silent wrote:Well I see WaltzCee is still at it. It seems like whenever we are cruising along enjoying reading posts and then suddenly things take a turn for the worse, you can always count on it being due to a select few posters.
Sometimes I get notifications of new posts and then when I log in, there is nothing there which tells me there has been yet another post from someone in my blocked list - which I highly recommend to everyone if you can't help but try to offer rebuttals. It'll get you nowhere - just more arguments from the armchair crowd. No wheel - NO expert.
Absolutely bang-on about the 'ignore' list, total god-send. I'm trying to only use it for malicious posters tho - 'dumb' is forgivable, but 'insulting' with it is the real rant-bait (cos
i will, can't help meself).
While a given poster might not very likely have any constructive feedback to offer, a chance to recap could benefit
someone else.. but i'll only repeat myself so many times before it gets irritating.. (Grrr!)
For Waltzee and anyone else struggling to keep up; the M.O. is simply plying gravity to eat our counter-forces / counter-momenta; the resulting momentum gain is
reactionless... and the value of 'reactionless momentum' is that its cost of accumulation needn't track ½mV² - ie. it circumvents the practical constraints that are usually responsible for causing the energy cost of momentum to increase with velocity. So, reactionless momentum is,
potentially, cheap momentum.
I say 'potentially' as, in all attempts thus far, nature has always found some other way of causing the energy cost to square up with velocity, regardless. Nonetheless, Bessler assures us that statorless momentum gains
are the key to his success ("
in a true PMM, everything must, of necessity, go around together"), and all his wheels
were statorless, so there
must be a permutation that actually works.
And again, the principles behind gaining momentum from gravity really are 'kids stuff' - if you can operate a park swing, you're already an old hand at this.
There's
two ways, broadly speaking, of gaining momentum from gravity:
• on a swing, we're performing work against centrifugal force, and the rotational kinetic energy gain is precisely equal to the net 'work done' against CF force
The
momentum gain, on the other hand, is precisely equal to the difference in period length between 'rising' and 'falling' phases of the swing, relative to gravity's constant acceleration. Spend more time falling and you gain momentum; more time rising and you shed it.
• however it's
also possible to eliminate the CF work component (see previous examples in this thread of changing GPE without changing MoI); in these instances, the rotational KE gain is precisely equal to the net work performed against gravity, while the momentum gain is, again, equal to the 'rising' vs 'falling' gravity / time delta.
I think that's enough of a recap for now, anyone still not following will just have to eat dust..
On a lighter note though, Mr.V I appreciate your approach to this problem using your math and intricate knowledge of the forces involved. I absolutely don't understand the math behind the physics and the physics behind the math. As I'm getting older, I have to pick and choose what I want to invest time in and at this stage of my life, trying to learn the maths involved is literally teaching an old dog new tricks. It ain't gonna happen and even when I was a younger man, it wouldn't have happened then either.
So I thank you for systematic approach to this Bessler puzzle. My attempts go in waves now of where I think I have a Eureka moment and then it fades.
Yesterday's moment was inspired by Bessler's quote: Alternately gravitating to the centre and climbing back up again." AP 291
I started imagining a wheel with pegs like a plinko board where the weights had arms like monkeys and as the wheel rotated and pegs went over the top and underneath any given peg with a weight, it would transfer itself around the wheel freely to do the bidding of the master.
Then I read Bessler's quote: “The causative principle of the movement, its ponderous impetus.� GB 56
So then I envisioned a big heavy wheel within a wheel where levers fall out on the upward (lighter) side and pry on the big weighted inner wheel to push it ahead like the child's hoop and stick toy.
As I approach my first year into this, I see why 300 years have transpired with still no expert on wheel construction to have come forth.
Finally what makes me want to bang my ahead against a wall are quotes like this:
“His Highness, who has a perfect understanding of mathematics, assured me that the machine is so simple that a carpenter’s boy could
understand and make it after having seen the inside of this wheel, and that he would not risk his name in giving these attestations, if he
did not have knowledge of the machine.� - PM 95 Joseph Fischer letter
“The Landgrave being, himself, present during my examination of this machine, I took the liberty to ask him, as he had seen the inside of
it, whether, after being in motion for a certain time, some alteration was made in the component parts; or whether one of these parts
might be suspected of concealing some fraud; on which His Serene Highness assured me to the contrary, and that the machine was
very simple.� - PM 97 Willem ‘sGravesande’s letter
“I have been assured that the secret was communicated to His Serene Highness, the Landgrave of Hesse, under an oath of silence, and
he was allowed to examine the internal structure of the wheel. Afterwards, his Serene Highness was quoted as saying to his ministers,
that he believed the machine to be a true perpetual motion machine, and in addition, it was so simple and easy to construct that he was
amazed that no one had managed to invent a similar machine before Herr Orffyreus.� - PM 137 Jean Bernoulli letter
The world should see this principle, in itself so simple, and yet at the same time so deeply hidden, of everlasting motion.� DT pg 209
SIMPLE SIMPLE SIMPLE SIMPLE Argh! All this simple talk, yet why is it so hard to solve? LOL! Anyone who claims to be an expert yet can't even construct the "simple" working wheel is no expert. You can be an expert in forces and mathematics, but to be an expert in Bessler wheel construction is altogether another matter.
