Author Topic: Ever heard of dynabeads?  (Read 45037 times)

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Offline mlinder

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Re: Ever heard of dynabeads?
« Reply #400 on: September 16, 2009, 12:59:45 PM »
Naw, I don't care about friction for this discussion. Besides, the beads roll instead of sliding, so there's very little friction in there. I'm just saying that the radial force will cause them to move outward to the wall of the inner tube, and the tangential force will cause them to migrate to balance. The only reason the beads don't move after balance is there is no tangential force to cause them to move, since there's no shock displacement after balancing. That's all. The radial force will keep the beads stuck to the side of the tube, but does NOT cause them to try to migrate to the heavy side of the tire. There is no force in the system causing movement toward the heavy side. Changes in radial force due to elliptical motion do NOT cause bead migration, they just cause a change in radial force of the bead pressing on the inner tube. Remember, radial force is acting straight INTO the tube, pressing the bead into the tube surface. A ball doesn't move if you push straight down on it. I've decoupled the motion of the shocks into radial (in-phase) and tangential (out-of-phase) components, and the tangential component is the one doing the bead-moving.

Bistro, the centrifugal force would send them to the point furthest from the rotation point as the wheel begins to speed up and centrifugal force becomes greater than gravitational force and whatever the force (or lack of) is that allows the beeds to rotate inside of the wheel. As speed increases, they will continue to pool at the point furthest away from the rotational center. Eventually we get to the point where your radial force causes them to stay where they are... at the point furthest from the rotational center, where they add to the imbalance. Is your tangential force greater than centrifugal force? Because according to you, they are working in direct opposition to each other.

However, I think I've figured out what people are saying contrary to this, and it does make sens in certain conditions. I'm gong to make a diagram and let you geniuses do the math for it, but it may take a bit to make, working with a graphics program I'm not proficient with.
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Offline bistromath

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Re: Ever heard of dynabeads?
« Reply #401 on: September 16, 2009, 01:09:34 PM »
Please, believe me on this one. The change in radial acceleration due to shock travel will not move them toward the heavy spot in the tire. Centrifugal force is radial acceleration, just so we're clear on terminology. The beads at the heavy spot have the greatest radial acceleration, this is true. It points straight out the tire. The beads 20 degrees away have slightly less radial acceleration. This acceleration vector still points STRAIGHT OUT THE TIRE. Since it points straight out the tire, and not toward the heavy spot, that force will NOT roll the beads toward the heavy spot. It is the tangential component that moves the beads.
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Offline mlinder

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Re: Ever heard of dynabeads?
« Reply #402 on: September 16, 2009, 01:11:50 PM »
So, you are saying that items with mass will not seek the furthest available space away from a rotational point?
Or am I misunderstanding?
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Offline bistromath

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Re: Ever heard of dynabeads?
« Reply #403 on: September 16, 2009, 01:13:58 PM »
You're misunderstanding. I don't know how to make it clearer... I'll try to draw up a diagram but my Photoshop skills aren't exactly solid.
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Offline IHWillys

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Re: Ever heard of dynabeads?
« Reply #404 on: September 16, 2009, 01:26:38 PM »
I will skip to the end and present someone else's version/demonstration of what's happening.  This is from the Centramatic site which is a similar product in that it uses many small balls that are free to distribute inside a torus intended to balance a rotating assembly.  I have some issues with some of what is shown in the the video but it does show a rather uneven distribution of the balancing balls while the assembly is under heavy imbalance without them and more even distribution while the assembly is closer to being balanced.  


I'm with the "science" guys here but I think, as mlinder has stated on multiple occasions, they/we may not be putting forth the full "story" when it comes to the physics involved.  I'm not going to try as I don't have enough formal training to argue and got lost in a few of them here so I simply can't argue/refute something I don't understand enough to see where any mistakes or deficiencies exist in said arguments.  Does that last sentence even make sense?  Oops, writing outloud again...

Goodness, some simple blinded tests sure would go a long way toward establishing a real effect or not, aside from explaining why/why not.

