‫Welcome back.
‫So this is the schematics for the plant again, and as you might have seen, we have pretty much covered
‫almost everything here in this plant.
‫We only have one more box to cover, and that's this omega box.
‫Let's find the relationship between the control inputs you one, you to Q3 and Q4 and the rotor angular
‫velocities, omega one, omega two, omega three and omega four so that we could then add them up and
‫then have this total omega that we can then direct into this data base equations.
‫So essentially what you want is a system of equations in this form where you have your omega one, two,
‫three and four, and then you will have four equations that contain you one, two, three and four.
‫So this is the top for you or your drone?
‫And let's now focus on one murder, that one murder has two blades.
‫And now let's focus on one blade.
‫Let's take this one.
‫So this would be a typical airfoil shape for the blade, and by the way, the word airfoil means that
‫airfoil is the shape of a wings cross section.
‫So if you look at this, this is a cross section.
‫So if I draw it like this.
‫And I only treat this cross section in two dimensions, then we say that it's an airfoil.
‫The other way to think about it is that the airfoil has an infinitesimally small width.
‫So if I imagine that this here this is some kind of with, then I'm going to say that this is, for
‫example, D.R.
‫And so this D-R is infinitesimally small.
‫So it's a differential with.
‫So that would be your airfoil.
‫And so this here, this is the top view of the blade.
‫And you can imagine that this blade is rotating like this.
‫So this here would be our aerofoil section with the with D-R, that's this one here.
‫So this point here, this is the center of the motor.
‫So it's this point here.
‫And let's say that the total length of the blade is our meters.
‫And the length from the center of the mortar till our airfoil, let's call it ah, but in this case,
‫we're going to call it a small ah.
‫And now we're going to take this side of the airfoil and we're going to represent it in 2D.
‫Like this, and so here this is the top few of the blade again, and now if we assume that this blade
‫is rotating like this.
‫With an Omega.
‫Radians per second.
‫Then what happens is that.
‫This blade will create a rotation disc.
‫So as this blade rotates, it will go in a circle and so all the area that the blade will cover, that's
‫what we call a rotation disc.
‫So it's this entire disk inside this green circle.
‫Now, if you know that the length of the blade is are.
‫Meters.
‫And you know that the blade is rotating at Omega radians per second, then, you know, at which speed
‫the tip of the blade is moving.
‫This dip here is moving at omega times, our meters per second.
‫Because if something goes in circles, then that's how you find out the translational velocity of its
‫tip, you take the length of this object from the center of rotation and you multiply it by the angular
‫velocity of this object.
‫And then you also know that your airfoil is moving at Omega times, lower case R meters per second.
‫And now if you look at your airfoil in 2D, like it's represented here in purple, if you look at it
‫from this angle, then this velocity omegle times, lowercase r here, it would be like this.
‫This purple airfoil would move in this direction at omegle times are meters per second.
‫And usually the airfoils are in this way because usually they have a twist, so that's why the nose
‫of the airfoil points up in the diagonal.
‫But the airfoil itself is moving in this direction, like this arrow is showing.
‫So if you look at it from this point of view, then this rotation disk, from this point of view, you
‫won't actually see it.
‫You would see it as a line, right?
‫So this would be your rotation disk from the side, this would be the top of you, maybe this would
‫be in 3D and this would be the same rotation disk, but from the side.
‫So you don't actually see the disk.
‫You only see the edge of the disk.
‫This one here.
‫And so the velocity here and here and at any other point on the blade, they all move on the surface
‫of the rotation disk.
‫However, what you need to know is that the court length here, that's measures like this.
‫From the nose of the airfoil till the end of the year, foiled till the very last tip, and that would
‫be a length.
‫And now let's take our airfoil and let's analyze what forces it experiences.
‫Let's do that in the next video.
‫Thank you very much.
‫And see you in the next one.