Toad Elevating Moment

[johannesbender]

i would guess that net torque direction would depent on the direction of friction , if i understand the drawing (and i do not understand the tecnical jargon) .

because to me you are using the counter result of torque on a lever ( the same as a helicopters tail ) , without friction this would not happen if i were to imagine the situation . so i presume the initial direction of spin and friction would determine the direction .

but how would such a spin be produced ?

[ruggerodk]

I've looked at yo-yo-ing over the last week - superficially attractive in that the weights might "climb back up to the center" by winding themselves up their spindles.

Apart from experimenting with the yo-yo set-up, I tried to reverse the it - that is, an Atwoods of the simple kind: A flywheel (the yo-yo, weight at rim) with the axle working as a pulley, from which a weight on a rope are winding down and back up.
The weight will 'climb back up' some 75-85%...depending on the axle radius.

Some very interesting things occour, as you can see from the attached spreadsheet (a revised copy of Wubbly's Atwoods experiment).

1. KE transfer from falling weight to flywheel
2. Large axle (pulley) radius = small KE transfer, high speed
3. Small axle (pulley) radius = high KE transfer, low speed
4. Small extra gain after a 4:1 ratio of radius (flywheel:pulley)

Perhaps time is the 'greedy, evil root' JB was referring to...

I considered rolling the weights out radially then dragging them along the bottom of the wheel, like a 'rolling road' to allow them to pick up even more energy before climbing back up, but concluded this was still a zero-sum deal.

If you consider an almost total KE transfer to the flywheel (and the wind up), the CF figures in the spreadsheet gives you a hint to something better than a zero-sum deal.

Best regards
ruggero ;-)

[ruggerodk]

There are some historical similarities between the spinning top and yo-yo.
And some connection to JB hints....:

The second oldest toy in the world is the yo-yo. The first was the doll.

The oldest Chinese yo-yo found in the Shanxi Province was believed to be over 4,000 years old.
It can also be called (kōngzhōng) or hollow bell or 'empty bell'. The name can be derived from the side of the top in which looks like a bell.
The Chinese yo-yo was introduced to Europe in 1700s.

A recent variation on the Chinese yo-yo is called the single-bell Chinese yo-yo (i.e. spinning top). The yo-yo consists of only one bell, and creates an uneven weight distribution. This makes a wider variety of tricks possible, including spinning the yo-yo as a top on the floor and recapturing it.

A Greek vase painting from 500 BC shows a boy playing yo-yo. Greek records from the period describe toys made out of wood, metal, or painted terra cotta (fired clay).

From HarvardYoyoClub:
Cut the bamboo like the shape of a hip drum.
Pull it with two pieces of string. It slowly moves. 
When the wind blows, it spins like flowing water. In the mountain temple, 
Hear the harmony of bells.
-An, from "the Description of Capitol Happenings"

regards
ruggero ;-)

[MrVibrating]

Right, result....

Last night i tried applying a torque via WM2D's 'Torque' widget, but for some reason this didn't apply any corresponding counter-force against the beam... as if the flywheel was being torqued against the vacuum or something.. initially thought it might be revealing a flaw in my thinking, but then this morning i tried using a motor instead, selecting 'Torque' as its type rather than acceleration or rotation etc., and voila - it works!

So just to recap; we have a pure moment counterbalancing a weighted lever, and, because this pure moment can be located anywhere along the lever's length - from its pivot to the weight itself and anywhere in-between, it can be positioned directly over the weight's center of mass, using the weight's own rotational inertia to apply the pure moment that counterbalances the weight! Nice and handy eh...


So the obvious thing to do now is search for a symmetry break between the spin-up energy required vs the GPE of the raised weight... presumably they're hard-coupled in an unwavering linear relationship, however this must be tested as such; varying the rot. inertia, mass, lever length etc. etc.

In the attached sim the weight's mass is focused around its periphery to maximise rot. inertia, the motor is applied directly to the weight's CoM & axis of rotation, and the main wheel is fixed to the background in order to verify the balance - again, unpin it to watch the weight rise.



Gotta go work now, back later..

[MrVibrating]

..on me netbook so very breifly: will respond to above posts later when i have time to fully digest them.. but for now, a quick summary of why i think this may be close to a breakthrough:

- during its acceleration phase, the point of application of the weight plus beam is at the far left side of the main wheel... even though the weight itself is over on the right. This alone is a cool feat, allowing the weight to lift itself..

- no stator required. All the forces involved can be applied from within the rotating frame.

