Flippin' Flywheels

[MrVibrating]

PS. the above sim is only half-populated as it runs at a crawl already. Each chain link however can mount a flail, so a maximum of 8 could be applied here, as four sets of two.

Also can't help notice they resemble the mysterious 'T'-shaped pendulums in the Merseburg engravings..

[daanopperman]

Hi Mr V

To me , the weights on the T bar could only add momentum to the pendulum if the pendulum was to stop before it's apex , and the only thing that could stop the pendulum before it reached it's apex was the cranck pin .
If the 2weights was on a bar not in line with the pendulum pivot , ( mabee a V shape ) and the pendulum was offset so that it hung not vertical , then by leverage one weight would change the pendulum's normal swing , for then one weight would be closer to the wheel axis always .

Daan .

[MrVibrating]

Cheers for the thinks, although i hadn't got as far as enabling gravity yet - the idea here was simply turning CF on and off without slowing down..

My thinking was that maybe we could use centrifugal force to fling a mass outwards, gaining free work from CF, and then pull the mass back in again for free when it's traveling along one side, without any CF...

It's the same concept i began this thread with - harnessing CF to perform work, which could be anything - spinning up a flywheel or loading a spring or raising some GPE or whatever... the problem i kept hitting with previous mechanisms was "how to retrieve the flung mass from the rim back to the center, against CF". So this idea here is simply making CF time-variant... basically, "free energy from switching a force on and off".

TL;DR - there's CF at the ends, but not at the middle. So, fling a mass outwards at the ends and drag it back in at the middle. Voila, free energy.

Maybe.

[MrVibrating]

...Obviously, allowing the mass to extend outwards under CF eats RKE to the same value of the CF PE.

However it doesn't eat momentum, which stays constant, albeit at a now-lower KE.

The rotational KE lost however may be temporarily sufferable, provided we use the CF PE to buy more momentum. Since momentum is otherwise conserved, if we add more - say, by converting CF PE to GPE (which could add momentum) - then net system momentum could increase with each full CF interaction.

Maybe..

[daanopperman]

Hi Mr V ,

If you had a grounded axel , and tethered the weight to the axel , after it was flung out by cf , it would speed up rotation and come back to the axel for free .

[MrVibrating]

..been thinking today that maybe if the arms are hinged allowing them to fold somewhat, then the chain could be slung over the axle, and just hang straight down, letting the slack rest on the inside floor of the wheel - ie. getting rid of the second, lower, sprocket.

This would prevent a mass being flung downwards, while still being able to fling another upwards - directly converting CF PE to GPE without the need for further weights and pulleys..

Originally i was thinking of running extra pulley strings off the flung weights in order to raise a separate weight, but this now seems needlessly complicated. If the objective is simply to convert CF PE to GPE, then it's already doing that, and all that is required is to convert that GPE back into RKE and momentum, perhaps via OB torque..

The chain clattering along the floor of the wheel, as well as the folding hinged poles, would be making the same kinds of sounds Bessler's wheel reportedly made.. Plus there'd be bangs from the flung weights landing on the descending side, which would get louder as RPM's rise..

Those all seem like encouraging consistencies, but the number of "bangs" per cycle doesn't seem to add up - we're looking for around 8 bangs per cycle, i currently have four poles attached, with room for another four, to make the total up to eight.

However the problem seems to be that the chain is rotating four times slower than the axles - so if the upper square axle was also the main wheel's axle, with the lower square hanging below, then one full revolution of the chain - making 8 bangs - would require 16 revolutions of the wheel itself. IOW, even with all 8 poles attached, we'd only get 2 bangs per cycle of the outer wheel. Getting the 8 bangs per cycle would mean adding another 3 identical chains, for a total of four running in timed phase, each holding 8 weight poles. So 8 bangs per cycle would be using a total of 32 weight poles...

This seems less encouraging. It's not prohibitively complex, just requiring multiple repetitions of the same mechanism. But they'd have to run side-by-side, and Bessler's wheel weren't very thick.

Another angle on this problem is that Bessler said that, given enough time, he could make a wheel that turned very slowly but with great power. This implies that there'd be many more interactions per cycle, accounting for the implied construction time, but also means it would need perhaps a dozen or more chains running side-by-side, so the wheel would need to be much thicker, more like a drum shape.

However a simpler interpretation would be that i have things back-to-front, somehow - what's needed is a way of making the chain rotate faster than the wheel, rather than the current inverse arrangement. Ie. if the chain ran twice as fast as the wheel, then one chain with four poles could make eight bangs per cycle, and likewise, a very slow but very powerful wheel could have umpteen bangs per cycle, from a higher gearing ratio..

However this would seem to mean that the chain's drive sprocket would need gearing up relative to the axle.

