Decoupling Per-Cycle Momemtum Yields From RPM

[MrVibrating]

Still at 32.765 kHz, 1 i-s/f:

internal accel factor = 10 m/s²

vMoI acts = 31.923277

lift act = 35.0311745
__

total in = 66.9544515 J



KE rise = 25.174

GPE gain = 51.781
__

total out = 76.955 J


..so still precisely 10 J over..!?

Final frame:



I left the meter ranges untouched for perspective in relation to the previous run - so as you can see, the green integral's larger, the red one smaller.. resulting in both the net input and net output being almost exactly 20 J less than the previous run, yet still precisely +10 J in excess..!?

OK so GPE and KE metrics surely cannot be wrong - the GPE is just the GMH of the weight plus that of the 'lift cage' floor and ceiling, and the net KE is just the "kinetic()" output..

..while the input integrals are just the force * velocities of the respective actuators.

All four metrics are using WM's standard formulas.

So where could i have introduced an 10 J error, that persists unchanged despite different internal acceleration factors?

Error's always more likely that genuine gain (if we needed reminding), but for now i'm not seeing it..

I guess it's probably high-time for that dry run, eh? Chop out the internal acceleration and see if the anomaly's still there..

[MrVibrating]

..well that didn't take long - you guessed it - i'd set the vMoI actuators to move their masses inward at 1 m/s, but hadn't added any initial radial velocity to the masses themselves.. just tangential velocity.

Thus on frame 0 "kinetic()" was showing "11 J", but on frame 1 the vMoI masses were instantly accelerated by 1 m/s radially.. they're 10 kg each so that's an additional 2 * 5 J = 10 J precisely.. so the starting KE from frame 1 was actually 21 J, not 11 J.

Duh.

When using the reactive feedback loop, initial radial velocity was near-zero - i did actually check for this at the time, but it wasn't an issue since the actuators began with near-zero speed, and so any radial acceleration of the masses should've registered as radial forces on the actuators.

Given that we got within 1.7 J of unity using the servo loop, i think that's probably as close as WM can manage under the circumstances.

Still, the idea of trying to gain height rather than direct acceleration seems worth further investigation, so i'll see what else i can come up with..

[MrVibrating]

Just thunk of summink - completely different and original in every detail:

• consider something like MT 133 / 134 - a pair of opposing lever weights, in transmission with a central, radially-sliding weight

• ok it's not that original; what's new tho is that the transmission ratio is now continuously-variable

• so when gravitationally-balanced in its default cross-shaped config, a given radial displacement only causes small angular displacements, but as the amount of radial displacement is increased, the ratio approaches, then exceeds, 1:1

• thus in its balanced state, the radial weight is balanced against a much-superior pair of angular GPE's, via this CVT: the system's thus at rest and has zero PE..

• ..give it a push-start tho and because the radial weight can move radially, thus lowering MoI and offering the system a lower-energy state, whereas the lever weights cause much less MoI change (none at all if radial rather than diametric), the rotation will inevitably apply CF force, able to perform more work against the radial weight than lever weights..

..in short the interconnected GPE's are in balance via the CVT, but will readily convert any applied rotational KE into GPE of the opposing lever weights..

..it'll do so with high efficiency (little reason for losses), yet no gain of course; the purpose however is this:

• to raise a GPE via an asymmetric pair of angular accelerations!

The thinking is this:

• because MoI increase caused by the radially-sliding weight applies negative inertial torque, and the system is statorless, the absolute change in angular momenta of the lever weights is asymmetric

The result, as i say, is simply to lift some weight, at cost, but via an asymmetric input of angular momenta to gravity / GPE; ie. one lever having contributed more work to the lift than the other.

Any weight so raised is then simply lowered again via regular overbalance.

The bobs on the levers could collide at some maximum angle, or else just pass by each other, with the amount of radial displacement possible only limited by the amount of angular momentum that can be transmitted to the levers in the available G-time per cycle.

