Toad Elevating Moment

[Ed]

Could use some help in WM...

WM is only so good and then one needs a more industry hardened sim program. Did you see my post earlier asking if you wanted help doing a 3d sim?

[Fletcher]

Could use some help in WM...

The test rig attached is designed to drop a weight from a spool, transfering that torque to the flyweight via a transmission wheel which shares an axis with the beam the pure moment is intended to balance.

The idea is to find the mass of the weight than needs to be dropped in order to generate a balancing pure moment, and integrate this over the drop distance to get a decisive input energy. This could eliminate any doubt that the difference between rotKE and transKE is free - ie. i expect the same input energy per unit time whether the pure moment is climbing or fixed to a stationary axle.

Worthwhile experiment, but the sim's crapping out on me - the chain is sinking through the spool... (if only this software had a proper spool widget!)

How do i get rid of this error? Raising the frictions and reducing elasticity doesn't seem to help.

Or can anyone think of better way to accurately manage input energy? I figued a weight drop is fairly conclusive, just as a proof-of-principle...

Does this help ?

[MrVibrating]

Fantastic work, cheers Fletch... must've taken a while (took me yonks to set up the original!)... weird results tho, for now.. can't seem to generate the balancing force regardless of the drop weight...

I suspect this may be an accurate side-effect of using a chain and sprocket - it's 'feeding' the beam downwards, regardless of any inertial counter-forces trying to keep it horizontal.. think i've inadvertently come across this effect before, but here it's a showstopper.. maybe there's a workaround or alternative method, have to sleep on it..

Cheers anyway!

[MrVibrating]

Could use some help in WM...

WM is only so good and then one needs a more industry hardened sim program. Did you see my post earlier asking if you wanted help doing a 3d sim?

Certainly it has its limits, but i think i might've bumped into a feature here, or rather a lack of foresight as to how chains and sprockets are supposed to work.. but yes thanks for the offer, however i wouldn't want to waste your time unless i had really compelling results...

Things are interesting ATM, but it could fizzle out any moment...

Aside from all the sim tediums, the thing i can't get off my mind is a sequence where the pure moment applies a balancing force - temporarily supporting its weight at the beam's axle - and thus allowing an equal opposite counter-weight to sink downwards, say from 12 to 6. If the PM was then disengaged, its effective weight is tranferred back to its actual position on the beam, which is thus balanced again... and could coast 180° to repeat the cycle.

Because the energy input to generate that pure moment decreases with both flyweight radius and RPM of the beam, this looks like a cycle that must break even beyond some threshold RPM and flyweight radius - the output energy curve is a flat line function of speed, but the input energy curve has a sharp gradient, hence should cross down through the flat-line output curve if speed and rot. inertia are sufficient...

The tricky bit would be coordinating the transfer of KE to a second flyweight, without applying a counter-torque that rakes back all our gain. A crank mechanism might do - if one flyweight goes CW and the other CCW, a 90° offset between the two crank positions would cause the bulk of RKE to manifest on one flyweight at a time, each in turn, CW then CCW... this could generate a fairly consistent torque through 360°..

Final thought for the night: consider the example where the pure-moment seems to cause a horizontally-suspended weight to levitate unsupported; all of the input energy is going to the flyweight, and none to the beam as it's balanced stationary. For a given mass, the energy per unit time needed to support that improbably-balanced weight decreases as a function of its radius! In reductio ad absurdum, an infinitely-wide radius would require an infinitesimal input energy to sustain that balance for infinity! Absurd, yet apparently that's the world we live in..

This alone is a fascinating meditation. To me, anyway.

Turning the whole thing on its side like this effectively rotates the world, too. The gravitational vector is now basically sideways, horizontal to the left. Max GPE is at 6 o'clock and 12, and if the self-balancing flyweight is nudged up or down it'll oscillate around the horizontal until settling back there. Allowing it to pass 12 o'clock flips the world again, and at 9 its weight is double its static GPE.

These are some of the spookiest mechanical properties i've encountered so far... if none of these effects are useful i'll be damned if i can find anything funkier...

