TINA SRIVASTAVA: All right. So as we discussed,
we're going to start off with the most basic question--
how do airplanes fly? It's a very critical question. I think everybody should
know the answer to this. Going back to the
comic that Minachi had with Calvin and Hobbes, and
not knowing how airplanes fly, and thinking that it's
magic is not the way that any MIT student should be. So we're going to cover
how airplanes fly. And we're actually
going to go beyond what the FAA requires you to know. Because frankly, you should
know how airplanes fly. So just so that we have a
common vocabulary with which to discuss, we're going
to talk a little bit about airplane parts. So here in my little
airplane, it's kind of a model there so you can see that at the
front you have your propeller. And so the engine and the
propeller in this little plane is up here at the front. Who knows what a fuselage is? Just shout it out. AUDIENCE: The middle part. TINA SRIVASTAVA:
The middle part. The body. It's where the passengers sit. Yeah, so that whole middle
part where people sit. So if you're thinking
about a big jet engine, it's where all the rows of
seats are where everybody sits. That tube in the middle
is called the fuselage. And the wings stick
out the sides. So the middle part
is the fuselage. And then one thing
that's interesting is the tail actually has
a lot more components. People kind of casually
refer to it as the tail. But there's a vertical
part that comes up in the back of the
vertical part of the tail can actually tilt side to side. And then you have a
flat horizontal part. And that actually has a back
part that can go down and up. And so we're going to talk
about what all of these are. So the back vertical part
when it goes side to side is your rudder. The flat part is your elevator
that you can move up and down, allows you to
control the airplane. We also have, of
course, the wings. Sometimes, there are struts
that support the wings. So they go from the wing
down to that fuselage. And then you have landing gear. In this case, you have these
wheels down at the bottom. We're also going to talk to you
during this course about sea planes. So they have slightly
different landing gear. But this is a good
place to start. The other thing that
we need to talk about are just the main four forces
that are on an airplane. So they're pretty
straightforward. So the force going up is lift. And that force is opposed by
the downward force of weight. And then when you're moving
the airplane forward, that's thrust. And it is opposed by drag. So what we're
going to talk about is that in order for
an airplane to go up, the lift has to exceed the drag. In order for the
airplane to go forward, the thrust has to exceed the-- excuse me. The lift has to
exceed the weight. And the thrust has
to exceed the drag. So those are the
main four forces we're going to be
working with today. So now I'm going to spend
a little bit of time over here on the blackboard. AUDIENCE: Hey video folks, is it
easier to use that blackboard? TINA SRIVASTAVA: They
said this blackboard. AUDIENCE: This one's better? TINA SRIVASTAVA: Yeah. AUDIENCE: These are
all chalks of color. TINA SRIVASTAVA: Yeah,
fancy-colored chalk. All right. AUDIENCE: Chalks of color. TINA SRIVASTAVA:
Chalks of color. All right. So I will preface the discussion
about lift with the fact that there are a lot of
theories of lift out there, some of which are wrong. So if you spent some
time googling lift before coming here, you
might have actually found a couple scenarios that
are completely false. So we're going to
focus on what's true, but I will cover least one
of those false theories to make sure you guys
don't get hung up on that. So in order to talk
about it, we're going to think
about an airplane. And we're going to do a
cross-section of the airplane. So if you took a saw,
and you cut off the wing, what are you left with? And I'll do it this way. So if you cut off the wing,
at the front of the wing is the leading edge. The back of the wing
is the trailing edge. If you did it-- if you cut that
off, what does it look like? So it looks like this. And this shape is
called an airfoil. And we'll get into
the specifics later. But first we'll just-- we'll talk about a simple way
to understand how lift works. So if this is the wing,
and you have air coming in, the air is pushed down by
the shape of this wing. So that means is as air flows
by, it gets pushed down. Now what is air? Air is not nothing. Air has molecules. It has mass. So if you think about
conservation of momentum, this is I think the easiest
way to think about lift. So conservation of momentum, you
have a bunch of air molecules. And those air molecules
are pushed down. So you have mass
being pushed down. So if mass is being pushed down
for conservation of momentum, something must be pushed up. And that's the wing. So that's the easiest
way to think about it that if you're deflecting the
air downward in order to have conservation of momentum,
the mass of the wing is lifted upwards. We're going to break
that down, but I think that's a good place to start. I'm just going to take
one moment to talk about an incorrect
theory of lift. So let me emphasize it's wrong. One of them is called
equal transit theory. Has anyone heard about this? Getting a lot of head nods. It's wrong. Equal transit theory,
which is incorrect, says that basically a molecule
of air that's coming over that starts over
here at the front has to go around the bottom and
meet the tail at the same time that a molecule that
goes over the top has to meet it at the back. There is no physical
principle that says that. It is false. And in fact, we have
measured that they don't. The molecules that
go under the bottom of the wing versus
the top of the wing don't actually reach the
end at the same time. But in this false theory,
equal transit theory, they say that you have to reach
the bottom at the same time. They also say that there
is more distance basically to cover because of the
shape of the airfoil. So in order for the
molecules going over the top to reach
at the same time as the molecules over the
bottom, they have to go faster. And so since the
air is moving faster over the top and the bottom,
that's what creates lift. So that's false. And there are many
reasons why it's false, the biggest one being that there
is no physical principle that says that two molecules starting
at the same time, one going over the top and one
going over the bottom, reaches the end
at the same time. That's just not true. And we'll show you some more
diagrams that show in fact it doesn't happen,
that molecules don't reach at the same time anyway. So please despite that being
very widely propagated, that is not true. And please don't spend
time on that theory. So let's focus on what is
true, how does it really work. Actually, let me give you one
more reason why that's false. The real reason that
equal transit theory is trying to tell you
that that generates lift is that because of the shape
of the airfoil, the shape of the wing, that's why the
distance that it has to travel is different over the
top versus the bottom. But one reason that's
wrong-- can you pass me that paper airplane please? Who has built a paper
airplane before? I see at least two people
who didn't raise their hand. Do we need to do
a class exercise? If you have not built
a paper airplane, it's really important that you
do just as a general childhood experience. Here's a paper airplane. Thank you, Minachi,