Would such a system exhibit the load-matching behaviours Wolff reported, i wonder? IE. it seems to me it might have a preferential speed, if it works - resisting over-acceleration (as more CF force = more negative inertial torque = more angular momentum asymmetry) - where 'working' simply means fixing the energy-cost of angular momentum across some RPM range..?

Only one way to find out..

Potential CVT options:

• spool the radial weight off of a cam-shaped reel to drive the weight levers

• or just a crank and conrod, perhaps making a variable crank via linear actuators sliding the conrod axis radially across the 'crank' wheel

• alternatively, how about entering a simple formula as a 'gear ratio' using WM's 'gears' constraint - make it an increasing function of the radially-sliding weight's displacement and voila..?


Another feature i anticipate is that it'll be internally balanced when turned 90°, yet while now in an overbalanced position (ie. "pounds in equilibrium" - which might answer to the question of how the one-way wheels maintained static overbalancing torque


More later..

[MrVibrating]

Well here's 60 secs you'll never get back:



As you can see, the ratio of radial to angular displacement's a non-linear function.. big whoop, not.

I've tried playing around with the slope and weight ratios (the lever bobs are 1 kg each), but it's basically conservatish, provided it maintains some kind of regular sync pattern.

Kinda scissorjack-y, i thought - a radial displacement converting to a pair of opposing angular ones (ie. the 'handles'), with a varying leverage ratio..

No idea what else to try with it for now tho..

[MrVibrating]

Had a new idea on the way to work earlier, been itching to get home just to get it down here before i forget it.

It's a fresh, slightly different approach to try and 'mechanise the maths'.

Instead of focusing on trying to increase G-times / per-cycle momentum yields to 'OU' levels (ie. in spite of rising RPM), this new approach will accept that diminishing G-times / AM yields is an inevitability of rising RPM..

..the new focus will be simply trying to achieve asymmetric redistribution of whatever momentum we already have!

It's basically a 'classic OB' wheel coupled to a vMoI on the same axis, via a clutch.. (yawn.. but stay with me, this is summink different!)

• suppose the vMoI has double or mebe 4x the base MoI of the OB half of the system

• so, gain some momentum from OB, then open the clutch and close the vMoI, to bring its MoI down to match that of the OB system

• this trades MoI for RPM, resulting in the vMoI out-accelerating the 'OB wheel' half of the system

• with the two MoI's now matched, apply the brake / clutch.. decelerating the vMoI, whilst accelerating the OB wheel

That's it, just rinse & repeat - the OB side of the system is getting slapped with momentum that was already part of the net system momentum; so instead of 'fresh' momentum from gravity and time, it's just the same old momentum it picked up from the previous OB cycles. But with the MoI's now even-stevens, the acceleration of one will be equal to the deceleration of the other..

The idea is to try cook up some internal 'relative momentum' between the two inertias, made from the absolute momentum gained from gravity and time. Equality of redistribution of this 'relative momentum' via inelastic collision (ie. braking) in the gravitating FoR is thus expected to cause an effective N3 break from the external / ground FoR.

Load o' hogwash i'm sure, but enough of a plan to get me teeth into.. got a couple of days off coming up too..

[MrVibrating]

Having slept on it, the more i think about it, the more compelling (& simple!) it seems..

• if it's mathematically impossible to decouple the unit energy cost from value of absolute angular momentum in the ground frame, for the same reasons, the unit energy cost of 'relative angular momentum' in the rotating frame is already naturally decoupled from its value in the ground frame


Thus, as an engineering proposition, the problem reduces to mechanising this concept of 'relative angular momentum'.

Going back to the proposed test rig of a vMoI clutched to an OB wheel:

• if the vMoI has twice the base MoI of the OB wheel, then halving its MoI will double its speed:

..if the base MoI were '1 kg-m²' and we thus reduce the vMoI from '2' to '1' from a starting speed of 1 rad/s, the OB wheel will thus 'see' an equal oncoming inertia at 1 rad/s (2 rad/s in the ground frame).. so it has a 'relative AM' of 1 L, no? Even tho it still has the same, conserved amount of AM in the ground frame; we've just generated some relative AM, no?

