Yes, the flywheel MoI's determine the efficiency of the CF PE to RKE conversion. If the mass is allowed to fly out too quickly then we won't have recouperated all the available momentum.ME wrote:Interesting theory, thanks for sharing !
When a weight travels from a low radius to a large radius because of a centrifugal force effect, then it's basically a change in position under influence of acceleration resulting in some predetermined velocity at such distance: Conservation of energy is still a mathematical consequence (at least for this part).
What happens with this rotating Atwood mechanism is that you actually make use of a desired effect which is: this weight should end up with some small velocity (preferably zero) at the rim, which also helps against structural damage by redirecting most if this hit momentum.
When I take Sleepy's yo-yo example and use the flywheel's velocity to bring this weight back to its smallest radius then the end result will also be that the flywheel's velocity becomes 0 (despite some losses).
yes, that's the whole point - we allow the MoI induced deceleration - nothing can be done about that for now - but in so doing, we're harvesting the CF PE to immediately store up some more RKE and angular momentum on the flywheels..Yes, but keeping RPM will also require the weight to gain in tangential velocity (and momentum)... That's why the wheel slows down in the first place: it tries to keep its momentum. So it's reversed: you need to add momentum to keep the RPM's.if we can slide out without sacrificing RPM, we gain momentum from the completed interaction
According to my unsubstantiated guess it could require the same amount of momentum as now stored in the flywheel, or the actual end-velocity of the weight at hit-point only directed inline with rotation to keep its RPM's (perhaps answers this: the brachistochrone)
So the intention is to simply brake the positive flywheel back to the main wheel, returning that positive momentum, and then flip the momentum or torque from the negatively-spun flywheel, and add that back as positive momentum too.
So all of the additional angular momentum generated by the CF workload gets sunk back into the main system as positive momentum.
Net effect = mass sent back out to rim with a higher final angular velocity than if the flywheels were locked to the main wheel, and the CF PE never collected.
I think we'll still have to lose a little bit of velocity, but i agree - it looks like we may be able to re-extend an MoI without suffering any significant drop in RPM.. and this is the basis of the propsed symmetry break.
The basic point is that an effective N3 violation gives us a perfectly elastic collision in which the distribution of momentum is no longer 50:50, but varied by whatever the degree of the inertial asymmetry, be it full or partial.I need to chew on this a bit more, it tastes either bitter or sweet.The energy asymmetry here varies as a function of RPM - it's principally an inertial asymmetry, an effective N3 violation, and so the energy efficiency follows the same pattern as any other putative N3 break - it has an arbitrarilly-low threshold RPM at which it is at unity, below this speed it is under-unity (so will resist gaining momentum, but the energy being lost isn't being dissipated as heat - it's not a frictional loss).. and above that threshold RPM it is progressively more OU the faster it rotates.
Edit to reply on upcoming post (I guess there's no need to add a new post):True.For starters though, just work out how you could gain energy from a violation of Newton's 3rd law; the game is principally momentum gain, and the energy gain falls out as an almost incidental consequence of that.
Energy as a number does some tricky stuff when brought out of frame, I'll only believe in a CoE violation when some mass gains in height (or something equivalent). But inside a frame a resulting acceleration over distance just leads to some new velocity, by definition.
If this asymmetry is applied repeatedly to one half of an interaction - so either the input stroke, or output stroke - the net system momentum rises. This means it is now its own, unique, reference frame. From inside this reference frame, the inertias remain constant, as inertia isn't momentum-dependent (a body's inertia doesn't change with its velocity, anymoreso than its mass). Thus the internal costs of mass displacements remains constant.
But from any external reference frame, the internal energies add to those of the accelerating system frame. A half-Joule will accelerate 1 kg by 1 m/s, but if i perform this acceleration on board a train travelling at 10 m/s, from the platform you see 1 kg accelerate from 10 m/s up to 11 m/s - a 10 Joule rise in energy, albeit, one which causes a corresponding 1 kg / m /s deceleration of the train's momentum.
Here however, in the rotating frame, we're applying equal opposite accelerations, so there is no net deceleration of the 'train' - in this case, our main wheel. And as with the train, the value of work performed in this accelerated reference frame is inflated relative to its value in our rest frame.
So in essence, we'd be gaining energy by piggybacking on a freely-accelerating reference frame - a free train, powered by the excess momentum accumulating each cycle.
Like i say, assume you have a free and controllable violation of N3 in an otherwise fully-elastic sequence of collisions - so you can easily gain or lose net momentum. But you don't want momentum - you care nothing for reactionless thrust or any of that guff, you just wanna da free energy, innit.. So how would you go about making free energy from an otherwise useless inertial asymmetry?
It's not hard, but results in thinking about energy symmetry in a different way to which we normally envisage ie. potential GPE asymmetries or what have you..
This type of energy asymmetry evolves in a signatory way, unlike, say, simply dropping something when its heavy and picking it up when its light, wherein the degree of asymmetry is constant, the I/O energy efficiency an N3 break is speed-dependent, rising exponentially with the rising net system momentum.
So what it all boils down to is whether or not we can genuinely raise the net system momentum, succesively over multiple cycles, without spending any PE.
The hope here is that if we can send a mass back out to the rim without incurring the full usual slowdown - albeit by slowing down at first, but while storing up the shed velocity in flywheels - then we might end an interation with more momentum than we began with. It's that simple - trying to generate a free train ride, and thus a licence to print money..
