Decoupling Per-Cycle Momemtum Yields From RPM

[Georg Künstler]

MrVibrating wrote:

More convinced now than ever that a 'Bessler wheel' is basically a gravity-assisted 'chicken run' from a few pages back - using gravity to sink counter-momentum, instead of animal cruelty. That's why it's 5-cycs-to-OU rather than just 3.

Here I disagree, it has OU after the first fall.
The function is catch the fall.
The Wheel is self accelerating after the first fall, impact.
The first fall is generating the assymetric torque.
This is the case for the bi-directionl Wheel.

The one directional Wheel is in its construction always out of balance, and therefore self starting. It is also using the fall in a tilting function.

[silent]

.

[MrVibrating]

OK just to clarify a few points, i'm going to run through some example 'gain trajectories'...


This is for everyone else's benefit, not mine, so hopefully it'll explain exactly what's happening, and what more needs to be done..



First off, let's look at the shortest theoretical route up the OU ladder..

You'll need Notepad, Calculator and the standard KE formula ½mV² (use this handy online calc here - i do!):


• Take two 1 kg masses. (They could be 1 kg-m² angular inertias - different dimensions, but same amount of inertia either way)

• Unhanging any portraits of sir Isaac you may have on display, and resting them face down whilst saying three hail Mary's, apply a unilateral force to one mass, accelerating it by 1 meter / sec.


So no drama here - just assume you have 1 kg moving at 1 m/s (or 1 kg-m² at 1 rad/s - same deal). How it got to that speed is incidental at this stage..


You should find that you currently have ½ Joule of KE.. and of course, that's also how much PE you've spent.



The second mass however is still stationary, so:

• inelastically splat the moving mass into the stationary one.

Bang! Now both inertias are moving or rotating at equal speed.

You had 1 kg-m/s of momentum, embodied on one 1 kg inertia, and now, post-collision, you still have that same 1 kg-m/s of momentum... only now it's distributed between two 1 kg inertias.

So, this means each mass is now moving at ½ m/s, right?

Applying the KE formula, 2 kg moving at 0.5 m/s has 0.25 J of KE..

..but we spent half a Joule, so 50% of our input energy has been dissipated by the collision. We've lost half our input energy. Bad start for a so-called 'gain-trajectory', eh?

What kind of idiot is gonna repeat the same mistake, expecting a different outcome..?


Exactly! Our kind! That's just what we do! It's what we're built for, derp!


So give it another whirl:

• add another 1 m/s of velocity to either mass

Again, this is a unilateral force we're somehow applying - not pushing or pulling against some other mass - and furthermore, in spite of that concession, we still only want to pay the same price for it, of half a Joule.

So now it's moving at 1.5 m/s, or 1.5 rad/s if you chose angular.

Current net input energy is two * ½ J accelerations, so 1 J total.

Again, crunch the accelerated mass into the non-accelerated one:

- so, without any bounce (crucial!), 1 kg moving at 1.5 m/s strikes 1 kg moving at 0.5 m/s; result? You should now find you have two 1 kg inertias moving at 1 m/s..

So how much KE do we have, according to the KE equation?

- Two 1 kg masses at 1 m/s have a total of 1 J of KE..

..and we've spent 2 * ½ J, so at the second cycle, we've gone from 50% down, to hitting unity! 1 J in for 1 J out..

So the efficeincy of the system is developing - we're not getting the same result each time! Who's the idjit now eh, mr so-called 'Einstein'..?

So we have to try a third cycle, to confirm where this is going..

• Again, accelerate one mass by another 1 m/s, for half a Joule..

• ..and again, prang it into the un-accelerated mass..

So now you should have two 1 kg masses moving at 1.5 m/s.

You've spent 3 * ½ J = 1.5 J.

How much KE does 2 kg moving at 1.5 m/s have?

It's 2.25 J, isn't it?

The ratio of 2.25 / 1.5 = 1.5.

That is, we're now at 150% of unity..

Enthused? Try adding further cycles, and watch in awe as your efficiency converges towards infinity..




However, Bessler does NOT indicate this interaction. His method reaches unity at four cycles, not two..

Why might that be? Obviously, the requisite conditions here of applying a unilateral force to cause the same acceleration each cycle, invariant of rising net speed, is a total sacrilege upon Newton's 3rd law.

And remember, N3 really IS inviolable, because of mass constancy. A 'genuine' N3 break is literally impossible..

..yet Bessler's wheels were statorless!

..but yet again, gaining height on a park swing is trivial! And that requires no stator either! Coincidence? No chance. No other alternative!

So the best we can hope for - and all Bessler managed - was an effective N3 break - something that achieved the same ends, albeit by alternate means...

..and thus we may conclude that this trick, of circumventing N3 by whatever devices, is inherently a "4 cycles to unity" optimum outcome - for some reason, it is intrinsic to the nature of the exploit - a built-in constraint.

