Decoupling Per-Cycle Momemtum Yields From RPM

[MrVibrating]

Preliminary, but from t=0 up to peak momentum, it's using around 11.1 J per L on the wheel axis.

Base rate per ½Iw² remember is just ½ J/L, so this certainly ain't cheap as a means to raise momentum, at least from a standing start..

Of course it's linearity of the cost that matters - IE. speed invariance; if we can maintain any constant J/L input efficiency, then there'll be some threshold RPM beyond which we're OU, and below which, under.

However part of the input workload here is CF force * radius, which obvs isn't speed invariant; that efficiency is thus expected to decrease as RPM's rise..

The principle workload however is those oscillating angular inertias - which seem responsible for causing most of the momentum variation; the vMoI just seems to enhance and clarify the result, no? Angular inertia is a speed-invariant workload; IE. 1 kg-m² in the wheel's frame is always just 1 kg-m², whatever the current RPM, so we'll have to see how these two costs stack as net momentum accumulates over successive cycles..

I'm gonna add a second plain disc, coaxial and connected via a clutch:

• its MoI equal to the wheel's at peak delta-L

• the clutch will be engaged during the 10° priming phase, then released from t=0

• the second rotor will thus coast at the constant starting speed of 1 rad/s, until the instant of peak dL per-cycle

• at peak dL the clutch bites, redistributing the wheel's gain in momentum back to the second rotor, IE. 'banking' half of it..

• ..then just looping that regime over N cycles, climbing the staircase plots


Again, decoupling CF PE from rotKE seems unlikely if not inherently paradoxical, so not much hope there.. best i've had in the past is constant CF work per cycle but for diminishing momentum yields, thus enforcing CoE regardless.

Angular inertia as the primary input workload however is much more promising.. (remember the 'chicken run' spoof?)

[MrVibrating]

..just a passing point of trivia, but if this is real - ie. an actual transient N1 violation - then Bessler must've been aware of this fact - IE. he obvs kept depicting diametric levers for good reason - but this means he would have to have been plotting angular momentum as a function of varying MoI and RPM.. using 18th century techniques that means tables of calcs, in much the same manner the sim progresses thru sequential 'frames'..

As ever, the potential room for an exploit here came to me during a nice soak in the bath (arm fracture's still healing, few more weeks free time left). The rationale's simple enough - big MoI vs little MoI, and rel vs abs angular momenta of paired angular accels under a net inertial torque as a 'stacking force'. Not the sort of thing you could empirically solve on the back of an envelope tho - too much to keep track of the varying torques and counter torques / momenta. Indeed, any sensible guestimate would likely proceed from the safe assumption of N1 as a first principle..

This is something you gotta measure to first find, and then, work with.. little opportunity for serendipity if you can't even see the effect from oggling alone.. thus would be further supporting the point that B. must've solved the vis viva dispute decades prior to his contemporaries, but the issue of linear vs squaring conserved properties was nothing less than the nuts and bolts of his exploit.. it would frame him squarely as a 'mathematician' over a mere tinkerer tho..

[MrVibrating]

Another thing - for years i've wondered why the diametric lever bobs in MT 133 are 'hammer' shaped, as if to signify directionality; yet as 'hammers' what would they strike, but one another? How would that cause or then rectify a net gain in AM in one direction over the other?

This essentially is 'MT 133' tho, right? The central radial displacement he depicts appears to be 'pneumatic' or maybe hydraulic, but nonetheless furnishing this same 'high-low-high' MoI variation..

..diametric levers + vMoI = effective N1 break.

Without gravity - that's the real coffee-splurter..

[MrVibrating]

Tried a run with the motors locked, just the vMoI on its own, and noticed that the momentum of the levers in the blue meter was decreasing.. derp - i'd subtracted the wheel speed from the motor speeds, instead of adding it..

The corrected final picture looks more like this:



..which makes a bit more sense eh - the variation on the wheel axis being the counter-momentum from that of the motor / lever axes.


As a final point of curiosity, here's the end result when only the vMoI is active:



Note the 'AM on Wheel Axis' meter on the lower left - now showing the correct label for AM, 'L' - i've zoomed right in, check the Y-axis scale on the left; there's this 0.1 L wobble... it looks insignificant in scale, yet it's anomalous - if the levers are perfectly stationary relative to the wheel, then its net momentum shouldn't waver, surely..?

IOW any apparent wobble in N1 from nothing more than the ice-skater effect suggests an issue.. which might also be affecting the result when the levers / motors are mobile.. if not amplifying it..

So before ploughing ahead with measuring energy efficiency i should prolly try eliminate that wobble eh..

