Hi Furcurequs/MrVibrating,
I tried to dig deeper about schniebe-käulgen. I asked a german friend of mine, but had no idea what can it mean actually.
I also noticed that google translate suggest did I mean "schiebe-kollegen". But I know that it tries to suggest a lot of crap when can't recognize the words to be translated.
On the other hand, I found a german word "Scheibenkeule" which means a kind of old/prehistoric mace with a disc shaped stone head similar to a grindstone, and possibly also used for grinding...
So, maybe in the 1700s on certain streets of Germany there was a kind of children's game played by a heavy "Scheibenkeule" type of club and small balls. Like a protogame or an alternate version for cricket or something else.
source links:
https://de.wikipedia.org/wiki/Ger%C3%B6llkeule
http://www.steinharteknochenarbeit.de/s ... eibenkeule
http://steinharteknochenarbeit.magix.ne ... 0Schleifen
http://www.pnp.de/region_und_lokal/land ... ropas.html
Does it make sense this way? Is it possible that "Schniebe-käulgen" and Scheibenkeulen are the same thing?
I am not sure about it and obviously my german knowledge is limited.
Otherwise it looks plausible for me as far as "Kinder spielen" goes.
Can someone with fluent german investigate this a little further?
Poss. Symmetry Break?
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re: Poss. Symmetry Break?
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MrVibrating
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re: Poss. Symmetry Break?
Cheers Gregory, like i keep saying, this would just be a consistency between the AP poem and certain MT images, but either way, moving masses (whatever their description) in and out varies their MoI and thus their speed / energy.
FWIW, i've even considered making the MoI-shifting masses into small wheels which ride the inside of the wheel face as they move in and out, as a way of transferring momentum between inner and outer radii - ie. small heavy flywheels riding the outer edge will be spun up to higher speed than identical wheels riding the inner edge. Couldn't find any particular benefit tho..
Something else i tried yesterday was masses that hang down from inside the top of the wheel, then, as it rotates, they hit the side of the wheel and come back down resting on the wheel's inner floor.
This results in the masses following an eye-shaped trajectory; the upper and lower arc are perfect semicircles, but with the middle lattitudes chopped out:
..the circle outline in the background is just there to provide a visual reference for how much MoI reduction can, in principle, be achieved using gravity alone.
I've tried a few variations on this so far - re-purposing the 'pods' concept i was playing with previously, which is slightly more elaborate than this 'eye' concept requires - WM2D can't easily do toroids, so getting a mass to 'ride the inside surface' of the wheel is tricky.. not that this concept can go anywhere, i think. Like i say tho it shows gravity's sufficient to selectively supress MoI.
TBH i'm still hovering around a certain crossroads, unsure which way to head - should i be trying to induce the positive torque directly into the wheel, while using gravity to re-accelerate another mass briefly slowed by the negative torque...?
Or else, sinking the positive torque into a smaller mass that is briefly accelerated ahead of the rest of the rotation?
Either way, the decelerated and accelerated rotating momentums then have to re-combine to a non-unity sum.. (because we can't have two infinitely diverging momentums).
So far, this only supposes that the two angular momentums in question are both co-axial - sharing the same axis of rotation. However there's also the possibility of orbiting axes..
This option would seem to provide a good consistency between witness testimonies (esp. Wolff's) and the latter option of applying the positive torque to a smaller mass which briefly accelerates before colliding with the rest of the wheel to share its profits.
The question of what to do with the negative torques tho is still left hanging..
I mean, logically, gravity must've assisted in dealing with this negative torque, somehow. Either precluding its induction in the first place, or else providing some kind of sink or reversal for it.
As i see it, confering and divvying out the positive torques inside the system is fairly trivial - we can apply gravity to help generate the positive torque via passive MoI reduction, and induce it directly into the main system or else via a smaller mass which then collides with the main system.
So the issue requiring more attention is what to do with these negative torques induced by extending masses back outwards again.
Presumably, there's some way gravity can help get rid of the effects of these negative torques.
The possibility that then first comes to mind is re-extending a mass radially, while it's rotating downwards, on the descending side of the wheel.
However, sliding outwards - even passively, under CF - while rotating downwards, inevitably means sliding downwards by some amount, once below the 90° horizontal mark, and so converting some GPE to MoI extension, and thus reducing the remainder available to angular acceleration. So this approach isn't without compromise.
Again, the thought arises that very rapid radial motions help to clean up the concept, if not the design. Shooting in and out very quickly means we can limit the corresponding arc segment of these actions, so improving our accuracy as to whether a mass is eg. extended straight upwards at 12 o' clock or suddenly retracted inwards at 9 o' clock or whatever, since GPE is not time-dependent.
This would mean that, conceptually at least, GPE inputs and outputs could be notionally considered as binary changes rather than having to be integrated over an angle. However this could also translate into as much practical utility as theoretical, since we want to harness the maximum MoI and GPE deltas at maximal RPM and thus minimal time. IOW, minimising the extent to which rising RPM closes our gain windows.
So this would provide good rationale for the use of something like scissorjacks.
But first we need to find a thermodynamic asymmetry between GPE-induced MoI changes, and MoI-induced RKE changes.
Two opposing workloads:
- we apply GPE to modify MoI, inducing inertial rather than OB torque
- we apply that inertial torque to modify GPE
...or some variation on this (ie. use GPE for OB torque, apply that to modify MoI and use a two-stage MoI change with inertial torque from the first driving radial variation of the second, which in turn converts back to GPE). Or something. Some permutation on these principles, exploiting a change in relative conditions.
One way or another, Bessler's success implies there's an asymmetry to be found between the energy scaling dimensions of these two workloads (ie. changes in one field change the scaling dimensions of the other). The asymmetry will also be interpretable in terms of a time-dependent asymmetry per Noether's theorem (ie. a variable determining energy in one field changes as a function of time in way that its equivalent in the other field does not).
