DaVinci-style drone with 600-year-old screw rotor design

It was hypothesized that a down facing lip would prevent air from escaping radially outward from the rotor, but this was proven incorrect. All rotors tested (3,4 and 5 in Figure 2.2) have 1 turn, a pitch of 100 mm (3.94 in), a radius of 76 mm (3 in), and a 1:1 taper ratio.

A downward facing lip showed reduced thrust and an upward facing lip showed negligible impact on thrust in Figure 2.7.

Flow visualization conducted during this trial revealed that air was being ingested radially inward during operation of the no lip and up facing lip aerial screws, and that this flow was disrupted by the down facing lip. These results support the findings of the CFD studies detailed in Chapter 3.

Figure 2.8 indicates that the presence of a lip in either direction increased the power requirement of the rotor. Figure 2.9 shows that the presence of a lip in either direction also reduced the FM of the aerial screw. Therefore, a lip is not a useful design feature at all, and was discarded.

http://vfs.umd.edu/assets/downloads/2020_elico.pdf

The key to this is that, for both ducted fans and props, a larger swept area is more efficient, while # of blades simply changes the torque/rpm ratio with negligible effect on efficiency. Thus, for a given torque, it's always better to drive two longer blades, than 3 shorter ones.

If you enjoy looking at pictures of WW2 fighters, you'll notice that the early planes had 2 bladed props, the midwar ones had 3 bladed props, and right at the end they jump to 4 and 5 blades - the reason being that the better engines got, the more torque they had to dissipate, and you can only make a propeller so big before you hit ground clearance problems. Helicopters, on the other hand, can make their rotors as large as they like - and so they do, and typically only have 2 blades. Only on helicopters like the Chinook, where they made the blades as long as they could feasibly engineer and still had torque to spare, do you see 3.

> Do ducted fans have similar changes in load-to-thrust ratio given an increase in blade count?

Not really. The parameter that describes how many blades are in a ducted fan is known as "solidity", and while it does have minor implications for blade shape the general efficiency is excellent no matter what. It's actually surprisingly insensitive - you can take a ducted fan designed with a 5 bladed rotor and just slap a 7 bladed rotor in there instead, without even redesigning the blades, and provided the power source is equally efficient at a somewhat lower RPM you basically won't be able to measure any difference in performance at all. Ducted fans can turn shaft power into air momentum with about 90% efficiency.

The reason that large swept areas are more efficient than small ones is simple physics and geometry. Energy (the thing you put in) is 1/2 mv^2, while momentum (the thing you get out) is simply mv. So for best efficiency you want to keep v as low as possible. It's better to get your momentum by moving a lot of air slowly, than a little air quickly.