Based on other answers I've read here (1)(2)(3), a single large blade propeller is the most efficient type of thrust you can get.
There are 2 reasons for this (as I understand it). Firstly, because each blade on the propeller causes wing-tip vortices when low pressure air meets high pressure air.
Secondly, each blade on the propeller adds surface area to the aircraft increasing parasitic drag.
So my question is what if both propellers are surrounded by a duct? Assuming it's a perfect fit, the duct will neutralize wing-tip vortices, so now all that's left is parasitic drag.
Now couldn't you just use 2 propellers that equal the surface area of a single large propeller and get the same efficiency with no added parasitic drag?
On a similar note, could you use just 1 small propeller surrounded by a duct and reach similar efficiency (if not better) than a large propeller surrounded by the same duct?
I say "if not better" because the smaller propeller would have less surface area, thus less parasitic drag.
