So How Does Yaw Work?

[Forrest Frantz]

It was suggested that I test an actual flight and find out, What is Up with Yaw?  Generate the data, and then present that to the group.  That this would be much more productive than talk.  So I set up a test ship and took 208 data points.

I'll be first to admit that physics can be surprising.

I recently put a chain in a box that was raised up on a pedestal.  Then I dropped one end of the chain over the edge of the box so that the chain would pull the rest of the chain out of the box.  What surprised me was that the chain, rather than slice the wall of the box in two as it ran out of the box, instead looped up and didn't touch the wall of the box.  The higher the box was raised off the floor, the higher the chain soured upwards into the air before it was pulled down to the floor. Once I saw this, the reason was obvious.  But it certainly was not obvious to me without seeing it first.  For your pleasure, here is the video.

https://www.youtube.com/watch?v=6ukMId5fIi0

Back to yaw.  The question the group has been struggling with is:

o Is Yaw force different than thrust force in how it should be treated?

o Is rotor yaw strongest when it's at the center?

My belief was that no.  Force is force is force.  While counter rotational forces of the motor are created quite differently than thrust forces, it's still a force.  But who cares what an old fart like me with dying brain cells thinks?  Let's do the damn test!

So here is the graph.

Here is the data

So what does this tell us.  It tells us two things:

o first, we can definitely reject the hypothesis that yaw force is strongest when the rotor is at the center of the ship.

o second, my premise might also be wrong, because there appears on the surface to be a slight increase in force as the rotor is moved away from center (remember that my prediction was that the force would not change; force is force is force).

So what's with this 0.3% upward slope?  There are two possible causes that my wee brain is aware:

1. Twisting the bar so the motor can tilt into yaw.  The bar, however, was a 1.5" aluminum extrusion that isn't going to twist enough when subjected to a mere 60 gram force.  So that's not a likely candidate.
2. Rotor tilt.

We all know how hard it is to create a thrust vector that is perfectly perpendicular to the rotor plane.  So could this be it? Did the rotor have a slight lean into the direction of yaw which would generate greater yaw torque the farther the rotor was from the center (same principle of physics when two kids of equal mass sit at different distances from the center of a teeter totter;  the kid nearest the center is going to get launched upwards)?

If the bias in slope is caused by a slight rotor tilt, how can one tell?  Easy ... fortunately.  Just slide the rotor across to the other side of the bar.  If it is thrust helping yaw on one end of the bar, on the opposite end, the tile will work against the yaw rotational force.

This is the result of that test.

Bingo.  The slope is zero.  So nothing surprising to me after all.  Darn.  I love being surprised like the magic trick above. The 0.3% bias was cause by a 0.34 degree tilt in the rotor.  Hey, that's as good as I could get it.  And as long as one tests along both ends of the bar, these minor biases can be averaged out.

What was the test procedure?  I'm hoping that someone will replicate this test to confirm the data, so we can correct the quad and octa V.  So there is a photo of the test setup and my messy mancave (please forgive me, I've been doing a ton of tests on custom mujlti-rotor Vs).

To help move this along, I'm also willing to host someone who is near to Hood River, Oregon, USA.  My wife's princess palace has a great suite upstairs.  We can repeat the test together.

Note:  Force was measured at a constant location on the T-Bar as can be seen in the photo.  To derive the correct units of force (versus proportional units), divide all data points by 19.5.

I'll let Leonard and others mull this over.  This data proves that:

o rotational force is constant no matter the location on the bar.

o rotational force is no different in treatment to thrust force that is also constant no matter the location along the bar.

o thrust force and rotational force are thus both governed by the same torque law.

o thereby, the APM/3DR is correct in code and procedure.  The factors "are set by their coordiantes."

o In the case of yaw, how far the motor is from the z-axis of rotation that goes through CG.***

o When any alternate approach to setting V yaw pitch and roll factors differs from the coordinate framework, we need to talk.

***Caveat:  Leonard, there is something that is strange about yaw that someone smart in math like you is needed to solve.  I'd like to make the following suggestion.  I'm going to friend you so we can work this together offline and come up with a unified approach.  Hopefully you will now let me work using geometry to solve for the coordinates of the quad and octa V as stated in 3DR/APM procedure, with your oversight.  If you want join with me to do this, I'll share this strange thing about yaw with you that doesn't impact regular ships but does impact some custom ships.  It might be nothing, but it also might be something we need to consider that no one else is.

