Think twice about what you think you know!

[sleepy]

Bear with me mathematicians,
The general consensus of the largest wheels' weight is 400 lbs.The general consensus of the speed of the wheel is 26 RPM.Once you have a 400 lb wheel moving at 20+ mph,it should put out a definite amount of force.Can it actually be stronger or weaker than another 400 lb. wheel at the same speed?I realize the internal drive mechanism would make a difference in maintaining speed under load,but as far as the force it would take to stop it immediately,wouldn't that be constant and identifiable?Can someone with some math knowledge figure out how much force it would take to stop the wheel at the current believed numbers.It would be enlightening to have a number to look at.In order for a wheel of that size and weight to reach those speeds within 2 revs,it must have had a lot of torque.And it was all it could do to move 15 lbs.?This just isn't adding up.Is it possible that either the perceived weight or the assumed speed is way off?Thanks in advance for the math help.

[jim_mich]

I'm sorry but the 20+ mph you keep quoting is wrong.

12 feet diameter x Pi = 36.699 feet circumference
x 26 rpm = 980.177 feet per minute
x 60 minutes = 58810.614 feet per hour
/ 5280 feet = 11.138 mph at outer rim.

Considering the weight would not be all on the rim I might guess it to be centered at about 8 foot diameter. This would put the speed equivalant at about 7.4 mph.

[Jonathan]

You're right, I used 12ft as the radius! How I frustrate myself...!

[rlortie]

Bill and Jonathan,

Help me out here.

Bills cut quote;

This wheel was obviously not very powerful and I don't think the depicted No.23 handle would present too many difficulties in stopping the wheel. Certainly the instantaneous stopping power required to overcome total wheel inertia (whatever that was) might be enough to lift someone off the ground if they were game enough to grab onto the moving rim.

Where and how do we explain the difference between torque, inertia and velocity? The handle is closer to the axis meaning less leverage for stopping the developed torque in total mass.

At the same time the outer radius, representing a longer lever offers less force required to stop wheel torque, but velocity of mass is faster. That is the same amount of mass present at lever, mass of wheel is constant.

Am I right or wrong in thinking that the closer or farther I am to axle the foot pounds of torque will equal the same? I would think that foot pounds would be the same and the added leverage compensates for velocity and not mass.

In my view it will take the same amount of energy to stop the wheel by handle or by rim. The latter taking longer but with less force. Using the formula for "work" both should equal out.

Do I have you confused yet? I know I sure the heck am and not ashamed to admit it.

Ralph

[ovyyus]

In my view it will take the same amount of energy to stop the wheel by handle or by rim...

I agree. IMO, it is a matter of convenience and safety. Grabbing onto a fast moving rim might prove tricky and, as Jonathan pointed out, splinter prone. Rather than risk friction burns at the rim I would rather brake the wheel slowly using the handle. Of course, the handle would be difficult and cumbersome if the wheel was very powerful, but that was not the case.

[John Collins]

Ovvyus wrote

Wolff is describing the action of the Merseburg wheel where the 6 inch diameter axle is used to raise a 60lb load with a (more than) 4 x reduction pulley. The wheel would have performed the same work if it was lifting a 15lb load (or less) directly from its axle with no pulley reduction.

If the wheel was rotating at a loaded speed of say 40 RPM, then the 60lb load weight would have been lifted about 15 feet (at best) in one minute.

Looking at the 4 x reduction to the pulley reminds me of something that occurred to me some time back. If, as Bill says, the weight was raised about 15 feet in approximately one minute, then removing the 4 x pulley reduction would create a demonstration lasting about 15 seconds - not a very impressive demonstration. I wonder if the pulley was reduced in order to provide a more lengthy demonstration of the potential uses for the wheel.

If this is so, then maybe we should consider that the wheel had more inherent power than we have given credit for? On the other hand the reduction in speed of 26 RPM to 20 RPM reported in the Kassel wheel when under a lifting load of 70 pounds may suggest that the reduction of the pulley was necessary after all. Perhaps it was a bit of both?

John Collins

[Jonathan]

"reduction in speed of 26 RPM to 20 RPM reported in the Kassel wheel when under a lifting load of 70 pounds"
I'm a little confused about this, was this really the case? Bill's site mentions the reduced speed only in reference to the Archimedean screw (it is a high-torque-low-speed device, so you would expect it to affect the wheel's rotation speed the most of all the demostrations).

[ovyyus]

To the best of my knowledge the Kassel wheel was not reported under load from lifting weights, but rather loaded with an Archimedean screw.

Jonathan, have you tried a guesstimate of the work done in turning the Archimedean screw based on it's depicted size and probable pitch and water content? IMO, not much water was transported by the screw at just 20RPM - maybe about 5 litres per revolution? (rope connection between screw and wheel looks close to 2:1 reduction which I won't take into account) = 100 litres per minute. The total water lift height looks about 4 feet at best. So, 100 litres = 220lbs lifted 4 feet per minute.

Compare Merseburg wheel lifting 60lbs to a height of 15 feet per minute with Kassel wheel lifting estimated 220lbs to a height of 4 feet per minute - about the same power.

PS: John, I think that if Bessler removed the 4 x pulley then the Merseburg wheel would not have been powerful enough to lift the 60lb load. Bessler obviously preferred to demonstrate a heavy slow lifting load rather than a light fast lifting load. Perhaps he felt it more impressive or convenient, or perhaps a 60lb box of bricks represented some 'norm' in the building trade of the time?

[John Collins]

Sorry Guys - you're right Bill, according to his letters the Kassel wheel load was described by von Erlach as an archimedes screw. However, I'm sure that a straight forward lift of a load would have been included although I can't find a reference at this time.

As for the Merseberg wheel and the pulley although I agree that the wheel might not have been able to lift a 60 pound weight unaided, I still think that the reduction pulley was useful for extending the time of the lift anyway.


John Collins

[Jonathan]

Yes Bill, here. I came to the conclusion of 24W and 160.8 liters per minute. But that should be an overestimate because I simplified the math. I also oversimplied the square pulleys, though I'm not sure at the moment which way that affects the outcome. To be conservative I would put it at 18W and 120lt/min.
That's a neat take John, it didn't occur to me that the pulley reduction might have been for show. But of course that is a trade-off, because it makes the wheel seem weaker to the observant.

[ovyyus]

Ah yes, sorry I'd forgotten about that - nice job Jonathan.

My own guestimate of 100 litres per minute does not take into account the reduction depicted between wheel and screw, where the screw looks like it will probably only turn about 1/2 to 2/3 the wheel speed. That correction added in would decrease flow rate to about 50 - 60 litres per minute. This is only about half of your own estimate, or about 10 watts, so maybe the truth lies somewhere in between.

Either way, it becomes obvious why Leibniz and Wolff questioned the utilitarian value of the machine in its present limited form. I think it would be fair to suggest that this criticism was one of Bessler's greatest obstacles and one that he was never able to fully address.