Decoupling Per-Cycle Momemtum Yields From RPM

[Leafy]

note that we have 3 formulas for energy.

PE and KE as you mentioned and the third one from Einstein
E = m* c * c
when we substitute the constant for light c by v then you see that we are missing the other half.

This energy is always transferred to the earth.
Half the energy to the object, the other half to the earth.

So if we do not direct the energy directly to the earth, we have won.
This will happen with a moveable carrier.
Therefore Bessler has used the wheel, a moveable carrier.

We don’t have to direct it to earth. Just don’t use it up.

Potential energy to Kinetic energy to torque.

KE to torque is easy. We can let KE stretch a mass. The problem is when it moves to the opposite side, how can it be limit so we gain a net torque.

[Leafy]

The energy distribution is a function of the mass / inertia distribution..

So for example if i expend ½ J accelerating a 1 kg rock, then i've imbued it with 1 kg-m/s of momentum, and also applied 1 kg-m/s of momentum to earth. The resulting counter-acceleration of the earth is found by dividing that metric '1' by earth's mass in kg - which'll give you something like 14 zeros before you see a number, an infinitesimal (but real and non-trivial) change in the planet's velocity. Applying the KE formula to that, would multiply half earth's mass by that 1e-14 infinitesimal, squared, which would be a KE below femtojoule range; this fleeting energy is subtracted from the KE of the rock, such that its real KE is only 0.5 J to say twelve zeros or so.. but you only perform exactly 0.5 J of work.

So no, energy distributions aren't automatically equal and opposite, precisely because momentum distributions are, and whereas momentum scales linearly with speed, KE squares.. so a non-linear relationship.

It’s coincidence that I’ve been thinking the same subject. The velocity of the earth is determine by conservation of momentum and conservation of energy. The force times the time of one mass is the same as the force timeS the time of the other mass. The force times the distance of one mass is the same as the force times the distance of the other mass. My problem is they have sign convention for momentum but no sign convention for energy. If we apply sign convention to energy then we may have gain and loss of energy during elastic collision.

[Johndoe2]

https://youtu.be/YZRY2i1W-vo

[Georg Künstler]

MrVibrating wrote:

So no, energy distributions aren't automatically equal and opposite, precisely because momentum distributions are, and whereas momentum scales linearly with speed, KE squares.. so a non-linear relationship.

In my construction I have both, an momentum transfer and an energy transfer to one side.

Whereas momentum scales linearly with speed, KE squares.. so a non-linear relationship.

The wheel itself is using a speed difference between carrier and internal mechanism.
The internal mechanism is falling faster than the carrier turns.
It can repeat the cycle again and again.

The speed difference from the first impact has the biggest value.
The speed difference will be reduced when the carrier accelerates.
The wheel will run,turn on its natural frequency.

[MrVibrating]

OK here's an interesting interaction; follow thru the implications for N3 if:

• cylindrical weights on either end of a leaf spring

• shaped such that they can take it in turns to act as bearings

• the 'bearing' end hooks into a rim-notch, the 'bob' end droops

• load the spring up with output GPE and/or the angular inertia of the bob

• thread the loaded leaf-spring through the axle..

• ..thus switching 'bearing' and 'bob' roles..

• ..and reversing the spring's torque profile when unloading!

In short, we could presumably load a leaf spring in one angular direction, then move it, whilst cocked, across the wheel, to unload an inverted pair of output torques, thus rectifying unilateral torques over a complete cycle..

Interesting proposition eh?

[agor95]

Now that is extremely cunning intellect.

Moriarty

[MrVibrating]

Hmmm - MT 134, the central Roberval linkage; for lifting a loaded leaf-spring vertically thru the axle? IE. all of the radial spokes are leaf springs, dropping and loading sprung PE at horizontal whilst simultaneously lifting a previously-loaded leaf-spring thru the axle to unload in the opposite (same? inverted, either way) angular direction to which it loaded, thus reversing the tor-- oh you get the idea..

[agor95]

Yes I understand the concept and the use of leaf springs.

All the Best

[agor95]

Duplicate - delete

[Johndoe2]

Good idea but I think the hook end will be heavier. At least from my understanding of what you said.

[MrVibrating]

So here's a pair of leaf springs attached to a basic vMoI:



..as the black weights alternate inner / outer positions, +/- inertial torques are produced, accelerating and decelerating the wheel, and thus with it, the spring axes.. it's the friggin' ice-skater effect, with all floppy arms, like, bashically.

I've tried every type of linkage from pulleys to cranks, but can only get 'em rolling consistently at best, with no kinds of gains.. obviously, it's not at all clear how you might go about rectifying a directional momentum bias here, there isn't even a collision, and no obvious way to apply one usefully anyway..


But then consider the options:

• all the clues - all of the big ones anyway - consistently point back to this kind of 'cross peice' arrangement, where you have a pair of equal opposing angular accelerations, coupled to a linear / radial one

• the de-facto objective is constant per-cycle momentum yields / costs, remember - this is just the literal embodiment of mech. OU

• so it's nothing to do with a putative GPE asymmetry; ie. the radial load cannot be another GPE, since Bessler would not be dropping two GPE's for the purposes of raising a third, since he knew too well the futility of such bunk

• hence my hitherto conclusion that it had to be for the purposes of an MoI variation, and harnessing the corresponding reactionless angular accelerations / decelerations of the wheel body


But just look at how that pans out above - where to go with it? How's that get us any nearer to our very specific objective WRT p-c momentum efficiency?


