BTW the physics of ducted fans and props was explored many years
ago by Kuchemann & Weber in their book The Aerodynamics of Propulsion.
The laws physics have not changed despite attempts by our government 
to legislate them out of existence.

As late as the Ultra High Bypass engine era of GE and others, the efficiency
of ducted fans was still 20% less than a prop with speeds lower than about
350 MPH. And that BTW was with very thin titanium fan blades running
tip speeds up to mach 1.4.

This chart from K&M  kind of sums up the low speed situation.

Paul Lamar
 
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