Ken

Offline Inigo Montoya

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Re: Ever heard of dynabeads?
« Reply #405 on: September 16, 2009, 02:06:42 PM »
How much that applies to the dynabeads is hard to say, appears to be the same basic idea. It was a very cool video though.

Offline dilbone

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Re: Ever heard of dynabeads?
« Reply #406 on: September 16, 2009, 02:11:25 PM »
Please, believe me on this one. The change in radial acceleration due to shock travel will not move them toward the heavy spot in the tire. Centrifugal force is radial acceleration, just so we're clear on terminology. The beads at the heavy spot have the greatest radial acceleration, this is true. It points straight out the tire. The beads 20 degrees away have slightly less radial acceleration. This acceleration vector still points STRAIGHT OUT THE TIRE. Since it points straight out the tire, and not toward the heavy spot, that force will NOT roll the beads toward the heavy spot. It is the tangential component that moves the beads.

centrifugal force is really no force at all...it is centripetal force...objects aren't being "thrown" to the outside by some mysterious force...it is the centripetal force of the tire/tube on the beads that pushes them into a circular path... Centripetal force and acceleration are both pointing into the center of the circle not the other way around.
the fact that the beads want to keep moving in a straight line tangent to the tire is what causes this thing you keep referring to as "centrifugal" force.  It "seems" as though the beads are cause of the force, but it is indeed the tire/tube...like a passenger in a car that is making a turn as I already mentioned.

Video was awesome IHWillys, very cool.

It's making me think a lot about all of this.

Also, amazing how civil now we all can be as we discuss...kinda nice huh?


Offline bistromath

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Re: Ever heard of dynabeads?
« Reply #407 on: September 16, 2009, 02:57:26 PM »
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centrifugal force is really no force at all...it is centripetal force...objects aren't being "thrown" to the outside by some mysterious force...it is the centripetal force of the tire/tube on the beads that pushes them into a circular path... Centripetal force and acceleration are both pointing into the center of the circle not the other way around.
the fact that the beads want to keep moving in a straight line tangent to the tire is what causes this thing you keep referring to as "centrifugal" force.  It "seems" as though the beads are cause of the force, but it is indeed the tire/tube...like a passenger in a car that is making a turn as I already mentioned.

Yeeaaaaahhh, I know. I figured someone would bring that one up, figures it's the physics teacher. ;D Centrifugal force is commonly used to refer to the equal reactive force opposing centripetal force, which becomes a "fictional force" when you have a rotating inertial frame. Just flip the sign and say "centripetal" instead if it makes you feel better. I'm using it because it's easier to conceptualize the action from the beads' perspective using a rotating inertial frame, and because people more commonly think about "centrifugal" rather than "centripetal" force.

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Also, amazing how civil now we all can be as we discuss...kinda nice huh?

Nooooo kidding. Much more pleasant in here.
« Last Edit: September 16, 2009, 02:59:07 PM by bistromath »
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Offline mlinder

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Re: Ever heard of dynabeads?
« Reply #408 on: September 16, 2009, 03:00:51 PM »
OK, so, I've been arguing that the heaviest part of the tire will be furthest away from the rotational center.

If so, I'm pretty sure that anything with mass will go to the furthest point available from that rotational center.


And it's true, I've seen it happen.

There are a lot of formulae that explain this. I just don't happen to know them off the top of my head.
Please excuse my crappy animated gifs, I made them in a program I've never used before for this kinda crap.


OK, so we see the ball as the 'heavy' point.

The forks extend and compress as the wheel spins, rotational and inertial (well, ok, rotational force, though it's just inertial force that's being redirected in a circular motion :P) force translated to straight inertial force at the forks, with the heavy spot distended beyond the average radius.

Far as I know, everything in that wheel is motivated to travel to that spot. Centripetal, centrifugal, wtf ever.



However, I think I figured out what they are saying is actually happening, and I know it CAN happen, because I've seen it happen, too..


In this, we see that the wheel is rotating around the middle of the entire wheels mass.

Enough of the lighter side has moved further away from the rotational center to offset the extra weight of it's opposite side, meaning that from a geometric center, it is not balanced, but from a mass center, it is.

