Aerodynamics in racing multirotors! Part 2.


In part 1 of this article on multirotor aerodynamics, some ideas on how to reduce the aerodynamic drag of racing multirotors was presented. I was also designing a tilted-body racing quadrotor called "Shrediquette DERBE". There were not yet any flow measurements of multirotors flying at high speeds. Therefore, I had to make quite a number of assumptions on the aerodynamics of a racing copter. This time, I am presenting some flow measurements, along with some potential optimizations for the next version of the "Shrediquette DERBE"


Recently, I had the opportunity to do some flow visualizations in a large wind tunnel at the Bremen university of Applied Sciences / Dept. of biomimetics (which is the place where I worked one year ago). I brought the Shrediquette DERBE and mounted it inside the wind tunnel. Prior to the measurements, I did some tests to determine a realistic flight speed and the appropriate pitch angle.
The measurements were performed at a pitch angle of 45 degrees with the motors running at full throttle (control loops are all turned off completely). Wind speed was set to 30 m/s. The Shrediquette DERBE was equipped with Graupner C-Prop 5.5x3", 4S 75C, Ultra 2806 2300 kV.

DERBE mounted inside the wind tunnel
The flow was visualized with a method called Particle Image Velocimetry (PIV). This allows to measure space- and time-resolved flow velocities in fluids: Some very small tracer particles are added to the air (e.g. oil droplets). These particles are illuminated by a laser in a very thin sheet. A camera is mounted perpendicular to this sheet, recording the motion of all the tracer particles. The discplacement of the particles is used to calculate the velocity of the fluid. During my PhD research, I was developing a tool (called 'PIVlab') to perform these kind of measurements within Matlab (see this article for more information).

Particle image velocimetry: Setup consisting of high-power laser, high-speed camera and particles in the fluid.

PIV measurement with a laser sheet
Here is a short clip that shows the copter 'flying' in the wind tunnel: Youtube Video

I measured the flow at four different locations (labelled A/B/C/D):

Top view of a multirotor. The green lines show the locations where flow velocities were determined.
This image sequence shows the laser sheet in position B.


The flow over the main frame is mostly horizontal - hence a tilted-body concept really makes sense. This concept aims to align the main frame parallel with the flow to reduce the frontal area and hence the aerodynamic drag (which is proportional to frontal area). The following image shows the flow velocities around the main frame (position A). The arrows indicate the direction, and the colors indicate the relative velocity magnitude:
Warm colors: Flow > 30 m/s
Cool colors: Flow < 30 m/s
Dark red: shadows / no measurements possible

PIV measurement around the main frame (position A): The flow is mostly horizontal in this plane.
 The flow under the propellers is actually highly assymmetric. It does not make sense to assume a constant flow velocity below the propellers. In measurement position B, the blades of the front propeller move forward, and the blades of the rear propeller move backward through the measurement plane (see the animated image sequence above). Therefore, the front propeller blades experience much higher flow velocities than the rear propeller blades. Hence, only the front propeller blades generate thrust in this plane. Furthermore, the assumption that the flow is perpendicular to the propeller disk below the propellers is only true for the regions of the propeller disk where the blades move forward.
The velocities in measurement position B are shown in the following image. Note the high flow acceleration (warm colors) behind the front propeller. Also note that the rear propeller does not accelerate the flow at this measurement position - it is almost passive.
Measurement position B: Only the blades that move forward through the plane (= the front propeller) generate thrust. 

Together with the results of the other measurement positions (not shown here), we can safely assume that only parts of the propeller (disk) generate thrust in high speed forward flight. This is very similar to the aerodynamics of large helicopters, where also the advancing and retreating blades experience very different flow velocities and generate different amounts of lift and drag). The importance of this effect (sometimes also called P-factor), is linked to the advance ratio of the propeller. Earlier, I actually thought that this effect might be negligible on multirotors, but this is clearly not true. A multirotor in fast forward flight only creates noteworthy lift in the green areas shown in the following image. In the centre of the red areas, the propellers might even create additional drag:

Multirotor in fast forward flight: The green areas create most lift, parts of the red areas might even create drag.
Note that this is only true for the propeller rotational directions shown in this image. If all propellers
rotate in the other directions, then red and green areas need to be inversed.


What does this mean for our racing multirotors? Tilted bodies make sense, as the flow is really horizontal at the main body. Vertical arms (as in the Shrediquette DERBE, see image below) are however problematic for two reasons:
  1. The flow will only be parallel to the arms at the front propellers. Because only these propellers do really accelerate the flow in fast flight. Below the rear propellers (the flow is not accelerated here), the flow will actually hit the arms from the side - which causes a large drag penalty.
  2. Multirotors use their motors to rotate around the pitch / roll / yaw axes. The force (or better: the moment) to rotate around the roll and pitch axis is induced by generating differential thrust between opposing propellers. Very large forces can be generated around these axes. As an extreme example: If both front motors run at full throttle, and the rear motors are off, then the pitch moment (moment = radius * force) could be around M = 0.12 meters * 12 Newtons = 1.4 Nm. But the force around the yaw axis is much lower because it is induced only by the torque of the motors - not by the thrust. If we assume the propellers to have a lift-to-drag ratio of 10:1 and a diameter of 5 inch, then the moment around the yaw axis is about 20 times lower than the moment around roll or pitch axes. Due to their orientation, vertical arms can however generate large forces around the yaw axis which can not be compensated by the small torque of the motors. In order to have a better control around yaw, it makes more sense to not rotate the arms.