Which is why i'm now reaching for some other function or ability i've missed there. One outstanding question - Bessler seems to intimate that the connection between the angular / linear motions should involve power conversion / leverage, per the scissorjacks, but how and why?


And so i got to thinking; what happens when we load one of these springs up, then move it through the axle, to then unload on the opposite side of the wheel?

To my addled thinking, it's similar to the effects of flipping the face of a spinning disc - translating clockwise into anticlockwise spin, for example... here, moving the loaded springs onto the opposite sides of the wheel will likewise translate what would've been a clockwise torque into a CCW one, or vice-versa, geddit? So the spring loading and unloading cycle would be applying consistent torques to the wheel in one direction.. ie. loading the spring might apply an anticlockwise torque to the wheel, but then unloading it on the opposite side of the axle would also apply another anticlockwise torque, and so each full spring cycle accelerates the whole system a lil' bit at a time.. constant input energy p-c, for squaring net rotKE, no?

Or am i talking complete shite again?

If the premise still seems semi-coherent tomorrow, i may make a start on trying to sim it. Sounds tricky to do tho eh.. Dunno, crazy talk prolly..

[MrVibrating]

FWIW here's an earlier, alternate phasing version, using pulleys:



Your basic permutations are:

• vMoI moves in same direction as levers

• vMoI moves in opposite direction to levers

• levers move apart / closer - ie. in both directions relative to the vMoI

So you've seen the first and third, and the second's pointless, so that's it; if there's some way of solving the thread topic here, i'm not quite seeing it yet.

But moving the springs around between loading and unloading.. that's potentially a way forwards, seemingly promising an effective N3 break...


Incidentally, this may be consistent with the reasons why MT 134, with the radial levers, is an improvement over the diametric levers of MT 133; if those levers are actually springy, then the droop of the two horizontal ones might also raise the vertical one, via the central Roberval or the pulleys, with the only missing detail being the curve of the levers - something he teasingly tells us he omits earlier on in MT 25.. which also appears to apply these leaf-springs!

"..the poles, when coming out, must not project so far out but must bend somewhat further inwardly. There is more to it than one supposes.."

MT 134 could be a fairly-complete prime-mover principle - weights taking turns to load springs when horizontal, whilst transferring a previously-loaded spring thru the axle in the vertical direction, essentially reversing the sign of its counter-torque when it's then unloaded..

[MrVibrating]

In the first sim there, the base wheel has an MoI of '1'.

In the second, it's given nearo-zero base MoI, purely to highlight the effects of the vMoI.

In both cases tho, you can discern that the counter-torques these levers apply back to the wheel are significant.

So you can imagine then, the gains that would be on offer if both the counter-torques from each full spring cycle were oriented in the same angular direction.. you'd have hard acceleration..

[Georg Künstler]

MrVibrating wrote:

And so i got to thinking; what happens when we load one of these springs up, then move it through the axle, to then unload on the opposite side of the wheel?

The above is nearly correct, I have problems with your wording "move it through the axle".
The construction has no axle as you use it.
I showed the type of construction already with the x-cross.
https://www.besslerwheel.com/forum/down ... p?id=20096

In the picture you see 4 cylindrical weights,
the cylinders above are compressing the springs,
during rotation springs are loaded on one side and released on the other.
So this construction is under stress from gravity even when it is not moving.
All 4 springs are already compressed.
It is a preloaded system.
The energy in the system is in balance until the first tilt.

[MrVibrating]

The 'axle' / axis / center of rotation - ie. simply moving it to the opposite side of the wheel.

The actual radial distance moved could be quite short - just enough to mean the spring's unloading in the opposite direction.

Unlike your build (v. well done BTW), the spring loading here is angular, rather than linear - to harness the counter-torques they're applying back to the wheel.

What i'm thinking now is that a scissorjack - some leverage, basically - could be used to convert a large droop of the horizontal weighted spring, into a smaller vertical lift of the previously-loaded spring; the degree of 'droop', and thus GPE output by the horizontal sprung weight, can be arbitrarily larger than the vertical distance the loaded spring needs moving through the axis in order to invert its unloading torque profile:



..no time now for a better sketch, but basically the horizontal drop distance can be greater than the vertical lift distance, hence using a small jack for the transmission, thus:

• horizontally-suspended weight droops, loading spring while lifting the previously-loaded one a short height

• after popping thru the axis the lifted spring unloads its inverted torque profile, accelerating the wheel

• repeat


In summary it's about using GPE to invert the torque profile of springs, such that they present positive torque to the system upon both loading and unloading, thus rendering an effective N3 break and per-cycle momentum rise - it is not an attempt at a GPE asymmetry, and superficial resemblances should be kept in context (as when considering many of the MT's such as MT 24 / 25 et al); the resulting energy gain would be rotKE, the mechanics of which do not follow from intuitive experience, as when considering the outcome of a prospective, albeit impossible, GPE asymmetry.. "drop when heavy, lift when light" is totally intuitive, if deceptively naive, but buying momentum for less PE than its KE value is a novel phenomenon that can only be considered and understood mathematically..