Bessler's (4th) Kassel wheel Archimedes screw pump calculations

[eccentrically1]

heh,heh gotcha ralphie

would it make any difference where the weights impacted on the descending side when they did impact? was that as specific as the witness got? just 'on the descending side'?

[cloud camper]

I love a great tapdance.

[daxwc]

Pole dance

[rlortie]

heh,heh gotcha ralphie

would it make any difference where the weights impacted on the descending side when they did impact? was that as specific as the witness got? just 'on the descending side'?

Even that is an assumption: The witnesses reported that they heard what sounded like weights falling, they did not see the weights in action. The sound may have been some sort of latching or release counter balance mechanism. nothing here that I would consider "objective" (based on observable phenomenon)...

"Tap-dance" "Pole-dance"?? IMO "Hopscotch" sounds more appropriate.

Ralph

[ovyyus]

The witnesses reported that they heard what sounded like weights falling, they did not see the weights in action.

...he [Bessler] did not disguise the fact that the mechanism is moved by weights. Several such weights, wrapped in his handkerchief, he let us weigh in our hands to estimate their weight. They were judged to be about four pounds each, and their shape was definately cylindrical. I conclude, not only from this but also from other circumstantial evidence, that the weights are attached to some movable or elastic arms on the periphery of the wheel. During rotation, one can clearly hear the weights hitting against wooden boards. I was able to observe these through a slit...

[jim_mich]

Jim, it's been 2 years since I estimated the water screw power at less than 25 Watts (on page 2). I note you haven't yet put forward your own power estimate. Did you give up on it?

Using the water screw as an indicator for the power output of the wheel has many flaws. A much more accurate wheel power calculation can be made from the lifting of the weight by wrapping a rope around the wheel axle. Or by the lifting of the hammer-mill weights. Each calculation, whether it be the rope lift, the hammer mills, or the water screw, requires some assumptions. The more things that are assumed, the less accurate becomes the final estimate of wheel power. Each assumption is based upon some source of information. Some information may be more accurate. For instance, if a witness or document states the wheel lifted a 'hundred-weight' then all we need do is determine the historical value of a 'hundred-weight' (about 112 lbs.). If we try to determine the weight of the hammer-mill stamps, then we might have their dimensions and type of wood, from which we can determine their weight. But then to determine the lift height we need to scale the drawings. With the water screw, all we have are in the drawings and one witness as to wheel speed.

The hundred-weight lifting was straight forward. It is described in a couple different documents. The axle size is noted. A rope is wrapped around the axle which is known, then over some pulleys, and directly lifts the hundred-weight.

The hammer-mill lifting height must be estimated from the pictures and the weight of the hammers are estimated. So again the calculations are simple, but a greater number of estimating is involved. A hammer-mill has more friction than two simple pulleys of the hundred-weight lift.

When trying to estimate the water-screw, there are a great number of things that need estimating, with the only source of information being the pictures. There are many more items that get estimated. And a water-screw has a lot more friction and resistance than the hammer-mill or the hundred-weight lift.

Calculating the water-screw can give results anywhere from 10 Watts to 80 Watts or even higher. Just by cherry-picking values for the water-screw, its calculated output can be almost anything. For instance, was the screw diameter 18 inches, as scaled on the drawing? Or might the screw have been 25% bigger, at 22.5 inch diameter? Or maybe 14 inch. At 22.5 inch the screw would pump 56% more water. Were those square pulleys really a 2:1 reduction, as in the picture? Or maybe they were the similar sizes, which would double the water-screw output. How much friction caused wasted energy with the water-screw? Water pumped by a water-screw has a lot of friction. The water must flow along the interior walls of the screw. And the primitive vee-belt drive also has a lot of friction as the rope squeezes into the vee then must be pulled out each time. And the rope rubs the side of the vee at it slides into the vee.

The bottom line is that there is no reliable way to estimate the wheel output or the friction involve by trying to use estimated water-screw data.

Bill, you have tried to use a small water-screw output as justification for your assumption that some sort of pulley reduction was used, and thus the wheel output was in the range of 25 Watts. I reject such assumption of pulley reductions. The wheel itself was a peritrochium, or axis in peritrochio. Three hundred year ago, this was a well-known means of gaining leverage. A large wheel was used to drive a small axle. Power was applied to the wheel, often by an animal or servant walking inside the large wheel. Then the small axle did the lifting or driving of machinery. The output was slow, put the torque was significant.

