# Where can I find info or techniques on calculating the influence of a duct on the thrust and efficiency of a propeller?

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!

• Apr 28, 2017 at 14:18
• Ducts offer improvements at low speed efficiency, "free" props better at higher speeds. There are graphs on this site, which also include fan jets and turbo jets in the subsonic range. Sep 8, 2019 at 15:43

1. If the duct is designed to prevent wake contraction, extra thrust is generated and less power is required to drive the propeller. The effects are computed with momentum theory, which is a simplification. For thrust T and power P, with $$T_D$$ and $$P_D$$ = ducted, $$T_U$$ and $$P_U$$ = unducted, $$a_w$$ = ratio of outlet/propeller area.:
$$\frac{T_D}{T_U} = \frac{1}{2a_w} \tag{1}$$ $$\frac{P_D}{P_U} = \frac{1}{\sqrt{2a_w}} \tag{2}$$