Now, I know both of these happen. But, I don't know enough to be able to tell you why one or the other happens in a given situation. I do know that the second is dependent upon rotational speed and amount of mass that is 'out' of balance. Speed up or slow down outside of that window and it goes to the first scenario up there.
My head is having a little trouble dealing with what would happen to the beads in this scenario, because I haven't had time to think about it yet, but soon as sort through 3 conflicting results I currently have, I'll post it or them.

« Last Edit: September 16, 2009, 03:03:23 PM by mlinder »
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Offline bistromath

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Re: Ever heard of dynabeads?
« Reply #409 on: September 16, 2009, 03:12:07 PM »
Nice animations! Really helps to conceptualize things. Thanks for putting those together, they're better than anything my meager photoshop skills could put together.

What I've been trying to put out there is that the beads in your first animation DON'T want to move toward the heaviest spot, because there's no force pushing them laterally in that direction. If the wheel were elliptical, you would be right, and if the wheel were free to move forward and backward as well as up and down, I believe you would also be right in that case. But in this case, and both videos posted back me up in this, there is no force pushing toward the heaviest point. There is in fact a tangent force in the opposite direction, strongest 90 degrees off from the heaviest point, and weakest at the heaviest and the lightest point. I'm not crazy! The math I posted above shows it.

Maybe I was confusing in my initial terminology, as I didn't fully understand it all yet at the time: the motion of the wheel is not strictly elliptical. It is circular, with an axis that is moving back and forth sinusoidally. The motion at the heaviest point can be termed elliptical, as can the motion at the lightest point, if you were to trace the motion of those points.

Your first image is the one that describes the unbalanced motion. I'm not sure what your second one describes. I believe in order for your second image to work you would have to have the axis at the center of mass, and the shock somehow connected to the center of rotation.
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Offline Slayer

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Re: Ever heard of dynabeads?
« Reply #410 on: September 16, 2009, 03:21:07 PM »

Offline paulages

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Re: Ever heard of dynabeads?
« Reply #411 on: September 16, 2009, 03:22:54 PM »
Mark- an analogy for what I believe bistromath is trying to say: imagine that you're on one of those space camp G-force rides (I grew up near huntsville, AL where NASA has their space camp museum  ;D), where it spins and spins until you're plastered to your chair. Now imagine overcoming that force to crawl around to wherever you imagine the analogous "heavy point" to be. The force keeping you from travelling radially past your chair is stronger than the force attempting to get you to that farthest point from the axis.

I think that's what he's saying anyway.
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Offline mlinder

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Re: Ever heard of dynabeads?
« Reply #412 on: September 16, 2009, 03:25:23 PM »
Nice animations! Really helps to conceptualize things. Thanks for putting those together, they're better than anything my meager photoshop skills could put together.

What I've been trying to put out there is that the beads in your first animation DON'T want to move toward the heaviest spot, because there's no force pushing them laterally in that direction. If the wheel were elliptical, you would be right,
But it doesn't mater if the wheel is elliptical. It only matters that the radius point furthest away from the axis is. As far as the beads are concerned it's the same thing.
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and if the wheel were free to move forward and backward as well as up and down, I believe you would also be right in that case.
But they can move in a radius of 360 degrees on cars, and these are made for cars.
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But in this case, and both videos posted back me up in this, there is no force pushing toward the heaviest point.
addressed this issue with the fact that the path of the 'heaviest point' is the same regardless of whether its the wheel itself that's elliptical with the heavy point following that ellipse, or the path of the heaviest point is elliptical.
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There is in fact a tangent force in the opposite direction, strongest 90 degrees off from the heaviest point, and weakest at the heaviest and the lightest point. I'm not crazy! The math I posted above shows it.
'K :)
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Maybe I was confusing in my initial terminology, as I didn't fully understand it all yet at the time: the motion of the wheel is not strictly elliptical. It is circular, with an axis that is moving back and forth sinusoidally. The motion at the heaviest point can be termed elliptical, as can the motion at the lightest point, if you were to trace the motion of those points.
Yeah, but the energy, or force, is pretty much elliptical.
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Your first image is the one that describes the unbalanced motion. I'm not sure what your second one describes. I believe in order for your second image to work you would have to have the axis at the center of mass, and the shock somehow connected to the center of rotation.

