Hi, everyone, and welcome to this new class in aerodynamics and specifically the description of lift
and drag.
So here we have what would be the schematic forces of left and right and how they are related to cruising
velocity of the aircraft.
Now, depending on the velocity, we will have more lift or less lift and more drag or less luck.
So drag has the same direction as the velocity.
While lift is perpendicular to the velocity.
And as you can see, depending on the design of the air for him, right?
We will be able to transform this velocity into lift.
And even if we don't want to, we will also have some drag.
OK, so you can see that the design of the fall will actually enable us to optimize the relation between
this lift and the drag.
So air foils, which are these over here, right?
Is actually the cross section of the wing now, depending on our lift requirements and drug.
We will be defining a type of airfoil or another depending on our actually considering all of these
variables, right?
So there's actually a lot of work in the aerospace industry in designing and optimizing exactly the
geometry of these air foils.
So let's see some air force parameters, which are interesting.
First of all, the court line, the core line is the distance, the line which relates to leading edge
and the trailing edge of these airfoil.
So in this case, it would be something like this.
This points over here, the leading edge towards the trailing edge, right?
So you just relayed the two points, you unite two points.
Draw a line and you will how the court line.
The next parameter is the Campbell line.
So it is this one over here.
OK.
As you can see, the Campbell line actually defines the center with respect to the lowest of surface
and the upper surface of the F1.
OK.
So as you can see, the geometry is not linear, such as in the cases before, but rather depends on
the geometry of the exterior bounce of the airfoil, right?
As you can see is simply this line, which is half way to the upper surface and the lower surface.
Then there's the thickness, the thickness, the fines, the literal thickness of the air foil.
OK, by definition.
And this point, for instance, is the maximum thickness.
OK.
It's also interesting to note this length over here is the maximum Kemba.
And the not the same, right?
So.
Really, like there's a lot of possibilities in terms of how you decide to design this type of airfoil,
and you'll probably need a lot of computational power and so on to actually provide an in-depth solution
to this problem.
As you can see, it becomes quite complex when you actually start playing around with the variables.
OK?
So another interesting thing to note is the angle of attack now angle of attack is a must know when
talking about aerospace engineering.
OK?
The angle of attack is the relation between the relative wind that is the direction of the wind with
respect to the airplane.
OK.
And the code line.
So the angle of the court line.
So one can think of it as a.
Angle, which simply relates the way in which the wind is interacting with the airfoil and the actual
air foil as being described by the court line.
OK.
So, in other words, simply take it as the wind, the villa in the direction of the wind and the direction
of the air for you.
OK.
Right.
So.
Now, let's try to understand two ways of visualizing how an airfoil is capable of providing lift.
The first one is through the angle of attack.
What this means is that having an angle of attack of the wind with respect to the court line, as we
mentioned before, allows for this air for this wind to move downwards.
What is called the down wash?
OK.
And so by changing the direction of this wind, this air foil, which is the actor changing the direction
of the wind, will receive necessarily a lift a force as a consequence, right?
You simply cannot change the angle of the wind without reacting to it.
And this is where Newton's third law comes to play, because because of this difference in direction,
there's necessarily a left force, OK?
And so the idea here is that this graph indicates how much these lift changes as a consequence of the
angle of attack.
All right.
And note that this is not the left, but rather the coefficients of lift.
However, the idea here is that if this angle of attack is around five degrees, we will have a certain
amount of lift.
OK, if we increase this angle of attack to 10 degrees, which would change would rotate these air airflow
in right, then what we would experiment is a higher lift.
And if we continue to increase more the angle of attack up to 12 degrees, 15 degrees, then what we
do is we enter to a condition which is known as stall, in which the it is not sustainable to continue
to increase the angle of attack and expect an increase of the left.
OK.
This is a direct consequence of the turbulence that the turbulent flow which appears downward.
OK.
And so.
Key thing to take into account the angle of attack is important in terms of generating lift.
Yes.
OK.
The difference in angle of attack has a direct effect on the lift.
Now the biannually effect.
OK, let's first focus again on this graph, and I just want to make one clarification.
Notice that at zero degrees of angle of attack, the lift is not zero.
The lift is actually it's a certain amount.
It's not that high, right?
And five degrees, it would be higher, but it's not zero, either.
Why is it that if we reduce this angle of attack to zero and we have the airfoil aligned with the wind,
we continue to perceive lift.
And this is one of the most important questions, OK?
And so what I would do, what I would like is for you to understand one thing.
When we were talking before about the geometry of the airfoil, we mentioned the Timberline right as
a way of designing these airfoil in this type of geometry.
However, my question would be, Well, why do we really need any type of Kimberlin or why do we need
this geometry in this shape, right?
Why not just make it symmetric?
Why not just cancel the difference between the Chamberlain and the code line and just have like a symmetric
airfoil?
And this is the clue.
By having a cable line, we are able to produce a certain lift even at zero degrees of angle of attack.
So in other words?
Even if there's no angle of attack, we continue to have a lift.
And this implies that we need a different explanation for this amount of lift at zero degrees.
And this is where the newly effect comes into play.
OK.
Intuitively, the most important thing to take into account is that the geometry of this cable line,
right, which makes these air fall in this complex that has these complex upper surface, right?
What happens is that the air.
Or the wind is moving right, as you can see here, but you are forcing the direction of the wind to
go down.
And this would actually implies is that, you know, the wind will try to keep its direction.
