Success..?

[MrVibrating]

Sometimes you loose a little GPE at sim run start because of elasticity effectively.

Let's say you place objects set to collide in your sim, but don't run it. And let's say elasticity is 0.5 and one object is above another on a common slot for instance. When the sim is run the top most object will "settle' against the lower loosing some GPE from initial conditions. It will 'settle' more with lesser elasticity factor.

fwiw.

Yep absolutely right, and good call - no collisions / contacts here, it just takes a moment for the solenoids' adaptive torques to kick in, because they're driven by the MoI delta, of course.. so the sim relies on gravity pulling on both weights, to produce the force feedback holding 'em in place..

..blind luck really that the gain didn't turn out to be unmetered GPE all along - like i say, an imperceptible (> 1 pixel, i guess) GPE change of -0.5 J is possible between start and end frames, even tho they look near-identical. It's another uncertainty removed..

Prepping chow now; will run that max freq sim, if it jells with the current hypothesis then i'll try correlate the gain back to the CF PE plots..

..at that point - if they match, i mean - wow. Interesting.

Almost seems uncannily close to an effective GPE asymmetry at the moment doesn't it? Where's the momentum gain that a KE gain would need to piggyback on? We appear to be looking at a completely different animal.. a GPE drops, making rotKE and thus CF-PE (which is just the same damned energy, albeit from the internal FoR), two masses get closer together, the other two get further apart, and in result, more work is output by the latter than input into the former.. yet for no net change in MoI either way - the interaction was designed to raise GPE without doing any net work against CF force - and yet in accomplishing the required MoI-constancy, it's doing the exact opposite; and not only is the net CF work non-zero... it's frickin' negative.. LOL i can't be the only one getting the impression there may be a beautiful logic resolving all these seeming contradictions - cos if it's real, then there must be..

[MrVibrating]

..if it's real, then the increase in gain could be correlated to a slight increase in MoI, caused by having to reduce the feedback multiplier in line with the lower sim frequency.

The feedback strength determines how rigidly the MoI is locked - too low and it starts to widen up as CF forces build, pulling each pair further apart..

..so i'll do the max-feq test after dinner, but might also finish off with a 1 kHz run, since it's only a few thousand frames.. or maybe even 200 Hz (real-time animation speeds) - why should we care if the ending MoI is completely different to the starting MoI if we're netting a closed-cycle energy gain? Doesn't matter if it needs resetting by hand each time, if the gain's robust.. just for a stand-alone energy gain that might be buildable as a desktop toy..

..on that note; why not just drop a weight, causing rotation, have two vMoI's and widen one whilst narrowing the other, whilst measuring carefully? Then we could try asymmetric inbound vs outbound speeds or whatever.. dunno.. just trying to get a feel for whatever it is we're dealing with here..

[MrVibrating]

freq: 32765 / 1.1261
i-s/f: 1
FFB: 1e9
turns: 0.25
no s&b cycs
no sprung timing


acts net P*t = 39.98313892

sol1 P*t = -4.866453819

sol2 P*t = 4.695350111

total in = 39.812035212
__

net GPE = -0.003819

KE rise = 39.989374

total out = 39.985555
__

diff = +0.173519788 J




See, i initially thought that raising the sim frequency should likewise be increasing the precision of the result...

But it's not the accuracy of the result that's changing with frequency, so much as the variation in MoI control - the gain being proportionate to the MoI variation.

IOW, the rig's designed from the ground up to prevent the very motion that's actually causing the gain.. the degree of accidental 'success' being a direct function of its degree of failure at fulfilling its intended purpose...

..and had i succeeded in reducing the constant-MoI function to a simpler equation that ran ideally at any frequency, the gain would've forever remained down in the noise floor!


So for good measure, let's see what a 200 Hz run throws up - this'll have lousy MoI lock, but should also pay out all the better for it..