Find the thermodynamic asymmetry and the requisite mechanism will spell itself out..
FWIW, i've even considered making the MoI-shifting masses into small wheels which ride the inside of the wheel face as they move in and out, as a way of transferring momentum between inner and outer radii - ie. small heavy flywheels riding the outer edge will be spun up to higher speed than identical wheels riding the inner edge. Couldn't find any particular benefit tho..
Something else i tried yesterday was masses that hang down from inside the top of the wheel, then, as it rotates, they hit the side of the wheel and come back down resting on the wheel's inner floor.
This results in the masses following an eye-shaped trajectory; the upper and lower arc are perfect semicircles, but with the middle lattitudes chopped out:
..the circle outline in the background is just there to provide a visual reference for how much MoI reduction can, in principle, be achieved using gravity alone.
I've tried a few variations on this so far - re-purposing the 'pods' concept i was playing with previously, which is slightly more elaborate than this 'eye' concept requires - WM2D can't easily do toroids, so getting a mass to 'ride the inside surface' of the wheel is tricky.. not that this concept can go anywhere, i think. Like i say tho it shows gravity's sufficient to selectively supress MoI.
TBH i'm still hovering around a certain crossroads, unsure which way to head - should i be trying to induce the positive torque directly into the wheel, while using gravity to re-accelerate another mass briefly slowed by the negative torque...?
Or else, sinking the positive torque into a smaller mass that is briefly accelerated ahead of the rest of the rotation?
Either way, the decelerated and accelerated rotating momentums then have to re-combine to a non-unity sum.. (because we can't have two infinitely diverging momentums).
So far, this only supposes that the two angular momentums in question are both co-axial - sharing the same axis of rotation. However there's also the possibility of orbiting axes..
This option would seem to provide a good consistency between witness testimonies (esp. Wolff's) and the latter option of applying the positive torque to a smaller mass which briefly accelerates before colliding with the rest of the wheel to share its profits.
The question of what to do with the negative torques tho is still left hanging..
I mean, logically, gravity must've assisted in dealing with this negative torque, somehow. Either precluding its induction in the first place, or else providing some kind of sink or reversal for it.
As i see it, confering and divvying out the positive torques inside the system is fairly trivial - we can apply gravity to help generate the positive torque via passive MoI reduction, and induce it directly into the main system or else via a smaller mass which then collides with the main system.
So the issue requiring more attention is what to do with these negative torques induced by extending masses back outwards again.
Presumably, there's some way gravity can help get rid of the effects of these negative torques.
The possibility that then first comes to mind is re-extending a mass radially, while it's rotating downwards, on the descending side of the wheel.
However, sliding outwards - even passively, under CF - while rotating downwards, inevitably means sliding downwards by some amount, once below the 90° horizontal mark, and so converting some GPE to MoI extension, and thus reducing the remainder available to angular acceleration. So this approach isn't without compromise.
Again, the thought arises that very rapid radial motions help to clean up the concept, if not the design. Shooting in and out very quickly means we can limit the corresponding arc segment of these actions, so improving our accuracy as to whether a mass is eg. extended straight upwards at 12 o' clock or suddenly retracted inwards at 9 o' clock or whatever, since GPE is not time-dependent.
This would mean that, conceptually at least, GPE inputs and outputs could be notionally considered as binary changes rather than having to be integrated over an angle. However this could also translate into as much practical utility as theoretical, since we want to harness the maximum MoI and GPE deltas at maximal RPM and thus minimal time. IOW, minimising the extent to which rising RPM closes our gain windows.
So this would provide good rationale for the use of something like scissorjacks.
But first we need to find a thermodynamic asymmetry between GPE-induced MoI changes, and MoI-induced RKE changes.
Two opposing workloads:
- we apply GPE to modify MoI, inducing inertial rather than OB torque
- we apply that inertial torque to modify GPE
...or some variation on this (ie. use GPE for OB torque, apply that to modify MoI and use a two-stage MoI change with inertial torque from the first driving radial variation of the second, which in turn converts back to GPE). Or something. Some permutation on these principles, exploiting a change in relative conditions.
One way or another, Bessler's success implies there's an asymmetry to be found between the energy scaling dimensions of these two workloads (ie. changes in one field change the scaling dimensions of the other). The asymmetry will also be interpretable in terms of a time-dependent asymmetry per Noether's theorem (ie. a variable determining energy in one field changes as a function of time in way that its equivalent in the other field does not).
Find the thermodynamic asymmetry and the requisite mechanism will spell itself out..
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MrVibrating
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LOL " a seer sees".
JK, don't wanna kick off any more translation debates. It's totally incidental, circumstantial and irrelevant to the physics - for a start, the above trajectory has no directional dependence, and is currently dependent upon a stator. Statorless is possible, however, by making the vertical hanging struts heavy enough to hang downwards somewhat stably. But for a directional dependence, the masses' deceleration on the way back out mustn't be applied to the system, while their effective weight remains balanced to the rising weight opposite - ie., conflicting requirements, i think..
JK, don't wanna kick off any more translation debates. It's totally incidental, circumstantial and irrelevant to the physics - for a start, the above trajectory has no directional dependence, and is currently dependent upon a stator. Statorless is possible, however, by making the vertical hanging struts heavy enough to hang downwards somewhat stably. But for a directional dependence, the masses' deceleration on the way back out mustn't be applied to the system, while their effective weight remains balanced to the rising weight opposite - ie., conflicting requirements, i think..
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re: Poss. Symmetry Break?
..quick followup to that last point:
- by varying the relative mass to RPM ratio, a vertical to horizontal momentum asymmetry can be introduced:
..here, MoI comes in quicker than it goes back out, however, as noted, the effective weight and thus OB workload is also asymmetric in the opposite direction; a hurdle many approaches to this principle in MT stumble at, including (potentially) MT 14, 15, 16, 18, 20, 22, 24, 25, 26, 27, 30 right thru to 42, and still recurring repeatedly even throughout the later, more abstract images.
