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Related thread from a few months ago discussed the Sharrow propeller mentioned in this article, which applies the same concept to boats: https://news.ycombinator.com/item?id=33949895

The difference in geometry for air vs. water propellers has a lot of complicated reasons but above all the fluid density of water is about 1000x air: ~1000kg/m3 for water vs ~1kg/m3 for air. Air propellers are optimized for very high-speed operation which is needed to produce any significant thrust in low-density fluid. Boat propellers are very "built up" and physically sturdy since they are used in low-speed operation with high torque.

I have seen people use RC airplane propellers in water for small autonomous boats -- They do work but look very comical (think 10x the size of a boat propeller, running at 1/10 intended speed)

Cavitation effects -- microscopic bursts of vacuum at low-pressure boundaries along the propeller -- come into play much sooner than with air propellers.

> Cavitation effects -- microscopic bursts of vacuum at low-pressure boundaries along the propeller -- come into play much sooner than with air propellers.

In liquids vapor-bubbles of the liquid (not vacuum) are caused by low pressure (or high temperature, boiling), and cavitation is the collapse of the vapor back to liquid state when pressure rises (or temperature drops).

Propellers in air do have issues with the speed of sound, but that's a different matter than cavitation in liquids.

Thanks for the corrections: So the bubbles are not a vacuum but low-pressure vapor and cavitation is the name for the collapse, not the bubble itself. And this can only happen in liquids where there is a potential phase transition. I've got a little marine knowledge but my physics is lacking so I appreciate the clarification!

I assumed cavitation had similar parallels in air propellers with high tip speeds (as you approach the speed of sound) but seems that is a different effect?

I would say it's still a vacuum in the more common meaning of the word: A reduction in pressure, not necessarily a complete vacuum.

They should produce more thrust per a given unit of energy than a conventional propeller by eliminating induced drag. Winglets on jet airliners work by the same principle, converting the wingtip vorticity, due to the pressure difference above and below the wing, into an apparent forward thrust.

I too was also expecting a same-thrust controlled study.

From the fundamental frequencies in the two graphs, we can see the toroidal propeller (72 Hz) is spinning slower than the traditional (88 Hz). Assuming, of course the same fundamental vs. rpm relationship -- the toroidal has twice the number of "blades" as standard, but I'm not sure how that manifests sonically. I wonder how a 3-blade or 4-blade propeller would compare to the standard 2-blade.

Also, a big difference between quadcopter and other propellers (boat, plane, heli) is that they use change speed to carefully control thrust - most quadcopters use fixed pitches. Adding mass to the propeller can reduce responsiveness, which means less stability ... but I don't know enough about the magnitude of this effect to know if that's a problem.

Propeller efficiency (both and air and water) are factors of torque, RPM, and advance speed (effectively the speed of the vehicle). You can't be efficient for all conditions. For example, a tug boat needs really high thrust at low and even zero advance speeds as it pushes up against a giant ship like a tanker. That design would be very different from what you'd need for a high speed boat with high advance speed. Similarly, props for drones can be designed for efficiency at hover (zero advance speed), or for going fast. Designing for noise will also have trade-offs for different conditions. Like it might be really quiet AND efficient in hover, but then be crap at when moving forward at high speed. Efficiency is always about trade-offs.

And one of those tradeoffs can be complexity. For example, you could integrate a variable pitch propeller with a control computer and your throttle to ensure you are always at the highest efficiency possible within the geometry constraints of the propeller.

> At a minimum, they should spin slower and/or strain the motor more for the same RPM. Maybe I'm completely off base.

Only when adjusting RPM. At constant RPM, a heavier properly will actually reduce impulses to the motor.

Someone simply needs to invent a motor that provides constant torque through a full revolution.

To control the amount of thrust changeable rpm is needed, or a changeable geometry, like pitch. I imagine the latter wouldn't be easy with the toroidal propellers.

You could mount each toroidal blade on an angled pivot and use rpm control to change the pitch. This enables thrust vectoring.

This might be what you're referring to, but Tom Stanton built a swashplateless 4 axis R/C helicopter (albeit not with toroidal blades) based on this principle: https://youtu.be/d80oXSCcHTk

In some applications warfare and anything in residential areas (e.g. thermal or roof damage inspection), I'd expect that pilots will gladly go for the lower noise even if it means a bit less flight time.

I'd expect commercial drone pilots to not give shit unless law tells them to give shit.

Less noise makes for less complaints by neighbors during longer flights in my experience.

Right, why would a contractor care? You flying your own drone in backyard, sure.

The main difference is compressibility, to the point that liquids are commonly used as air analogs in wind tunnels.

Ship propellers end up working in different density material, with also different speed requirements and that's why they are differently shaped even if the equations are the same.

air is compressible, water is not. This effects not only the mechanics, but also the acoustics. Air is actually a much worse conductor of sound so making a quieter propeller should be easier.

The principle of using a toroidal shape to reduce creation of vortices and thus sound should hold for either medium and may even be more efficient since a vortex causes drag and they are known to improve efficiency in boats.