[MrVibrating]

Further gains, getting more confident now that we might be closing in on a solution.

I've found a much simpler configuration; instead of torquing the flyweight, NOT torquing it.

In the attached sim, two identical wheels have a flyweight attached at 12 o'clock TDC. The only difference being that the one on the left is allowed to freely rotate, and the one on the right is fixed, unable to rotate.

This results in the left wheel reaching a higher energy at 6 o'clock BDC.

Hence, at 6 o'clock BDC we can lock the flyweight on the left-hand wheel, and ascend needing only the energy of the R/H wheel. Thus when the L/H wheel returns to 12 o'clock TDC, it now has its original GPE plus the excess RKE.

This can be repeated for multiple cycles, gaining a wee bit of energy each cycle. Just pause the sim at BDC/TDC and add/remove a rigid joint anywhere to the flyweight.



There's also a second slightly more complex version i'll post shortly, with a higher gain, via the addition of a lever and spring...

[MrVibrating]

Just a thought - may be rubbish but it led to the current config - the mysterious Weissenstein pendulums - those big unweildy 'T' shaped things...

I think each one is two things; a minimal flyweight, and a beam. Their lengths are in a 2:1 ratio - the beam is twice the length of the flyweight. This ratio relates to radius and diameter - the beam's length is the diameter of the wheel and the flyweight's length is equal to its radius.

The conflicting details at the tops of each of the three pendulums are clues to deciphering the components' actual purpose (rather than the ostensible pendulum red-herring):

Left to right, the occlusion error shows that the pendulum can't collide with the post its otherwise aligned to rest on - this, because it's not a pendulum, and rather the flyweight needs to rotate, as described above. IE. if the occlussion error wasn't there, then the flyweight wouldn't be able to rotate. This is why the 'hanging post' obtrudes in front of the 'pendulum'.

The center pendulum shows that the flyweight-end of the beam needs some degree of freedom to move laterally. In other words, the diametric beam the flyweight is attached to needs a slightly flexible fixture to the main wheel.

And finally the rightmost pendulum indicates more clearly that the horizontal part of the 'T' is pivoted to the vertical section, and able to rotate upon it.

As i say, this may be entirely spurious conjecture, but the present config is an interpretation of it... and it seems to be doing something interesting..!

[Dunesbury]

you mean Meresburg pendulum? Kassel drawing is one pendulum.
Weights on pendulums not rotate around pendulum. They adjust in and out for regulation, if need.

[MrVibrating]

Yes, sorry, i mean the 'Mereseburg' images:





..and yes, they're ostensibly pendulums, to regulate the motion. However they're mysterious in that they were never described by any of the witnesses, and also because as i've described above, there's discrepancies between how the tops of them are depicted.

As JC recently clarified, when Bessler wrote that

"...no illustration by itself contains a description of the motion; however, taking various illustrations together and combining them with a discerning mind, it will indeed be possible to look for a movement and, finally to find one in them'."

..he was likely refering to the images in his published works (MT hadn't been published). Hence why these anomalies in the images could be intentional clues - hidden in plain sight - to solving the working principle.

As i say, my speculations might be complete bunkum, but either way the above posted config seems to be demonstrating clear gains...

[MrVibrating]

Attached is the beam & spring version, in which i initially noticed the anomaly.

I was playing with the pure moment, using it to balance a beam attached to the wheel. The idea was that a perfect-balancing pure moment causes the weight of the flywheel to be borne at the opposite end of the beam, at its pivot to the wheel, causing the weight to lift itself. This was the first of these configs i originally posted on this subject, a couple of pages back.

I went back to it, to see if adding a supporting spring to the beam reduced the input energy required to generate the balancing pure moment. It didn't, and on a whim i instead decided to test the freely-pivoted flywheel vs the static one, with the above results..

Still figuring it all out, so for now, in the current enquiry, the spring and beam may be superfluous... they're clearly not critical to the gain, and any benefits they may convey are currently inconclusive...

[ovyyus]

Further demonstrations regarding the possibility and impossibility of perpetual motion.

