MTM5

[MrVibrating]

OK here's a reference interaction, first whole then split into four parts - i don't know how useful the CF-PE metric is; it's the 'G-force on weight' in Newtons integrated over the weight's change in radius relative to the main wheel.

2 rad/s, 8x spin-up, one full cycle:

freq = 7554

initial KE = 23.005015119
final KE = 31.990645943
KE delta = +8.985630824

kiiking motor P*t = 8.984514562
kiiking motor T*dØ = 8.987831603
wheel motor P*t = -6.153193057
wheel motor T*dØ = -6.153193057
CF-PE = -0.000000144043

net output = 8.985630824 + 6.153193057 = 15.138823881
net input = 8.987831603
unaccounted = +6.150992278
CoP = 1.68




Now broken down into four quadrants:

first 90° from TDC to 9 o' clock, weight spinning up:

frames 0 - 25529

initial KE = 23.005015119
final KE = 50.484938090
KE delta = +27.479922971

kiiking motor P*t = 8.058564295
kiiking motor T*dØ = 8.058851727
wheel motor P*t = 14.94369735
wheel motor T*dØ = 14.94369735
CF-PE = -3.999035259




from 9 o' clock to BDC, weight spinning down:

frames 25530 - 28841

initial KE = 50.490765015
final KE = 68.035451655
KE delta = +17.54468664

kiiking motor P*t = -0.990851783
kiiking motor T*dØ = -0.990118136
wheel motor P*t = 19.9334119
wheel motor T*dØ = 19.9334119
CF-PE = -3.999776579




BDC to 3 o' clock, spinning up in opposite direction:

frames 28842 - 30664

initial KE = 68.038354164
final KE = 54.800859208
KE delta = -13.237494956

kiiking motor P*t = 3.979474622
kiiking motor T*dØ = 3.980893831
wheel motor P*t = -21.69102873
wheel motor T*dØ = -21.69102873
CF-PE = 3.998057936




3 o' clock to TDC, final de-spin:

frames 30665 - 32765

initial KE = 54.780963992
final KE = 31.990645943
KE delta = -22.790318049

kiiking motor P*t = -2.064790714
kiiking motor T*dØ = -2.06391498
wheel motor P*t = -19.32456473
wheel motor T*dØ = -19.32456473
CF-PE = 3.998289143


So this should help track the development of this 6.15 J gain, if anyone can make sense of it..

[MrVibrating]

Q1:
total in = 8.058851727 + 14.94369735 + 3.999035259 = 27.001584336
total out = 27.479922971

So +0.478338635 J up



Q2:
total in = 19.9334119 + 3.999776579 = 23.933188479
total out = 17.54468664 + 0.990118136 = 18.534804776

-5.398383703 J down



Q3:
total in = 13.237494956 + 3.98089383 = 17.218388786
total out = 21.69102873

+4.472639944 J up



Q4:
total in = 22.790318049 + 3.998289143 = 26.788607192
total out = 2.06391498 + 19.32456473 = 21.38847971

-5.400127482 J down


(+0.478338635) + (-5.398383703) + (+4.472639944) + (-5.400127482) = -5.847532606

But this is still -0.303459672 J down on the 6.15 J gain..

Or is trying to sum the results from each quadrant like this a nonsense? Can anyone else make better sense of it?

[Fletcher]

I dunno if this is helpful or not MrV .. pic and sim included ..

I metered Power (Watts) to/from Wheel and Kiiking Motors, and plotted them (hidden) - I then summed them for total draw etc then divided that summed total by 10 to get a better scale effect ( can't find an average function in the WM program ) ..

The idea was to try and establish a Power usage and surplus trend from the motors doing the work ..

[MrVibrating]

Perfectly valid to sum P*t integrals, even from different mixes of actuators and motors, and will give a bottom line i guess. I'm completely focused on auditing it for now tho.. It's looking more compelling with each passing day, but also, more familiar - getting over the initial shock (and number-intimidation), it's apparently reducing to precisely the mathematics i've been espousing all this time. I suspect we're already seeing a level of consistency that increasingly precludes error or oversight..

Ok, so.. let's look at energy cost of momentum as a function of speed - this is ultimately the intended exploit after all.

I'm metering the compound angular momentum of the kiiking rotor relative to the wheel - as if the CF force were just ordinary gravity. I've added a kiiking startup speed input, so i'll do a batch of tests, incrementing the initial kiiking speed by 1 rad/s each run, and then calculating the e/p.