Because otherwise, OU in three cycles would be possible, as Bessler would have quickly discovered! Yet evidently, it isn't.. Bessler's ideal solution (as portrayed on the Toys page), necessitates a "4 cycles to unity" ('4 c/u') trajectory..


So why might that be? Let's frickin' sim one on the back of a fag packet and find out eh..?


• Let's concede that in order to apply a force to an inertia, it has to be applied between it and some other inertia.

There may be examples of 'effectively' unilateral forces under certain given conditions (inertial torques, OB torques or whatever), but let's just assume we have to incur an equal opposite counter-momentum, as per normal, for this current example...


so to accelerate 1 kg by 1 m/s in one direction, we also have to accelerate the other 1 kg in the oopposite direction..

..so we now have 1 kg at 1 m/s with ½ J going on one direction, and then another, equal mass, speed and KE going the other way..

..so we've initially spent 1 J, with zero net momentum to show for it..


• Now kill that counter-momentum. Destroy, annihilate, liquidate that mofo. However. You work it out. Just, make it happen..


• Now do the collision.


Rinse, repeat and calculate...


If you actually do that calc, it's precisely the same interaction as before, except half the net momentum and input energy is lost each cycle.

So, 1 kg at 1 m/s meets 1 kg at 0 m/s, resulting in 2 kg at ½ m/s, and 0.25 J net KE, from 1 J of spent PE; ie. 25% efficiency, 75% loss.

Then, 2nd cyc, 1 kg at 1.5 m/s strikes 1 kg at ½ m/s, resulting in 2kg at 1 m/s and 1 J net KE, for 2 J net input PE, so, 50% efficiency at this stage.

3rd cyc: 1 kg @ 2 m/s hits 1 kg @ 1 m/s - resulting in 2 kg @ 1.5 m/s, so 2.25 J of KE, for 3 J total input PE.

2.25 J out / 3 J in = 0.75% efficiency, so far..

As you can see, net efficiency is increasing by a steady 25% per cycle...

At the fourth cycle, 1 kg @ 2.5 m/s tangles with 1 kg @ 1.5 m/s, leaving both at 2 m/s, and so posessing a net kinetic energy of 4 J, my idjit friends..

We've spent 4 J too, so it's a '4 c/u' (four cycles to unity) result.


Let's just spend one more Joule, to witness first-hand the true miracle of back-of-fag-packet OU for ourselves:

1 kg @ 3 m/s snags 1 kg @ 2 m/s; result = 2 kg @ 2.5 m/s = 6.25 J... but we've only spent 5 J in total..

6.25 / 5 = 1.25, or 125% of unity




So, that's the gig.

The 2 c/u possibility is apparently too good to be true, but the 4 c/u is friggin' spelled out in pictures on the Toys page, from 300 years ago..

..so it's totally game on, people!

There IS a physical mechanism possible, that embodies the 4 c/u trajectory above... and the Toys page, in conjuntion with MT's 30 thru 42 and 133 - 134 etc., describe the nature of the interaction that accomplishes this result.

Thus, each 'bang!' emanating from his wheels was dissipating half the per-cycle input energy..

..his wheels contained sufficient PE to cover the first 5 cycles.. (which, with multiple mechs per wheel could be half a turn or less, it's quite arbitrary, build-time aside)..

..Bessler's unit energy cost of momentum was effectively 1 J per kg-m/s or kg-m²-rad/s.. within a limited RPM range anyway.. (efficacy of the exploit was evidently still somewhat RPM-dependent, since a) his wheels didn't explode, and b) he explicitly wrote that they "gained further advantage from applied loads" - implying that their peak efficiency was at a lower speed than that which they were able to coast at, but with efficiency decreasing - the unit energy cost of momentum nonetheless rising - with increasing RPM.

So, the surgically-clean theoretical 4 c/u trajectory evidently comes with certain constraints when realised practically... the take-home being that there's a 'sweet spot' RPM margin for optimal momentum gains / counter-momentum destruction.


Note also that simply inverting the sign of counter-momentum - such as by aiming it upwards, to be returned by gravity, is NOT the exploit, since that would conserve all of the momentum and so yield a 2 c/u result instead. The 4 c/u outcome can only arise under two possible conditions: destruction / sinking / expunging the system of counter-momentum on a per-cycle basis.. and also, one further set of circumstances:

• Try repeating the first, 2 c/u example, only this time, make the non-accelerated mass 3 kg. Keep the accelerted one at 1 kg


• You should now find that, despite conserving all momentum and counter-momentum within the system, it's now been drawn out to a 4 c/u trajectory! You get the 25% accumulator again..


In fact, there's a simple back-of-envelope calc you can do to predict the gain trajectory / no. of cycles to unity / OU:

• simply add the ratio of the two interacting inertias together!


So with two equal inertias, 1 + 1 = 2 c/u (their actual masses or MoI's are irrelevant).

If one mass is 1 kg, and the other's 2 kg, then 1 + 2 = 3, so the system will reach unity after three cycles, and 130% at the fourth!

