Toad Elevating Moment

[Dunesbury]

Does your sim resemble one of these?

http://physics.kenyon.edu/EarlyApparatu ... scope.html

[MrVibrating]

It resembles a lollipop. It's a beam; one end is pivoted to a wall or post, and the other end has a vertical wheel attached, on a good bearing.


See the following page:

http://www.brown.edu/Departments/Engine ... couple.htm

Scroll down to "pure moments".

A pure moment is a torque applied to a balance beam or lever. If the torque magnitude is equal to an unbalancing force on the beam, it will balance it - regardless of its location along the beam... even if it's directly aligned to the overbalancing force that it's cancelling.

Because of this ability, i realised that a counter-torque generated on the beam by accelerating or decelerating the spin of the weight itself could supply the pure moment needed to lift itself.

This much is simple enough - and the simulation and theory are in perfect agreement.

However, if the radius of the weight increases, then so does its moment of inertia, and thus the torque needed to accelerate or decelerate it, and the corresponding counter-torque on the beam.


So for a given mass, a high radius flywheel can generate the same pure moment magnitude at a slow rate of velocity change, as a smaller-radius flywheel at much higher rates of change.

Likewise, the amount of energy that needs to be input to the flywheel to generate the required pure moment decreases inversely to radius - doubling the radius reduces the required input energy by a factor of four, to generate the same force.

Conversely, halving the flywheel's radius increases the amount of energy required to make it balance itself, by a factor of four.


All of the above points are demonstrated in my preceeding sims - they seem pretty solid conclusions and i trust them.


The upshot then is that if the beam IS balanced (and all available evidence confirms this) then we can reposition it vertically... basically for free.

So we have a lollipop, hanging upside down. Like a bicycle or motorbike's front forks, or rear swingarm. It's just a wheel, hanging from a beam, with a pivot at the other end of the beam. We spin up the wheel, which applies a counter-torque to the beam, hence, if the wheel's inertia is high enough, and we accelerate or decelerate it hard enough, then this counter-torque will reach a magnitude sufficient to balance the beam, even though the pure moment is aligned to the overbalancing force, as explained at the above webpage. Thus, perfectly counter-balancing its own weight, the accelerating or decelerating flywheel can lift the whole lollipop, rotating it about its pivot, which bears all of the weight while the pure moment is being applied.

In summary, it's a hanging lollipop, or pendulum, that only gravitates when it isn't balancing itself, but the cost of balancing itself is substantially less than the GPE we can gain by lifting it while it's balanced.

[ruggerodk]

MrVibrating:

Perhaps this will help...?

regards
ruggero ;-)

[johannesbender]

mr.v I completely get what you are saying and how it is remarkable , in many ways we could perhaps draw a few similarities with the actions of tops if we were not concerned about details .(just an example of what happens to your beam if we consider the top's point to be the pivot of the beam) although not the same thing I just made a simple visual connection to how a top rises. .

however it is the spin wich needs to be figured out , how to get the amount of spin needed to achieve the goal , I am sure you have ideas for this.

[MrVibrating]

That's the cool thing - no actual 'spin' is required... in the above sims, the 8 m flywheel can lift itself and the swing arm for just 15° of rotation.

The degree of angular displacement required is dependent on the relative radii of the flywheel and swingarm.

If negative torque is used, then the flywheel only needs 33°/s of spin, which can be applied while the thing is still hanging vertically. From thereafter, it only needs to brake itself against the swingarm.

If it's done the other way, with positive torque, the self-balancing pure moment for a 6 kg flywheel can also lift a 3 kg un-spinning load (ie a motor, rotational spring or whatever) attached at the flywheel's axis.

So, still some way from seeing a full mechanism but in theory at least, the requirements aren't particularly demanding, and no high speeds are required. Just a matter of careful calculation and coordination..

[johannesbender]

mr.v perhaps a simple physical experiment would be of higher value , if your correct then yes thats not really alot of spin needed

[Fletcher]

Mr.V .. I've been racking my brains to find a method in WM to act as a brake, other than the rotational damper etc - every friction method didn't work - I'll keep thinking on it.

What does occur to me is that I often only use the Translational energy of rotating masses in rotation because I once suspected the sim wasn't giving correct results for RKE.

I suggest you test the basics - build a ramp & roll the same dimensions & mass flywheel down it - see how much GPE is lost to give it the required RKE/RPM & make an adjustment for the translational Energy in your sums.

N.B. remember to put dynamic friction & static friction to 1.0 to stop any slippage.

Then repeat on up-ramp to see how high the flywheel will rise & the gain in GPE, for comparison.

N.B. you know how to place a flywheel on a ramp & alter its initial conditions already so that it can start from a standing start.

[MrVibrating]

MrVibrating:

Perhaps this will help...?

regards
ruggero ;-)

Hi mate, and thanks for giving it some thought!

