Motor Arms: Round or Flat???

“I know, let’s put a flat front on this speed boat!” said no one ever.

Update December 8, 2017: I rewrote this section slightly (I’ve been meaning to for a while). What is most important to note here (when talking about the arms only) is reducing drag relative to the prop wash, not relative to the direction of movement.

  • Thanks to “Ed” who reminded me to change this point.

I am a fairly reserved person, but as an engineer, it is frustrating to see what are considered to be the top quadcopter “racing” frames. Unfortunately for us, there isn’t much of a choice when it comes to a smart design. The main performance destroying design flaw on these frames are the arms.

Strange Animals:

Quadcopters are strange animals – they behave absolutely nothing like a conventional aircraft. Airfoil shapes work excellent in the case of airplanes since the axis of the airfoil  shaped structures (fuselage, wing, etc.) are, in general, parallel with the direction of movement/air flow. If this parallelism deviates much (angle of attack increases too much), then the airfoil goes into a stall which is where turbulent air dominates and causes immense drag. This is why flat shaped arms (oriented horizontally) will never work well for quads since the thrust from the propellers is hitting the broad side of the arms. However, if we consider the “fuselage” of the quad only, airfoil streamlining works great in the case in which you plan on staying at a relatively fixed pitch such as speed runs.

Reasons for Using Round Arms:

  1. Large flat surface under arms = air brakes.
  2. Large flat surface under the props = thrust blockers.
  3. They have nearly half the drag coefficient of a flat plate.
  4. They are the best way to reduce arm drag regardless of pitch angle. However:
    • This is only true for any part of the arm not in the prop wash or for quads with inverted motors.
    • If the arm is in the prop wash (95% of quads on the market), reducing the surface area perpendicular to the thrust and streamlining the surface area is best.
  5. They are a great way to rout wires to the motors which further reduces drag.
  6. The projected area (see concepts) is 1/2 that of an air brake (flat arm) which effectively makes the overall drag force 1/4 that of a flat arm.

For flat arms not in the prop wash, it is understood that the large face of a flat arm will not always be perpendicular to the direction of movement, flat arms are still extremely inefficient. Actually, as your quadcopter gains speed (and pitch angle increases), the face of the arm gets closer to being perpendicular to the air flow which in turn increases the inefficiency of the flat armIn the prop wash, the thrust created by the props is always (theoretically) perpendicular to the surface of the arms.

Are Round Arms as Strong as a Flat Arm?

To understand how much deflection an arm will have (a measurement of how stiff the object is), the formula for calculating beam (the arm) deflection can be used. Without getting into detail, the only term that we need to use as a comparison between a tube and rectangular arm is the I term which is called the second moment of inertia.

For a rectangle, the direction of deflection makes a difference in calculating I. There are still many assumptions to be made here, but in general, we are only concerned with deflection along the direction of thrust.

For this calculation, I used a tube that has a 10mm outer diameter and a 8mm inner diameter. Then using algebra, I calculated the thickness a flat arm would have to be to equal the strength of the tube. For the width of the flat arm, I used the average of a typical flat quadcopter arm which is 22mm. Using these numbers, a flat arm would have to be 5.41mm thick to equal the strength of the 10mm tube arm. 5.41mm is very hefty for an arm. However, when comparing arms of the same length, this flat arm has the following drawbacks:

  • The flat arm is 4.2 times heavier than the tube
  • The flat arm has 2.2 times the projected surface area of the tube (in the direction of thrust)
  • The flat arm is obstructing 2.2 times the amount of thrust that the round arm blocks.
  • The flat arm has a 66% greater drag coefficient.
  • Matters only get worse once the motor wires are run down the flat arm (motor wires for a tube arm are run down the inside).

The same calculation can be carried out for a solid cylindrical arm:

  • The solid cylindrical arm is 2.6 times heavier than the tube
  • The solid cylindrical arm has .88 times the area of the projected surface area of the tube (in the direction of thrust)
  • Although it is .88 times the surface area, this will be thrown out the window (along with the drag coefficient) once the motor wires are run down the arm.

What if I’m Not Going for Speed and my Pitch Angle Stays Low?

At a pitch angle of 0°, the 5.4mm thick arm is a little more than half the projected area of the round 10mm arm. However, as that pitch angle increases, the projected area increases. At around 13.5° of pitch, the projected area equals the 10mm tube and it only gets worse as pitch increases. However, it also gets worse due to the motor wires running across the arm. With the motor wires added, we can only reach a pitch of 7-8° before the projected area equals the 10mm tube.

For a more in-depth understanding of drag, please see sections 4 and 5 of the Speed Optimization series.

drag-coefficient-chart

9 thoughts on “Motor Arms: Round or Flat???

  1. Really informative and the right balance of detail without kicking the arse out of it, and losing my interest. Well done, I look forward to more of your work.

  2. I Don’t think it’s really relevant what angle your quad is flying at as the air flow over the arms is always essentially straight over them due to the props creating much faster air flow than the air speed from forward movement.
    Correct me if I’m wrong?

    1. You are absolutely correct – I have been meaning to update this for a while now. Thanks for reminding me! Very busy here, but it is definitely an important point so I changed it right away.
      Maybe I will run across the study again, but a study was done to reduce as much drag on a wing sitting behind a propeller by changing the shape of the wing. Since the thrust behind the prop moves (mostly) perpendicular to the prop, the wing shape they came up with changed only slightly. but it was still oddly shaped.

  3. Such great stuff here, Im currently attempting to design a race quad from tube, its challenging fitting everything in whilst keeping it lightweight, strong and relatively easy to work on.
    what do you think about + style quads in terms of aerodynamics? would be interesting to look at the black box of one to see how hard each motor has to work.

    thanks for updating, such good information, many people just stab in the dark at these things lol

  4. How do you think a 14mm flat arm (5mm thick) would compare to a 12mm round tube in tersm of drag?

    1. It depends – if it is laid out like a normal quad, it would be worse to have a flat arm. Vertically mounted, it would depend on the pitch angle which would have to be nearly 90°. But since the arm is mainly seeing thrust from the props, the air flow would be theoretically parallel with the arms. It is still up for debate though. Most of this stuff would be better measured in a wind tunnel – best thing is to try it out. That’s my issue: I’m mostly theory, not enough practice. However, most things I have tried have worked well 🙂

  5. It sure does seem to be working for you and I did mean flat horizontal (standard layout arm) thanks.

    There really isn’t enough research done for these things, so many forces and most of them are misunderstood like thrust.
    Thank you for the quick reply, have you ever tried a plus style quad or have any theories about the potential issues with them?

    1. I never tried a plus style. Originally I thought they wouldn’t be as responsive, but they do have a reduced moment of inertia (if talking purely pitch and roll, 2 motors will be on the rotating axis) so that might make up for it. About the only issue I’ve seen are designs where the front motor arm is extended – this leads to an imbalance in motor work load and top speed and response suffers.
      I’ve been working on a part 2 to the “choosing the right motor” blog since I wanted to go over efficiency and effects of motor weight – but the motor weight snowballed and I’m not sure how to slice it up yet. I’m still working out some of the physics, etc (this will also help figure out effects of the + style layout).
      This reply was quicker, caught me at a good time!

  6. Thank you, really can’t get this information anywhere else and also your analogies to help simplify things are great 🙂

    Look forward to reading it!

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