2016 update: David has produced a great customizable OpenSCAD file based on the study referenced in this post. The file can be found over at thingiverse here (thing:1535549).
In a previous post I discussed how the addition of a well designed duct can reduce hovering power consumption of a rotor by over 60% or alternatively nearly double the thrust if power consumption is kept at the same level as the unducted rotor. These claims are based on a scientific study conducted on this very topic which can be found here (Mirror here) (Jason L. Pereira 2008).
If you want to have a go at testing these claims for yourself then this post will hopefully give you an idea of what kind of shape that duct needs to be and also suggest some possible ways to construct it.
The perfect duct for hovering
Below is an cross-sectional view of a duct taken from the reference above. It outlines the critical parameters that affect performance: Diffuser included angle (θd), diffuser length (Ld), inlet lip radius ( r lip), blade tip clearance (δ tip).
According to the study the optimal optimal configuration found experimentally includes a δtip = 0.1%Dt, rlip = 13%Dt, θd = 10◦ and Ld = 50% to 72%Dt. I have used sketchup to mockup what such a duct would look like for a 5″ rotor as seen below. Note that I went with Ld = 50% to try and keep the overall length to a minimum and also made it a single surface by using the inner wall only.
The same duct can also be extended slightly for a contra-rotating setup and shown below.
The dimensions for a single rotor duct are shown below (larger views available) for a 5″ rotor. Scale accordingly for a rotor of your choosing, but be sure to measure your rotor first as it may not be quite what you expect.
You can find a copy of the sketchup model here.
The most difficult part about making a duct for a multirotor will be keeping it light enough that you do not offset the respective gains. Thankfully, the literature suggests that when done correctly the additional thrust gained is so large (~90%) that you would need to nearly double the weight of your multirotor to cancel out the gains.
Remember though, if you only want to bench test the thrust or efficiency improvements (as I hope to do eventually) then the duct can weigh whatever you want, it doesn’t matter. The following is a list of suggestions for how you could achieve a lightweight duct.
- Carbon fiber – The ideal solution: In an ideal world you would construct your duct out of a single piece of 0.5mm thick pre-impregnated vacuum bagged and autoclaved carbon fiber. If have access to this equipment then look no further.
- Fiberglass reinforced foam – The realistic option: A more DIY solution would be to purchase some styrofoam blocks and carve them into the desired shape. For added rigidity you could also layer fiberglass on the surface like you would for a RC boat hull or model plane wing.
- Cheapest possible or just for testing – If you just want to test out the idea then really anything will do the job, balsa wood, cardstock, old drink bottles, paper mache, gap filling foam etc.
The most difficult part of the build would be getting the blade tip clearances as close as possible, as this has a big impact on efficiency but also requires very tight tolerances. One way around this problem is to build the duct quite roughly and then line the inside of the duct where the rotor will be placed with a material that can be scraped away by the rotor as it turns. Something like expanding gap filling foam may be perfect for this. Once the rotor scrapes away the excess foam you should be left with blade clearances measured in fractions of a millimeter.
If you do end up trying something let me know as I would be really interested to see what you came up with and how you went.