- again, for clarity - it is NOT necessary for the weight to spin in order to apply a pure moment. Indeed, the PM can be applied ANYWHERE along the beam, without altering either the PM torque or the beam's balance. If you don't know what a "pure moment" is, Google it; it's interesting and won't take a second (i gave links in a previous post). The PM is just a static force - no displacement is required in order to manifest it. Here, we're simply exploiting the convenient position-agnostic nature of the pure-moment to not only position it directly over the weight, but in addition, then using the counter-force to the weight's own rotational inertia, to manifest the PM and thus counter-balance the down-force due to gravity. Hence, the entire weight of the beam and flyweight is borne on the pivot at the far left... nothing's 'levitated', as such, rather, the beam is balanced at the pivot despite having the weight positioned at its unsupported end. Thus the weight lifts itself.

- this whole point about the weight lifting itself is really only applicable if there's a symmetry break between the requisite RKE of the flyweight vs the output RKE on the main wheel. Otherwise one might just as well assume the pure moment is lifting the weight, and the distinction becomes more academic, if you follow my drift.

Still, i'm excited by the current prospects... can't wait to get back to this later..

[Fletcher]

Mr V ..

Just an observation & perhaps a few questions from your last few posts.

Your rotational torque device reminded me of how a motorbike can change orientation while jumping in the air - you rev the engine which spins up the back wheel or you apply the rear brake to slow the back wheel i.e. pitch control - this 'torquing' raises or lowers the front end so you can land flat with a ramp etc.

Did you establish whether a spinning wheel on the end of a rod was easier to raise than a non spinning one ? - IIRC WM2D didn't show any variance when I built the sims to test this some years ago - perhaps real world shows something different ? [N.B. not including Magnus Effect etc from air friction].

Yes, there needs to be a clear advantage in less energy required to spin up the device [overcoming inertia & air frictions] verses the GPE achieved to be of any practical use IMO - funnily enough this energy asymmetry is one I'm also pursuing with my models, but using a slightly different approach to you - hopefully I'll have something to share & discuss soon enough.

[MrVibrating]

OK i'm getting massive OU from a crazily simple configuration here.

For the first cycle (one complete revolution of the main wheel) an input of 3.243 J yields an output of 89.616 J.

After the 2nd cycle the running total is now 7.103 J in, to 179.523 J out.

3rd cycle: 11.087 on the flywheel / 269.059 on the main wheel.

The trend so far seems to indicate progressively less input energy is required to maintain the pure moment the faster the wheel rotates (a time/speed thing?), and also that the rate of RKE increase on the main wheel decreases per cycle as speed increases. At this rate of change though any eventual equalisation point will be orders of magnitude beyond the safe operating speed of the flywheel... ie. you'd collect and reset after each cycle, presumably, rather than letting it accelerate up to infinity..

So anyway, here's what i'm doing... i got rid of the beam, attaching the flywheel directly to the main wheel. Then i found the torque value for the perfectly-balanced pure moment. At this point, the flywheel is positioned at 3 o'clock on the right side of the wheel, like this:



Incidentally, if we briefly remove the pure moment and instead lock the flywheel to the main wheel, the total GPE of the system at this position
is just 14.091 Joules - that's how much we could collect if we let the wheel rotate 90° so that the flywheight falls from its current 3 o'clock position, down to 6 o'clock. 14.091 J....

So anyway, in the position pictured above, if we apply a clockwise torque of precisely 14.8 N-m to the flywheel, it spins up, applying an equal and opposite counter-torque - a pure moment - that precisely equals the flyweight's downforce due to gravity. Hence as the flywheel accelerates, the main wheel remains perfectly balanced - all of the flywheel's weight is being borne at the main wheel's axle. Thus there's zero torque on the main wheel.

Also, as an attempt at a sanity check, i've attached an identical flywheel under identical torque, to the background, to ensure it has the same energy as the one mounted on the wheel. This was meant to eliminate the possibility that the gain on the main wheel is due to additional input energy that might be slipping in unnoticed, however i'm doubtful this is sufficiently rigorous, given the results. Still, FWIW both flywheels, mounted and unmounted, always show the same RKE.

So, after finding the perfectly-balancing pure moment, i invert it, from negative to positive. Now, the weight is exerting a downforce significantly greater than its static weight...

After 90° of clockwise rotation, the energy input to the flywheel has been 0.572 J (ditto the 2nd flywheel stuck to the wall). The energy on the main wheel however is 36.659 J.

So recall that the dead GPE was 14.091 J. We've input 0.572 J. Total input energy so far should be 14.663 J, yet we have 36.659 J on the main wheel - precisely 2.5 x OU for some reason!

The sim accuracy is cranked up to 2000/s : 1.000e+006, BTW.




