jim_mich wrote:Bill wrote: He was 65 years old at the time. He died 2 years later in 1723. Perhaps something to consider in relation to his difficulty handling the big Kassel wheel?
Is this an example of a typical younger persons warped perspective towards older people?
Bessler was age 65 when he died. Same age as Fischer when he inspected Bessler's wheel. Do you suppose Bessler was also weak? After all Bessler died at age 65. But wait. Bessler was building windmills at age 65. So a 65 year old man need not be weak. But then Bessler dropped dead, literally.
My point is that age 65 does not imply a person is frail and weak. So I don't think anyone needs to consider Fischer's age in relation to his difficulty handling the big Kassel wheel. Only an ill-informed young person would suggest such a thought. Enough said.
Its obvious we will never know the weight of Bessler's Kassel wheel. But from all indications, its upper upper weight limit might be about 1000 lbs. Numerous times the weight of just the wheel has been estimated. John Collins in PM-AAMS estimated the empty wheel at about 500 lbs. John estimated 192 lbs of weight. You can read how he arrived at his figures on page 173 of PM-AAMS. John assumed weights 2-1/2 inches, which fit inside a 15 inches of interior space of the wheel, making the total wheel about 700 lbs.
But suppose the weights were about 4 inch OD by 3/4 inch thick, thus still weighing about 4 lbs. This would allow 20 weight-disks within the 15 inches, which would increase the weight of the weights to about 640 lbs. Then add the weight of the wheel itself and the total assembled working wheel might tip the scale somewhere around 1140 lbs.
What I take from all this is exactly what Bessler wrote, "the empty wheel was so heavy that it could hardly be lifted to its new bearings. With the weights it would have needed the Devil to lift it."
Bessler's empty wheel was probably somewhere between 350 to 500 lbs. This would make it difficult but not impossible to move to its new bearings.
I would put the upper limit for the total weight of the assembled 12 ft "difficult to stop" wheel, to be somewhere around 900 to 1200 lbs. Such would be the line where Bessler's wheel crossed into the impossible to stop realm. If any heavier then the wheel would be become impossible for Fisher or Bessler or Bessler's assistant to stop it.
http://singaporeseen.stomp.com.sg/singa ... 336769.jpg
;)
...anyway...
Having too massive a wheel may not be consistent with other accounts we have about it, though. Remember, according to descriptions by Fischer and 's Gravesande, the wheel would accelerate from a near standstill to its full rotational speed within just two or three rotations - when, of course, it was given a good enough initial push to get it started from a full stop.
If we were to assume some sort of intrinsic motion and/or gravity powered device, it might also then be somewhat safe to assume a limited amount of available energy PER REVOLUTION to accelerate the wheel up to speed. If that limited amount of energy per revolution was approximately equivalent to that which we can determine from the calculated power output in the load tests, then we can perhaps determine an upper limit to the wheel's moment of inertia, too, which would give us an idea as to the amount of mass for a given mass distribution in the wheel.
As an example I'll just grab the figures of 106 watts at 20 RPM for the Kassel wheel from here:
http://www.besslerwheel.com/wiki/index. ... eel_Output
I chose the 20 RPM figure to work with because that just happens to give us a whole number of 3 seconds per revolution.
106 watts times 3 seconds gives us 318 Joules per revolution which is 318 Joules * 0.7376 foot* pounds / Joule or about 235 foot * pounds per revolution.
If we use the above assumptions, then, 2 to 3 times 235 foot-pounds would approximately equal the energy stored in the wheel's rotation at 26 RPM.
So, if we go with three revolutions, we have 3 * 235 foot-pounds or 705 foot - pounds of energy to get our wheel up to speed.
Where 1/2 * I * w^2 is our rotational kinetic energy and w (I'm using that for omega - the rate of rotation in radians/sec) is 2 * pi * 26 rot/min * 1 min / 60 secs or 2.72 radians / sec,
The moment of inertia of our wheel will be I = 705 * 2 / 2.72^2 or 190 slugs * ft^2
If we divide this by our wheel radius squared we get 190 slugs - ft^2 / 36 ft^2 or 5.28 slugs, which is 5.28 slugs * 32.17 lbs / slug or 170 pounds mass.
That would mean that if our wheel had ALL its mass at the rim, it would weigh about 170 pounds. If the wheel were more like a solid disk, however, with the mass distributed equally throughout, for it to have the same moment of inertia it would weigh 340 pounds.
With our 235 foot-pounds of energy per revolution, that's like having 235 foot-pounds / (12 ft * pi) or 6.23 pounds of force applied at the rim throughout a revolution.
So, we can use that force and the equivalent mass at the rim for our calculated moment of inertia to determine the time it takes for the wheel to spin up to speed.
F = m * a, 6.23 pounds = 5.28 slugs * a, a = 1.18 ft / sec^2
V = a * t, 16.3 ft / sec = 1.18 ft / sec^2 * t , t = 13.8 seconds
So, the wheel would take a total of about 13.8 seconds to do it's first three turns.
If it could get up to speed in two turns, of course, it would have a smaller moment of inertia and might be considerably lighter, like I = 126 slugs - ft^2 and 113 lbm if all the mass were at the rim and 226 lbm if distributed throughout a disk. ...and it would take about 9.2 seconds to do the first two turns.
Now, if one could think of a mechanism that provided more energy per revolution at start up and so at slow speeds than under normal operating conditions, one might consider a more massive wheel. ...or, of course, if the energy source was time dependent rather than rotation dependent, like one might have with a hidden chemical combustion fuel source, then the moment of inertia of the wheel could also be greater.
...and just some more things to think about.
Dwayne