If you just roughly plot forwards over n cycles, the unit energy cost of this 'relative 1 L' as a function of work done against CF force in the absolute frame is reduced because each collision (ie. engaging the clutch) equalises the speed difference, 50% of it accelerating the 'OB wheel', the other half decelerating the vMoI wheel, so ie. we have to pay in at the absolute FoR cost for the first cycle from say 1 to 2 rad/s absolute, but thereafter a subsequent 1 rad/s relative begins at an absolute of 1.5 rad/s, not 2 rad/s.

'Relative AM' is of course a horseshit concept - angular momentum's absolute; either there's CF force or there isn't - but still, if it can nonetheless be accumulated at profit, it'd look like closed system gains from a divergent input FoR..

[MrVibrating]

It'd also avoid the issue of having to store onboard PE to complete say 5 cycles before payoff; instead only the first input cycle would be at unity, thereafter reduced by the net deceleration caused by each inelastic collision.

So maybe this provides the context for the central radially-sliding GPE (ie. the 'stampers') - these drops powering the vMoI retractions / 'relative AM' rises..? A scissorjack-type transmission might thus solve for the fact that, whilst we cannot increase the amount of mass being dropped each cycle to match the climbing CF work costs, we could allow the 'height' component of that GPE to increase with RPM / CF force..? (I still like the last concept of using a scissorjack-type of power conversion to counter-balance unequal radial vs angular weights, precisely because of its self-regulating characteristics..)

[MrVibrating]

OK first attempt at accumulating relative momentum:




@ 4.5 kHz, 1 i-s/f:

Clutch = -155.8383404 J

vMoI CF-PE = 111.1983648 J

OB Sys = 173.1025789 J

KE Rise = 138.2916 J

111.1983648 + 173.1025789 = 284.3009437 in

138.2916 + 155.8383404 = 294.1299404 out


..another day, another 10 J magical free rounding error from nowhere, but instead of trying to make it go away i'm gonna indulge in a Peter Griffin-style day-dreamy cutaway of free chicks and hot beer for life, at least until the weekend (i just need the lift).. :P



Idiot-guide explanation of the interaction:

- the vMoI starts out riding with the OB wheel, but has four times the base inertia, hence helping itself to 4x its share of momentum

- pockets full, the clutch disengages and the vMoI squeezes itself into accelerating - conserving absolute angular momentum, yet gaining 'relative' AM, relative to the OB wheel..

- ..which it then re-collides with, by dropping the clutch, now at a 1:1 MoI ratio and so equitably redistributing the 'velocity' component of that relative momentum gain

- clutch still locked, the vMoI re-extends to 4x that of the OB wheel, and the cycle repeats


One issue thus far is that i've inadvertently set it up to gain more 'relative AM' each successive cycle, whereas ideally i want to buy the same, fixed quantity of relative AM each cycle.. will have to refine the code a bit, the basic MO is there tho..

[MrVibrating]

Polished it up a bit - measurements are still coming in a little over or under but i think it's yet another zero-sum:


..i tried calculating the forces acting on the OB actuators from 1st principles, multiplying the masses by the sine of the actuator angles, then adding the CF force per mr²w, but this only plots the instantaneous effective gravitational force + CF force, while the net force on each actuator includes the radial inertial forces from accelerating 'em inwards & outwards, which means the full equation for both GPE actuators is too long for one meter, tho could perhaps be built up from nested & hidden meters... dunno.. the point would be to calculate the work done from boiler-plate physics, instead of relying on directly measuring the forces acting on each actuator, which is where the variance / error margin arises when using complex functions for active constraints. This, incidentally, is how the 'vMoI CF P*t' integral works - it's not 'sensing' the forces on the actuators via the 'constraintforce[n].x' function, which actually only puts out junk data under these control conditions, but obvs for exactly the same reasons it'd also seem the more reliable method for measuring the work done by the OB mech..