[MrVibrating]

freq: 200 Hz
i-s/f: 1
FFB: 10,000
turns: 0.25
no s&b cycs
no sprung timing




acts net P*t = 39.20336015


sol1 P*t = -4.122281245


sol2 P*t = 4.131307055


total in = 39.21238596
__

net GPE = -0.555044

KE rise = 40.111740

total out = 39.556696
__

diff = +0.34431004 J




OK turns out another consequence of weaker MoI lock is more output GPE; weights 1 and 2 are obviously not finishing at equal radii, both sagging slightly under gravity..

..and since the gain depends upon those weights getting further apart, we need to supply enough input energy to accomplish that displacement - it'll be discounted by CF force, but has to actually happen first.

Let's see what happens at 1 kHz / 1e6 FFB..

[MrVibrating]

freq: 1 kHz
i-s/f: 1
FFB: 1e6
turns: 0.25
no s&b cycs
no sprung timing


acts net P*t = 39.84350632

sol1 P*t = -4.529553927

sol2 P*t = 4.44047122

total in = 39.754423613
__

net GPE = -0.111126

KE rise = 40.025828

total out = 39.914702
__

diff = +0.160278387 J


Hmm... less GPE out, less MoI drift.. but also less gain..

So the hypothesis isn't bearing out..

Let's go back to the 3.2 J config to see if the CF integrals match up with the solenoid plots.. cos if they don't, then it's looking more like a frequency-dependent error.. as in, not the 'serendipitous' kind..


Trying to think of potential modes of failure, as much as plausible-ish gain principles... the solenoids are basically sending a series of fluctuating positive & negative forces to the weights - why might an aberrant asymmetry arise, and why might higher frequencies exacerbate it? Dunno, let's see if there's any consistency to be found in the CF plots..

[MrVibrating]

Bingo..?


The 'gain' is the persistent non-cancellation of the solenoid work integrals...

..one's substantially more negative than the other is positive..

Using the recent 3.2 J example:

Code: Select all

Solenoids torque * angle:
-------------------------


Solenoid 1 T*a = -11.86803455

Solenoid 2 T*a = 8.608218143
__________________________

Diff = -3.259816407





Solenoids P*t = time integral of torque * angular vel:
------------------------------------------------------


Solenoid 1 P*t = -11.86713399

Solenoid 2 P*t = 8.608454476
__________________________

Diff = -3.258679514
 

..i've yet to make full sense of the CF PE workloads, but here they are anyway:

Code: Select all

CF F*d = radial displacement integral of mass * ang vel² * radius:
------------------------------------------------------------------

Weight 1 CF F*d = 5.785514836

Weight 2 CF F*d = -5.785514259

Weight 3 CF F*d = 2.091526537

Weight 4 CF F*d = -2.091531385




CF P*t = time integral of mass * ang vel² * radius * radial vel:
----------------------------------------------------------------
 
Weight 1 CF P*t = 5.785635425

Weight 2 CF P*t = -5.785656591

Weight 3 CF P*t = 2.095351461

Weight 4 CF P*t = -2.091418786 

..the rest of the stats, incidentally, were:

Code: Select all

freq: 32765 / 1.614 
i-s/f: 1
FFB: 8e8
turns: 0.25
no s&b cycs
no sprung timing



All solutions are in units of Joules
------------------------------------


Torque * angle of OB axis = 31.52624219

Rot KE of OB axis = 31.524276

Radial KE = 8.466819




Net input energy:
-----------------

Actuators Net P*t = 39.98208583

Solenoids Net P*t = -3.258679515

Total input = 36.723406315



Net output energy:
------------------

Net GPE = -0.005474

KE rise = 39.991096

Total out = 39.985622
__________________________

Diff = +3.262215685




Actuators F*d = radial displacement integral of radial force:
-------------------------------------------------------------

Actuator 1 F*d = 28.05445649

Actuator 2 F*d = 11.92763307

...but now ponder this following question carefully:

• surely, the more salient question is not why the two solenoid workloads are non-cancelling...

