Why only four pounds?

[jim_mich]

Suppose Bessler wanted an eight pound weight and a twelve pound weight? He might put two 4 pound weights together (with a bolt or axle-pin through the center) to form a twelve pound weight-stack. And then put three 4 pound weights together in like manner. Thus Bessler could make any 4 pound increment for any weight-stack.

Thus we cannot assume with any certainty how much weight-mass was in each weight-stack. Bessler's Merseburg wheel was about 18 inches thick and covered with canvas. Thus the interior was almost 18 inches thick. Assuming that half the interior space was used for a CW working portion and the other half was for the CCW portion, and assuming the weights were on some sort of levers which took some space, and allowing for some clearance, then we might assume a usable space for each weight-stack of maybe 5 to 7 inches. And assuming each four-pound weight was 1" thick by 3-1/2" diameter, each weight-stack might weigh 16 to 28 pounds.

Now suppose each weight was only 3/4 inch thick. A four pound weight 3/4 inch thick would be slightly over 4 inches diameter. A weight-stack of 9 such weights would be 6-3/4 inch thick and would weigh 36 pounds.

Also, Bessler might have used weights all of the same diameter but of various thicknesses. In this way he could make a weight-stack weigh whatever he wanted.

With many 16 to 36 lb weight-stacks riding around inside a 26 RPM rotating wheel with ordinary centrifugal forces that at the bottom of the rotation can easily cause each weight to exert more than twice it normal downward force, then Bessler would probably need a rather sturdy wheel.

A sturdy wheel without interior weights might be difficult but not impossible to move. But filled with some large unknown quantity of four pound weights would probably make it near imposable to move. A flimsy wheel filled with just a few 4 pound weights would not need to be emptied of weights so as to be moved.

So I'm of the opinion that Bessler used multiple weight disks bundled together into "weight-stacks", and that there might have been different thicknesses of weights and thus weights that were different than 4 pounds, and that his wheel was built strong and sturdy to handle a lot of weight.

[johannesbender]

yes this is what I mean , if there were a collection of weights of 4 pounds only each "a stack or pairs" then it would be in multiples of 4 such as
4 8 12 16....

this is where it becomes difficult though , if we
consider how many possible variables there could be ( variables of weights and values) we
cannot establish anything as a sure thing , maby
the 4 pounds were the heaviest of a bunch of different sized/weighing masses .

maby it had to do with the specific requirements
of the wheel , work-load / energy / size etc.

if it were leverage then yet again we have to many possibilities to play with .

what is there that may give substantial evidence to a theory such as "because he had to be able to move it " except the fact that there were more than one pair of pillar supports at a certain demonstration , wich he used to demonstrate by moving the wheel to the other pillars , for this reason it was perhaps designed such that by splitting his weight requirements into smaller ones he could group together "stack" and then remove with ease again if needed.

a bunch of small weights are easier handled than one large single weight .

edit , lets not forget that the closer towards the center an area within a wheel gets , the less space there is , that would need smaller weights if we were to concider the "ap wheel" areas as areas possibly filled.

jb

[Dunesbury]

Thus we cannot assume with any certainty how much weight-mass was in each weight-stack.

Clue to how much mass his wheel had is provided by account of assistant stopping his wheel. How much spinning 12 foot mass could man stop as easily as he did? Has anyone built wheel that massive, spun it to 26 rpm, and tried to stop it? I don't know. Who has the biggest one here?

[jim_mich]

It all depends upon the method used to stop the wheel. Does the assistant grab the wheel just once at the rim, and thus stop it within about 1/10 of a rotation? Or does he grab the wheel hand over hand so as to bring it to a stop within say 1/2 a rotation or so? Or maybe he stops the wheel using the handle-rod on the axle? After you assume the method of stopping the wheel, and assume the weight and strength of the assistant, then one can back figure the upper limit of the wheel mass.

[Dunesbury]

Wasn't handle rod put there for that purpose?
Assume this method.
Assume man was 150 lbs and normal strength.
How much mass could he stop in short time?

