Poss. Symmetry Break?

[Furcurequs]

This post in a community buzz thread may be where I got the wiki link for quarkkäulgen:

http://www.besslerwheel.com/forum/viewt ... 105#115105

Those interested might want to check that out and read through the thread.

The poster, I believe, is German and argues that he is pretty confident that Bessler was simply referring to what we know of as marbles when he used "schniebe-käulgen. If he's familiar with the area from which the word originated, which he seemed to be, then I'd have to say his input would hold much more weight than mine.

[MrVibrating]

MrVibrating:

So this tells us two things - as he also mentions elsewhere, these wheels take time to construct. But furthermore, a higher-power, slower wheel that takes even longer to build, implies many more MoI to RKE interactions per cycle. It seems highly consistent to suppose that what he was considering here is a system with many scissorjacks

I too have wondered in posts about Bessler’s such long times needed to build a wheel. I am not sure many sissorjacks is the answer. If you asked me what would take me 6 months to build I would tell you it would be a wheel that incorporates a spiral. Maybe you were on the right trail before just purely looking at time.

That's an excellent point. He also makes pains to point out that while the principle may appear disarmingly simple, it took much calculation to develop, which would be consistent with determining a precise geometry such as a varying angle of curvature for multiple mechanisms.

My doubts re. the value of curved trajectories however comes back to a point i made earler, which is that a given amount of input PE (gravitational or otherwise) can, in the first instance, only convert to an equal amount of output KE in another field - so that work could be in the form of OB torque, or inertially-induced torque, or else shared between them.

This matters with regards to the question of how many individual masses are required to generate and harness a potential asymmetry - Jim for instance thinks it's two, but i disagree...

This is because i spent some weeks puzzling over the rising weights in the one-way wheels - when the Gera wheel, say, was tied off stationary, yet under constant static torque, that torque can only have come from an OB weight, requiring rotation to get lower, and without the use of a stator.

So, if the principle requires only two masses, what was the other, underbalanced mass doing at this static interval? Was it already raised, using excess energy it already had before being stopped? Perhaps forcibly halting the wheel caused an internal part to overshoot the rotation and thus cock a spring with some PE or else directly raise a load, using its own braking momentum? This is one possibility. But then, surely, an 'under-balanced' load already lifted is now a de-facto OB load..

This isn't necessarily a contradiction, but seems to narrow the chances of it being correct.

The only other alternative is that dropping a single OB weight generates sufficient advantage to then raise itself or another (per Jim's theory). However if this advantage depends upon MoI-reduction, which itself requires energy, then we have less available for either workload.

So either way, restricting ourselves to just two opposing masses is a bit of a conceptual straightjacket, compromising conflicting needs.

Four individual masses however allow us to separate their functional requirements. Long weight levers arranged around the perimeter per MT 133 / 134 have maximal GPE but negligible radial motion and thus MoI-RKE conversion, whereas opposing MoI-reducing masses per MT 134 have maximal MoI-RKE conversion but negligible GPE. So their requirements and trajectories needn't conflict or compromise one another.

And so this is the reason i suspect the apparent plausibility of spiral trajectories may represent an invalid set of assumptions; on the one hand, combining axial and radial displacements may seem to kill two birds with one stone, but if we also need to pop a gopher then it's a two-stone job.

As a final thought on this, any axial velocity we add from a spiralling trajectory - at first glance, reducing the RPM delta between an outbound mass and the rim of the wheel - has a sting in the tail, in the form of inertial counter-torque applied back to the wheel as the outbound mass's 'rides' the curve.. so, in applying angular acceleration to the extending mass we'd also be applying negative torque to the rest of the system, apparently defeating the purpose.

However my latest thinking is that applying the negative torque to the wheel is an inevitability, and that the exploit must be an asymmetry of induced +/- torque magnitudes in the first place, rather than a different way of dealing with equal opposite torques.

As i adjust to this new realisation, spiralling trajectories may yet have merit. If there is no way to avoid inducing equal opposite angular momentums from equal opposite inertial torques, then our only remaining option is to try to induce unequal inertial torques in the first place.

So, what would unequal inertial torques imply, if the masses causing them nonetheless still have to follow a closed-loop trajectory between inner and outer radii? I don't currently have any good answers for this, so spiralling trajectories should probably remain on the table of potentially-useful principles, even if it's not yet clear how or why...

