Into the Vanishing Point..

[MrVibrating]

I find myself holding my breath with you MrV.

Looking forward to future installments.

Surprised you're not turning blue at the snail's pace i'm going..

Still, 8 months left for a 2017 success...

[MrVibrating]

...Imagine this cycle in reverse - let the mass fling outwards on the corners, loading a spring, say, then retracting on the straights... in principle, you could stop a freight train without generating a Joule of heat, i think... just sinking its momentum away over successive term changes..

IOW, it looks consistent with a non-dissipative loss mechanism, able to destroy momentum... maybe..

Wouldn't be the first time i've been wrong about this sort of thing tho...

..hopefully i can find a slightly more useful (ie. gainful) application of it..

[MrVibrating]

...just remembered, if i'd followed Fletch's advice and started out with a single mass in the first place i might've had this working months ago.. instead i was too caught up in trying to fit the concept to Bessler clues - especially inner / outer masses acting in pairs..

Still, now that it's working, what to do next?

The original idea was to bank the energy in a variable-MoI flywheel, to prevent runaway acceleration and thus the input work against centrifugal force from spiraling. However the variable-MoI flywheel stores not just momentum but also potential energy in its loaded springs - ie. that portion of its energy contained in the springs isn't momentum, so this wouldn't be banking momentum at a fixed energy rate as intended..

The aim was to be able to keep buying momentum at a fixed rate, and so circumventing the usual half-square accumulator (KE = 1/2mV^2) on rising velocity. I'm now unsure the variable-MoI flywheel can fulfill that requirement, so need to reconsider what possible use this Robernoster contraption could have...

We have full, 100% accurate rectification of inertial torque of one sign only, able to accelerate to any speed, without inducing equal opposite counter-momentum. Something so novel and controversial must have some practical application?

And the things to look out for in a reactionless interaction are the unit energy costs of momentum, and of course divergent net momentum. But i'm not sure how either result could be pursued from here at this stage..

Superficially, it may seem no more remarkable than any other conventional torque and angular acceleration, but the difference here is the reactionless factor - when the hands on a clock turn, a counter-torque is being applied back to the clock and wall its mounted on. But here, the hand on our clock is turning itself, and the only corresponding counterforce is centripetal / radial, not angular..

So what to do with it then - how to benefit from it?

Perhaps there's something useful that can be done via gravity with it? Some kind of balance or lift / drop advantage, or god-knows what?

[MrVibrating]

Just blue-skying here...

How about gearing the Robernoster to a flywheel, to keep it at constant speed as the flywheel accelerates faster?

Could be a constantly-variable transmission (CVT) or just discrete ratios..

If the RN's operating at constant speed, then supposing it costs 1 J to pull the mass inwards each time, this is all we can add to the flywheel each stroke. Pull it in 5 times, adds 5 * 1 J to the flywheel...

Obviously that's not useful. The whole concept was to add consistent units of momentum, at a constant energy cost, in spite of rising velocity.

So what i need to be juggling around is momentum, not energy.

If i can keep buying 1 kg-m/s of momentum for 1 Joule, cumulatively, then that would be over-unity. Or whatever the energy cost, so long as it's constant, not rising with speed.

If however i'm only adding energy to the flywheel, then the amount of momentum i'm buying for that energy is ever-decreasing, by the inverse of the half-square of rising flywheel velocity.

So i need some kind of conceptual leap here, that i'm currently missing..

IIRC i previously deduced that there were two possible routes to OU from inertial torques: either being able to pull mass inwards freely, without performing net work against centrifugal force, or else by being able to re-extend the mass without causing the usual deceleration this applies.

It's this latter feat that i've now accomplished - i can speed up the RN by pulling the mass inwards, and then re-extend it without causing a deceleration.. However i can't for the life of me see how to get OU from this at the moment.. I'm still convinced this has to be a route to some kind of exploit, but for now i'm just not seeing it.

Whither / wherefore the advantage here, if any?

[MrVibrating]

OK here's another angle on this thing...

...pulling the mass inwards while it's rounding the corners raises linear momentum without raising angular momentum, and also does so without applying counter-torque..

...equally tho, re-extending the mass on the straights raises angular momentum, but without raising linear momentum... and also incurs no counter-torque..

..plus it costs no energy!

Think about it - pulling the mass in on the corners does cost energy - the work involved in displacing the mass against CF...

..however re-extending the mass on the straight is not performing work against CF - it's simply a small linear translation, and whatever it costs to set the mass in motion on its outwards journey is recouped when it reaches full extension - the net cost for which is thus zero.

