Function for the Thrust of a Ducted Fan

[Blanchdog]

TL;DR

Trying to come up with an equation for the thrust of a ducted fan in terms of fan radius, rpm, angle of attack, width between rotor and duct, and any other relative variables.

I'd like to design a ducted fan capable of generating 800 N of thrust. Though I can do fairly high level math, I just really don't even know where to start in calculating (or at least relatively accurately estimating the thrust generated by a propeller, particularly a ducted one (as I understand it ducted fans produce a greater amount of thrust if made correctly).

So I need an equation for thrust as a function of the radius of the prop, rpm, angle of attack of the propeller, number of blades, width between the prop and the duct, and any other relative variables. Angle of attack is a bit over simplified for a geometrically complex surface like a turbine blade, so if there's some optimal geometry then a number representing that is just fine.

As a secondary interest, I'd like to know the power of the engine necessary to drive such a turbine.

Any help/instruction is appreciated!

 

[Bystander]

https://en.wikipedia.org/wiki/Hiller_VZ-1_Pawnee

 

[JBA]

You may find the information and calculations at the below site helpful.

https://en.wikipedia.org/wiki/Axial_fan_design