I think the best way to get a quiet craft is to make one whose primary
movers don't make very much noise. Engine exhaust, you have to
muffle. Propeller blades, though, can be made noisy or quiet. The
VERY noisy ones are probably bad designs in my opinion. The noise is
a sign of non-laminar flow over the surfaces, or some other bad
thing. Fix problems with the prop and you fix at least some of the
problems with the noise.
That's not to say that all changes which reduce noise improve
performance though. Some changes could be made which make the prop
quieter but cost energy in some way. In my understanding, the
MultiWing company does this with their fans, since they are primarily
used in heating and air conditioning applications.
The same thing could be said for ducts. The duct shape determines how
well air sticks to the walls of the duct going through, and that
inevitably could either make noise or could cause turbulence which the
prop must travel through, which would also make noise. Does make
noise, I should say, since I've heard that noise.
You've said in the past that time and money aren't much of an issue
for you. So the best thing you could do here is make a test
platform. Make maybe a 24" duct and start playing with straws and
screens to see what happens. Make a mechanism that allows you to test
thrust and power while you're at it. Then you can not only test to
see whether your idea works, you can also test real world performance
in unexpected situations, like when you get leaves or grass in there.
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