Yet as it enters the next corner, now at full radius again, its angular momentum has been raised!

For free!

Am i wrong?

Surely this is a bona fide symmetry break? I mean the raising-angular-momentum-without-cost part is almost tangential - the broken symmetry part is in re-extending the mass without incurring counter-torque, while retracting does cause torque.

But we also have this raising of angular momentum, without inducing counter-torque or costing energy...

The sole energy cost is in pulling the mass inwards while rotating. So we're paying for the rise in linear momentum this causes. Even though this doesn't raise angular momentum.

But when we do then raise angular momentum, by extending on the straight, there is no similar corresponding energy cost. It's effectively free...

I do appreciate why everyone's withholding judgement for now - the demonstration seems singularly underwhelming as-is.. and admittedly i'm struggling to work out how to proceed with it so far.. yet it has these very interesting, if not controversial properties.. reactionless torque, reactionless momentum rise and also free rise in angular momentum... only the rise in linear momentum is paid for.

So on the one hand it's a very simple mechanism, yet it's doing things you do not see every day... if ever!?

[Gregory]

Hey MrVibrating,

Great to see you continue! Sorry for not responding much, I am busy with my own research and other stuff...

...Imagine this cycle in reverse - let the mass fling outwards on the corners, loading a spring, say, then retracting on the straights... in principle, you could stop a freight train without generating a Joule of heat, i think... just sinking its momentum away over successive term changes..

IOW, it looks consistent with a non-dissipative loss mechanism, able to destroy momentum... maybe..

Yeah, we discussed this before. I can only say the same.
You have come up with an inertial brake, just like I did. The mechanical realization does not matter… If you push out a mass on greater angular V than the angular V of the same mass while being pulled in, then you create an inertial brake due to solely the principles of CoAM. And because your angular V is zero at the straigth line path, it will be a very efficient inertial brake.

The cycle: L = I * W
Mass m pushed out and radius r increase, therefore I = I + xi; W = W - xw; L is constant as of yet, but after you retract at the straight path you decrease I, now I = I - xi, but without changing W, so W stays at its decreased state, therefore L decreases. Then the cycle repeats, I = I + xi increases with the same fixed amount and after retraction this causes a decrease of the already decreased W and L, and so on… Basically, this is similar to a mass flying out on a spoke to an infinite radius, we only designed it in a cyclical way via a mass periodically moving through a radius length of R2-R1.

So, as I see this is not a question, but this is a fact, a direct consequence of CoAM. We forced CoAM to do something it usually doesn’t do by itself. Or perhaps better to think about it like this:
CoAM works the same all the time, it is impossible to break it. We just created a situation where one part of its play can’t be realized, as there is no angular quantities on a straight line path.

...pulling the mass inwards while it's rounding the corners raises linear momentum without raising angular momentum, and also does so without applying counter-torque..

...equally tho, re-extending the mass on the straights raises angular momentum, but without raising linear momentum... and also incurs no counter-torque..

Correct. I see it the same way.

..plus it costs no energy!

Think about it - pulling the mass in on the corners does cost energy - the work involved in displacing the mass against CF...

..however re-extending the mass on the straight is not performing work against CF - it's simply a small linear translation, and whatever it costs to set the mass in motion on its outwards journey is recouped when it reaches full extension - the net cost for which is thus zero.

Yet as it enters the next corner, now at full radius again, its angular momentum has been raised!

For free!

Am i wrong?

Surely this is a bona fide symmetry break? I mean the raising-angular-momentum-without-cost part is almost tangential - the broken symmetry part is in re-extending the mass without incurring counter-torque, while retracting does cause torque.

Yes, angular momentum rises, but when you look at the full cycle it is not for free. It costs a very little to overcome the inertia of mass while it starts moving outward (cf would do it anyway). But what is much more important, you have to pull the mass inwards in the first place, working against CF. This is the cost of the rising angular momentum.

And if we have a math guy here, he can surely show us whether the rise in angular momentum equals the energy needed to pull the mass inwards in the first place. I suspect this will be the case as our mother nature always tries to balance out things, but I haven’t checked the math for this in details.

Otherwise what you are doing is absolutely great work.
Your way of introducing that straight line path, ingenius I can say! :)

[MrVibrating]

Thank you, i needed that, just to know i'm not making up whatever fantasy i want to believe in..

I like the analogy of an infinitely-long radial translation, too - which works both ways, as if the mass can also be pulled in an infinite distance..

After going to bed last night, i also came to the same conclusion, that the rise in AM has been paid for by pulling the mass in on the corners, since it depends not only on the rise in radius, which is free, but also the rise in velocity, which is not free.