It's funny, the second one is the explanation from teh manufacturer of why they do work. They are saying the wheel will travel around the central point of the mass. Or that the beads cause the wheel to travel around the central point of mass. I'm not sure yet.
Still working on this in my head.
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Offline mlinder

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Re: Ever heard of dynabeads?
« Reply #413 on: September 16, 2009, 03:30:21 PM »
Mark- an analogy for what I believe bistromath is trying to say: imagine that you're on one of those space camp G-force rides (I grew up near huntsville, AL where NASA has their space camp museum  ;D), where it spins and spins until you're plastered to your chair. Now imagine overcoming that force to crawl around to wherever you imagine the analogous "heavy point" to be. The force keeping you from travelling radially past your chair is stronger than the force attempting to get you to that farthest point from the axis.

I think that's what he's saying anyway.

Yes, he did say that, but that's only true if acceleration is instantaneous from a standstill to whatever the speed may be that I can no longer move from my chair.

Hi Paul :)
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Offline bistromath

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Re: Ever heard of dynabeads?
« Reply #414 on: September 16, 2009, 03:32:44 PM »
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Mark- an analogy for what I believe bistromath is trying to say: imagine that you're on one of those space camp G-force rides (I grew up near huntsville, AL where NASA has their space camp museum  ;D ), where it spins and spins until you're plastered to your chair. Now imagine overcoming that force to crawl around to wherever you imagine the analogous "heavy point" to be. The force keeping you from travelling radially past your chair is stronger than the force attempting to get you to that farthest point from the axis.

Hell, I'm not sure what YOU'RE saying!  ;D ;D ;D

I'm gonna leave this one alone until my skull stops hurting. I'm pretty sure I got it with my math above, though, and it works out well with the explanation on the Dyna Beads site itself as well as the two videos. Still, a fun problem!

Whoop! I'll reply to mlinder's last one here. Have to get SOME work done today....

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But it doesn't mater if the wheel is elliptical. It only matters that the radius point furthest away from the axis is. As far as the beads are concerned it's the same thing.

No, it isn't. It really isn't. Plot the motion of a bead 20 degrees off axis from the heaviest point, and you'll see. It really, really isn't.

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But they can move in a radius of 360 degrees on cars, and these are made for cars.

That supposition of mine was wrong, then, also shown by the first posted video, which clearly showed a 2-axis-free system that still balanced. Ignore me! ;D

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Yeah, but the energy, or force, is pretty much elliptical.

No, the force is not elliptical, or at least not the same ellipse at all points -- "pretty much" isn't close enough. Energy has nothing to do with this.

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It's funny, the second one is the explanation from teh manufacturer of why they do work. They are saying the wheel will travel around the central point of the mass. Or that the beads cause the wheel to travel around the central point of mass. I'm not sure yet.

The latter. What they really do is cause the center of mass to coincide with the axis of rotation.

I mean, I've shown math that describes the motion of the beads in a way that reflects the videos that were posted, and the purpose of the invention itself. If you're trying to prove they don't work, it'll be hard, because it's apparent that they do. I'm really just trying to find the mechanism behind it, and I think I did.
« Last Edit: September 16, 2009, 03:37:27 PM by bistromath »
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Offline BVCB650

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Re: Ever heard of dynabeads?
« Reply #415 on: September 16, 2009, 03:44:03 PM »
Holy Crap!! This stupid thread is still going strong? Let me make it simple......I lied. Lied, lied, lied. The stupid balls suck. My tires wore out before I even got home. Damn thing was vibrating so badly, I had to pull over and push the bike home. I will demand a refund dammit!!!
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Offline mlinder

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Re: Ever heard of dynabeads?
« Reply #416 on: September 16, 2009, 03:50:18 PM »
Quote
Mark- an analogy for what I believe bistromath is trying to say: imagine that you're on one of those space camp G-force rides (I grew up near huntsville, AL where NASA has their space camp museum  ;D ), where it spins and spins until you're plastered to your chair. Now imagine overcoming that force to crawl around to wherever you imagine the analogous "heavy point" to be. The force keeping you from travelling radially past your chair is stronger than the force attempting to get you to that farthest point from the axis.

