Inegnuity v's Entropy 2 - Observations & Questions

[Wubbly]

Reply to post from Thu Aug 12, 2015 here: http://www.besslerwheel.com/forum/viewt ... 911#135911

(I believe Gearing is squared in the formula because KE Output for CoE is a squared term).

e.g. for Driver mass 4.0kg and Lateral Load mass of 0.5kg with 4 x Gearing ...

* Driver Acc = 'g' / ( Gearing^2 * Lateral Load mass to Driver mass Ratio + 1 ) => -10 / ( 4^2 x 0.125 + 1 ) = -3.333 m/s^2

The Lateral Load Acc is 4 x the Driver Acc because of the gearing used.

Can someone please explain to me why we have to square the Gearing factor when considering the inertia quotient effect on the new acceleration of the Driver ?????????

I hope you will both have a say in explaining to me the inertial factoring of my formula's.

Fletcher,
Your driver acceleration equation is identical to the Atwoods acceleration equation.
The derivation of the Atwoods acceleration equation for 3 hanging masses was done in this post here using free body diagram analysis:
http://www.besslerwheel.com/forum/download.php?id=10709

If you set m2 and m3 to zero, you get a simpler form of the equation as shown in this diagram here:

http://www.besslerwheel.com/forum/downl ... er=user_id

The acceleration equation for one hanging mass is:
a = (g * driver_mass) / (driver_mass + I/r1²)

This equation is basically: a=F/m
Linear acceleration = Linear Force / Linear Mass

• The acceleration is the linear acceleration of the driver mass.
  The linear force on the system is the driver mass x acceleration due to gravity.
  The linear mass of the system is: (the driver mass) plus (the moment of inertia of the Flywheel divided by the radius squared), where the radius is the radius of the driver mass.

Note: when you take the moment of inertia of the flywheel and divide it by the driver radius squared, you get the "linear mass" of the flywheel that is felt by the driver mass during the acceleration.
To equate this to your gearing problem, the flywheel rim mass represents your lateral load mass.

If you take the right hand side of the equation and divide the numerator and the denominator by the driver_mass, you get:
a = g / {1 + [I/(driver_mass * driver_radius²)]}

Your lateral load mass is the flywheel rim mass. It has a "rotational mass" or moment of inertia of "I".
If you take a moment of inertia and divide it by a radius squared, you get a linear mass.
So the denominator of this acceleration equation is looking a lot like:
(lateral_load_mass/driver_mass) + 1)
But we need to do a little more algebra to get the gearing factor in there.
r1 = radius of driver mass
r2 = radius of flywheel rim mass (or lateral load mass in your case).
If you take r1 and multiply it by some scaling factor (or gearing factor), you get r2.
r2 = C * r1
or:
r2² = C² * r1²

almost there ...
The moment of inertia of a rim mass is I = mr²
If your load_mass was a point mass at radius r2, the moment of inertia of your load_mass would be
I = load_mass * (r2)²
or
I = load_mass * C² * r1²

so the denominator term of the acceleration equation would be

{1 + [I/(driver_mass * driver_radius²)]}
={1 + [load_mass * C² * r1²/(driver_mass * r1²)]}
={1 + [load_mass * C² /(driver_mass )]}
={1 + [C² * load_mass /(driver_mass )]}

Which would make my acceleration equation equal to:
a = g / {1 + [C² * load_mass /(driver_mass )]}

Which matches your acceleration equation of:
Driver Acc = 'g' / ( Gearing^2 * Lateral Load mass to Driver mass Ratio + 1 )

[ME]

Fletcher, perhaps I misunderstood; you mean it was the whole exercise to find these initial conditions?
In that case I need some more time for the right-side.
At this moment I take the initial angle is the just same, the left vertical at 1m to the left, and the right vertical at (8/9) meter to the right, and see what will happen.
If -as you suggest- rotational-inertia is an issue there'll be the metric of Mass-radius plus guessing if you either used a disc or sphere, while even without inertia I expect the width of the lever should also play some role; I don't know yet.

I label the vertical axis the y axis and the horizontal axis the x axis. In sim world 3 o'cl is zero degrees and it goes CCW. I think mathematicians use a different coordinate orientation.