[MrVibrating]

Practically every German to English dictionary I've seen, though, seems to translate schnip or schnipp to "snap."

Coincidence no doubt, but back when i first saw the Toys page, the term that originally sprung to mind for the hammer toys was "snap toys"..

[MrVibrating]

This post in a community buzz thread may be where I got the wiki link for quarkkäulgen:

http://www.besslerwheel.com/forum/viewt ... 105#115105

Those interested might want to check that out and read through the thread.

The poster, I believe, is German and argues that he is pretty confident that Bessler was simply referring to what we know of as marbles when he used "schniebe-käulgen. If he's familiar with the area from which the word originated, which he seemed to be, then I'd have to say his input would hold much more weight than mine.

Good find!

So maybe "marbles" implies the game is momentum transfer..

This would be consistent with Wolff's interpretation / deduction of the masses somehow gaining additional energy while falling, then imparting that gain to the wheel in their landing upon the radial slats (mis-translated in JC's book as "slightly warped boards").

It also tallies with the hammer-shaped weights of MT 133 / 134, implying that the direction of rotation is towards the flat ends of the hammers.

So, if the MoI-RKE conversion is applied to an orbiting mass on some kind of lever, then in the first instance that positive torque is not being applied to the wheel - rather, the angular velocity of the mass in question is accelerating ahead of the rotation.

This in turn raises the likelihood that the negative torques were also induced into similar masses & armatures, rather than being sunk directly into the main system.

So the implication then would be a system wherein the impact from the accelerated mass adds more RKE than the impact with the decelerated mass consumes.

Which would mean that rather than trying to induce unequal inertial torques, we'd be back to treating equal opposite torques differently.

My initial thinking here followed directly on from the previous 'discs' experiments, which suggested that although it was impossible to induce unequal opposing angular momentums, unequal RKE's were quite plausible.

What put me off that conclusion is that it's only really momentum that matters - the excess of RKE from a falling mass would ultimately just mean more heat and noise from that side of the wheel, if the up vs down momentums are nonetheless equal.

Then again, suppose we have equal opposite momenta with unequal KE's - we can't convert that directly into a net change in momentum... but we can convert the excess into GPE and let gravity do the rest..

I'm fairly confused right now to be honest, but what seems fairly concrete is that an asymmetric distribution of CW to CCW momentum appears to be as unattainable as ever, while an asymmetric distribution of CW to CCW RKE is a much more tangible propostion. Pefectly do-able, i'd say.

So i think it's fairly trivial to have more clockwise RKE than counter-clockwise, for instance, despite the respective angular momentums remaining equal and opposite.

Assuming a direct conversion of those unequal RKE's to GPE's, we can in principle raise more mass with one angular momentum than the other.

It would be that same apparent anomally that got Wubbly's attention - the net angular momentum would be zero, but the net RKE would not be. In a direct collision between two such masses, the system comes to a complete halt, and whether the heat dissipated came principally from an excess of CW or CCW KE would be entirely moot.

But maybe if we do something else with that energy difference, besides a dumb collision, such as raising a weight with the greater RKE, and dropping one onto the lower RKE.. we might come out ahead?

[daxwc]

This would be consistent with Wolff's interpretation / deduction of the masses somehow gaining additional energy while falling, then imparting that gain to the wheel in their landing upon the radial slats (mis-translated in JC's book as "slightly warped boards").

Is there evidence they were radial? I thought the new translation was just short boards.

Sorry don't mean to nit-pick your post.

[MrVibrating]

A directional asymmetry of braking momentum would be a whole new way of looking at things...

It would either mean:

- a preponderance of braking momentum on the descending side

- a preponderance of CW to CCW braking momentum

[MrVibrating]

This would be consistent with Wolff's interpretation / deduction of the masses somehow gaining additional energy while falling, then imparting that gain to the wheel in their landing upon the radial slats (mis-translated in JC's book as "slightly warped boards").

Is there evidence they were radial? I thought the new translation was just short boards.

Sorry don't mean to nit-pick your post.

IIRC the original text was specifying "normal" as in its original meaning of orthogonal, which, to the axial plane, implies radial.

[daxwc]

Stewart:

In fact in the periphery [of the wheel] here and there small 'normal' beams were attached, which on rotation of the wheel ~it was evident~ were quite clearly perceived to be hit by weights. I have noticed those small beams [while] looking through a crack, although from a distance.