Hell, I'm not sure what YOU'RE saying!  ;D ;D ;D

I'm gonna leave this one alone until my skull stops hurting. I'm pretty sure I got it with my math above, though, and it works out well with the explanation on the Dyna Beads site itself as well as the two videos. Still, a fun problem!

Whoop! I'll reply to mlinder's last one here. Have to get SOME work done today....

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But it doesn't mater if the wheel is elliptical. It only matters that the radius point furthest away from the axis is. As far as the beads are concerned it's the same thing.

No, it isn't. It really isn't. Plot the motion of a bead 20 degrees off axis from the heaviest point, and you'll see. It really, really isn't.

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But they can move in a radius of 360 degrees on cars, and these are made for cars.

That supposition of mine was wrong, then, also shown by the first posted video, which clearly showed a 2-axis-free system that still balanced. Ignore me! ;D

Quote
Yeah, but the energy, or force, is pretty much elliptical.

No, the force is not elliptical, or at least not the same ellipse at all points -- "pretty much" isn't close enough. Energy has nothing to do with this.

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It's funny, the second one is the explanation from teh manufacturer of why they do work. They are saying the wheel will travel around the central point of the mass. Or that the beads cause the wheel to travel around the central point of mass. I'm not sure yet.

The latter. What they really do is cause the center of mass to coincide with the axis of rotation.

I mean, I've shown math that describes the motion of the beads in a way that reflects the videos that were posted, and the purpose of the invention itself. If you're trying to prove they don't work, it'll be hard, because it's apparent that they do. I'm really just trying to find the mechanism behind it, and I think I did.

Will respond in a sec..
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Offline Duke McDukiedook

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Re: Ever heard of dynabeads?
« Reply #417 on: September 16, 2009, 03:52:37 PM »
The plane will not fly...

The plane will not fly...
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Offline Simpson

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Re: Ever heard of dynabeads?
« Reply #418 on: September 16, 2009, 03:56:00 PM »
I see this topic plagues many forums.
http://www.advrider.com/forums/showthread.php?t=353020

Perhaps when mankind finally develops the grand unified theory of the universe Dynabeads will be explained also.
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Re: Ever heard of dynabeads?
« Reply #419 on: September 16, 2009, 04:04:44 PM »
Definition

A placebo effect occurs when a treatment or medication with no therapeutic value (a placebo) is administered to a patient and the patient's symptoms improve. The patient believes and expects that the treatment is going to work, therefore it does.

The placebo effect is also a factor to some degree in clinically effective therapies, and explains why patients respond better than others to treatment despite similar symptoms and illnesses.



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Re: Ever heard of dynabeads?
« Reply #420 on: September 16, 2009, 04:06:21 PM »
Hey Bob, most of us are trying to have a reasonable discussion about these friggin beads and old "silicon dick" can't help himself stirring sh1t at every step of his illiterate  and undecipherable rants. I would like to see what the outcome is or general consensus on these things and i have added "critical" and :informed" info to help people make up there minds. Until this cretin joined the thread all was fine. I think its a bit heavy to tar us all with the same brush so how about letting us get on with this and maybe have a word to silicon dick.

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Re: Ever heard of dynabeads?
« Reply #421 on: September 16, 2009, 04:09:39 PM »
I see this topic plagues many forums.
http://www.advrider.com/forums/showthread.php?t=353020

Perhaps when mankind finally develops the grand unified theory of the universe Dynabeads will be explained also.


I liked this post & response from that forum......

Quote
Quote:
Originally Posted by SOMNuts
Can't give you any science behind them. However, I've tried them and they are #$%*.......excuse me they are CAPITAL #$%*!


We've a lack of communications, here  I'm an old fart meaning that when I hear something is #$%* it means something is bad as in not good. Unless, of course, it was "good #$%*" or "bad #$%*" where #$%* described what was good or bad, not its goodness or badness. Got that?

However, I often read on this site words like "it's the #$%*" meaning "it's very good". So which #$%* is your #$%*?

