Wheel acceleration...

[Jonathan]

This is also interesting, but it is the same problem as before, though in this case it is a little harder to explain, because before I made reference to simple fractions relating the mass going up and down, and the rates at which they do so, but I can't in this case. But I do have a proof via reductio ad absurdum: if this device did work, then it should also work if all the yellow balls were purple. I find that quite interesting. :) If you label all the balls on the right, 1, and the ones on the left, 2, and in the middle they alternate, then it is easier to see what I mean. If your version works, then the energy of the balls on one side falling is enough to lift half the balls in the column. In the all purple version, the column is twice as heavy, but there are twice as many balls falling, so it should still work. But I think it pretty clear that the all purple version won't work.

[Wheeler]

Hello I have what may be considered a known fact for Ken and all who have studied his idea, but I could not see it clearly.
Ken if your latest posted design did work, which way would it turn?
I was looking at the left and right sides, and thought that it may just turn horizontal when it did begin to rotate.
Would the left side have a left force, and the right a right force?
I am not completely sure I understand, it may be due to my immature scientific mind. Thanks for the wonderful posts, I love this stuff.

[bluesgtr44]

WARNING!! Be advised that my books have arrived. I am now considered "armed and a danger to myself and society". Thank you Mr. Collins!

Steve

[Jonathan]

Wheeler, the device is stationary, it is the balls that should move. If it did work I imagine that the power would be taken off by an inside-out paddle wheel, the paddles of which would fold out of the way when ascending past the yellow balls.

[Jonathan]

A few posts back I said: "...they assume dα/dt=0."
That's all wrong and I've gotten to sit down and look at that paper more carefully. They assume dα/dω=-1. From this assumption I have derived the following:
θ(t)=A(t-1+e^(-t))
ω(t)=A(1-e^(-t))
α(t)=Ae^(-t)
Where A is the initial angular acceleration. I am aware that the units only work out for α(t), this is because the "-1" of "dα/dω=-1" has units of 1/s. If you change it to dα/dω=k (which is just as legitimate a starting assumption), where k is measured in 1/s, then the equations are:
θ(t)=A((e^(kt)-1)/k-t)/k
ω(t)=A(e^(kt)-1)/k
α(t)=Ae^(kt)
I have qualms about the following equations:
3) Assumes constant acceleration.
4) Relies on 3.
6) Assumes rotational inertia is constant (which is okay if noted).
7) Assumes constant acceleration.
8) Relies on 7, and mistake is repeated.
9) Relies on 8.

[ken_behrendt]

Jonathan...

I read your reductio ad absurdum treatment for my second "spacer ball design" and I think I have to disagree. IF all of the balls were purple weight balls, I do not think anything would happen. However, from studying the design it is obvious that the total weight of the center channel balls is ALWAYS less than the weight of the right circular channel balls. Therefore, I would expect motion.

However, in thinking over this design I quickly realized that the bottom "Mixer" mechanism is really the weak link in the whole thing. In order to alternate a light weight yellow spacer ball with the heavy metal purple weight balls, the mixer mechanism must momentarily STOP the descending motion of the right circular channel weight balls while simultaneouly LIFTING the center channel column of mixed balls so that the spacer ball can be inserted into its place at the bottom of the column.

That insertion process requires energy during a phase of operation when the right circular channel balls are motionless. Perhaps the motion of the right channel weight balls could rev up a flywheel whose rotational energy would be tapped by the mixer mechanism during spacer ball insertion.

The question then is whether or not the descending motion of the purple weight balls between spacer ball insertions would supply enough energy to the flywheel to operate the mixer mechanism. Right now I am of the opinion that it would supply more than enough energy although constructing a working model of the design I attached would be a real headache!

As far as the "Separator" at the top of the center channel is concerned, it would use minimal energy...just enough to push balls to the right and then the left.

ken

P.S. I've been thinking about the "Spacer Ball Insertion" designs for the last few days and have a weird design for a gadget using magnets that would essentially work exactly like the one attached above. Only this design would require NO mixer or separator mechanisms! If I find the time I've seen if I can do a quick Paint program sketch of it. It's kind of unique...

[Wheeler]

Jonathan
Thanks for the clarification on this, I have been studying the mechanics of the whole process, and I am not convinced we are looking in the right area.

I think we are not able to find the answer, because we have not used what is needed to understand how this actually could happen.
Is it possible that it did not happen in the way we are thinking? If we are not able to find the answer to a basic physics arrangement, then we may want to rethink our approach.

[Wheeler]

This ball system is on my paintbrush program also, and I agree with you that something is unique about the possibilities. I have the wm demo, but have to do the learning curve for awhile first before I can assemble what I want faster than paintbrush.