I think the original confusing translation of 'warped boards' must be related to the words 'trabeculae normales'. I still can't see how someone would arrive at a translation of 'warped' though. 'Trabeculae' is diminutive plural of 'trabs' which means a beam or plank etc., so we get small beams/planks. 'normales' is an adjective (normalis/normale) which means "right angled, made according to a carpenter's square". The word 'normal' in English wasn't used to mean "conforming to common standards, usual" until the early 1800s. So when talking about 'normal' beams/lines in a wheel/circle I would think this would mean beams/lines at right-angles to the tangent.

http://www.besslerwheel.com/forum/viewt ... f&start=15

[MrVibrating]

There's another, very compelling reason why sinking the inertial torque into a lone mass which then impacts the rest of the wheel, is superior to inducing the toruqe directly into the wheel:

Suppose we have a long weight lever, with a heavy bob fixed to one end. A second weight can slide up and down the lever shaft during its rotation, varying the net MoI and thus RKE of the swing.

However, the more non-radially-translating mass this torque is sunk into, the less velocity / RKE we get.

We get the same net change in momentum either way, but the change in RKE is dependent upon the specific distribution of inertia and velocity.

In other words, we get maximal conversion of MoI to RKE when the corresponding torque is only sunk into the radially-translating mass itself.


This principal applies equally in the other direction - if we sink our negative torque into the net system, we've induced less RKE in that angular direction.

So, for example, we'd want to send a minimal inertia going CW, and a maximal inertia going CCW. The same change in radius of the same amount of mass, inbound or outbound, causing the same changes in CW to CCW angular momentums, but potentially, vastly unequal distributions of CW to CCW RKE.

As noted already, a simple collision merely equalises the momentums, and the difference in directional energy would be irrelevant. But a conversion of that RKE difference into a GPE advantage might be a possibility..

[daxwc]

Doesn’t that make the boards right angled according to periphery of the wheel?

[Gregory]

Hi Furcurequs,

Great findings on your part, thanks for the input.
Actually I found out that I know Quarkkäulchen, althought I had no idea about how it is called in german. I know the recipe without cheese, but yeah... I will give it a try with cheese, sure to be yummy.

Pancake headed club... There might be a little connection as Käulchen alternatively/wrongly also spelled Keulchen. http://www.wissen.de/rechtschreibung/kaeulchen
While frying the Quarkkäulchen it is usually very hard if not impossible to stick to a ball shape, and this is how balls become disc shaped, leads to scheibe and "Scheibenkeule". But now I think it is otherwise probably not much related to "schniebe-käulgen", so it was possibly an inappropriate find on my part.

"Schnieben" is an alternate version of "Schnauben" which means snore, snort, puff, wheeze, blow, breathe.
Here are some example sentences about "schnieben" I collected from different google books, all related to problems with breathing and such:

"...geschnöben, so viel als schnauben, schnaufen, doch nur von einem gelindern und feineren Geräusch; mit der Nase schnieben, wenn man etwas darin hat, was man mit der Luft ausstoßen will."

"Wer dies Schnieben oder Schnarchen zum erstenmal hört, glaubt durchaus keinen Vogel, sondern das Schnieben eines schlafenden Menschen zu hören und wirb diesen ganz in der Nahe suchen, während jene! sonderbaren Töne vom..."

"...der Appetit ziemlich gut; früher hartleibig, seit dem Gebrauch von Karlsbad oft zu 8 Tagen Diarrhoe'; bei Anstrengung Drücken und Stechen in der Brust, Knrzathmigkeit, Schnieben durch die Nase; um ruhiger Schlaf mit angstlichen Träumen"

About "käulgen"... these are definitely (small) balls, or ball shaped objects/structures. I read a lot of different examples like bees collecting nectar dust in the form of small balls sticking to their legs, or maggots develop for nine days inside a yellow "käulge". Also grape berry referred as "käulge" and other similar stuff.