for building it for me. If we took this paper airplane
instead of this fancy airplane, and we did a cross-section
of this wing, what would it look like? Yes. You demonstrated with your
hands, but shout it out. AUDIENCE: It's going to be the
same at the top and the bottom. It's just a piece of paper. TINA SRIVASTAVA:
Yeah, it's going to be the same at the
top and the bottom. It's just a piece of paper. Exactly. It's just like a
little flat rectangle. So instead of this fancy
shape that you have here-- we're going to use
red for wrong-- it's like a little rectangle. That's what a paper airplane's
cross-section of its wing looks like. Well, surprise. Surprise. As you said, it's the same
at the top and the bottom. So the distance
that a air molecule would have to travel over
the top and the bottom is identical. So really, the equal transit
theory completely falls apart. Yet, a paper
airplane still flies. So why is that the case? Again, remember
the actual reason is that if this paper
airplane is inclined, it is pushing air down. So air that's coming
up is bumping into it and being pushed down. And therefore, as you
deflect air molecules down, conservation of momentum--
the wing is lifted up. So now we're going to break
this down in a little bit more detail. And I'm going to go back
over here to the slides. So one thing that's
important, as I said, a really detailed
mathematical description is not really necessary to
fly a plane or become a pilot. The FAA doesn't require
some of this detail. But it is important to
know it to the extent that it helps you control
the airplane and fly it. So here's a good reference
in terms of that. But one of the biggest things
is just that for lift, you have to increase that
downward momentum of the air. And airfoils are--
the shape which is called an airfoil
is a type of shape that is very efficient at increasing
that downward momentum. Now, who knows what
Bernoulli's principle is? Who's heard of Bernoulli? Good. Everyone's heard of Bernoulli. Can anyone articulate
Bernoulli's principle? Yes. AUDIENCE: I think it's like
p plus one half of mv squared equals constant the
difference squared. So when the pressure
goes down somewhere, the speed of the
particle has to go up. TINA SRIVASTAVA: Yes. Absolutely. Absolutely. So what Bernoulli
observed was the case that when there is a
decrease in pressure, there's an increase in velocity. That's the core concept
that you have to understand. And so when we think about an
airfoil, when we see that-- and I'll draw another
airfoil for us to talk about. When we have air
that's moving very fast over the top
of the wing, that means an increase
in velocity means there's a decrease in pressure. So this is the extent
to which you really need to know it for the FAA exam. So which statement relates
to Bernoulli's principle? I'll let you read those answers. So is it A, B, or C? Shout it out. AUDIENCE: C. TINA SRIVASTAVA: C. Good job. Well done. We're going to discuss a
little bit more details though. In order for any wing
to generate lift, it has to be in a fluid. If this airplane was in
space or in a vacuum, and there wasn't any
fluid passing by it, then there wouldn't be any
molecules to deflect downward. And therefore, you
couldn't push the wing up. But the fluid doesn't
always have to be air. You might see similar
designs underwater for underwater drones. It just has to be a fluid
that's passing by the object. So when you have this airfoil in
a fluid, when the fluid is not moving, when it's stationary,
then all of the fluid is exerting pressure
on the airfoil. So you get all these
little normal forces exerting pressure. When the fluid is not
moving, and the airfoil is stationary in the fluid,
then all of those pressure forces, all those normal
forces or forces perpendicular, sum to zero because
there's no net force. It's just sitting in the fluid. But when that fluid is
moving, it generates a force. So that's the force it
generates generally when the fluid is moving forward. And a force is a vector. So it has direction
as well as magnitude. So there is a vertical component
and a horizontal component to that. So we call the vertical
component the lift. Does anyone know what we call
the horizontal component? AUDIENCE: Drag. TINA SRIVASTAVA: Drag. Good job. Now, here's a dumb question. What part of the
aircraft generates lift? Yes. AUDIENCE: The whole aircraft. TINA SRIVASTAVA:
The whole aircraft. Good job. So a lot of people might
be under the misimpression that it's only the wings
that are generating the lift. Well, actually, the whole
aircraft is generating lift. And it's not just aircraft. Any objects that are
moving through fluid have this phenomenon. And sometimes, it's
not a good thing. So what is this a picture of? A race car. Come on, guys. I know we're in an
airplane class but-- who can tell me what is
that thing sticking up at the back of the race car? AUDIENCE: A spoiler. TINA SRIVASTAVA: A spoiler. What's a spoiler? AUDIENCE: It spoils the airflow. TINA SRIVASTAVA: It
spoils the airflow. So when a race car is
driving on a race track, and it's going through the
air-- the fluid is air-- actually just the race car
itself is generating lift. And that lift can cause the
race car to kind of lift upward and not be as much
in traction with the ground. And when you're a race car, and
you want to go really, really fast, you want to have
very good traction with your wheels
against the ground so you can go as
fast as you can. So the reason that you
have a spoiler at the back is actually to counteract the
lift that's being generated by the race car. So it's not just airplanes
and wings that generate lift, but really anything
moving through a fluid can generate lift. So we're going to talk a
little bit about equations. Don't get scared here. We'll just dive into
it step by step. So we have f equals ma. Hopefully, this is
not the first time you're hearing
about that equation. So can somebody just shout
out what is acceleration? AUDIENCE: Change in velocity
with respect to time. TINA SRIVASTAVA: Change
in velocity over time. Very good. So velocity again
is also a vector. So velocity being a vector has
both a magnitude and direction. So you can change
the velocity either by changing the magnitude
or the direction. In the case of an
airfoil, we're changing the direction of the air. So the air has velocity. It's coming in. We're changing the
direction of that air. And that's generating the lift. So because we changed the
direction of the velocity, that creates a force. That's our force f. So f is actually
here representing the rate of change of
momentum of pushing those air molecules down and
generating a force, creating the airfoil
to be lifted up. So that's why we discussed
again that equal transit theory is false. Because even an paper airplane
with a completely flat cross-section of
its wing, as long as it's inclined upward
such that the air is being pushed down will fly. So here's another question. Which moves faster--
the wing through the air or the air past the wing? Wow, you're very quiet. Which moves faster? Yes. AUDIENCE: The air over the wing. TINA SRIVASTAVA: The
air over the wing. We have one for the air over
the wing is moving faster than the wing through the air. Anyone else? Yes. AUDIENCE: Depends on where on
the wing you're talking about. TINA SRIVASTAVA: Depends
on where on the wing you're talking about. Yes. AUDIENCE: Because
if you define air to be the air that's