NB. 1st May, 1733. Due to the arrest, I burned and buried all papers that prove the possibility. However, I have left all demonstrations and experiments, since it would be difficult for anybody to see or learn anything about a perpetual motion from them or to decide whether there was any truth in them because no illustration by itself contains a description of the motion; however, taking various illustrations together and combining them with a discerning mind, it will indeed be possible to look for a movement and, finally to find one in them.

..he was likely refering to the images in his published works (MT hadn't been published).

I don't agree. The above quote is a translation of the hand written cover page of the MT illustrations. It therefore seems more likely that Bessler was specifically referring to the MT illustrations and not his other published works.

...However they're mysterious [pendulums] in that they were never described by any of the witnesses.

Yes, but given Bessler had trouble convincing people his wheel could perform practical work (his wheels were criticised as being very weak) then he might have viewed demonstration of a pendulum wheel speed governor as being secondary, or even pointless.

[MrVibrating]

Found that the last gain is probably sim error - it depended on whereabouts the rigid joint was placed on the flywheel. I'd been placing it at the periphery, but when i tried putting it at dead center the behaviour went away...

However the difference in energy is still larger than one might expect from simple error - when pinned at the edges, the wheel gains a Joule or so per cycle, but when pinned dead center it barely makes 270° of rotation... so it might still be worth trying to understand why the discrepancy is so large - perhaps it hints at something useful..

[MrVibrating]

@Ovyyus

I've not disregarded MT entirely, but since JC's post last November i've been trying to resolve the witness clues with the Meresburg prints.

The clue that got me thinking about high rotational inertia was cylindrical hollow weights. Then last week, trying to maximise rot. inertia i ended up playing with a long beam with a weight on each end, and noticed that it looked a lot like the horizontal section of the Meresburg pendulums..

And all the while, my overarching aim was to identify an alternative field for a workload independent of gravity, my logic being that if either input or output was a GMH workload, then the reciprocal workload must be in some other field. Thus, discovering a rotational inertia effect that also generates a strong vertical force seemed like a prayer answered..!

However it also seemed consistent with the general progression of MT, which includes lots of later references to flywheels, which also have bulbous ends (like the Meresburg pendulums), optimised for rot. inertia.

So for the last few weeks i've been playing with rot. inertia, until a couple of weekends ago i realised that input energy needed to generate a given vertical force via rot. inertia decreases as a function of radius. That's when i noticed that the Meresburg pendulums have radii almost as wide as the wheel itself - which seemed to be screaming off the page confirmation that this is the non-linearity that leads to the asymmetry..!

But coming back full-circle, what initially sent me in this direction was those much smaller hollow lead cylinders... so i'm currently unable to resolve this difference in scale - if rot. inertia is key, and Bessler's weights seem designed to maximise their own axial rot. inertia, then maybe 2 meter-long flyweights are superfluous and the pendulums' inertia is incidental to the core asymmetry... i still haven't found any potential exploits using these much smaller radii - generating a self-balancing pure moment with a small radius requires more RKE than seems practical, for instance.

But the possibility remains that rot. inertia of the lead cyclinders is incidental, even though it led me to notice the much more important rot. inertia of those pendulums... so i'm at a bit of a crossroads - high radii rot. inertia IS useful (it generates substantial vertical forces) but the rationale that led to the discovery was serendipitous and possibly a misgiving..

If i could find some similarly compelling use for the shape of the lead cylinders i'd jump on it, but right now i'm thinking their shape owes more to other considerations, but that nonetheless rot. inertia IS potentially useful, even if i got here via a dodgy interpretation.. However JC's suggestion that Bessler was refering to the published illustrations, if correct, would be a further consistency that rot. inertia is indeed a key element. I find the very deliberate anomalies between the tops of the three pendulums to be another very compelling set of clues, and it seems a remarkable consistency that this particular pendulum shape would be ideal for generating maximum vertical force for minimum input energy...



