Toad Elevating Moment

[MrVibrating]

Presumably (ain't checked yet) the flywheel's RKE when unlocked is negative relative to the wheel, and when it is braked to a standstill against it, the net energy squares with the locked run.

However, if correct, would that preclude tapping the asymmetry? Could we dump this negative RKE without transferring it back to the main wheel? Slap it against something, or something?

Anyone willing to hedge bets on what the direct-drive version will do?

[MrVibrating]

Example:

Before



After


Weird huh? The net for the locked run is 44.949 J... 1.139 J more than the unlocked run.

Yet the unlocked run has more on the wheel, where it probably counts...

I mean, why couldn't we put all of that 43.81 J into a second flywheel, before braking the first one..? This could prevent the braking flywheel from clawing back the excess, since we'd already have it, safely out of its reach on a second flywheel.. Or what if the braking mechanism lifts a weight, or tensions a spring, or something.. ? Is that a way of tapping off the excess?

Of course if the direct-drive version takes off all these questions become moot...

[Fletcher]

I don't know if this has any relevance Mr V .. BUT .. this is a sim I built a long time ago - updated with some colours.

The bottom pendulum bob is free to rotate until bdc then is locked.

There are the other two comparisons.

The idea was to periodically lock & unlock the bob strategically & investigate if there were any energy gains [height above horizontal] or not etc.

Because they all arrived at bdc at different times & had different periods then the inertia's must have been different - I was looking to exploit this if I could.

N.B. of course Total KE = Trans KE + Rot KE [same GPE]

[MrVibrating]

Quick update (will have more time for this tomorrow):

Spent this eve running some tests.

The locked vs unlocked tests were a dead end - locked and unlocked systems have equal net energies. This is still slightly less than the net translational, and i'm still unsure why, though it's doubtless a trivial detail - the difference is tiny at any rate.


Pure moments, OTOH.... it seems the only triviality is getting OU out of them... it is literally a piece of piss.

Tonight's measurements only confirm the previous results, however i can now characterise the asymmetry in slightly more detail:

For some, presently inexplicable, reason, the peak efficiency converges to a little over 1:1.6 I/O, or 1.6x unity, per cycle.

In the current config, a cycle consists of a 90° drop from horizontal down to vertical, followed by relifting back to that position.

No need for a piccy or sim - it's just a horizontal beam with a wheel on one end. The other end is fixed to a wall, post, obliging assistant or whatever.

Basically a horizontal lollipop, on a hinge. For its output stroke, it drops down to vertical. For our input stroke, we get it to lift up again... but by applying torque to the weight, rather than the pivot.

This causes the weight to lift itself upwards, and the total amount of energy required to make it do this is a variable.

The amount of output energy when it drops back down is a constant - a product of mass and vertical distance. Mass doesn't change, and neither does the drop height, so the drop energy is fixed, and doesn't vary with weight radius, density or inertia etc..

But input energy is of another form - and it's variable, not fixed. Specifically, it varies as a function of the radius of the weight. We can always make a weight lift istelf by spinning it up, but weights with smaller radii need more spin-up energy to lift themselves than larger ones.

This much is just a summary of previous findings... however the apparent trend there raises the seemingly-absurd implication that an infinitely-wide radius flywheel would need infinitely-little energy to suspend its own weight for infinity - clearly a troubling conclusion.

So tonight i narrowed things down a little, and kept raising the flywheel radius and plotting the results. What i found was that the required input energy converges towards a minimum, and then only increases by progressively-smaller increments as radius continues to rise.

The trend thus appears to indicate an optimum 1 to 1.6 ratio of input to output energies.... scale invariantly (at least for the scales tested).

Energy density is currently quite low (3.3 J / cycle for a 32 meter wheel!), but for a first foot in the door it's something..


Basic example of a cycle: lollipop drops from horizontal to vertical, energy is harvested and stored, then at BDC it is used to spin up the flywheel, causing it to re-lift back to horizontal. Rinse and repeat ad infinitum. Each drop pays out 1.6x more than the spin-up energy needed to relift.

I'm bombing tonight's data here just for posterity, no need to read it... but independent replication of the asymmetry would be good, if anyone's interested enough...