But again, I found a few likely words for "schniebe-käulgen" in this list from the other thread:
http://www.murmelwelt.de/namen.html

You mentioned "Schnippskugeln" and the other one is "Schippelkugeln". Both leads to snip/slice/scrap balls as far as I could translate. And back in the 1700s these marbles are most likely hand made, therefore the word "snip" makes some sense. I found two books where there is even some description about the game and the balls. Only someone would need to translate it properly, perhaps it could add something of value to our understanding:
https://books.google.hu/books?id=sh1qAw ... er&f=false
https://books.google.hu/books?id=zHBqAw ... ln&f=false

Also there is another game called "Schusser" which is kind of a crossbow with clay balls for hunting birds:
https://translate.googleusercontent.com ... UW-q1WBfcA

I think we can conclude that Bessler was referring to children playing a game with some kind of marbles or stone/clay balls. There were and are a lot of different (children) games like that all around the globe with various rules. Marble games:
https://translate.google.com/translate? ... torie.html
https://translate.google.com/translate? ... &sandbox=1
http://www.murmelwelt.de/stein.html

So... "The children play on the pillars with loud heavy marbles/stone/clay balls."
An additional possibility is the snow/hailstone related meaning. Furthermore if we want to consider the translation snoring/snorting, that may refer to the sound the balls make or simply a kind of artistic meaning.

So, perhaps we can now stop hijacking MrVibrating's thread so much. :)
Sorry MrVibrating!

[MrVibrating]

Doesn’t that make the boards right angled according to periphery of the wheel?

IOW the conundrum is whether the impact is vertical, horizontal, or some combination..


The case i'm trying to make is that the most consistent interpretation would see the inertial torque, in the first instance, applied only and exclusively to the inbound mass, in order to maximise the divergence of inertia to velocity, and thus maximise the potential 'gain' margin.

If the impact was from a purely radial motion, this would imply that the corresponding negative torque was being applied to the whole wheel, in real time, as the torque itself is generated. This minimises the MoI to RKE conversion efficiency, narrowing our potential 'loss' margin.

In other words, if the impact on the descending side is from a radial motion, from something coming outwards and colliding perpendularly to the rim, then that means the negative inertial torque is applied to the descending side of the wheel.

This in turn would imply that gravity is indeed assisting by way of re-accelerating the inertially-decelerated angular momentum, as previously outlined.

Equally, on the opposite side of the wheel, it would mean that the positive inertial torque from an inbound mass overlaps with the negative gravitational torque from re-lifting a previously-lowered weight.

So some good consistencies with the Toys page here.. this interaction precisely fits the (+G) + (-I) > (-G) + (+I) profile.


If however the impact is from an axial collision upon a radial surface, then it's either from an upwards or downwards CW or CCW motion.

This would still be consistent with the common principle here of divvying up equal opposite torques into unequal inertias for unequal RKE's in opposite directions, but would be applying a different permutation - for instance if the colliding body's motion was downwards in the common direction of rotation, it would be consistent with Wolff's deductions of the weights seeming to gain energy over and above their GPE while otherwise in freefall. This in turn however would mean that the negative torque was applied to the ascending side of the wheel, fitting the (+g) + (+I) > (-G) + (-I) profile.

Since the other two remaining profiles are simply the inverse of these two above, one or other of them must be wrong, whilst the other produces an energy asymmetry of one sign or the other..

[MrVibrating]

So, perhaps we can now stop hijacking MrVibrating's thread so much. :)
Sorry MrVibrating!

No need, it's a fascinating sideline and may yet have further relevance.




And at least it's not a flame war.

[daxwc]

MrVibrating

IOW the conundrum is whether the impact is vertical, horizontal, or some combination..
The case i'm trying to make is that the most consistent interpretation would see the inertial torque, in the first instance, applied only and exclusively to the inbound mass, in order to maximise the divergence of inertia to velocity, and thus maximise the potential 'gain' margin.

"Here I will say only this
much: no wheel is moved by heavy blows, which are more likely to
dash the paddles of the wheel into a 1000 pieces, as though with
bullets. MT 152"
I wish we knew how loud it was. Did the weights sound like they were being used for maximum impact or were they just being landed? I myself doubt very much it was an impact wheel principle in the true sense.

[Fletcher]

I agree with you dax on that one.

It seems that weights had to be stopped in translation somehow, in a manner that didn't entirely waste the KE of movement (e.g. say as a weight hitting the rim at right angles would). Striking a right-angle short board would salvage some energy I guess and is consistent with Wolff's account.

We also know that JB used felt initially to reduce noise because of all the banging and clattering. In later wheels he abandoned the felt covering, and they were heard to make scratching noises etc.

So it seems the striking of the short boards was not a true impact derivative wheel like MT52 which describes heavy hitting as a waste of time.