However since we know already that the '2 c/u' possibility is simply not on the cards - the exploit necessitates cancellation or destruction of counter-torque or counter-momentum - we can just double that sum - so 1 Kg playing kiss-chase with 2 kg will reach unity at 6 cycles and be making ever-fatter OU babies from cycle #7 onwards.

Likewise, a 2 kg-m² MoI in a series of 'spin & brake' cycles with a 10 kg-m² MoI has an inertia ratio of 1:5, and 1 + 5 = 6, so allowing for the requisite 50% momentum loss per cycle, the system would hit unity at the twelfth cycle, and 112% at the 13th... Geddit? Piss-easy huh?




So that's full disclosure. MT, and all the clues, are about the means to harness this KE gain principle.

If you really think it through (seriously, take a hot bath / sunbathe or whatever to dwell on it) - it's hard to disagree with Bessler's point that in "all true PMM's, everything must, of necessity, go around together" - in other words, that KE gains from a statorless wheel / effective N3 break really are the only game in town. There simply is no other possibility - no margins for doubt, even - anywhere else in mechanics / classical physics.

KE gains / mechanical OU is frickin' kids stuff - just fling & bang, repeatedly... flinging and banging, and flinging again.. so long as the 'flings' are reactionless, somehow (?), you can't not make energy. :|



So, obvioushly, gravity-assisted asymmetric inertial interactions are the name of the game. Gravity can be used to cyclically sink counter-momentum, or else, prevent its generation in the first place, such as by cancelling counter-torques. Spin & bang / brake / clutch / splat / crunch / land gracefully upon - basically any collision except bounces / boings - and you get a constant per-cycle efficeincy accumulator.

Just find some mechanism that literally articulates the accelerate & brake maths above, and you'll know it's working when it loses 75% input energy the first cycle, but only 50% on the second..

The Toys page and MT are obviously explaining a mechanism/s for achieving this.

The key for us is to understand what the gain principle is - the only thing it can be - because this is the context in which to be viewing MT and the Kassel engravings etc.

A pendulum with a wheel is a gravitating inertia with a non-gravitating one.

A wheel biased by a bucket spooling off the axle is a wheel biased to sink counter-torques applied to that axis, to gravity.

A scissorjack is a frickin' linear lever - it just converts a high-displacement, low force action into a low-displacement, high-force one. MT repeatedly shows us ways this can be used to couple GPE and MoI interactions.

We already know that GPE-GPE interactions are a zero sum, and that inertial interactions are likewise symmetry-bound by N3. Obviously, then, the symmetry break depends upon the interaction of gravity and inertia. Obviously, it's a gravity-assisted asymmetric inertial interaction, derp.

That's all it can be.

It's a wheat-and-chaff game, in every sense, but threshing momenta from counter-momenta is what this is all about..

"Driver" vs "driven", or sources / sinks, or causes / effects might be better fits to Bessler's thought processes than our modern concepts of "inputs" and "outputs". Likewise, he wouldn't have recognised the term "rectification" as we do, but that's precisely what he was doing.

My best bet is "sinking counter-torques to gravity on a per-cycle basis".

The GPE-MoI coupling afforded by the scissorjack is the key to decoupling the momentum yield from RPM - ie. gaining the same momentum, for the same PE cost, in spite of rising RPM, across some useful RPM range.

Obviously, those diametric or radial weighted levers have high MoI, but small displacements.

One or other of the torques or counter-torques involved in their operation is being somehow sunk to gravity.

This yields a constant momentum gain per cycle, which has a relatively small 'velocity' component, but high 'inertia' component.

Its constant, speed-invariant energy cost is the speed-invariant GPE of the 'angular lift & radial drop'.

So that same GPE output buys the same rise in net system momentum per cycle, or at least, at a rate that doesn't diminish by the square of velocity, across some useful RPM range.

Somehow, the confluence of 'over-balancing' torque, coupled with the sequence of positive-then-negative inertial torques caused by the radial translations, combined with radial GPE outputs, hustles a per-cycle net momentum rise from those weighted levers.. levers which are, more specifically, heavy angular inertias..


Finally, note also that this GPE-MoI coupling is going to transition every 180° - each time it rotates around 180°, the radial GPE drops, applying two opposing torques and their respective counter-torques to those high-MoI armatures..

..yet the Toys page shows two 'impetuses' for 180°, then only one for the next 180°..

..therefore it is evident that the asymmetric inertial interaction depends upon the different ways gravity interacts with the mechanism, when oriented in the two 180° phases..

..so it's not simply the same interaction repeated twice per rotation - rather, the momentum gain is the result of one complete turn of a given mechanism. Something happens differently when rotating 'under' compared to 'over'.. and the momentum gain through the full 360° is the result of that difference.


(Apologies to anyone who wanted 50,000 words or less. It's worse than that - you need a calculator! Eek! But hey precious little jargon, plain-english and just one equation.. all i currently have is summarised right here.)

