On Fri, 5 Jun 2020 13:27:23 -0700 (PDT), wrote:

I've read that ships at sea, because of wave action, tend to rock from side to side, causing the paddles to lose contact with the water, sometimes 50% of the time greatly affecting the efficiency. Screw props are always in full contact with the water. In my opinion, the main reason paddlewheels fell out of favor is that the mechanisms are more complex and most importantly, take up a lot of space.

I believe that there are still Paddle Wheel vessels operating. See
https://en.wikipedia.org/wiki/Paddle_steamer
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cheers,

John B.