On the one hand, adding in your own physics is kinda subverting the whole purpose of simming, relegating it almost to an animation software, and likewise running the risk of introducing your own stupid errors, but when all the other metrics fit while the time integral of constraintforce * constraint velocity for the OB mech's coming in at over 3 kJ (seriously, that's how bad WM's error was for the vMoI work integral), you gotta wonder how reliable its force data on the OB actuators is, too - and since i'm still getting +/- 3-10 J over or under, i'm guessing that's where it's arising..


Still, gonna peg this 'un down to unity for now, as i think i see the fundamental reason it can't cause a divergent FoR - and it's because i'm using CF work to gain velocity, which remains locked to the absolute frame, instead of regular torque, which doesn't (ie. per the 'chicken run' demo)..

As such, i've a new concept to test:

• spin up a rotor, against a 'stator' comprised of a weighted vMoI

• open & close the vMoI while the weight drops, and whilst torquing the rotor

• spin'n'brake, rinse & repeat

It's basically 'sinking counter-momentum to a vMoI + gravity * time' - but whereas previously when sinking counter-momentum to a vMoI i either opened it, or closed it, with the momentum gain on the rotor only ever equal to the momentum lost to the MoI change, now the interaction will start and end with the same MoI's. Opening and closing the vMoI will still prolong the drop's G-time, during which the torque * angle applied to the rotor should be the same per rad/s of relative acceleration whatever the actual speed in the ground frame. That's the thinking anyway.. day off tomorrow, so will prolly just bolt the above two parts together, and add a plain disc as a 2nd rotor, via a motor. Then it's just a case of syncing it up..

[MrVibrating]

Tried it:

It says i made 2 mJ.

I think it's just trying to spare my feelings.

[MrVibrating]

Thinking about it, this idea of trying to shift focus away from G-times / RPM towards simply asymmetrically redistributing the momentum i already have is ill-conceived:

• how else you gonna fashion an internal asymmetric inertial interaction without recourse to some external stacking force such as gravity and time? IE. 'shifting focus away from G*t' towards what, pixie dust?

• if the only way to internally redistribute extant momentum asymmetrically is by leaning on G*t, then any asymmetry (and thus non-cancelling remainder) so obtained is, effectively, momentum from G*t regardless..

So, back to square one.. the value of accumulating this momentum would have to be decoupled from its GPE cost or GKE value in the ground FoR.

Yet all the while we're using a weight as a 'stator', it's falling, and the faster we turn the less G-time it spends falling, or else the further it falls (ie. if spooling off of a reel, say)..


The weights heard landing on the descending side of B's wheels seem to meet much of the implicit requirements of a diverging inertial frame, since you have an inelastic collision instantaneously redistributing internal momenta, whilst gravitating; keys steps, surely, in migrating the FoR of the input-energy workload into the gravitating FoR, wherein a relative internal acceleration of 1 kg-m²-rad/s costing ½ J may have a much higher KE value in the external static frame.

We need to cause auto-acceleration of the FoR of the input-energy workload; ie. whatever it is we're doing to gain momentum, that process must itself be accelerating a little each cycle, accumulating speed relative to the ground FoR.

Conventional torque, as from a motor or rotary spring, is obviously preferable as an input workload since angular inertia's speed invariant, so a 1 rad/s acceleration of 1 kg-m² could conceivably cost ½ J every cycle, regardless of its absolute speed in the static FoR.

Inertial torque OTOH (ie. from the ice-skater effect) is speed-dependent, due to CF force squaring with RPM.

Then again, using CF force to harness and recycle an energy gain is one of few options in a statorless system.. it's basically that, or else weight lifts, but inevitably will involve both either way - ie. we know his wheels over-balanced, which means internal weights were changing radius in the presence of CF force, meaning an MoI decrease then increase, but the decrease phase costs energy which must've been harnessed from rotKE by an MoI increase somewhere else, and if they're both in the same FoR then the efficiency of that exchange is 1:1 etc. etc.

Fundamentally, remember, an OU system is one in which the input energy costs sum with rising RPM, while output energy value squares. At least, across some useful range of RPM..