--------
warning, drab data dump follows
--------


Flyweight suspending itself at 90° horizontal:
-----------------------------------------------


flyweight mass = 0.393 kg

flyweight radius = 0.5 m

armature dimensions = 2 m x 25 mm

armature mass = 0.025 kg

drop time = 0.8454 seconds (for 0.5 m radius, no applied torque)

applied torque = 7.948 N/m

input KE = 459.984 J total balancing energy

armature output KE = ~200 mJ

output KE = 7.787 J (from dropping un-torqued flyweight or equivalent mass)


--------------------------


As above, changing only flywheel radius to:


1 m, input KE = 114.908 J

2 m = 28.727 J

4 m = 7.182 J with slight drop of armature - increased torque by +0.006 N/m to 7.954 N/m to compensate

8 m = 1.798 J total balancing energy (armature is balanced stationary hence no displacement to measure)

Dramatic drop in input KE with increasing radius (OU from 4 m onwards)!



Now lifting itself from BDC to 90° horizontal:
-----------------------------------------------

still at 8 m; total re-lift energy (rot + trans) = 6.683 J

armature KE = 0.094 J

..and staying with re-lift energy, keeping all else as is:

16 m = 5.042 J

32 m = 4.640 J (armature KE still constant at 0.094 J)

64 m = 4.552 J

128 m = 4.585 J

256 m = 4.812 J


conclusion: peak efficiency converges towards a high ratio between armature and flyweight radii, reducing above and below this sweet zone.

4.640 + 0.094 = 4.734 J total input, for 7.787 J total output = 1.64 x unity at peak efficiency


--------------------------------------------------




Armature reduced to 200 mm x 25 mm

armature mass = 30 grams

flyweight radius = 32 mm

flyweight mass still 0.393

torque = 0.774

output KE (90° drop) = 2 mJ armature + 772 mJ = 774 mJ total


as before, self-raising input KE from vertical to horizontal:

flyweight KE = 133.973 J

armature KE = 9.4 mJ


x2 Radius 64 mm = 33.824 J

x4, 128 mm = 8.787 J

256 mm = 2.528 J

512 mm = 0.963 J

1024 mm = 0.572 J (armature KE still 9.4 mJ)

2048 mm = 0.474 J (best run; ~300 mJ OU per cycle)

4 m = 450 mJ

8 m = 444 mJ

etc..

-------------------------

armature = 10 mm

torque = 0.039 N/m

radius = 0.025

90° drop KE = 39 mJ

re-lift KE = 50 mJ

radius = 50 mm = 30 mJ

r = 100 mm, 24 mJ

r = 150 mm, 23 mJ

r = 200 mm, 23 mJ

400 mm, 23 mJ

800 / 23

1.6 m / 23 mJ

...seems pointless continuing there, well converged at 23 mJ... optimum run is therefore 100 mm for 24 mJ.

39 mJ output divided by 24 mJ input, again gives 1.62 x OU. Asymmetry appears scale invariant, converges to a little over 1:1.6..

_____________


In conclusion...

Energy source is apparently gravity - it does more work on the drop, than the re-lift. The accelerating flywheel doesn't get lighter; it just shifts its weight over to the pivot between the armature and wall or post or whatever. Basically, sinking the effective weight thru the pivot and post to Earth. In a nutshell, pure moments can sink effective weight on a balance beam to earth, for less energy than the overbalanced beam generates.

Hence neither the mass or weight changes - rather, the point of application of the weight shifts between its location on the over-balanced armature, and the armature's pivot point.

So we drop the weight when its where the mass is, and then relift it when the weight's centered on the axle instead. We still pay input RKE and translational, but no need to pay for GPE since the weight itself isn't subject to gravitation when we're lifting it.

[MrVibrating]

Heh just noticed the balancing RKE drops off at a factor of four to the doubling radius.

Doubling the weight's radius = 4x less inut energy to levitate the same mass. At least, until it starts to converge...


I wonder if this relates to Bessler's factor-of-four hints? Currently it seems hard to reconcile the rest of this config with Bessler's stuff, beyond the most circumstantial consistencies.. then again, assuming this is a valid symmetry break, how many more can there be..?

[Fletcher]

Can I just pass a logic test past you, for my benefit ?

Using the Lollipop Test as the thought experiment.