[MrVibrating]

MrVibrating : I've also thought the 2 opposing levers with knobs looked like a couple of the hammer toy guys. So are you implying then that the movement of the weights was like in MT40 where one is going up while one goes down and this too is going on in the bottom half of the wheel but just the opposite? That's more or less like some kind of pumping action akin to the dodecagram is it not?

Silent

I don't know mate, i'm just relating the rationale that seems to jel..


Usually i'm cooking up and then testing prospective gain mechs based on attempts to 'actualise' the above maths..

..here however i'm digging for inspiration, trying to glean clues from Bessler about how these de facto components of a gain interaction might be fitted together.

The only real guiding objective is thus the thread topic, of regulating per-cycle momentum yields invariant of RPM, across some finite-but-practical RPM range. Accumulating equal momenta for equal costs is an inherently OU process - it literally manufactures kinetic energy from its raw components..


How exactly those lever arms operate in the working solution, is what i too am trying to ascertain. I simply don't know at this stage, only having deduced that they must, somehow, be causing a per-cycle net momentum rise via their interactions with gravity and inertial torques whilst overbalancing... but beyond that..??

Do the arms have to operate in opposite directions (clockwise vs counter-clockwise), or the same direction (like the prior chicken run mock-up), and what collides with what, exactly? Do the 'bulbs' terminating each lever strike the cross-bar, or what? Is it yet a literal design, or still somewhat figurative / demonstrative rather than strictly practical, with significant further refinements required?

I'm honestly not keeping anything back - least of all anything i think might be useful.

Get calculating KE gains from momentum gains from hypothetical N3 breaks, familiarise yourself with the way their efficiencies develop over successive cycles, then try deduce mechs that fulfill those conditions...

Soz it's so vague and general, for now, i'm sharing it cos it seems like concrete foundations; i still fully expect to fully and inevitably solve it, and this seems to me like the end-game - if it ain't done in this thread, it'll be the next one..

So, not exactly iron-clad, but either the Toys page is a red herring or else it really does depict an interaction culminating in "something extraordinary" arising in a 5-cycle envelope.. and if it's a KE gain, then it has to be a means for decoupling per-cycle momentum yields from RPM - because that's what 'mechanical OU' IS; the only physical embodiment it can plausibly hold, since KE=½mV², and thus "excess KE" - the notion that a mass or system could somehow possess more KE than half the product of its inertia times its velocity squared - is inherently oxymoronic, and not logically consistent. A system can only ever have precisely the right amount of KE for its given distribution of inertia and velocity. Whatever their product, half that squared is its KE, period. Thus 'mechanical OU' can only mean we've somehow paid less for our KE than it's worth... and that can only mean an effective N3 break, which in turn can only be attributed to vertical, statorless rotation in a gravity field.

To wit, "..it is elementary, Dear Watson!"

[MrVibrating]

..one further point to reiterate (which may involve MT 134, as you'll see)

• Once at its 'unity threshold', it makes not a jot of difference how the system arrived at that state..!


In other words, if you've spent 4 J of PE, and you have 4 J of KE, then what's it matter if it started out with 75% loss, or was simply accelerated straight up to its current speed via any conventional (ie. N3-respecting) means..?


What i'm driving at is that MT 134 may be making the point that in say a 4 c/u trajectory, the system (the pair of interacting inertias) could be primed up to its 'unity threshold' by any means whatsoever... it is only the 'fifth' cycle that requires a reactionless acceleration and collision..

And so that 'fifth' cycle could actually be the first, after having accelerated both inertias up to their unity threshold quite conventionally (and simply!)..

..the first 4 cycles in a 4 c/u trajectory are redundant! There may be no need to endure them or their losses... just spend 4 J to make 4 J KE any way you like, then input one more to add another 2.25 J (so 4 J to prime, then a further 1 J reactionless acceleration and collision raises the system KE to 6.25 J), and thus a 125% gain from the first cycle..

Again, simple stuff that just becomes obvious when you think about it.. (and i'm honestly not quick on the uptake)..

[MrVibrating]

Just pulling these outa me arse now - quite at random: MT 96.


MT 96 = same shite as the Toys page etc., using fluids instead.

• the water screw 'A' is the driver / input source

• its MoI is massively boosted by an attached 'flywheel'

What is a high MoI good for, but inducing counter-momenta and / or banking momentum?

So, like the input GPE's indicated in MT 40 et al, this water screw has maximal MoI, relative to its GPE load..

• the water is obviously the GPE

• it is output by being poured over two water wheels

Why two? Why double 'em up like this? It would have no obvious benefit to the energy efficiency of the interaction - no more work is going to be done by the falling water than its GPE, either way..

..unless it's not really about hydrodynamics at all, but rather a vessel for communicating a more abstract, general, point..

..the same message mirrored elsewhere in other related images?

..for instance, maybe they're paired up in analogy to the paired weight levers in so many of the other MT's?

In other words, maybe they come as a couple because paired output torques are the key to rectifying a constant per-cycle momentum gain..?