--

W. Forrest Frantz

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[Greg Fletcher]

Forrest, please! Go to the used book store and spend a few bucks on a HS physics book. Read the part on force and torque.
If you don't get it, let me know and I would be glad to help.
Torque = Force x Distance. You are not measuring torque unless you include the distance from the pivot point to where your string is tied. Your set up is converting torque back into a force. The original torque results from the blades pushing on the air thru the motor into your frame. Your units of grams force/watt is not a torque. A torque value by definition is Force x Distance, and the units are then gram*cm/watt. I would suggest you make your rig better with a proper pivot point instead of duct tape and repeat your experiment, noting the distance from the  pivot to the string. Run your motor at a constant power setting. Then vary the distance from the pivot to the motor.
Oh ya, How do you measure a 0.34 degree tilt error. You must have some expensive instruments.
Latter, Greg

[Jonathan Challinger]

It isn't acceptable to continue to make ad hominem attacks. If you don't like him, ignore him. If you don't like his argument, refute it. If both, pick one (the former is probably the better choice).

I haven't investigated this in-depth so I won't make judgement either way, but I just want this stupid flamewar to stop. If he isn't being civil, remove him from the list. If he is, stop making attack posts. He certainly seems civil enough at the moment.

Forrest, in an open source environment, if you want to make change happen, you have to:
1. Supply code (for us this means making a pull request)
2. Convince the maintainer to incorporate your code. In this case that means randy, and randy trusts Leonard. You've somehow managed to lose credibility with Leonard and completely piss him off, so you might want to tread carefully in deciding what to send him.

I'm sorry your experience here has been so poor, but I don't doubt for a second that that is your fault.

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[Jonathan Challinger]

And I'm sure his expensive instrument is called a trig function, by the way.

[Greg Fletcher]

Oh ya, I forgot. IMHO your data has low slope is your mechanical setup can't be trusted. You are maybe just hitting a limit when the tape stretches tight.
I doubt any one will repeat your experiment, because we don't need to. We get it. You need to do the experiment to be convinced.
That's fine then do them, just go for a little more precision. Don't make me do it for you ;) Cause I can if I have to.

[Greg Fletcher]

Sorry, you are right Jonathan. I was overly harsh, but I realy just want to help. Forrest, I will repeat your experiment and post it on youtube. I still have that test rig, so I will try turning the motor sideways and vary the distance.

[Ritchie Wilson]

I'm unsure because I'm looking on my phone but is the length (to motor) measured from a freely rotating point? If not any force value will have to include to structural rigidity of the test rig so its deflections are translated to actual torque of the system.

Regards

Ritchie.

On 14 Aug 2013, at 08:09, Greg Fletcher <gafle...@att.net> wrote:

Sorry, you are right Jonathan. I was overly harsh, but I realy just want to help. Forrest, I will repeat your experiment and post it on youtube. I still have that test rig, so I will try turning the motor sideways and vary the distance.

--

[Leonard Hall]

Forrest this is exactly what we have been trying to explain to you. I think your experiment demonstrates the point that Robert and I have been trying to explain.

The toque the motor creates is not changed by the position it has on the arm. This is why the yaw toque coefficients that I calculate in my code are not dependent on the position of the motor. I use 4 equations:

1. Yaw Toque: this is the sum of each motor toque multiplied by the direction (+1 or -1). As you have demonstrated here.

2 & 3. Roll and Pitch Toque: This is the motor distance from the roll/pitch axis multiplied by the lifting force of the propeller.

4. Lift Force: This is the sum of all lifting forces from all propellers.

There are 3 different relationships here.

Toque = Toque (Yaw)

Toque = Force x Distance (Roll and Pitch)

Force = Force (lift).

Toque and Force are two different things.

I think I have invested enough time in this. Good luck.

Leonard

[Forrest Frantz]

For those wanting to replicate the test of How Does Yaw Work ... here is some key additional information, critical to:

o increase signal/noise of the data

o reduce variance

Cheers.  I'll put together the code for not just the Vs, but in addition, the framework for any custom quad, hexa, or octa.  I'll then as requested, submit a pull request.