immediately next to the-- that is in contact with
the wing or the general air as in the air space. TINA SRIVASTAVA: Yes. AUDIENCE: If it's the air
that's in contact with the wing, they're going at the same speed. TINA SRIVASTAVA: So it
depends on which air you're talking about. True. Actually, what we're discussing
is about frame of reference. So depending on your
frame of reference, if your frame of
reference is the airfoil, you can take it to be that
the airfoil is stationary. And you see the wing to
be stationary and the air to be moving past you. If your frame of
reference is out here, you might see the air to be
stationary and the airplane to be moving through it. So depending on what your
frame of reference is, you can actually have
the identical result. So the answer is actually
that it's the same. So depending on your
frame of reference, it's exactly the same the
speed of the air moving past the airfoil versus the
airfoil moving through the air. And the reason-- so does anyone
want to dive more into that? Are you guys familiar with this
concept of frame of reference? Yes. A lot of head nodding. Great. So the reason that's significant
is that as we learn about lift and as we study
this, we actually could create a whole bunch
of different airfoils, and then build airplanes, and
then fly them through the air, and measure them. But that's very expensive. So instead, what we do is we
basically take the airfoil. And we put it on a
stick, and then we put it inside a wind tunnel. Has anyone been
in a wind tunnel? Got a couple people. Hey, we saw that like over 60
of you guys were aero-astro. You need to go to your
Wright brothers wind tunnel. It's being upgraded
actually right now over in your building 33. So because it's
exactly identical, the air moving past the
airfoil or the airfoil moving through the
air, it's a lot cheaper to put the airfoil on a
stick in a wind tunnel, and then shoot air past it,
and then do your measurements rather than continuing to take
off airplanes and fly them through the air. So we're going to be talking
about that a little bit. So the question is, what
factors affect lift? So there are a lot of
things that affect lift. So one has to do with
the object itself. So I was talking about
the shape of the airfoil. So we talked about
a different shape, which is just a
flat piece of paper or a rectangle as a shape. You can have a
more slender shape. And the way that
you modify the shape can significantly
impact your lift. So for example, one
of the modifications can be back here at the end. If you made your
airfoil longer like this and point even
farther down, then it would push the air in a
slightly different way. So that would affect the
lift that that airfoil could generate. It would also affect the
drag that it induces. Another aspect is just
the size of the wing and the shape of the wing. So we see a lot of
different kinds. So this is a big
rectangular wing. In a jet, you might
see a swept wing. There are different
types of shapes. And then there's
also just the area. So regardless of whether-- if this is your-- if you're looking
down at an airplane-- so this is kind of
the broad, flat wings, or you could have very
thin, skinny wings that you might see on a glider. Regardless, there is a
surface area of the wing. That area also impacts
the lift quite a bit. And the aspect ratio as we
just discussed in the shape can affect lift. The other thing other
than the object itself, other than the
wing itself, motion can affect lift, so the
velocity of the air. And the very
importantly is what's called the angle of attack. So it's the angle with which
this airfoil has to the air. So if you had one airfoil
that was pointed up like this versus one, the same
one but it was not tilted up, this airfoil would be having a
higher angle of attack or angle to the wind than this one. Now, this might seem like
a very fancy description, but who has been in a car
driving down the highway, and you stuck your
hand out outside? And if you tilt your
hand up a little bit, you'll see that the wind
kind of pushes your hand up. And if you tilt it down,
your hand pushes up. And you kind of glide
your hand out the window. So I'm getting a
lot of head nods. So that's really all
that angle of attack is talking about that if
you angle your hand up, it gets pushed up a lot more. If you angle it down,
it gets pushed down. That's the angle of attack. And we're going to define
it more specifically when we talk about the
terms associated with an airfoil in
the shape, but it's good to get the
general concept first. And then another
factor affecting lift is the air, the fluid
that it's in, so the actual mass of the
airflow coming around you. So there are a lot
of aspects to that. We talked about whether
you're in water, whether you're in air, or
the density of the air. Another component of that
air is the viscosity. Does anyone know
what viscosity is? Yes. AUDIENCE: Resistance to flow. TINA SRIVASTAVA:
Resistance to flow. The way I like to
think about it is if you've ever baked brownies,
and you have your mixing bowl and your spatula in
there, and if you just have the water and
the oil and eggs, and you're mixing it around,
you can mix pretty quickly. And it doesn't stick to
the spatula that much. But if you were mixing
molasses or once you get all that brownie batter in
there, it's harder to do it. And it sticks to the spatula. So that's what we're
talking about when we're talking about viscosity. So it's the tendency
for these molecules to stick to each other and
to stick to the object that's moving through them. So with the case of the
airfoil, we're talking about-- and we were discussing this
just a moment ago about which air were we talking about. So some air that
might be very close might kind of stick
to that airfoil or stick to the wing versus
just moving smoothly past it. So viscosity has a big impact. And then compressibility
also affects lift. So the compressibility
of the air-- did I turn off my mic? So certain types of
fluids are compressible. So you could take
a balloon of air. And you can move it
into a cold environment and have it shrink or
in a hot environment and have it expand while
having the same amount of mass inside the balloon. So I'm getting a
lot of head nods. So that just shows the
compressibility of the air, whereas some types of
fluids are not compressible. They're incompressible. And they affect lift
in a different way. So although I've told
you all these things that affects lift, one
thing I will admit to you is that calculating lift is
difficult. It's very difficult. In fact, we don't really
know how to do it properly. This is a snapshot
from Wikipedia of all the different
theories of lift. So there are a lot
of different ways that people go about
trying to calculate lift. And it turns out that
it's very hard to do. So one that you see up
there is Navier-Stokes. So Navier-Stokes is
a set of equations that does a really good
job of predicting lift. And it really takes into
account a lot of things. It takes into account
conservation of energy, conservation of mass,
conservation of momentum, viscosity, even a lot of things
like thermal conductivity and a whole bunch
of considerations. But the problem is that solving
those equations is very hard. We try to use supercomputers to
estimate every little aspect. And it's very difficult to do. And we're not
really able to solve those equations to determine
precisely what the lift is going to be. Let me talk about some