Oh, and how do dynabeads work, anyway?

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Offline Retro Rocket

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Re: Ever heard of dynabeads?
« Reply #422 on: September 16, 2009, 04:14:01 PM »
I read that yesterday, did you see the follow up?

"
Quote
The most functional word in English!!!!!!>

Well, it’s #$%* … that’s right, #$%*!


#$%* may just be the most functional word in the English language.

Consider:
You can get #$%*-faced, Be #$%*-out-of-luck, Or have #$%* for brains.

With a little effort, you can get your #$%* together, find a place for your #$%*, or be asked to #$%* or get off the pot.

You can smoke #$%*, buy #$%*, sell #$%*, lose #$%*, find #$%*, forget #$%*, and tell others to eat #$%*.

Some people know their #$%*, while others can’t tell the difference between #$%* and shineola.

There are lucky #$%*s, dumb #$%*s, and crazy #$%*s. There is bull #$%*, horse #$%*, and chicken #$%*.

You can throw #$%*, sling #$%*, catch #$%*, shoot the #$%*, or duck when the #$%* hits the fan.

You can give a #$%* or serve #$%* on a shingle.

You can find yourself in deep #$%* or be happier than a pig in #$%*.

Some days are colder than #$%*, some days are hotter than #$%*, nd some days are just plain #$%*ty.

Some music sounds like #$%*, things can look like #$%*, and there are times when you feel like #$%*.

You can have too much #$%*, not enough #$%*, the right #$%*, the wrong #$%* or a lot of weird #$%*.

You can carry #$%*, have a mountain of #$%*, or find yourself up #$%* creek without a paddle.

Sometimes everything you touch turns to #$%* and other times you fall in a bucket of #$%* and come out smelling like a rose.


When you stop to consider all the facts, it’s the basic building block of the English language.

And remember, once you know your #$%*, you don’t need to know anything else!!

You could pass this along, if you give a #$%*; or not do so if you don’t give a #$%*!


Well, #$%*, it’s time for me to go. Just wanted you to know that I do give a #$%* and hope you had a nice day, without a bunch of #$%*. But, if you happened to catch a load of #$%* from some #$%*-head……….

Well, #$%* Happens!!!


I loved it.... ;D
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Re: Ever heard of dynabeads?
« Reply #423 on: September 16, 2009, 04:16:46 PM »
I read that yesterday, did you see the follow up?

"
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The most functional word in English!!!!!!>

Well, it’s #$%* … that’s right, #$%*!


#$%* may just be the most functional word in the English language.

Consider:
You can get #$%*-faced, Be #$%*-out-of-luck, Or have #$%* for brains.

With a little effort, you can get your #$%* together, find a place for your #$%*, or be asked to #$%* or get off the pot.

You can smoke #$%*, buy #$%*, sell #$%*, lose #$%*, find #$%*, forget #$%*, and tell others to eat #$%*.

Some people know their #$%*, while others can’t tell the difference between #$%* and shineola.

There are lucky #$%*s, dumb #$%*s, and crazy #$%*s. There is bull #$%*, horse #$%*, and chicken #$%*.

You can throw #$%*, sling #$%*, catch #$%*, shoot the #$%*, or duck when the #$%* hits the fan.

You can give a #$%* or serve #$%* on a shingle.

You can find yourself in deep #$%* or be happier than a pig in #$%*.

Some days are colder than #$%*, some days are hotter than #$%*, nd some days are just plain #$%*ty.

Some music sounds like #$%*, things can look like #$%*, and there are times when you feel like #$%*.

You can have too much #$%*, not enough #$%*, the right #$%*, the wrong #$%* or a lot of weird #$%*.

You can carry #$%*, have a mountain of #$%*, or find yourself up #$%* creek without a paddle.

Sometimes everything you touch turns to #$%* and other times you fall in a bucket of #$%* and come out smelling like a rose.


When you stop to consider all the facts, it’s the basic building block of the English language.

And remember, once you know your #$%*, you don’t need to know anything else!!

You could pass this along, if you give a #$%*; or not do so if you don’t give a #$%*!


