Decoupling Per-Cycle Momemtum Yields From RPM

[MrVibrating]

In order to better budget the distribution of a given RPM's available momentum-from-gravity yield, perhaps it can first be 'buffered' into a vMoI; then it could be collected in a single swift action and released as required, thus somewhat independently of the timing or angle of the GPE output it was sourced from..?

For example, we could use a drop-weight over some finite height to accelerate a wheel with a widening MoI, the negative inertial torque perfectly cancelling gravity's acceleration, and thus collecting all of the output GPE as CF PE - as by loading a spring, say - with zero rise in rotKE..

..then, setting the fallen weight aside but without yet re-lifting it..

..we're left with the spinning wheel - all of the drop's G*t momentum yield has been gained in the 'MoI', rather than 'velocity' component, so, we have it already onboard, regardless of the ensuing RPM rise relative to the ground frame / G vector.. we're not yet relifting nor re-dropping the weight remember..

So we could now use that 'stored' momentum from the drop to sink counter-momenta - applying torque to an onboard fixed MoI, against the positive inertial torque from retracting the variable-MoI - the latter is thus losing momentum from having its MoI reduced while being prevented from accelerating to conserve AM, while the former is 'changing it up' into 'velocity' form, thus progressively inching-up its velocity and thus squaring KE value in the ground frame, yet at linearly-summing PE cost..

Bashically: use a vMoI to swiftly buffer output momentum from gravity, then use its controlled release to cancel counter-momenta from internal angular accelerations - a kind of two-step 'chicken run', thus isolating momentum yields as a function of RPM, from the inevitable angular accelerations - and thus accelerating rate of GPE interactions that would otherwise entail - caused by their accumulation.. IOW allowing some breathing room, or 'free displacement space', with which to simply express and manifest a KE gain in the first place, without causing it to extinguish its own ultimate momentum source..


"Mmm - momentum sauce".. must be dinnertime..

[agor95]

Hi MrVibrating

A person has 1 bugger and cooks it to perfection in a set period of time.

Then 4 buggers at four times that period.

Oops - cooked to much.

:)

Anyway your are a little text heavy for me. However you are going in the right direction.

P.S. The dropped weight is lifted with spring. The K.E. is stored in rotation. vMoI always useful.

Cheers

[MrVibrating]

..just for a visual re-cap of what i'm currently considering, from earlier related examples:

Here's a basic G*t to MoI exchange:



..as i say, this can be idealised in any way, so, controlling negative inertial torque to hold say speed or rotKE constant against gravity's acceleration.. gaining all momentum in the 'MoI' dept. instead..

Next, here's a fixed MoI being accelerated against the positive inertial torque from moving radial masses back in:



..thus successfully sinking all counter-momentum to inertial torque, but at expense of sacrificing precisely as much angular momentum in the 'gain' direction as had been 'reactionlessly'-imparted to the fixed MoI.. no actual momentum gain, or, thus, energy gain, possible without gravity in the picture..

The difference this time of course being that the vMoI will only be shedding angular momentum sourced from gravity, periodically going back to scoop more, just, not before the asymmetric inertial interactions are OU..

And finally, here's a 'chicken run' - a spoofed 'OU' system that's actually grounding counter-momenta via a hidden motor:



..why so gake and fay? It's just a visual reference for what mech. OU would look like, if the stacking force wasn't actually also performing displacement, as here.. (and yes the metering's a little flaky but a) WM sucks at variable handling and b) can't polish diarrhea)..

So basically the full cycle i'm considering is: load the vMoI with the momentum from gravity, use it to sink CM's from a 4x4 inertial acceleration, thus bagging the PE discount / 'KE gain', before finally resetting the GPE with it..

No so ambitious, really - bit busy tomorrow (fracture clinic), but unless a better plan becomes apparent i should make a start within days..

[MrVibrating]

Hi MrVibrating

A person has 1 bugger and cooks it to perfection in a set period of time.

Then 4 buggers at four times that period.

Oops - cooked to much.

:)

Anyway your are a little text heavy for me. However you are going in the right direction.

P.S. The dropped weight is lifted with spring. The K.E. is stored in rotation. vMoI always useful.

Cheers

Cheers guy, but first and foremost this is my ongoing research notes for me - for my project - not pre-releasing a book here..

..on a roll right now and barely wasting a word imho.. seem to be making real progress..

Buggered if i quite get your riddle but sounds eye-watering..

