IntroductionIn 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"
MethodsRecently, 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|
|Particle image velocimetry: Setup consisting of high-power laser, high-speed camera and particles in the fluid.|
|PIV measurement with a laser sheet|
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.|
ResultsThe 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 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:
ConclusionsWhat 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:
- 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.
- 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...|
|Shrediquette 0815, a standard racing quadrotor that I designed for training and to learn more about|
lightweight and rigid plastic construction.