and the resulting energy anomaly.

That will be cause to proceed to physical experiments..

[MrVibrating]

I may finally have calibrated the momentum meter - the result is a mish-mash of derived and calculated momenta, which - for reasons i'm uncertain of - finally appears to display some kind of appreciable symmetry when the central axis is both free and locked; the calibration run is an acceleration of the k-motor, then coasting a while, then locking the blue axis, and then finally locking the green one too.

When i say 'appreciable symmetry' however, i don't mean a mutual-cancellation; the following demo is running in super-slo-mo just to give the eyes time to take in the data (watch the momentum plot):



Et voila, N3 symmetry. Kinda.

The reason i was having such difficulty calculating the instantaneous zero-sum is because there isn't one, apparently - the symmetry we see above starts to diverge as the weight's translational motion transitions from mostly x-plane - when it's thus pushing the wheel in the opposite direction - to mostly y-plane as the green disc rotates around, thus reducing the counter-torque being applied to the wheel, however this initial symmetry we see above cannot be coincidental; the meter, finally, appears to be correct, and is showing us a rotational momentum on the main wheel that is a counter-momentum to another counter-momentum that has already cancelled the primary momentum!

So a momentum that's being mutually cancelled in real-time is nonetheless inducing a kind of shadow momentum that is entirely orphaned from a reciprocal quantity. The N3 break manifests immediately, and is intrinsic to this arrangement of a satellite motor torquing the three underlying discs.

Recall that the weight's rotational dp is balanced in the first instance not by the rotor's rotational dp but by its trans dp; that is, torquing the weight CCW initially applies a rightwards translational force to the rotor, which in turn causes it to begin rotating, so N3 symmetry is primarily acting between the weight's moment and the rotor's translational motion.

The wheel thus in turn responds to these translational momenta being applied to the rotor, mirroring them - just as N3 says it should - even though they're already mutually cancelled by the weight's angular momentum.

In short, cancelling a rotational dp with a translational one induces a third, extraneous and orphaned translational counter-momentum.

Moreover, this is happening not in spite of N3, but because of it. You got your N3, then your N -1.5, N4.5, and so on.. (JK)

Surprising results eh? Yet entirely physical, apparently, and following from the simplest fundamentals..

I need to test this finding further, but it seems to jell - not least in explaining why i've been finding it impossible to derive mutually-cancelling components; it's a closed system of masses interacting about a common axis, yet - audacious as it sounds - having a non-constant net momentum.. An N3 break resulting in an N1 break (as i've suspected for the last week or so).

So my initial intention of gaining discount momentum from the I/O F*t asymmetry is not what's causing the gain - serendipitously, i've stumbled across an N3 / N1 violation that is present constantly the entire time the satellite motor's engaged; as the first-quadrant results affirm, the system's already OU long before a complete cycle of the intended exploit, in a single stroke of the full four-stroke cycle. For its part, the cycle may likewise be a lucky roll of the die insofar as successfully rectifying a consistent gain from the unintended effect, although obviously, now that we have a better idea of what's really going on, more-optimal cycles may become apparent..

The upshot's that non-constant system momentum is the first step towards rectifying energy gains. You can't do that by juggling internal momenta when the net system's constant regardless, but when it isn't, just about any inertial interaction, elastic or inelastic, has the potential to break CoE..

I'll want to check quads 2 thru 4 to make sure its this same rot-trans bastard running amok, but it seems inevitable - the data above's just too convincing..


Updated sim's attached, will probably be w/e before i get time to do much more..

[MrVibrating]

..wait, wait, no - so desperate was i to see some kind of balancing sum, i forgot to ask the all-important question; if there's an unbalanced momentum, why's everything freeze when the two satellite axes are locked? That simple test seems to unambiguously certify the system as N3 & N1-compliant. In which case, there must be a mutually-cancelling sum in there, no?