1. from 90 degrees [shaft horizontal] we know the lost GPE at bdc

2. starting from bdc [vertical] we apply a motor that supplies torque to the bob [radius to be determined]

3. we adjust torque till the pendulum can raise 90 degrees to horizontal, replenishing the GPE

4. we note the RKE gained by the bob & also note that the iinertia of the bob [mass distribution] determines how much rpm it has & how much RKE it has - larger inertia means less RPM & RKE acquired ?!

5. we note that the RKE is substantially less than the GPE able to be extracted

.........................

Comments:

A. Convention would say, I think, that to raise the lollipop to horizontal it has acquired RKE + GPE = Total E & this is greater than just the RKE alone.

B. However your point is made that applying a torque only gives the bob rotation & RKE & the by-product is that it lifts gaining GPE for free ? - and this is a break in symmetry.

C. assuming a 100% efficient motor able to deliver torque to the bob it should only consume the RKE amount of energy ?

D. have you any examples in real world that can apply a pure-moment torque force like you propose, & if so, what are the general efficiencies ?

E. Have I understood you correctly ?

[MrVibrating]

I don't know if this has any relevance Mr V .. BUT .. this is a sim I built a long time ago - updated with some colours.

The bottom pendulum bob is free to rotate until bdc then is locked.

There are the other two comparisons.

The idea was to periodically lock & unlock the bob strategically & investigate if there were any energy gains [height above horizontal] or not etc.

Because they all arrived at bdc at different times & had different periods then the inertia's must have been different - I was looking to exploit this if I could.

N.B. of course Total KE = Trans KE + Rot KE [same GPE]

I can load the sim, and from the look of it you were playing with similar dynamics... however it crashes when i try to run it..


The tests i ran yesterday began with the attached config - two identical bobs, the left one drops to BDC revealing the net energy of the system for a conventional drop. The right one applies a counterbalancing pure moment for the duration of the left one's drop.

As you can see, the dropped bob outputs just 7.787 Joules, while the self-levitating bob draws a whopping 460 Joules over the same period.

This initial baseline test doesn't look particularly promising. However, now try doubling the radius of the right-side bob - keeping its mass, torque and everything else unchanged...

Now, the left bob still outputs the same 7.787 J. But the energy drawn by the levitating bob over the same period had reduced by a factor of four, to 115.082 J.

Still wildly inefficient as a transaction, however keep doubling that right bob and comparing the reduction in input energy. 2 meter radius draws only 28.770 J - a factor of four less again...

With just one more doubling of the right bob's radius, now 4 meters wide, the energy drawn to levitate it has dropped below the 7.787 J output energy of the left bob, to just 7.193 J.

So now we have a much more agreeable transaction.. with 595 mJ excess! However we've only dipped a toe in the water at this point - the asymmetry can be further widened in step with the radius of the levitating flywheel.

Obviously a 4 meter-wide flywheel for a half-Joule gain is pitiful energy density. Reducing the armature length as an alternative to increasing the flywheel radius is one possibility, however this also reduces the drop height and thus output energy.

Still, as i say, for a first step this seems a very tangible asymmetry. Presumably it can be further optimised, but the basic disunity seems incontrovertible - input energy is an inverse function of rotational inertia!

[MrVibrating]

Can I just pass a logic test past you, for my benefit ?

Using the Lollipop Test as the thought experiment.

1. from 90 degrees [shaft horizontal] we know the lost GPE at bdc

Sorry, got a throbbing hangover here - not sure what you mean, but we determine the output GPE by dropping the un-torqued bob from horizontal to vertical. Just as an easy reference output.

2. starting from bdc [vertical] we apply a motor that supplies torque to the bob [radius to be determined]

Yes, pretty much, although to keep the variables meaningfully relative to one another, i begin by finding the torque required for levitating the default mass radius.

I then use this 'perfect balancing' torque as the reference input torque for the self-lifting tests, from vertical to horizontal. However it may be that the self-lifting torque could be somewhat less than this self-levitating value - also, precision limits mean the 'perfect' balancing torque is usually unobtainable, hence i take a conservative measure - preferring that the bob will eventually rise slightly, rather than drop slightly.

I can envisage two different types of gain cycle - one using the self-balancing torque, and another using the self-lifting torque. Here i've simply established the former, and used it for the latter, even though the latter may require less torque and thus energy...