It is basic (math-)geometry, where the angle is actually measured in radians. I personally use degrees because the angles don't fraction-up so fast. So the angle-coordinate system is: x=Cos(alpha), y=sin(alpha).
That's why I'm a bit surprised to see a fractional angle.
So basically your starting-point is the height (set to 0.8015) which has its fraction close to the amount of significant numbers; So I wonder why didn't just choose 0.8000? (blabla..etc).
I'll see how far I get.

Marchello E.

[ME]

Fletcher, as I look at it this will becomes more-and-more a guessing game to reconstruct what you did, before I even try to apply some calculations.
For the right-side I guess the initial lever angle is slightly higher. It should be obvious that the mass-radius is important to know because of its side effect when getting larger the left-side gets less initial-leverage, and the right-side gets more initial-leverage. As suggested earlier, the width of your beam becomes more important as it changes the distance from the pivot point.
And then I also assume you didn't drop the weights onto the beam.

I did three or four guesses in WM2D, and these are the current metrics,
(actually the result is closer than expected after setting g to 10kgm/s^2):
Beam-rectangle, Size:(3m x 0.04m), Angle:(+25°), weight:(0.001 kg)
Left-Mass(m1):(1kg), Planar, position:(x = -1m), r:(0.1m)
Right-Mass(m4):(4kg), Planar, position:(x = 8/9m), r:(0.1m)

For the y-position: just drop on a fixed beam, and kill all rotation and velocities it has. Then continue the simulation with a free rotating beam.

Final Sim-result on (t=0.54 s)
v1=3.499 m/s, v4=-2.815 m/s
dh1=0.895, dh4=-0.798 (difference due to change in point of contact)
dPE1=8.846, dPE4=-31.928, Total.dPE=-22.982
(as you'll see: I'm not there yet in reconstruction)

As much as you would like to address moments-of-inertia (rotational KE), there first need to be some basic-understanding of your presentation. I guess some rotational-KE is the lesser factor in the found discrepancies, perhaps even on the edge of the significant numbers used.

Marchello E.

[ME]

ey, Me again... (3 in a row, I must be getting annoying now)

I just looked at the sim (with previous parameters).
Here's an animation of the lifting-side (it steps a bit fast at the end).
As can be seen the weight starts closer to the axle, and ends further away; despite the constraint of having a constant x-location.
Also there's no significant rotation. It rotates a bit down when low, and then rotates back when leaving the horizontal.

Marchello E.

[Fletcher]

Update :

Thanks ME for the comments.

No offence intended but I will leave your animation example for the moment as it's direction is taking me away from the path I'm on which is taking all my concentration.

......................

Thanks Wubbly also, much appreciated.

I read thru your explanations and math earlier this week, which were well presented as always. I intend to re-read it again in the next few days and see if I have any extra thoughts the second time around over and above my initial ones as I first read it. A little time often clears my head which makes for clearer thoughts in my case usually. I greatly appreciate anyone who knows their subject and can articulate it well so that goes for ME and Mr V as well.

.......................

Soon I will continue my story of searching for a physics and mechanics anomaly (as is so fashionable a term at the moment).

And addressing whether WM2D (a sim re: possible programming limitations or restrictions) could ever show a legitimate violation of CoE (e.g. KE and momentum gain) without the addition of fake extraneous forces added to a wheel system to cause self sustaining rotation.

i.e. Could a configuration or arrangement of mechanics in WM2D (or real world) using gravity force and inertia gain rotation and then accelerate (consistently increase its RPM) to a geometrically determined operating speed with no further external source of energy given to the system once in motion ?

My investigations obviously involve the basic pantograph mechanism and its many and varied guises and names such as scissors, storksbills, student forceps, 'x's' and 'v' sections, etc, and their functional performances under certain conditions and arrangements.

I continue to look for a potential 'loophole'. The fat man is still singing - at least in my mind ;7)

[ME]

No offence intended but I will leave your animation example for the moment as it's direction is taking me away from the path I'm on which is taking all my concentration.

No problem; As you probably noticed I was bit puzzled how to reproduce your experiment and unable to see what I thought you intended.

So I guess there will be at least three new topics from your hand?

My short ideas:
WM2D-simulation-limits
My best guess: WM2D determines the next time-steps based on some previous events. Simply explained by constructing a polynomial of positions. Velocities, accelerations and higher powers are thus automatically included and determinable by basic differentials down to a certain level. This means when things accelerate and time goes by, the preceding condition gets out-of-(polynomial)-scope and will therefore not be used to balance energies to counteract probable PM-mechanisms.

