Toad Elevating Moment

[MrVibrating]

V .. I think you are forgetting a couple of things.

1. The vertical attachment rod has mass so when it is in the up position [north] it has RKE aswell.

You're right, although it hadn't escaped me - if accounted for it'll actually add to the efficiency rather than detract from it, too. However it's more practical just to counterbalance this mass, such as by using a wheel instead of a half-beam like that.

2. the polygon rod & the attachment rod both have increased GPE, which should be factored.

Yes - again, the GPE of the vertical beam represents more output work for the given input, and so the 550mj disunity is a conservative measure. However this additional load can be counterbalanced away, it's incidental to the main focus.

3. Force [albeit torque] is not energy.

Only looking at energies here! Specifically, the RKE of the flyweight vs that of the main wheel or beam (or in this case the raised flywheel's static GPE). Any attention i'm paying to forces is strictly in regards to the resulting I/O energies.

Just my prelim observations - sim attached where I remade the polygons more accurately.

P.S. you could extend the attachment shaft so that it was pivoted in the middle [counterbalanced] so that you could remove the GPE gain from this in the energy budget.

Yep right there with ya, and well done for tidying the polygon - couldn't suss how to do that myself... the 'snap to' function is a bit hit'n'miss...

I came up with a simplified design at work earlier, gotta try simming it yet but it's basically a big Superman "S" for a one-peice flywheel, counter-balancing an off-center rectangle for the main rotor. Ugly but simple, easily adjustable and keeps the two RKE measures nice and neat. Will have at it later...

[MrVibrating]

Go to this post and download the zip file. There is a script I created for making clutches in WM2D and it builds one dynamically. Try that and let me know if it works for you.

Brilliant work and much appreciated; it throws a few errors i think due to my flaky old copy of WM, but i can get toroids out of it. However they're composed of two halves - my thinking is that force and energy measurements are going to be more reliable if they're related to a single object, rather than a composite one. Eg. it'll need spokes or some form of radial support so i want them to be integral and symmetrical / fully balanced.

I figured a big angular 'S' shape, with thicker curves and a narrower diagonal section, is probably the simplest flywheel to draw with the polygon tool.

The ideal however would be a torus that can be pivoted at its central axis without the need for spokes (not for a physical model, just for simming of course). Lack of a toroid tool is a real weakness in WM's abilities.. just my luck it's also the optimum shape for maximising rot. inertia...

[Ed]

WM is limited in the kind of geometry it can import, hence the two halves. It should treat it like a ring as long as you lock the two halves together.

I believe (not sure about your version) there is a property of an object that can be changed that can simulate a hollow sphere, ring or disk.

[MrVibrating]

Sorry for being an AH to spoil your coffee ...but you still have to spin up the flywheel - by 500mj
regards ruggero

By 1.254 J you mean...

550mj is a conservative measure of the difference between the RKE and the GPE, although in restrospect, the output 1.7 J also needs to be input, unless the static flywheel was perfectly counterbalanced - in which case that 550mj is free.

Without counterbalancing though, input and output would be equal - provided we recovered the RKE input to the flywheel. Indeed, my hope is that conservation of this quantity could reduce the input energy required for subsequent cycles..

Ultimately, no matter how high the flywheel's rot. inertia, or how low the resulting input RKE needed to apply 100% weight cancellation, the faster the main wheel turns, the less time per cycle the pure moment needs to be applied for - eg. assuming a 50% duty cycle at 30 RPM the pure-moment needs to be applied for a maximum of one second per cycle. However at 60 RPM it only needs to be on for half a sec per cycle. If faster speeds are possible then the per-cycle input energy continues to drop accordingly, hence per-cycle I/O efficiency increases with speed. This is just a cool consequence of the fact that we only need the flywheels to reach a theshold torque; their actual RKE consumption at any given RPM of the main wheel is incidental and time dependent... whereas, the output GPE is temporally invariant. At least, up to relativistic speeds, anyway.

Which is nice. :)

[MrVibrating]

WM is limited in the kind of geometry it can import, hence the two halves. It should treat it like a ring as long as you lock the two halves together.

I believe (not sure about your version) there is a property of an object that can be changed that can simulate a hollow sphere, ring or disk.

Ah that's what 'shell' and '3D/sphere' are for (i'd guessed as much, tho hadn't tried using 'em yet).