From there, i start increasing the flywheel radius, keeping the mass and torque constant (as things get larger torque may need tweaking, as evinced by last night's data - presumably this is due to increasing scales amplifying the aforementioned imprecision.. probably a 32bit limit or something)..

3. we adjust torque till the pendulum can raise 90 degrees to horizontal, replenishing the GPE

As i say, could do it that way, but that's not the way i've been doing it. You've got the basic principle though.

4. we note the RKE gained by the bob & also note that the iinertia of the bob [mass distribution] determines how much rpm it has & how much RKE it has - larger inertia means less RPM & RKE acquired ?!

Yes, pretty much - the way i look at it, the radius determines the rot inertia and thus the lifting force for a given mass and RKE. However this is just quibbling over semantics - we're on the same page.

5. we note that the RKE is substantially less than the GPE able to be extracted

"That's a bingo!"

.........................

Comments:

A. Convention would say, I think, that to raise the lollipop to horizontal it has acquired RKE + GPE = Total E & this is greater than just the RKE alone.

Precisely. The translational (lift) energy IS an additional load over and above the rot. inertial / RKE workload. However, the whole point of establishing the 'perfect balancing torque' first is that at this value, the effective weight of the bob is borne at the beam's opposite end, at its pivot to the wall.

This almost eliminates the input translational workload, since under this condition, the bob has near-zero GPE. It's not really 'lifting' itself, since its effective weight is over at the pivot end of the beam.

Example: using the previous posted sim, the perfect-balancing pure moment for a 500 mm bob is 7.954 N/m. This raises the bob to horizontal in 944 ms, for a total of 578.276 J. However this includes RKE and translational - rot alone is 573.829 J, and trans = 4.447 J.

However, note that the trans builds up to that maximum...

For comparison, let's reduce the torque to less than the perfect-balancing pure moment... leaving just enough for the bob to raise itself to horizontal...

I find this to be 5.065 N/m. This increases the lift period to 1.788 seconds, and the net input energy tp 834.293 J... however, not only has the required input energy increased, but also we see that all of it ends up on the wheel - trans hits a peak of ~1.6 J about halfway up at 45°, but tends towards zero as the bob approaches horizontal.

Now, keeping the torque at that minimum 5.065 N/m, try increasing the bob radius to 8 meters. We find that the trans follows the exact same dynamic as before, hitting a peak of 1.6 J halfway up, then tending back to zero approaching the 90° mark.. now, the total input energy is 3.201, and all of it is RKE on the bob.

Now, try bringing the torque back up to the perfect-balacing moment, 7.954 N/m - keeping the bob radius at 8 m. Now we find that the total input energy is 6.686 J, however only 2.239 J of this is RKE on the bob - the rest, 4.447 J, is translational... if we disengage the motor (replace it with a pin joint), the bob continues to rise up to ~135°, then falls back down. When it returns to BDC it now has 14.475 J - rot remains 2.239 J (the flywheel's coasting, conserving AM), trans = 12.236 J.

If we only take the trans, leaving the RKE on the bob, we have nearly twice as much energy output as input; 12.236 out from 6.686 in leaves 5.55 Joules excess (yikes all the fives!).

Finally; 8m radius, 7.954 N/m, perfectly balanced at 90°, trans thus equals zero, total input energy for 846 ms (equivalent to drop time for equal mass with 500 mm radius) is 1.798 J, all RKE. Output trans when torque is removed is 7.788 at BDC.

This last condition helps illustrate that the trans and RKE can be, effectively, thermodynamically decoupled. The only real impracticality is that the flywheel RPM keeps rising towards infinity with every cycle. Nonetheless, each time we're able to accelerate it hard enough, it'll rise for less input RKE than resulting output trans.

I do acknowledge that getting rid of this ever-increasing RKE is a real practical problem, but in principle we could simply brake it after extracting many cycles of gain from the system. The resulting counter-torque could then perform similar asymmetric interactions in the opposite direction... so i think this is more of an engineering issue than a symmetry-enforcer.

Indeed, the asymmetry itself seems disarmingly-simple to exploit...

B. However your point is made that applying a torque only gives the bob rotation & RKE & the by-product is that it lifts gaining GPE for free ? - and this is a break in symmetry.