Without that paid-for rise in velocity, the free rise in radius would only reduce angular momentum.

Likewise tho, if we had the paid rise in velocity without the free rise in radius, angular momentum would be constant - remaining the same as from the previous corner. We'd have the paid rise in linear momentum, but no rise in angular momentum.

So although i agree that the angular momentum rise has ultimately been paid for, and would not have been possible without prior input energy to raise velocity, if we didn't extend on the straight, which is free, there'd be no rise in angular momentum.

So the prior energy input provides the potential to raise angular momentum, but does not do so directly. What makes the binary difference between AM-rise vs no-AM-rise is this free rise in radius - that's the decisive condition causing it to manifest.

Paying for the velocity rise is a necessary condition for the AM rise, but not a sufficient condition, which ultimately depends on the free change in radius..

So in consideration of a complete cycle, yes, the AM rise is not free. But broken down into discrete strokes / phases, the instantaneous input energy is only invested in a velocity rise and thus linear momentum rise - which itself depends upon CoAM and angular momentum remaining constant.

In other words, it costs the same energy to pull the mass in, regardless of whether we then extend on the straight to raise angular momentum, or not.

So breaking it down into discrete strokes / phases, the AM rise does appear to be free, contingent as it is on the free rise in radius.

If we simply accept the velocity rise as the paid-for component, we're cornering ourselves into a paradox, in which the instantaneous workload of raising velocity is directly caused by CoAM, and angular momentum remaining constant - ie. we'd have "paid to raise angular momentum by the process of conserving it". This is clearly an oxymoron.

Still, without some kind of further innovation this is so much semantics. We're in interesting territory, a hall of mirrors.. but for now it seems there's only one entrance / exit..

My original goal was to try and lower the cost of accumulating momentum, to break from the 1/2 inertia * V^2 base rate. This seems like a step in that direction, if not quite there yet.

Assuming that's even a viable goal in the first place..

A free rise in velocity would seem the more promising advantage, but i see no path to that end thus far..

Nonetheless, Bessler seems to have been interested in the interplay of linear and angular components of motion, as denoted by the scissorjacks, so this seems to be on the right track.. and if so, at some point, gravitational interactions should become a further interesting factor into the mix.. although for now, i have no idea as to how or why...

[ME]

I just drew the following thing.
In blue the path a tri-robernostered weight would likely follow. It has the same shape as that black belt.

[MrVibrating]

Thanks Marcello, great stuff!

I have however already considered such a config, prior to conceiving the slot-joint version, when i was still playing with paternosters back in January:



...and couldn't see any immediate benefit..

Obviously this was inspired by the 'AP wheel' motif, but was more exploratory than reasoned conjecture..

In principle however you're correct - there's no apparent requirement or limitation on the number of strokes / phases per cycle, as yet..

[MrVibrating]

Just returned from my personal thinkbox (a hot bubble bath, tall scotch and a fat stogie), with a possible breakthrough realisation...


RKE = 1/2 MoI * angular V^2...

WM2D doesn't by default monitor angular properties of orbiting masses - i suppose i could in principle make such a meter, by multiplying the 'actuator length' by the rest mass and change in angle / time of the armature... however as-is, i'm only metering linear properties - rest mass times absolute X + Y velocity.

So for now we're left to surmise angular momentum and KE from first principles...

However, considering this point that the paid for rise in linear velocity is a necessary but insufficient condition for a rise in angular momentum, which only becomes manifest when the free rise in radius also occurs, it now seems apparent that this is not only causing a free rise in angular momentum, but also a free rise in RKE!

Think about it - if we're raising MoI without reducing angular velocity, then we're raising both angular momentum along with RKE!!!


At this point it seems obvious that the way to harness this is to book-end the cycle with a gravitational interaction - dropping a mass against a low MoI, then freely raising MoI before re-lifting the weight again...

Unless i'm mistaken (again (per usual)), we could be further along here than i originally envisaged..

In short, re-extending on the straight means we enter the next curve with both a rise in angular momentum and RKE!

If i'm right on this, this could be our meal ticket..

[MrVibrating]

...I've also realised a correction to a previous false conclusion regarding my earlier attempts at this, here:




...the reason it doesn't work is not because i pulled the masses in too far - the change in radius is roughly the same as in the working version...

The real causative difference is in trying to close-loop what needs to be an open-ended cycle - CoAM here is causing both an acceleration, but also a corresponding deceleration along the straights.

In order to rectify a consistent gain in velocity would've required the masses to run off onto concentric tracks at ever-rising velocity, something like this:



..and so an open-ended cycle.