Could a configuration or arrangement of mechanics accelerate
I would like to simplify this to: Is it possible for a mechanism to be overbalanced most of the time during a single rotation.

Ah well, I hear something similar or perhaps the same...

Marchello E.

[Fletcher]

It depends on what we call overbalanced ME .. Bessler said his wheels were driven by imbalance.

But he also said for example ...

No. 4: Here the lines curve a great deal and are made up of half circles. It was imagined without doubt that movement could be obtained in this way; but the former invention and the latter are the same thing.

Granted! One finds out through calculation and on paper, on one side somewhat more than on the other side, that a superior weight equalizes; observe! Thus there will always be stability and no mobility; why?

Answer: because the friction, owing to the machine's own weight and heaviness, eats away all the supposed superior weight; sufficiently understood.

- Johann Bessler

Today, especially here, we would say that friction was best kept low in all situations as it robs any system of energy but that there was never any enduring superior weight from weight imbalance force. (N.B. image of MT4 shown near the keel position of least GPE) And that segment positive torque always equals segment negative torque with position of zero torque (equilibrium of forces) in between these maximums, in supposed weight force OOB wheels.


So .. I say differently that a generic force imbalance potentially could make a gravity-motion wheel (the mechanism) imbalanced most of the time during a single rotation. There is a difference !

ETA: then again, today we are mentally hamstrung by our modern education and tolerance for CoE doctrine which wasn't common knowledge in the 1700's.

[ME]

In notice here with MT004 the same issue as seen in MT013 with Bessler's use of the term 'friction'. Friction is not the root-cause why those things fail (as you point out): 'Friction' translates best as negative torque. Although MT030 and MT032 smell like the common use of 'friction'.

There's by the way a whole train of cause-effect relation which eventually could be something like: gravity -> <unknown> -> mech.imbalance -> mech.torque -> wheel torque -> wheel rotation -> perpetual motion -> ...

[Fletcher]

I agree. There is little doubt in my mind that Bessler's wheels (assuming they were genuine) comprised two separate mechanical systems that interacted in a cause and effect relationship.

1. the Prime Mover structure which was the cause.

2. the secondary weight imbalance mechanism which was the effect.

Bessler wiki MT's re MT15:

"From this drawing alone, however, nothing of the prime mover's source can be seen or deduced although the figure shows the superior weight."

- Johann Bessler

Bessler wiki MT's re MT48:

"The principle is good, but this figure will bring about no mobility by itself until completely different, additional structures have been provided."

- Johann Bessler

I have been vocal about this for many years. Mainly because MT48's rolling balls and elevator OOB system is so overtly different from the stock and standard weighted levers types etc.

Neither OOB type works (is self sustaining where torques are not canceled) on their own without additional 'help' in the form of extra Rotational Inertia given to a wheel; or extra KE and momentum given to a wheel; or internal parts given additional GPE.

All of these things require Work to be done on the system. For any of those three things to occur in reality it would mean a violation of the Work Energy Equivalence Principle [WEEP], or said differently that WEEP does not hold for all mechanical situations. This has consequences for our understanding of physics and gravity as a conservative force, not to mention CoE.

Work done is of course force x displacement and we often cite Law of Levers as an example of a balanced situation => F1 x D2 = F2 x D1

Here is an interesting recent article about non-conserved work http://revolution-green.com/some-philos ... -for-free/

The question that has always plagued me is could the Prime Mover be OU capable on its own and self sustain its own rotation ? Or, is the secondary OOB system absolutely necessary because the Prime Mover structure can not be both cause and effect in one ?

I lean towards that it could operate by itself but I suspect Bessler promotes it as a bolt-on addition to other common garden sub-OU systems to make the story more complex to hide his secret (the deflection).

[ME]

Perhaps Prime* and Second* switch function somehow somewhere...

[Fletcher]

Yeah .. that's a natural conclusion I think. That there is some sort of positive feedback occurring between systems that reinforces into some small gain. Like in phase wave forms.

I've looked for such systems for years.

But still, I have to think that the Prime Mover must have been OU capable on its own.

Especially in light that Bessler wanted to establish a Christian School of mechanics etc after he sold his wheel IIRC.

Although what is known here as MT was not published by Bessler it is believed by many that this was to be at least one of the texts and subjects he would use and cover at his school.