Unfortunately WM doesn't support spools / spindles - something it sorely misses.. i've tried improvising them from chains but with limited success.


However, as useful as this would be as an accurate way of measuring / limiting input energy, there's certain issues to consider:

- the pure moment only exists when the flywheel is changing angular velocity, accelerating or decelerating... but rotation itself is incidental, almost a by-product. We don't need the weight to spin, but rather to change its rate of spin. Even then, 'spin' implies multiple revolutions, which we don't need; the most effective flywheels - those with high rotational inertia - only need to rotate by tiny increments... in the above examples the 6 kg mass raises itself 2 meters by rotating only 15 degrees.. provided it's speeding up or slowing down, it just needs a high moment of inertia to keep the angular displacements small, manageable and most importantly, cheap!

Applying this constant torque by dropping a weight during the lift could be tricky... but perhaps not insurmountably so.

And it would actually be a good methd for a real test rig running the negative torque version.. however this would still leave the question of how to apply a consistent braking torque. But simply for accurate energy accounting, it's definitely a good idea.

- For the accelerating version however, the further point to remember is that the torque has to be applied between the flywheel and the beam. It's no good accelerating the flywheel unless it's pushing against anything other than the beam, since the only reason we're doing it is to generate a corresponding counter-torque on the beam... and it's that counter-torque we're really after - the flywheel is just something for it to bounce off.

So i wouldn't expect any lifting force from accelerating the flywheel via a spool, unless it was arranged in such a way as to apply a force between the beam and wheel.



You're thinking along the right lines though.. FWIW i've played a little with WM's rotational spring constraint, which works fine for a narrow but useful range of response. So that's another potential way to go... but you've got the gist - there should be almost twice as much energy in the drop, as the spin-up / down... easily enough to reset whatever mechanism we can find.

Simple cycle eh? There's gotta be an easy way to implement it!

[MrVibrating]

mr.v perhaps a simple physical experiment would be of higher value , if your correct then yes thats not really alot of spin needed

Definitely. I've only given it scant consideration as i can't yet decide how to proceed with the basics - how to apply torque, + or - etc.

I don't want to resort to motors or any electronics if they're unnecessary. For a high-moment flyweight i'm considering a 1 meter balsa beam with flat lead squares nailed to each end, like a stretch TIE-fighter type shape...

But i'm unsure about what to try and build, or what the options are. Brake tests seem the best way to go - eliminating any possibility of further energy input, and only requiring controlled friction...

But even then, what to use as a constant-torque brake? Doubtless there's a simple way to improvise one.... but how?

[rlortie]

Have you considered a Prony Brake?

http://en.wikipedia.org/wiki/De_Prony_brake

A search here in "general Discussion" shows 18 hits!

[MrVibrating]

Mr.V .. I've been racking my brains to find a method in WM to act as a brake, other than the rotational damper etc - every friction method didn't work - I'll keep thinking on it.

What does occur to me is that I often only use the Translational energy of rotating masses in rotation because I once suspected the sim wasn't giving correct results for RKE.

I suggest you test the basics - build a ramp & roll the same dimensions & mass flywheel down it - see how much GPE is lost to give it the required RKE/RPM & make an adjustment for the translational Energy in your sums.

N.B. remember to put dynamic friction & static friction to 1.0 to stop any slippage.

Then repeat on up-ramp to see how high the flywheel will rise & the gain in GPE, for comparison.

N.B. you know how to place a flywheel on a ramp & alter its initial conditions already so that it can start from a standing start.

Not sure i'm following (it's late sorry, bit frazzled) - you're suggesting drawing the RKE from a consistent GPE, but then won't all the diferent wheels reach that same RKE at the bottom of the ramp? We could just check the energies from first principles (half inertia times angular velocity^2 or whatver the formula) to confirm they're correct. However the 'requisite' input RPM and RKE are almost secondary and tertiary issues to the requisite counter-torque, since this is what balances the beam and exempts us from inputting GPE.

I admit i don't fully comprehend this apparent inverse-cube relationship between MoI and RKE - IIRC it's limited, as previous tests show it converges beyond about 16 - 32 x the default radius. However it seems to make sense that higher MoI means more output force for less change in RPM, and that consequently lower RPM means lower input energy.

Dunno. Needs nailing down, for sure. But this was precisely the reason i stopped using compound objects as flyweights - too many variables to slip up on. And i stopped making one-peice polygon flyweights because they don't resize consistently and it's too much hassle to make umpteen different ones for each batch of tests... so i'm sticking with homogenous discs until i find a design worth more effort.