of the limitations that we have in solving
these equations. So first of all, it
has to do with how the air flows over the wing. If the air is moving very
smoothly past the airfoil, then it's very easy to come up-- not easy, but it's
easier to approximate. We can predict what a particular
air molecule is going to do. But as you see there, when
it starts spinning around and becoming turbulent-- so if you start seeing a
particular air molecule that's moving around, and becoming
turbulent, so not doing laminar flow but turbulent,
and moving around, and bumping into other air molecules,
then predicting what that molecule does and
what all the molecules do around it become very, very
difficult. In fact, we have a very hard
time doing that. And so instead, we
basically assume that that doesn't happen. And we impose some
limitations or conditions on the airflow which
are not actually true but help us with
approximating lift. So one of those is
the Kutta condition that you see at the bottom left,
which is this smooth flow off. So basically, you say that
none of this turbulence is happening. And the air moves
very cleanly off. And you also have a couple
other specific requirements such as that no air
molecule from the top comes over to the bottom, and
no air molecule from the bottom goes around to the top. And you just assume that
they move smoothly off. And so that Kutta
condition is actually very helpful in
approximating lift. We also make other assumptions
that there's no viscosity or that the fluid
is not compressible. Sometimes, these
assumptions are appropriate. And sometimes, they're not. Another thing that's really
critical about our ability to estimate lift is that as
I've been talking to you here on the blackboard, I have
talked about a cross-section, that you just-- you cut off the wing. And you're only looking
at one cross-section. So since we're talking
about a cross-section, we're talking in
two-dimensional space. Well, we can actually
do a pretty good job of estimating lift in a
two-dimensional environment. But the fact of the matter is
wings are not two dimensional. And the wing comes
out into the classroom and back into the blackboard. And to estimate actually
how all these air flows work at the edge of the
wing is very difficult. Has anyone heard
about tip vortices? Couple head nods. So we have a picture
there that shows a jet to just show a
little bit about what the air does when it comes off
the edge, the end of the wing. We're going to talk about
tip vortices a little bit. But the problem is that
it no longer is adhering to all of our conditions. Now, we don't have smooth flow. We definitely have
turbulent flow. We have spinning flow. And we have air molecules
hitting other air molecules. And it becomes extremely
difficult for us to model all of
those air molecules. We really can't do it. So going from two dimensions
to three dimensions is really a limitation
of a lot of the equations that we have to
approximate lift. So what do we do? Well, first of all, we go back
to our two-dimensional surface. And we talked about all
of these normal forces, so when you have all
the fluid going past, and it has pressure,
and it's supplying all these forces perpendicular
to the airfoil all around. So how do you approximate lift? Well, you say, oh, that's fine. You just sum all
those forces around. Well, that's great if you know
what all of those forces are, but it's not great if you don't
know what all of them are. So what is the
solution that we-- what we do? Basically, we
calculate what we can, and then we measure the
rest experimentally. So in this equation of lift,
for example, so we have L is for lift. Some of the other terms
that you have there-- rho is the one that
looks like a p. So rho is talking
about the air density. You have velocity. And A is the wing
area we talked about. And then we have this fancy
little symbol there C sub L or the coefficient of lift. And basically, we
say that I don't know how to come up
with characterizing all those complications
about viscosity and some of the effects like
that have to do with turbulence and shock waves, Mach
number, Reynolds number, all these types of things. And so we say we'll
measure what we can, and then we'll-- or we'll
calculate what we can, and then we'll actually, in a
wind tunnel where we put this guy on a stick, we'll actually
measure the coefficient of lift. And that's how we
really calculate lift these days is using
a lot of measurement to inform what's actually
happening because it's just very complicated. AUDIENCE: Tina, that
velocity is squared, right? So if you go twice as fast, you
get four times as much lift. TINA SRIVASTAVA: That
is the relationship. Absolutely. And the other thing
that's really important is that that coefficient
of lift is measured for a given angle of attack. So we talked a little
bit about angle of attack with your hand
outside the window. So let's get into defining it
a little bit more in detail. So in order to describe it,
I have to come up with a few more terms that have
to do with the airfoil. So we talked about
the very front of the airfoil or
the front of the wing is called the leading
edge, and then the back is the trailing edge. And we talked about the
trailing edge a little bit when we were talking
about the Kutta condition that no air molecule-- we're
assuming no air molecule can cross the trailing
edge to the other side. So then the camber is in there. So that's just talking
about really representing the curvature of that
airfoil and then a chord line that goes in between so you
can measure how that is. So try and do your
little zoom in fanciness that you were doing. AUDIENCE: I think I set--
yeah, maybe it went to sleep. Giving up? TINA SRIVASTAVA: I'll
just point at it. So this is the chord
line of the wing. So you can see that
this is a full airplane. The airfoil is right here. And you see this chord
line going from the back to the front. Is somebody trying to
come in the door there? Great. And then we'll talk about
some of these terms. Basically, the most important
thing to think about is the angle of attack. Thank you for
checking on the door. So talking about how we
can control the lift, so some of the
things we can do have to do with the aircraft design. So we can build an airfoil. And we can talk about how curved
that airfoil is, the curvature on the top, how curved it is. We can design the wing area. When we're flying, we
can control the airspeed. And then the angle of
attack is something that you can control when
you're in the airplane by pitching down or pitching up. And we'll describe pitching
and how you control an airplane in more detail. Another thing that's
relevant is flaps. So I talked about in
this drawing right here where I added this white
part of the trailing edge that moves down, that really is
kind of similar to flaps. So when your flaps are up,
they're sort of in line with the rest of the wing. But when your flaps
are down, it's the effective thing
like pushing-- pulling a piece of your
trailing edge downward, which causes again more of that
air to be deflected downward. So it increases your
drag, but it also increases your lift because
you're deflecting more air molecules down. And then we also talked
about spoilers, for example, as something that
can, like on a car, that can actually disrupt the
lift by disrupting the airflow. And when we talked about
the four forces of flight, if you're doing steady
flight, you're not climbing or you're descending, but
