Decoupling Per-Cycle Momemtum Yields From RPM

[MrVibrating]

I've been investigating various different conservative interpretations of the 'quarters' riddle, playing with both angular and linear systems (too much to document now)..

..however one discovery is that a scissorjack can form a kind of linear 'vMoI':



..due to varying leverage as a function of the changing ratio of angular to linear displacement of the scissor sections..

..and lo and behold, a seemingly-intrinsic 'four-factor' emerges in the time rate of change of momentum, beginning at 8 p/s when the links are mostly-vertical and dropping down to 2 p/s approaching horizontal / full extension!

Possible tie-in with MT 41; 'vertical application' having 'more inertia' (as opposed to 'more friction' as translated)..?

'Inertia', remember, effectively being a function of acceleration and not just mass; power conversion - ie. leverage ratio - between the dropping and horizontally-translating masses is changing throughout the interaction - in essentially the same way as a rotating 'variable moment of inertia'.

Makes you wonder if closed-loop 'kiiking' can't also be achieved in a linear or mixed linear / rotating system to dodge CF force and thus the absolute / ground FoR..?

IOW, potentially, 'relative', rather than absolute, kiiking, hence decoupling PE in the accelerating frame from KE in the ground frame..?

If the drop-weight were replaced by a swinging pendulum, might the whole thing - jack plus swinging pendulum - gain linear horizontal momentum, driving itself along sideways, in much the same way a weighted vMoI spins up..?

Again it'd be a matter of phasing the 'left vs right' or 'upswing vs downswing' accelerations relative to the variations in effective inertia, only without rising system velocity compounding the internal workload via CF force.. any moreso than 'a crab, crawling from side-to-side'..

IOW, then, kicking out tangentially in a rotating FoR; 'sideways' / linear action being automatically translated into angular counter-momentum of a rotating system about its axis..?

IOW inducing linear momenta from G&t in the first instance, via CF-force-exempt asymmetric inertial interactions in the tangential plane, rather than CF-force-facing radial plane..

IOW the asymmetric inertial interaction 'thinks' it's only moving sideways.. so holds the same internal efficiency, invariant of rising RPM..?

Think about it - a sideways-scooting asymmetric inertial interaction - still gaining momentum from gravity and time, via an under-slung pendulum, but in the linear / tangential plane (ie. orthogonal to radial) - thus applying 'top-spin' / 'bottom-spin' and 'side-spin' counter-momenta to a wheel system..?

Note that such a pendulum needn't be driven by gravity alone - a motor could supply it the necessary input torque * angle; the objective would simply be to pit up or down-swings against more or less linear inertia, thus causing asymmetric distributions and consistent per-cycle yields / PE costs..


Gonna play around with this, see if i can't make a linear scooter on a rail accumulate horizontal momentum.. cuz if that works, then damn.. elegant solution, no? OU linear motion may yet precede angular..

[Tarsier79]

I like your thinking.

I investigated different MOI wheels geared together etc. I managed to make it look like energy disappeared, but couldn't reverse that interaction.

I believe any theory of operation, linear or rotational MOI should be interchangeable.

I also believe MOI is directly related to energy.

[MrVibrating]

Here's the effect using a regular pulley instead:



..causing less of a variation; the decreasing ratio of angular to horizontal displacement of a simple lever or scissor link really seems to be the key - and for that matter it looks like you can get more variation from a single well-placed lever than an entire scissorjack..

Comparing the previous 'OB redux' drops that exhibited constant dp/dt - even in spite of changing MoI - here it's variable..

One big difference tho is that in the previous tests the weight was pulling directly on the non-gravitating mass; here it's leveraging against the jack's fulcrum, which is anchored stationary, as to earth.. So, if this is gonna work, that anchor point needs to be horizontally mobile - the pendulum swinging from it, hopefully propelling the whole thing sideways at an accumulating velocity each full cycle..

Definitely in 'crazy' mode here i think, but will try take a go at it tomorrow..

[Tarsier79]

It will always be variable due to the angle of the levers. As yo push a scissor jack out, it becomes easier at the end. It is directly due to leverage. Also, your first green lever doesn't appear to be at the same angle as the blue levers to start with,.

[Art]

Here's the effect using a regular pulley instead:



..causing less of a variation; the decreasing ratio of angular to horizontal displacement of a simple lever or scissor link really seems to be the key - and for that matter it looks like you can get more variation from a single well-placed lever than an entire scissorjack..

Comparing the previous 'OB redux' drops that exhibited constant dp/dt - even in spite of changing MoI - here it's variable..

One big difference tho is that in the previous tests the weight was pulling directly on the non-gravitating mass; here it's leveraging against the jack's fulcrum, which is anchored stationary, as to earth.. So, if this is gonna work, that anchor point needs to be horizontally mobile - the pendulum swinging from it, hopefully propelling the whole thing sideways at an accumulating velocity each full cycle..

Definitely in 'crazy' mode here i think, but will try take a go at it tomorrow..

