Arm Design: Thrust Stand Tests
What's the best arm shape for a racing quad?
Most people think of skinny frames as 'light' frames, but as we tested Flaco it became clear that light weight wasn't its greatest asset. It was just a few grams lighter than a Full Tilt Boogie, but it was so much more agile and powerful. Clearly the thrust gains far outweighed the weight savings. I wanted to quantify this, so I built a thrust stand.
The stand is just a long Flaco arm with a TPU pivot in the middle, and a TPU paddle on the other end for pushing on a scale. The paddle and motor are equidistant to the pivot. I printed up multiple arm shapes to slide over the arm, and a Philips head screwdriver turned out to be the perfect 5mm smooth axle.
The fairings sat halfway down the arm, so half their weight was added to the final thrust numbers. Each configuration was tested three times on the same three batteries, 1300 Bonkas that were recharged for each test (one battery proved to be worse than the other two). Each run was 5 seconds at full throttle, recorded on video. I advanced the video frame by frame until a max reading was reached, then a reading was taken every 1/2 second (15 frames) for 5 seconds. The 30 readings from each configuration were averaged and adjusted for fairing weight for a final result. The raw data is here, each run looked like this.
I tested the bare Flaco arm and simple flat 15mm and 22mm arms. The 6mm Flaco arm yielded 1408 g, followed by 1384 g for the 15mm and 1337 g for the 22mm. I also did a quick mockup of the unblocked prop disk area for each configuration by counting pixels in Photoshop.
A 6mm arm blocks 2.4% of the prop disk, followed by 6.3% and 9.3% for 15mm and 22mm. There's no thrust data for an arm-less configuration, so I compared them to each other. When you compare 6mm to 15mm, the 15mm has 98% of the thrust, and 96% prop disk area. 6 v 22, the 22 has 95% of the thrust, 92.9% of the area. 15 v 22, exactly 96.6% of both. So it seems the two track pretty closely (duh). An arm that's considered 'pretty narrow' could still cost you 100 grams of thrust when you add up the four motors. Flaco vs Mixuko? About 280 g. This shows how it's silly to obsess over 2 or 3 grams on a frame when there's hundreds of grams of thrust to be gained.
The full Flaco fairing, including a trailing edge cone for the motor, yielded 1416 g vs 1408 g for the bare arm. Unfortunately, the fairing weighs 10 g. This isn't the best test of the concept of a fairing, however, since it has almost double the frontal area of the bare arm (it has to wrap around the arm, after all). The glass half-full interpretation of this would be: the Flaco fairing must be a really good shape, 'cause it increases thrust by 8 g even though its frontal area is much bigger. If only it could be made much lighter.
This is perhaps a better apples to apples comparison. A 15mm airfoil yielded 1393 g vs 1384 g for a flat 15mm arm. A 9 g, or .3% improvement seems too small, given what we know about the drag of flat planes vs airfoils. A better way to think about it might be this. If we assume the 1384 g corresponds to the unblocked prop disk area, or 93.7%, then the total possible thrust is 1477 g. That means the flat 15mm arm is sucking up 93 g of thrust. If that's the case then a 9 g improvement is a 9.7% improvement on the arm. That's better, but still nowhere near what you'd expect an airfoil to do compared to a flat board.
Maybe this is just a matter of my data being lousy, but I think there might be another reason. I suspect that propwash is so turbulent that normal aero calculations don't apply – just think about how inefficient props are when they have to fly through their own propwash. To put it another way, I'm guessing that while coefficient of drag (Cd) and frontal area are equally important in clean air, frontal area takes precedence over Cd in dirty air.
I spoke with a product designer at Horizon Hobby and he said the angled struts in the Inductrix are very important, I believe he said they straightened the flow from the props. The Inductrix's struts are perpendicular to the prop pitch. I decided to check this out with a straight fairing and a 45 degree fairing, cut to the same profile. By pure dumb luck the straight fairing broke loose and angled itself in the opposite direction of the Inductrix's struts, parallel to the prop. I found this rather surprising, since that means the Inductrix's struts are lying at 90 degrees to the airflow off the props, and would present a much larger frontal area and thus impede more flow. I printed up one more fairing, one which would rotate freely and find the path of least resistance. It was pretty cool to watch the fairing lock in at around 45 degrees the other way once throttle was applied.
Another freaky discovery: the fairing that was locked at 45 degrees perpendicular to the prop broke free a few times, and rotated 'til it became...HORIZONTAL. I have no idea.
The straight fairing won, with 1393 g, followed by 1386 g for the rotating fairing, then 1318 g for the perpendicular fairing. Does this mean you gain thrust by directing the prop wash straight down?
I flew a Tiny Whoop on my own frame with the struts angled both ways, thinking I'd made a great discovery, but it flew much better with the struts perpendicular. With the struts parallel it would just fall out of the air every once in a while, like it was caught in its own propwash. Clearly there's something more complicated going on here, and, also, Horizon obviously know what they're doing.
I strapped an entire whoop on the stand, balanced it 'til the pusher read 0 on the scale, and ran through a few variations. The thrust numbers seemed to be the same no matter what, so the effect from the angled struts must go beyond mere thrust.
I remember reading on the interwebs ages ago about a guy who put his motors on pedestals to get more separation between the props and the arms. The goal there was to eliminate vibration and jello on a video rig, but I've always wondered if there was an effect on thrust as well. I made a flat 22mm arm that was elevated 15mm, so that it was very close to the propeller. 1337 for the low arm, 1339 for the high arm, so basically no difference. Apparently blocked thrust is blocked thrust. Obviously you can't extrapolate this to a meter below the prop, but it sure seems that within the height of the motor bell there isn't a big difference in arm placement.
Leading or Trailing Edge?
A Mifune-esque profile on a 22mm arm yielded 1385 g angled parallel, and 1369 g perpendicular. Both an improvement over 1337 g for a flat 22mm arm. The 160 g increase in thrust (1385 x 2 + 1369 x 2 - 1337 x 4) and its overall slippery shape certainly explains why I love flying Mifune so much.
After the first day of testing I remembered all the times people told me that the trailing edge is more important than the leading edge while I was working on Mifune. I argued that if that was the case, then why do cars have sharp noses and chopped off rears – there's no such thing as a Kamm nose. I printed up a 22mm trailing edge and tested it against the same flat 22mm arm and got 1323 for the trailing edge, 1330 for the flat (I re-ran the flat 22mm arm because it was on a different day). So it appears that if you can only have half an airfoil (because a full airfoil frame is hella hard to make), it's better to have the front.
Push or Pull?
This is one of the burning questions of our time. I ran the bare arm and the 22mm flat arm both ways. The 22mm arm gained 53 g (!) from being a pusher, while the bare arm lost 5 g. I'm guessing that means that means it's better to push than to pull, but the difference at 6mm is so minimal it falls in my margin of error.
In the air of the turbulent the skinny arm is king. Skinny and streamlined is better, but not by much. Streamlining is difficult, possibly more expensive, and may not be worth the weight gain. If you must run a wider arm, a half airfoil is better than flat.