This is an analysis of the variables which affect the ability to control a multi-rotor as the size is scaled up.
This will show why at some point, variable pitch must be introduced.
I hope to follow this with another article which includes Phase Margin and Gain Margin, but right now I'm trying to refresh my memory from 30 years ago on Laplace transforms and Bode Plots. Ugh!
I hope this makes some sense.
Comments
Neat analysis. I like that someone went out of their way to document this stuff.
The last sentence, "This is primarily due to the exponential increase in the polar inertia of the rotor blade", leaves a bad taste. P^5 is not exponential, 5^P is. If you want to write a technical paper, don't use "exponential" to mean "fast-growing".
Interesting work Randy. As you may know, I'm a proponent of helicopters. Anything we can do to put the brakes on the out of control multirotor bandwagon is good. :) It is my belief, and I think that anybody who seriously considers the situation would agree, that once you get to the point of needing variable pitch propellers on a quadcopter, there is simply no point to it's existence. Multirotors have the advantage of extreme mechanical simplicity. 4 sticks. 4 direct drive brushless motors. 4 fixed pitch props. And a microcontroller. Beautiful. They are not more efficient than a helicopter. They really don't do anything better than a helicopter other than being simple (and being new). Once you take away the simplicity there is no good reason to build them. Adding 4 servos, 4 variable pitch mechanisms, and possibly 4 powertrains for central power distribution, they have lost all their simplicity.
Now, a few comments, I only skimmed over it. First, the R22 is a 2 seater. Secondly, you aren't actually coming to a conclusion about where to draw the line in multirotor scale? You also do not address the scale factor of external disturbance force which may actually help larger machines. ie: A 40 km/h wind gust should have less effect on a large multirotor than a small one, requiring less control response. I think. I'm not sure how to model this.
Thanks for the analysis. I'm trying to see how to tally this with real-world experience. My "quad" is 13kg (a big quadplane) and has arm spacing of 1m. My 250 racing quad is 4x smaller in arm spacing, and 10x smaller in weight. Going by the table on page 9 would I expect 1024x smaller roll response? That doesn't seem to tally with what I see in practice.
What have I missed?
Randy - Nice analysis. I wrote an a paper a few years ago about a control system for large multicopter. One of the most interesting issues is the scalability of the differential torque yaw method used on multicopters and how its effect diminishes to almost nothing with scale.
We ended up tilting the props with actuators to get sufficient yaw authority.
Here's a link to the paper if you are interested.
-Rusty
-
1
-
2
-
3
of 3 Next