Decoupling RKE from GPE, for fun and profit

[jdelaney]

Mr. Vibrating,
The Pacific Science Center in Seattle, Wa. used to have an exhibit where a person could ride your idea.

edited to add; What you're describing was also used as a governor on generators in the early 20th century. This is because as something accelerates, it's kinetic potential increases. And since generators didn't run at a constant rpm like they do today, this extra served the same purpose as Bessler's pendulums.

[MrVibrating]

Joule is a newton * meter. Momentum is the newton * second.

I'm thinking in terms of power and acceleration as well as energy - ie. maintaining equal torque inputs across a changing speed curve means that we need to increase our input force to compensate for the speed and so apply the same impulse to the wheel's inertia. So we apply more force but for less displacement of the lever end, over equal time. However, even though the shortening end of the lever is undergoing progressively smaller displacements, we're simply torquing the wheel closer to its center - the angular displacement of the whole wheel for each successive acceleration remains equal, as does the drop time.

Although on reflection, it occurred to me later last night that perhaps there's more time flexibility on the input sides of things - why not just torque the wheel from the center right off the bat, since 1J is 1kg/m regardless of how long it takes to drop? Input time only starts to become a factor as speed rises - it's at the tail end of the process that we make the gains, by maintaining GPE / RKE conversion efficiency when returns would otherwise be diminishing.



It ultimately all boils down to this:

1J accelerates 1kg by 1m/s.
If it is only mechanical expediency that precludes maintaining a 1:1 GPE to RKE conversion across an RPM range, then the door is wide open.

If there is some geometric, spatial / dimensional or other practical limitation that prohibits this, i'm not yet seeing it. Undoubtedly there is - i must be wrong, this all seems far too naive.

There certainly is for the linear scenario. However in a rotary system it seems those limitations instead turn to our advantage - in a nutshell, the distance between the mutually-accelerating masses never changes, allowing us to chase the inertia via the torquing arc radius instead of physically chasing a linear mass.

And as the speed builds, the RKE squares, while the per-cycle input energy does not, breaking unity after three cycles and smashing it by half a power of ten shortly thereafter.


Again, it all boils down to the ability (or not!) to sustain I/O efficiency across a climbing speed range - which needn't be large, especially for a high MoI design.


Stuff to do now, back later...

[pequaide]

If I understand you correctly I think your system will work. Because: A drive force makes a consistent quantity of momentum at the rim, it does not make a consistent quantity of energy at the rim. For example: A drive force (torque) will rotationally accelerate 1 kilogram at 10 decimeters (radius) as easily as it will rotationally accelerate 10 kilograms an one decimeter. The momentum (10kg *1m/sec and 1 kg *10 m/sec) is equal; but the energy is not. I have proven this ease of rotational acceleration with photo gate timers.

When you reduce the drive radius by half you are making the force double the speed of the same mass; this is the same as doubling the rim mass while keeping the drive force in the same place. It is the same mv but you are doubling the v instead of doubling the mass.

[MrVibrating]

Pretty much, i think... the way i see it, the effective dimensions of the input energy are equivalent to those of momentum - we're accelerating the same amount of mass by the same velocity, so we're literally building up its RKE, but basically input in the units of momentum. So RKE squares as velocity accumulates, while the input energy sums linearly.

It's all about playing frames of reference off against each other - kinetic energy is measured as relative to inertial reference frames.

Here we have two, seperate frames of reference, and thus two distinct energy quantities, nonetheless manifested in the same mass - that of the wheel's MoI, for the input integral, and that of the Earth's inertia for the output integral.

By progressively compensating the torque radius to the rising speed we stay right on the six of the wheel's MoI, tucking in behind it just as deftly as a chase plane. Thus we're effectively treating an accelerating reference frame as if it were stationary - functionally equivalent to running along behind a linearly-moving mass, keeping it stationary relative to us, but by merely raising our prodding finger closer to the axle - no Lycra required. In both cases, the inertia remains constant.

If that linear mass began to get away from us, this acceleration relative to us subtracts from the acceleration component of any additional F=mA we try to apply, diluting its work potential.

A rotor / stator system eliminates this change in distance - the two masses always remain equal distance apart. Hence the inertia we wish to perform work upon never goes anywhere. It's always right next to us, no matter how fast it goes.

So, how do we keep our applied energy in this sweet spot without having to literally spin our stator in the same direction? Torque radius determines force and displacement following the basic laws of levers. Basic gearing is all we need.

Ideal, it seems, would be the kind of constantly variable transmission commonly used in scooters and mopeds. In fact we see just such an equivalent mechanism on page 141 of Das Triumphirende in the depiction of Wagner's roasting spit contraption, in the form of a spiral spindle. Such a transmission system would allow continuous input rather than step-wise inputs.

Instead of drop weights, we might even substitute a simple motor-generator interaction paired via such a gearing system - perhaps using permanent magnets, electromagnets or simply springs... gravity is entirely incidental to the asymmetry, asides from assisting us with an alternative reference frame.