Here's the first example:



And here's the data from a max-freq run:

initial kiiking speed = 1

final KE = 32.037434361
initial KE = 23.500086157
KE delta = +8.537348204

kiiking motor P*t = 8.536108068
wheel motor P*t = -6.152402227

final kiiking AM = 3.188790105
initial kiiking AM = 0.749967712
kiiking AM delta = +2.438822393

e/p = 3.5000

..yes, it actually came out square to 4 digits like that. Neat huh?

It's those same numbers again - we converge towards 350% efficiency, the wheel is 3m radius, the green disc's 1m radius and the blue one's 0.5m. This hint of a relationship between relative radii and CoP needs further investigation..

..but for now, how will this e/p efficiency change as initial kiiking speed is increased? I honestly haven't checked any further than this, so far - nail-biter eh? - but i'm gonna stay up a bit longer and run off a short batch of these; results to follow..

[MrVibrating]

initial kiiking speed = 1:

final KE = 32.037434361
initial KE = 23.500086157
KE delta = +8.537348204

kiiking motor P*t = 8.536108068
wheel motor P*t = -6.152402227

final kiiking AM = 3.188790105
initial kiiking AM = 0.749967712
kiiking AM delta = +2.438822393

e/p = 3.5000 J/kg-m²-rad/s



initial kiiking speed = 2:

final KE = 32.493777964
initial KE = 25.000132317
KE delta = +7.493645647

kiiking motor P*t = 7.491510283
wheel motor P*t = -6.152206202

final kiiking AM = 3.268031592
initial kiiking AM = 1.499950424
kiiking AM delta = +1.768081168

e/p = 4.2370



initial kiiking speed = 3:

final KE = 33.841102360
initial KE = 27.500162081
KE delta = +6.340940279

kiiking motor P*t = 6.339618043
wheel motor P*t = -6.152386651

final kiiking AM = 3.492518487
initial kiiking AM = 2.249939286
kiiking AM delta = +1.242579201

e/p = 5.1019





initial kiiking speed = 4:

final KE = 36.337566981
initial KE = 31.000181171
KE delta = +5.33738581

kiiking motor P*t = 5.33642258
wheel motor P*t = -6.152423411

final kiiking AM = 3.873882080
initial kiiking AM = 2.999932150
kiiking AM delta = +0.87394993

e/p = 6.1061




initial kiiking speed = 5:

final KE = 40.037077107
initial KE = 35.500193179
KE delta = +4.536883928

kiiking motor P*t = 4.535479147
wheel motor P*t = -6.152105054

final kiiking AM = 4.377963689
initial kiiking AM = 3.749927668
kiiking AM delta = +0.628036021

e/p = 7.2217


So the energy cost of momentum is increasing with speed, yet there's this persistent 6.152 J gain each cycle, invariant of speed..

In an independent sim i set up a motorised wheel with the same 0.75 kg-m² as the kiiking rotor, gradually accelerating it between the momentum gains for each of the above cycles whilst monitoring kinetic() - it turns out these e/p rates above are actually greater than their baseline ½mV² values, at least in relation to the kiiking motor workload i've referenced them against, though i'm not sure what to make of that at this point..

The 6.152 J gain, we already know from previous analysis, is already present as KE upon reaching BDC, so the momentum yield - which at that juncture is still incomplete until the weight rises back to TDC - seems somewhat academic.. yet 6 J of anomalous KE obviously has a corresponding momentum component, so there must be some way of calculating or deriving this..

[MrVibrating]

That's it - since we know the MoI we can invert the rotKE equation to solve for a velocity delta, which we can then re-multiply by the MoI to find the momentum gain corresponding to each 6.152 J KE gain.

Throbbing headache at this stage so packing it in for the night..

[Fletcher]

Don't blame you ..

If this analysis methodology is all legit (just saying) then could you not turn gravity back ON and put a pinned freewheeling rim weight just after tdc - cycle the sim up on motor input for some revolutions and then turn OFF the big wheel motor .. gravity is conservative so with no losses what goes down must come up - and the KE (momentum) gain should still be there and continue accumulating ?

Maybe I'm going off the reservation ..

ETA ..

Still spinning my wheels here ;7)

Even simpler still - maybe do both - take the current sim and analysis methodology, and just turn Gravity ON - since everything is coordinated to velocity shifts then the KE gain trend should continue - right ?

[agor95]

Hi

You are giving us an example of high level research.

P.S. I'm going off the reservation at the moment.