Right. Using the minimum 5.065 N/m torque required to lift an 8 m radius 393 gram mass to horizontal on a 2 m beam, we have 3.08 J on the flywheel and zero trans at precisely 90°. Trans hits a peak of 1.64 J on the way up, following a shallow parabola. That's all of our input energy, yet output in pure trans (replacing the motor with a pin joint once it's reached horizontal) is 7.790 J

That's 4.7 Joules gained at the beam's pivot... and we still have the 3.08 J input energy there on the flywheel..

C. assuming a 100% efficient motor able to deliver torque to the bob it should only consume the RKE amount of energy ?

We do pay for trans - it does increase the input energy. But crucially, this translation is not subject to gravitation during the flywheel's acceleration, hence the total vertical translational KE is heavilly subsidised by this transient exemption to gravitation. The effective weight of the bob, during the lift, is instead borne at the beam's pivot to earth. When we reach 90° we stop applying torque to the flywheel, allowing it to coast... it now bears its weight at its actual location, as it would spinning or not. Hence now vertical trans is subject to gravitation again, and we're thus perfectly entitled to GPE on the way down that we haven't paid for on the way up.

D. have you any examples in real world that can apply a pure-moment torque force like you propose, & if so, what are the general efficiencies ?

Besides inertial counter-torque from an angularly-accelerating mass, nope. First thing i thought of, and only thing i've currently tried.

In principle though, because the pure moment is just a torque, rather than an associated displacement, the implication remains that there may be a more practical means, circumventing the whole issue of spinning up a flywheel (and thus what to do with the surplus RKE afterwards). All the pure moment needs to do is momentarilly shift the point of application of the weight from the rim to the axle. Furthermore, assuming the source is active (such as in the present iteration) - requiring input energy for the duration of the applied moment - the per-cycle input energy period drops in step with increasing RPM - at higher RPM the input energy only needs applying for shorter bursts, while the output energy remains a speed-invariant function of conventional GMH.

So yes, there may be a better way of doing this.

E. Have I understood you correctly ?

I think so. The central thesis and core exploit is simply the fact that a pure moment can counter-balance a beam regardless of where it's located along it - including directly aligned to the overbalancing force it's equalizing.

In such a condition, clearly the net weight of the system hasn't got lighter; rather, the weight of the overbalancing force is now being borne at the beam's fulcrum.

Hence this enables us to 'lift' without lifting (props to Bruce Lee). A vertical translation under such circumstances is thus more equivalent to a horizontal one, since there is no effective change in GPE while a perfectly-counterbalancing pure-moment is still being applied.

When that pure moment is removed however - bam! - the point of application of the weight shifts from the beam's fulcrum back to its flyweight end, and thus GPE spontaneously re-applies... basically conjuring (or conning) free GPE from the subsidised lift condition..

[MrVibrating]

...just got to thinking, the energy density's so paltry because i started with a 'reasonable' mass density but then increased its area of distribution to something like expanded foam... if not aerogel.

But given that previous tests have confirmed the asymmetry scales linearly with mass, it'd make much more sense to use denser material. Duh. So staying with an 8 meter radius, just for benchmark purposes:

mass = 1608.495 kg (8 m radius steel disk)

perfect balancing torque = 3.155e+004 N/m

un-torqued drop time for 90° Horizontal to Vertical = 838 ms

total output KE for un-torqued 90° H to V drop = 3.155e+004 J

total input KE for 838 ms weight suspension = 6790.271 J

Difference = 24,759.729 or 24.7 kJ per cycle.

Thus assuming 2 seconds / cycle we get 12,379.8 J /s, or 12.3 kW from a 16 meter diameter 1.6 tonne behemoth...

Still not brilliant, though.. is it?

At the moment we've only counted 90° drops, so a full 180° drop arc could double the power density again..

But to really significantly improve the efficiency, the per-cycle input energy needs to drop with rising RPM, hence a fully rotary implementation is necessary, rather than the present oscillating version. Also the flywheel RKE needs some means of being usefully recycled rather than just wasted or allowed to rise to mechanical failure. A means of circumventing flywheels altogether would seem preferable.

If this IS Bessler's asymmetry, then one can immediately appreciate why he wasn't tauting it for locomotion, or why for example Leibniz didn't persuade his royal patrons to buy it for their garden fountains etc. It seems a firm and consistnent asymmetry, but the power density can't compete with more conventional engines, at least while using gravity rather than say magnetic force..