[MrVibrating]

Right, tried a variety of measures to stabilise the vMoI-only baseline:

• pinning the levers and their bobs directly to the wheel with rigid joints when their motors are switched off

No effect on the wobble

• set lever masses to nearo-zero (bobs still kept at 1 kg each)

Wobble eliminated.


This is obvs an error in WM2D. While slight, and inconsequential to the net result, the levers are just inert rectangles, previously set as 'steel' and leaving the corresponding default properties and mass as a function of their 20 mm thickness and 1.9 m length; none of which should affect MoI when they're entirely static relative to and rigidly affixed to the wheel.

The MoI calc is not in error - again, it's just the mr² sum of all six inner components, plus the MoI of the wheel disc itself.

That supposedly-perfect MoI sum is simply multiplied by the wheel speed - and obviously the levers speeds when rigidly affixed and static relative to the wheel is simply the wheel speed, so.. dodgy error on WM's part, but insignificant in the scheme of things; here's the anomaly now, with nearo-zero lever masses (still incorporated in the calcs, just below the displayed 4 digits):



..if anything, this has only enhanced the clarity of the effect.

Since the principle mr² of interest about the motor axes is that of the end-bobs on the levers - which remain 1 kg each - it would seem equally legitimate to replace the lever bodies with 'rigid rod' constraints, which are themselves treated as massless - previously tried and tested w/o issue - but for now i'll just leave 'em as solid bodies, albeit with only token masses.

Just for closure on this lil' niggle, here's that vMoI-only baseline run again:



..as you can see, the Y-axis on the lower left meter is zoomed in to three sig figs and perfectly flat-lined.

Since none of these revisions affect the net result, and i can see no further error sources, the anomaly still stands; we appear to have N1 on the ropes here..



Latest sim revision attached.

[MrVibrating]

..found one more error:

• i was previously summing the wheel plus motor axes momenta, assuming positive vs negative plots would cancel to zero..

(on the 'yellow' meter)

This works out wrong tho, as both are metered as 'positive' - the correct operation is thus subtraction.. i think..


Here's the (further) 'corrected' vMoI-only baseline:



..so 'relative' and 'absolute' metrics correctly adjusted on the Y-scale, and now here's 'the full effect' again:




So, regardless of this last correction, the absolute +/- dL/dt (green trace on the yellow meter) appears to be non-constant.

That is, the instantaneous dL/dt on the wheel axis minus the dL/dt on the motor axes are not equal and opposite, and not cancelling to a net zero..


ETA: eek! one tiny oversight - the yellow meter is labelled with the inverted subtraction; the function actually being plotted there is 'dL motor axes minus dL wheel axis'; just a typo tho, corrected in the attached sim.

rev 4.3 attached

[MrVibrating]

Looking ahead to the likely outcome of the intended second rotor and its 'inelastic collisions' via a clutch bite at 'peak L'

• even if the transient variation in net L is real, siphoning it off onto a second, equal, MoI will inevitably result in the 'primary' rotor here reverting back to a proportionately-lower L than it began with..

• IOW precisely because of N1, you'd expect that the two rotors will reach a stable range of speed, minus any losses from the clutch

IE. won't the asymmetry, if it's even 'real', simply take with one hand what it gives with the other?

[MrVibrating]

Just for completeness, here's the 3rd case again in the latest sim (more stable, attached):



• 'L' on wheel axis rock-solid as it should be

• levers nonetheless appear to smoothly gain then lose net momentum

• the MoI variation preventing their mutual cancellation.. & seemingly boosting their resulting sum..

[MrVibrating]

OK tried every type of clutch sync, but it makes no difference; it just wobbles around the starting speed range, IE. momentum's constant, duh, you didn't seriously think i might be on to something?



The only condition under which it's able to gain momentum is when gravity's enabled, and 'opposing sync' is selected, which causes a GPE variation as both levers stay on the same side of the wheel; even then, only making unity minus losses.

You can see the sync applied here - the clutch activation is tied to the angular direction of one of the levers; active only when it's moving in one direction (but not the other), and accelerating on its way into the center (but not when decelerating / after passing the center). Like i say, tried a bunch of other rules, no difference either way..

[MrVibrating]

..just for completeness / morbid curiosity, here's the opposing lever sync, same clutching rule, gravity still off:




..IE. nowt there, never was.

[MrVibrating]

I've been mulling over MT 41 - 42 again.

As noted previously, these are showing radial - angular interactions.

In MT 41, the left and right sides are symmetrical, yet denoted by an inflected 'A' on the left side.

Inflected 'A' denotes a driver, and straight 'A', something driven.

