In reference to helicopters and helicopter propulsion . . .
could there be any serious benefits to using a propeller that was of
increased surface area, so that it resembled almost a complete circle
with slots missing to allow lift, so it was more like 10 or 12 blades
rather than the standard 2 or 4??
Neat idea, a little late. Leonardo di Vinci drew pictures of this a few
hundred years ago. Engineers have not chosen to pursue this design. Likely a
matter of the parasitic drag created by the larger spinning surface.
Perhaps it is time for someone (you?) to revive the idea and see what happens.
Consider building a model from Leonardo's drawings.
You might find "Modern Airmanship" by van Sickle to be a good source of
information on aerodynamic drag.
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Update: June 2012