One of the last things MT seems to culminate in is the possibility of some kind of inertial counter-balancing principle, emdodied figuratively if not literally in the Robervals of MT 134 and MT 143. Intriguingly, if again, coincidentally, the preceding image, MT 142, seems to show a similar apparatus to the 'eye' trajectory rig i was playing with earlier..
Coincidence or not, i think there's good reason to suppose that MoI-induced torques isn't some late-stage, closing theme in Machinen Tractate, as one of the most consistent narrative ideas throughout it.. it is the "aspect not readilly apparent", the point that requires "further speculation", when a "superior weight may be apparent, yet nothing can be seen or deduced of the prime mover".. it is the "special thing behind the scissorjacks", the rationale behind the "connectedness principle" and "correct handle-construction", the "thing that can be learned, to be treated later", the thing "said" more than "shown", the "horse" before the "cart". Inertial torque is the elephant in the shadows, explicitly mentioned nowhere, yet implied everywhere, thinly veiled as issues of static balance.
As MT confirms, any static field's effects on energy balance are a zero-sum deal. But gravity's effects on conservation of angular momentum, and those of CoAM with regard to RKE, opens up a whole new vista of dynamical fields and potential inequilibira..
- by varying the relative mass to RPM ratio, a vertical to horizontal momentum asymmetry can be introduced:
..here, MoI comes in quicker than it goes back out, however, as noted, the effective weight and thus OB workload is also asymmetric in the opposite direction; a hurdle many approaches to this principle in MT stumble at, including (potentially) MT 14, 15, 16, 18, 20, 22, 24, 25, 26, 27, 30 right thru to 42, and still recurring repeatedly even throughout the later, more abstract images.
One of the last things MT seems to culminate in is the possibility of some kind of inertial counter-balancing principle, emdodied figuratively if not literally in the Robervals of MT 134 and MT 143. Intriguingly, if again, coincidentally, the preceding image, MT 142, seems to show a similar apparatus to the 'eye' trajectory rig i was playing with earlier..
Coincidence or not, i think there's good reason to suppose that MoI-induced torques isn't some late-stage, closing theme in Machinen Tractate, as one of the most consistent narrative ideas throughout it.. it is the "aspect not readilly apparent", the point that requires "further speculation", when a "superior weight may be apparent, yet nothing can be seen or deduced of the prime mover".. it is the "special thing behind the scissorjacks", the rationale behind the "connectedness principle" and "correct handle-construction", the "thing that can be learned, to be treated later", the thing "said" more than "shown", the "horse" before the "cart". Inertial torque is the elephant in the shadows, explicitly mentioned nowhere, yet implied everywhere, thinly veiled as issues of static balance.
As MT confirms, any static field's effects on energy balance are a zero-sum deal. But gravity's effects on conservation of angular momentum, and those of CoAM with regard to RKE, opens up a whole new vista of dynamical fields and potential inequilibira..
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re: Poss. Symmetry Break?
I should probably just at least make a mention of spiral trajectories - per the first instance of the variant-type "A" in MT 16:
A spiral trajectory is interesting as, while varying the radius, it also varies the angular velocity of the masses, relative to the rest of the wheel.
If we pull a mass straight outwards radially, its angular trajectory is lengthened and so it must be accelerated in order to maintain the same RPM it had at the previous lower radius. This resistance to acceleration is the reason the RPM's drop as the mass's radius increases - ie. the reason why MoI squares with radius.
But a spiralling outbound trajectory, combining radial with axial motion, as shown here in MT 16, means the extended mass is also imparted with an angular acceleration.
The helps to maintain the effective weight of the outbound mass (and thus the wheel's state of balance), while limiting the deceleration of the wheel during the extension, at a cost of the some of the outer weight's OB GPE.
For now, i suspect spiralling trajectories are muddying the waters, making visual integration confusing, whereas rapid, straight radial motions, such as from scissorjacks, are cleaner.
They're worth mentioning however simply because they embody all of these principles..
A spiral trajectory is interesting as, while varying the radius, it also varies the angular velocity of the masses, relative to the rest of the wheel.
If we pull a mass straight outwards radially, its angular trajectory is lengthened and so it must be accelerated in order to maintain the same RPM it had at the previous lower radius. This resistance to acceleration is the reason the RPM's drop as the mass's radius increases - ie. the reason why MoI squares with radius.
But a spiralling outbound trajectory, combining radial with axial motion, as shown here in MT 16, means the extended mass is also imparted with an angular acceleration.
The helps to maintain the effective weight of the outbound mass (and thus the wheel's state of balance), while limiting the deceleration of the wheel during the extension, at a cost of the some of the outer weight's OB GPE.
For now, i suspect spiralling trajectories are muddying the waters, making visual integration confusing, whereas rapid, straight radial motions, such as from scissorjacks, are cleaner.
They're worth mentioning however simply because they embody all of these principles..
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Furcurequs
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Re: re: Poss. Symmetry Break?
Hello Gregory,Gregory wrote:Hi Furcurequs/MrVibrating,
I tried to dig deeper about schniebe-käulgen. I asked a german friend of mine, but had no idea what can it mean actually.
I also noticed that google translate suggest did I mean "schiebe-kollegen". But I know that it tries to suggest a lot of crap when can't recognize the words to be translated.
On the other hand, I found a german word "Scheibenkeule" which means a kind of old/prehistoric mace with a disc shaped stone head similar to a grindstone, and possibly also used for grinding...
So, maybe in the 1700s on certain streets of Germany there was a kind of children's game played by a heavy "Scheibenkeule" type of club and small balls. Like a protogame or an alternate version for cricket or something else.
source links:
https://de.wikipedia.org/wiki/Ger%C3%B6llkeule
http://www.steinharteknochenarbeit.de/s ... eibenkeule
http://steinharteknochenarbeit.magix.ne ... 0Schleifen
http://www.pnp.de/region_und_lokal/land ... ropas.html
Does it make sense this way? Is it possible that "Schniebe-käulgen" and Scheibenkeulen are the same thing?