Moving on, another 90° later we have:



44.840 J output on the main wheel, for 1.296 J input on the flywheel.

Now that the system has completed 180°, the pure moment is acting upwards, and the wheel is perfectly balanced and coasting. The flywheel's entire weight is only being borne at the main wheel's axle, not out at the flywheel's actual position. Which is kind of cool.

Another 90°:



2.252 J in / 52.997 J out.

And after one complete rotation:



3.246 J in for 89.768 J back out. 27.65x OU, apparently... something's not right.

Aside from the fact that this constant pure moment couldn't be sustained for more than a cycle or two, i'm thinking that this must mean the flywheel energy isn't a clean representation of the input energy, which is also going to the main wheel? In other words both RKEs are inputs, and their sum is the output.. that would explain it. I'm not sure how to proceed though...

Can anyone see a way to decisively delineate input from output energies? Is the extra energy manifested on the wheel also imparted to the Earth when the unmounted flywheel spins up? The inputs at the axles are torques, rather than energies, but we're only reading energies of the wheels... but if OTOH we input RKE to the flywheel at a constant gain per cycle (although i don't know how to do that) would that still exert the counter-torque needed to generate the pure moment?

Maybe i've hit a limitation of the sim? Is there a simple test rig i could build? Need to simplify the issue somehow..

[MrVibrating]

..here's the thing i don't get - if some of the input energy is going directly to the main wheel, it must be in the form of torque over angular distance, right? Yet if some of our 14.8 N-m of input torque was being applied to the main wheel instead of just the flywheel, then the flywheel should have that much less, and so accelerate more slowly than the unmounted flywheel.

In other words, if both mounted and unmounted flywheels have the same energy, then they're both receiving all of the input torque, whereas if some of it was instead torquing the main wheel, the unmounted flywheel should race ahead of the mounted one.. see what i mean? Nightmare.. I'm so confused right now...

[MrVibrating]

@ruggerodk

fascinating stuff, thanks for sharing... i'm sure inertial forces or their counter-forces are key to the solution. The Toys page seems to be shouting it, along with many of the later MT systems, expecially the final ones.. it's a shame the experiments get so much more complex. For now i'm just chuffed i found an inertial effect i can sim in 2D, even if it's outputting garbage..

I'll probably come back to yo-yos at some point when this pure-moment guff has run its course.. the climbing back up thing is tantalising... but then this pure-moment thing can do that too, if only i could work out why...!

[MrVibrating]

Mr V ..

Just an observation & perhaps a few questions from your last few posts.

Your rotational torque device reminded me of how a motorbike can change orientation while jumping in the air - you rev the engine which spins up the back wheel or you apply the rear brake to slow the back wheel i.e. pitch control - this 'torquing' raises or lowers the front end so you can land flat with a ramp etc.

Did you establish whether a spinning wheel on the end of a rod was easier to raise than a non spinning one ? - IIRC WM2D didn't show any variance when I built the sims to test this some years ago - perhaps real world shows something different ? [N.B. not including Magnus Effect etc from air friction].

I always considered that moto X pitch-control effect to be due to aerodynamic drag of the tire, however now that you mention it pure moments may play a significant role... however insofar as they apply to counter-forces during acceleration / deceleration, there'll be no effect from a spinning mass that's just coasting or slowly changing speed.

Varying the radius of a given mass varies its rotational inertia and thus provides another means of manipulating a pure moment for a given rate of rotation.

So short answer; nope, haven't done the physical experiment yet, though it'd be interesting to do so... The WM2D sim is simple enough though, just remove the main wheel from my earlier sim, leaving the lever attached to the background at one end and the accelerating flywheel at the other. I achieved the same effect by simply pinning the main wheel to the background. It is fascinating to play around with, but the principle's simple enough, as described here:

Yes, there needs to be a clear advantage in less energy required to spin up the device [overcoming inertia & air frictions] verses the GPE achieved to be of any practical use IMO - funnily enough this energy asymmetry is one I'm also pursuing with my models, but using a slightly different approach to you - hopefully I'll have something to share & discuss soon enough.

Wahey, great minds eh.. ;) Look forward to reading about it..

[ruggerodk]

...if we apply a clockwise torque of precisely 14.8 N-m to the flywheel, it spins up...

How do you intend to apply torque or spin to the flywheel?
How much energy do you need to accomplish exactly that?

A test rig could be to speed up a small motor which axle are pinned (fixed) to the main wheel.

Apart from that it's a very interesting subject ;-)

Though, two opposite and equal force - as mentioned in your linkpage - sounds much like Centrifugal opposing Centripetal forces.