Bessler's drawing of the storkbill on the toy page , has a very definite taper from the bottom "cell" attached to the handles to the top cell with attached weight (point / arrowhead).

Each cell differs from the previous one by roughly about a factor of 20 % .

This would mean that each cell feels an increase of approximately 20% more
leverage than the previous cell , ( look at each cross across the pivot in each cell as being a lever around a fulcrum with the input end of the lever being 20 % greater (longer) than the output end of the lever )

I have frequently wrestled with trying to figure out what effect this would have on the MOI of the weight on the storksbill and have never managed to explain it to myself with much confidence.

It would be really nice to see it compared to the above scissor jack using the same constraints .

I bet you could do that VB with one arm tied behind your back ! : )


----

Tarsier --"I managed to make it look like energy disappeared, "--

Yes , --I can show you countless builds where the energy does more than it "looks like" disappearing ! : )

[daxwc]

Art:

Each cell differs from the previous one by roughly about a factor of 20 % .

There is also a Phi connection in that the first two diamonds is Phi to the previous two. It only works in pairs and it only works backwards.

[MrVibrating]

Happy hols everyone!

Minor update:

• trying to accumulate linear horizontal momentum from G*t is of course an act of futility, as best i can see..

..ie. consider a pendulum that's also hanging from a horizontally-sliding carriage on a slot, and interacting via a linear force with a non-gravitating mass also sliding horizontally on the same or a parallel slot: the system reduces to a basic linear interaction respecting N3, plus an angular interaction between the pendulum and slot / earth, also obeying N3.

It makes no difference if the conrod connects the sliding mass to the pendulum's bob or shaft, or likewise if the conrod's also a linear actuator (so for instance you could apply an internal linear force that cancels gravity's downwards acceleration of the pendulum, just accelerating the non-gravitating mass instead); no matter, N3 don't even blink..


It does segue neatly into the next avenue of investigation tho:

• is it possible to cause a divergent inertial FoR in the radial plane, instead of the rotating plane?

This obvs can't simply be an inertial interaction with the earth via the wheel's fixed axis / support posts - rather, we want to accelerate a mass in the radial plane, against some other mass also in the radial plane, 'reactionlessly' - ie. roping in gravity and CF forces, somehow..

Will be following up this question next..

[MrVibrating]

Last idea was stoopid - no way to decouple the radial and rotational KE changes if using CF force as a 'stacking force', so it's a hiding to nowhere..

Since then i've gone back to what seems the crucible 'cross-piece' in MT, of radial action coupled to paired angular displacements.

Not expecting to get far before hitting the "Doh!" moment on this one, but in particular i've been wondering some more about diametric weight levers.

IE. weight levers spanning the diameter, rather than just radius, and so passing thru the axle.

Consider a pair of such levers pivoting at opposite sides of a wheel, oscillating / swinging through small, equal arcs in synchronised motion.

They could both swing in the same angular direction, or opposing directions.

To spice things up, add a vMoI to the wheel - IE. a balanced pair of masses that can be drawn inwards and outwards radially, substantially changing the wheel's MoI and so causing +/- inertial torques per the ice skater effect.

Because the diametric weight levers are oscillating / swinging, they reach peak velocity at the 'top' of their swings, IE. mid-way between apices.

Likewise, the vMoI is phased to match this speed variation; arriving at the center / minimum MoI at the same time that the levers are at the peaks of their swings.

You can probably already see the 'logic' going on here:

• if the diametric weight levers are swinging in alternate directions, then their counter-torques should cancel out, the wheel continuing to rotate at constant speed

• if the net system's accelerating however from the additional inertial torques, the two levers will be undergoing asymmetric / non-cancelling changes in +/- momentum about their respective axes / pivots..

• ..that non-zero sum causing a corresponding equal opposite change in momentum on the main wheel axis, per N3


IOW it seems like it might be possible to vary net momentum, without recourse to an I/O gravity * time asymmetry.

IE., non-constant momentum, despite the absence of gravity from the equation.

If such a transient variation in net system momentum is possible without even using gravity or 'weights', might they yet have some use in rectifying a constant time-rate of change of momentum each cycle?

IE. might such closed-system momentum variations, in conjunction with inelastic collisions and/or GPE interactions, present a potential gradient upon which we can carve out a 'staircase plot' of constant per-cycle momentum gain at constant input energy / work done?



In every past instance i thought i'd found a way to vary net momentum - violating N1 - without using gravity, it turned out to have been a stupid mistake.

The hard lesson learned each time is that whether 'gravity' is present or not is a sure-fire indicator of whether the supposed CoM violation is real or not..

So, caveat emptor, as usual - i'm a complete idiot and this whole thing's nuts..

Next i'm gonna methodically work thru a set of sims, without gravity, metering MoI and angular velocity - both about the central wheel axis, as well as the diametric lever axes; the levers will be powered by 'motors' / rotary servos, as i'm interested in their respective momentum variations about those axes, and their equality, especially when under the additional inertial torque on the main axis.