I am not sure about it and obviously my german knowledge is limited.
Otherwise it looks plausible for me as far as "Kinder spielen" goes.
Can someone with fluent german investigate this a little further?
I believe we've had other German speakers who didn't really know what "Schniebe-käulgen" meant, either. One seemed to understand that "Shnipp-käulgen" might mean "marble," however, which from that one reference I found seems to have been the case.
When searching Google Books, I used the time range of 1650 to 1800, I think, and I saw many uses of the word "käulgen" and also uses of "Schnieben," so I personally don't believe those words were misspelled by Bessler. What they referred to then when used together or what they might have morphed into more recently, I don't know.
We've had posters in the past here who were concentrated on learning the old German and translating the Bessler texts, but I haven't seem them in a while.
"Scheiben" and "keule" both seem to have been used around Bessler's time, also, from my quick Google Book search. So, "scheibenkeule" could have a fairly old origin. Whether it's the same thing and an alternate name for what Bessler was referring to, I certainly don't know. It's anyone's guess, I suppose, until we find something definitive.
Thanks.
Oh, Google Translate doesn't seem to have some old German words in its vocabulary, so it will offer similarly spelled new German words as suggestions.
Dwayne
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Furcurequs
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re: Poss. Symmetry Break?
I just happened to see this German Wikipedia page in my bookmarks:
Quarkkäulchen
https://de.wikipedia.org/wiki/Quarkk%C3%A4ulchen
From Google's translation, quarkkäulchen is apparently some type of dessert from Saxony. It's a type of fried dumpling where the dough is made from potatoes, lean curd, eggs and flour.
The "käulchen" part of the word seems to be our old familiar "little balls." In modern German the "gen" has become "chen."
Google translation of the page:
https://translate.google.com/translate? ... edit-text=
I just found this, too:
I also found this:
So, "cheese balls"?
We can see, then, that käulchen (käulgen) was a word used in Saxony.
Youtube video of kids making quarkkäulchen:
"Quarkkäulchen. Simply Saxony. (EN)" (...with recipe)
https://www.youtube.com/watch?v=g1TiGZeyrHs
Google+ references to Quarkkäulchen with lots of pictures. (I'm getting hungry!)
https://plus.google.com/wm/4/app/basic/ ... %A4ulchen/
Quarkkäulchen
https://de.wikipedia.org/wiki/Quarkk%C3%A4ulchen
From Google's translation, quarkkäulchen is apparently some type of dessert from Saxony. It's a type of fried dumpling where the dough is made from potatoes, lean curd, eggs and flour.
The "käulchen" part of the word seems to be our old familiar "little balls." In modern German the "gen" has become "chen."
Google translation of the page:
https://translate.google.com/translate? ... edit-text=
I just found this, too:
http://www.journeytoberlin.com/content/ ... rkkeulchenWhat gets sold in Berlin as Quarkkeulchen is something quite different to the Saxon pancakes. They still contain quark, but there's no potato in the dough and they're deep fried as balls. The result is more like a doughnut, though they're often flavoured with lemon zest and cinnamon, giving them quite a different flavour, plus of course the quark gives them a heavier texture.
The word 'keule' in the context of food is normally a leg (e.g. Lammkeule - leg of lamb), but the name of these has nothing to do with legs! It comes from the middle German word for a ball - 'Kaule' - which, if used in the diminutive form, becomes Käulchen (little ball), which sounds the same as Keulchen.
I also found this:
http://frederiqueandfriends.blogspot.co ... ion-7.htmlThis is a very traditional dish served in the eastern part of Germany, in the federal state of saxony. I tried to translate it but without a lot of success ;) Quark is the german word for curd cheese and käulchen is the form of the dish - at least that's what I think.
So, "cheese balls"?
We can see, then, that käulchen (käulgen) was a word used in Saxony.
Youtube video of kids making quarkkäulchen:
"Quarkkäulchen. Simply Saxony. (EN)" (...with recipe)
https://www.youtube.com/watch?v=g1TiGZeyrHs
Google+ references to Quarkkäulchen with lots of pictures. (I'm getting hungry!)
https://plus.google.com/wm/4/app/basic/ ... %A4ulchen/
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MrVibrating
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..couple of quick late night thoughts:
- potential energy density of a rig powered by OU inertial torques
Basically, much, much higher than for a gravity-powered device. Gravity presumably sets some limit on the amount of MoI variation it can provide for a given mass and radius, but just generally, the strength of torque that can be generated by pulling a heavy mass inwards quickly is, potentially, surprisingly powerful.
If anyone's skeptical that this could generate high torque, simply consider any arbitrary wheel size, loaded with any arbitrary amount of radially-moveable mass at its perimeter, rotating at any arbitrary RPM... MoI equals mass times radius squared, and RKE equals half the MoI times RPM squared.
But you don't need to worry about that for now, just pick a number.
Next, we reduce the radius of that mass by just 30%. This howver halves the system's MoI. Since angular momentum is MoI times RPM, and must be conserved, if MoI halves, RPM doubles to conserve net momentum, and half the inertia at twice the velocity has twice the energy.
So, whatever number you picked for the baseline RKE... it's just doubled.
Frictional losses notwithstanding, there's no time-dependency to this formula - it doesn't matter if the mass is drawn inwards quickly or gradually - the same change in MoI causes the same change in RKE, regardless of how long it takes..
Which means it can also happen very quickly. You could employ springs as buffers to limit collision losses (so the incoming masses would be progressively braked instead of slamming into the hub and wasting KE). So the power is determined by how many MoI cycles we can fit into a full rotation of the net system, at a given RPM.