you're just flying straight, that means that your
lift and your weight basically cancel each other out. If your lift is greater
than your weight, then you can climb. And if your weight is
greater than your lift, then you descend. But if you're just
flying straight, you're in an equilibrium where
those two forces cancel out. So good. I have a more detailed
diagram of angle of attack. So you can see here
the chord line. You can also see the
relative wind and same things that I drew here-- the lift and the drag and then
that resultant force vector. So you can actually
control the angle of attack in a number of ways. One of the ways that we
talked about is pitching down. So pushing your yoke
forward causes the airplane to pitch down. And it does that by
changing the elevator at the back of the airplane. We'll describe that
in more detail. But the other things that can
affect the angle of attack, you can actually affect
before you even take off. So it has to do with
your aircraft weight, for example, and the
center of gravity, as well as your airspeed
when you're flying. So here are a couple of
diagrams that show you how the lift changes with the
effective angle of attack, and then there is a
critical angle of attack. So that's when you can
keep climbing for a while. But if you get too
steep, what happens? Who knows what happens
when you go to steep? AUDIENCE: You stall. TINA SRIVASTAVA: You stall. That's right. So the air can't really
effectively go over the wing. And it starts separating. And so you're no
longer effectively pushing the air down. And you lose the lift
that you were generating. And one thing I also
want to point out here in these diagrams is you see
with these little colored lines the air that's coming in. And it's going out. And you can see
that in this case, the blue lines are
showing that the air that went over the top of the airfoil
went faster and actually got to the back faster than the
air that went from the bottom. So again, please don't fall
for the equal transit theory. So practice question. A, B, or C? AUDIENCE: A. TINA SRIVASTAVA: A. Good. So the angle of attack
is defined there. And one thing that I
would like to point out is that this is also the
case for a propeller. So your propeller also
looks a lot like an airfoil or like a wing that's
sideways and spinning around. And so also the angle of
attack for a propeller is defined basically
the same way is the angle between
the propeller's chord line and the relative wind. So let's define the
center of pressure. So it's basically
the point on the wing where the lift is centered. And so that can actually move
as you can see in this figure. Based on the angle of attack,
the center of pressure can act in a different location. And that's really important
to understand also that it's not that the
lift is always coming right at the front. Depending on where you are,
it might be pulling you in different directions. And that can affect
the maneuverability of your aircraft. And we'll get into
that in more detail. So we talked a little
bit about flaps, that flaps actually
can increase the lift that you're able to produce. But it's a trade-off because
it also increases the drag. So when in the course of
the flight, takeoff, cruise, or landing, when
do you use flaps? Does anyone know? AUDIENCE: Takeoff and landing. TINA SRIVASTAVA:
Takeoff and landing. Landing. Yeah, the reason that you,
especially on landing-- many times people use
flaps on takeoff as well. But the reason is
just that you like to have your aircraft
configured that in case you didn't take off, you
can land without making a lot of dramatic changes. The reason that you
do that is basically that by increasing your lift
but also increasing the drag, drag affects how fast
you're moving forward. And so you can actually
have the airspeed be higher with the
ground speed being lower. What it does is it allows you to
go very slow without stalling. And so that really helps
you land an airplane. So basically, it
allows you to come in at a kind of
steeper angle to land, maintaining the airspeed that
you need in order to do that. And you'll notice that there
are different flap settings. So you can either have flaps
at 10 degrees, 20 degrees, 30 degrees. We'll discuss that
in more detail. And Phillip will talk
about it in terms of performance I think as well. Thrust-- so we talked about
that forward force thrust. In this type of an aircraft,
a single engine propeller aircraft, it's the
propeller that's rotating that is really
producing the thrust. And it's really, as I
said, the propeller blades are kind of like
an airplane wing-- it's a good way to
think about it-- that are just spinning round
and round and generating lift. But in this case, it's
moving air molecules front to behind your airplane. And then although this is
also just a force, instead of talking about it
in pounds, we usually talk about the
horsepower required to drive the propeller. So let me also talk about drag. So there are a couple
different types of drag. So one drag is just what's
called parasitic drag or parasite drag. It's basically when the aircraft
is moving through the air that you get some kind
of resistance to that. That's parasitic drag, whereas
this drag is induced drag, which is the drag that's created
by the lift, so this backwards D. And so you can
see in this figure that the total drag is a
sum of that induced drag and the parasite drag. AUDIENCE: Do we also call
the induced drag just lift in an unwanted direction? TINA SRIVASTAVA: Lift in
an unwanted direction. Sure, whatever can have
you associate induced drag with lift. That's the drag created by lift. Ground effect-- does anyone
know a ground effect is? Only a couple of you. So let's talk about
it a little bit. So basically, when you're very
close to the ground within one wing span of the
ground, you actually have some of the airflow
going on with your airplane is blocked by the ground. And so your induced
drag decreases. Now, with the induced
drag decreases, it's actually the case
that your airplane can become airborne at a lower
speed than it's supposed to. So what you might
notice is that when you're on the
runway taking off-- this is probably the first
part of your flights. After you did your
pre-flight, your engine runup, you pulled out onto the runway. And you'll have
determined in advance what is the air speed at
which you should rotate. Now, that's really important. With a Cessna 172, for
example, it's around 55 knots. And you want to look at
your airspeed indicator. Because if you
just feel yourself, you might notice that
much lower, like 40 knots, that the plane has
already taken off. You're already floating. You're flying. And you might be very
excited about that. And you might want to just pull
back on your yoke to take off. Well, you won't be
able to sustain flight. And so this is what why ground
effect is really important is that you can kind of
float over the ground because you're so
close to the ground that the ground is blocking
some of the effects of the air. And so what you want to
do is really make sure that you continue your
ground roll, continue. Even if you're a
little bit airborne, stay close to the ground
until your airspeed comes up to that rotate speed, so
in this case, 55 knots, and then you pull back
on your yoke to take off. So again, so when does
ground effect happen? When you're close
to the ground-- when you're within one
wing span of the ground So let's talk a little