[johannesbender]

or rather should one not ask , how much spinning mass could lift a man of such weight and stop, rather than the other way around.

by the way the reduction in rotational speed
when lifting the box , can one not say that if it took X amount to drop N amount of rpm that it would
take X times W amount to stop the wheel ?

jb

[Dunesbury]

A man in good shape can lift more than own weight.
If assistant caught handle rod at top of revolution and applied force up, he could stop 150 lbs in < 1 revolution. But since wheel was spinning so fast, depending on which wheel we are talking about, 26 to 40-50 rpm, it would be much more difficult, because mass is moving.
That account of assistant stopping wheel so easily indicates wheel didn't have much mass.
In my opinion.

[Furcurequs]

Dwayne, I have mentioned this before, but it has always seemed to me that Fischer von Erlach, having spent two hours examining the wheel in detail, recording the wheels rpm both loaded and unloaded, was only able to state the one could hear the sound of about eight weights landing gently on the side towards which the wheel turned.

I've checked and double checked and the word 'about' is quite clearly written, (in French). It seems to me that in line with the rest of his report he would have stated clearly that he heard eight weights if he was certain of that. One could conclude that the sounds were indistinct or merged with other less clear sounds. Bessler said that he had occasionally muffled the sound of the weights with felt, and it seems quite possible to me that he did this in this case too. Perhaps he did not wish people to think he might have used five or ten weights.

JC

Hey John,

Thanks for answering my question, and sorry I didn't get back to you sooner.

Do you know if Fischer von Erlach said anything about whether the sounds of supposed weights landing gently came at steady, regular intervals or not? If he didn't mention it, I would assume that the sounds did provide a steady pulse and that the timing wasn't erratic. ...which would make it hard for me to believe that the "about eight" could be ten with maybe a couple missing or, of course, your five.

I seem to remember, too, reading that Bessler had left the felt out of some of the later wheels and that they were noisier, presumably due to the hitting weights, but maybe he still put some in there to be deceptive.

Anyway, I had also wondered whether there was any significance to the "about" in von Erlach's account. Actually, I can think of some other reasons as to why it could be "about eight" rather than precisely eight, but I'll not get into them at the moment.

Thanks again,

Dwayne

[johannesbender]

dwayne wow the more we learn ,the less we know. . :-(

dunesbury , I have no idea how to calculate such things , but I imagine only that if the man was lifted up before the wheel were stopped , that the
man's weight were the limit the wheel could not drive , thereby saying if you were to know how
well fed this man were , you would have an upper limit (more or less) , but since we do not know
how average his weight were then its a gamble too.

jb

[Furcurequs]

It is also quite possible that these 4# weights were merely intended as a distraction. In that Bessler wouldn't allow the witnesses to feel the ends of the weights, it has been assumed here that perhaps they were bored through their length like beads on an abicus whose sole purpose was to produce the sound heard as eight weights falling on the descending side.

A reasonable exercise for those better versed in math than I, would be to calculate how much mass was necessary, at 26 RPM turning in a 12-foot diameter wheel, to lift an adult (say 200#) off his feet when this person attempted to stop the wheel by force.

Hey Unbalanced,

I thought I'd give your calculation a try and run a few numbers.

If we had eight 4 pound masses riding on the rim of a 12 foot diameter wheel that was turning at 26 RPM, that would be 32 pounds of mass or approximately 1 slug of mass moving at about 16.3 feet per second (12 ft * pi * 26 rot / min * 1 min / 60 sec).

If we use slugs and feet per second in the kinetic energy equation we get units of foot-pounds of energy.

So, 1/2 * 1 slug * ( 16.3 ft / sec )^2 is about 132 foot-pounds

We can then divide that by 200 pounds for your person and convert to inches.

132 foot-pounds / 200 pounds * 12 inches / foot = 7.9 inches

So, that means that just the 32 pounds of weights alone moving on the rim of the 12 foot diameter wheel rotating at 26 RPM would have enough kinetic energy to lift your 200 pound person about 8 inches into the air.