This, in turn, provides an answer for another issue that must be consistent with any viable solution:
- Bessler says, given enough time, he could construct a wheel that turns very slowly, but with great power
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.
These would operate at similar, maximal speed to the regular wheels, there'd just be more of them. This is simply an implicit property of a higher-power system nonetheless running at lower speed. More energy at lower velocity for a give amount of mass and radial travel means more such interactions per given angle or cycle.
But then this also reveals a further insight - how can such a system remain turning slowly despite its high power? Why doesn't it just take off, accelerating up to silly speeds - not least since, there's no stator..?
The only possible resolution is that, as suggested previously, the positive torques are accompanied by negative torques. If the positive and negative torques are then applied in series, rather than parallel, the net system now has a 'notchy' rotation with a self-imposed RPM limit.
So this may also help illuminate a third issue - of what to do with these negative torques. I've been looking for ways to avoid sinking them into the net system, trying to only 'rectify' the positive torques while somehow discarding or avoiding the production of negative ones. Or using gravity to re-accelerate the slowed mass. None of which has borne fruit yet.
What the above conclusions point to is another path - both torques can be sunk into the net system.. they're just already asymmetric. The asymmetry is formed by generating a greater positive than negative torque in the first place, not by treating equal opposite torques differently.
So the question we should be asking is not what to do with the negative torques, but what to do differently to avoid inducing as much.
Another aspect of this performance characteristic is the observed RPM stability when raising or lowering a load, or runnning unloaded, which, as previously noted, implies that the direction of the torque asymmetry is dynamically variable - negative torques can trump positive when lowering a load, which could correspond to either an over-speed condition (driving the wheel faster than it wants to go), or else a reversal of the mechanism (ie. if the rope spooled off the axle in a consistent direction then the wheel must've run backwards when lowering the load).
So that's a few more dots joined, and a helpful signpost marking the path at this juncture.. i now have a better idea of what the target looks like, and so what to be aiming for...
- potential energy density of a rig powered by OU inertial torques
Basically, much, much higher than for a gravity-powered device. Gravity presumably sets some limit on the amount of MoI variation it can provide for a given mass and radius, but just generally, the strength of torque that can be generated by pulling a heavy mass inwards quickly is, potentially, surprisingly powerful.
If anyone's skeptical that this could generate high torque, simply consider any arbitrary wheel size, loaded with any arbitrary amount of radially-moveable mass at its perimeter, rotating at any arbitrary RPM... MoI equals mass times radius squared, and RKE equals half the MoI times RPM squared.
But you don't need to worry about that for now, just pick a number.
Next, we reduce the radius of that mass by just 30%. This howver halves the system's MoI. Since angular momentum is MoI times RPM, and must be conserved, if MoI halves, RPM doubles to conserve net momentum, and half the inertia at twice the velocity has twice the energy.
So, whatever number you picked for the baseline RKE... it's just doubled.
Frictional losses notwithstanding, there's no time-dependency to this formula - it doesn't matter if the mass is drawn inwards quickly or gradually - the same change in MoI causes the same change in RKE, regardless of how long it takes..
Which means it can also happen very quickly. You could employ springs as buffers to limit collision losses (so the incoming masses would be progressively braked instead of slamming into the hub and wasting KE). So the power is determined by how many MoI cycles we can fit into a full rotation of the net system, at a given RPM.
This, in turn, provides an answer for another issue that must be consistent with any viable solution:
- Bessler says, given enough time, he could construct a wheel that turns very slowly, but with great power
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.
These would operate at similar, maximal speed to the regular wheels, there'd just be more of them. This is simply an implicit property of a higher-power system nonetheless running at lower speed. More energy at lower velocity for a give amount of mass and radial travel means more such interactions per given angle or cycle.
But then this also reveals a further insight - how can such a system remain turning slowly despite its high power? Why doesn't it just take off, accelerating up to silly speeds - not least since, there's no stator..?
The only possible resolution is that, as suggested previously, the positive torques are accompanied by negative torques. If the positive and negative torques are then applied in series, rather than parallel, the net system now has a 'notchy' rotation with a self-imposed RPM limit.
So this may also help illuminate a third issue - of what to do with these negative torques. I've been looking for ways to avoid sinking them into the net system, trying to only 'rectify' the positive torques while somehow discarding or avoiding the production of negative ones. Or using gravity to re-accelerate the slowed mass. None of which has borne fruit yet.
What the above conclusions point to is another path - both torques can be sunk into the net system.. they're just already asymmetric. The asymmetry is formed by generating a greater positive than negative torque in the first place, not by treating equal opposite torques differently.
So the question we should be asking is not what to do with the negative torques, but what to do differently to avoid inducing as much.
Another aspect of this performance characteristic is the observed RPM stability when raising or lowering a load, or runnning unloaded, which, as previously noted, implies that the direction of the torque asymmetry is dynamically variable - negative torques can trump positive when lowering a load, which could correspond to either an over-speed condition (driving the wheel faster than it wants to go), or else a reversal of the mechanism (ie. if the rope spooled off the axle in a consistent direction then the wheel must've run backwards when lowering the load).
So that's a few more dots joined, and a helpful signpost marking the path at this juncture.. i now have a better idea of what the target looks like, and so what to be aiming for...
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daanopperman
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re: Poss. Symmetry Break?
Mr V ,
Have you ever considered that the spiked weights on the outside of MT 134 and 144 to be break shoes .
Have you ever considered that the spiked weights on the outside of MT 134 and 144 to be break shoes .
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MrVibrating
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You mean 133/134 - but yes, interesting proposition. Although i'd previously wondered if the similarity between the hammer shape of the long levers in the lower section of MT 133, and the lower hammer toy's hammers on the toys page, suggests that the negative torques might be of more value that the positive ones, in retrospect both positive and negative are equally important.
I think their shape may correspond to a directionality between the two torques, and that this directionality is contingent upon a condition set by the other, smaller levers..
