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‫Welcome back.

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‫So this is the schematics for the plant again, and as you might have seen, we have pretty much covered

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‫almost everything here in this plant.

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‫We only have one more box to cover, and that's this omega box.

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‫Let's find the relationship between the control inputs you one, you to Q3 and Q4 and the rotor angular

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‫velocities, omega one, omega two, omega three and omega four so that we could then add them up and

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‫then have this total omega that we can then direct into this data base equations.

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‫So essentially what you want is a system of equations in this form where you have your omega one, two,

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‫three and four, and then you will have four equations that contain you one, two, three and four.

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‫So this is the top for you or your drone?

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‫And let's now focus on one murder, that one murder has two blades.

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‫And now let's focus on one blade.

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‫Let's take this one.

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‫So this would be a typical airfoil shape for the blade, and by the way, the word airfoil means that

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‫airfoil is the shape of a wings cross section.

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‫So if you look at this, this is a cross section.

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‫So if I draw it like this.

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‫And I only treat this cross section in two dimensions, then we say that it's an airfoil.

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‫The other way to think about it is that the airfoil has an infinitesimally small width.

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‫So if I imagine that this here this is some kind of with, then I'm going to say that this is, for

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‫example, D.R.

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‫And so this D-R is infinitesimally small.

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‫So it's a differential with.

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‫So that would be your airfoil.

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‫And so this here, this is the top view of the blade.

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‫And you can imagine that this blade is rotating like this.

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‫So this here would be our aerofoil section with the with D-R, that's this one here.

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‫So this point here, this is the center of the motor.

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‫So it's this point here.

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‫And let's say that the total length of the blade is our meters.

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‫And the length from the center of the mortar till our airfoil, let's call it ah, but in this case,

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‫we're going to call it a small ah.

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‫And now we're going to take this side of the airfoil and we're going to represent it in 2D.

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‫Like this, and so here this is the top few of the blade again, and now if we assume that this blade

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‫is rotating like this.

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‫With an Omega.

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‫Radians per second.

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‫Then what happens is that.

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‫This blade will create a rotation disc.

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‫So as this blade rotates, it will go in a circle and so all the area that the blade will cover, that's

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‫what we call a rotation disc.

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‫So it's this entire disk inside this green circle.

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‫Now, if you know that the length of the blade is are.

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‫Meters.

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‫And you know that the blade is rotating at Omega radians per second, then, you know, at which speed

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‫the tip of the blade is moving.

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‫This dip here is moving at omega times, our meters per second.

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‫Because if something goes in circles, then that's how you find out the translational velocity of its

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‫tip, you take the length of this object from the center of rotation and you multiply it by the angular

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‫velocity of this object.

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‫And then you also know that your airfoil is moving at Omega times, lower case R meters per second.

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‫And now if you look at your airfoil in 2D, like it's represented here in purple, if you look at it

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‫from this angle, then this velocity omegle times, lowercase r here, it would be like this.

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‫This purple airfoil would move in this direction at omegle times are meters per second.

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‫And usually the airfoils are in this way because usually they have a twist, so that's why the nose

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‫of the airfoil points up in the diagonal.

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‫But the airfoil itself is moving in this direction, like this arrow is showing.

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‫So if you look at it from this point of view, then this rotation disk, from this point of view, you

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‫won't actually see it.

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‫You would see it as a line, right?

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‫So this would be your rotation disk from the side, this would be the top of you, maybe this would

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‫be in 3D and this would be the same rotation disk, but from the side.

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‫So you don't actually see the disk.

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‫You only see the edge of the disk.

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‫This one here.

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‫And so the velocity here and here and at any other point on the blade, they all move on the surface

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‫of the rotation disk.

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‫However, what you need to know is that the court length here, that's measures like this.

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‫From the nose of the airfoil till the end of the year, foiled till the very last tip, and that would

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‫be a length.

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‫And now let's take our airfoil and let's analyze what forces it experiences.

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‫Let's do that in the next video.

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‫Thank you very much.

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‫And see you in the next one.