It is, however, an incontestable truth that my much-mentioned Wheel deserves not only the name of the long-sought Perpetual Motion, but also, just as much, the name (Perpetual) Mover; since it is an example of one of the best-known of all mechanical appliances, namely a peritrochium.

Leibniz used the Latin word "trochlearum" to describe a reduction of speed. Bessler used "peritrochium" (English: Axis in peritrochio) in describing his wheel. I maintain they all mean the same thing, which is as pictured by Bessler.

So Bill asks, "Jim, it's been 2 years since I estimated the water screw power at less than 25 Watts (on page 2). I note you haven't yet put forward your own power estimate. Did you give up on it?"
Yes, I gave up on it when I realized that the variables and assumptions were such as to make any estimate for the water-screw worthless. I can make the output estimate at say 9 Watt, and thus about 1/3 of Bills, or 75 to 80 Watts, and thus about 3 times of Bills, simple by assuming the variables are a little bigger or smaller.

[Oystein]

This is what Working model say about the power.

Here showing equivalent/needed average unbalance/leverage from 8 pcs. 4 pound weights.

The power is then of course easy to calculate for those interested.

It is unlikely that all the wheels used a 4:1 reduction pulley, as many reports would have reported that. They would have used anything against him. I am more with Jim on this at the moment.

[ovyyus]

Bill, you have tried to use a small water-screw output as justification for your assumption that some sort of pulley reduction was used...

I estimated the power of the water screw based on typical water screw construction and on the relatively precise sizes given in Bessler's scaled drawing. To imply that I manipulated my estimate in order to justify anything is a lie.

The hundred-weight lifting was straight forward. It is described in a couple different documents. The axle size is noted. A rope is wrapped around the axle which is known, then over some pulleys, and directly lifts the hundred-weight.

To estimate power we need to know the rate at which the hundred-weight was lifted and also if that rate was constant or not. Which documents give a straight forward description of the rate at which the hundred-weight was lifted?

[Furcurequs]

If we were to all get onto a large merry-go-round (not that we aren't sort of on one already, I guess, lol) and let it get up to a fairly high and constant speed and then decide that its rotating platform was to be our new frame of reference, what would we see and feel there?

Well, as we stood on the rotating platform, we would quickly realize that we each felt a strange new mysterious horizontal force. If we compared notes, we would have to agree that each of us were feeling a force directed in a different horizontal direction, however, but after a little more deliberation we would come to the conclusion that there was something in common about the forces we were all feeling and that for each of us it is a horizontal force pulling us directly away from the center of the platform.

This new and mysterious horizontal force that each of us now feels doesn't seem to be described by Newton's laws of motion, though, in this strange new reference frame of ours. This new type of force in the horizontal is as seemingly mysterious, then, as the gravitational force in the vertical. So, scientists would call this new mysterious force that can't be accounted for by Newton's laws of motion in this particular reference frame the "fictitious" centrifugal force - since, again, it is a force that is seemingly pulling us away from the center and Newton's laws of motion alone don't account for it here.

Now that that's understood, WOAH!, we seem to be growing weary having to contend with this new horizontal centrifugal force. Apparently our bodies and muscles just aren't adapted to this force since we grew up in a different sort of world and reference frame in which such a force was essentially nonexistent. So, as we grow fatigued we might decide we'll just give in to this new force and go with it and so walk in the direction it seems to be pulling us and toward the outer railing on the platform where we think we can then at least let the force just hold us there against the railing where we might be able to rest from all our exertion.

UH OH! WOAH AGAIN! What's going on now?! We can't seem to walk straight! We started out walking in the direction the centrifugal force was obviously pulling us but apparently there is now another sideways horizontal force forcing us to walk in strange spiraling paths! This is pure craziness! This is not right! This is not what we are used to!

This other strange new force we now seemingly have to contend with as we move across and relative to the platform would be called the "fictitious" coriolis force by physicists because it is not accounted for by Newton's laws of motion in this new noninertial reference frame, either.

It's almost like this new reference frame is a whole different world, huh?