On that last point, EM force is, what - a billion times stronger than gravity? Something like that. In which case, make up a number for your desired power density, double it and add a few zeros...

[Tarsier79]

Im not getting the concept of your advantage. When your cross is locked, there is more inertia, and the potential energy goes into rotation of the cross as well. The total system energy remains the same. You can tap the high inertia energy to the low inertia flywheel, and theoretically make it spin faster, but it will have no more energy. If you suddenly lock the cross when it is spinning, the inertia will suddenly increase and it will slow down.

I also don't get how you think spinning the cross/weight makes it easier to lift? Have you got a sim showing exactly that?

[MrVibrating]

@Tarsier

- yep your're exactly right, that one was a dead end as i've since acknowledged. The net energy is equal between locked and free runs - though still less than net translational.. however this anomaly is probably trivial, it's certainly small and wasn't the subject of my curiosity. I mistakenly jumped on the RKE of the main wheel as a potential exploit, which it isn't.


That whole locked vs unlocked flywheel thing was a diversion from the current (prospective) symmetry break; which compares the amount of spin-up energy required to make a weight effectively levitate or lift itself, against the GPE available from dropping it over the same height.

The basic point is that we now have two independent mechanical fields in which to differentiate input and output workloads; both of them render a vertical force component, and one of them is temporally invariant, and so we're using it for output work (time and speed invariant because GPE doesn't change over time).

The other one however, that we're using for an input workload, is time dependent. As the radius of a given mass increases, the effective 'edge speed' of the disc rises, for a given RPM. In the same way, the given mass is accelerated a greater distance over the given time, hence it has a higher effective rotational inertia - the inertia per mass*acceleration is constant, but as the radius of that mass increases, so does the amount of space it's accelerated through, for a given RPM.

Hence as flywheel radius increases, the RPM required to accelerate a given mass by a given speed decreases accordingly - at 500 mm radius we're accelerating the same amount of mass the same distance drawing almost 460 J of RKE, as when an 8 meter wheel of the same mass draws less than 1.8 J. P=MV, but KE=MV^2...

I do believe the sims are demonstrating an asymmetry, however i'm at the stage now of waiting for others to confirm or refute this. It's been three weeks now... so if it's delusion it's the longest bout i've had so far.. normally clears up in a day or two! I've been dismisive of it at times, but on closer examination it shrugs off every potential problem i can think of... but it's far from qualifying as 'unassailable' yet.. i don't even have a closed-loop sim... that would be a good start...

[MrVibrating]

Still no closed-loop sim - can't suss out how to do a clean transmission system; the chain & sprocket method introduces unwanted off-axis torque.

Had one cool idea to eliminate the possibility that extra energy could be sneaking in un-noticed - spin up the flywheel at vertical, then make it climb to horizontal using braking torque only...

Problem is i get inconsistent results from WM's rot damper constraint - RTFM and it says it only applies torque if the difference in speed between the moving parts is within a limited range... so not sure how to apply a consistent negative torque, that also eliminates further energy input..

The attached sim shows the general idea - as the radius increases, keeping mass the same, the initial RKE / RPM can be dropped accordingly. However i expected the results to mirror the inverse test, when the wheel accelerates at constant torque. Instead something else seems to be happening, and i'm not sure what or why..

[MrVibrating]

Still trying to find a definitive way of ruling out the possibility of extra energy input.

How hard can this be? It's seriously doing my nut in.

WM2D's rotational damper is evidently non-linear in response, and it's certainly dissipative. That makes it useless as an accurate brake.


So the only way i can see to apply an accurate braking torque is again, using the motor.

Consider the following experiment:

- Find the self balancing torque for a standard radius flywheel (ie. 500 mm steel @ 6.283 kg = 123.480 N/m on a 2 m beam)

- Then increase its radius to 8 m, keeping its mass the same at 6.283 kg and torque the same at 123.480 N/m

- Determine the spin rate of the flywheel when it has lifted itself from vertical to 90° horizontal, from a static start (ie. in the attached sim it's 33.539°/s)

- Finally, input that spin rate as the flywheel's starting condition, and invert the sign of the torque.

Now the wheel begins with all its input energy already there, and the motor only acts to reduce the wheel's energy. The wheel lifts itself from spinning at vertical, to stationary at 90° horizontal... scrubbing off energy all the way up.