• the water wheels are also connected to a high MoI rotor (on the far left side of the page), via high-ratio gears

So one turn of the water wheels causes many rotations of that vertical 'flywheel' - IE. serving no other purpose than accumulating prodigious angular momentum, from gravity...

• "gears" = "scissorjacks" = power conversion, transforming low-force high-displacement work into a 'one-inch punch'

• the water wheels are in turn connected back to the water screw


There doesn't appear to be much if any power conversion in the gearing connecting the water wheels back to the water screw..

..also, it may be worth noting that being angled diagonally, half of the screw's momentum - and the counter-momenta being induced to the stator / frame - are aligned with those of the vertical high-MoI rotor driven by the water wheels, the other half being in the horizontal plane. Both high-MoI rotors turn in the same direction..

So in summary, Mt 96 shows a water pump / GPE interaction, with massively boosted MoI's for both the input and output workloads, accumulating maximal momentum from gravity - and quite probably, either showing an input / output momentum asymmetry (ie. more momentum is to be gained from the GPE drop than is invested in its lift, an 'up' vs 'down' momentum asymmetry), or an attempt to generate or harness or just allude to such a momentum gain..

• does the "NB.i" on the original print mean "nota bene"?

Either way it would appear the intention is to mark this interaction as significant, in some way.

Not to suggest there's anything viable about MT 96 itself - it's dependent upon a stator, so cannot isolate its system momentum, and can never achieve OU. However, if it's not intended as an actual prospect, but merely as a guide to the physics of interest, then its efficiency is moot..

TL;DR - MT 96 is 'about' generating a momentum asymmetry between input and output legs of a GPE interaction. It has the same fundamental physics components as the Toys page - power conversion / leverage, paired output torques, and high MoI values relative to the GPE loads for both input and output strokes of the interaction.



There's another little mystery in this particular series of MT's - the 'square vs circle' dichotomy, whatever this is meant to refer to...

For instance MT's 94 & 95 feature this 'square' vs ' circle' distinction...

..and what is the fundamental (if not sole) difference between MT 94 and 95, but their relative aspect ratios?

It's the same 'mechanism' (tho i hestitate to consider any of these as prospective 'mechs' so much as Kircher-era hieroglyphs, using much the same kind of basic logic as Carl Sagan's Pioneer plaque); the same interaction in both figures, but 94 is tall and slim with 'circular' axis, while 95 is short and fat and has a 'square' axis...


Now, just roll with me a minute, cos this might sound nuts at first..

..but in WM2D, 'square' vs 'circular' axes denote rigid joints versus pin joints - that is, if Bessler is using this same convention then in MT 94 the two GPE loads 'C' are free to rotate about their axes, while in MT 95 they're forced to rotate with the water wheel 'A' (which is inflected, ie. indicating an 'input')..

So how could such a convention arise? Again, an answer's suggested by WM2D - which re-uses it for slot joints, which can have free axes, able to rotate as they slide, and indicated by circular joints, as well as 'keyed slot joints', denoted with square axes, which slide but preclude rotation...

..so perhaps this notion of a 'keyed axis' - ie. a square axle thru a square hole in a wheel, thus preventing rotation, is somehow part of the solution to this particular symbolism..?

MT 100 features a prominent 'circle in a square' (item 'P') - so might this imply that a circle signifies torque applied or induced to an internal axis, with a square meaning a torque applied or induced to the net system?

Obviously, the hammer toys on the Toys page also feature this dichotomy, and the interpretation would seem consistent - the upper toy 'C' has a circular anvil, and causes internal rotations of the long weight-levers denoted by the lower toy 'D', which has a square anvil because it induces torques / momenta to the net system?


I'm doubtful further clues are even necessary, given how far we seem to have come; there's really only so many variations on the MT 40 / Toys page interaction, and one of them must produce a constant per-cycle momentum yield.. the efforts to decode everything will undoubtedly increase after we've replicated, and might take years.. but i don't see that we need much more from him to attain OU..

[silent]

.

[silent]

.

[agor95]

I know it sounds crazy, but maybe causing a mechanism to wobble slightly has something to it?

If you can't be crazy here were else could you go and not get locked up :-)

Look at the second smaller weighted toy - notice the twists in their bodies.

Then again a top that is going through an inversion, rotates faster along it's length with the energy gained from it's primary protation axis.

Good Searching

[MrVibrating]

@Silent - thanks for your thoughts mate, the interaction has to be a succession of reactionless accelerations and collisions though, since that's what makes mechanical OU. I'm fairly certain it only requires two dimensions, but we'll see..


Don't take this the wrong way - however you're still looking for the processes that fit together to actually cause and substantiate an energy gain; it's a mystery to you, as everyone else here, so you're looking to identify the elements that might somehow be indicated by the abstract clues, the interpretations of which might reveal a mechanism..


..and i'm kinda doing the same thing, except i've already identified the gain principle - albeit, as a general solution, that simply shows how KE 'gains' can only be manifested in terms of PE discounts on the energy cost of buying momentum. IOW, OU = cut-price momentum.

That process is simply a series of reactionless accelerations and collisions.