Thing is, the only reason i want a ring shape is to concentrate the mass of the flywheel around its periphery. For a given mass and radius, the further out to the perimeter you can focus the mass, the greater the distance it has to be accelerated for a given torque. Conversely, if the mass is focused towards the axis, or uniformly distrubuted as in a solid disc, then all or some of the mass only needs accelerating a shorter angular distance, reducing inertia and increasing the input energy required to generate a counter-inertia equal and opposite to the flywheel's weight.

If it was just for collision geometry then a disc-shaped shell would suffice, but i'm after maximum possible rotational inertia for a given mass, hence a big thin ring is the optimum shape in 2D...

In 3D of course, thin lead cyclinders would be the optimum shape, since for a given radius (perhaps due to space constraints) you could continue raising their rot. inertia by extending their length... It was this realisation that led me down this path in the first place...!

[Ed]

I could do a 3d test for you in simwise? Just figure out what it is you want to test and let me know. It can import wm2d files, so make one of those, post it, and then tell me what you want substituted with 3d geometry and what you want the dimensions of the 3d geometry to be.

[ruggerodk]

Sorry for being an AH to spoil your coffee ...but you still have to spin up the flywheel - by 500mj
regards ruggero

By 1.254 J you mean...

550mj is a conservative measure of the difference between the RKE and the GPE, although in restrospect, the output 1.7 J also needs to be input, unless the static flywheel was perfectly counterbalanced - in which case that 550mj is free.

No - I mean that the 500mj gain of the first cycle is what you have as input to start up the next cycles.

Unless you repeat the initial input for every new cycle....;-)

That's OK with me

ruggero

[MrVibrating]

Those Weissenstein pendulums...


Funny shape for a pendulum...

Perfect shape for a nice hefty pure moment... !

[MrVibrating]

Sorry for being an AH to spoil your coffee ...but you still have to spin up the flywheel - by 500mj
regards ruggero

By 1.254 J you mean...

550mj is a conservative measure of the difference between the RKE and the GPE, although in restrospect, the output 1.7 J also needs to be input, unless the static flywheel was perfectly counterbalanced - in which case that 550mj is free.

No - I mean that the 500mj gain of the first cycle is what you have as input to start up the next cycles.

Unless you repeat the initial input for every new cycle....;-)

That's OK with me

ruggero

Well if experience thus far is anything to go by, i'm never more right than when i realise what i previously thought right is flat wrong. Nonetheless, if i really AM right this time, then the difference between the rotational KE and translational KE is free. Granted i've been wrong every time so far, i'm just saying, IF. I'll graciously (or sheepishly) retract if/when i discover my error.

My thinking for now though is that if i was sitting on the main wheel, and it was my job to apply torque to the flyweight, my job wouldn't be made harder or easier if that torque results in the wheel rotating CW or CCW. All i need to input is the RKE - the flyweight's rotational inertia is unaffected by the weight or its axis rising or falling, and remains a fixed force regardless.

This means all my input energy is going to RKE - that's all the system's input energy - and the resultant rise in GPE in the system's output energy.

Or to put it the other way round, the RKE of the flyweight represents all of MY output energy, and its total energy (RKE+transKE) is the sum of that input energy plus the resulting rise in translational GPE.

This GPE change is decoupled from the RKE change because the vertical force generated by the accelerating flyweight is a counter-force. Hence the GPE rise is a reaction to my input energy - effectively, inverted counter-work (since it works for us, raising the system's net energy).

I'll be testing this shortly - my expectation is that the input workload required to manifest the pure moment will not change with the resultant change in height. Will post results as i get 'em.

In the meantime though, remember the accounts of B's wheel running at the same speed regardless of whether it was raising or lowering a load, or unloaded? This characteristic would be consistent with a prime-mover being driven by counter-forces; the output workload thus presenting no load upon the moving weights inside...

[Ed]

No, I can't remember that. Can you cite your source? Here is a reference for when lifting water. (In a letter from Fischer to Desaguliers)

This wheel turns with astonishing rapidity, making twenty-six turns in a minute, when the axle works unrestricted. Having tied a cord to the axle, to turn an archimedean screw for raising water, the wheel then made twenty turns a minute.

[MrVibrating]

As predicted by previous tests, the energies scale pretty much linearly to mass - there is a slight variation, the source of which i'm unsure of but which is nonetheless immaterial - however increasing the mass of the flyweight by a factor of ten to 8.8 kg (much more realistic for its size), increases the energy difference accordingly:

rot = 122.790 J
trans = 170.088 J

Hence the system energy has increased by 47.298 J - we still have the 122.790 J on the flyweight (it doesn't magically vanish).