The long vertical levers connecting the jacks to the axle are kind of apocryphal or symbolic, rather than literal - ie. applying torque against a stator locks the input and output workloads to the same, terrestrial, FoR, thus precluding any thermodynamic decoupling. Thus the more salient point being portrayed is simply the angular-to-radial transmission.

This same point may apply equally to scissorjacks per se - perhaps they're being established as metaphors for angular to radial transmission per se.. rather than literal mechanical solutions / applications..

Thus the essential 'lesson' of MT 41 is that we can ply radial drops to drive angular lifts (left side), or equally, angular drops to drive radial lifts..

MT 42 makes a decision between these two options - going with radial drops (inflected 'A') driving the rotation. This inevitably means the weight is raised in the angular plane, by the rotation driven by the radial drops.

If you're following this logic, MT 42 is basically depicting reversed 'classic OB' - angular lifts with radial drops..

We know this can't be alluding to an energy advantage - GPE in/out is path-invariant.. so IE. left and right sides of MT 41 both achieve unity efficiency minus losses..

..hence what is the 'horizontal vs vertical friction' advantage Bessler refers to?

Logically, MT 42 must be singling out the aforementioned 'horizontal application' - IE. the vertical disposition of the jacks is not the plane of action he's referring to..

..rather, it is the prospect of driving the rotation with radial, rather than angular, drops. This is why MT 42 carries over the inflected 'A' from the left side of MT 41.

The only advantage possible, is in the resulting momentum yield.

Mechanical over-unity is only possible if we can buy equal momentum each cycle, for equal work done; IE. the conversion of input work to output momentum rise must be speed-invariant, not decreasing with RPM.

If we went with the right-side solution to MT 41 instead, we have basic OB - the energy cost of each radial lift is constant, so it always costs IE. 9.81 J to lift 1 kg by 1 meter, however the amount of momentum gain each successive lift can buy is decreasing with RPM, per the thread title..

..to recap that point, briefly: if we attach a weight to a wheel at 12 o' clock, and let it rotate down to the 6 o' clock position, it will imbue the wheel with a certain amount of momentum increase.. but if we begin at a speed of say, 4 RPM, then the weight will spend half as much time under gravity's constant acceleration as when beginning from 2 RPM.

Each doubling of RPM halves the 'positive G-time' per cycle, thus halving the momentum yield from the same input GPE.

Hence the right side of MT 41 is showing a regime that suffers reducing momentum yields with rising RPM - IE. 'classic OB' is condemned to always produce diminishing momentum returns with rising RPM, so is intrinsically bound to I/O energy unity.

The left side solution thus must be offering some kind of alternative to that dead-end - IE. some way of maintaining momentum yields in spite of rising RPM..

As noted previously, removing a drop-weight from the descending side of the wheel, in principle, isolates its potential momentum yield from the rotation speed - it's no longer being thrust downwards with the descending side of the wheel, which thus no longer adds to its absolute velocity, nor thus detracting from its potential G-time per cycle.

In a nutshell, if we're to cleave equal momenta from gravity & time each cycle, invariant of rising RPM's, then radial drops with angular lifts - 'reverse OB', basically - is the de facto way to go.


Yet we also know that Bessler's wheels did indeed continually over-balance regardless - the one-way wheels were under static torque when tied off stationary.

Only classic OB can produce such static torque in a statorless system - IE. a weight can only be suspended in a radial drop position against a stator.

Hence they surely must've used both regimes - just as MT 41 does - at the same time..

Please, anyone - refute me on this..? At least render it an open question rather than a statement of fact? IE. just show how a radial drop could provide static torque in a statorless system..

..which brings me to my final point, for now: as noted, the long levers connecting the jacks to the axle cannot be literal - instead representing some means of transmission that would be viable in a statorless wheel..

This, surely, can only be CF workloads? IE:

• CF force can pull masses outwards, thus powering a radial lift

• conversely, a radial drop can power retraction of those same masses inwards, against CF force

In the former case, we get an ideally-perfect conversion of rotational KE into GPE.

In the latter, we likewise obtain an ideal conversion of GPE into rotKE.


The only functional distinction that would seem to matter to us is the prospects for speed-invariance of the resulting momentum potentials..


FFWD to the Toys page - again, the scissorjack must denote some means of converting radial drops into discrete rises in system angular momentum.. some kind of transmission system between radial and angular workloads.

Each successive radial drop has to furnish a momentum rise, the cost/benefit of which must be RPM-invariant; the same work done each cycle buying the same amount of angular momentum.

The solution, whatever it is, has to be here, somewhere.. simply because there isn't anything else - we're down to bedrock here; these are the functional elements of the problem, and thus, whatever its solution..


As an aside - does anyone know if we have original German texts of Machinen Tractate? I've looked but can't find.. my concern being that the translations might include suppositions / inadvertent projections of the interpreter, as we've seen in the 'quarters' riddle..?