Strictly, only the former are needed to produce OU - if you are able to cause a reactionless acceleration, then the greater the starting velocity at which the reactionless acceleration is made, the greater its KE value / gain, relative to the fixed-price input energy cost of the momentum.

So for example if we can buy 1 kg-m/s of momentum for ½ J, regardless of our current velocity, then that reactionless acceleration from a standing start has a KE value of ½ J, or unity... but from an initial velocity of 1 m/s, it has a value of 2 J, so 2x OU (since we began with ½ J, spent another ½ J, and ended up with 2 J.


From an initial velocity of 3 m/s, that single reactionless acceleration of 1 kg by 1 more m/s has a KE value of 3.5 J (since we begin with 4.5 J, then spend ½ J to end up with 8 J), hence 7x OU.

From an initial velocity of 10 m/s, that single reactionless 1 kg / 1 m/s acceleration, costing ½ J, has a KE value of 10.5 J, since we began with 50 J, then spent ½ J to end up with 60.5 J, so 10.5 / 0.5 = 21x OU.

This is just using KE=½mV², and the simple indulgence of a hypothetical N3 break. Nothing else required - the 'KE gain mechanism' is simply the standard KE formula, applied to reactionless accelerations.

However to accumulate such momentum gains in a statorless system requires it to evolve over a succession of reactionless accelerations and collisions. This is how you build the principle into an auto-rotating PMM.


So the things i'm looking to interpret - the clues of interest - are anything that might be relevant to this necessity for accumulating momentum gains from gravity via a series of RA's and collisions.

So it's a guided search, rather than a blind one. I know exactly what it is i'm looking for. It has definite, unambiguous kinematic properties - there's zero fuzziness here; only a series of RA's and collisions can accumulate reactionless momentum from gravity for less PE than its resulting KE value. These facts are axiomatic.


So the kinematic elements of interest are torques, and the various available sources and types of them. Principally we're looking for an interplay of torques from different fields, interacting to yield a net gain.

These two fields can only be OB torque, and inertial torque, because that's all that's possible in a statorless wheel.

So the next step (for me at least) is to suss out how these two torque sources conspire to produce a per-cycle momentum rise with constant energy cost...

..but how those accumulations cause KE gains / OU is already fully solved. There is no mystery of how the energy gains were achieved - KE is substantiated / enumerated by the standard KE equation, ½mV², as it ever was.

Honestly mate, please don't take offence but you're still scrambling around in the dark looking for mystery magic, when all you need do is start actually using the standard KE equations, and calculating for yourself the KE value, and PE costs, of reactionless accelerations and collisions. That's it. That's what makes mechanical OU, period.

With that understanding it's simply a matter of applying the two types of torque in different sequences until you / i / we work one out that's viable - ie. having constant, speed-invariant energy cost across some RPM range.

Bessler didn't receive the working design from a burning bush, he instead worked it out from an understanding of the conservation of momentum and its hold over the conservation of energy / work potential.

Seriously - everyone! - you should all be playing with RA's, collisions and the KE formulas. That's all you need to demystify mechanical OU. Then it's simply a matter of identifying the general interactions that actually replicate what your maths results are doing.

Inertial torques are reactionless and conserve momentum, whereas gravitational torques are also reactionless but do not conserve momentum.

The really central, pivotal point underlying all this - and the core of the exploit - is that gravitational interactions are trivially capable of violating CoM, gaining or losing momentum over successive cycles. This momentum change is reactionless, incurring no counter-momentum.

So, use a time-delay to rinse momentum from gravity, then collide it into more inertia, rinse and repeat. That's all we're looking for. Accelerate, bang!, calculate, & repeat. Fill a page with quick calcs, then work out another alternative interaction and do another page of them. What we're looking for is lying under one of these rocks.. we just need to turn enough of 'em over.. and when you think you might've found it, then go back to Bessler's woodcuts to look for relevancy / confirmation.

[MrVibrating]

OK MT 43.. the seemingly out-of-place spirally thing attributed to "the well-known Professor Mangold at Rintein"

Just a real quickie this time - the 'flat A' used to denote the wheel body identifies it as an output field.

Thus it rotates counter-clockwise, caused by the weights getting lower by displacing the spiral track of the wheel beneath them; the ball-weights are pulled downward by gravity, so roll 'downhill' by causing the wheel to rotate, instead of moving around themselves with the wheel, they just want to drop straight downwards.

At the bottom, running off the end of their spiral tracks, they pass through a hole / gap (not apparently drawn / visible) in one radial beam, before being caught and re-lifted in the angular plane by the next radial beam, now lying in front of the spiral tracks, and able to roll back into the center as that beam they're caught on rotates upwards (per the lone weight on the right).


Previously i'd thought the interaction was supposed to be read in the clockwise direction, so this is another new revelation for me - a new way of applying OB torque / GPE interactions!