So we can re-use that stored RKE to apply another pure moment - this time by braking it, inverting the torque and decelerating the flyweight, applying a second pure moment equal in magnitude to the first.

This is just 'in-principle' reasoning of course - no idea what the actual mechanism would look like. But it may mean we could have two 47 J payouts per cycle - one for accelerating the flyweight, another for decelerating it again.

This "twice per cycle" dynamic would be another strong consistency with Bessler's wheel!

[MrVibrating]

No, I can't remember that. Can you cite your source? Here is a reference for when lifting water. (In a letter from Fischer to Desaguliers)

This wheel turns with astonishing rapidity, making twenty-six turns in a minute, when the axle works unrestricted. Having tied a cord to the axle, to turn an archimedean screw for raising water, the wheel then made twenty turns a minute.

I think we have at least two sources for this detail, Weise and Wolff.

From Weise's testimony in Grundlicher Bericht (p. 68 of JC's edition), and also Das Triumphirende (p. 238 of JC's edition):

This far end was attached to a chest full of bricks - about 70 lb weight in all – and this load was raised and lowered several times by the machine. The most noteworthy detail regarding this particular experiment was that the wheel, while under this considerable load, continued to rotate at exactly the same rate as when it was running “empty�.

In fact, below this we have the Third testimony, "Issued on the consensus of the entire official body of witnesses":

The machine then gradually began, of its own accord, to revolve faster and faster, soon acquiring a speedy and regular rate of rotation in which it persisted until it was stopped by the application of very considerable effort. It also retained this same speed and regularity of rotation when it was used to lift a chest containing 6 heavy wall-bricks (the total weight being about 70 lbs).

Offhand i can't find Wolff's testimony, but there's two refs already.

I'm not suggesting this behaviour is exclusive to a counter-force as prime mover, however it's the most self-consistent explanation, i believe. Otherwise, if the prime-mover was an overbalancing weight then the wheel would noticeably decelerate under such load, and accelerate when that load is reversed. In essence, OB weights would be leveraged directly against the 70 lb applied load. Instead however, we have this IMO very strong evidence that the applied load was NOT directly coupled to the internally moving masses.

[MrVibrating]

in restrospect, the output 1.7 J also needs to be input, unless the static flywheel was perfectly counterbalanced

Lost the plot there somewhat - the 1.7 J transKE is already 'input' via the 1.254 J rotKE - the difference is free.

I made the mistake of thinking that rotKE only represented part of the input energy, and that i must also have been inputting transKE that wasn't being measured.

Just an assumption, but it was wrong, and unecessary. And anyway, counterbalancing just leaves the question of how to re-raise the counter-balance.

Given the implications a few brain farts are only to be expected, but for now i stand by the measurements - the elevated GPE is an output of the system, not an input... it can nonetheless be re-input, and the half-Joule difference between trans and rot KE is a free gift to all mankind, 71 picojoules each for every man, woman and child, to be dispensed as they see fit.

[MrVibrating]

This wheel turns with astonishing rapidity, making twenty-six turns in a minute, when the axle works unrestricted. Having tied a cord to the axle, to turn an archimedean screw for raising water, the wheel then made twenty turns a minute.

..just to acknowledge the witnessed slow-down - undoubtedly there's no conflict of witness statements if they pertain to different demonstrations, and one would expect that even when no such deceleration was noticed, a more accurate measure might detect one. Nonetheless, it seems evident the slow-down is not in the direct linear proprtion one would expect if the prime mover were directly attached to the applied load.

And if for example the prime mover WAS a pure moment as i'm suggesting, the applied load (to the net system) presents no load at all upon the flyweight, the workload of which remains a fixed function of its rot. inertia.

[MrVibrating]

Could use some help in WM...

The test rig attached is designed to drop a weight from a spool, transfering that torque to the flyweight via a transmission wheel which shares an axis with the beam the pure moment is intended to balance.

The idea is to find the mass of the weight than needs to be dropped in order to generate a balancing pure moment, and integrate this over the drop distance to get a decisive input energy. This could eliminate any doubt that the difference between rotKE and transKE is free - ie. i expect the same input energy per unit time whether the pure moment is climbing or fixed to a stationary axle.

Worthwhile experiment, but the sim's crapping out on me - the chain is sinking through the spool... (if only this software had a proper spool widget!)

How do i get rid of this error? Raising the frictions and reducing elasticity doesn't seem to help.

Or can anyone think of better way to accurately manage input energy? I figued a weight drop is fairly conclusive, just as a proof-of-principle...