Toad Elevating Moment

[MrVibrating]

Soz mate, this type of scheme:

[rlortie]

You paint a very good example of why I hate scissors. Can you calculate the force required to set your scissors in motion with the excessive acute angle you depict? That is why the lock.

Experience has lead me to believe that they must not close more than 40 degrees, otherwise it takes more force (mass) to open them than gained by the extended weight.

http://www.mathopenref.com/angleacute.html

Ralph

[ruggerodk]

Way to go MrVibrating - appreciate it ;-)

[MrVibrating]

You paint a very good example of why I hate scissors. Can you calculate the force required to set your scissors in motion with the excessive acute angle you depict? That is why the lock.

Experience has lead me to believe that they must not close more than 40 degrees, otherwise it takes more force (mass) to open them than gained by the extended weight.

http://www.mathopenref.com/angleacute.html

Ralph

Yep, like i said i tried opening up the angles - under-extended, over, and midway (90° angles between the scissors), but with no change - i think the reason is that the GPE can't reduce as its own weight is forcing it upwards (as hoped for, only no more than it's being pulled down, unfortunately)..

[daxwc]

Maybe the scissor angle has to do with Bessler’s greed statement.

[jim_mich]

Maybe the scissor angle has to do with Bessler’s greed statement.

No, no. Bessler's greed statement concerned Bessler's enemies being greedy by wanting to see how his wheel worked without paying the asking price. It was Bessler's enemies that were being the greedy ones for expecting to be told how the wheel worked without compensating Bessler for his ten year long search. Would you expect a laborer to work for nothing? This is what Bessler's enemies were suggesting. And Bessler called them out for being greedy...

Let a Gartner be no breaker of fences, even if a Wagner leaves ruts in the road.. For greed is an evil plant.

[daxwc]

...My work will not be revealed prematurely.
Should anyone wish to speculate about the truth, let him just
ponder on the rich pageantry of words which I now cause to
shower down upon him! Let a Gartner be no breaker of fences,
even if a Wagner leaves ruts in the road..

For greed is an evil plant. An anvil receives many blows. A
driver drives. A runner runs. The seer sees. The buyer buys.
The rain drips down. Snow falls. The shotgun shoots. The bow
twangs...

You seem to have forgotten it is in a different paragraph and hardly an open and shut case. Here is the quote straight from JC's book.

[jim_mich]

Sorry Daxwc, but in the original text, these lines are not separate paragraphs. They run right together. John Collins separated them into different paragraphs. This is the original German:

Ein Gärtner sei kein Zaunabbrecher,
Ein Wagner wolle bohren Löcher.
Der Geiz ist eine Wurzel böß’

And below is the image of the AP page, with the text in question boxed in red.

So, I have NOT forgotten that it is in a different paragraph in John's book. And I'm well aware that some people attribute a different meaning to these three lines. I'm also know that the actual original German has a slightly different meaning than JC's translation. But JC's translations in this case is plenty close enough. The slight difference simple reinforces that Bessler was writing about the greed of Wagner and Gartner



Edit:

The German word for greed is 'Gier'. Bessler does not use such a word here.
Bessler uses the word 'Geiz', which translate more into stinginess, miserliness, meanness, tightness.

Bessler was bitching that Gardner wanted to break down the fence that Bessler erected to protect his wheel, and Wagner wanted to bore holes in his wheel to look inside.
These guys wanted Bessler's secret, but were too mean, miserly, and stingy to pay the asking price.

[MrVibrating]

Just found a back-of-envelope non-dissipative loss:

Imagine an 8 meter wheel.

Running radially through the axle is a 7 meter pole, a la MT135.

This means the pole has 1 meter of radial motion available - it can be lifted or dropped 1 meter.

Suppose the pole weighs 1 kg per meter (obviously these units are for ease's sake)..

Hence the 7 meter pole falling 1 meter has a GPE of 7 Joules available.

But instead of re-lifting it, we rotate the wheel 180°. Because the pole is sitting on the bottom of the wheel, but running up through the axle, the axle divides the pole into 4 kg to be lifted, while 3 kg drops. Hence rotating the wheel this way is equivalent to raising 1 kg, 8 meters... ie. rotation by 180° costs 8 joules.

Hence we've got 7 Joules out, but 8 joules in. The missing Joule has been sunk into an unconserved GPE loss.

So this is interesting - it appears to be an energy asymmetry, that effectively destroys mechanical energy.

I'll have to try simming it later, just wanted to share for now..

[MrVibrating]

Right, simmed it, nada.