[MrVibrating]

SN8 15 km hop imminent:

https://www.youtube.com/watch?v=OLpN8Cco3mU

..look at 'em paying for 'velocity' relative to the ground, derp..



"What if i were to teach the proper method of mechanical application?"

[agor95]

Hi M

I am watching the StarShip - yer right which star is this heading for Sol?

[MrVibrating]

As previously noted, the absolute amount of momentum that can be obtained from a given drop is somewhat arbitrary, if we're prepared to collect it all in the form of raised MoI instead of velocity..

..however there's a minimum amount we're going to need to sink the counter-momentum from the inertial interactions:

• each 1 rad/s acceleration of 4 kg-m² is 4 kg-m²-rad/s of momentum..

• ..times four, means we need to scoop 16 kg-m²-rad/s from each GPE drop, to sink all 16 kg-m²-rad/s of counter-momentum that's going to be produced

Thus it's perhaps feasible to automate the scooping to open the MoI as far as required in order to collect that 16 L each drop..

..the instant the weight lands / reaches BDC, detach it, then begin the spin'n'brake cycles whilst cancelling their counter-momenta with the ice-skater effect, ie. by pulling the masses back in..

Might as well make the four rotors also double-up as the 'vMoI' masses - ie. moving the rotors themselves in and out to produce the inertial torques..

So basic systm i think could look like this:

• central 'hub' MoI = 1 kg-m², and comprised of:

• ..4x 4 kg-m² radially-sliding 'rotors'..

• ..their radii controlled by linear actuators..

• ..their spin'n'brake cycles by motors..

• ..plus a 1 kg drop-weight, spooling off the wheel over 1 meter of height


Pretty simple & familiar stuff, shouldn't be a problem.. (and yes, axial MoI's can be > orbital MoI, just a consequence of MoI=mr²)

[MrVibrating]

Hi M

I am watching the StarShip - yer right which star is this heading for Sol?

i think the Sol colonisation plan's much later - the immediate objective basically just 'falling, with style'..

Looks almost ready... tenterhooks, eh!?

[MrVibrating]

Well so much for flying soda cans eh..

Still, better news here - i've just confirmed that the energy cost of reducing MoI at 1 rad/s from any initial value (i began at 200 kg-m² * 1 rad/s) by precise 1 L units is exactly ½ J each.. rising linearly with RPM; so if RPM doubles, so does the energy cost of cancelling 1 L of counter-momentum.. IOW not squaring!

If instead of making the MoI of the central 'orbital' axis 4x lower, i make it equal to the net of the four axial MoI's - so a 1:1 MoI ratio - each braking phase will accelerate the net system by 50% of the per-cycle relative acceleration - so if both net axial and orbital MoI's are 1 kg-m² and each cycle causes a 1 rad/s reactionless acceleration, sinking 1 L of CM and accelerating the net system by ½ rad/s, that only raises the cost of the exploit to ¾ J / L.. yet that could accelerate the axial MoI's by twice the KE..

Prolly make a start in the next few days..

[Tarsier79]

That is odd, because when I was playing with MOI, the inertia aligned with COE.

Also, If you think a spring can transfer momentum, just test it. Compress a spring to the same amount and shoot 2 different weights vertically to calculate GPE.

[MrVibrating]

"MoI aligns wth CoE"

Inertia is a component of energy and momentum; ratio of interacting inertias determines collision losses.

CoE is broken by an effective N3 break - ie. by a CoM violation - not by 'inertia' or any MoI change.

Raising MoI while rotating can perform work loading a spring - ie. loading it with 'CF PE' - and whether it's going in or out, each ½ J change in CF PE at a constant RPM of 1 rad/s for a 1 kg radially-sliding mass causes a 1 kg-m²-rad/s change in angular momentum.

Basically, radial translations only conserve angular momentum if the rotation is allowed to accelerate or decelerate in response to changes in MoI..

..whereas here, those inertial torques are going to be perfectly cancelled by counter-torque from spinning up the onboard rotors - basically using the vMoI as a kind of co-rotating 'stator' - something to push or launch off against, that will be unyielding - not counter-accelerating per N3, as a fixed-MoI would, but rather holding constant RPM, due to these compensating inertial torques counter-balancing the counter-torques.


