I'm new to UAV's, but have been researching enough to see that there are a multiplicity of designs available. One item I've come across is dihedral quad/hex/octo frames, where the motors are tilted inboard slightly, thus vectoring the thrust slightly outboard, rather than straight down. It is claimed to provide a smoother and more controllable platform. On an instinctive level, it seems right. But what about from an engineering perspective... can it be verified by modeling it through equations?

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If the motors are tilted 10 degrees inboard and the copter gets tilted 10 degrees, the lower arm will now have its motor's thrust vector vertical while the upper motor is now 20 degrees from vertical. The vertical component of thrust is thus reduced on the upper motor, which will cause it to lower and while the other side has 100% of its thrust vertical so it raises. So here we have positive stability creating a self righting frame, without even changing the differential thrust output of the motors. This is good for a stable hovering platform and bad for maneuverability.

Hmmm... OK, I get the stable hovering, but I think the "bad" for maneuverability may prove a matter of taste more than a hard technical problem. At least my rudimentary understanding of the physics involved seems to point to that. From what I've read, it increases thrust efficiency for X & Y vectors, while maybe decreasing it for Z very slightly. But shouldn't tuning take care of any issues the design imposes? 

I know this is an old discussion thread, but I have recently found a research report from 2017 on the math involved here:

A Unified Approach to Configuration-based Dynamic Analysis of Quadcopters for Optimal Stability https://arxiv.org/abs/1709.07936

And, I have seen one commercial drone that appears to be quite stable when compared to the majority of drones. But it never made it to market. it is called the CyPhy LVL 1 https://www.youtube.com/watch?v=HCHoTIsCtio

This discussion raises a question about the widespread adoption of dihedral in multirotor drones. If this design technique improves stability of a multirotor, what is holding back a widespread adoption? I really think it is the fact that the commercial designers are not as eager to try new things. And then, to verify that the theory matches the practical application, this would require a lot of testing.

So I asked in another discussion forum, and one of the respondents simplified the answer to: "It is too complicated. Just make the thing flat and let the Flight Controller stabilize the drone." Another respondent wrote: "multirotors are already stable."   WOW! There sure seems to be a general misunderstanding about stability.

But the next question is: If the design configuration with dihedral is inherently more stable, does this mean that the motors work less and use less power, and will the flights last longer? I have not been able to find anything that addresses this question.

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