7 meter bar weighing 7 kilos on an 8 meter diameter wheel weighing 100 kg

Got 53.8 J for 180° rotation, 55.6 J for linear reset of the bar. The 1.8 J difference is probably error - i'll try and fine tune a final bout of measurements and make it go away...

Edit, i get a persistent error of up to a joule, and not less than about 400mj, despite maxing the accuracy. However i'm using a pulley to torque the wheel for the linear drop, and the error varies depending on where the pulley attaches to the wheel along its central vertical line - the error reduces when it's attached by the rim, and increases when it's attached closer in, 1 meter from the axle, so behaves like an integration error...

Either way, my back-of-envelope calculation was way out!

[MrVibrating]

Found something interesting a while back that i've been toying with today:

- hang a weight off a chord, via a pulley, and you can lift and/or drop the pulley instead of moving the weight. Cool huh?


I tested this again earlier using a balance beam - drawing in the chord overbalances an otherwise-balanced beam, effectively pulling the beam down towards the weight, without the weight changing height.

If the weight hasn't changed its GPE, and the beam/wheel is otherwise balanced, then we've converted some GPE to RKE without actualy spending any of it - which seems weird..! In effect we've taken up some slack, and this requires an input of energy equal to the RKE imparted... but we still have the raised weight...

Dunno if this goes anywhere, will investigate further, later....

[MrVibrating]

Well it was inertia providing the torque - the rotor / balance beam was being pulled by the weight's resistance to acceleration; at a constant speed the force disappears, so this is probably just another dead end - unless B's 'principle of excess weight' was inertial, rather than gravitational. I rather think he'd've described it more appropriately had that been the case...


I've found something else interesting though last night - a vertical wheel with two pendulums at equal radii opposite each other. If the timings can be synched reliably, loss and gain appear to be possible; the arc-lengths of the swings don't appear to shorten in relation to the imparted RKE, so it's not a simple trade-off; rather it looks as though these systems have a non-constant energy! At least until i can establish otherwise...

TTFN

[MrVibrating]

Minor update; the briefly-interesting pendulum-thingy was just a resonance effect, and i haven't had a good clue since....

Found a neat way of affixing scissorjacks tho using a cross-shaped pair of sliders, but that's trivial. I've been trying to interpret the left-side occlusion error repeated in the Merseburg illustrations - perhaps this somehow indicates that the supports and entire room are a metaphor for a co-rotating component?

There's also a similar occlusion clue in the illustration featuring the Archimedes screw - the transmission rope swaps front-to-back between plan and profile views. The way they cross seems to mirror the stamper levers opposite - and these too feature an occlusion error - are they likewise abstract reproductions of the scissor mechanism?

And what's up with the top-left window pane - is he thinking in terms of quadrants of an interaction? This seems tentative since calculus wasn't yet widely appreciated, but then again he was personal friends with Leibniz, who of course claimed priority on its invention... more likely tho is that it's nonetheless a reference to a quadrant of the cycle in practical terms..

Hey, one thing i've been meaning to ask - anyone know the provenance of the picture mersburghmore.jpg, depicting Bessler triumphantly holding a scissorjack aloft, in some kind of fairground - is this an official (ie. Bessler-sanctioned) illustration? If so there's a few clues here..

Right now all i'm thinking about is weights, pulleys and levers, with axial pass-thrus (thus necessitating the co-rotating axle). If the scissorjack performs a real, or at least potential, useful purpose then i'm still unsure of its role, but i suspect it might be moving a chord, rather than a weight... all just hunches of course..

[rlortie]

Resonance:

Minor update; the briefly-interesting pendulum-thingy was just a resonance effect, and i haven't had a good clue since....

A now deceased partner of mine (James Kelly) built a four pendulum device as you describe. A widower, he would often bring his work inside the house.

He stated that whenever his top load washing machine went into spin cycle, the pendulum-ed wheel would start rotation. He then modified it by duplicating a small framing square pivoting at the heel, blade down and tongue horizontal to the right for clockwise motion.

Weights for bobs were installed to blade with 1/2 size weights attached to tongue extending past the wheel radius. A common bristle basting brush was fixed in place at nine o'clock to rub the horizontal weights, giving a small amount of impetus to the swing. He claimed that it worked!

Disclaimer: I never saw it working nor do I have objective proof that it worked as claimed.

As for you above picture, I question its authenticity.

Ralph

[AB Hammer]

MrVibrating

Even though I like the picture, I have to agree with Ralph. I believe it is a later artist drawing and no connection to Bessler's origin.

Alan