What impact does a shroud have on the torque produced by the prop(s) of a multirotor that incorporates a properly designed shouded propeller?

Question

Based on the research presented here: "Hover and wind-tunnel testing of shrouded rotors for improved micro air vehicle design" and other reading that translates similarly well-designed shroud and rotor combinations into more general layman's terms, I have found that some authors indicate that there is a performance increase of 40% to 60% in static thrust for such a configuration. One source has indicated a theoretical increase in static thrust as much as 80%.

If we focus our attention on a multirotor design that is intended as a craft whose principal purpose is for inspections of stationary objects such as buildings and stationary infrastructure, and it is not expected to fly fast nor fly far, then the primary benefit from the shrouded rotor is the improvement of static thrust. Flight in translation will be rare and incidental to maneuvering around the object being inspected.

And assuming that the shroud can be manufactured with a mass that is less that the incremental improvement in thrust, this design will serve its intended purpose with the significant benefit of having some built-in protection from horizontal impact with obstacles.

The need for maneuverability will be equal to most other multirotor applications intended for inspections and as such yaw will still need to be produced by controlling the speed of the propellers by the flight controller.

What impact will the shroud have on the production of yaw by the torque produced by the propellers (rotors)?

Answer 1

Ducts and shrouds reduce tip losses; the reason we don't see them more often is that a well designed propeller should not have large tip losses.

Tip losses are greatest when there's a large pressure differential between the upper and lower side of the blade. In other words, the blade is highly loaded.

This question explains why large, lightly loaded blades are more efficient than smaller, faster spinning blades:

Why are larger propellers generally more efficient than smaller ones?

Notice that none of the answers mention tip losses - they're not the reason the small, fast prop is inefficient, they're just an extra problem. Fixing that extra problem with a shroud still leave you with fundamentally inefficient system.

assuming that the shroud can be manufactured with a mass that is less that the incremental improvement in thrust,

For a well designed prop, a shroud adds more weight that it saves - and it's usually better to use that weight to increase the diameter of the prop instead of adding a shroud.

significant benefit of having some built-in protection from horizontal impact with obstacles.

To work well, a shroud needs to have very little clearance from the blades. That means that if you hit anything, the shroud will hit the blades. You might cause less damage to the thing you hit, but you're still going to crash.

Answer 2

There are two possibilities, depending on how ducts increase efficiency, but the end result should be the same. It could reduce torque required to spin the motor at a given RPM and thrust, or it could increase the thrust per RPM of the propeller with a constant torque. In either case the torque required to spin the propeller for hover thrust goes down.

For the given hover thrust the yaw torque caused by propeller drag as described above would then go down. The yaw torque produced by the inertia of the propeller and motor changing speed would remain constant (assuming the moment of inertia of that system is the same).

I'm not sure what the ratio of yaw torque generated by propeller drag is to the yaw torque generated by accelerating the propeller, but the inertia based one would eventually saturate like a reaction wheel on a space craft does.

This means that your maximum yaw steady state angular acceleration would go down if weight of the aircraft was exactly equal. I'm not sure how often multirotors get to this point. For smaller movements my intuition says that it would come down to flight controller tuning to get similar yaw performance.