Regards

[MrVibrating]

@Fletch - as things stand currently it's a delicately coordinated dance, so simply switching gravity on is chucking a big spanner in the works; about the only good reason for going vertical would be to attach an OB system - which is obviously a legit ambition - but the gravity-independence is frankly there to be exploited.. i'm personally more keen to see a small, robust high-power unit driven by sprung forces..

Because the current sim's designed for asynchronous internal / external wheel speeds, you could perhaps look for the least-disruptive angular velocities that resonate somewhat with the tumbling gravity vector, but it'd obviously be better to spin a balanced system rather than one that's gonna shred its bearings.

That's all jumping far ahead for now - the only FoR of interest or use at the moment remains the internal, rotating one, treating CF as gravity. Watching the action from the ground FoR doesn't necessarily even hint at what an actual application of the effect may look like.


@All - I understand that since the energy's patently there, there's nothing to stop us trying to harness it already, just using suck-it-and-see engineering (lift a weight, tension a spring or whatevs) - who cares how or why it works, let's get plugged in, right?

Anyone thinking like this needs to take a deep breath and a step back, because the first priority is basic theoretical comprehension; we need to grasp exactly how and why it works before proceeding further. Remember, Bessler said the power can be multiplied up to a precisely-calculated degree, implicating a maximum of four-fold, with the 'quarters' riddle implying a factor of sixteen. Anyone here see what might be involved in such an optimisation? This simple question's a good example of the current gap between our knowledge and ambitions..

We've seen hints of where to look however, because of the noted recurrence of CoP variables that seem to correlate to the relative radii involved. If you recall, i did try increasing the green wheel's radius to half that of the main wheel, finding that this slashed CoP, but this leaves open the implication that going to even greater radius ratios may improve CoP further beyond this apparent 350% convergent maximum at the current dimensions. It may be that having many, much smaller kiiking rotors around the periphery significantly boosts energy and power densities (just for example, this will minimise the relative CF delta throughout a cycle).

When we truly have a handle on it, then we'll also be able to multiply it up to a precisely-calculated degree.. and at that point we'll know enough about what we're talking about to begin designing applications.

Make no mistake however, float tests are going to go hand-in-hand with every development, and if the only way to do this safely is in counter-rotating pairs, we have to take that on as a blessing rather than curse.. (Anyone blasé about inadvertently piloting the planet can GTFO right now..)

[MrVibrating]

Previously i've only tried raising wheel speed in doubles, noting diminishing efficiency, so here's a closer look at the lower speed ranges up to 5 rad/s..

kiiking speed 1, 8x spin-up; incrementing wheel speed in single-cycles from an initial value of 1:

initial KE = 6.250081805
final KE = 10.829918766
KE delta = +4.579836961

kiiking P*t = 4.578485231
wheel P*t = -3.076550615

in = 4.578485231
out = 4.579836961 + 3.076550615 = 7.656387576
diff = +3.077902345
CoP 1.67


2 rad/s:

initial KE = 23.500086157
final KE = 32.038717062
KE delta = +8.538630905

kiiking P*t = 8.536108068
wheel P*t = -6.152402227

in = 8.536108068
out = 8.538630905 + 6.152402227 = 14.691033132
diff = +6.154925064
CoP = 1.72


3 rad/s:

initial KE = 52.250092045
final KE = 65.089186438
KE delta = +12.839094393

kiiking P*t = 12.83623347
wheel P*t = -9.228476384

in = 12.83623347
out = 12.839094393 + 9.228476384 = 22.067570777
diff = +9.231337307
CoP = 1.71


4 rad/s:

initial KE = 92.500122741
final KE = 109.832148920
KE delta = +17.332026179

kiiking P*t = 17.32844479
wheel P*t = -12.30499906

in = 17.32844479
out = 17.332026179 + 12.30499906 = 29.637025239
diff = +12.308580449
CoP = 1.71


5 rad/s:

initial KE = 144.250101462
final KE = 166.202224470
KE delta = +21.952123008

kiiking P*t = 21.94835651
wheel P*t = -15.3807135

in = 21.94835651
out = 21.952123008 + 15.3807135 = 37.332836508
diff = 15.384479998
CoP = 1.70


Conclusion: around 2 rad/s seems to be a sweet spot for the current dimensions.


Not sure what to try next - the 6.152 J per-cycle gain from the previous reference run correlates to an angular velocity delta of +4.050 rad/s from a relative standing start, an AM delta of +0.786 L, implying that this is the size of the divergent inertial frame causing the gain.