[Georg Künstler]

MrVibrating wrote:

The weights heard landing on the descending side of B's wheels seem to meet much of the implicit requirements of a diverging inertial frame, since you have an inelastic collision instantaneously redistributing internal momenta, whilst gravitating; keys steps, surely, in migrating the FoR of the input-energy workload into the gravitating FoR, wherein a relative internal acceleration of 1 kg-m²-rad/s costing ½ J may have a much higher KE value in the external static frame.

I can mostly agree on that.
there are 3 types of an collisions.
1. is the direct impact, one against the other, destroy material, produce heat

2. the masses make a collision with a spring in between, the forces where redirected
and the

3. the indirect collision while the masses are gravitating, lifted against gravity with a flash.

So this indirect collision is the way to look for the function of the Bessler wheel.
Masses are lifted against gravity with a flash on the descending side of the wheel.
This leads to an amplification of the forces on the downgoing side, supported from gravity.

You can compare this function with a men hanging on the pipe slide.
At the end of the pipe slide the man is making a upswing with a flash.

I will remember here Bessler's words, the force must be applied in the correct angle.

All this above will lead you to a parasitic oscillation.

A turning wheel will make a parametric oscillation,
an indirect impact in the same time when the wheel is turning will make an additional parametric oscillation, a pendulum on an internal carrier will make also an move, an parasitic oscillation.

[MrVibrating]

Thanks, and i'm sure reciprocating / swinging actions play a part in a working wheel, however concepts like 'parametric oscillation' are completely meaningless to me; there's inertial interactions, and gravitational interactions: our goal is to gain angular momentum, which always has a corresponding kinetic-energy value in the ground FoR, hence, more to the point, we want to pay less energy for its purchase, which in turn means avoiding the V² multiplier on the cost of accumulating it.

This is how you frame the problem in a manner that's intrinsically resolvable - by definition, Bessler found some way of fixing the input energy costs of accumulating angular momentum from gravity and time. There are inertial interactions, and gravitational ones; everything else being but variation on those two types of fundamental interaction - so a 'swinging' action is more meaningfully treated as either an inertial interaction, or else a combined gravito-inertial interaction, having an input phase and an output phase, or input workloads and output workloads, which always refer to some reference frame against which we / they enumerate measurements / momenta / energies. CoE is caused by both input and output FoR's being one and the same, interlinked via the effects of Newton's 3rd law.


These are the concepts, terms and conditions with which to understand and ruminate meaningfully on the prospects for mathematical OU. "Parametric oscillation" / harmonic resonance etc. etc. just seems like navel-gazing under a star-spangled sky.. jumping in puddles at a sign-posted channel swim..

[Georg Künstler]

I understand your words, but that don't happen in Bessler's wheels.

He created a moveable FoR. You look at a fix FoR.

In his wheel everything is on the move, nothing stays stationary.

An indirect impact leads to an flash movement against gravity. gravity has to make the work again.

What you need is the right handle condition of this movement.
You have to find where the impact in the wheel will occur, and under which angle.

The wheel lives from the speed difference between inner and outer construction.

[MrVibrating]

Yes, he created a rotating FoR, but it was still rotating relative to the ground FoR, and it is in this, external FoR that the KE gain exists and is harvested. The energy gain is the difference between the input work costs in the rotating FoR, and their KE value in the ground FoR.

You need to think in more fundamental terms - an impact implies a preceding velocity difference prior to the collision (ie. something was traveling faster), followed by a redistribution of internal momentum post-collision (so the lighter mass or MoI was slowed down, and the heavier one sped up). Yet these are just the terms of basic inertial interactions, in which net momentum is strictly constant / net zero. Momentum can only be gained from gravity and time - specifically from a rising vs falling G-time asymmetry (because if 'up' & 'down' G-times are symmetrical you just have a pendulum).

Hence on the one hand, the mathematical solution is "OU = the efficiency of accumulating reactionless momentum rises", but in practice, it's a case of "OU = fixing the unit energy cost of momentum from gravity and time" (ie. invariant of rising RPM).

So concepts like 'parametric oscillation' and even 'collisions' per se, are but side issues, at best; the fundamental problem must be framed and addressed under its express terms, concisely grabbing the bull by the horns..