Hi, everyone, and welcome to this new class and this new section regarding flight mechanics, in this
case, we will be studying a bit of the ideas and the fundamentals of stability of an aircraft.
So let's start by defining what is the center of gravity.
OK, most of you, I guess, already know, but it's kind of an important concept.
So just checking, OK, this center of gravity is actually defined as the average point of all the mass
distribution of a given aircraft.
OK, so you would have the tail, you would have the cockpit, the different passengers and cargo and
all of that.
And if you add all these masses, you would get a center of mass.
OK, an overall geometric gravity center.
OK, now the limits for the center of gravity must always be met and defined in the flight.
What I mean by this is that you cannot consider a center of mass which goes further to the back of further
to the to the start of the of the aircraft, because if that were to be the case, the aircraft might
become completely unstable.
OK, so if you are, for instance, allocating different passengers in an aircraft and there's not a
lot of passengers, you cannot consider putting them all on the on the front, OK, on the back, because
that would that would stabilize the aircraft, possibly due to the position of the center of mass.
So it is a really an important concept to take into account.
And pilots and and all the staff have to are required to check with a flight manual all the allocations
of their passengers.
OK, this is important.
Stability depends on the allocation of the center of mass.
OK.
The center of gravity, as I mentioned.
So, as we said, passengers must be seated in a specific way.
Now, let's define another concept center of pressure.
This is a really interesting topic, which is well discussed in all papers regarding aviation.
OK, and regarding the stability of aircraft.
And it's basically the center or the position at which all the force, all the lift that is produced
by the wing can be considered to be applied to.
OK, so the idea, as you can imagine, is that if we have a big wing, we would have different amounts
of lift on different points on top of the wing.
OK, but as an overall as a kind of an average, we can consider just one point and the total amount
of lift of that wing.
OK, on one specific position.
Alright, this is a quite interesting topic because it is kind of a simplification, as you may understand,
but it is quite useful to understand this in terms of stability of the aircraft.
So usually it should be around one fourth of the cord of the wing.
OK, and this also depends on.
So what I mean with it, the idea is that the cord is that the line which unites the front of the wing
and the end of the wing.
OK, so if I say it should be on one fourth, this means that it should be allocated quite on the front.
OK, as you can see, two fourths will be in the middle, three fourths over here.
Right.
So one fourth is over here.
The idea this can be reduced mathematically and is usually approached for many problems.
But the idea is that this kind of C.M.A all kind of very, very close to one fourth of the cord.
OK, this specially depends on the on the geometry of the wing itself.
OK, depends on the camera.
So and actually the form, the geometry of the wing right.
What s stability depends on the location of the center of pressure.
And it actually depends by comparing the center of pressure, the position of the center of pressure
with the center of gravity.
So basically you have to compare one to another.
Let's say this.
OK, so here we have some illustrations of what this would look like, OK, let's see, the center of
gravity should be located closer to the front for stability purposes.
OK, this is kind of a definition of stability.
I'll just take a minute to talk about stability.
But before I want to, I want to kind of relate what the tail and the left actually do.
OK, so first of all, in an aircraft, as we mentioned before, we need an equilibrium of forces.
We need the lift.
We need the weight.
We need the drug and we need the thrust.
Right.
So all these forces should be completely equilibrium.
Now, the aircraft should also consider an equilibrium in terms of movement.
OK, what I mean by this is that a moment I don't know if you know this, but a moment is defined as
the force multiplied by the distance of the force, the perpendicular distance of the force, respect
to the center of rotation.
So.
As I said, our rotation off the aircraft actually takes place around all respect to the center of gravity.
So this is why the center of gravity is so important.
You can imagine this aircraft OK, moving in anyway, but respects to the center of mass.
OK, now the idea here is that if we need moment equilibrium, we need all the moments to compensate
one another.
OK, the same way that the lift and weights had to be the same so that the some of the lift and the
weight would be zero.
Now what we need is the product of L times the distance of L..
OK, which I defined as the L should be actually equal to T alright.
Multiplied by the distance of T.
So first of all, you may notice that T has to be defined in the negative direction, OK, because the
left is defined in this way and the lift would actually imply that the aircraft moves in this direction.
However, if we need to compensate for this movement because of the lift, OK, we have to compensate
it with a tail force.
