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Lorenz Waterwheel

PostPosted: July 8th, 2019, 10:27 pm
by BadgerJelly
Not sure where to post this (move if necessary)

How much, and how fast, would water have to flow for a Lorenz Waterwheel that was 200m high in order to reach a chaotic state? I was thinking the size of the buckets would be roughly 20,000 litres but have no idea how to calculate the amount of water required.

I’m talking about a river here. What scale of river would meet these requirements?

Thanks

Re: Lorenz Waterwheel

PostPosted: July 10th, 2019, 7:48 am
by Dave_C
It would depend on your specific wheel. There's a number of design features that go into the wheel which will influence the motion. I thought about modeling the wheel and in so doing, I realized there were a host of factors that would need to be taken into account, such as:
1. Rotational inertia of wheel
2. Friction of wheel
3. Size of buckets
4. Size of hole in bottom of bucket
5. Spacing of water buckets (ie: is there always a bucket under the water or are there gaps?)
6. Angle wheel makes with vertical (I read some experimenters tried to limit rotational forces by tilting the wheel)
7. Where around the circle the buckets are being filled
etc...

One web page suggested that their attempts to model this wheel required tilting the wheel over to minimize rotational torque from the water and minimizing flow. They also had problems with friction of the wheel.
http://www.ace.gatech.edu/experiments2/ ... nz/fall02/

Re: Lorenz Waterwheel

PostPosted: July 10th, 2019, 9:54 pm
by BadgerJelly
The scale I was thinking was a 200+ metre high wheel. The river flowing into it would act like a ‘normal’ waterwheel for part of the year and when the rainfall increased it would move into chaotic motion.

Basically would upscaling too much dull the effects? I’m thinking in terms of friction and/or a large volume of the falling water being blown away on the wind - imagine a wheel 200-300 metres in diameter embedded in the cliff face at Angel Falls.

Theoretically speaking could such a waterwheel ‘move chaotically’ as seen on a smaller scale? I don’t see a reason why it wouldn’t, but just want to make sure I’m not overlooking how chaotic systems may differ due to scale.

Thanks

Re: Lorenz Waterwheel

PostPosted: July 10th, 2019, 11:21 pm
by Dave_C
Without developing an analysis of the motion, I can't offer you proof that larger wheels can exhibit chaotic motion just like smaller ones, but I don't see any reason to think that simply scaling up the different variables would change the motion. Some may scale differently than others but the exhibition of chaotic motion should be independent of scale.

Re: Lorenz Waterwheel

PostPosted: July 10th, 2019, 11:32 pm
by BadgerJelly
Dave_C » July 11th, 2019, 11:21 am wrote:Without developing an analysis of the motion, I can't offer you proof that larger wheels can exhibit chaotic motion just like smaller ones, but I don't see any reason to think that simply scaling up the different variables would change the motion. Some may scale differently than others but the exhibition of chaotic motion should be independent of scale.


That was my thinking. After all such patterns show across different scales ... so that is why I intuitively assumed it would be okay. The weirdness makes me doubt though.