The exploit is this:

• each kg-m²-rad/s of 'reactionless' AM applied to the onboard rotor/s will require a 1 kg-m²-rad/s loss of momentum on the shrinking-at-fixed RPM vMoI

So no momentum rise at this stage, just transferring it from the vMoI, to the onboard rotor/s.

• each such transfer costs say ½ J per 1 kg-m²-rad/s of input work against CF PE on the vMoI, plus the torque * angle in the rotating FoR.. however the rotKE rise on the rotors can be more than this, because KE squares with RPM

• each braking phase redistributes that momentum back to the central 'hub' axis accumulating it

So net speed and energy evolution will be characterised by staircase plots..

Note, there will only be one, initial GPE output - all but a formality (since it'd make little difference no matter how the initial 9.81 J of KE was imbued to the wheel) - but 1 kg will drop 1 meter onto some kind of resting surface and then, just sit there for the rest of the action..

The onboard rotors will be given MoI's of 4 kg-m² net, which will be asymmetrically-accelerated then braked by 1.1 rad/s, four times in succession, using only the angular momentum picked up by the initial 9.81 J GPE output.

Thus the full interaction will try to follow the riddle - or at least its offered solution - as closely as possible.

The preliminary test i ran before bed last night simply checked that each 1 kg-m²-rad/s of AM bled from the vMoI when held at a constant 1 rad/s had a cost of exactly ½ J - so, fixing the energy cost of momentum, even as a function of changing MoI / radius.. so, 1 kg-m²-rad/s taken from out by the rim has the same cost as 1 kg-m²-rad/s taken from closer to the axis.

As the intention is to use the inertial torque / AM from reducing MoI at fixed RPM - as sourced from the initial GPE output - to counter-balance the CM from a series of 4 asymmetric angular inertial interactions, each will consume an increasing amount of radial travel of the vMoI mass, following the contour of MoI=mr², so, four, unevenly-sliced chunks of radial travel, each worth 1 kg-m²-rad/s of inertial asymmetry, for ½ J per kg-m²-rad/s at 1 rad/s - plus the T*a on the motor/s - and tracking ½Iw² with RPM thereafter.

If that's still not clear enough, just have to wait'n'see, or else beat me to the punch..

[MrVibrating]

..basically: scoop m from the G&t, then disengage from the GPE system so it's no longer at cross-purposes with the KE gain principle it would otherwise interfere with.. then simply spin'n'brake, as ever.. unrestricted by decreasing momentum availability as a function of rising RPM and thus shortening per-cycle G-times.

Simples. Decouple the two systems, for now: nail the gain, then think about how to recombine 'em..


For instance, an OB weight is also changing radius.. so, might the OB weight also be the vMoI? etc. Bessler intimates that significant simplification IS possible, so you never know.. but that's for later (if this even works)..

[Robinhood46]

Simples. Decouple the two systems, for now: nail the gain, then think about how to recombine 'em..

When you recombine 'em (the two systems) if they are not recombined at the same position, with regard each other, you will have a gravity wheel with a fundamental difference.
This is the only way, in my opinion, that PM can be acheived.
But, as you say, how do we recombine them?

[MrVibrating]

Just back from fracture clinic - as i suspected it ain't held position so gotta go in for an op to pin it on Friday. Felt it slip a few days back when unscrewing a bottle of milk - they said 'no twisting forces' but the pain had subsided and i'm right-handed so instinct got the better of me.. been killing ever since tho, swollen right back up.. tsk..

Still, did some head-maths on the Tube and in retrospect i'm doubtful the proposed rig can actually work..

The issue of course is that the proposed solution doesn't involve any deceleration / collision step - it just divides any given output GPE into four equal portions, and calculates how much acceleration each ¼ portion can impart to 4x the mass... 4x in succession.

It's that last step that's the problem - ie. having accelerated four 1 kg-m² rotors by 1.1 rad/s for the first 2.45 J, they now need decelerating back down to zero velocity relative to the vMoI, in order to reset the cost of the next 1.1 rad/s acceleration to that same 2.45 J base value.. and obviously doing likewise for the final two identical spin-ups..

..in short you gotta brake and redistribute each asymmetric rotor acceleration back against the vMoI 'co-rotating stator' to complete / consolidate each momentum rise for the minimum-possible expenditure.

Otherwise, if relative speed between the thing you're accelerating and the thing it's being accelerated against is just allowed to accumulate, the PE cost of the momentum is simply squaring right alongside its KE value.

So the mooted solution is either flat wrong, or at least, incomplete..