bit about stability. And we'll start by just talking
about the three axes of flight. So there is a
longitudinal axis, which is basically from the nose
to the tail of your airplane. And there's a
lateral axis, which is from wingtip to wingtip and
then vertical going straight through the plane. So you have the ability
to control all three of those axes. So the elevator, which I keep
talking about is like your yoke where you push it forward
or you pull it back, that allows you to
pitch the airplane. So pitch nose up,
pitch nose down-- that's you controlling the
back part of this tail, the elevator, which
allows you to have motion in this direction,
so pitch nose down. So you might hear that a lot. In case you're getting
close to stalling because your angle of
attack is getting too high, they might say, nose
down or pitch nose down. You also have
ailerons, which are out on the side of your wings. And those ailerons
control the roll. So that's rolling along
the longitudinal axis. And then your rudder, which
is at the back of the tail, the vertical part of the tail-- that controls yaw. So this is called yaw,
this type of motion. So when you're turning, you
actually kind of do a roll and yaw usually to enact a turn. There are some cases
where you actually want to have adverse
yaw or you actually-- adverse yaw means
basically you're using the yaw direction in maybe
the opposite direction at which you're trying to turn with
the roll or other angles of your plane. And so this just talks
about an adverse yaw is when you're not turning the
rudder in the same direction that you're using your aileron. And so this is where you
talk about coordinated flight or uncoordinated flight. When you're actually in an
airplane, the rudder or the yaw is controlled by your feet. So you have feet pedals
that control the rudder. And the yoke that
you're holding onto or a joystick that you're
holding onto front and back controls the pitch. And then turning it like in
the steering wheel of a car is only controlling the roll. So you actually
also use your feet for that third
direction of the yaw. So just talking about
stability in general, this isn't going to dive
into a whole diffy q discussion or anything. But just in general,
something that's stable-- so it's just talking
about like a little bowl if you have a ball in a bowl,
even if the ball gets jostled around, it'll return
to the center point. Unstable would be the opposite. So if you have a convex
surface, then if the ball moves even just a little
bit, it'll really get moved out of control. So the reason that
we talk about this is basically when you're
flying in an airplane, and you're talking
about stable aircraft, for example, the reason I really
love flying a Cessna 172, even though it's kind of
the training airplane, is that the-- as people
call it, it flies itself. So if you notice the plane's
doing something weird and turning, almost the
best thing you can do is just let go. And the controls will
normalize, and then the plane will fly straight and level,
which is really great. There are other
types of aircraft that are inherently unstable. So we have Minachi
and Oxsana over here who do aerobatic flights. And Mark will be talking
about that tomorrow. So that's where
you actually want an airplane that's not
so stable so that you can cause it to do all kinds
of crazy maneuvers and turns and twists very easily. You pretty much can't
get a Cessna to do that. It really wants to fly
straight and level. So then there are
also other aspects that can affect stability,
such as your center of gravity, so how you load the airplane. We'll have a specific
lecture that just talks about weight and balance. But one thing to keep in
mind is that as people sit in your airplane
or as you put bags in the baggage compartment,
you're loading the airplane. And so if you have too
much weight aft of the CG or behind the center
of gravity, you can cause the plane
to basically go like this, which isn't very
helpful when you're flying. If you have things a
little too forward, it actually pushes
the nose down. In general, the nose
down is a little bit more stable from the
perspective of lift and getting air to fly over. You don't want
something that keeps trying to stall whenever
you let go of it. And then similarly, you can
talk about the stability in the lateral direction
in the roll direction. And some of these things
like swept-back wings like you see on a jet can
affect that type of stability. And then finally,
there's stability about the vertical axes. Generally, this is going to
be kind of fixed for the given aircraft that you're in. But you can affect it as
you design an aircraft. So we started talking
about stall already. So when you have
your angle of attack past its so-called
critical angle of attack, it can cause the air to
basically no longer be able to flow over the top and
no longer be able to effectively deflect air down. And so the air
kind of separates. And you can stall. So it's really important to
know that you can actually stall at any airspeed. Even with full
power, you can stall. In fact, one of the
maneuvers you'll have to do in order to
get your pilot's license is a power on stall. So you can stall both
where your engine is idle, like you're coming in for a
landing, and you get too steep, but you can also
stall with full power. And you just made your
angle go too steep. So it's really affecting that
critical angle of attack. And again, once you have that
angle of attack too steep, then there's a very significant
loss of lift, which is not good when you're flying an airplane. So when can you stall? At any airspeed and
any power setting, and it's really based
on the angle of attack. So if you-- yes, go ahead. AUDIENCE: So what happens
after the end of the graph? Does it just plunge zero? Is it not like any solution? Like why does it stall? TINA SRIVASTAVA:
Yeah, basically, it's not generating any lift. Right. You can see this like
with a paper airplane. Sometimes, if you-- it kind
of stops and kind of crashes. We'll see how Minachi's
paper airplane does here. Well, that one-- I definitely had a low angle of
attack, so it flew very well. Let's see if I can
get it to stall or if it's too stable
of an airplane. That one-- basically,
after it stalled, it basically went nose
down, which is good. It has a little extra
paper folding at the front so that the nose will go down. But it's really bad basically. If you stall, it
can go that way. The other thing that can
happen after you stall a lot usually is you can
enter a spin, which is actually the next case. So this is when you're
uncoordinated in your stall. So what I mean by uncoordinated? So that's what I was just
talking about before, where your roll and
your yaw are not going in the same direction. And here you can have
a situation where both of the wings have stalled. So the airflow has separated
over both of the wings. But one may be more
stalled than the other. And it causes the airplane to
have a very, very hazardous condition or an
intentional condition if you're Oxsana over
there, and you're trying to spin your airplane
to do a fancy trick. This is very dangerous
close to the ground. As you'll hear, you
only intentionally do this in certain
types of aircraft when you're wearing
parachutes in certain airspace when you're very high
above the ground. You don't want to do this. And in fact, if you're just
getting your private pilot's license or your PPL,
you're not going to practice a spin because
