<p>The starting point is working out the speed of air through your rotor disk(s). This air starts stationary at some point above the disk, and is pushed down by the disk. The force required to accelerate the air is what lifts a helicopter, and you can modify the usual Force = Mass * Acceleration equation to Force = Mass per second * change in speed to work out the vertical speed of air past the blades.</p>
<p>Note that this approach is independent of blade design, which is why we start with it. It tells you the conditions that you need to design for, based purely on the disk diameter and the required lift.</p>
<p>It also gives you an idea of the top speed, because you can't go faster than the air you're pushing against. (just an idea though, because you're not flying straight up!)</p>
<p>There a more complete guide with equations <a href="https://cdn.intechopen.com/pdfs/57483.pdf" rel="nofollow noreferrer">here</a></p>
<p>You can also use that change in speed to work out the power required to fly, from the kinetic energy that needs to be supplied every second to the air as it is accelerated to the required speed. It's worth working out the numbers for a few different disk diameters, to compare hovering power (and thus duration) vs top speed.</p>
<p>Most aerofoils stall at around 15 degrees, which sets the limit for the maximum angle of the blades. If you assume they're going to be at that angle, and you have just worked out the vertical air speed, you can multiply by 1/Tan(15) or 3.7 to get the minimum forward speed of the blade.</p>
<p>You can plug that speed into the <a href="https://www.grc.nasa.gov/WWW/K-12/airplane/lifteq.html" rel="nofollow noreferrer">lift equation for fixed wings</a> to work out the blade area and lift coefficient you need to generated the required lift.</p>
<p>You'll probably find that you don't need anything like 13 blades and a coaxial rotor.</p>
<p>This is really just scratching the surface though. You could do a whole aerospace engineering degree and still not cover everything you have asked for. FWIW, the text book I used was <a href="https://www.amazon.co.uk/Foundations-Helicopter-Flight-Simon-Newman/dp/0340587024" rel="nofollow noreferrer">The Foundations of Helicopter Flight by Simon Newman</a>.</p>

CC BY-SA 4.0
2021-12-08T20:35:42.110Z
You'll probably find that you don't need anything like 13 blades and a coaxial rotor. Can I turn that on its head, and say its what I want to use and configure the motor KV to suit? I need two contra-rotating, because that the basis of yaw control. I want two different, prime numbered blade counts to reduce/eliminate harmonic 'beats'. (My primary goal is "quiet".)
Buk
CC BY-SA 4.0
2021-12-10T09:08:13.807Z
Sure, the above process doesn't tell you anything about the number of blades, only their total area. You can run the numbers and split that area any way you want, although it may result in very thin blades. You should note that noise is mainly related to power and air speed, and the best way to reduce them is to increase the disk diameter. HBR turbofans are only quiet when compared to the supersonic exhaust of a turbojet. Lots of people have build drones that use EDF units, and they're always loud.
Robin Bennett
CC BY-SA 4.0
2021-12-12T00:50:26.777Z
"noise is mainly related to power and air speed"; Could you elaborate on that a little please? Starting with a given mass -- say 500g -- and the need to hover that. Steady state. The power requirement is essentially fixed; but there are several (a continuum) of ways to achieve that delivery. (Many) small diameter at high speed. One large at (much) lower speed. Lower speed tends to produce less noise. Wrap it in a shroud, and less noise still is radiated. Size limited+plus yaw control requirement suggests 2, contra rotating props. More blades; lower speed (but more torque).
Buk
CC BY-SA 4.0
2021-12-13T08:52:42.163Z
The power requirement is absolutely not fixed. If you double the rotor disk area, you halve the downwash speed required for the same lift. The mass flow is the same but the speed term in the energy equation is squared, so the power is halved. That power makes air move, and as that moving air mixes with stationary air its energy gets turned into noise and heat. Ducts and multiple blades can change the character of the noise, but reducing power addresses the root of the problem.
Robin Bennett
CC BY-SA 4.0
2021-12-14T09:06:34.587Z
The size limitation is fixed, unchangable. I cannot double it. I also want the duct. For the safety of totally enclosed rotor(s) amongst other reasons. (Thanks for your attempt to help, but I'd really like soome help to do what I described in teh OP; not do it your way.! I'll stop wasting our time now.
Buk
CC BY-SA 4.0
2021-12-08T12:52:11.487Z
2021-12-08T12:52:11.487Z
Robin Bennett
<p>I want to design and make my own Dronut-like drone. The size will be limited by my LCD printer.</p>
<p>My goals are:</p>
<ol>
<li>quiet. 2) safe. 3) duration.</li>
</ol>
<p>I'd like to use a pair of HBR turbofan style fans to extract power from low-speed high torque motors; with (say) 17 and 13 blades to minimise harmonic resonance.</p>
<p>My question is, how to go about choosing the aerofoil profile, AoA twist, etc. of the blades?</p>
<p>This doesn't fit with either normal airplane propellers, helicopter rotors nor quad/hex/etc. ; so where to start? Is there any software, spreadsheets, websites that can help me with this?</p>
<p>I found <a href="http://www.starlino.com/power2thrust.html" rel="nofollow noreferrer">this site</a> which make a useful start on the math. At least up to the point he switches into units of Inch/grams, at which point I loose my will to live.</p>
<p>Do you know somewhere that does similar calculations with explanations but stick to sensible units?</p>

<propellers><building><design><resources>
Contra-rotating coaxial shrouded fans: design guidelines
Buk
# Contra-rotating coaxial shrouded fans: design guidelines

(Asked by: username_0 on 2021-12-07)

I want to design and make my own Dronut-like drone. The size will be limited by my LCD printer.

