Johann Bessler's Perpetual Motion Wheels Part V

The pendulums of Johann Bessler's Weissenstein wheel

In the surviving drawings of both the Merseburg wheel and the Weissenstein wheel, pendulums are shown mechanically connected to the wheels, presumably as speed regulators. See for example http://www.besslerwheel.com/images/Kassel-2ndFigure.jpg

From these drawings, we can see from the way the pendulums are connected, that they must complete exactly one oscillation per wheel revolution.

From John Collins' re-publication of Bessler's Gründlicher Bericht ("Thorough Report") p57, it seems that these pendulums may not have been essential components. The translated description of them is:—

"N.8. Are the 2 pendula for balance, which allow the motion to continue, but without hindering the running, but which can be taken down, yes, but which in truth hinder the speed of revolution, if they are attached, very slightly."

Pendulums — modelling

Since we know the size of these wheels, we can also estimate the size of their pendulums, by scaling from the drawings. If we assign reasonable values to the pendulum masses, it is then possible to make a computer model, and compare the periodic time of a pendulum with the rotational speed of a wheel.

(Yes, I know that scaling from drawings is a very bad thing to do, when anything important depends on it, but that isn't really the case here).

For this periodic time comparison, it is only necessary to model a single pendulum, since an identical second pendulum must have an identical periodic time.

Weissenstein wheel and pendulum

Observers said the 12ft diameter Weissenstein wheel rotated at 25 to 26rpm, corresponding to a period of 2.3077 to 2.4 seconds per revolution. The silux model that I built (below) shows that the period of the pendulum by itself is 3.8278 seconds.

Silux model of the Weissenstein wheel pendulum. The macro has stopped the simulation after exactly one oscillation.

So, if the wheel was actually connected to the pendulum as drawn, it would have been trying to drive the pendulum quite a lot above its natural frequency, and well outside of the range where any forced oscillations/resonance situation could be occurring between the wheel and the pendulum.

Further details

T-shaped frame: assumed to be hardwood, total mass 18.2kg.
Top 2 masses: assumed to be brass spheres 8 inch dia, mass 37.34kg each.
Bottom mass: assumed to be 50% heavier than top mass; 56kg.
Distance from pivot to either top mass: 38 inches.
Distance from pivot to bottom mass: 122 inches.
Total amplitude of swing (bearing in mind that the end of the crank is not shown at quite its lowest position in the drawing): ±45°.

Halving the amplitude to only ±22.5° reduces the period from 3.8278 to 3.7163 seconds, only a 2.9% drop. It is also very insensitive to changes in the masses.

Conclusions

I conclude that as drawn, and connected to a wheel turning at 25 to 26rpm, the pendulum could at best be only a bit of essentially useless mechanism, wasting energy, with no useful regulatory function.

Assuming the eyewitness accounts of the wheel's speed and its size are reliable (and I see no reason to doubt them), and assuming the drawings are correct in showing pendulums, there are only two options:—

Either — For whatever reason, Bessler made these pendulums as drawn, but did not connect them to the Weissenstein wheel. It does appear, from Bessler's description quoted above, that the wheel was run at least on some occasions without the pendulums. In that case it must have had some other internal method of speed regulation.

Or — The pendulums were connected and operating on some occasions, but for whatever reason they were not drawn "as built". They could have been given the required 2.3 to 2.4 second period if their masses had been placed much closer to the pivot, rather than at the extreme ends of the frame as shown in the drawings. In my model, I found that if all the masses are moved in to only 0.3 of their original distance, i.e. 11.4 inches from the pivot for the top masses and 36.6 inches for the bottom mass, the periodic time is reduced to 2.3505 seconds.