So that's getting even more complicated. I like this concept, it seems to have a lot of consistencies going for it. But if it is on the right track, it's obviously not quite there yet..

[MrVibrating]

...on a whim, i remembered that the AP wheel features squares so thought it might be worth knocking up an "AP wheel paternoster":





..the sprockets rotate in sprung slot joints, to keep the chain tensioned - it's a longer path side-to-side than corner-to-corner, so the chain alternates from too tight to too slack otherwise.

The gears there are just to keep the sprocket angles synced.

However i didn't bother attaching the weight poles yet, as having half-built it i fail to see any special benefit from having three sprockets. I was thinking about JC's hint that odd numbers of mechanisms, such as 3 but especially 5, might generate interesting properties. But this sort of thing doesn't seem to be what he had in mind...

[MrVibrating]

...waiting for the latest sim to run (2 square sprockets, 8 poles which fold in on the ascending side) - it's slooow to process, will maybe post later tho..

However i realised last night that there's two potential routes to an inertial asymmetry if CF can be switched on and off without changing RPM;

1) being able to pull a mass back in, without performing work against CF (the thing i'm trying currently)

Or:

2) being able to send a mass back out to the rim, but without incurring the usual deceleration.!


For instance, pull the masses inwards whilst they're going around one of the end points, causing an acceleration (ice-skater effect) - however the whole chain and sprocket system is being accelerated by this... including the weights traveling up and down the flat sides... which aren't subject to CF... so they can be moved back outwards to the 'rim' without causing an angular deceleration (cos they're not changing angle in the first place)..

Something else to try later..

[agor95]

Hi MrVibrating

I am reading your tread with interest.

Good Luck - There is more than one way to spin a wheel.

[MrVibrating]

Cheers mate.

Currently seeing if a paternoster can be used as a 360° Roberval - if so, that could make a gravitational asymmetry possible.

The basic idea is a paternoster with radial weight poles, which remains balanced regardless of how far in or out the weights slide on the poles. Then we could 'lightly' raise a heavy weight..

Also, noticed a cool fact about paternosters - they seem to violate conservation of momentum!

Consider this - a paternoster as shown previously with radial weight poles. The weights are flung outwards at the top of the ascending side. As their poles rotate around the upper sprocket, CF is generated, and if at this moment we pull the masses back inwards, we generate an acceleration, per the ice skater effect.

Again, remember that the skater accelerates when she pulls her limbs inwards, precisely because of conservation of momentum; by reducing her angular inertia, her velocity and thus energy increase to compensate, and so maintaining constant angular momentum, which is just MoI times RPM.

However, when this occurs aboard the rounded ends of a paternoster, something remarkable happens...

Get ready, cos this is where it gets weird:

Because the whole chain and sprocket system is accelerated by this inertial torque - including the linear sections, which aren't generating centrifugal force - we're also applying linear accelerations to the masses traveling up and down the sides... and linear momentum is simply a function of mass times velocity! MoI is no longer a factor for these masses, until they reach the next bend..

And since their mass is constant, but their velocity is increasing... their momentum is increasing!!!

We're raising the net momentum of a closed system!!! How badass is that?

Think about it - if the masses remain in that extended position as they reach the bottom and track round to come back up, while we're applying inertial accelerations to the ones coming around the top, then we're also applying an angular acceleration at the lower end, but without further raising MoI to compensate (the masses are already fully extended anyway)... so we're also creating angular momentum down below!

Then, on the ascending side, we can pull the masses back in as soon as they've cleared the corner and are heading back up the straight. As they crest the top they get flung back out and the cycle repeats.. each time adding momentum to the net system.

Remember, pulling the mass inwards under CF causes acceleration. But sending the mass back out while it's traveling in a straight line doesn't involve CF, so doesn't cause a corresponding deceleration. We get to keep the momentum we've added!!

We can create momentum in a closed system!


"But wait", you're thinking.. "it'll cost more energy to retract the masses as velocity and thus CF build up".. and yes, yes it would. The cost would rise in step with the rising system velocity - CF will double with RPM and it will cost all the KE we're gaining to keep pulling the masses back in.

Which would be a total showstopper.. unless.. there was some way of raising momentum without raising velocity?


So.. if you'd been wondering where the scissorjack might crop up in all this, here we are: a jack spinning about its center with equal masses on either end, moving equal distance in and out as the jack expands and contracts.. et voila, a variable MoI flywheel!

We can spin it up while we extend its MoI!!!

So we can dump more and more momentum into it, without raising velocity, and thus without raising the cost of retracting the weights coming around the top of the paternoster!

This variable-MoI flywheel could be coaxial to the main system axle, it's just a scissorjack pivoting around its central linkage. We could let it expand against a spring in response to rising CF - if both the spring constant and CF square with radius, then they can remain in balance across a useful radius.

