Bessler Wheel Math

[Jonathan]

Here's that paper I promised.

[jim_mich]

Jonathan,
Very well writen paper, but I think your coefficient numbers are a little high. I would assume that the bearings were lubricated. My trusty Machinery's Handbook has 3 pages on bearing friction, 11 pages on journal bearings (like Bessler's?), 14 pages on ball bearings, and 5 pages on bearing lubricants. The relevent charts say for sliding friction at 14 to 20 pounds square inch, for bronze on bronze dry is 0.20, for cast iron on cast iron slightly lubricated is 0.15, and wrought iron on hard wood well lubricated is 0.08, and (for reference) leather on cast iron dry is 0.56.

I would think Bessler had journal type bearings. Journal bearing with oil bath ranges from 0.015 to 0.0009 depending on speed, pressure and lubricant.

For reference the coefficient of ball bearings range from 0.0011 to 0.0095.

[Jonathan]

Thanks Jim.
I did a search through both John's book and Bill's website, and it just seemed like I read somewhere that the bearings were "clean" or "dry", but I can't find it so maybe you're right. Also, I personally find the 700lb estimate for the wheel a little high, as that seems like a lot for two men to translocate, even if you removed the weights; I lean more toward 400lb (=1,779.3N). Keeping that and continuing to make this more conservative, we could change mu to be .1, and maintain the .25 pulley coefficient, and get
P=19.5W=14.4 ft-lb
E(@6h)=.42MJ=.31 million ft-lb/s
No matter how small the power is, the stored energy would still have to be pretty big. There is reason to believe that the wheel ran for far more than 6 hours too, since the experts could find no way to put energy in, and it was sealed in a stone-walled room. And of course, how would he store the energy? Best would be a spring, but he claims that some people were allowed to grope inside his wheel, and they would have noticed that. Not to mention that a blacksmith couldn't keep the making of a =<12ft spring a secret for long. I can't remember if Bessler had blacksmith skills, if he did you'd think someone would notice him slaving over a giant spring. In fact, I wonder if they had the technology to make a spring so big back then?
Note: I forgot to say in the note in the paper, that since the value for R is a little fuzzier than most, I used 3in over, say 4in, because that is more conservative.
EDIT
I also forgot to mention that if there was a fourfold pulley reduction, the upward velocity v of the load weight would be .0893mph (=1.6in/s), and would take a little under four minutes to rise to the third floor (remember that the third floor example is just an arbitrary guess).

[Kirk]

Until I am finished all I can say is I believe his wheel was powered by gravity. I am convinced enough to invest time and money in a prototype. Health has slowed me down but I'm not stopped yet.

Kirk

[epistemologicide]

great read jonathen, and great work!!

[Jonathan]

I was just going to post the following technicality in the math I did, but in the process of making it I noticed a glaring error that I've been making for some time, and no one's called me on it!
But first the technicality. I overlooked this because the numbers are fuzzy enough that this doesn't change things much, and theta is definitely pretty small anyway. The correct form of the relevant equations are listed there.
But that was just for completeness, the error is a bigger deal. I used r=.75in, when in fact this was the diameter, it should be .375in! So here are the correct values (E is still taken at 6 hours),
without pulley reduction:
P=74.5W=55 ft-lb/s
E=1.61MJ=1.19 million ft-lb
with pulley reduction:
P=37.5W=27.5 ft-lb/s
E=.80MJ=.59 million ft-lb
with more conservative values (as per my previous post):
P=16W=11.8 ft-lb/s
E=.35MJ=.26 million ft-lb

[Jonathan]

BTW, F_g2T is the perpendicular component of the second gravitational force, the "T" should be upside-down to indicate perpendicular, but of course Paint doesn't have the ability to make that symbol. It only occurs to me now that I could have selected and rotated it, but it's too late now. :)

[Michael]

Jonathan,

I haven't read your paper but if it's been done on your past summation that 2/3 was wasted in axel friction I ask you to think about this. No matter how much weight is on the wheel, if it has even slightly more mass on one side, and if this side started at the twelve oclock position, and the wheel rotated, under your summation the weight would only reach the 8.00 to 8.30 position on the other side. I use an unbalanced wheel only as a reference. Do you think that this is what would happen?

