Center of Gyration

[fAtnhapy]

Hello everyone. First post, been lurking for a while. I wanted to introduce myself. Good looking guy with rippling muscles, pearly white teeth, azure blue eyes and hair that reminds people of the black Bavarian forest at the height of the spring rainy season after a particularly heavy downpour. I can barely get to 40 on an IQ test even after three consecutive nights at a Holiday inn but I do own a business with a machine shop that would be very profitable if I didn't have my guys spending half their time making Bessler parts. Clever guy that Bessler whether his wheel was the real deal or not. Couldn't reproduce those results with a diehard. I am of the opinion that "fall like a snowflake" may be the key here. The only way I know how to make a weight fall like a snowflake is to make a yo-yo. Does the wheel care if the weight is forced to spin on the way down? Would it not still apply it's weight and and stored angular momentum amount to a two for one? Question for the physics gurus. If I put an 8" diameter weight on a 10 degree ramp a foot long and let it roll to the bottom it will land at a fairly high velocity with few revolutions. If I put a 1/8" diameter axel in the middle of my 8" diameter weight and let it roll down the same ramp it will hit the bottom at a lower velocity but have much more angular velocity. Will the two senerios add up to the same?
Velocity1+Angular velocity1 = Velocity2 + angular velocity2 ??
fAt
P.S. I spell like a third grader.

[Mr.Umez]

I've been studying this lately having pendula with same mass and center of mass but different rotational inertias collide into one another and see how they react. My hypothesis is that changing to a smaller rotational inertia will/should make the upswing easier because it effectively has 'less mass' and is easier to accelerate.

My last experiments only lead me to conduct more experiments, but I can post what I've working at so far. Just give me some time to create graphics to explain stuff more clearly.

I don't know if this is the way, but I do know it it way ahead in potential than any off-balance design.

Mr.Umez

[SeaWasp]

don't know if this is the way, but I do know it it way ahead in potential than any off-balance design.

Mr.Umez

I aggree with you totally in that respect!

[jim_mich]

Ralph,

Let me address your concerns first. As a pair of weights spread apart each weight also moves outward. Then as a pair of weights contract together each weight also moves inward. The spreading and contracting balance out producing zero net torque. But it is the moving inward and outward that I'm looking at. The red circular lines are the Radius of Gyration, which is in the center of the mass as it rotates. The difference between the two red lines represents how much the weights move inward and outward. As they move inward and outward the weights MUST speed up and slow down in order to match the wheel speed. As I said this will tend to push and pull or 'pump' the wheel faster and slower. I don't think this alone will do anything. Maybe if it is coupled with something else who knows at this point?

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fAtnhapy,

Welcome to the Bessler forum. I think I understand your concept and I've given it some brief thought in the past. It's after midnight now. I'll think about it and get back tomorrow afternoon.

[Jonathan]

I don't know if it is relevant any longer Jim, but your original design with the diamonds doesn't have variable inertia.
fAt, are you working on a GIT?

[jim_mich]

Jonathan, I disagree. As the diamonds get stretched in a tangent direction and squeezed in a radial direction the two tangent direction weights move away from each other and farther away from the axle center. This makes them need to speed up to match their new larger radius. Inertia makes them want to stay the same speed. So they compromise and the weights speed up some and the wheel slows down some. Of course the weight assembly on the other side is doing the opposite so things balance out. The inertia of each weight assembly pumps the wheel faster and slower. When all weight assemblies are considered then the wheel as a whole would average a same speed and inertia.

The radial direction weights balance each other when they move if the two are the same weight and size. If they are different then they will cause out of balance and variable inertia.

My original design is here.

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fAtnhapy,
A while back I ran (but did not post) some wm2d simulations and both scenarios that you describe produced equal total energies.