[MrVibrating]

What i can't work out is how a radial drop can result in a momentum gain, if all it can do is drive an MoI retraction?

Retracting MoI can apply a positive inertial torque, which can be used to drive an angular lift.. but then that GPE has to be the source of any momentum gain, right? Back to square one..

So an angular drop can cause angular acceleration, which raises CF force and can thus drive an extending MoI, thus an output of CF work which in turn can raise a radial GPE.. which is then dropped again in the angular plane..?

..or else conversely, a radial drop can cause an MoI retraction which causes angular acceleration which raises a GPE in the angular plane.. then what - to be dropped in the radial plane?

I don't see how either option can cause RPM-invariant momentum gains..


The only other option just seems pointless - IE. a radial drop could be used to drive an MoI extension, but this would be pushing masses outwards in the same direction they're already being pulled by CF force, right? It seems redundant, and moreover, still doesn't seem to help with gaining momentum, let alone at constant energy cost..

I feel like a complete idiot here.. i know i'm looking at all the pieces of whatever the solution must be - there can't be anything missing.. but i just can't see how they fit together to solve the problem.

You've got the ice-skater effect, with positive and negative inertial torques, but which on their own conserve momentum..

..and then you've got GPE inputs and outputs - radial lifts with angular drops gain momentum, and the opposite cycle sheds it back to gravity.

Soz, nothin' doin here for now.. just trying to lay out the jigsaw pieces to try force meself into staring at the problem.. FA idea how to solve it for now tho..

[MrVibrating]

Consider a simple OB wheel, rotating a weight from 12 o' clock down to 6 o' clock.

Suppose it costs 1 Joule to raise initially.

No matter what RPM we begin at, the weight will only add that same 1 J of rotational KE to the wheel.

If we began at 1 rad/s, the wheel will only gain enough momentum from the drop to raise its rotKE by 1 J.

But likewise, if we began at 2 rad/s or 4 rad/s - we'll get a 1 J gain in rotKE each time, the only difference being that the associated momentum rise will be halving each time we double the speed, right?

We could increase the momentum yield of any drop by raising MoI on the way down, thus applying negative inertial torque and so slowing the descent..

..but then any increase in momentum is in the form of increased MoI - not speed..

..and besides, we still only gain the same 1 J per drop, only now it's partially in the form of CF PE, rather than rotKE. So for example the extending MoI could load a spring or something - maybe raising a weight or whatever - but then we'd still need to cash in that PE to get the rotKE..

I don't get it.

I feel like doing a series of real-dumb sims - just the above examples, simmed out and metered up, just to try lay it all down clearly - but have no idea what i expect to find, in terms of opportunities for fixing momentum costs.. besides, what haven't i done already in terms of measuring these types of exchange? What's the point?

Maybe if i just make a start on it anyways some kind of point will become apparent?

[Fletcher]

I feel like a complete idiot here.. i know i'm looking at all the pieces of whatever the solution must be - there can't be anything missing.. but i just can't see how they fit together to solve the problem.

...

Soz, nothin' doin here for now.. just trying to lay out the jigsaw pieces to try force meself into staring at the problem.. FA idea how to solve it for now tho..

...

I don't get it.

I feel like doing a series of real-dumb sims - just the above examples, simmed out and metered up, just to try lay it all down clearly - but have no idea what i expect to find, in terms of opportunities for fixing momentum costs.. besides, what haven't i done already in terms of measuring these types of exchange? What's the point?

Maybe if i just make a start on it anyways some kind of point will become apparent?

How many times have I hit a brick wall - gone back to basics, for lack of any other inspiration and direction to explore - looking for WHAT, I ask myself ?

The Bessler answer is simple !

Somewhere in the basic mechanical interactions we explore is a chink in the Newtonian armour.

I think only by revisting things over and over, do we have the opportunity to perhaps one day examine relationships and cause and effect in a different light and perspective. And maybe in that tedious analysis and familiarity find the chink and exploit it.

So no effort, or backtracking and examination, is ever a waste, IMO !

But it does take will power to do it.

Remember, that B. did some experiments, that looked postive. He didn't build a runner wheel at that time. He got married and went on honeymoon etc. Did some doctoring. Then he set to work and built his first fully functional runner, derived from those experiments. He confirmed the chink was real !

[Robinhood46]

I think only by revisting things over and over, do we have the opportunity to perhaps one day examine relationships and cause and effect in a different light and perspective. And maybe in that tedious analysis and familiarity find the chink and exploit it.

We need to look at every aspect with absolute objectivity and the biggest obstacle to overcome to achieve absolute objectivity is the illusion that we already have it.