So, as we're applying inertial accelerations at the top of the paternoster, the spinning scissorjack is extending under its own induced CF, raising its own MoI, and hence braking against the paternoster's acceleration.

In short, instead of inducing our extra momentum into the chain and paternoster system, which would also raise our operating costs, wiping out any benefit.. we can feed that momentum into an expanding flywheel, raising the system momentum without raising velocity and running costs!

If input energy per unit of momentum remains constant, then we have an effective N3 break, in that we can buy more momentum than we should be able to afford if velocity was increasing with successive acquisitions of momentum.

This looks like mathematical OU. Variable MoI and CF are the keys to the prime mover, and OB is just the payout currency...

[MrVibrating]

"Centrifugal governor". That's the kind of thing i'm thinking of - raising its own MoI under CF to maintain RPM while yet gaining momentum.

Momentum without velocity is cheaper to buy! Whereas, if you're lumbered with ever-more velocity the more momentum you buy, the more expensive it gets - following the half-square of static MoI times rising velocity.

In principle, keeping V constant while raising MoI instead yields the same kind of energy result as an effective N3 violation.. the unit energy cost of momentum stays constant so long as velocity does! Nice eh?

[MrVibrating]

Managed to find a way to implement a frictionless paternoster in WM2D - no collisions to calculate! Yipee..! It's so smooth it almost processes in real-time at 200 Hz. I raised it to 400 Hz just to slow it down enough to see clearly:




...no weights attached to the poles yet, but the basic apparatus is there to pursue either of the asymmetries described above.

The grey ghosted box in the middle is just to highlight the "zero CF" zone, where we can change radius of the weights for free (once they're attached).

Curved slot joints combined with radial slots were the key. Pretty sexy motion nuh? Perfectly lossless, simplifying everything. It oscillates slightly, here between 19 and 23 RPM, but holds that range indefinitely. The raison d'etre of the whole show of course tho is the CF the tips of the poles are subject to, ranging from ludicrous, to zero, in one smooth seamless and lossless transition.

As you can see, if the sliding weights (once fitted) are attached to one another in 90° couplings (via pulleys, say), then the one being flung outwards can retract its CF-free companion, for effectively no cost besides its linear inertia.

Similarly, if we retract a weight inwards at 12 o' clock TDC, when it is at maximum angular velocity and thus CF, the corresponding acceleration is applied to the whole system, regardless of whether the weights at 6 o' clock BDC, or traveling up or down the linear sides, extended or retracted.

And because of that little twist, although that inertial acceleration depends upon CoM doing its thang, and remaining constant around that 180° arc segment, everywhere else on the rotating part of the system is gaining momentum! So we can turn CoM against itself, and use it to create momentum from inside the closed system. Again, if we then re-extend the mass in the CF-free zone, we don't incur the reciprocal deceleration, and thus we don't remove the extra momentum we just added!

Haven't added the governor mechanism yet either, although in retrospect scissorjacks are needlessly over elaborate, and further slot joints should suffice. As i see things so far, this will be a separate rotor, possibly co-axial to the main rotor, and the trick will be simply to add momentum to it without speeding it up. As mentioned, balancing CF against springs seems the way to go.

Once we have our momentum sink, we can fill it up with momentum, by applying un-reciprocated inertial accelerations to the paternoster.

The governor would also be consistent with Bessler's claimed load-matching properties - ie. benefiting from applied loads, in that any negative torque decelerating a governor rotor will allow the spring to retract the MoI, and thus applying a counter-acceleration that resists the applied deceleration.

As mentioned earlier in the thread tho, weights sliding on radial poles can also fulfill this function - plus i still have no major role for gravity yet. So hopefully there'll be some opportunity to optimise and simplify further down the line, as things become clearer..

For now, though, we have a passive variation in force. CF is a fairly arbitrary function of mass, radius and RPM, but whatever the max force selected, it can be varied between that, and zero, passively.

Today was a good day.

[Fletcher]

You've gotta celebrate the good days Mr V.

I will have to re-read your last few posts again tomorrow to digest them properly - too rushed over the weekend so that my concentration was lacking.

Best as always.

[MrVibrating]

Cheers mate, but you're gonna love this..

[ME]

Managed to find a way to implement a frictionless paternoster in WM2D - no collisions to calculate! Yipee..! It's so smooth it almost processes in real-time at 200 Hz. I raised it to 400 Hz just to slow it down enough to see clearly:
...
Curved slot joints combined with radial slots were the key. Pretty sexy motion nuh?

Wow... that's very nice!! I guess you use three joints per bar there?
Is that manual labor or programmed? Congratz anyway, very handy!

but you're gonna love this..

Please continue.