If it throws any light however, there's a rational inclination to assume that input energy and output force magnitude should be tightly bound, yet this isn't generally the case - for instance a finely-wound solenoid could generate a higher field density and resulting force at lower input energy than a coarsely-wound higher-energy one... what really matters is not the energy required to manifest a force or feild, but simply the work that is done against that field. In principle, simply manifesting a field costs nothing. Only the work it subsequently does counts. And in our case, here, it's a counter-balancing force that obviates input GPE (and into the bargain, having to re-lift a conventional counterbalance) - but the actual work that is done via it is negligible, equivalent to a horizontal translation..

The current test rigs are beguiling, misleading - one has to keep reminding oneself that the weight isn't where it appears to be. It's not where the mass is, but over at the other end of the beam, at the pivot. Put the mass on the right side of a wheel, and fix the beam's pivot to its left side, then apply a pure moment and the weight 'lifts' itself, because it's really balancing itself,.. we see the 'weight' over on the right, but our eyes decieve, and the wheel knows better, turning anti-clockwise because all of the weight, beam plus flywheel, is actually borne on its left side. There is no weight on the right side. No 'weight' has been 'lifted' - all of the weight fell! Nonetheless the mass generating that weight has risen....

That thought experiment pretty much summarises the exploit here.


Braking torque is a finnicky problem though isn't it..? I considered using WM's friction, but figured getting a linear response would be too hit'n'miss.. there's gotta be a more elegant solution...

[MrVibrating]

Have you considered a Prony Brake?

http://en.wikipedia.org/wiki/De_Prony_brake

A search here in "general Discussion" shows 18 hits!

Hadn't, good call. Can it apply a constant force across a range of speeds though? I'm thinking friction usually increases with speed..

It's a start though, something to chew on, cheers...

[Fletcher]

OK .. here's a sim I quickly modified with some output cross checks - it has pulleys & pulley ratios etc PLUS Pin Friction Coefficient & Pin Radius etc - pull it apart & use what you can to make a pin friction brake response & also a traditional pulley.

ETA: to make a pin with friction use the bottom left symbol - the one with the question mark [generic pin] - under properties enable friction & add values for pin friction coefficient & pin radius - it helps to link these fields to input boxes - this should make a friction brake

[MrVibrating]

Minor update - realised an interpretation of the Meresburg illustrations that seems highly consistent with the current config:




I was initially skeptical that this could've been what Bessler was doing, however in light of this i'm much more confident..

Also, i realised that there's another very simple cycle available:

- Drop the empty beam end (the pivot) while the pure moment is being applied

- then stop the pure moment, and allow the flywheel end to drop.

Et Voila! We've dropped two weights from one mass - effectively dropping the same thing twice.... but we only need to re-lift it once!


Finally, included is a (very) lossy brake test - the purpose of which is not the energy lost by the crappy non-linear rotational damper, but rather tha input vs output F x D integrals for the beam alone...

The thinking is, if the beam is balanced on the way up, as anticipated, then there's less force acting on it, and conversely more force acting on it as it falls back down.

Plotting the line integral seems to strongly support this asymmetry being real:



The first bump on the left is the up-swing, and the second along is the down-swing. Again, this work integral is just for the beam, not the weight, but both bumps represent the same 90° of angular displacement - it swings up to horizontal, then back down to vertical again. The displacements are equal but the integrals aren't, and the additional force in the second bump is gravitational weight, absent from the first bump (the subsequent bumps are just the residual swinging after the interesting action has played out).



Do i win the £5 yet..?

[MrVibrating]

OK .. here's a sim I quickly modified with some output cross checks - it has pulleys & pulley ratios etc PLUS Pin Friction Coefficient & Pin Radius etc - pull it apart & use what you can to make a pin friction brake response & also a traditional pulley.

ETA: to make a pin with friction use the bottom left symbol - the one with the question mark [generic pin] - under properties enable friction & add values for pin friction coefficient & pin radius - it helps to link these fields to input boxes - this should make a friction brake

Fletch you genius you.. no need to wait for me, just go for it! Let's get this thing over with...

Just give the wheel an arbitrarilly high rate of spin to begin with, set the beam horizontal and find the friction necessary to hold the beam stable and horizontal for as long as is possible - you now have a perfect balancing pure moment using only negative torque.

Then set the beam vertical and find the RPM reached when the beam has climbed back to horizontal by applying that same torque via a motor.

Finally replace the motor with the brake again, input that RPM as a starting condition and the thing should climb back to horizontal just as the flywheel comes to a halt.

If it doesn't make it back to horizontal then we can draw the firm conclusion that the rotor energy is doing lifting work, and full GPE applies to the weight during the lift. I'll just be glad for the closure.


However if it DOES lift itself all the way back up then the £5 is mine, all mine, and i'm blowing the lot on chocolate and fizzy pop, bwahaha etc.



Thanks for providing the toolkit, and i will have a play with it, provided it doesn't crash my WM. But from hereon, your kung fu is clearly better than my kung fu and there's no point holding out for me to catch up... i'm really not bothered who's first across the finish line...