Of course, though, that would be IF you could transfer all that energy to your person.

If the person were to just suddenly latch onto the side of the rim, however, we would have to consider the conservation of momentum and could assume his attachment to the rim to be a perfectly inelastic collision.

Since the distances we are concerned with here are in inches and the wheel is a huge 12 feet in diameter, I'll just approximate things by treating it as a linear problem.

So, our slug - our 32 pounds of mass - times it's speed of 16.3 ft /sec is the momentum before the collision which must equal the momentum of the person and the weights after the collision.

Our person is about 6.2 slugs (200 lbs/32.17 lbs/slug), so...

16.3 slug - ft / sec = (1 slug + 6.2 slugs) * person's launch speed

launch speed = 2.26 ft / sec !

So, how high will our person fly off the ground?

Well, we have his weight decelerating him, but it is also decelerating the mass of the rim at the same time. So, he's not being decelerated at 1 g.

So, let's see what his deceleration rate is now.

F = m * a , a = F / m

a = 200 lbf / (1 slug + 6.2 slugs) = 28 ft / sec^2 ... 1 g = 32.17 ft /sec^2

Now, let's calculate how far the person moves upward before coming to a stop.

v = a * t, s = 1/2 * a * t^2 , s = 1/2 * v^2 / a

s = 1/2 * (2.26 ft / sec)^2 / 28 ft / sec^2 = 0.092 feet!!

0.092 ft * 12 inches / ft = 1.1 inches!

So, although the 32 pounds of mass on the rim would have enough kinetic energy to lift the 200 pound person about 8 inches into the air, the person would only be lifted about 1 inch by suddenly grabbing hold of the rim.

This, of course, was neglecting the mass of the wheel itself, which most likely would dominate when it comes to our person launching.

I'll spare you the details on this one, but using the moment of inertia equation for a solid disk, one in which there is a uniform mass distribution throughout the volume, I calculated the numbers for a 300 pound wheel of the same dimensions and speed as before.

A 300 pound, 12 foot diameter solid disk rotating at 26 RPM should, then, have enough kinetic energy to lift the 200 pound person 3 feet 1 inch into the air, but for the person grabbing onto the rim where we have to consider the conservation of momentum, the person would only be lifted 1 foot 1 inch.

These calculations, of course, don't take into account any extra drive force, but only the stored kinetic energy in the flywheel.

Now, if there was a little bit of swinging involved or the person were to use pequaide's tether so as to perhaps more efficiently transfer kinetic energy from the wheel to the person, one might be able to get more height. I've not done the experiment, though.

Dwayne

ETA: Thinking about this reminded me of a Wheel of Death video where a guy mounted the spinning "wheel" by grabbing the rim of the cage. This link should start 10 seconds before he grabs hold: http://www.youtube.com/watch?feature=pl ... VAlNA#t=70

[Dunesbury]

He jumps on about 1:20.

Those numbers sound right to me. A 1 foot lift would make me say "attempting to stop wheel by grabbing rim could lift man in air". More than 1 foot you might say "man could barely stop it". If it lifted him 6 feet off ground, then you might say "probably not good way to stop it".

[ovyyus]

Dwayne, you might like to read the below topic, if you haven't done so already. I'd be interested to hear you views on the matter.

http://besslerwheel.com/forum/viewtopic.php?t=4925

[Ed]

Bill, do you really thing that little return trough was catching all the water that was sploshing and splashing out of the water screw?

Did anyone stop to think about how much slippage and friction would have been present with the square pulley and rope drive system?

Makes you stop to think if some people could ever solve this thing.

Bessler either shows a "little return trough" so that none of the other parts are occluded, or he actually used a glass tank to house the water screw. ;-)

[Mark]

But, Ed...

"there's a scale at the bottom, so it must all be drawn precisely....."

wait... do red herrings grow that large?


edited to add:
Just another of Bessler's many red herrings, imho.

[Ed]

Only the feathered kind... they can get up to about four pounds.