OK, a tail lift, which actually goes in the opposite direction.
Why is this work?
Because if you had the tail going up also, you would have a very severe movement of the aircraft.
You would see that it is completely unstable, you see.
So you need one to compensate the other.
And the second idea here is that the lift is very big.
OK, it is much higher than the than the tail in the lift on the tail.
Why is that?
Well, the idea is that you have to compensate for the moment.
OK, so l times D.L. should be the same as the Times.
And as you can see in this image, D.L. is very, very lower compared to DETI.
OK, so in the end you end up with a lift, which is very big an idea which is quite small and a T which
is kind of small.
OK, but our duty, which is very large compared to the other.
So this is kind of what you need to know in terms of of the moment.
OK.
Let's see now how how this actually affects stability of the aircraft now.
Depending on the position of the center of gravity, our aircraft will be stable.
OK, so to understand this, what I propose is that you actually look for this over here.
OK, imagine that you have a point, all right.
Or that you or I don't know, this could be a ball, could be a heavy ball, could be some metal ball.
And you're holding the ball from this point.
So imagine your fingers over here kind of supporting the weight of these ball, OK?
You can imagine that.
And this works as a pendulum.
OK, so you could actually move the ball and it would be stable regarding the center of rotation over
here.
Right.
It would move this way.
Now, imagine that you have that you are actually.
You know, you're.
The ball is over here on the top and you're holding the ball on this point, which doesn't really make
sense, does it?
Right.
OK, so the idea would be.
Considering that this would be a solid beam, OK, in this case, you would actually have completely
unstable movement.
OK, and why is that?
Well, the idea would be that if you're trying to hold this ball from below, if you try to move the
ball a bit, the ball will completely fall and move to the other part.
Right.
And move to the lower part, OK.
And would start rotating here.
And why is this?
Well, this is the basic of stability.
So it depends on where you're holding the ball and where the ball is actually moving.
This would be completely unstable.
This element over here, as you can see, as you can imagine.
OK.
And this one would be stable because it would rotate, but it would be in you know, it would be kept
in a certain range of angles.
OK, so it will rotate, but it would be stable and this one will be unstable.
OK, so why why am I talking about this?
Well, the idea is that the position of the center of mass is actually where we would be actually calling
the ball.
OK, so we would kind of imagine that we we are calling the aircraft in this point over here.
So.
If we have a perturbation of the lift, for instance, so if the lift were to increase a bit for one
moment, you can see easily that the aircraft would actually move.
But since the center of mass is on the front, right, respect to the velocity, OK, respect to the
velocity that would be coming over here, you can see that automatically kind of stabilize or right
over here.
So this is the same idea as this one over here.
OK.
In addition, as you can see, the lift in the tail would be would have the different directions, OK,
because we have to compensate the aircraft and if there's a perturbation in the lift, the most possible
one, probably the tail will automatically compensate for that.
OK, now let's see the other case, the case that we have at the center of gravity actually positioned
farther away from the front of the vehicle.
OK, then the lift.
OK, so let's say now the lift increases a bit.
So if you imagine that you're holding the aircraft on this point, what would happen is actually the
aircraft would start to rotate and unless the tail can provide stability, which probably wouldn't,
OK, the aircraft would just be completely unstable.
OK, just move around in the same way that we defined this over here.
Right.
So imagine taking the aircraft on this point, holding the aircraft in this point and actually putting
an additional force to this so the aircraft would be completely unstable considering the velocity.
Right.
It's pretty clear.
I think if you have any doubts regarding this, just let me know and I'll make sure to send to you some
more examples and ideas on stability, OK?
Because it is an interesting topic and it is very important, of course, for aircraft that they are
stable.
In fact, if you wanted to know.
There's also a military aircraft which are designed for them to be unstable, naturally unstable.
And this is because it may improve the amount of ability of the aircraft itself.
So sometimes it may be interesting for us to make the aircraft and stable.
But as you can imagine, just as in terms of a commercial aircraft, of course, we needed to be incredibly
stable.
OK.
What else?
Yeah, so if we do find the center of gravity, as we mentioned, after the sense of pressure, OK,
then the acquisition naturally unstable, even though the tail may try to stabilize it, but the aircraft
is unstable.
OK, so this is what you need to know.