‫Welcome back.
‫So this is our airfoil here, and like mentioned before, the airfoil moves due to the rotation of the
‫blade in this direction, like this horizontal arrow at or Megahed, times are meters per second.
‫However, what we want to do now, we want to analyze what aerodynamic forces this airfoil is experiencing.
‫And that is done in such a way that we imagine that our object that in reality is moving, we imagine
‫that this object is addressed and then we imagine that the air is coming added.
‫In reality, of course, the air is at rest, for example, if you have an airplane and this airplane
‫is moving in this direction, then obviously the airplane is the one that is moving and then the air
‫is at rest.
‫However, in aerodynamics, we assume that the airplane is at rest and then the air is moving at the
‫airplane.
‫And from the aerodynamics point of view, it really doesn't matter because.
‫Either you move through the air or the air moves through you, the aerodynamic forces will be the same.
‫And that's how wind tunnels work, they put some kind of wing inside a wind tunnel, let's say that
‫this is a wind tunnel and then this is your wing here, and then you have some kind of huge propeller.
‫Or a huge fan.
‫And that fan rotates very fast and creates a lot of wind towards the wing and then the wing is stationary
‫and then the air will go over the wing and under the wing and then they analyze what kind of aerodynamic
‫forces the wing is experiencing.
‫But the wing would experience the same forces if the air was at rest and then the wing flew in this
‫direction at the same velocity, then the wing would experience the same aerodynamic force.
‫And that's why in our air foil, instead of representing this velocity vector like this.
‫We're going to represent it like this, but the velocity still or mega times are meters per second is
‫just now.
‫We are assuming that the airfoil is stationary and then the air is moving towards the wing, towards
‫the airfoil, and that's the air moving towards the airfoil due to the fact that this rotor is rotating.
‫And that's why you have this velocity vector along this rotation disk that you don't see here, because
‫you're looking at it from the side, but in fact, it would be a rotation disk.
‫But since you're looking at it from the side, then you don't see that it's a disc.
‫You only see that it's line.
‫So if you're looking at the top view of the rotor and you say that it is rotating at Omega radians per
‫second like this, then at this time instant you're assuming that the rotor is at rest and then the
‫air is moving at the rotor like this at Omega.
‫Times are meters per second also when the mortar rotates like this at omega radians per second.
‫Then this would be your rotation disc.
‫And this rotation will form something called a stream tube with the air, so the air will have this
‫kind of pattern down.
‫So from the side, it would look something like this.
‫Meaning that the rotation of the motor will force some of the air to go down like this in this pattern,
‫and that means that this blade, when it rotates, it will also see some kind of velocity from the air.
‫But vertically like this and let's call this velocity the sub, the meters per second.
‫So obviously, the rotation of the model will produce some kind of thrust upwards.
‫But also because of that, the air will be pushed down like this, so the blades, they will see this
‫velocity here, this vertical velocity, which would be VSP meters per second.
‫So that means that this airfoil also sees a velocity.
‫Like this, the use of the meters per second, so this airfoil sees air coming at it from two directions,
‫it has two components.
‫One component of the air velocity comes from the fact that the motor is rotating.
‫And so as the Air Force rotates through the air at omega radians per second, then this specific airfoil,
‫because of that rotation, sees air velocity at omegle times are meters per second.
‫But because of the fact that you also have this stream tube effect due to the rotation of the motor
‫because of that fact, this airfoil also sees this VSA V meters per second.
‫So it sees another.
‫Air velocity component.
‫So they can be thought of as two components of one air velocity vector, and this would be the resultant
‫air velocity vector.
‫So this white vector and red vector, they are just the components of this general resultant vector.
‫And we call this resultant vector, you meters per second.
‫So this result on Vector now takes into account both velocity vectors from the rotation and from this
‫extreme tube effect.
‫And you can compute the magnitude of this new vector using the Pythagoras theorem, so you equals the
‫square root of.
‫The sum of squared plus.
‫Oh, my God.
‫Times are squared and of course, that would be meters per second.
‫And so now you have that total air velocity vector that the airfoil sees.
‫Because of this air velocity, this is what will happen, you will have high air pressure below the
‫airfoil.
‫And you will have low air pressure above the airfoil.
‫And that happens because of how the airfoils are designed, they simply have this kind of shape that
‫when this air velocity goes through the air fall from this direction as shown here, or in reality,
‫of course, when the air foil goes through the air in the opposite direction, then you have high air
‫pressure here and you have low air pressure here.
‫And so you have pressure difference, and that pressure difference will give you an IRA dynamic force
‫and let's call this force D F sub A and note that this is a differential force.
‫Why?
‫Because our airfoil has a differential with.
‫That was the answer because of the fact that our airfoil has this differential with because of that
‫fact, our force is also a differential force.
‫So you can imagine that on a blade you will have many airfoils with differential widths and each airfoil
‫will have some kind of differential force.
‫And so in the end, what you're going to end up doing, you're going to end up integrating these airfoils
‫from the center of rotation up until the end of the blade.
‫And that's when you will get the total force that the blade will produce.
‫But we're going to get there now in the next video where we're going to do we're going to decompose
‫this DFS up a into several components and then we'll see how this thrust force is generated.