[fAtnhapy]

Jim... I believe that I am working on a GIT.....Ah....er....what exactly is a GIT? :0)
fAt

[fAtnhapy]

Umm my last post should have been to Johnaton, Jim is the one dashing my dreams.... :0)
At least tell me that the 1/8 axel gave me a ton more angular momentum!
fAt

[Jonathan]

fAt, click the word GIT in my earlier post.
Well Jim, then you'd be mistaken; the problem is here:
>The radial direction weights balance each other when they move if the two are the same weight and size. If they are different then they will cause out of balance and variable inertia.<
Inertia is proportional to the square of the radius, so moving one weight out and another in by equal amounts changes the inertia.
a=2rcos(&#952;)
b=2rsin(&#952;)
I=m((R-a)²+(R+a)²+2(R²+b²))=m(R²-2aR+a²+R²+2aR+a²+2R²+2b²)=m(4R²+2(a²+b²))=4m(R²+2r²)
Notice that a²+b²=4r², that the square of the radius of the tangential weights is R²+b² (via Pythagoras), and that the final equation is not a function of &#952;.

[fAtnhapy]

Ah... thank you Jonathon, no I am not working on a GIT but I do believe that a spin is imparted to some or all of the weights on the decending side storing energy to be used to get back over the hump on the accending side. Close is easy I've done it with numerous concepts, heck an empty well balanced wheel is close. But there is a whole lot of real estate between close and actually running more less making energy. One thing I have noticed is that if I put the wheel in a position where it should run it turns into a gorilla and starts fighting harder than would be expected to obtain equalibrium. I'm starting to think there's some phenomina involved ala latent vs specific heat. Never seen mention of it but I've had 20 lb weights flipped over inexplicably. If nothing else I've grown to appreciate why Bessler took an axe to his wheel.
fAt

[jim_mich]

You are right Jonathan, when two weights move equal distance but opposite directions in & out then the inertia changes.

If the weights are different mass amounts then I think changes need to be made. You use a single 'm' and I think the mass of each weight would need to be used. Or I could be confussed. (It don't take much to confooze me!)



PS. What keystrokes are needed to make a square root symbol?

[ken_behrendt]

Jim...

I could not find an HTML code for the square root sign.

How about just using (x)^1/2 ?


ken

[Jonathan]

I used charmap (thanks again to Stewart, IIRC). But the number is 8730, in the form of "&#NNNN;".

[Fletcher]

I'll have to read thru this whole thread again later today to try & keep up with the play.

If I understand you correctly (& I probably don't yet) then there may be some compromise where the CoG can shift in or out (by having different opposing masses located on the shifting diamond) but the inertia doesn't change ?

If that were possible it certainly would fit the scenario of small magnitude of power available to JB's wheels, as it would be a ratio giving a small advantage.

[jim_mich]

Fletcher, you understand it correctly.

There are two scenarios that I'm looking at. The first is as you said, "The CoG can shift in or out but the inertia doesn't change". The second is the reverse where the inertia changes while the CoG stays more or less fixed.

The diamond pattern mechanism is NOT the only way to do this. It is just the easiest to demonstrate.



Some random thoughts...

Another hurdle seems to be symmetry. Wheels that have symmetry of movement seem to have symmetry of balance. It may be that the weights need to be forced into a non-symmetrical pattern of movement? The weights would move about the wheel in one manner on the descending side, then move in a different manner on the ascending side, the two manners of movement being NOT symmetrical while returning the weights back to the start location.

Another thought is a wheel within a wheel where the inner wheel turns faster or slower than the outer wheel.

I know Ken will jump in and state that it must be, "Simple." To that I say "Hog Wash!" Simplicity is in the eye of the beholder. An apprentice (carpenter's boy) would be skilled in woodworking and could be expected to build most anything out of wood. His skill might not be fully developed into the fine details of polishing and finishing wood, or selecting and buying wood but I'm quite sure an apprentice could build most anything that doesn't require great precision. If Bessler's wheel was made like a Swiss watch or a steam engine then a carpenter's boy would not be experienced enough.