Yet more N3 guff..

[MrVibrating]

Pendulums: use them as reaction mass, and they swing up to some apex, then turn around and come right back at you.

Useless for a linearly-accelerated mass, because you end up flying away from the pendulum. One shot deal.

But not if we're accelerating a vertical wheel, sharing the same axle as the pendulum.

Suppose both have equal inertias and radii - at rest, the bob hangs down at the 6 o'clock BDC position.

We apply an impulse of energy between the wheel and the left side of the pendulum bob. So the bob swings to the right, and the wheel is accelerated clockwise.

Then the bob reaches the apex of its arc and reverses direction, swinging back down.

If the inertias were matched, then upon return to the BDC position, the bob is stationary relative to the wheel, although both are moving at equal speed relative to a stationary observer.

We now apply a second, identical, impulse, this time to the right side of the pendulum bob, further accelerating it in the direction it was already travelling, towards the right, but in the opposite direction to the wheel's rotation - a counter-clockwise torque, bringing it back to a full stop from the stationary perspective.

If the inertias were equal then so was the division of energy, and if each impulse of energy input was equal to one Joule, then each mass received half a Joule per impulse. We've input 2 Joules total, the wheel is stationary so all of that 2J is on the pendulum.

At this point we have an effective violation of Newton's 3rd law - we've applied 2J of impulse energy between two equal inertias, but all of it now resides in only one mass - the reaction mass - in this case the wheel - is stationary.

So we can keep inputting energy this way, linearly - when the pendulum reaches its next apex on the right, we input a 3rd Joule as previously, so now we have 2.5J on the pendulum and 0.5J on the wheel.

And again, next apex on the left, wheel's turning slowly CCW but as the bob starts its descent back down it briefly speed-matches the wheel again, and bam! - we input a 4th Joule right at that moment; applying a counter-torque to the wheel and braking it back down to stationary, while further accelerating the pendulum. All 4 Joules of input energy are now on the pendulum, and the wheel is not rotating.

Because we've been inputting 1J at a time, and the pendulum and wheel were always stationary relative to each other when we did so, our input energy has scaled linearly - we've only input 4 Joules.

But KE and RKE scale by the square of velocity - if the two inertias were each equal to 1kg then each 1J input impulse yielded 2 meters /sec of acceleration, and we now have a peak 8 m/s of velocity on our pendulum bob, for our 4J of input energy...

1kg at 8 meters per second has 32 Joules of KE.

We would thus have 28 Joules of excess energy.

The roles can be reversed - halting the pendulum while further accelerating the wheel. Same principle - each swing cycle has moments of maximum relative speed, alternating between moments of zero relative speed, and good ol' gravity keeps faithfully reversing the sign of the reaction mass each time the pendulum reaches an apex..

Probably just BS but thought it worth sharing, will try to overturn it over the next few days... It's basically just a minimalist implementation of the ideas i've been kicking about in recent weeks..

[MrVibrating]

Simulation has confirmed the first half of the theory, results below.

A motor is used to apply a torque between the wheel and pendulum bob.

The mass of the pendulum arm is minimal, so that the interaction is primarily between the wheel's inertia, and that of the bob.

Because we want to apply all of our input energy at the instants when the relative velocity of the two masses is zero, we need to input it quickly, before the relative speed has had time to change. For this reason, a brief burst of high torque is used, rather than a lower torque over a wider angle; ie. inputting a given energy over less time and angle of displacement.

Obviously, all the quantities and dimensions here are optimised for mathematical simplicity, not practical construction.

The wheel mass is 10 kg, with a 6 meter radius.

The pendulum radius is also 6 meters, and the bob mass is then tuned so that its inertia matches that of the wheel. This figure comes out at 5.922 kg.

1 kN/m of force is then applied at the axis, for 100 milliseconds.

Note that the interaction is exclusively between the wheel and pendulum - none of the interaction energy is earthed. The results would be identical in zero-G.

At the moment the system returns to its initial condition, with the bob at bottom dead-center (BDC), all of the energy that has been input between these two masses is vectored in the same direction, and in the same location.