Now, if we want to stay in this reference frame and world in which these forces are seemingly very real to us, then we will need to make the necessary modifications to Newton's laws so that we can actually apply them somehow.

Personally, though, I would rather just get off the merry-go-round and stay in the reference frame I'm more familiar with and in which Newton's laws actually do apply as I was taught them and then analyze the problem from there, where I can better keep track of what's really going on.

...including how the motion of the apparently muscle powered (or not) masses on the platform affect the motion (and kinetic energy) of even the platform itself.

It is here in my reference frame on the surface of the earth in which I need whatever excess energy I might find, of course. ...hmmm... ...but do you think that the gravitational force is actually a "real" force or but a "fictitious" force as Einstein's work would suggest?

...hehe

Take care.

;)

Dwayne

[Furcurequs]

A good summation of the current predicament Dwayne. I guess the moral of the story is that intelligence doesn't always inoculate us against stupid :D

ovyyus,

Thanks. We all need to try to be careful, I guess.

...and in regards to your other comment (that you may have now edited out?), I thought you might like that one.

;)

...lol

Btw, I'm still working on other posts including one specifically about the Finsrud stuff. Sadly, due to my discomfort I often am either slow to respond or I don't get around to responding at all.

I was actually reluctant to make this previous post to which you responded for fear it might be too wordy or incoherent.

Reading it again, I guess it's okay.

TC

Dwayne

[jim_mich]

To estimate power we need to know the rate at which the hundred-weight was lifted and also if that rate was constant or not. Which documents give a straight forward description of the rate at which the hundred-weight was lifted?

The same drawing that you use to justify the screw dimensions show the rope wrapped around the axle,then hanging straight down to lift a bucket. The other drawings show the rope again wrapped around the axle, then under a pulley near the floor, then the rope crosses the room, then over a pulley near the roof, and then a straight lift of a box of weights. Nowhere is there shown any "block and tackle" type of pulley reduction. The wheel rotation speed is known. The axle size is known, the load is know. From those THREE pieces of data it is very simple to calculate the speed at which the weight is lifted, and from that the HP or Watts produced. Again, let me repeat. The 8 inch axle size is known. The 26 RPM speed is known. Or you can assume the wheel slows down to 20 RPM water pumping speed. The hundred-weight 112 lb load is know. Lifting speed would be pi × 8 × 26 = 653.5 inch/min (0.9076 ft/sec) at 26 RPM or pi × 8 × 20 = 502.7 inch/min (0.6981 inch/sec) at 20 RPM.
HP formula = Lb × Velocity_Ft/Sec ÷ 550.
112 × 0.9076 ÷ 550 = 0.1848 HP. (Equals 137.82 Watts)
112 × 0.6981 ÷ 550 = 0.1422 HP. (Equals 106.01 Watts)

So this is a straight forward calculation using the known weight lifted, the known wheel axle size, and the known wheel RPM, and an alternate slower wheel RPM witnessed when pumping water, which we do not know if the wheel slowed down while lifting the 112 lb hundred-weight. Only when you ASSUME some sort of ADDED wheel reduction can the wheel output be different. Only THREE well known pieces of data are needed to determine wheel output.

I estimated the power of the water screw based on typical water screw construction and on the relatively precise sizes given in Bessler's scaled drawing. To imply that I manipulated my estimate in order to justify anything is a lie.

First off, I did not imply that YOU manipulated your estimate. What I was saying was the there are so many pieces of data that are estimated by scaling the drawing, that the end result could be very different than Bessler's actual wheel. We have no assurance that the water screw in the drawing is drawn properly to scale. Bessler may have drawn the wheel and hammer-mill to scale and then drawn the water screw half scale because it might have dominated the drawing if drawn full scale. I'm not saying this was the case. I'm saying that we DO NOT KNOW. This could be the case.