...but rather, why either are frickin' non-zero in the first place?


Because, what is their workload, but to apply an inertial interaction between each mass in a pair; ie. accelerating and braking them in relation to one another..?

• all GPE is input by the actuators

• neither solenoid performs any net work against CF force

..so what workload is left to them, bar the linear / radial inertia of the weights they're controlling?


In short, why isn't the net work performed by each solenoid zero???


Is this some kind of second-derivative of CF PE, caused by the angular acceleration..?

Grimer = 1

Everyone else = 0

?

[MrVibrating]

..this is so exciting, i got halfway to work and thought 'eff it, this is more important...

• We are seeing energy gains from 'reactionless' spin'n'brake cycles!

• They're coming from the solenoid spin'n'brake cycles, not those of the weight axes!

• It's an angular-to-linear conversion of work, from a principally linear asymmetric inertial interaction!

• The inertial interaction between each weight in a pair is being augmented by CF force!

• Weights 1 & 2 cost less energy to accelerate than they pay out upon braking!

• Weights 3 & 4 cost more to accelerate than they pay out when braking!

• Yet zero net work is performed against CF force relative to the OB axis! No inertial torques are induced!

• The current asymmetry between the two anomalous-but-opposing workloads is small, yet is being constrained by the positive workload... which may not even be necessary!

• IOW, why not employ the constant-MoI gapping function for harvesting the negative integral only? At that point we've netted our gain, and can reset without having to worry about any MoI variation or corresponding inertial torques?

• IOW, the 'reset stroke' following a gain interaction needn't necessarily have a positive energy cost at all, and could be a zero-sum..


Could this, finally, be a consistent hypothesis..?

[Fletcher]

Now that you are narrowing things down.

Have you tried as a control turning Gravity OFF ?

Does it perform the same ?

[MrVibrating]

This is currently as clear-cut a picture i can make of it:



..if that's too fast, here's a slo-mo version:

https://i.ibb.co/dKBNd8L/3260m-J-long.gif

..and here's all the integrals in one easy reference:

Code: Select all

freq: 32765 / 1.614 
i-s/f: 1
FFB: 8e8
turns: 0.25
no s&b cycs
no sprung timing



All solutions are in units of Joules
------------------------------------


Torque * angle of OB axis = 31.52624219

Rot KE of OB axis = 31.524276

Radial KE = 8.466819




Net input energy:
-----------------

Actuators Net P*t = 39.98208583

Solenoids Net P*t = -3.258679515

Total input = 36.723406315



Net output energy:
------------------

Net GPE = -0.005474

KE rise = 39.991096

Total out = 39.985622
__________________________

Diff = +3.262215685




Actuators F*d = radial displacement integral of radial force:
-------------------------------------------------------------

Actuator 1 F*d = 28.05445649

Actuator 2 F*d = 11.92763307



CF F*d = radial displacement integral of mass * ang vel² * radius:
------------------------------------------------------------------

Weight 1 CF F*d = 5.785514836

Weight 2 CF F*d = -5.785514259

Weight 3 CF F*d = 2.091526537

Weight 4 CF F*d = -2.091531385




CF P*t = time integral of mass * ang vel² * radius * radial vel:
----------------------------------------------------------------
 
Weight 1 CF P*t = 5.785635425

Weight 2 CF P*t = -5.785656591

Weight 3 CF P*t = 2.095351461

Weight 4 CF P*t = -2.091418786





Solenoids torque * angle:
-------------------------


Solenoid 1 T*a = -11.86803455

Solenoid 2 T*a = 8.608218143
__________________________

Diff = -3.259816407





Solenoids P*t = time integral of torque * angular vel:
------------------------------------------------------


Solenoid 1 P*t = -11.86713399

Solenoid 2 P*t = 8.608454476
__________________________

Diff = -3.258679514

...again, the exciting thing is not that the sum of the solenoid workloads is persistently negative.. but simply that either is positive or negative in the first place!

