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I have seen that a new electric airplane design has decided to a choose ducted propeller design somewhat similar to the one of jet engines, explaining this design choice with the fact the ducted design would avoid loss of thrust from edges of propellers channeling thrust more efficiently.

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I don't know how this could be calculated, but it's obvious this structure will add weight, and I'm wondering how it can be determined whether the gain in thrust efficiency compensates for the added weight and whether it makes sense to use a similar design on small drones.

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If the ducted propeller really increases efficiency, we would see more of these

Fanliner

Rhein Flugzeugbau Fanliner (picture source)

and fewer of these:

Socata TB-9

Socata TB-9 (picture source)

The ducting has benefits when

  • the disk loading is very high. This means the propeller diameter is small for a reason. Since efficiency tanks with decreasing propeller size, another consideration forces the propeller to be small. This would be the tip Mach number.
  • the propeller noise would be unbearable without the fairing. Again, this is the realm of highly loaded propellers with high tip Mach numbers.
  • the flow passing through the propeller needs to be conditioned such that regardless of flight speed the flow speed at the disk is almost constant.

In short, this benefits turbofans which fly at transsonic speed.

For slower vehicles with less power hungry propulsion systems, the disadvantages will prevail:

  • Friction losses on both surfaces of the fairing easily eat up any gain from reduced tip losses.
  • The weight of the fairing creates induced drag.
  • Also, the fairing costs more to build and maintain than leaving it off and using a larger, more efficient propeller.

Could ducted propellers improve efficiency in small drones?

Clearly no!

I'm wondering how it can be determined whether the gain in thrust efficiency compensates for the added weight and whether it makes sense to use a similar design on small drones.

The authors of XFOIL, Mark Drela and Hal "Guppy" Youngren, have published and open-sourced a design code for ducted propellers. This article describes the process. For a good overview of other computational methods I recommend chapter 3 of this report. In short, you need a panel code to capture the complex interaction between duct and propeller blades.

In a very simplified form, a ducted propeller is equivalent to a slightly larger unducted propeller due to the reduction of tip losses. However, with increasing speed the added surface of the duct will add a drag component that is absent from the unducted propeller. In off-design conditions, the duct helps to normalize the flow through the propeller but becomes a liability with flow separation in the duct at higher angles of attack to the oncoming flow. There is no simple factor between ducted and unducted propellers and which is better depends on the operating conditions and the design preferences of each individual case.

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    $\begingroup$ Another benefit of the ducting is if you want to create a media buzz and lure gullible investors to support your hare-brained (or criminal?) scheme for a personal transport. $\endgroup$ Jul 4 at 22:04
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    $\begingroup$ Ducted propellers were the same in the past as electric commuter planes are now. Investor baits. $\endgroup$
    – Jpe61
    Jul 4 at 22:28
  • $\begingroup$ @PeterKämpf you mean this: (unfortunately german) aerokurier.de/elektroflug/lilium-jet-dossier ? $\endgroup$
    – U_flow
    Jul 5 at 7:26
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    $\begingroup$ Thanks for the clarification, but still remain obscure how the ducting gain should be calculated, so that numbers can be drawn to demonstrate when a configuration is not achieving any significant benefits from ducting or it's disadvantageous. The fact the Lilium data that doesn't add app is interesting, but still, it doesn't seem to mention anything on ducting vs non ducting matter. I mean the fact that they have inflated the data neither deny nor confirms if their choice of using ducted propulsion is advantageous or not compared to having open propellers. $\endgroup$
    – AndreaF
    Jul 5 at 11:18
  • $\begingroup$ @U_flow Yes, of course. You do so, too. It is obviously hare-brained. Same with the Cargolifter three decades back. That one started with honest intentions and was then hijacked by criminal New Economy MBAs. Interestingly, you linked to one of the non-fawning articles about Lilium. Well done! $\endgroup$ Jul 5 at 15:12
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It is actually suprisingly easy to give a lower boundary and therefore an estimate of the power consumption in hover for any thruster. It is given by momentum theory which correlates the size of an idealized rotor disk with its power consumption:

$$P = \sqrt{\frac{T^3}{2 \rho A}}$$

where:

  • T is the thrust
  • $\rho$ is the density of air (or other medium)
  • A is the area of the rotor disc (or diameter of thrust tube)
  • P is power

You can directly see that the bigger the rotor disc $A$, the lower the power consumption during hover. Now, this is idealized in the sense that an ideal propeller accelerating air, would need this much power. Real propeller need more power, because of real world effects such as losses at the tip of the propeller or not-ideal drivetrain, mach effects and so forth and so on. These effects can be captured by correction terms such as $\eta_{tip}$ or $\eta_{drivetrain}$ ($\leq1$). Therefore the equation becomes. $$P = \sqrt{\frac{T^3}{2 \rho A}} \cdot \frac{1}{\eta_{tip} \cdot \eta_{drivetrain}}$$

Therefore back to your question: All you do by adding a ducted fan, is to increase the efficiency of your propeller. Thus, for example $\eta_{tip}$ will rise perhaps from 0.8 to 0.95 or so (values are given only as an example). But the ducts you depicted serve two purposes:

  1. They maximize tip efficiency, therefore decreasing power consumption
  2. They increase the diameter $A$ by "spreading out" the flow of air (for example with the big lip you see at the front of the duct), therefore further decreasing power consumption

Still, small propellers mean insane amounts of power. So much so, that there even was a discussion if for example this concept would even work or if it was fraudulant (unfortunately in german). I strongly encourage you to plug in some values for your favourite upcoming E-VTOL.

However, note the following: Helicopter have big rotors exactly to minimize power consumption during hover. EVTOL concepts plan to spend only very little time in hover, so for some cases it makes sense to take the efficiency hit of higher power consumption during hover in order to avoid having a big rotor during the high-speed portion of flight, because this also comes with a performance penalty.

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    $\begingroup$ Thanks for the explaination but remain the problem of the calc of η parameters you have mentioned, Knowing the way to calculate them it would be possible to determine the efficency gain of ducted solution and so know when the gain compensate the added weight and whether the added design complication is worth it $\endgroup$
    – AndreaF
    Jul 4 at 20:50
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    $\begingroup$ Also, the power/mass ratio of a combustion engine is a big part of the aircrafts mass budget, right? But electric motors are lighter (and outweighed by the batteries) so you could see a motor with lots of reserve power that's just used to take off? $\endgroup$
    – Rich
    Jul 5 at 1:36
  • $\begingroup$ @AndreaF: Unfortunately there is no "easy" way to calculate $\eta$, this is normally done empirically. To make things worse, it also depens how you construct your duct. If you do it wrong, the efficiency might even go down (see this post aviation.stackexchange.com/questions/88170/…) $\endgroup$
    – U_flow
    Jul 5 at 7:23

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