I thought it might be useful to rehearse my own thoughts here as I have not written about this subject for a long time, although it's in my mind constantly.
Bessler's largest wheel, the Kassel wheel, was approximately 12 feet in diameter, and 18 imches thick. It turned at 26 RPM unloaded and 20 RPM when lifting a heavy box of stones. It could turn in either direction if given a slight nudge in one direction or the other, after which it accelerated to its full speed in 2 to 3 turns. This wheel's predecessor, the Merseberg wheel, was of a similar size but thinner at only a little over 11 inches thick. It could turn at 40 RPM and was also able to turn in either direction.
These two wheels were designed and built to answer the accusation that the earlier ones were driven by clockwork. The earlier ones were able to begin to spin immediately their brakes were released. This fact suggests that they were in a permanent state of imbalance - or that a weight was always able to fall at the exact point that the wheel reached a balanced position thus continuing the imbalance. In the Merseberg and Kassel wheels I visualise there being two sets of weights - one for each direction, a kind of mirror image arrangement. The two-directional wheels obviously would not turn without a nudge in one direction, because the weight which fell as soon as balance was reached was counteracted by the weight which fell into position to turn the wheel the other way.
Once the wheel was turning, howver, one of the weights would move backward and therefore have no positive effect on rotation, while the other continued the imbalancing process. That's the theory; of course designing an arrangement of weights which fulfills the theory and works is another matter.
It seems clear that there were several variables which could be applied to the design of the wheel, which could make it turn faster or slower, using weights of varying size. Bessler claims such in his Apologia Poetica, and his demonstrations seem to prove that. The obvious variables include weights of different sizes and more or less of them; thinner and thicker wheels and large diameter wheels and potentially more mechanisms.
In my opinion the first one-way wheels hold the key to success, assuming that the internal mechanisms in the later ones were based on the earlier ones. Although we know that the Kassel wheel produced about eight bangs on its falling side, we have no knowledge of how many noises accompanied the spinning of the earlier ones - just that a loud noise was produced. I mention this because it might be wise to leave aside any assumption that there would need to be eight bangs to somehow include in the earlier more basic wheel. Bessler implied that he was able to barely induce a wheel to turn with just one cross-bar inside it, which could mean one pair of weights operating within a single but complete mechanism.
So I, at least, continue to work on producing a one-way wheel, but with five mechanisms which I believe Bessler indicated, is the most that can be fitted into the wheel. That indicates to me that the more mechanisms the better - and five seems to me to be the answer, or part of it. So four would not produce as much torque as five and three even less.
Many people work on the theory that because there were about eight bangs on the side towards which the Kassel wheel turned, that fact can be assumed as relevant to the other wheels, but I believe that the earlier ones were simpler with less mechanisms inside and therefore fewer sources of noise. Being of a simpler design they should be easier to replicate - why try to build a two-way wheel when a one-way wheel would prove the point.
JC