He is not trying to change his direction, but it is forced to change its direction because of the convex
geometry of the upper surface of this iPhone.
Therefore, what will happen is that we will have a suction over here, OK, the pressure will be very
low.
This can be shown of the hill, so imagine that you go to a laboratory and you want to conduct some
experiments with your iPhone to see how the velocities around the Airfoil behave and also the pressure.
This would be the velocities.
OK.
And this would be the pressure that you will identify in the laboratory.
And the first thing you, you ask yourself is, well, you know, it seems like we have this high pressure
over here, which is indicated by these arrows, which are moving towards the F1, right?
This implies a very high pressure wells on the part above the upper surface.
We have low pressure.
And not only is it low pressure, but it's very low pressure in the sense that you know it's higher
in magnitude.
Right?
The suction here, the reduction in pressure here is higher in magnitude.
The high pressure that we perceive here.
So in other words.
Even if, intuitively, the this works as a way to understand how the airfoil is capable of generating
lift because the wind pretty much crashes into the for it right and down washed in this direction,
perhaps a better explanation for it is that actually the wind is moving.
Tries to keep its direction, but because it's forced to go down towards the airfoil, it receives all
experiments a lift.
OK, so this is important.
This is an important thing to to note again.
So because of the change of direction that he's forced by defining this cable line, which produces
this convex geometry on the upper surface, what ends up happening is that there's a lift production
because of the suction of this lower pressure over here.
OK.
So, Bernoulli, why has been really important?
Well, the idea of Bernoulli effect is that.
There's always a relation between, you know, the flow.
Either the wind particles over here, the wind particles over here or the wind particles interacting
with the body.
You can make a model in which no viscosity is considered.
No thermal variations are considered OK.
It's a simple model in which we are trying to understand how the velocity changes around the airfoil
and how the pressure is determined by the A4 in geometry.
OK.
And what we see is that if we want to the laboratory, we would experiment this difference in velocity
from the upper surface and the lower surface.
And this difference in pressure on the upper surface and lower surface and the newly effect.
What it really implicates is that the some of the pressure plus one half of the density time is the
velocity of the flow squared.
This for any particle wind particle over here is constant.
Either this particle over here, all these particles over here, OK?
Considering the assumptions mentioned before.
So what ends up happening is that there's a direct relation between what an inverse relation right between
velocity and pressure.
And you can see this when comparing these two graphs.
For instance, they take this point this wind particle black one over here, OK?
It slows down over here, and the pressure is very high.
So what this means is that because the pressure is very high, the velocity must be very low.
The particle is moving very slowly over him, whereas in the opposing case, these particles are moving
very fast.
Why?
Because the pressure is very low, because we are experimenting this suction behavior over here.
OK.
In other words, this geometry, this complex geometry over here forces the particles to accelerate.
And because they accelerate, it implies there is a lower pressure and having a lower pressure implies
that they will be left OK.
And another way to think about it is that the pressure, the difference in pressure between the upper
surface and the lower surface, if you compute the difference in pressure, you will end up with the
lift.
So the lift to some extent is nothing else but the difference in pressure between the upper and the
lower surfaces.
OK, so my question will be what if instead of having this Kimberlin, we have a symmetric profile,
right?
Airfoil?
Well, in that case?
You wouldn't be you wouldn't notice the change in velocity in the way that we notice it here.
OK?
We notice it because there's a cable line.
And another thing would be what if we just drew the cable line in the opposite direction?
Right?
Like, just have these airfoil, but we geometry make it so that it's in reverse.
Kind of.
Well, what would happen in that case is that the velocity distribution would be inverse.
OK.
So.
I hope this is clear to variables angle of attack, which relates just the angle with respect to the
wind, and this generates this profile between the left and the alpha.
Also considering the stall conditions and the biannually effect.
Which is simply the fact that by having this geometry, we increase.
We have some lift only because of the fact that we have a cable line.
All right.
So the cable line directly links to this initial amount of lift.
I hope that that is clear.
All right.
Again, if you have any doubts, if you want some more clarifications, just let me know.
It's always a bit difficult to explain this topics and for sure, just like.
Be patient in the sense that one does not simply learn fluid dynamics and aerodynamics in just 10 minutes.
OK, like you said, you have to grasp it.
I would suggest also, if you go through other sources over you look at you look up and Google for similar
ideas, then that will start to form and you will grasp that with more conviction.
OK.
And so I would really encourage you to do so.
OK, another thing to take into account is that the the way in which we calculate the lift and the track,
all right, can be related to this formula.
And basically what we're taking this one half of the density times, the square of the velocity of the
flow around the F1 times, the surface of the wing, which is capable of generating the lift.
And multiply that for a coefficient of light of the lift.
OK, so the lift coefficient increases with the angle of attack, and it's also different to zero at
zero degrees, right because of the cable line.
Right.
And in the same way, we could calculate the drag of that wing.
OK.
Considering the surface of the wing, I've been asked a few times this and what I mean by the surface
of the wing.
And what does what this means is taking the code line.
OK.
And multiplying it by the length of the wing, OK, and considering, of course, if it's an elliptical
wing, you should take into account the surface of an elliptical wing and so on.
OK, so the surface, you know, is really related to the total surface of the wing, which is producing
lift, right?
I hope that this class is clear again, as always, these are some pretty difficult topics, but I'm
sure you'll get through it and you'll understand fine, OK, so yeah, with this, we can move to the
next class.