The implication being that there doesn't appear - for now - to be any particular reason we need to generate the positive solenoid integral in the first place - either way, no net work's done against CF force - so why not try to generate only the negative integral in an otherwise-closed loop interaction?

A start/stop rig's fine if it's a solid per-cycle energy gain.. ain't gotta be constant motion for an initial proof-of-principle..

[MrVibrating]

Now that you are narrowing things down.

Have you tried as a control turning Gravity OFF ?

Does it perform the same ?

Good Q.

It relies on the angular acceleration of the system, so sans gravity some other source of torque would be required.. perhaps it'd work in an actually-accelerating FoR (per the gravity / inertia equivalence principle), dunno, early days..


One thing to check though might be whether or not the solenoid anomaly is riding on the actuator workload - IOW, is the negative solenoid workload presenting as a positive workload on the actuator, such that the actuator must perform more work over and above the weights' GPE?

I can check for this by independently metering all four GPE's - the work done by both actuators summed together is equal to the GPE in/out, but are they independently at unity? Ie. is 'actuator 1 P*t' equal to the net change in GPE of weights 1 & 2?

If the gainy solenoid integral is a cost to its actuator, and the lossy one a credit to its actuator, then doing away with the latter will leave us with a deficit and we'll likely have robbed Peter to pay Paul..

If OTOH the solenoid workloads are fully independent of whatever the linear actuators are doing, then we have an open door..


So this evening i'll try resolve each actuator's workload with the respective changes in GPE of each weight pair.. touch wood it'll be 1:1, and we're go for launch on v3..



If this is it, then it neatly solves the paradoxes i've been facing lately - did i not say the gain interaction had to be linear / radial, since if it were angular the per-cycle momentum yield inevitably diminishes by the inverse square of RPM, enforcing unity regardless of other considerations? Likewise, if the gain were rotational KE then this causes the rate of GPE in/out to increase in lock-step, such that they're impossible to decouple..

In light of these known constraints, it was pretty desperate even attempting to break unity using asymmetric angular inertial interactions.. and little surprise they didn't succeed..

But linear asymmetric inertial interactions - where the biasing is provided by CF force rather than gravity - appear to be the ticket..

At least, that's the current hypothesis. Will try to ascertain definitively one way or the other, ASAP..

Presumably though, once we know all four independent GPE changes, we should be able to make better sense of the CF integrals, and whether they affect the actuator workloads..

[MrVibrating]

OK here's a thought experiment:

• gravity off

• wheel turned by constant torque from a motor

• one weight pair, controlled by one actuator and rot. solenoid, as a function of wheel angle as previously

• thus the motor's applying a constant torque to a constant MoI

• let's make it 1 N-m and 1 kg-m²

• so upon reaching 1 rad/s we'll've spent ½ J of torque * angle on the motor

• we'll likewise have ½ J of rot KE on our constant-MoI rotor

• ..plus we'll also have a negative solenoid integral..?


Is that sound logic? It' s pretty much the hypothesis we're looking at, innit?

Mebe a good v3 candidate, after checking the actautor / GPE symmetry here..

[MrVibrating]

LOL, just check those digits - the "3.2 J" run didn't make just 3.2 J..


..it actually 'created' 11.8 J!


However it also 'destroyed' - quite unnecessarily, i suspect - 8.6 J..


The key here is that neither involved any change in MoI.. net work against CF was zero, not simply in their combined efforts but individually as each weight pair / solenoid workload in their own right..


The implication is that there's a CF-PE associated with the distance between each weight in a pair, that is independent of their net CF-PE as a function of their combined MoI...

Incredible, huh?