For the water screw we need to estimate a whole slew of dimensions...
To determine water pumping output, you need to know the screw rotation speed, the total weight of water being lifted, the rate at which the water is lifted and expelled, and the lift height. To know the screw rotation speed, you need to know the wheel speed, driving pulley size and the driven pulley size. To know the weight of the water lifted, you need to know the volume of each screw "bucket" size. To know that you need to know the screw diameter, the screw lead (the spacing from one "bucket" to the next) and the clearance between the screw vane and the screw axle. If there is no clearance then the water in the screw will siphon back down. And to a lesser extent you need to know the screw vane thickness and the screw wall thickness. The screw lead is a pure guess. There is a notch shown at the bottom end of the screw, which is about 6 inches long. You need to know the water pumping height. This must be scaled from the drawing. There is no accurate way to determine how high the water is pumped. According to the drawing, the screw would suck a significant amount of water out of the small water tank box, and the water level would drop quite a bit.

My point about the water screw estimate is that there are a LOT of variables that get estimated by scaling the drawing. If only a few, or even one, of those dimension are estimated wrong, then the results will be wrong. The hundred-weight lift calculations agree closely with the hammer-mill calculation. But then the water-pumping calculations are way the hell different. This leads me to think the picture of the water screw is not scaled properly. Suppose the water screw drawing is half-size for appearance sake. That would make the screw twice the size shown. That would make the water volume 4 times as much and the water pumping height 2 times as high. The pulley twice as big on the screw, which would reduce screw rotation speed. The output would be 4×2÷2 = 4 times your calculated output. So your 25 Watts would be in the range of 100 Watts. Plus the friction of a water screw is much greater than that of the other devices shown, thus eating up more power.

So, simply assuming the water screw was draw half scale causes the water screw output to be in the general range of the hammer-mills and the hundred-weight lift. Now don't crucify me. I'm just speculating as to why the difference between the other two calculations verse the water screw calculation.

[ovyyus]

The same drawing that you use to justify the screw dimensions show the rope wrapped around the axle,then hanging straight down to lift a bucket.

You question the accuracy of dimensions derived from the scale drawing for the water screw and then assume the rope and bucket load configuration is exactly right. The bucket is drawn empty! :D

The 26 RPM speed is known. Or you can assume the wheel slows down to 20 RPM water pumping speed.

You want me to assume that wheel speed under the water screw load would be the same as wheel speed lifting a hundred-weight directly from the axle??? So much for 'straight forward'.

What I was saying was the there are so many pieces of data that are estimated by scaling the drawing, that the end result could be very different than Bessler's actual wheel.

The scale drawing provides water screw length, diameter, water lift height, speed coupling and loaded wheel speed was measured and reported. Factor in typical and sensible construction techniques and materials (these pumps had been built for centuries) and there seems no reason why a reasonably accurate power estimate can not be made.

This leads me to think the picture of the water screw is not scaled properly. Suppose the water screw drawing is half-size for appearance sake. That would make the screw twice the size shown. That would make the water volume 4 times as much and the water pumping height 2 times as high. The pulley twice as big on the screw, which would reduce screw rotation speed...

Did you actually say that... yes you did. It boggles my mind that as a last resort you might suggest changing Bessler's scale drawing to suit your needs.

No wonder Stewart left the forum in disgust. Sensible discussion with you is clearly impossible. I'm done trying. Good luck.

[eccentrically1]

all forces cancel, and a wheel and axle at the end of the day is just a lever. it's not alive like we are, capable of motion. unless it has energy in some form it can transform continuously. no sticky points from throwing mass around and expecting a different result from any arrangement or position, thank you.
it was transforming energy external to it, an environmental engine. i don't like the stored internal energy approach, that would have been a clear fraud, and karl would have called him out on it.

maybe the best estimate of its power could be based on its weight, which has a range itself, but maybe not as wide as the assumptions for the other estimates. the power to weight ratio is the cube square law. i'll try the math later.

i think the wheel wasn't as heavy as we think, and most of its weight was at the rim. as it started up, the weights rolled out to the rim to help start it and make it have more inertia, and stayed there while it coasted, making small rocking motions in small arcs following the rim, so they wouldn't throw it out of balance, or lose energy due to excessive backwards motion.

in my own one very humble 4.5 star opinion.

[jim_mich]

It boggles my mind that as a last resort you might suggest changing Bessler's scale drawing to suit your needs.

It boggles my mind that as a last resort you might suggest the lifting of weight was slowed by being reduced by some sort of pulley arrangement, when it is obvious that the pulley speed reduction mentioned by Leibnez was the peritrochium style of the wheel itself.