TBH i really think the best source of answers regarding the meanings of MT 133 and 134 are potential correlations with the Toys page.
I think a full understanding of the Toys page is close at hand..
The scissorjacks, (E), represent inertial force.
This is why it has the square tip - symbolising inertial force both in terms of the predominant force their operation generates, as well as the square tip indicating a force that squares with displacement (as inertial force does).
Its vertical orientation also provides the reference frame for understanding the lower hammer toy, (D).
Like (E), it has handles. So both are operated by the same form of input work.
Stayiing with (D), its handles are orthogonal to the vertical vector indicated by the jacks (E). This is consistent with inertially-induced torques - if the inertial vector is vertical then vertical motion of the lower toy (D) induces horizontal inertial forces.
When it moves upwards, both hammers are pulled sideways in the same direction.
When it moves downwards, both hammers are pulled sideways back in the opposite direction.
Coming back to the jacks (E), their handles too are operated by a horizontal action, orthogonal to the main inertial vector.
This could be suggestive of a two-stage inertial interaction - vertical motion of the lower toy (D) induces horizontal forces which in turn could operate the jacks, ie. varying the net MoI.
The lower toy (D) also has a square anvil, and preceding images seem to establish a convention wherein square axles correspond to principally inertial forces.
The rounded bobs on the upper toy (C), by contrast, fit an established pattern of gravitationally-operated actions. However it, too, could be subject to the same horizontal inertias induced by the interaction between (E) and (D).
So, with these points in mind, consider that as the two hammer toys (C) and (D) move a little way up and down, horizontal inertias cause them to snap left and right, alternating their positions.
If we squeeze the jack handles (E), while the whole system is rotating about the bottom of the page (the axis pointed to by the whistling top), then the two hammer toys are pumped inwards and outwards in turn, and this radial (ie. vertical, here) cycling induces axial (ie. horizontal, here) forces, AKA 'torques'.
As such, if we assume CW rotation (of the whole system around the afformentioned lower main axis), then squeezing the toys upwards and outwards causes the upper toy (C) to flip its condition.
At this point, the lower toy (D) is already oriented in that direction (to the left, trailing the rotation), so does nothing (it can't move any further left).
Next, we open the jack handles, pulling the toys back inwards towards the system's center of rotation.
This now induces a CW (rightwards) inertial force, causing the lower toy to flip its condition, while the upper toy, already biased to the right, does nothing, until the jacks are squeezed again, moving the toys back outwards radially.
I remain less certain about items (A) and (B) - they most obviously seem to describe aspects of the axle, and how the above mentioned forces integrate with it, implying its vertical orientation is not to be confused with the inertial vector indicated by (E). My instinct is that they describe how the two afformention postive and negative inertial and gravitational torques are alternated between opposite sides of the axle between inbound and outboud phases of the operation of the jacks (E).
It seems likely that the opposing alternate eyelets on the shaft (B) imply that, for example , a positve gravitational torque combined with a negative inertial torque is applied to one side of the axle, before the inverse halves of the same interactions - the negative gravitational torque combined with the positive inertial torque - are applied to the other side of the axle.
The 'chain' item (A) might thus represent these alternate 'odd couple' pairings of opposing inertial and gravitational torques.
These torques can be simply itemised as: +G, -G, +I and -I.
So the first pairing might be +G & -I, then followed by the inverse coupling of -G & +I.
This means there is already an implicit asymmetry to be found within one of these four possible permutations.
While i accept John Collins' annotations that the four hand-written numbers on the Toys page may not even be in Bessler's hand, it would nonetheless seem fitting that there may be four possible solutions to the implied propostiion:
Assuming no particular priority they could be numbered thus:
MT 138 = (+G) + (+I) > (-G) + (-I)
MT 139 = (-G) + (+I) > (+G) + (-I)
MT 140 = (-G) + (-I) > (+G) + (+I)
MT 141 = (+G) + (-I) > (-G) + (+I)
Logically, if any one of these conditions is true, then so is its inverse (ie. the same asymmetry reversed), while the other two must be false.
It also goes without saying that +/-(G) ≠ -/+(I) - ie. there is already an implicit asymmetry between inertial and gravitational torques, whatever their respective signs.
Which in turn would confirm my suspicion that isolation of inertial and gravitational torque-inducing apparatuses is paramount. (Meaning a minimum of four masses are required, not two.)
On that count, i have one particular stone left unturned - i've previously looked into the gravitational properties of diametric weight levers, but not their inertial properties. It seems perfectly obvious that their radial displacements are minimal, so any MoI-induced torques from their changes in radial distance must also be minimal.
However they do have significant axial motion, and this also varies their instantaneous angular momentum.
This detail may or may not be tangential - simply isolating radial from axial displacements my be sufficient to enable a divergence of gravitational and inertial energies. But either way, i need to spend some time playing with these longer weight poles, to familiarise myself with their inertial effects..
I think their shape may correspond to a directionality between the two torques, and that this directionality is contingent upon a condition set by the other, smaller levers..
TBH i really think the best source of answers regarding the meanings of MT 133 and 134 are potential correlations with the Toys page.
I think a full understanding of the Toys page is close at hand..
The scissorjacks, (E), represent inertial force.
This is why it has the square tip - symbolising inertial force both in terms of the predominant force their operation generates, as well as the square tip indicating a force that squares with displacement (as inertial force does).
Its vertical orientation also provides the reference frame for understanding the lower hammer toy, (D).
Like (E), it has handles. So both are operated by the same form of input work.
Stayiing with (D), its handles are orthogonal to the vertical vector indicated by the jacks (E). This is consistent with inertially-induced torques - if the inertial vector is vertical then vertical motion of the lower toy (D) induces horizontal inertial forces.
When it moves upwards, both hammers are pulled sideways in the same direction.