The best way to try to overcome the cognitive dissonance that a single mass can have two wildly-differing energies at the same time is to keep in mind the hypothetical violation of Newton's 3rd in the linear scenario - a pair of perfectly elastic masses oscillate back and forth, and every alternate stroke is reactionless, causing a net acceleration in the non-inertial frame, but none in the inertial frame - the two masses are undergoing the same net displacement each cycle, it's just asymmetrically apportioned between them, hence the gain in KE from the non-inertial frame is attributable to the unequal division of momentum and not the work being done by the masses, which is just a perfectly elastic collision and needs no further input energy after the first cycle... as far as they're concerned, they're not going anywhere.

In the rotational system we're gaining all the advantages of a real N3 break, without actually having one - it makes no difference if we drop and then relift a weight, magnetc flux or spring - these input interactions remain symmetrical, practical entropic losses notwithstanding. In other words if friction etc. can be eliminated then the net input energy remains zero - whatver we put in comes right back out on the rotor, only multiplied by up to half the input squared.

Pulling all these conclusions together, an optimum implementaion would seem to comprise a pair of lead tubes (maximising the MoI's), a rotary spring, a spiral spindle and belt; the spring-wound tube drives the other via the spiral spindle (or similar mechanism), applying input energy in the static MoI FoR, while gaining from the stator's FoR and so rewinding the spring.

No weights, magnets or electronics are required - indeed, all seem inferior to the advantages of a simple spring.

So the crux of the matter is that this inherent mechanical ability to chase the MoI curve and so stabilise the input work efficiency offers us an additional KE reference frame that we would otherwise be denied by sheer practical inconsistencies in a linear scenario. We can input energy in this reference frame, while harvesting the excess from the alternate frame of the Earth's surface.

Both input and output integrals remain wholly conservative, but their sum is not - the area under the latter curve being up to fifty times greater than that of the former.

My initial incredulity is also waning... :o

Lil' help here, anyone?

[MrVibrating]

Interesting Mr V .. giving it some thought I hope. Will add anything I think might aid your thread.

Cool, Fletch is on the case (you da man)!

;)

[MrVibrating]

Mr Vibrating,

I think your a genius.
It seems to me that your mathematics concur very neatly with the current design that I am busy with. I have a little bit of work to do on it and the design stage (technical drawings and all) is complete.
Then the build will begin.

I must have over 400 wheels (some concepts similar to others) drawn on my PC today. I've buildt about
12 of them because I thought the warranted a build. Needless to say, up until now they have been stillborn.

Granted, I have not been too active on the forum in the past but, I aim to change that and start posting some of the ideas that I felt warranted building.

Fletcher, I think you and your contributions are marvelous.

Zy

You're far too kind for such a wild hypothesis. If this is real it's so kick-yourself-obvious i'd need a few slaps to the face before any pats on the back... an inertial exploit was my first suspicion, then i wasted 2 years getting sidetracked with eliminating gravitational interactions. I even knew the required input / output dimensions - temporal variance vs spatial - but still didn't put two and two together.

Not that it would've helped - 2+2 still equals four. It's only when we add 1+2 and get 4.5 that things start to get interesting, and we realise that in fact, 5+5 can equal 50 using the same metric and all without cooking the books. 5=12 and 10=50, all at the same time and with no contradictions. Any crazy person could've solved this centuries ago..

The maths i make no claim to - it's just the basic bog-standard energy terms, with a little twist, in both senses of the word.

I look forward to reading about your own work...

[MrVibrating]

won't work, sorry. you missed something basic. I'll let Fletcher explain. There's actually 2 points that you missed on. Happens with lack of experience.

Indubitably so.

Either way, time will tell...

[Fletcher]

Carry on Mr V. Your comments and speculations are infinitely more interesting and thought provoking than many.

[MrVibrating]

Cheers mate.. One more thing that might be worth clarifying is that the angle over which a torque curve operates doesn't change with radius - a 20° arc at wide radius is still 20° closer in, and likewise 360° is a full cycle regardless of whether at the narrow or thick end of a spiral spindle. So we're not necessarily trading force for displacement here - we get the full equal angular increments for each unit of input energy... only the force varies. Except it's actually kept in balance with the wheel's MoI, ensuring we get consistent kg/m/s acceleration per unit of input energy.

You could say that we're simulating the effects of a static reference frame, in one that's actually accelerating.. except rather than co-rotating with it, we're simply gearing the power ratio, maintaining a constant rotor MoI load upon the falling weight when it would otherwise be doing less work on the wheel the further it fell and the faster the wheel spun.

The end result is that we have two reference frames against which total KE is relative - one's stationary, but the other's only quasi-static... allowing us to flit between its inertial and non-inertial modes at will.

Of course the mere fact that any mass has myriad KE's from different FoR's is nothing controversial - the ony real novelty here is the realisation that we can sustain the static inertia of a non-inertial frame in one that's actually accelerating.

I'm still undecided about how best to implement constant torque, but the step-wise example with a wheel and long lever seems to remain the easiest to get to grips with (although i wouldn't be surprised if an obvious use for scissorjacks became apparent at some point)...

I'm also still thinking about the possibilities for propulsion, if any, though it seems unlikely as it's only a pseudo-N3 break, not a real one.

