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Drone Physics

iahmed.me

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Re: Drone Physics

#31

Post by cpgxiii »

fragmede wrote: post #10
ivanjermakov wrote: post #8

I studied this subject when I was building FPV sim from scratch. I noticed that yaw action is often misunderstood, falsely believing that it's caused by a change in angular momentum (think reaction wheels). There is a good SE answer about deriving net torques given each props' thrust force in less PhD language than this article: https://drones.stackexchange.com/a/416/11402 If anyone is interested in tackling UAV simu…

Why does four seem optimal? Why not three or five? or eight?

If you look at larger multi-copters, 6 and 8 are quite common since they allow for some redundancy, allowing for safe landing and/or continued flight following the failure of one of the rotors.

As other replies note, 4 is the simplest arrangement mechanically and control-wise, as the control math is quite simple (just rotor speeds/torque) and the only moving parts are the fixed-pitch rotors.

The minimum, as seen in real (and model) helicopters, is either two (approximately) constant-speed rotors with swashplate control, or one (approximately) constant-speed rotor with swashplate control and one tail rotor, either with (approximately) constant speed and variable pitch, or with variable speed. At the scale of real helicopters, two rotors may often be more powerful and efficient (e.g. CH-47, V-22) but the size and weight of the gearbox needed to transmit so much power is a significant contribution to the weight and cost of the helicopter, and thus having a single main gearbox is much lighter and cheaper. The notable difficulties of shaft drive between multi-rotor helicopters, particularly with distributed engines (see a number of V-22 issues) strongly discourages helicopters with more than 2 rotors.

Re: Drone Physics

#32

Post by bigiain »

hnuser123456 wrote: post #13
chasd00 wrote: post #12

Earlier quoted context omitted.

Why not just flip over and accelerate? I bet some in the drone racing crowd do this.

You could, but once you need to turn around and thrust upwards to avoid hitting the ground, you'll need to run the motors HARD, which will make a lot of turbulence right below you, which you then fall into. So you're falling into wind that is already blowing towards the ground, so you need to push it down even faster, and so on. Ducted fans might help a little, since they can send the turbulence further away faster,…

I wonder if, for autonomous (or semi autonomous) flight, there's a way to make the drone flip and "power dive" then fly a carefully configured/programmed half-loop at the bottom? Seems there might be scope that way to have an autonomous "reduce altitude as rapidly as possible to 5m" function on a button that'd fly a full power j shape and compensate for the semicircular radius of the "deceleration without flying through your own prop wash" part of the maneuver? Similar (but more complex) to the "flip" and auto land functions on "toy" drones?

(I wonder if the drone people from Ukraine already have this? I suspect it'd make drones even harder to defend against with anti aircraft system designed and optimised to shoot down fighter/bomber planes instead of swarms of inexpensive drones.)

Re: Drone Physics

#33

Post by montymintypie »

hnuser123456 wrote: post #28
montymintypie wrote: post #26

Earlier quoted context omitted.

> Two is possible if the payload hangs below the props I think this is incorrect, it's the somewhat unintuitive rocket pendulum fallacy.

Here is a video of one: https://www.youtube.com/watch?v=qO747JB4Nr8 There's a few demonstrated here (26-32 seconds in): https://www.youtube.com/watch?v=vBsyFj8bEJk And here's one that uses the ailerons instead of being able to tilt the motors: https://www.youtube.com/watch?v=L2fgL97rgK0 I could've sworn Peter Sripol built one while on Flite Test too, but I can't find it atm. Looks like the rocket pendulum fallacy is…

Sorry, I wasn't arguing against bicopters being possible, obviously something like the osprey exists.

> the air resistance of swinging back and fourth really does help dampen oscillations passively

But they don't swing back and forth like a pendulum (unless your PIDs are off) because of the center of mass, that is the entire issue with the fallacy.

Re: Drone Physics

#34

Post by montymintypie »

elictronic wrote: post #29
montymintypie wrote: post #26

Earlier quoted context omitted.

> Two is possible if the payload hangs below the props I think this is incorrect, it's the somewhat unintuitive rocket pendulum fallacy.

He specifically says if the motors independently tilt. This is active control. The Rocket pendulum fallacy is only valid for systems requiring passive stability. Tandem rotor helicopters exist.

Rockets also have active control via gimballing motors. Bicopters tilt their motors to control pitch and yaw, roll is still governed by motor speed.

I was arguing against the COG of the payload, not of the existence of bicopters entirely.

Re: Drone Physics

#35

Post by hnuser123456 »

hnuser123456 wrote: post #19
fragmede wrote: post #10

Earlier quoted context omitted.

Why does four seem optimal? Why not three or five? or eight?

4, 6, and 8 are all fairly standard, as quadcopter, hexacopter, and octacopter, because you have a pair of motors rotating in each direction, which allows you to slow down all the motors spinning in one direction and speed up the others (as long as each set spinning the same direction is on opposite sides of the center of gravity), to maintain constant lift while yawing left or right. Tricopters are possible as tilt-…

Too late to edit, but I meant cyclic pitch, not collective pitch.

Re: Drone Physics

#37

Post by hazrmard »

huqedato wrote: post #2

I would have liked to understand this, but the math behind it is overkill. One may need a PhD in aerospace to digest it.

Hello, blog author here. I agree the math appears overkill. I wrote this as a learning aid for myself with the benefit of hindsight of having worked with some drone sims. I wanted to dispel any doubt in my mind that I could derive drone physics from basic principles, instead of copy-pasting state equations. I went further and tried to motivate transport theorem, rotational analog of F=ma etc from scratch.

In summary: I take F=ma and extend it for rotational motion. (1) Calculating linear motion when the vehicle containing sensors is rotating. (2) Calculating rotation of the vehicle itself due to thrust/yaw force acting about its center of mass.

I'll echo what the other commenter said: this is no way PhD math. It may appear so - but I'm only being verbose with simpler concepts like cross products and rotation matrices.

Re: Drone Physics

#38

Post by hazrmard »

the__alchemist wrote: post #3
huqedato wrote: post #2

I would have liked to understand this, but the math behind it is overkill. One may need a PhD in aerospace to digest it.

Yes and no. The math here is useful, albeit not required. It is not specialized PhD material; it's linear algebra. (And not the abstract quantum mechanics/chem kind!) What I mean by not required is, I've written drone firmware and didn't directly use this; the core can be done with a PID for rate controls (Compare measured rate along each axis with commanded; nudge motor power proportional to the diff), and commandin…

You'd be right to be surprised by lack of mention of quaternions. I (blog author) was not too familiar with them when I did the work this post is based on. With the benefit of hindsight, I may yet revise the post.

Re: Drone Physics

#39

Post by huqedato »

hazrmard wrote: post #37
huqedato wrote: post #2

I would have liked to understand this, but the math behind it is overkill. One may need a PhD in aerospace to digest it.

Hello, blog author here. I agree the math appears overkill. I wrote this as a learning aid for myself with the benefit of hindsight of having worked with some drone sims. I wanted to dispel any doubt in my mind that I could derive drone physics from basic principles, instead of copy-pasting state equations. I went further and tried to motivate transport theorem, rotational analog of F=ma etc from scratch. In summary:…

Ok man, for me it's PhD math. Waaaay above my high school level math. Perhaps you will write a version for layman like me, without advanced math and rather with more verbal explanations and animations.
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