Is 1 large propeller more efficient than 2 smaller propellers (if both cover the same area)?

Question

Is there a reason in efficiency to prefer 1 large propeller over 2 smaller propellers, when both cover the same area?

With same area, I mean i.e.

$ r_{small} = 1 $

$ A_{small} = \pi * r^2 = \pi * 1^2 = \pi $

$ A_{large} = 2 * A_{small} = 2 * \pi $

$ \pi r_{large}^2 = 2 \pi $

$ r_{large} = \sqrt {2} $

Some boundary condition/simplification: The 2 smaller propellers do not interfere each other

PS.: This is related to: multirotor - Why are larger propellers generally more efficient than smaller ones? - Drones and Model Aircraft Stack Exchange Why are larger propellers generally more efficient than smaller ones?

Answer 1

Propeller momentum theory is only concerned about total area, so you can split the area up over any number of propellers and the maths works out the same.

It calculates the mass of air moving through the propeller every second, and thus the speed it must be moving. It doesn't consider things like the blade efficiency or number of blades - any prop inefficiency needs to be deducted from the results.