it's pretty dangerous thing to do in many aircraft. But you do have
to learn about it and make sure you
don't get into a spin. So let's talk a little bit
about maneuvering flight. So basically, that
means when you were flying straight
and level, that's kind of when you're at
an equilibrium where your lift and your weight
kind of cancel out. And the plane's just
going straight and level at the same altitude. But climbing is when your lift
temporarily exceeds the weight so you can actually climb. So once you are
in a steady climb, then you can actually still have
your forces be in equilibrium. So remember f equals ma. So a is acceleration, which
is a change in velocity. So if you're not
changing your velocity, and you're just
in a steady climb, then you're also
not accelerating. Now, this is a little
bit complicated, so I will say this is
a little bit tricky. There is a tendency for
these airplanes to turn left. And there are actually
multiple things that contribute to this
left-turning tendency. And when you're in
an airplane flying, you might hear your
instructor say right rudder. And it is really
to counteract some of these left-turning
tendencies. So we're going to break them
down and talk about them. But this can be a
very in-depth subject, so I will definitely
refer to the PHAK, which is the Pilot Handbook of
Aeronautical Knowledge. Chapter 5 goes
into all of these. So the first one is torque. So basically, the thing is
when you're-- if you're sitting in the airplane, and
you're looking forward at your propeller, most
US engines actually have the propeller
rotating clockwise. So and you can see that
arrow that says action. That's the propeller
rotating clockwise. And so because of Newton,
we know for every action, there's an equal and
opposite reaction. So because the propeller
is turning to the right, the whole airplane is
trying to roll to the left. So that is the first
left-turning tendency. Before we move to the next
one, are there any questions on this left-turning tendency? Great. So the next one
is p-factor, which is an asymmetrical thrust. This happens when the airplane
has a high angle of attack, so either when it's climbing
or in this condition called slow flight, which is where it's
kind of an uncomfortable thing. You have to do this in
your flight training. So basically, you have your
power setting pretty high, but you've kind of
pitched the airplane up. And so you're not getting as
much airflow over your control surfaces like your
ailerons and your elevator. So they call your
controls mushy. So it's hard to kind of
coordinate your airplane. But you kind of sit
in that environment to basically understand how
it's difficult to control the airplane in
that environment. So if you're pitched up, and
you have a-- so you have a high angle of attack, and you're
either climbing or in slow flight, you have this
tendency where the-- because you're
angled to the wind, the right propeller blade,
which is descending, is kind of cutting into
the air as it's coming in. So it's actually
generating more thrust, whereas the ascending
left propeller blade, so the propeller blade that's
going up on the left side is kind of coming away from
the wind that's coming at it. And so it's not
generating as much thrust as the right propeller blade. So that causes the
center of thrust to move towards the right. And that creates a little bit of
a yaw tendency of the airplane. Does that make sense? Great. Lot of head nods. P-factor was one that
both Phillip and I spent quite a bit of time
getting our heads around. And Professor Hansman
helped us out there. So another one is called
the corkscrew effect. Sometimes, it's
called slipstream or spiraling slipstream. It basically has
to do with the fact that that propeller remember is
just kind of like a wing that's spinning around. And so it's basically
pushing the air back. And since the propeller
is spinning around, that air that's coming
back from the propeller is spinning around the airplane. And as it spins around, when
it comes up to the back, it pushes on the vertical
stabilizer, that tail piece, and causes the plane
also to do a left yaw. Does that make sense? Some good head nods. Yes. AUDIENCE: Why doesn't it
also cause it to roll? TINA SRIVASTAVA: Why doesn't
it also cause it to roll was the question. And it could, especially
if it's hitting the wing. But in general,
what we've seen is that it can depend
on whether you're in a high wing or low wing. But the biggest thing that
it sort of hits is here. Now, in general, when
you get to a left yaw, you sort of kind of roll. These are connected angles. But I think just
what we've observed is primarily that
the air, when it hits the vertical stabilizer, is
the biggest surface that's kind of pushing it and
the angle that it's at. So if you sum it
all together, yes. I'm actually quite confident
you'll get some roll, but the biggest thing that
you notice is the yaw. So let's see if we
understood p-factor as well as we think we did. A, B, or C? AUDIENCE: A. TINA SRIVASTAVA: A. Good job. I actually have my little hint
there that the B is actually talking about torque, which
is a different left-turning tendency. And then finally, we're
going to talk a little bit about gyroscopic precession. It's a little bit
complicated if you're not familiar with the gyroscope. But when Phillip
talks to you about all the different controls
in your airplane, you'll have to learn
about gyroscopes all over again in a little bit. But in general, what do you
need to know about a gyroscope? What is a gyroscope? A gyroscope is
something you can hold. It's spinning. You can play with them. What they allow you to do
is have rigidity in space. And they also have this
concept of precession. And precession is basically
that the resultant action of a spinning rotor when a
deflecting force is applied happens 90 degrees
ahead of that rotation. And so because of that,
you can consider that the-- you have the propeller
spinning, and that causes this gyroscopic precession. And that basically
causes 90 degrees out of that sink is this
force which causes a yawing movement, a pitching
and a yawing in this case. Once we talk more about
gyroscopes and how they work, you'll also learn
different flight controls that you look at in the plane,
leverage these gyroscopes. And we'll come back
and circle back to making sure we understand the
key fundamentals of gyroscopes. Yes. AUDIENCE: So why is p-factor
a left-turning tendency and not a pitch up tendency? TINA SRIVASTAVA: Sure. So let's go back to p-factor. So what we're talking
about is the difference in the center of thrust. So the thrust, when
you're straight and level, the thrust is just forward. But what we're seeing is
that when the right blade, because when you're in
a high angle of attack, the right blade is
generating more thrust than the left blade. So the center of thrust
is slightly to the right. So that is why because it's to
the right and not up or down. Up or down would cause
a pitch up or down. But since it's to
the right, that's why it's causing the yaw action. AUDIENCE: So it is not
90 degrees ahead because of precession. TINA SRIVASTAVA: So
precession is separate. It is generating its own
factors and dynamics. So both of these things are
acting at the same time. So precession does
in fact affect pitch just like you
correctly recognized. But this is an
additional factor that's happening is that since
the center of thrust is actually moved to the