When it moves downwards, both hammers are pulled sideways back in the opposite direction.
Coming back to the jacks (E), their handles too are operated by a horizontal action, orthogonal to the main inertial vector.
This could be suggestive of a two-stage inertial interaction - vertical motion of the lower toy (D) induces horizontal forces which in turn could operate the jacks, ie. varying the net MoI.
The lower toy (D) also has a square anvil, and preceding images seem to establish a convention wherein square axles correspond to principally inertial forces.
The rounded bobs on the upper toy (C), by contrast, fit an established pattern of gravitationally-operated actions. However it, too, could be subject to the same horizontal inertias induced by the interaction between (E) and (D).
So, with these points in mind, consider that as the two hammer toys (C) and (D) move a little way up and down, horizontal inertias cause them to snap left and right, alternating their positions.
If we squeeze the jack handles (E), while the whole system is rotating about the bottom of the page (the axis pointed to by the whistling top), then the two hammer toys are pumped inwards and outwards in turn, and this radial (ie. vertical, here) cycling induces axial (ie. horizontal, here) forces, AKA 'torques'.
As such, if we assume CW rotation (of the whole system around the afformentioned lower main axis), then squeezing the toys upwards and outwards causes the upper toy (C) to flip its condition.
At this point, the lower toy (D) is already oriented in that direction (to the left, trailing the rotation), so does nothing (it can't move any further left).
Next, we open the jack handles, pulling the toys back inwards towards the system's center of rotation.
This now induces a CW (rightwards) inertial force, causing the lower toy to flip its condition, while the upper toy, already biased to the right, does nothing, until the jacks are squeezed again, moving the toys back outwards radially.
I remain less certain about items (A) and (B) - they most obviously seem to describe aspects of the axle, and how the above mentioned forces integrate with it, implying its vertical orientation is not to be confused with the inertial vector indicated by (E). My instinct is that they describe how the two afformention postive and negative inertial and gravitational torques are alternated between opposite sides of the axle between inbound and outboud phases of the operation of the jacks (E).
It seems likely that the opposing alternate eyelets on the shaft (B) imply that, for example , a positve gravitational torque combined with a negative inertial torque is applied to one side of the axle, before the inverse halves of the same interactions - the negative gravitational torque combined with the positive inertial torque - are applied to the other side of the axle.
The 'chain' item (A) might thus represent these alternate 'odd couple' pairings of opposing inertial and gravitational torques.
These torques can be simply itemised as: +G, -G, +I and -I.
So the first pairing might be +G & -I, then followed by the inverse coupling of -G & +I.
This means there is already an implicit asymmetry to be found within one of these four possible permutations.
While i accept John Collins' annotations that the four hand-written numbers on the Toys page may not even be in Bessler's hand, it would nonetheless seem fitting that there may be four possible solutions to the implied propostiion:
Assuming no particular priority they could be numbered thus:
MT 138 = (+G) + (+I) > (-G) + (-I)
MT 139 = (-G) + (+I) > (+G) + (-I)
MT 140 = (-G) + (-I) > (+G) + (+I)
MT 141 = (+G) + (-I) > (-G) + (+I)
Logically, if any one of these conditions is true, then so is its inverse (ie. the same asymmetry reversed), while the other two must be false.
It also goes without saying that +/-(G) ≠ -/+(I) - ie. there is already an implicit asymmetry between inertial and gravitational torques, whatever their respective signs.
Which in turn would confirm my suspicion that isolation of inertial and gravitational torque-inducing apparatuses is paramount. (Meaning a minimum of four masses are required, not two.)
On that count, i have one particular stone left unturned - i've previously looked into the gravitational properties of diametric weight levers, but not their inertial properties. It seems perfectly obvious that their radial displacements are minimal, so any MoI-induced torques from their changes in radial distance must also be minimal.
However they do have significant axial motion, and this also varies their instantaneous angular momentum.
This detail may or may not be tangential - simply isolating radial from axial displacements my be sufficient to enable a divergence of gravitational and inertial energies. But either way, i need to spend some time playing with these longer weight poles, to familiarise myself with their inertial effects..
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Furcurequs
- Devotee
- Posts: 1605
- Joined: Sat Mar 17, 2012 4:50 am
re: Poss. Symmetry Break?
Gregory,
I thought I would point out that the words "quarkkeulchen" and "quarkkäulchen," though spelled differently, appear to both refer to the same thing in modern German.
https://www.google.com/search?q=quarkke ... n&tbm=isch
...yum...
https://www.google.com/search?q=-quarkk ... n&tbm=isch
...yum...
If I do a Google search with "-quarkkeulchen quarkkäulchen," I get about 16,500 results.
(A search with a minus sign before a word means to return results that do not have that word, btw.)
If I do a Google search with "quarkkeulchen -quarkkäulchen," I get about 43,200 results.
So, "quarkkeulchen" seems to be the more common spelling now.
It would be interesting to know if the spelling is different in different areas of Germany.
I tried to use a Google n-gram search to verify which spelling came first, but it didn't return any results.
According to a quote in a post of mine above, though, the "quarkkäulchen" would have been closer to the original spelling (apparently from Saxony) - referring to "little balls" - and the "quarkkeulchen" spelling was what it morphed into (in some locations?) due to the way the original word sounded.
I suppose that the word you suggested, "scheibenkeule," could have morphed in spelling in a similar way, perhaps. Again, I don't know, though.
A pancake headed club? ...lol
Some of those quarkkeulchen/quarkkäulchen pictured in the Google image search were, of course, more ball shaped than others.
I thought I would point out that the words "quarkkeulchen" and "quarkkäulchen," though spelled differently, appear to both refer to the same thing in modern German.
https://www.google.com/search?q=quarkke ... n&tbm=isch
...yum...
https://www.google.com/search?q=-quarkk ... n&tbm=isch
...yum...
If I do a Google search with "-quarkkeulchen quarkkäulchen," I get about 16,500 results.
