Leonardo da Vinci's Perpetual Motion Wheels Part II

Leonardo's "J-tube" wheel

Here is the second of Leonardo da Vinci's perpetual motion machines to be analysed, again from Codex Forster II.

An animation has been made of this machine, at http://www.youtube.com/watch?v=GhR-K10UjnY, but obviously not in a "true" way. The falling weights don't accelerate correctly, and the wheel's rotational speed seems to remain unchanged, even though energy must be lost from the weight impacts. So, let's make the silux model:—

Silux model of Leonardo's "J-tube" machine, at start of simulation

I decided to make the model as the minimum necessary for testing. The circular part of the wheel is 1m diameter, of mass 10kg. In the model, it is made as Positive, Functional in the Edit Object box, whereas the J-shaped tubular part that carries the weight is made as Neutral, Functional, so that it cannot influence the wheel balance. The spherical weight is 4kg. Gravity is active; friction is negligible.

Results

Model at maximum wheel angle reached, with graph of wheel angle vs time

As expected, the weight falls at its maximum radius while the wheel turns through the first 90 degrees. Then it rises at a lesser, generally diminishing radius in the curved part of the tube, while the wheel turns another 147.94 degrees, to a maximum angle of 4.153 radians, i.e. 237.94 degrees, in 1.848 seconds. Thus it doesn't quite reach the 240 degrees necessary to complete a cycle, and so it fails to deliver any net energy. I tried a few variations, e.g. varying the wheel mass, which for some values allows a moderate exchange of energy between the wheel and the weight. The weight then oscillates slightly, as it rises in the curved part of the tube. But none of these variations could complete a cycle of operation.

Reference, and miscellaneous remarks

This completes my comments on Leonardo da Vinci's wheels. For more on his work, check out http://www.leonardodigitale.com/index.php?lang=ENG  (thanks to Ed, for the reference).

I should mention that I currently regard my gmail as a "read-only" inbox for emails. I'll read anything posted there, but I'll reply if necessary in this blog.

Recently I've been making a new blog post every five days, so I'll try to keep to that schedule, for a while anyway. Next time: a "wider issues" post.