I saw this question Is there a rule of thumb for spacing between jet engines?, which referred to How do you choose engine placement for under wings engines?, but I was wondering how the engine spacing is approached for propeller aircraft. There are some examples as shown in this question (How far should the two propellers on a twin-engine plane be apart?), but I'm looking for a more systematic approach.
Compared to jet engines, propeller engines are larger, and have a much larger stream tube going into the engines. This will probably make their performance much more sensitive to the lateral gap between the engines.
I found this paper Aerodynamic interaction between propellers of a distributed-propulsion system in forward flight, which indicates for a three propeller setup:
At the thrust setting corresponding to maximum efficiency, the efficiency of the middle propeller is found to drop by 1.5% due to the interaction with the adjacent propellers, for a tip clearance equal to 4% of the propeller radius.
This is one data point, but I wonder how the influence varies with prop spacing. It makes sense to me that at a far-enough spacing, the engine can be treated as independent. I'm wondering what this far-enough spacing is, and how the influences vary with prop spacing.
There is a wide range of gaps available, some aircraft, such as the X-57, have a spacing that is very small - the tips are touching.
So my question is:
What is the aerodynamic influence of prop spacing (to each other and to the engine) in multi-prop engine setups?