One more time: It's not a "tacking propeller", it's a "propeller". It's as if the last few pages of this thread never happened.
You're just being deliberately obtuse now. You are pretending not to understand just to avoid admitting you are wrong, just like your earlier "it's complicated" evasion when attempting to squirm out of admitting you made a mistake about stacking pairs of weighing scales. It's painful to read.
I have already told you some primary differences between a sail and a prop.
A tacking boat takes energy from the wind, uses the lift force derived from crossing the ddw wind path, and taking a longer path because of that. More work is done that way. The center of mass does not move ddw.
Props transmit energy to the air, do not cross the ddw path, the centre of mass moves along the axis, so ddw. The ddw path is the shortest possible, and work is f*d where d is the displacement of the hub and not the tips.
You make analogies between props and tacking boats, so one would expect to find them in a text book on aerodynamics, or in a sailing book describing tacking, by making references to a propeller.
Find such references...JBTH.
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