right, it's causing the yawing. Did that answer your question? AUDIENCE: No, but that's OK. TINA SRIVASTAVA: You want
to chime in, Phillip? AUDIENCE: It's an external
force, as opposed to generating by the propeller. PHILLIP GREENSPUN: It's
a little bit tough. I think, yeah, we should
table it and refer you to that physics book See How
It Flies, which has some of it. But the one thing I
would add on p-factor is another thing
to keep in mind is whether the propeller is
advancing or retreating into the wind. So if you think about it,
when the airplane is level, the propeller is not moving
relative to the oncoming wind. But if you tilt the airplane
up, as the propeller goes down, it's actually
advancing into the wind and getting a little bit of
an efficiency boost that way. Whereas when it's
coming up, it's going from the front of the
airplane towards the back of the airplane. So it's retreating TINA SRIVASTAVA: Yeah, so
what Phillip's describing is why the right propeller
blade is generating more thrust than the left propeller
blade, which is what's moving the center of thrust. So I think the real thing
to answer your question is that there's more
than one effect happening simultaneously. Yeah, so the-- PHILLIP GREENSPUN:
I'm not sure that you get gyroscopic precession
from that action here because it's generating
lift by pushing air. I'm not sure that
all the thrust really has to go through,
for p-factor at least, through the center of
the spinning propeller. Also, I know in helicopters,
the physics 101 answer is 90 degrees. But the real answer for
engineering it is 72 degrees. So it does get complicated. Fortunately, it's beyond the
scope of what the FAA tests you on because they
themselves, I'm sure, don't understand it fully. TINA SRIVASTAVA: Yeah. How about we come back after
we've talked about gyroscopes in excruciating detail and then
we have a set of terminology to talk about, let's come
back to discussing that more. Thanks. AUDIENCE: I have a simple
question for you maybe. TINA SRIVASTAVA: Yes. AUDIENCE: Just to
help me remember, why is it called p-factor? What is the p for? TINA SRIVASTAVA:
Power or propeller. So the p is referring
to that propeller, right propeller
more than the left. It also usually happens when
you're at a higher power. So some flight
instructors like you to think about when you have
higher power in the airplane, you need to put on
more right rudder to counteract that
left-turning tendency. PHILLIP GREENSPUN: We're
a little bit behind. Should we take our bathroom
break now and then-- TINA SRIVASTAVA: I'm
actually almost done, so I think we can finish there. So one thing is to talk-- so
we talked about with climbing flight, f equals ma. So once you're done
changing the velocity, and you don't have a
change in velocity, your forces are in equilibrium. So the same is the case
with a descending flight. When you're actually
turning, your forces are not in equilibrium
because you're having this change in velocity. And so you actually have a
number of changes happening. And it's basically considered
accelerated flight, which is same as when you're
driving if you're turning. So when you're flying,
when you're doing a turn, you're accelerating because
you're constantly changing the direction of your velocity. You also have load
factor, which we'll get into in more detail when
we talk about performance of an aircraft and how the
load affects your performance. But another thing
to think about back when we were talking about that
zero gravity flight and a plane flying in a parabolic
trajectory or a roller coaster when you're at the top. But when you're at the
bottom of the roller coaster, you really feel like
you're being pressed down into your seat. In fact, when we run
that zero gravity flight, although at the top, we had
30 seconds of weightlessness so we could do our
experiments, when you go to the bottom
of the parabola, you basically get 2G or
twice what you normally feel. And so you have to kind of
lay down and let that happen before you come up again. And so when you think
about load factor, just think about you
being at the bottom of your roller coaster
and really feeling a kind of twice
that force on you. And then just to
kind of end, we want to talk about most of the time
we're talking about the planes that you'd be flying, but
another type of aircraft altogether is a blended
wing body aircraft. So just like this is
one example of that. So what it means is
that that fuselage or that kind of tube in
the middle that you sit in is blended into the wings
so that the whole body is generating more lift
because the whole surface is kind of designed that way. It's really kind of cool. And from an aerodynamic
perspective, it's got a much better
lift to drag ratio because the whole
thing is really deflecting the air molecules
downward and generating that lift. So I just asked kind
of a thought question. If this is so much better, it's
more efficient of an aircraft and aerodynamically has much
better properties, why do you-- it actually-- we've
also found that it's better in terms
of fuel efficiency because it has less
drag and more lift. Why do you think that
JetBlue and American Airlines don't fly aircraft
that look like this? AUDIENCE: They don't have routes
with a thousand passengers. TINA SRIVASTAVA: They
don't have routes with a thousand passengers? Well, you could make a smaller
blended wing body aircraft. Yes. AUDIENCE: Passengers
like windows. TINA SRIVASTAVA:
Passengers like windows. That's actually a big-- it's a big reason truthfully. Yes. AUDIENCE: It's very different
from what's currently made, so the development would
be expensive and risky. TINA SRIVASTAVA: So it's
very different from what's currently made. And then you said
so the development would be very risky. Actually, I think it's more
than just the development. Because it's different
from what's currently made, the entire infrastructure
supports the current format of an airplane with
a tube and wings. So we're talking about
airports, jet bridges, the way that people load
food carts onto a plane, the way that passengers
get on and off, the fact the
passengers don't have as many windows on
this type of aircraft. It's unfortunately that
whole infrastructure that surrounds it that is a
big contributing factor to why, even though there's
a better design, why we don't move towards that. So this was a big,
big thing for me when I was an undergrad
at MIT aero-astro. I'm thinking I'm going to design
the next best amazing airplane. But even if you do design the
next best amazing airplane, it may not be widely
deployed because of these other infrastructure
aspects, which really got me into systems engineering. But enough with that
thought exercise. For time, we'll just summarize
what did we learn today. So we talked about how does
an airplane generate lift? And we talked about different
factors that affect lift. We also discussed that lift
is very hard to calculate. And so we experimentally
measure a lot of aspects of it. And we discussed the different
forces on an airplane-- stability, and kind of this
left-turning tendencies, and some of the different
aircraft configurations. So are there any
questions about that? PHILLIP GREENSPUN:
Yeah, Tina, what do you think about
let's do questions, let's take a bathroom
break, and then-- TINA SRIVASTAVA: Yeah, so
you can think about it. PHILLIP GREENSPUN: People
with questions talk. I'm going to call
the pizza people and give them my credit card.