As they're not actually 'going around together' with the wheel itself, they're under no CF force.. and contributing only their axial MoI's (about their own axes) to that of the net system, hence here is a way of using weight drops to generate torque without causing inertial torques! An alternative to radial lifts / angular drops and their inverse..

Obviously it's not OU (not an asymmetric gravitational interaction WRT energy), but as a potential momentum asymmetry it might show a bit more promise..

Will have a play in WM tomoz and see what falls out...

[silent]

.

[MrVibrating]

Been having a bit of a stupid fortnight meself here, zero progress since last updates..

..just one idea keeps bubbling up - probably nothing, but it's a slight variation on the discussed 'MT-40-ish' proposal:

• as before, a radial GPE drops down the centerline

• but instead of connecting to those diametric weight levers, these are replaced with scissorjacks..

• so you have a pair of diametric scissorjacks, which function in exactly the same way as diametric weight levers, except now their length is variable on the fly..


You can prolly see where this is going:

• MT 40 et al convert that radial GPE drop into paired lifts of those diametric weight levers. MT 133 also features the diametric levers, however MT 134 ditches them in favour of radial weight levers - ie. pivoting from the hub, rather than from the opposite rim... surely then this is a development?

• So what can radial weight levers do that diametric ones cannot?

Answer - rotate in one direction only!

•• Diameteric weight levers require a 'reset' stroke

•• So if the radial GPE drop converts to a 'one inch punch' via a scissorjack, used to apply counter-torque to the net system by lifting one or both of those diametric levers, any momentum so produced is gonna be undone by the reset stroke 180° later.

IOW, diametric weight levers seem useless for applying a consistent torque / momenta in one direction. If you can get a clockwise impulse from the first 180° cycle, you'll inevitably have to incur a counter-clockwise one 180° later, in order to manifest the clockwise one again after a full 360°.

This is obviously useless for generating a consistent impulse in either direction. Diametric weight levers, in terms of being a heavy MoI to torque the net system against, only seem good for wobblers, not runners.

Besides, Bessler seems to always show them in opposed pairs, both activated together, hence each radial GPE drop would be applying equal opposing torques by activating both diametric levers at the same time...

..the problem then would be, how to rectify a net torque in one direction? Doesn't seem possible, does it?


So, on the one hand, diameteric weight levers maximise the MoI that can be fitted inside a given wheel size, and so maximising the counter-torques / counter-momenta that can be induced to the net system..

..but they seem futile for doing so in a consistent angular direction!

•• Whereas, radial weight levers (per MT 134) can be consistently torqued in one direction!

So in the first 180°, the radial GPE drops, using the scissorjack to apply a 'one inch punch' to a radial weight lever, and in the next 180°, the GPE undergoes an angular lift then radial drop, again converting via the jack to another one-inch-punch, again torquing the radial weight levers in the same direction as the previous one.

So two impulses per 360°, both in the same angular direction.

We'd be compromising the absolute magnitudes of the impulses possible - basically halving them - but gaining the ability to apply torque in one direction only..

Of course, this still assumes we have some way of sinking the counter-momenta to gravity, however... so not any kind of done deal, yet..


Essentially, we're talking about torquing the net system in one direction, by torquing these internal radial weight levers in the other direction, whilst somehow sinking the counter-momenta to gravity. It's still not exactly compelling progress is it...


But then another idea occurred to me; what if we stick with diametric weight levers after all - since he keeps depicting them all over the place in so many different MT's from start to finish - but modify them slightly...

I'll just throw it out there:

• what if the diametric weight levers are instead composed of scissorjacks? Then their lengths are adjustable..

So they're still pivoted on opposite sides of the rim, and still require a 'reset' stroke every 180°, however now, their lengths can be changed between each 180° stroke, thus:

• Radial GPE drops, again converting to a 'one-inch-punch' via central vertical jacks

• But one diameteric weight lever-come-scissorjack is short, whilst the other is long; activating both together thus yields a net torque in one direction

• 180° later, having been lifted in the angular plane, the radial GPE drops a second time, but now the diametric jack-levers have swapped lengths - one's retracted, the other's extended - and so now the second stroke also produces a net torque in the same consistent direction as the first..

This preserves the benefit of being 'diametric' and so maximising the MoI in the available wheel-space, whilst also applying consistent net torques in one direction...


LOL when i made this doodle all those years ago:



.. i got the interaction back-asswards, thinking the levers were inputs rather than outputs (duh!)... but maybe that wasn't the half of it... maybe they're just stand-ins / placeholders for diametric weight levers with adjustable lengths, and thus alternating MoI's..?

So, on the first 180° the left one's long and the right one's short, then 180° later they swap lengths - ie. one extends, the other retracts - and so again the left one is long and the right one's short...

..thus each time they're activated (together as a pair, by the radial GPE drop), a consistent torque in one direction is produced..?


Maybe something for the weekend...

[MrVibrating]

..cuz how else could you get a momentum gain from paired opposing MoI's?

MT 133 & 134 both indicate a uniform directional bias, in the shape of the hammers around the circumference, yet if the levers on opposite sides move at the same time in opposite directions, it's a zero sum..?