At this precise instant, if we're riding the rim of the wheel then we're looking out on an effective N3 violation - all of our reaction mass is right there with us - travelling at the same speed alongside us!

The same is also true from the external stationary frame (per the simulation below).

So the next half of the theory is that successive interactions under these conditions will cause an exponential rise in output energy, for a linear rise in input energy...

More to follow...

-----------------------

Initial condition:




After one half oscillation of pendulum:




Anim:



Sim encl.

[MrVibrating]

So, quick recap:

It looks like Newton's 3rd law does not apply strictly to gravity-assisted rotating systems. At least, we appear to have a transient exception - applying only for a brief instant. The intention, as outlined in the OP, is that subsequent identical energy inputs will result in an N3 break that is permanent, not time-dependent.

So the expectation is that an identical torque applied at the final frame in the above sim will decelerate the pendulum to a standstill, while further accelerating the wheel, such that all of the energy so far input now resides on the wheel. Conversely, if the sign of the torque is reversed then the wheel will be halted and all of the energy that has been input will reside on the pendulum.

Either way, this will consitute an effective violation of Newton's 3rd law. In short, gravity turns our reaction mass into a 100% efficient boomerang. If we can keep our reaction mass with us as the net system KE rises, then our input energy remains a linear function of relative velocity while our output energy squares with net system velocity. As such, GPE and RKE would be thermodynamically decoupled, and can hence evolve via these diverging energy terms.

The same mass, at a given velocity, will have two different energies at the same time - both perfectly and equally valid, under their respective terms, but differing by up to half a power of ten.

At least, that's the direct implication of a usefully-meaningful N3 break. Whether this is one or not remains to be seen.. Place your bets now gents..

[MrVibrating]

Also, just to quickly note that the slight (25 mJ) mis-match in rotor/bob energies is due to the sim ending with the pendulum a fraction of a degree off vertical (0.020°). The sim is already running at 1 kHz, and raising the time resolution further will likely only result in the mis-match narrowing down to upteen significant digits, as is typical for WM2D. So it's basically accurate enough to stand in for a perfect 50:50 division of inertia and energy.

The same limitation will apply for further steps - there might be a teeny amount of residual motion one way or another, but regardless, the sim is accurate to at least 99.98% above error margins, and infinitesimal accuracy is unnecessary.

I'll post the next batch of results later...

[Trevor Lyn Whatford]

Hi Mr V,

that is similar to what I am trying to do here,
http://www.besslerwheel.com/forum/viewtopic.php?t=6503

The gravity assisted Outer rim torque verses gear ratios. Once set in motion with a push, any lifting from the flywheel driven weighted gear hamster, is transferred to outer rim torque on the flywheel, which then drives the weighted gear hamster some more, and so on. There is more to it than that though.

[MrVibrating]

Interesting concept, thanks for sharing!

On second thoughts i should probably have described this as a "pendulum assisted" rather than "gravity assisted" rotary system, since it doesn't depend on gravity to add or remove energy, but simply to flip its sign.

If this approach works, the energy gain will come from the N3 violation, not from gravity - it'll be caused by diverging reference frames, where CoE holds true differently in each. This will result in a single mass having two alternate energies at the same time - one as measured from the system's internal frame, and another from the static external frame - with this latter measure boosted by a net system acceleration.

Gravity here is almost incidental.. just something to bounce off.

[MrVibrating]

OK this next step picks up where the last one left off - an impulse of energy has been applied between two masses, and both have equal energy and momentum:



There's 27.685 Joules on the wheel, and 27.660 J on the pendulum bob (aforementioned error margins notwithstanding), so our initial impulse has input around 55.345 J of work.

The wheel is coasting clockwise, and the pendulum has swung out to the right, then fallen back to BDC where we've freeze-framed. So the pendulum has maximum momentum, and it's vectored clockwise, towards the left.

At this stage we now have two options:

Option 1:

A second identical impulse will again push the pendulum to the right, against its leftwards momentum, and bringing it to a full stop. It will also further accelerate the wheel in the same clockwise direction it's already turning.

