I am trying to run numbers on a concept VTOL fixed-wing aircraft, and I am looking at having fans or props positioned inside the wings, (which would therefore make the wings relatively thick for a fixed-wing aircraft). Naturally this would see the fans/props enjoying the benefits of a duct, but with minimal downsides such as the need to add weight/material as the wing is already going to be there.
I am using Blade Element Theory to trial propeller dimensions/numbers to see what kind of sizes I would need to achieve the VTOL (if I can minimize the radius of the VTOL fans then I can the wings thinner or with a smaller chord), but I don't know of any way to estimate the influence that the duct would have on the final thrust/power values.
If there is a rule of thumb for this, or a database, or some equation or anything, that would be a great help!