...as well as lifting itself, this geometry causes the weight of the rotating flyweight to be 'felt' on the wrong side of the wheel, ie. although the weight is physically on the right, it's nevertheless borne on the left of the wheel. This is interesting because, if the wheel was fixed, unable to rotate, then we'd have to increase the RKE of the flyweight to make it rise. However, if the wheel can rotate then we only need to give the flyweight enough RKE to balance itself, which in turn causes the effective weight to shift position to the opposite side of the wheel, thus allowing the weight to lift itself for even less input energy.

So very circular logic, but even if the insipiration and rationale is slightly ad hoc, for now this remains a fascinating line of enquiry...!

[Ed]

conclude from circumstantial evidence that the weights were pierced in the middle and attached by connecting springs

It's hardly definitive that the weights were hollow. Middle could mean along the length or just the center of the bottom but not all the way through, etc.

The weights Bessler removed may not have been all of the active weights in the wheel, for all we know. There is also evidence that, at least the descriptions for, many of the drawings comes much later than his other published works.

I agree with Bill that the 1733 note was related to MT. Despite what John said in that blog post, there is more evidence the note goes with MT than his other published works. Remember the note itself was printed on the back of a duplicate MT page.

As for your "answered prayer", I would stop with the sims for a bit and answer whether this works in reality before spending more time building up ideas based on it in the simulator.

Always use a motor and real weights for your "moments" (I know you have in some of your sims), because the rotational torque constraint always acts on the central pivot of a body and not wherever you place it. At the moment I can't find the reference in the docs where I read that, but if you are quickly using them to represent your moments, you may be getting positive results that are not real. Just something to keep in mind.

[ovyyus]

It's hardly definitive that the weights were hollow.

Yes. A translation of Christian Wolff's description/speculation of the Merseburg wheel:

...I conclude, not only from this but also from other circumstantial evidence, that the weights are attached to some moveable or elastic arms on the periphery of the wheel. During rotation, one can clearly hear the weights hitting against the wooden boards...

Wolf described seeing (through a slit or crack) short boards attached at the rim of the wheel. He speculated that the weights hit these boards and that they must be attached in some way (pierced) to movable arms.

[MrVibrating]

Going back to the most recent sim, where a cross-shaped flywheel overbalances a wheel in locked vs unlocked half-cycles...

We still have a potentially interesting anomaly, that needs resolving:

Bearing in mind that the ideal flywheel shape would be toroidal, the starting and ending positions of both runs, locked vs unlocked, are identical - the same parts are in the same positions before and after.

Initial GPE is identical.

The only difference is whether, once falling, the flywheel has RKE relative to us, externally (ie. when it's locked), or to the wheel (when it's unlocked, its rot. inertia keeps its RKE at zero relative to us, but positive relative to the wheel).


Think about that for a second - dead simple rig, free vs locked flyweight.

Any reasonable person would expect that in the unlocked run, any RKE picked up by the flywheel would have to subtract from the final RKE of the main wheel, no? So the flywheel has some RKE, and the main wheel has that much less. CoE - it's a foregone conclusion eh..?

But this doesn't happen. With the flywheel unlocked, when it reaches BDC the main wheel actually has MORE energy.

So to recap; starting and ending positions are the same, GPE / translational should be identical, and any RKE gained by the flywheel should come at the expense of the main wheel's RKE. Because there's only so much GPE there to begin with, and it's the same amount in both locked vs unlocked runs.. right?

So check this:

43.813 J unlocked
38.557 J locked

Quite aside from how suprising this is (it's back-arsewards!), this characteristic bears all the hallmarks of a symmetry-break exploit. One interaction, two different energies, separated by a detail trivial to their conventional FxD integrals.

The only explanation i can currently see is that the direction of this flywheel RKE relative to the wheel is gear-wise - if the wheel turns CW, then the flywheel is turning CCW relative to it (even though its RKE is zero relative to us).. hence this exerts a small pure moment oriented downwards - in effect, the flyweight's resistance to spinning relative to us directly causes a spin relative to the wheel, exerting a downforce that adds to the G vector...

If this interpretation is valid then we can harness the effect via a hanging stator transmission between the flywheel and main wheel... will have to try this.. meantime, there's still a suggestion of a potential exploit here... this system's net GPE at TDC is evidently not constant..!