Since the initial impulse performed a little over 55 J of work, we can expect that a second, identical impulse will produce an identical work yield, and if the pendulum is stopped then all of that work must be bound up in the wheel. This means the wheel's KE should rise to over 110 J.

So let's try that:






Success! The small error has multiplied slightly, but the bob returns to BDC with only 119 mJ, while the wheel has pretty much the full energy anticipated - 110.741 J.




And option 2 is simply the reciprocal interaction, with the sign of the applied torque reversed; braking the wheel and further accelerating the pendulum by equal and opposite amounts:






Again, perfect agreement with the hypothesis, resulting in 110.519 J on the pendulum bob, and an infinitesimal RKE. The very slight discrepancy between the two results is due to insignificant timing inaccuracies in the simulation stop points. The bottom line is simply that we've input 110 Joules of work between two masses, and all of it is in one mass, while the other is stationary.

As predictable and trivial as all this may seem, it may represent an important breakthrough: the main implication being that the net system momentum is not conserved.

For example, suppose we now lock the pendulum to the wheel - the 110 J will thus be shared between them; the wheel will become part of the pendulum and the whole system will rock gently. But this is an acceleration of the net system - the two masses are now stationary relative to eachother, but both are moving relative to us stationary observers.

And this is how an N3 break generates free energy. Successive impulses under these conditions will continue to perform 55 J of work in the internal, on-board frame, but the rise in system RKE will evolve following the square of angular velocity... If sufficient velocity is attained, 55 J of on-board work could be worth over 2 kJ of RKE! Sounds crazy, but this is precisely why Newton's 3rd is a conservation law - mechanical CoE depends upon it!

So... N3 appears dead in the water, here. At best it's splashing around ineffectively but the main defences are down and the writing's on the wall - this system's wide open to an exploit...

...anyone for kiiking? :)

[Trevor Lyn Whatford]

Hi Mr V,

Newton's third Law, I do not see the need to break it to enable a Gravity or motion wheel. All we need to do is have a greater force on one side of the wheel than the other, Job done.

[MrVibrating]

I only meant that it's one way, not the only way.

Having said that, i've come to conclude that a gravitational asymmetry is not on the cards - gravitational interactions appear to be intractably time-symmetric, so an excess or deficit of GPE is intrinsically and by definition not possible. For any gravitational system to perform work, a weight must get lower - it is insufficient for it to merely bear static force; that force must cause a displacement of the weight itself for its output work to be harnessed - and so equal work must be done to restore its height, and any form of counterbalance merely multiplies the problem.

I don't like it any more than anyone else here, but i think it's a fact..

Whereas what i'm presenting here seems to show that an N3 break is viable:

- the first interaction above applies a kick of energy between two equal inertias that are free to rotate, yet results in both travelling at the same speed in the same direction and in the same location

- the second reverses the first, resulting in all of the net energy exerted between two free masses manifesting in only one of them, while the other remains stationary

Both of these results individually contravene the usual consequences of Newton's 3rd law, as they would apply to linear mutual accelerations; here we have perfectly elastic collisions between equal inertias, resulting in accelerations of the net system... in other words, momentum is not conserved.

So yep, a gravitational asymmetry would work too, if you can find one... but for a Sunday afternoon sideline, here's an inertial asymmetry, for whatever edification, elucidation or indeed echolocation one may cast upon it.

[MrVibrating]

So the 2.1 result above ended with a stationary pendulum, and all of the input energy left coasting on the wheel. But N3 or no, it's a hollow victory as there's nowhere else left to go - we can't repeat the trick as now the two masses are moving at constant speed relative to one another. It's a dead end.

But the final 2.2 result gave us a static wheel, and all the energy on the pendulum... which has apices - and thus transient moments of relative stasis with the wheel - on both the left and right side of it. So we could input further identical impulses at either loci, and perform another 55 J of work, accelerating the masses in either direction...

So provided we can keep pumping the swing under these conditions of relative stasis, the net system KE should start to square up with velocity...

For a better mental picture of where this is headed, if we plot the on-board input energy per cycle as a function of rising speed, we get a flat line graph. But plotting the output KE from the external frame, we get a 45° slope. Superimposing the two plots, there's inevitably some threshold intersection where the latter smashes straight through the former and keeps climbing...