I guess a sim is on the cards... maybe next week.

[Fletcher]

I think a picture of what you are proposing is simple terms would be helpful for most to follow.

If the math is correct (the horse) then a mechanism (the cart) should be conceivable and able to manifest it in reality.

I am having thoughts back to a thread of about 6 months ago about Cf's wasting energy at the rim in mass transition and where I was looking at resultant vectors and adding them consecutively IIRC.

IINM (Dwayne was involved in the discussion) the problem or objection was that trying to accelerate a moving mass with a set force ran out of legs and was always a losing proposition.

You may have the work-around with your different approach ?!!!

[ME]

Mr V.
Nice read !

Reference frames

In the end we would just like to use it in our own frame of reference. Perhaps it makes calculations and solving easier, but action-wise it doesn't matter?

the angle over which a torque curve operates doesn't change with radius - a 20° arc at wide radius is still 20° closer in

You just mean torque works parallel to gravity? or..

I think a picture of what you are proposing in simple terms would be helpful for most to follow.

Count me in.

[MrVibrating]

@Fletch

Yep i'll try formulate some sims over next week, will post up any results and piccies.

On the one hand i cannot believe this could possibly work - the expectation that a Joule in equals a Joule out is just too reflexive to be able to suspend disbelief. If we input 10J then that's all we have. One wheel can't have 10J and 50J at the same time. That way madness lies.

But then i keep coming back to the linear equivalent, based on a notional N3 break - the prospect of a reactionless impulse, while clearly impossible, is yet easy enough to indulge for arguments' sake. It only really becomes stupefying when you realise that its incontrovertible consequence is a reference frame split between inertial and non-inertial frames, resulting in a thermodynamically-closed and finite interaction internally, while at the same time having potentially infinite energy from a non-inertial frame.

As befuddling at that seems, it's nevertheless textbook. The only legitimate objection is that N3 is, in reality, immutable. But controlling rotary inertia allows us to emulate the effects of a reactionless impulse and loop the two ends of that infinite KE vector together. Point is, the impossible part was the N3 break, not the diverging FoR's - we've swapped the miracle for something trivial, yet still have them, and both are concurrently valid and accurate energy references.... massively out of agreement, but neither's wrong. 10J can accelerate 1kg of rotor mass by 10m/s, and half of ten squared is 50J RKE.

A sim should be simple - set up a wheel that already has say 2J, and a 1kg * 1m GPE input. If i can get the transmission ratio right, this should raise the wheel's energy to 3J in the rotating frame but 4.5J in the stationary one. I haven't used FoR's in WM2D yet but have noticed the function...should be a doddle.

Power ratios. Everything about Bessler's wheel has always screamed it. It's all about the torque control. And by definition, any working wheel has alternate energy FoR's internally vs externally. Please let this be it, please let this be it dear God... finally...?

[Fletcher]

Amen to that !

Yes, in WM you can change the player mode to a different FoR.

[MrVibrating]

Mr V.
Nice read !

Ta mate, first real brainstorm this year, nice to feel back in the game however briefly..

In the end we would just like to use it in our own frame of reference. Perhaps it makes calculations and solving easier, but action-wise it doesn't matter?

Yup the RKE is in our FoR (Earth's surface). The input energy is in the pseudo-static FoR of the accelerating flywheel. It's basically full-fat output energy, with discount input energy - kinda like taking the special-introductory one-time only offer of 1J/1kg/1m/s and then rejoining the back of the queue in a ropey disguise.

You just mean torque works parallel to gravity? or..

A conventional lever trades force for displacement, so i thought it worth emphasising that varying the torque radius doesn't mean sacrificing torque angle / duty cycle - that only the force is varied, not the angular displacement over which it acts. This matters as we want to accelerate a consistent amount of rotor mass by a consistent amount of velocity for each input stroke, and a diminishing torque angle would hinder this.

I think a picture of what you are proposing in simple terms would be helpful for most to follow.

Count me in.

Honestly, the only mental image i have for now is the one already described - a circle adjacent to a variable balance beam acting as a lever - drop a weight on the end and the other end turns the wheel, via a peg on its face. The peg can be repositioned radially, and the lever horizontally. All we're doing is converting a 1kg / 1 meter GPE drop into a 1kg / 1m/s acceleration of the wheel - 1J in, 1J out, but regardless of the changing speed, which would otherwise defeat this objective. After just 3J in we have an extra 1.5J on the wheel - energy which would never have existed if we hadn't matched our input torque to the accelerating MoI, but which must exist because of it, at least according to the standard SI system definitions.

One wheel, one lever, one weight. Same size. Side-by-side. Interacting.

Or else you could picture the spiral gear from Wagner's roasting spit - maybe a pair of 'em, to keep the torque curve from the GPE drop equal to the accelerating MoI. Again, we'd be 50% OU after dropping three Joules, with 4.5J of RKE on the wheel.

For now that's all i got..

[Fletcher]

Hope you don't have any other important things to think about this week Mr V. It's gonna keep you occupied in the day and awake in the middle of the night.