I think the most tantalising prospect might be to pull on this thread of an implied relationship between CoP and relative radii by going for a higher ratio, ie. a relatively smaller kiiking rotor, to explore the possibility of trading absolute quantity of gain for potentially better CoP quality..

[Fletcher]

Appreciate what you are saying MrV .. you are running sensitivity analysis to various inputs and dimensions, ratio's, masses etc - the idea being to identify any firm trends in Outputs when Inputs are changed - a logical process of change of Inputs should give a logical change in Outputs i.e. trend analysis - then you can identify (as you are doing) pessimistic, realistic, and optimistic ranges and conditions for such, IN THIS MODEL ..

It's a process of what I like to call "Stress Testing" the sim model and the assumptions .. stress it till it breaks, and then back off ..

IMO one of those important changes is testing the reliability of the inertia's .. the program automatically computes the MOI for each object based on a mathematical formula .. in the real world MOI's are determined by experimentation and the math model gives a good approximation - this is due to not all objects being totally uniform homogeneous materials etc ..

So can I suggest that you swap out the Kiiking Wheel for a rectangular pendulum rod etc etc - vary the diameter of the pendulum bob (blue kiiking weight - maybe try a square rather than a circle ?) - these small structural changes will change the MOI's somewhat, but should help stress test the sim model and your assumptions and methodology so far .. if the trends continue true to form all well and good for your hypothesis ..

[MrVibrating]

..having just consulted the oracle of the bathtub and scotch, it may be time for a scratch rebuild with the following features:

• input-selectable radii all round

• a duplicate reciprocating system (might as well start how we mean to go on)..

• ..attached to a 'spaceship' mass, that can be unanchored (we can beam our energy gains safely back down to Earth, in principle)

..poor old Greta would have an aneurysm if she could see what we're doing right now..

This will mean lengthening all the formulas to incorporate the additional spaceship FoR, but this way we can lift anchor and let it flop around or go wherever the impetus takes it, without the mechanism getting in a muddle..

Switching from discs to adjustable beams also clears away all the dead mass; MoI's can be implemented via counter-balanced 'flyweights' with adjustable mass and radii..

[Fletcher]

Evolution and Negentropy at the same time - evolution to simplify, casting out redundancies and distractions, and automating; and negentropy to dial-in and make things more complex and ordered ..

Hope your computer processing and memory can handle the workload .. may need to dial-back the accuracies etc while in development and de-bugging phase ..

[MrVibrating]

Evolution and Negentropy at the same time - evolution to simplify, casting out redundancies and distractions, and automating; and negentropy to dial-in and make things more complex and ordered ..

It's coalescing - emerging - pretty much on its own from here on, i'm just the monkey pulling the levers..

Hope your computer processing and memory can handle the workload .. may need to dial-back the accuracies etc while in development and de-bugging phase ..

Yup, i'm now settling on 8 sig-figs as an acceptable balance between accuracy, time and clutter..



..before boarding the spaceship however, there's just one more thing to check - this hypothesis that the weight's orbital momentum is being harnessed by the wheel motor, whereas its axial momentum is recouped by the kiiking motor: if true, then eliminating the weight's orbital angular momentum component will also eliminate the gain..

To that end, in the following sim the weight's been outsourced to radially-sliding masses; it's the same net amount of weight, under the same CF force and undergoing the same 1 m radial displacement. The green disc radius has been reduced to 0.5 m to limit the cranking length to 1 m, while the 'weight' has become a flywheel with selectable MoI, currently set to match that of the original weight:



..hence kinematically, this is the identical interaction, but for the elimination of the weight's orbital angular momentum component.

Here's the outcome:

initial KE = 19.83333336
final KE = 29.73804178
KE delta = +9.90470842

kiiking motor P*t = 5.679746241
wheel motor P*t = 4.311490382

in = 5.679746241 + 4.311490382 = 9.991236623
out = 9.90470842
diff = -0.086528203

..and surprise.. there ain't a wet fart left in the thing. Doesn't necessarily prove the hypothesis in and of itself, but certainly seems to support it. Make of it what you will.


So we'll stick with what works for now. From hereon i'm moving to floating dual-rotor systems, so that any config can be float-tested on the button. Gimme some time to knock something up..

[MrVibrating]

Aha - not so fast with those conclusions; there is another key difference in the above design..




..the kiiking rotor's no longer inertially isolated from the wheel!

So scratch what i said about orbital vs axial momenta - the conrods are grounding the kiiking rotor's inertia that we want to diverge from the wheel / absolute frame..

What EMGAT really means is 'everything (that is OU) must go around together'..