(A search with a minus sign before a word means to return results that do not have that word, btw.)
If I do a Google search with "quarkkeulchen -quarkkäulchen," I get about 43,200 results.
So, "quarkkeulchen" seems to be the more common spelling now.
It would be interesting to know if the spelling is different in different areas of Germany.
I tried to use a Google n-gram search to verify which spelling came first, but it didn't return any results.
According to a quote in a post of mine above, though, the "quarkkäulchen" would have been closer to the original spelling (apparently from Saxony) - referring to "little balls" - and the "quarkkeulchen" spelling was what it morphed into (in some locations?) due to the way the original word sounded.
I suppose that the word you suggested, "scheibenkeule," could have morphed in spelling in a similar way, perhaps. Again, I don't know, though.
A pancake headed club? ...lol
Some of those quarkkeulchen/quarkkäulchen pictured in the Google image search were, of course, more ball shaped than others.
I don't believe in conspiracies!
I prefer working alone.
I prefer working alone.
-
daanopperman
- Devotee
- Posts: 1548
- Joined: Wed Oct 27, 2010 7:43 pm
re: Poss. Symmetry Break?
Hi Furcurequs , Gregory
Schlosen , Grand houses or palaces .
Anno 1693
" Denselben Sommer waren schreckliche Donner-Wetter, und fielen einst [einmal] auch Schloßen, wie Schnip-Käulgen [Murmeln] so groß, welche den Fenstern in der ganzen Stadt großen Schaden taten. "
In Afrikaans ,
Dieselfde Somer waarin verskriklike Donner - Weer val teen aan Woonings , waar veryste balle so groot welke die vensters in die ganse Stad groot skade besorg.
If I look at this quote , then the only thing that " Schnip Kaulgen " could indicate to is frozen balls , like hail stones .
In English
In The same summer in the presence of terrible Thunder (Weather) Storms , fell against the residence frozen balls so great that the windows in the entire city lots of damage receive .
If we then look at Schnip and Schniebe then the latter is more likely to be snow or sleat related .
So it is not impossible for the children to have been playing with clubs made of snow , not throwing snowballs but hitting with snow .
Schlosen , Grand houses or palaces .
Anno 1693
" Denselben Sommer waren schreckliche Donner-Wetter, und fielen einst [einmal] auch Schloßen, wie Schnip-Käulgen [Murmeln] so groß, welche den Fenstern in der ganzen Stadt großen Schaden taten. "
In Afrikaans ,
Dieselfde Somer waarin verskriklike Donner - Weer val teen aan Woonings , waar veryste balle so groot welke die vensters in die ganse Stad groot skade besorg.
If I look at this quote , then the only thing that " Schnip Kaulgen " could indicate to is frozen balls , like hail stones .
In English
In The same summer in the presence of terrible Thunder (Weather) Storms , fell against the residence frozen balls so great that the windows in the entire city lots of damage receive .
If we then look at Schnip and Schniebe then the latter is more likely to be snow or sleat related .
So it is not impossible for the children to have been playing with clubs made of snow , not throwing snowballs but hitting with snow .
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Furcurequs
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- Joined: Sat Mar 17, 2012 4:50 am
re: Poss. Symmetry Break?
Hey daanopperman,
The way that's worded, it looks like that could make sense. Murmeln, the German word for marble, was apparently added by an editor - possibly in 1973.
I'll have to look to see what sort of words are in those middle German dictionaries for "snow," "ice," "frozen" and whatnot.
I did find another quote from 1711 that uses "Schnip-Käulgen":
"Barmherzigkeit ihre Zuflucht nehmen könne. Ich will die Anmerkungen, welche hierüber zu machen wären, diesesmahl zurücke lassen, und den geneigten Leser nur allein daran erinnern, daß viele fowohl Geistliche als Weltlichemit denen Worten zu spielen pflegen, wie die Kinder mit denen Schnip-Käulgen; absonderich aber ist man aus Franckreich dergleichen Wort-Spiele bißhero fo fehr gewohnt worden, daß sichverhoffentlich niemand dadurch verblendenläffet. . . . . ."
https://books.google.com/books?id=WvNYA ... en&f=false
Can you tell in what context it's being used here?
Something like "playing with words like children with those schnip-kaulgen"?
Practically every German to English dictionary I've seen, though, seems to translate schnip or schnipp to "snap."
Here are other examples using "Schnippkäulchen":
https://www.google.com/search?q=schnipp ... hen&tbas=0
The way that's worded, it looks like that could make sense. Murmeln, the German word for marble, was apparently added by an editor - possibly in 1973.
I'll have to look to see what sort of words are in those middle German dictionaries for "snow," "ice," "frozen" and whatnot.
I did find another quote from 1711 that uses "Schnip-Käulgen":
"Barmherzigkeit ihre Zuflucht nehmen könne. Ich will die Anmerkungen, welche hierüber zu machen wären, diesesmahl zurücke lassen, und den geneigten Leser nur allein daran erinnern, daß viele fowohl Geistliche als Weltlichemit denen Worten zu spielen pflegen, wie die Kinder mit denen Schnip-Käulgen; absonderich aber ist man aus Franckreich dergleichen Wort-Spiele bißhero fo fehr gewohnt worden, daß sichverhoffentlich niemand dadurch verblendenläffet. . . . . ."
https://books.google.com/books?id=WvNYA ... en&f=false
Can you tell in what context it's being used here?
Something like "playing with words like children with those schnip-kaulgen"?
Practically every German to English dictionary I've seen, though, seems to translate schnip or schnipp to "snap."
Here are other examples using "Schnippkäulchen":
https://www.google.com/search?q=schnipp ... hen&tbas=0
I don't believe in conspiracies!
I prefer working alone.
I prefer working alone.
re: Poss. Symmetry Break?
MrVibrating:
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.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
What goes around, comes around.