Well, #$%*, it’s time for me to go. Just wanted you to know that I do give a #$%* and hope you had a nice day, without a bunch of #$%*. But, if you happened to catch a load of #$%* from some #$%*-head……….

Well, #$%* Happens!!!


I loved it.... ;D

Yeah, ;D I believe that should be credited to Mr. George Carlin as I think it's one of his comedy bits.
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Offline mlinder

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Re: Ever heard of dynabeads?
« Reply #424 on: September 16, 2009, 04:21:14 PM »
OK, someone posted this and then deleted it:
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Did anyone read the site?
http://www.innovativebalancing.com/HowItWorks2.html

"
Paul was telling us about tire beads, free moving weights  inside a tire that continuously seek the location which counterweights a tire imbalance.
I wondered why they helped as opposed to making matters worse.
So here goes.
First I want to frame the question.  Wide low profile tires and wheels entail three dimensional complications which we should leave out.  Also, the beads are recognized as not solving "lateral imbalance".
Also I think we should exclude out-of-round tires.
So, if a tire is geometrically circular and properly centered in its axle but is out of balance so that a segment has greater mass than other geometrically equal segments, do the beads self-locate so as to correct the imbalance?
Yes.
The beads feel the so-called centrifugal force in the rotating tire and, if they can, they will role to the place farthest from the Axis of rotation (like rolling downhill).  We have said, however, that the tire is properly round and centered, so, at first glance, we can see no preferred collection point for the beads.  Each spot around the tire is equidistant from the axle.
Now, if the axle was hard fixed in a bearing with no chance of movement that would end the discussion.  The bearing would be forced to handle the imbalance and the beads would do nothing significant.
But our vehicle has a suspension system and the axle moves as required.  As the vehicle speeds up, the force of the imbalance increases.  This is the tire's increasing preference to rotate around its own centre of mass, and, because the tire is out of balance, its centre of mass is not exactly at the centre of the axle.
At sufficiently high speed, the axis of rotation moves away from the axle centre towards the centre of the rotating mass.
Obviously, the centre of mass is on the heavy side of the wheel with respect to the centre of the axle.
So we have our whole wheel and tire rotating around a spot that is slightly off the axle centre, and the part that is farthest away from the new axis of rotation  is on the opposite side from the overweight sector.  But this is precisely where the beads will roll...  to the spot farthest from the axis of rotation.
To repeat: it is because the centre of mass becomes the axis of rotation that the points around the tire are no longer equidistant from the axis of rotation.
So we have a positive result.

From above,
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Also I think we should exclude out-of-round tires.

OK, so we can't use them in wheels that are out of round. Not a problem, you shouldn't be running out of round tires anyway.

But, this brings up something that Bistro and I were talking about.
Does a point in space traveling in the same elliptical orbit around a center of rotation care whether that ellipse is caused by being at a certain point along the curve of the  small end of another, physical ellipse , or by being at a certain point along the curve of a perfect circle, both being rotated around the same center point? I guess it depends. It would take more energy to move it [away[/i] from that point on the ellipse. But the amount of force holding them there in each scenario is the same, assuming rotational speed is the same.

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The beads feel the so-called centrifugal force in the rotating tire and, if they can, they will role to the place farthest from the Axis of rotation (like rolling downhill).  We have said, however, that the tire is properly round and centered, so, at first glance, we can see no preferred collection point for the beads.
But again, this assumes that all the radii are equidistant from the mass center of rotation, which they are not, because the tire is out of balance, therefore there is a single radius point that is further away from the physical point of rotation.
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At sufficiently high speed, the axis of rotation moves away from the axle centre towards the centre of the rotating mass.
OK, so heres the schpiel written down.
At sufficiently high speed....
What does that mean? It's variable. It's also not a static condition once it reaches this nebulous velocity. The window in which this happens could be of any range, at any beginning or ending, all dependent on how out of balance the thing is to begin with, and many other factors.

OK, I understand now that water, beads, whatever, will travel to what is physically the furthest distance from the center of mass in the wheel. I can actually understand the beads working in this case to a degree, as they will travel there, though I'm not sure how to calculate how much it will move there in terms of less than all of it.

OK, still have some thinking to do.

No.