However multiple cycles are unnecessary - a single cycle book-ended by a gravitational interaction to provide initial input and final output energy integrals would seem sufficient to harness a gain..

Pulling the mass in too far would also preclude the effect from working, so my initial experiments in this thread weren't entirely a wasted effort - it was still a valuable lesson learned. But my prior failure was simply caused by trying to reach too far too soon, ignoring Fletcher's good advice to take it one mechanism at a time..

[MrVibrating]

Also, for completeness (and because i previously said i'd post it), here's the failed attempt at applying it as an inertial motor:



...as you can see, the amplitude of the wobble increases with rising internal velocity, but if i pause it and clamp the masses to the base, the net momentum remains at the 0.1 kg-m/s it begins with - there's no gain in net linear velocity of the system.

Still, couldn't hurt to try, and i still share John Collin's conjecture that if Bessler's succes does or did depend on an effective N3 violation, an inertial motor may yet be in the offing..

FWIW i also tried it with the RN's aligned in the horizontal plane, attempting to 'row' upwards (although gravity's still disabled here), but with identical negative results.

[MrVibrating]

...So.. back on-track (pun), if we do indeed have a free rise in RKE here, then it's time to couple the effect to a gravitational exchange, dropping a mass when RKE is low, then raising it when RKE is high...

As ever, devising a simple practical mechanism that fulfills that objective may take some more time and effort, but at least we have the brief..

[Gregory]

RKE? I didn't thought about it, but yeah I am not surprised...
RKE is subject to V^2, and Angular momentum is subject to V.
After that it sounds logical that RKE rises if L rises via V. And in this case, yes our L rises because we also increas V by pulling in the mass repeatedly...

About gravity...
I forgot, but I wanted to suggest this to you. Perhaps it would be a good idea to try using gravity around 12 o'clock to push the mass inwards, and then let it slide out below 3 o'clock on a straight path, and repeat. There are drawbacks to this, and it may work only at a limited RPM range, but might well worth a try.

[MrVibrating]

..basically, by switching our 'inertia' terms between that of rest mass for linear and MoI for angular, we're not just switching momentum terms but also energy terms.

After the first input stroke on the right hand side, we leave that corner with a raised V and if we don't extend on the straight, we enter the left hand corner with the same amount of momentum and KE we had upon leaving the right hand corner..

..but if we do extend on the straight, then we enter the left side corner with more angular momentum and RKE than we had upon leaving the right hand corner.

So we're 'creating' angular momentum and RKE merely by extending on the straight - without applying torque, or, thus, counter torque! We just 'magic' it from nowhere by flipping the 'inertia' component of both fields, from rest mass, to MoI.

This seems really exciting..

As for gravity, i've considered your suggestion already, but haven't (yet) found a promising trajectory that can be constrained to the Robernoster itself - if we retract at 12 o' clock, we'd need to extend again before entering the corner. Entering the corner at full extension seems to be a necessary condition.

Similarly, we could apply gravity to extend at 6 o' clock, but as noted, the cost for extending on the straights is negligible anyway, so this doesn't appear to convey any particular advantage.

What i'm thinking instead is that perhaps we have a "prime mover" mechanism here, that connects up to a gravitational interaction facilitated by some other, separate mechanism. Translation errors notwithstanding, Bessler did say "all the internal parts, and the perpetual motion structures, retain the power of free movement" - seemingly differentiating between two component mechanisms.

It seems likely that if this is the basis of his exploit, he'd've been using something more like a paternoster, with a belt or chains running between wheels, which could in turn commute with other components via suitable transmission systems.

The only reason i gave up on such designs was their computational complexity in terms of simulation - the key problem the Robernoster was intended to solve, insofar as involving no collisions or friction. One full cycle of a simulated paternoster can take many hours to complete, if at all, half the time bugging out due to collision errors, either spontaneously exploding, or else the belt / chain falling through the wheels / sprockets. Just try making a sprocket and chain assembly and you'll see what i mean..

I suspect there's probably better, cleaner ways to effect a more traditional paternoster in WM2D, using formulas for inputs and outputs, but the Robernoster seemed like an ideal solution for my needs at the time. The tricky part now however would be harnessing the angular motion components, which i currently can't even meter..

Fundamentally tho, the motion can be reduced to just a single wheel which slides from side to side, performing a 180° turn at each stop. If such a mechanism can be easily fashioned in WM, then this may open up further opportunities, both for metering the angular momentum and KE, as well as interconnecting a linear (ie. vertical) GPE interaction via gearing / pulleys / rack and pinion or whatever..