Original subtitles

[MUSIC]

In this module we're gonna explore how a quad rotor work.

We're gonna look at the basic mechanics and

draw some conclusions about how to design quad rotors.

So we'll first start discussing the basic mechanics underlying a quad rotor.

We'll discuss some very, very simple approaches to control.

We'll outline some basic design considerations.

Talk a little bit about maneuverability and agility, and

think about the components we might want to select to build a quad rotor.

And in the end we finally want to explore the effects of size.

So what does it mean to create a bigger quad rotor, and how does that impact

performance and, conversely, how do things scale down and you decrease the size?

Let's start with the basic mechanics.

As we discussed before,

a quad rotor has four rotors that support the vehicle's weight.

So each rotor spins and generates the thrust.

If you plot the thrust, or the thrust force,

against the RPMs of the motor or the angular velocity.

You'll find that this relationship is approximately quadratic.

Every time a rotor spins, there's also a drag that the rotor has to overcome.

And that drag moment is also quadratic.

So if you think about a quad rotor,

every rotor has to support roughly one fourth of the weight in equilibrium.

Which means by looking at the thrust forces of rpm curve,

you can determine speed that'll be required to produce one fourth the weight.

So that gives you omega zero the operating speed.

But of course, that operating speed produces a drag moment and

every rotor has to overcome the drag moment.

And that's where motors come in, you have to size the motor, so

that they can produce the torque to overcome this drag moment.

So when the robot is hovering, the rotor speeds compensate for the weight.

Using the weight you can determine the basic operating speed for every rotor.

And that in turn tells you what torque you need to apply at every motor.

The equations are fairly simple, if you assume that you know

the constant of proportionality between the force and the square of the RPM.

And the constant of proportionality between the drag moment and

the square of the RPM.

You can calculate the resultant force quite easily.

It's the sum of the four thrusts and the gravity force.

And if you know where the center of mass is,

you can quickly calculate moments about the center of mass.

And of course the total moment is obtained by calculating

the moments due to the forces exerted by the rotors and the reactions

due to the rotors spinning in counterclockwise or clockwise directions.

Those reactions are moments, and they add to the net moment

In equilibrium, the resultant force is obviously zero.

And the result in moment is also zero.

But what happens when these resultant forces in moments are non-zero?

Well you get acceleration.

To keep things simple let's first look at the acceleration

in the vertical direction.

So in the vertical direction, again,

every motor thrust is the same, and they'll add up to support the weight.

But if you increase the motor speeds, then the robot accelerates up.

If you decrease the motor speeds, obviously the robot will accelerate down.

So a combination of motor thrusts and

the weight determines which way the robot accelerates.