Drone #3: The simple physics


So I determined for sure that I'm going to build a multicopter, most likely a quadcopter.

A simple model of the physics of the quadcopter is surprisingly simple. Contrary to an ordinary airplane there's only two forces working on the quadcopter: Thrust and weight. Weight is unsurprisingly always pointing towards the center of the Earth, where as thrust can be directed using the propellers.

How exactly does this work?

A typical quadcopter configuration could be the X as seen below.
A drone

It would seem that if all motors m1-m4 are running at equal speeds the quadcopter would go straight up. And yes that is correct, but it's important to realize that in order for the quadcopter to not start turning about its y-axis (what's known as yaw) the motors needs to run pairwise in opposite directions. Such that e.g. m1and m3 runs clockwise and m2and m4runs counterclockwise.

So now we have the quadcopter in the air. How do we get it to turn?

My first thought here was that I would need some servo motors to angle the motors driving the propellers hence pushing the drone in a different direction. It turns out that this is one way to do it. See this video of Team Blacksheeps Gemini drone that can fly over 90+ km/h - it tilts it's propellers to achieve this.
But there's a simpler way.

By simply lowering the speed of the motors in the direction that you want to go, the body of the drone on this side will obviously drop which will make it go side ways in the direction of "the drop". But lowering the speed of two of the motors would probably also lower the overall altitude of the quadcopter so I would probably need to raise the speed of the two other motors the same amount to keep it around the same height. So in this way we're actually using the gravity to angle the propellers in the way we want to go. Clever!

So if I wanted the drone in the figure above to go to the left I would simply lower the speed on m1 and m2 and raise the speed on m3 and m4 by the same amount. This would cause the left side to drop hence angling the propellers to the left in reference to the ground hence the craft would move to the left.

But is it really that simple?

The physics is, but controlling the engines is not. They will almost certainly not have exactly the same output or well almost certainly not be completely in sync. And in order to perform something as simple as a straight climb they would need to be that. So for that I will need an elaborate control system that can make sure the engines stays in sync.

I will need what's known as an Inertial Measurement Unit that using a gyroscope and accelerometer (and other sensors I think) can measure how the craft is moving and depending on that the control system can calculate whether to turn the motors up or down. Probably using a PID controller.

Hmm.. Perhaps I should try and build a small software model of the quadcopter to learn how to control it...

Michael Reibel Boesen

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