Reg.

Mike

[Jonathan]

I'm not sure, it's hard to say, but that doesn't sound too far off.
However, the percent of the energy wasted is: without pulley reduction: %E=33.33%; with pulley reduction: %E=66.67%; with more conservative values (includes pulley reduction): %E=22.22%.

[Michael]

Jonathan,
An average bearing will bring the wheel to the 10.00 oclock position. A very good one will bring it near 11.00 oclock. An axel resting in a socket will come somewhere close between the two. That's about 1/5th wasted from various frictions.

Regards,

Michael

[Jonathan]

Which is exactly how much the most conservative values put the percent of energy lost due to friction as (1/5=20%). But what is your point? Clearly Bessler's wheel didn't have a lone point on the periphery causing the torque, and ultimately his wheel ran for much longer than 6 hours. There may be more things in heaven and earth than are dreamt of in my philosophy, but I'm quite certain that not enough could be in the wheel.

[Michael]

Actually the loss is closer to 1/6th to 1/8th. I may have missed something in the postings but you stated the losses due to axel friction were 2/3'rds.

Thanks for the references on the grim link.

Reg.

Michael

[Jonathan]

2/3 was a guess based on nonconservative values (including 700lb wheel weight) and my mistake that R=3/4in. 1/2 was a guess based on nonconservative values except 400lb wheel weight, and the R=3/4in mistake. My previous post is the actual math using various levels of conservative values and the correct R=3/8in.

[Jonathan]

And I thought this was pretty convincing before...I just finished John's new book, Das Triumphirende, and on pg 244 it says (about the Merseburg wheel):
"...it then began to rotate of its own accord with such force that within a minute it had rotated 40 and more times, ... The far end was attached to a chest full of bricks - about 70 lb weight in all - and this load was raised and lowered several times by the machine. The most noteworthy detail regarding this particular experiment was that the wheel, while under this considerable load, continued to rotate at exactly the same rate as when it was running "empty"."
(It should be mentioned that this testimony doesn't mention pulley reduction.) From this account we have the Merseburg wheel turning at 40rpm give or take a little. This can be found on ovyyus' website, and yet somehow I managed to overlook this, because had I realized it I would have done the math on the Merseburg wheel originally. Having realized this, the energy and power for the Weissenstein wheel listed in one of my above posts should be about twice as great in the case of the Merseburg wheel (since the math for each wheel is essentially the same, except for the rotation speed (and the wooden axle radius, but that is a little fuzzy in the first place, and it is more conservative to just assume they were both 3in)).
The "noteworthy detail" tells me that there is something odd about the Merseburg wheel, that one can load it and it continues to turn at the same rate. (In hindsight one could have deduced the existence of a similar oddity from the fact that the Archimedian screw only slowed down, but did not stop, the Weissenstein wheel (maybe it was only I who hadn't noticed this yet?)). These facts tell us that the torques from his wheels were dependent on their angular velocity or the wheels could detect a load and would increase torque so as to maintain that velocity. Unfortunately that is a pretty vague hint, which coupled with the fact that the wheels used varying versions of the principle, make this the almost unsolvable mystery it is.

[VergingOnDone]

Jonathan,
Very well writen paper, but I think your coefficient numbers are a little high. I would assume that the bearings were lubricated. My trusty Machinery's Handbook has 3 pages on bearing friction, 11 pages on journal bearings (like Bessler's?), 14 pages on ball bearings, and 5 pages on bearing lubricants. The relevent charts say for sliding friction at 14 to 20 pounds square inch, for bronze on bronze dry is 0.20, for cast iron on cast iron slightly lubricated is 0.15, and wrought iron on hard wood well lubricated is 0.08, and (for reference) leather on cast iron dry is 0.56.

I would think Bessler had journal type bearings. Journal bearing with oil bath ranges from 0.015 to 0.0009 depending on speed, pressure and lubricant.

For reference the coefficient of ball bearings range from 0.0011 to 0.0095.

Hi Jim, from my understanding the bearings were dry and they were kind of like sets of planetary gears, the teeth edges being covered? ( silver foiled ) for less friction. Loose enough to only slightly rest on the edges.