[MrVibrating]

Here's the rig:



Pretty self-explanatory, but for clarity:

• the mr² of all six components are summed to give the wheel's instantaneous MoI

• that MoI gets multiplied by the wheel speed to plot net momentum about the wheel's axis

• likewise the fixed MoI's of the levers are multiplied by their motor speeds to plot their momenta relative to those motor axes; additionally plotting their 'absolute' momenta as a function of thier MoI times the motor speeds plus wheel speeds

• finally, those two momentum meters on the wheel and levers' axes are simply summed together - the right meter summing the outputs from the blue and green ones to its left - again, using both 'relative' and 'absolute' metrics of the levers' momenta

The parts are basic:

• the levers are thin steel 'poles'

• both bobs, and vMoI masses, are 1 kg each

• the wheel body is 1 kg * 1 m radius disc, planar MoI

• there's a motor (rotary servo!) swinging each lever

• and also a pair of linear actuators for the 'vMoI' masses


Final points:

• not interested in energy / CoE for now, just CoM

• the wheel begins askew as the first 10° of rotation are used to initialise the system, so that it begins each run from the same initial coasting speed, in whichever mode of lever sync is selected; to this end a central motor drives the system up to a starting speed of 1 rad/s, upon which it disables and is replaced by a basic pin joint: the system then pauses, primed and ready to run, the clock at 't=0'

Gravity is off, remember..

So next, i'll begin by looking at examples of equal vs opposing lever directions, first with a constant wheel MoI / no inertial torque, and then with it; this, hopefully, unpicking the causes and effects of any resulting anomaly.. or lack thereof.

Again, i'm an idiot - and gravity is disabled. Just to keep both points in the forefront, here.. IE. by all rational expectations, N3 and N1 should be respected and observed..

[MrVibrating]

So here's the first run, opposing lever directions, thru 180° of system angle:




..Pretty much the expected result - the bobs' arcs bringing them in slightly closer to the wheel center, causing a slight drop in wheel MoI, but the net momentum's basically pegged. There is a slight variation in net momentum on the wheel axis - i don't know if it's realistic or not, but it's nothing to write home about either way; enough to write down to imprecision (tho i can see no error source thus far).

Note how the relative vs absolute metrics on the levers' momenta about the motor axes are comprised of equal opposing components.

The instantaneous 'delta-L' sum is likewise constant.

So, apparently nothing to challenge Newton here..


Next, the lever directions will be matched, such that both swing in the same angular directions at the same time.

Then the same two tests will be repeated, whilst also applying inertial torques from the vMoI..

[MrVibrating]

So, inverting the lever sync:



Egads! If there's an error here, it's getting harder to ignore..

No matter which frame we take, we're apparently seeing non-constant net momentum in an ostensibly closed system..!?

Just to be clear, the purpose of summing the wheel and motor changes in momentum was that if net total was constant then any variations in that of the wheel or motor axes would cancel to net zero..

..and as you can see, if they did before.. they don't now!

So, umm... let's bring the vMoI into play, see how that affects these two results..

[MrVibrating]

And now things start getting really weird:



• again, very slight variation on the wheel axis

• the strange thing tho, is that while relative I/O +/-dL/dt was nigh-on constant, the frickin' absolute value, in the external, ground FoR, smoothly rises then falls again!


Yes i've triple-checked they're not labelled back-to-front - i'll attach the sim at the end so anyone can see for themselves - but it looks for all the world as if CoM in the absolute frame has somehow been supplanted by CoM in the relative frame.. yielding a transient net rise!?

If we just bang that there lump on the 'ead, mightn't we siphon some off the top, like?

But i'm getting ahead of meself; one more round: levers in same direction, with inertial torque from the vMoI..

[MrVibrating]

Lordy!



..so the absolute momentum variation on the lever axes has now also been applied to the wheel axis!


What dark magic is this? Eyeballing it, but looks to be around a 50% fluctuation in net momentum there..


No gravity. Just two swinging weight levers, and the ice skater effect. Plus one idiot.


Is this real? If so, can it be rectified and accumulated at fixed unit energy cost? Stick around to find out..


Sim attached.. have at it!

[MrVibrating]

Here's the final freeze-frame, just panned out in time a bit:




..really puts the anomaly in perspective..

..one hell of a blip in N1 there, no?

[MrVibrating]

Right then, whack-a-mole time; if we keep boshing it on 'ead at its climactic peak, like, we should be able to cream off the difference into a co-rotating / coaxial MoI; per usual, if this secondary MoI is in 1:1 ratio with the wheel MoI, then the pair o' them, as a 'net system', should accelerate by half the peak per-cycle variation, dissipating half its energy while net momentum climbs one step at a time, typical staircase plot style-e..

First off tho i should prolly set up some energy metrics, see what kind of efficiency we're currently looking at for this so-called reactionless AM..