And then, why use hammers to depict this directional bias, unless impacts are involved? And we know impacts are an essential ingredient for consolidating per-cycle momentum gains; no impacts / collisions, no closed-loop momentum or energy gains...

I think this is something i'm only gonna puzzle out by experimenting.. will just have to sim it to see what happens..

[MrVibrating]

..just for completeness, here's that last rig i was working on, with dual metrics on everything (net P*t integrals, plus discrete F*d integrals on every constraint):







MoI Act 1 = 768.2431817

MoI Act 2 = 771.0684407

GPE Act 1 = 105.5792823

GPE ACt 2 = 123.154366

Spring 1 = 0.570052622

Spring 2 = 9.728299083

Spring 3 = -9.222925453

Spring 4 = 8.962049633

Damper 1 = -396.0768097

Damper 2 = -406.8696886

Damper 3 = -395.6678295

Damper 4 = -405.8276746

Brake 1 = -0.220322397

Brake 2 = -0.298670443

Brake 3 = -0.471863647

Brake 4 = -0.106597081

Net Losses P*t = -1605.185163

Net Acts P*t = 1766.150143

Net Spring P*t = 10.02715926

KE Rise = 168.51752

EPE change from: 82.41801 to: 76.58822




Mech 1 MoI control:

MoI Act 1 = 768.2431817 - Damper 1 = -396.0768097 - Damper 2 = -406.8696886

Dissipated = 802.9464983 = 34.7033166 more than MoI Act 1 supplied

Springs 1 & 2 output 0.570052622 + 9.728299083 = 10.298351705

34.7033166 - 10.298351705 = 24.404964895 J excess




Mech 2 MoI control:

MoI Act 2 = 771.0684407 - Damper 3 = -395.6678295 - Damper 4 = -405.8276746

Dissipated = 801.4955041 = 30.4270634 J more than MoI Act 2 supplied

Springs 3 & 4 absorbed -9.222925453 + 8.962049633 = -0.26087582

30.4270634 + 0.26087582 = 30.68793922 J excess



Total 24.404964895 + 30.68793922 = 55.092904115 J more energy dissipated by the two MoI-control dampers than generated by the two MoI-control actuators




OB / GPE Mechs 1 + 2 = 105.5792823 + 123.154366 = 228.7336483 J

Net Brakes F*d = -0.220322397 + -0.298670443 + -0.471863647 + -0.106597081

= -1.097453568 J dissipated

Plus KE rise = 169.614973568 J net output on GPE mechs 1 & 2

228.7336483 - 169.614973568 = 59.118674732 J input so far unaccounted

Minus the excess from the MoI mechs = 4.025770617 J loss from the GPE mechs



Net Acts F*d = 1768.0452707

Net Acts P*t = 1766.150143

diff = 1.8951277 J




Net Brakes F*d -1.097453568 + Net Dampers F*d 1604.4420024 = 1605.539455968

Net Losses P*t = -1605.185163

diff = 0.354292968 J


Net Acts P*t minus Net Losses p*t = 1766.150143 - 1605.185163 = 160.96498

KE rise = 168.51752 = 7.55254 J

Minus Net spring P*t = 10.02715926 J

diff = -2.47461926 J loss



In summary the '10 turns' target was completely arbitrary; over single cycles (or parts thereof) i'm satisfied this solves to unity.

I'd previously been concerned that F*d integrals over looping displacements mightn't be valid (since we're no longer looking at an 'area under a curve' in the traditional sense), however having actually gone ahead and tried it anyway, it does appear to be a legit procedure.

..which in turn means that there's no system now that can't be solved reliably. Lotta work doing it this way, but needs must..


The latest interaction i've been considering is still too wooly to dive into straight away, since:

• alternately varying the lengths of the paired diametric weight levers cannot, in and of itself, cause a momentum rise.. (duh)

Obviously, when such a lever is pressed into motion, counter-momenta are induced, and when that motion ceases, we again induce equal opposing counter-momenta, so no net change.

So varying the lengths of the diametric levers ain't gonna be enough, by itself; counter-momenta still need sinking to gravity..

..this makes me doubt that it's even worth trying, for now.. what really matters is precisely how any counter-torques are being earthed..

Plus, no MT seems to show anything like this - that is, diametric levers with varying lengths. Could this be because they're too close to the mark and were removed "following the arrest"? Or else, it's just another false start, perhaps..





But if the diametric levers have fixed equal lengths, then there's doesn't seem any way to selectively sink their counter-momenta to gravity if both are activated at the same time!? They'd just be irrelevant, wasting energy for no net momentum gain...

..so i'm currently back to a blank page. 'radial GPE output to one-inch-punch via scissorjack' seems like a good start... it's just a matter of figuring out what the hell that 'punch' is supposed to be displacing, in order to rectify a net momentum gain from it.

Soon as i think of something (or likewise, anyone else following), i'll jump to it. For now, though, it's chin-scratching time.. (no longer having a beard to stroke)..