Anyway, thanks for tolerating my ramblings. I always look forward to reading your well-thought-out posts. It's something positive and refreshing and it gives me something new to ponder and think on while I'm at work.
Cheers.
silent
Thank you mate, i assure you
you can follow the maths, it really is just the KE equation - multiplying half the inertia by the velocity squared - and the momentum formula, which simply multiplies inertia by velocity; the latter's conserved, the former, only if the interaction's 'elastic', which here, they're not.. so momentum's conserved, but KE isn't. I won't condescend you with more examples; like i say, i always check everything with an
online calculator myself anyway (no shame in it!).
Those limited maths aside, the mechanics really are simplicity itself - just like the 'red vs green' examples on the previous page - gravity absorbs counter-forces / counter-momenta! So we can use an internal, transiently-gravitating weight as a 'stator' to torque the wheel against; when it's aligned to the gravitating plane we apply torque, and when it
isn't, we don't. Colliding with it in-between torques, we share the momentum gains back with it, bringing it back up to speed with the wheel.
Because the energy cost of momentum squares with velocity, by constantly resetting the relative speed between 'stator' and 'rotor' back to zero we're effectively playing snakes'n'ladders with the
V² multiplier in the
KE=½mV² equation, and repeatedly rejoining the front of the queue to take advantage of the 'special introductory offer' of ½ J per kg-m/s of momentum. Thus, because the relative speed between 'rotor' and 'stator' is always zero at the start of each cycle / 'power stroke', the energy cost of buying more momentum never gets more expensive..
..at least, that's the idea. In practice, as seen throughout this thread, what happens instead is that there's simply less time available per cycle for 'gravitating', as RPM's build up, and so rather than the required
input energy rising by the square of increasing RPM's, we're seeing the actual
momentum yield decreasing by the inverse-square of RPM, to the same net effect.
And
this is what i'm hoping to overcome using these diametric weight levers...
Having
said that, i've no clue how or why they should help in this regard, simply having deduced that it
must be so because so much of MT seems to be reiterating their usage.
And now, having finally measured their respective MoI's relative to that of the net system, it seems they could be ideally-suited, insofar as enabling the optimum 1:1 ratio between the two interacting inertias in a reactionless accelerate-and-brake cycle; the quickest route to OU, in the shortest-possible number of successive cycles.
Compared to say a radial lever weight (pivoted at the hub, or indeed anywhere else on the wheel, per MT 19 & 20, etc.), which would necessarily have a much lower MoI than that of the net system; for instance if each lever had only 10% of the MoI relative to that of the net system, then each accelerate-and-brake cycle would be at a 10:1 ratio, and since the number of cycles (threshold speed, basically) to reach OU is equal to the
sum of the MoI ratio, it'd take 10 + 1 = 11 cycles to reach unity, and 12 to reach 110%; furthermore if the exploit required sinking half the per-cycle momentum gains to gravity (ie. all of the counter-momentum), then those figures likewise double; so 22 cycles to break-even, and 23 to reach slightly-OU.
So, even though i
don't know exactly
how to apply them yet, there's good reason to suppose they're key to a working system; cos Bessler daubed 'em
everywhere, eight ways from Sunday, and also because they're able to furnish the optimum MoI ratio for the most-efficient OU performance envelope (maximal energy gain, in minimal time / speed / number of cycles).
Again, the 'red vs green' examples on the previous page
really do amount to all the mechanical complexity required. All i'm going to be trying next is
precisely the same interaction, but replacing the 'red' and 'green' inertias with those of the diametric levers, versus that of the wheel containing them. So, same basic interaction, just with different shapes..!
Clear as mud no doubt.. but
i've got a rough idea what i'm on about, anyway, so that's all that really matters for now; hopefully the following experiments will speak for themselves..
I've been lucky enough to finish work early enough to get some work done this evening, so gimme a chance to stuff me face and i'll get settled down with some sims..