EDIT: Are the direction of rotation of the flywheel vs mainwheel significant?
If spinning the flywheel on a not-pinned main wheel are balanced (i.e. the gravity weight of the flywheel on the main wheel are cancelled out), then what makes the main wheel rotate?

regards
ruggero ;-)

[Fletcher]

Aside from the fact that this constant pure moment couldn't be sustained for more than a cycle or two, i'm thinking that this must mean the flywheel energy isn't a clean representation of the input energy, which is also going to the main wheel? In other words both RKEs are inputs, and their sum is the output.. that would explain it. I'm not sure how to proceed though...

Can anyone see a way to decisively delineate input from output energies? Is the extra energy manifested on the wheel also imparted to the Earth when the unmounted flywheel spins up? The inputs at the axles are torques, rather than energies, but we're only reading energies of the wheels... but if OTOH we input RKE to the flywheel at a constant gain per cycle (although i don't know how to do that) would that still exert the counter-torque needed to generate the pure moment?

Maybe i've hit a limitation of the sim? Is there a simple test rig i could build? Need to simplify the issue somehow..

Hi .. can you post the actual WM sim file that you used here - I'd like to pull it apart & rebuild it to see if I get the same results - I need your original for direct comparison - ta.

[johannesbender]

A couple is used to describe the
rotational effect of two equal forces
that do not share a line of action. A
couple (or torque) is much used in
mechanical engineering. For
example, a combustion engine
delivers torque at its shaft, which
can be used to drive equipment. As
stated, a couple is a pure moment
and as such can only be destroyed
by a couple with a counter effect.
Otherwise, the total sum of the
forces will not be zero.
Example
We examine the tail rotor of a
helicopter. This rotor is also called
the anti torque rotor, as its purpose
is to counteract the reaction torque
on the fuselage as a result of the
applied torque to the main rotor by
the engine and transmission. When
this reaction torque is not
cancelled, the fuselage will rotate.
The anti torque rotor functions by
introducing a moment, which
consists of a thrust vector F which
works over the arm 'l' with origin
O. This origin O lies on the main
rotor shaft. We assume a right
angle between the arm 'l' and the
tail rotor thrust vector F. The
helicopter engine produces a torque
of 500 Nm during a hover. The
length of 'l' is 5 metres. What force
F is needed to prevent the fuselage
from spinning?
When we assume a right angle
between the arm 'r' and the tail
rotor thrust vector F, so the vector
products of F and r resolve to the
product of their magnitudes. The
moment M must counteract the
torque of 500Nm; in other words,
the sum of the torque and the
moment must be zero. This leads to
the equation 500 + 5F = 0 -> F =
-100N. The minus sign indicates the
direction needed to cancel out the
effect of the applied engine torque.

....

this is why i talked about a helicopter tail .
if i am off base i oppologize.

http://www.helistart.com/momentCouple.aspx

[MrVibrating]

@Fletch

Cheers mate, sorry meant to attach it last night...


Still, there's only three steps

1) horizontal beam, supported by pivot one end, other end has wheel attached

2) find the self-balancing pure moment (a constant torque) - this can be applied anywhere along the beam (ie. including directly over the weight wheel - hence we can use the weight wheel itself to generate it in the first place. However only the torque widget is strictly needed, no rotation required. After finding the pure moment via the torque widget, i switched it out for a motor instead, applying the same torque to the wheel)

3) invert the sign of that pure moment, so now the weight wheel is exerting twice its static weight

And that's it... two moving parts, massive OU...

[MrVibrating]

..Obvioushly, not-at-all OU really - both RKEs are inputs, i'm sure of it.

The thing is, when the pure moment is perfectly counter-balancing the flyweight, no work is being done on the beam; all of it is imparted to the flyweight and the beam remains motionless.

Yet rotate the beam 180 degrees, or invert the pure moment, and the rate of acceleration of the flyweight drops in relation to the acceleration of the beam. The net torque hasn't changed, but the distribution of output work has.

Therefore, the only way to preclude input energy going to the beam is to only apply the pure moment when it's perfectly counter-balancing the flyweight; breifly, for just a few degrees of rotation around the horizontal phase. Otherwise, if the PM can perform work on the beam, it will...

I'll try this later. This should still produce a net acceleration of the beam/main wheel, but presumably the gain will equal the work done on the flywheel...

So yep, bit of a confusing mess ATM but i'm getting a handle on it...



Edit: but hang on a minute - if the above reasoning is sound, then why doesn't the mounted flyweight lag the unmounted one? That was the whole point of having an identical unmounted flyweight.. it's not like i didn't think of this at the time. The unmounted flyweight was meant to eliminate such confusions. It's as if the sim is applying more torque than the 14.8 N-m it's supposed to hold constant - supplementing the torque leaked to the main wheel..

Logically though you'd expect the unmounted flyweight to advance over the mounted one, all else being equal...