My goals are:

1. quiet. 2) safe. 3) duration.

I'd like to use a pair of HBR turbofan style fans to extract power from low-speed high torque motors; with (say) 17 and 13 blades to minimise harmonic resonance.

My question is, how to go about choosing the aerofoil profile, AoA twist, etc. of the blades?

This doesn't fit with either normal airplane propellers, helicopter rotors nor quad/hex/etc. ; so where to start? Is there any software, spreadsheets, websites that can help me with this?

I found [this site](http://www.starlino.com/power2thrust.html) which make a useful start on the math. At least up to the point he switches into units of Inch/grams, at which point I loose my will to live.

Do you know somewhere that does similar calculations with explanations but stick to sensible units?

**Tags:** propellers, building, design, resources


---

## 1 answers

### Answer by username_1 on 2021-12-08. Score: 4

The starting point is working out the speed of air through your rotor disk(s). This air starts stationary at some point above the disk, and is pushed down by the disk. The force required to accelerate the air is what lifts a helicopter, and you can modify the usual Force = Mass \* Acceleration equation to Force = Mass per second \* change in speed to work out the vertical speed of air past the blades.

Note that this approach is independent of blade design, which is why we start with it. It tells you the conditions that you need to design for, based purely on the disk diameter and the required lift.

It also gives you an idea of the top speed, because you can't go faster than the air you're pushing against. (just an idea though, because you're not flying straight up!)

There a more complete guide with equations [here](https://cdn.intechopen.com/pdfs/57483.pdf)

You can also use that change in speed to work out the power required to fly, from the kinetic energy that needs to be supplied every second to the air as it is accelerated to the required speed. It's worth working out the numbers for a few different disk diameters, to compare hovering power (and thus duration) vs top speed.

Most aerofoils stall at around 15 degrees, which sets the limit for the maximum angle of the blades. If you assume they're going to be at that angle, and you have just worked out the vertical air speed, you can multiply by 1/Tan(15) or 3.7 to get the minimum forward speed of the blade.

You can plug that speed into the [lift equation for fixed wings](https://www.grc.nasa.gov/WWW/K-12/airplane/lifteq.html) to work out the blade area and lift coefficient you need to generated the required lift.

You'll probably find that you don't need anything like 13 blades and a coaxial rotor.

This is really just scratching the surface though. You could do a whole aerospace engineering degree and still not cover everything you have asked for. FWIW, the text book I used was [The Foundations of Helicopter Flight by Simon Newman](https://www.amazon.co.uk/Foundations-Helicopter-Flight-Simon-Newman/dp/0340587024).

> **Comments:**
> **username_0**: You'll probably find that you don't need anything like 13 blades and a coaxial rotor. Can I turn that on its head, and say its what I want to use and configure the motor KV to suit? I need two contra-rotating, because that the basis of yaw control. I want two different, prime numbered blade counts to reduce/eliminate harmonic 'beats'. (My primary goal is "quiet".)  
> **username_1**: Sure, the above process doesn't tell you anything about the number of blades, only their total area. You can run the numbers and split that area any way you want, although it may result in very thin blades. You should note that noise is mainly related to power and air speed, and the best way to reduce them is to increase the disk diameter. HBR turbofans are only quiet when compared to the supersonic exhaust of a turbojet. Lots of people have build drones that use EDF units, and they're always loud.  
> **username_0**: "noise is mainly related to power and air speed"; Could you elaborate on that a little please? Starting with a given mass -- say 500g -- and the need to hover that. Steady state. The power requirement is essentially fixed; but there are several (a continuum) of ways to achieve that delivery. (Many) small diameter at high speed. One large at (much) lower speed. Lower speed tends to produce less noise. Wrap it in a shroud, and less noise still is radiated. Size limited+plus yaw control requirement suggests 2, contra rotating props. More blades; lower speed (but more torque).  
> **username_1**: The power requirement is absolutely not fixed. If you double the rotor disk area, you halve the downwash speed required for the same lift. The mass flow is the same but the speed term in the energy equation is squared, so the power is halved. That power makes air move, and as that moving air mixes with stationary air its energy gets turned into noise and heat. Ducts and multiple blades can change the character of the noise, but reducing power addresses the root of the problem.  
> **username_0**: The size limitation is fixed, unchangable. I cannot double it. I also want the duct. For the safety of totally enclosed rotor(s) amongst other reasons. (Thanks for your attempt to help, but I'd really like soome help to do what I described in teh OP; not do it your way.! I'll stop wasting our time now.  

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