Do vertical arms make sense...? Not really...
In the last weeks, I designed a standard racing quadrotor (called 'Shrediquette 0815') that I use to test the properties of 3D printed frames. I learnt how to design a very rigid and lightweight plastic frame. I will use this knowledge to improve the design of the Shrediquette DERBE II.

Shrediquette 0815, a standard racing quadrotor that I designed for training and to learn more about
lightweight and rigid plastic construction.


  1. Looking at the Derbe in Forward Flight with a level body, it looks like the arms are effectively flat plates (ignoring motor wires) with a high Angle of Attack. Wouldn't traditional flat arms have a similar frontal area but providing down force rather than, albeit with a terrible lift to drag ratio, positive lift? Are you suggesting that the rear arms should maybe be parallel to the FF flow (or with a slight AoA) rather than vertical or horizontal?
    Did you ever manage to test the air brakes? I wonder if control surfaces could also prove useful for better yaw authority in FF. Have you noticed yaw issues with Derbe in actual flight?

    1. Dear Alex,
      I agree that they're flat plates with a l/d of maybe 1... I guess mounting the arms the way I did makes sense from the aerodynamic point of view, but it is very bad for yaw control (because this axis is soooo weak...). There should be as little area in the "yaw plane" (the plane parallel to the motor axes) as possible, otherwise the copter might experience yaw outs in some situations. The DERBE had this when doing fast turns (but never in straight forward flight).
      I did not test the airbrakes yet. In my next design, I'll try to make the arms as aerodynamically passive as possible.

    2. Yaw outs did not happen in fast flight, because in that case, the flow was pretty much parallel to the arms. But in turns, when throttle is reduced but the forward speed is still high, the flow hits the arms almost perpendicular. And that creates too much (asymmetric) force on the yaw axis and could sometimes not be compensated anymore.

  2. Thanks for your information and research! :-)

    I am just wondering why use 5.5x3 prop at 30m/s? Why not usual 5045 or 5045BN for example?

    1. I simply prefer the Graupner props... I also couldn't measure any differences in flight speed when comparing them to 5045 bullnose props. These props turns at lower RPM, so there might be no advantage of the larger propeller pitch.

  3. hi William, huge compliments for your professional works and measurements here! We need better highspeed copters! I love to dive fast in the alps (dont know if you know my RCSchim videos). I cant do as much diving as I want to - but this is the best part in FPV for me ;-) Last time I had a crash with my Black Bullet (esc burnt) but the bullet (fwd tilted arms) had some issues for me in the beginning. mainly the sudden 90 degree yaw issues on fast forward were terrible. I got it down to flyable behaviour but never 100% rid of it. I used cleanflight on the naze32 with luxfloat - that made the quad behave better, and I also had better results with bigger props (going from 5x4.5 to 6x4.5 gave more yaw stability were everything else failed).
    Ultimately however the props killed the ESCs ;-)

    So not sure atm. what's better, tilted arms, or conventional...
    Vortex 250pro, which is looking good, is back at conventional; some others hop on the train of fwd tilted quads...

    However, keep researching!
    Mario / RCSchim from Austria

    1. Hi Mario, thanks for your feedback! I am currently also flying with a conventional design, but I don't like it. I simply cannot 'accept' that a standard racing multirotor looks almost symmetrical, but flies everything else than symmetrically: It goes forward all the time.
      There simply must be a good solution for a racing copter with an aerodynamically good body... I'll keep on trying to make something like this despite my limited time.

  4. is your quad motor layout orientation different from Naze or CC3D?
    From that image it seems yes. That might explain why your say this in image #8: "this is only true for the propeller rotational directions shown in this image. If all propellers
    rotate in the other directions, then red and green areas need to be inversed."

    1. Yes, I think my props all spin in the other direction of what is "standard". But I don't think that this has an effect.

    2. it has no effect, it's that I started sketching frame design over your images. I will need to change the image around to start sketching again. Basically, I put the arms in the red area and not the green.

  5. An issue I have with the test setup is you fixed the Prop speeds as all equal. By using a BlackBox logger that data shows that when a quad is in forward flight the rear motors run at a higher speed. I think this does create lift, downward thrust vector, else the quad would not hold a forward pitch angle and must rotate back to level.
    Interesting data and flow measurements.
    I would like to see those done with an active Flight controller. Maybe mount the quad on a pivot to allow it to rotate in pitch. Then use the RC controls to command the FC to pitch into forward flight. My bet is that you will see an different flow.
    waltr on RCgroups forum

  6. I would love to see some drag data on something newer than the ZMR250 (Luminere QAV-X or kraken or Shuriken X1

    I'm also very curious what's the Derbe weight (without the LiPo)


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