I’ve been on and off lurking around this site for quite a while and still haven’t seen a particularly good answer regarding whether overlap would be a benefit, a wash, or a negative. Given the size of the propellers currently being used, a small increase in diameter and chord could result in a considerable increase in prop efficiency.
All of the propellers are already flying in turbulent air - the protective netting ensures that. They’re also in pusher configuration so they’re getting turbulent air off of the arms.
You’ll notice in @Beachbum s drawing that the overlapping props are actually moving in the same direction which I would consider beneficial in this condition because it will avoid a hard “slap” against air that’s been accelerated the opposite way. Trying to accelerate already accelerated air is a problem, but it will also be dispersing tip vortices generated in that area of the arc (this is likely already happening some on the current X4 design).
I’m not sure if my lazy drawing will attach to this post, but the eyeball calculation on a maximum overlap situation shows half of each arc of each propeller will experience some overlap, but the total area of overlap is less than one propeller swept area. In other words, <1/4 total swept area is actually overlapped.
Free-stream vs Slipstream. This is where things get interesting - a huge area of that overlap is in the slipstream of the pilot. At least 50% but possibly 75%. Are the propellers far enough back that re-accelerating the air will cause a beneficial pressure recovery? Is having overlap in areas of slipstream beneficial while leaving areas of non-overlap in free-stream air? How bad will the harmonics be from the blades going in and out of the slipstream and through areas of overlap?
It will probably take someone building one to actually find out, though if anyone has some fancy fluid dynamics software and the time to throw at it, it might give something of an idea.