[MrVibrating]

OK, so, duh - weights 1 & 2 get lifted by the same amount 3 & 4 are lowered; likewise 1 & 2 begin at zero height, then 1 is lowered by the same amount 2 is raised, such that both end at equal height above and below the zero line.. whilst 3 & 4 go from being at equal distance either side of zero, to both aligned at zero:




..so apparently it's impossible to determine this way if the GPE work done by each actuator was augmented by solenoid work..

..after all, only part of the lift is accomplished by the actuators; the weight is also partly rotated upwards, and likewise for the drop, which is mostly angular but also partly radial..


However the same effect could be tested for with gravity out of the picture - such as with the v3 rig mooted earlier:


• spin up a rotor with a constant torque motor

• use FFB to move a single pair of masses from position '1 & 2' into position '3 & 4'

• thus rotor MoI stays locked to 1 kg-m², in spite of the gap between the weights increasing by sqrt(2) of radius.. this gap increase representing a net output of work by CF force

• because MoI is constant, accelerating 1 kg-m² to 1 rad/s will cost precisely ½ J, and we'll have ½ J of rot KE

• but we'll also have that negative CF integral from opening up the weight gap..

• without gravity, the only loads on the solenoid and actuator are inertial..

• ..hence if the solenoid gain comes at expense of an actuator cost, a clear correlation should be evident!


I have to go work all day tomorrow, so as ever, lil' patience.. unless i think of any show-stoppers between now and tomorrow night, i'll make a start on it when i get in..

[MrVibrating]

..two tests to try with v3:

• measure the solenoid integral at constant RPM (ie. zero applied torque / wheel is coasting) - so logically, if MoI's constant then angular velocity should also remain constant; will the solenoid integral still be negative?

• measure again when accelerating under constant torque; is the gain dependent upon the axis accelerating when the radial voodoo's being applied?


..and anything else we think up on the way..

[MrVibrating]

So here's a start on v3 with gravity still enabled:



Nice and basic, just the bare essentials..

Here's the digits for that run:


act = 7.257261093

sol = -1.511606451

total in = 5.745654642

KE = 5.80407

GPE = -0.00039

total out = 5.80368

diff = +0.058025358


..so the gain's down to 58 millijoules there.. and it does look as if the actuator input workload is increased by the solenoid output workload.. it's more than the KE rise anyway, but of course this isn't the test the rig's intended for, so a number of points to consider in relation to this preliminary run:

• Previously, with two reciprocating mechs, input torque was constant, hence the wheel was still accelerating when that solenoid was outputting work..

..whereas here, the OB torque goes to zero as the masses enter their centrally-balanced position, so there's less CF force and thus less output work done..

With gravity off, and constant torque provided by a motor instead, the expectation is that the solenoid integral will still be getting pumped up as it was previously under constant OB torque..


• The really exciting point to keep in mind is that even in the above, near-unity result, this negative solenoid integral clearly isn't an error..

..and it can only be caused by an output of work under CF force..

..yet MoI is held constant throughout! This CF-PE integral is decoupled from MoI and thus rot KE! Under any normal circumstances, an output of CF-PE means an increase in MoI and a corresponding drop in velocity to conserve net angular momentum (the ice skater effect); and that drop in velocity is the cause of the drop in rot KE corresponding to the withdrawn CF-PE.. in a nutshell, if we take out 1 J of CF-PE, we expect a 1 J drop in rot KE, right?

Whereas here, we're looking at an output of CF-PE that doesn't cause a rise in MoI, and so doesn't cause an angular deceleration, and so doesn't cause a drop in rot KE equal to the CF-PE yield, get it?

Obviously, if it causes an equal opposite rise in actuator workload instead then we're seemingly no better off, however this is yet be determined..


So anyways, din-dins & a movie (watching 2010: The year We Make Contact again, all-round best sci fi ever), then i'll start retesting with a motor..

..also wanna try the 'coasting only' version - no applied torque - give it a 1 rad/s starting velocity and see if we still get this negative solenoid workload.. and how it affects the actuator workload..