The 26 RPM speed is known. Or you can assume the wheel slows down to 20 RPM water pumping speed.

You want me to assume that wheel speed under the water screw load would be the same as wheel speed lifting a hundred-weight directly from the axle??? So much for 'straight forward'.

No, I did not say the water screw ran the same speed all the time or that the water screw ran the same speed as the weight-lifting. But you want me to ASSUME that the wheel speed was slowed while lifting the hundred-weight load, when there is no witness to such.

The scale drawing provides water screw length, diameter, water lift height, speed coupling

Yes, you are right. But my point is that there is nothing saying that the water screw part of the drawing is to a correct scale. It is pure assumption as to the size of the water screw. No written documents back up the assumed water screw dimensions. The dimensions of the hammer lifts were described. The arrangement and the dimensions of the weight lifting were described. But the ONLY written description of the water wheel was how fast it caused the wheel to rotate. ALL of the rest is speculation based on a drawing that is SPECULATED to be correct. And if the SPECULATED lead pitch hidden inside the water screw was more or less, then the water output is more or less at any given speed. And if the pulley sizes, which are derived ONLY by scaling the drawing, were to be more or less than the ASSUMED sizes, then the screw speed would also be more or less than SPECULATED.

This was the point I was trying to make. Using a LARGE QUANTITY of ESTIMATED SPECULATED values coupled with a known wheel speed DOES NOT produce a reliable ESTIMATED SPECULATED result.

Logically the wheel output should be the same when presented with a same load, regardless of whether the load be lifting weights through the window, be lifting hammer-mill weights, or be lifting water.

The window lift was straight forward. It presents the most accurate calculation, unless of course we assume addition pulley reduction.

The lifting of the hammer-mill weights was straight forward. It gives a similar result. Its calculation requires added assumptions as to the height the hammers were lifted and how much they weighed.

But then when we come to the water-screw. The wheel was obviously being loaded and made to work. Are we to assume that a very small amount of water pumping slowed the wheel so much that it was noticeable, while the hammer mill was able to run OK, requiring about 5 times as much input to operate as your wimpy water screw calculation. Are you telling me that the hammer-mill also required some sort of pulley reduction?

The hundred-weight lifting also required about 5 times as much for the lift as your wimpy water screw calculation, while matching rather closely with the hundred-weight straight simple lift. But you dismiss this by saying the hundred-weight lifting was reduced by pulleys. Where was the pulley reduction for the hammer-mill?

Such does not make sense. The logical assumption to be made would be that the water screw drawing is out-of-scale and that more water was being lifted than ASSUMED by a typical water screw calculation that is based upon scaling the drawing. If the water screw size was actually bigger than shown on the drawing, then all three devices would agree as to wheel output. Thus one single simple assumption as to size of the water screw would bring all three devices into agreement. This is logical thinking. Assuming a much slower hundred-weight lifting based upon one sentence by Leibniz, which can be explained as being the same "fourfold pulley speed reduction" as Bessler's very plainly shown peritrochium pulley speed reduction, while ignoring the hammer-weight lifting goes against logic.

No wonder Stewart left the forum in disgust. Sensible discussion with you is clearly impossible.

And so you stick your fingers in your ears and say, "No, no, no!" You have formed an opinion. And you refuse to look at anything that might change your opinion. A more powerful wheel would upset your assumptions. You ignore basic logic and cling to your past assumptions. Logic says that all know facts and assumption must agree. If the calculated wheel output of the hammer-mill matches the calculated wheel output of the hundred-weight lift, but the calculated wheel output of the water screw does not match either of the other two, then logic says that the water screw calculation is more likely wrong than that the other two are wrong.

Stick your fingers in your ears. Flee, while yelling, "No, no, no! Jim is wrong." It is no sweat off my brow whether you think I write truth or fantasy.

[ovyyus]

Bessler's added description of the scale drawing:

NB. from the small measure stick, which is 3 Ells or 6 feet long, everything else can be accurately measured, it will all be true/correct. Made by Orffyre g.

But Jim sticks his fingers in his ears while yelling, "No, no, no! Bill is wrong". What ridiculous thing will he have us believe next? :D



PS: thanks to Stewart for the above translation.