It would be a boring read indeed if the MT book/instructional text contained just one picture of a Prime Mover. Much more interesting to include all other sub-OU types of Perpetual Motion Machines attempted thru history, including his personal history of the search.

Then you could lead the pupil thru the pitfalls and dead ends whilst learning some mechanics along the way. It would be hard not to be impressed with the author after the solution was revealed having seen the prior art in this area and the utter lack of success that only his persistence conquered, it seems.

[ME]

Like in phase wave forms

The problem with that it still needs some "offset" (like the attempts to use a second wheel). Oscillations on itself will average to zero.

I guess there's a need for some sort of implied resonance, because we can't directly use the wheel to phase-lock the mechanism: it'll keel or simply balance. That almost leaves the solution in a way of phase-locking it to the only constant force: gravity. And once it moves it locks itself to the wheel going the max RPM. Nothing new as we all tried this one way or the other.
This mechanism -on one rotation- it is not allowed to loose potential, while it must loose potential to enforce wheel rotation. So the mechanism might be a confused one, where it can't decide what to do; and when it does decide , or gets decided by perhaps a little persuasion or a locked gate, and hopefully uses the wheel to accomplish this task, it'll (suddenly) find itself situated in the same position needing to make the same decision how to loose potential, only some (partial) rotation further.

With this line of thinking it's getting more interesting to read about his 'Fortress of God' instead of his mechanics to find and extract some metaphorical guidelines how to "move forward" in life like: do you lead your own and what happens to the one you drag along or must one move in pairs persé, is there equality or similarities between these two; Is one allowed to dance and swing; and when will which door open or be closed...
Any research on this?

[Fletcher]

I have definite thoughts on your last paragraph. Though I confess I hadn't thought about the religious connotations and any metaphorical significance in those terms. Bessler did say that the solution came to him in a dream as a gift from God, so there is a master servant pairing acknowledged there.

Bessler does give a description of a pairing in AP.

AP XLIII http://www.besslerwheel.com/forum/viewt ... 182#128182

snip ...

I'd like, at this point, to give a brief description of it.
So then, a work of this kind of craftsmanship has, as its basis of motion,
many separate pieces of lead.
These come in pairs, such that, as one of them takes up an outer position,
the other takes up a position nearer the axle.
Later, they swap places, and so they go on and on changing places all the time.

... snip

[ME]

Yes, that's the text I had in mind (also another).

As old-christian churches tend to be strict, that 'snip' gets more interesting when combining this with his intention to 'church'-up his epiphany.

Bessler states that the wheel was a gift from God; He find people who are blind to the truth of PM; he wants to build a school to educate people, so I guess it's an obvious assumption to 'rescue' people while being busy anyway. And it can't deviate too much from his personal message... (unless he's a scam, then things are a bit different).

- For an 18th cent. church to say a 'pair' is of equal weight, and 'able to swap places' etc is quite revolutionary I guess (let's project this pair as man and woman)
- A less revolutionary way, but still a good advice, is that everyone (man) needs to be a leader and a servant from time to time (and swap regularly).
- or much less inspiring: one is either a leader or a servant (and this leader determines the way to go, as that's the reason to swap)...
I could get creative with this stuff myself and say something like: When those pairs do their "work" with the ground (gravity), they'll speed up on their path and be lifted by the wheel (circle of life? God?) itself. And who knows what happens when no "work" is done...?

The projectability of such metaphors depend on Bessler's view and insights, if he used metaphors in his religious texts at all (I don't know).
(ie: Das Evangelische sondersame Grosse Jubel-Jahr 1717 - can't find an online version)

[Fletcher]

And so we find ourselves led in this discussion in a round about way to the toy page. (see attachment form wiki)

In there you will find two pairs of items.

The first, A & B, supposed to be views of a Jacob's ladder (which I do not doubt). You know the one; where angels alight on the rungs to do God's bidding and ascend to heaven etc.

The second pair being, C & D; the Hammermen toys.

.......................

I will shortly go back to Wubbly's analysis and make some observations and perhaps reach some conclusions for my own satisfaction about scissors and storksbills mechs.

The objective of studying them in some detail was to find if there was anything that pointed to some sort of hidden (unaccounted for) physical anomaly. Perhaps an ability to transfer more Momentum than other mechanical arrangements can do; so churning out more KE than CoE allows for ?

Perhaps they are just extra_ordinary after all ?