'1 lb falling 1 quarter' has to be a GPE output.

'1 quarter' thus has to have dimensions equivalent to gravity or force * displacement - ie. work / energy.

Suppose the drop's 1 kg over 1 meter, hence '1 quarter' = 9.81 J

The riddle is thus saying that 9.81 J, invested in the acceleration of either four 1 kg masses, or else one 4 kg mass, can yield 4 * 9.81 = 39.24 J of KE / output work potential.. (i'm hesitant whether it can be output / harnessed as PE as the form of gain seems intrinsically velocity - and, thus, KE - dependent.)

39.24 J = 4 kg (or 4 * 1 kg) at 4.4 m/s. Or equivalently, 4 kg-m² (or 4 * 1 kg-m²) at 4.4 rad/s.


So the riddle seems to solve very neatly / consistently / self-referentially, even - i mean, that's a pretty circular little maths loop, no? A perfectly closed-loop gain, in terms of weight, inertia and velocity..

It just implies however that all output GPE does useful work - without dissipation (so, no inelastic collisions / braking) - and furthermore without paying anything for whatever causes the inertial asymmetry / N3 break; only meeting the cost of the actual accelerations, but nothing else.

And despite these restrictions, the energy cost of the momentum / accelerations has to stay pegged at its 'quarters' value - so for a 9.81 J GPE, we only get to spend 2.45 J on each acceleration; the 'right amount' for the first acceleration, but if it also has to buy the next three at the same efficiency despite rising RPM yet without inelastic collisions or braking..(?)

It's a whole 'nother conundrum - how can the maths fit so perfectly, in spite of these outstanding practical hurdles?


If i went ahead with the rig as proposed, half the input energy will be getting dissipated, the vMoI inevitably has to gain RPM, and with it, the PE cost of momentum.. and i'd imagine that'll quickly be the end of any so-called 400% - it's obvs. gonna be unity minus brake dust, just hours of work in vain..


If buffering momentum into a vMoI is no use, then the riddle only seems practicable by sinking CM to a weight / using it as a 'stator' - whilst it's still gravitating..

..despite the (accelerating) rotation.. this was why i thought vMoI buffering might help - grab the momentum in a flash, then dole it out at leisure, freed from the complications..

Remember, the final, decisive action flipping a system into OU efficiency can only be an asymmetric acceleration or deceleration - not a GPE or CF PE input or output..

..so even if asymmetric inertial interactions can be implemented (which this thread has shown can be trivial), if the first thing a successful momentum asymmetry has to do is accelerate the rate at which the system's lifting and dropping weights, it hard to see how these piecemeal momenta can ever accumulate to significance - that is, exceeding the 'threshold' or 'unity' velocity at which the squaring net KE value intersects / clears the linearly-summing net input PE plot.

Quite simply, the elementary physical requirements for manifesting OU - that is, buying piecemeal unilateral momenta for less than their cumulative net KE value - depends upon fixing the unit-energy cost of those momenta from within the accelerating reference frame, while the only possible external source / sink for momentum is G&t, thus necessitating a GPE cycle, yet which cannot interfere with the accumulation of velocity under conditions of inertial isolation from the environment.. (!)

The maths solution fits snug as a bug in a rug, but the mechanical constraints still all seem to be mutually-exclusive..

Any thoughts besides 'too wordy' welcomed..

[MrVibrating]

Simples. Decouple the two systems, for now: nail the gain, then think about how to recombine 'em..

When you recombine 'em (the two systems) if they are not recombined at the same position, with regard each other, you will have a gravity wheel with a fundamental difference.
This is the only way, in my opinion, that PM can be acheived.
But, as you say, how do we recombine them?

I was kinda hoping that'd become clear after isolating a gain, if by any contrived means..

..i've little idea how to resolve these points with the EMGAT principle at this stage, basically - on the one hand, N1 rules without gravity & time in the mix - we ain't getting anywhere without weights and thus a GPE cycle - yet i can't think of an N3 break that can develop to fruition with a bleedin' GPE system blocking the road, yet no GPE system = no N3 break..

Like i say, perhaps the over-balancing / under-balancing displacements can also be tapped for corresponding +/- inertial torques, eliminating a need for dedicated vMoI masses (if even useful at all).. dunno.

It would be nice if a better solution to the riddle led us to that implementation so simple "the machine can be serviced while running", but right now i've little idea what that might look like..