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‫Welcome back.

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‫So this is our airfoil here, and like mentioned before, the airfoil moves due to the rotation of the

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‫blade in this direction, like this horizontal arrow at or Megahed, times are meters per second.

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‫However, what we want to do now, we want to analyze what aerodynamic forces this airfoil is experiencing.

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‫And that is done in such a way that we imagine that our object that in reality is moving, we imagine

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‫that this object is addressed and then we imagine that the air is coming added.

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‫In reality, of course, the air is at rest, for example, if you have an airplane and this airplane

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‫is moving in this direction, then obviously the airplane is the one that is moving and then the air

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‫is at rest.

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‫However, in aerodynamics, we assume that the airplane is at rest and then the air is moving at the

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‫airplane.

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‫And from the aerodynamics point of view, it really doesn't matter because.

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‫Either you move through the air or the air moves through you, the aerodynamic forces will be the same.

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‫And that's how wind tunnels work, they put some kind of wing inside a wind tunnel, let's say that

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‫this is a wind tunnel and then this is your wing here, and then you have some kind of huge propeller.

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‫Or a huge fan.

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‫And that fan rotates very fast and creates a lot of wind towards the wing and then the wing is stationary

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‫and then the air will go over the wing and under the wing and then they analyze what kind of aerodynamic

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‫forces the wing is experiencing.

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‫But the wing would experience the same forces if the air was at rest and then the wing flew in this

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‫direction at the same velocity, then the wing would experience the same aerodynamic force.

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‫And that's why in our air foil, instead of representing this velocity vector like this.

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‫We're going to represent it like this, but the velocity still or mega times are meters per second is

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‫just now.

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‫We are assuming that the airfoil is stationary and then the air is moving towards the wing, towards

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‫the airfoil, and that's the air moving towards the airfoil due to the fact that this rotor is rotating.

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‫And that's why you have this velocity vector along this rotation disk that you don't see here, because

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‫you're looking at it from the side, but in fact, it would be a rotation disk.

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‫But since you're looking at it from the side, then you don't see that it's a disc.

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‫You only see that it's line.

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‫So if you're looking at the top view of the rotor and you say that it is rotating at Omega radians per

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‫second like this, then at this time instant you're assuming that the rotor is at rest and then the

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‫air is moving at the rotor like this at Omega.

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‫Times are meters per second also when the mortar rotates like this at omega radians per second.

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‫Then this would be your rotation disc.

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‫And this rotation will form something called a stream tube with the air, so the air will have this

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‫kind of pattern down.

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‫So from the side, it would look something like this.

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‫Meaning that the rotation of the motor will force some of the air to go down like this in this pattern,

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‫and that means that this blade, when it rotates, it will also see some kind of velocity from the air.

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‫But vertically like this and let's call this velocity the sub, the meters per second.

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‫So obviously, the rotation of the model will produce some kind of thrust upwards.

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‫But also because of that, the air will be pushed down like this, so the blades, they will see this

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‫velocity here, this vertical velocity, which would be VSP meters per second.

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‫So that means that this airfoil also sees a velocity.

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‫Like this, the use of the meters per second, so this airfoil sees air coming at it from two directions,

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‫it has two components.

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‫One component of the air velocity comes from the fact that the motor is rotating.

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‫And so as the Air Force rotates through the air at omega radians per second, then this specific airfoil,

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‫because of that rotation, sees air velocity at omegle times are meters per second.

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‫But because of the fact that you also have this stream tube effect due to the rotation of the motor

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‫because of that fact, this airfoil also sees this VSA V meters per second.

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‫So it sees another.

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‫Air velocity component.

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‫So they can be thought of as two components of one air velocity vector, and this would be the resultant

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‫air velocity vector.

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‫So this white vector and red vector, they are just the components of this general resultant vector.

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‫And we call this resultant vector, you meters per second.

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‫So this result on Vector now takes into account both velocity vectors from the rotation and from this

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‫extreme tube effect.

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‫And you can compute the magnitude of this new vector using the Pythagoras theorem, so you equals the

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‫square root of.

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‫The sum of squared plus.

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‫Oh, my God.

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‫Times are squared and of course, that would be meters per second.

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‫And so now you have that total air velocity vector that the airfoil sees.

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‫Because of this air velocity, this is what will happen, you will have high air pressure below the

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‫airfoil.

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‫And you will have low air pressure above the airfoil.

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‫And that happens because of how the airfoils are designed, they simply have this kind of shape that

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‫when this air velocity goes through the air fall from this direction as shown here, or in reality,

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‫of course, when the air foil goes through the air in the opposite direction, then you have high air

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‫pressure here and you have low air pressure here.

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‫And so you have pressure difference, and that pressure difference will give you an IRA dynamic force

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‫and let's call this force D F sub A and note that this is a differential force.

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‫Why?

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‫Because our airfoil has a differential with.

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‫That was the answer because of the fact that our airfoil has this differential with because of that

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‫fact, our force is also a differential force.

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‫So you can imagine that on a blade you will have many airfoils with differential widths and each airfoil

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‫will have some kind of differential force.

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‫And so in the end, what you're going to end up doing, you're going to end up integrating these airfoils

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‫from the center of rotation up until the end of the blade.

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‫And that's when you will get the total force that the blade will produce.

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‫But we're going to get there now in the next video where we're going to do we're going to decompose

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‫this DFS up a into several components and then we'll see how this thrust force is generated.