The only limitation will be the ability, or not, to maintain these transient moments of relative stasis between the mutually-accelerating inertias, as the net KE builds up...

So the final step here is to simply keep repeating the exploit a sufficient number of times, until we either break unity, or find we can no longer maintain the required input conditions..

More later..

[WaltzCee]

Simulation has confirmed the first half of the theory, . . .

In simulation, I have taken a 4 inch diameter disc and with weights around .03 pounds had that sucker spinning @ 9.2 million rpm.

I had iterations set @ 25K per second.
And all this in 0.068 seg's.

You really need to take simulation with a grain of salt or perhaps a shot of jack.

¯\_(ツ)_/¯

[Trevor Lyn Whatford]

Hi Mr V,

your quote,

I only meant that it's one way, not the only way.

Having said that, i've come to conclude that a gravitational asymmetry is not on the cards - gravitational interactions appear to be intractably time-symmetric, so an excess or deficit of GPE is intrinsically and by definition not possible. For any gravitational system to perform work, a weight must get lower - it is insufficient for it to merely bear static force; that force must cause a displacement of the weight itself for its output work to be harnessed - and so equal work must be done to restore its height, and any form of counterbalance merely multiplies the problem.

I don't like it any more than anyone else here, but i think it's a fact..

I do not think it is a fact. I think I can get around it, there are a lot of way to make the reset more efficient, and more efficient use of the weights PE conversion into GKE. Hopefully I can show you lots more after my next two builds. I hope to get them finished in the Christmas break.

[WaltzCee]

. . .

<edit> opps, that's the shot where I took it to 100K.

I then took it to 1 million iterations a seg. Holy cow. You'd never believe me when I told you what I saw. </edit>

[MrVibrating]

Simulation has confirmed the first half of the theory, . . .

In simulation, I have taken a 4 inch diameter disc and with weights around .03 pounds had that sucker spinning @ 9.2 million rpm.

I had iterations set @ 25K per second.
And all this in 0.068 seg's.

You really need to take simulation with a grain of salt or perhaps a shot of jack.

¯\_(&#12484;)_/¯

LOL it's just an equal and opposite reaction between identical inertias - they fly apart with equal energy, but then one stops, turns around and heads back the way it came... because it's a pendulum.

So my auspicious little 'breakthrough' here has proven two things - Newton's 3rd law, and also the existence of gravity; what goes up must come down.

It only gets controversial when we put the two together and the latter reverses the former - the inescapable result being Newton's 3rd law can be sidestepped.

So although the claim may seem extraordinary, it's all really rather pedestrian: raise a weight as reaction mass, and it'll only go so high before falling back down. Gravity's conservative so it'll still have all of its energy when it returns, and if the second mass it's propelled against is just a vertical wheel then it never actually goes anywhere either, and the two masses can remain in the same reference frame as their net energy increases.

I haven't started adding energy to the system yet, so there's no efficiency results to consider - so far, if i put in 55 Joules then we have 55 J of action, no more or less. The only point of interest is that both masses can remain in the same vector and location, or alternately one mass can remain stationary while the other has all of the given energy - because gravity has reversed the direction of one half of a regular equal-and-opposite reaction, effectively cancelling it.

So it's kind of an extraordinary result, yet an incontrovertible consequence of basic first principles. However the intention is that it lays the ground for an energy asymmetry - provided the principle can be repeated enough times as the system accelerates.

I'm in no hurry here - i'm trying to think why it can't work before actually simming it. But it's such a simple principle, there's almost nothing to it - it's just two colliding masses, and gravity. Hardly pushing the envelope of extreme physics here..

[Grimer]

Pendulums: use them as reaction mass, and they swing up to some apex, then turn around and come right back at you.

Useless for a linearly-accelerated mass, because you end up flying away from the pendulum. One shot deal.

But not if we're accelerating a vertical wheel, sharing the same axle as the pendulum.
...

What about using the earth as a reaction mass and don't share the same axis?