[bluesgtr44]

Excellent Jonathan! There had to be some assumptions made, I'm sure you are very aware of that. The things you list that you have qualms about....most are cited in examinations of the wheel. Why the qualms? There seems to have been some mention that the acceleration seemed to be "fluid"...pretty smooth, so to speak.

Going from the information that has already been provided (I was impressed with the work these two genlemen did)...How about alleviating some of your "qualms" and fill in some of the blanks (assumptions) with your idea of what may actually be there.

As I have stated before, I am interested in the uni-directional wheel. This information was based on the reports for the last wheel. This was the most documented wheel and of course that is why they used this one for their analysis. It doesn't matter....the acceleration was the same for ALL wheels...because that aspect was the same. It didn't change. The only change was he made it bi-directional...Does not change the basic principle of "acceleration" that he applied within his work. Once he found the secret it applied across all spectrums of what was designed after that. Sure, some of the numbers changed, but the principle did not!

Jonathan, the reason I ask you to plug in some of your thoughts on this, Maybe the two guys who figured this up were merely doing the math from the challenge of...."providing a person with these figures, what can you deduct mathematically is happening"....as to where YOUR thought process might be...."provided with this information, what assumptions can be made to assist a person is search of PPM." They were looking for a mathematical result...you are looking for PPM.

Steve

[Jonathan]

Steve,
The observed smoothness is pretty subjective I think. However, that is somewhat beyond the point because we know for certain that the acceleration was not constant. If the acceleration were constant, then the angular speed would increase without bound.
I've never taken this route of analysis because I didn't like how many assumptions had to be made to come to a conclusion, and specifically assumptions that are guaranteed to be violated: "I" is not known and certaintly changed with time, and dα/dω could be any function at all, as long as it crosses the ω-axis once from [0,Ω] at Ω (the final angular speed).

Ken,
>IF all of the balls were purple weight balls, I do not think anything would happen.<
That was my point.
>However, from studying the design it is obvious that the total weight of the center channel balls is ALWAYS less than the weight of the right circular channel balls.<
That is canceled by the channel balls being forced to move faster.
Unfortunately I don't have time at the moment to show a different proof.

[Silver Eyes]

Steve, you say the only thing that didn't change was the acceleration aspect but 2-3 rotations isn't very accurate. I mean- You have from 2 to 3 . I also don't remember this being said for every single wheel so you can't assume because it was not said that it was true. I also haven't seen how the acceleration happened so you have to consider this too. Did the wheel start from a major thrust and gradually loose that stored torque as is reached its main speed (doubtful because of the first wheels) was the acceleration constant, or was the acceleration constant not a constant at all, but also increased as the wheel increased until it reached a set limit?

[Jonathan]

I'm back, here's the proof: given the diameter d, linear mass density &#955;, then the mass that falls is given by &#955;&#960;d/2, and the mass that rises is given by &#955;d. The net migration of the balls must be zero or else it keels, and this implies that the net momentum of the system is zero too. Momentum is p=mv, so we have &#955;&#960;vd/2=&#955;dv'. Cancelling gives &#960;v/2=v', and rearranging gives v'/v=&#960;/2>0, for nonzero v. Thus, though there is less mass rising in the middle than falling at the side, it rises faster. Note that rising faster is like being on a longer lever arm, the longer the arm the faster it rises at a given angular speed. Ulitmately this proof can be generalized to show all gravity powered perpetual motion is impossible, because a closed-loop cycle of weights in a wheel is logically required to have no net linear momentum. Also, I am aware that I simplistically made reference to v even though it is representing the speed of an object that is following a curved path, and would intermittantly have to be zero for the mixer to work. In the former it is okay via the post-definition, pre-mathematical explaination re: zero net momentum, and of course in the latter case it is no big deal because if half the device isn't moving then no disproof of perpetual motion is necessary.

[Fletcher]

You guys may like to study (sic) Jan Kowiski's designs on his Auzzy web site (Jonathan can probably give you the link). They are very similar to what you are proposing but with a mechanical solution to the lifting/mixing suggested. A little time there & I think you will quickly see why his ideas won't/don't work & the inherent problems in this approach. JMHO.

[bluesgtr44]

OK gentlemen...I advised you that I had recieved my books and am now "armed and a danger to myself".

From page 64 of PPM AAMS...this is the Merseberg wheel..."Within about one revolution, the machine acquired a strong and even rotation, even when a box was lifted..."

From page 69...Still the Merseberg wheel..."The inventor started it with the merest little effort. As soon as just one of the internal weights began to fall, the machine started to revolve with such strength that it turned forty or more times a minute."

WOW!

Steve

[Jonathan]

I think you mean Jan Rutkowski. Also these animations (one and another two posts later).