This SEEMS to eliminate the possibility that extra input work is being done. We start out inputting just 34.078 Joules as RKE, but after lifting to horizontal the flywheel has zero RKE and a translational GPE of 123.312 Joules... a gain of 89.234 J per cycle, or 3.618 times unity.

Again, this ostensibly occurs because during the lift, the flywheel's weight is borne at the beam's pivot - the beam was perfectly balanced, as if it was counterweighted. Hence 'lifting' the weight was, in practice, no different to rotating a balanced wheel 90° - if we maintained the input torque with the flywheel latched up at 90°, it has not gained GPE in any meaningful sense, since it will not drop when unlatched.. because the beam's balanced by the pure moment.. The GPE gain only actually materialises the moment the torque is removed, at which point the beam is instantly unbalanced and wants to drop the weight.

However, there remains a valid contention that the system still uses a motor.... so even though it's evidently reducing the flywheel's RKE, we cannot be certain that it isn't inputting energy to the beam.

Logically, it cannot be - the pure moment in this scenario depends on negative torque, braking the wheel, removing energy from the system. It only lifts the wheel because it balances the beam, negating its own weight. That much seems incontrovertible. Nonetheless, skeptics will argue that motors consume energy, and they're right of course.


It's SO frustrating. Spent the last month staring at a symmetry break yet can't work out how to prove it. And all it needs is a simple linear brake.

If there was some way of applying a constant braking force to the flywheel, then we could spin it up, remove any and all forms of further input work, and then make it lift itself exclusively by braking, thus proving that the gained GPE is truly free energy....


Can't believe i'm stuck on something so simple.. it's just a brake FFS. All i need to do is decisively REMOVE energy from the system, in order to reveal the resulting gain.. can't give up when things seem so tantalisingly close to success... but how to proceed?

[Dunesbury]

Mr. Vibrating,
I can't believe you stuck either. I like to help, but I no have WM2D.
It sound like sim is giving a false positive.
Dunes

[MrVibrating]

LOL cheers mate.

I don't think the sim is giving an error - the question is simply whether or not the motor is also performing work on the beam... specifically, 90 J of work... that isn't being monitored or measured.

I've explained why this isn't a necessary condition - the beam is balanced during the lift, by the torque on its unsuspended end.

And attached is a similar brake-lift, using the rotational damper constraint.

This is dissipative and non-linear in response, so useless for conserving work / energy.

Because of this limitation, the flywheel needs almost 9 kJ starting RKE to lift itself all the way up. So there's no gain here (quite the opposite in fact), and indeed, no point increasing the radius - i've thus kept it at the default 500 mm.

What it DOES show however - the only useful thing it can demonstrate - is that it's possible to perform the lift under braking forces only.... ie. the rotational damper definitely, positively isn't inputting energy to the beam. The lifting force is manifested wholly and exclusively by braking the flywheel.

So this proves that braking torque is a viable means of aquiring lift - that it's a satisfactory condition. In principle at least, no further input of energy is required to cause the lift.


But it cannot prove that further input work isn't being performed by the motorised version... since adding more input work is also a perfectly viable means of causing the lift.

And as i say, regardless... it's massively under-unity because it's dissipative and non-linear wrt to RPM.

So it proves very little, other than the fact that the weight can be lifted using only its pre-set RKE. However to prove that the previous motorised sim is only lifting by such means requires replacing the motor with a constant-force brake.

Again, the motorised version is only applying negative torque, decelerating the flywheel, and it is the wheel's rotational inertia that shifts its weight over to the opposite end of the beam - as conclusively proven by the positive-torque lift test.

Here, we've simply given the wheel its energy first, and then reversed the motor's torque, to drain that energy away.. this lifts the weight, and once it's lifted, all of its initial RKE has been removed from the system. The GPE during the lift didn't change, because the beam was balanced by the torque.

However once it's lifted and we then remove that torque, the weight shifts back over to the flywheel's position, unbalancing the beam, and thus it now has GPE that simply wasn't there during the lift.


In a nutshell, i'm saying we can breifly switch off gravitation for less energy than the resulting GPE attained.

But to prove this, i either need a way of applying a constant negative torque WITHOUT consuming external input energy (ie. a simple brake), or some way of re-imagining the whole system or the means of measurement...