2. Airplane Aerodynamics

Alright, as we discussed, we'll start with the most basic question: how do

airplane

s fly? It is a very critical question. I think everyone should know the answer to this, going back to the comic Meenakshi had with Calvin and Hobbes and not knowing it. how

airplane

s fly. I think their magic is not the way MIT students should be, so we're going to cover how airplanes fly and actually go beyond what the FAA requires you to know because, frankly, you should know how. Airplanes fly so we have a common vocabulary to discuss, we're going to talk a little bit about the parts of airplanes, so here on my little airplane there's kind of a model, so you can see it on the front. you have your propeller and then the engine, the propeller and this little plane is here in the front, who knows what a fuselage is, just shout it in the middle part, the body, that's where the passengers sit, yeah, so that whole middle part where people sit, so if you're thinking about a big jet engine, that's where all the rows of seats are, where everyone sits.

That tube in the middle is called the fuselage and the wings stick out the sides, so the middle part is a fuselage and then a thing. The interesting thing is that the tail actually has many more components, people casually refer to it as the tail, but there is a vertical part that comes out at the back of the vertical part of the tail that can actually tilt from side to side. side and then you have a flat horizontal part and it actually has a rear part that can go up and down, so let's talk about what all of these are, so the rear vertical part when it goes from side to side is the rudder, The flat part is your elevator that you can move up and down allowing you to control the plane.

We also have, of course, the wings. Sometimes there are struts that support the wings, so they go from the wing to the fuselage and then you have landing gear. In this case, you have these wheels at the bottom. We'll also talk to you during this course about seaplanes, so they have slightly different landing gears, but this is a good place to start. Well, the other thing we have to talk about. they're just the four main forces that are in an airplane, so they're pretty simple, so the upward force is the lift and that force opposes the downward force of the weight, okay, and then when you're moving the plane forward that is thrust and it opposes drag, so what we are going to talk about is that for a plane to go up, the lift has to exceed the resistance for the plane to move forward, the thrust has to exceed the dress Excuse me, lift has to exceed weight and thrust has to exceed resistance, so those are the four main forces that we're going to be working with today, so now I'm going to spend a little bit of time here at the whiteboard. video platform people said this way boy, this one is better, yes, fancy colored truck, okay, color clashes, okay, so I will start the discussion about lifting with the fact that there are many theories about lifting, some of which are incorrect, so if you spend some time searching on Google lift before coming here, you may have come across a couple of scenarios that are completely false, so we'll focus on what's true, but I'll cover the At least one of those bogus theories to make sure you don't understand.

I hung up on that, so to talk about it we're going to think about an airplane and we're going to make a cross section of the airplane, so if you take a saw and cut off the wing, what are they? You went with I don't do it this way, so if you cut the wing, the front of the wing is the leading edge, the back of the wing is the trailing edge, if you did that, if you cut that, how do you go? So it looks like this and this shape is called the airfoil and we'll get into the details later, but first we'll talk about a simple way to understand how lift works, so if this is the wing and you The air coming into the air is pushed down by the shape of this wing, meaning that as the air flows, it is pushed down.

Now, what is air? The air is nothing. Air has molecules, it has mass, so if you think about conservation of momentum, this I think the easiest way to think about lips is conservation of momentum, you have a bunch of air molecules and those air molecules push each other around. down so mass is pushed down so if mass is pushed down to conserve momentum something must be pushed up and that's the wing so that's the easiest way to think of it On it. If you're deflecting air downward to conserve momentum, the mass of the wing rises upward, we're going to break that down, but I think that's a good place to start.

I'm going to take a moment to talk about an incorrect theory of lift, so let me emphasize that it is wrong. One of them is called equal transit theory. Has anyone heard of this? The equal transit theory, which is incorrect, says that basically an air molecule that comes and starts here at the front has to go around the bottom and meet the tail at the same time that a molecule that comes over the top has to meet the tail. her on At the back there's no physical principle that says it's false and we've actually measured that the molecules that go under the wing versus the top of the wing don't actually get to the end at the same time. time, but in this false theory Transit Theory they still say that you have to get to the bottom at the same time.

They also say that there is more distance to cover basically because of the shape of the airfoil, so for the molecules to pass over it. to arrive at the same time as the molecules above the bottom they have to go faster and since the air moves faster over the top and bottom that is what creates lift so that is false and there are many reasons why it is false, you already know the most important one. One is that there is no physical principle that says that two molecules that start at the same time, one going up and one going down, reach the end at the same time.

That's simply not true and we'll show you some more diagrams that show that in fact it's not the case that the molecules don't arrive at the same time anyway, so even though that spreads widely, that's not true and, Please don't waste time on that theory, okay, so let's focus on what it is. That's right, how does it really work? Actually, let me give you one more reason why that is false. The real reason that traffic 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 it has to travel is different at the top and at the bottom, but there's a reason it's wrong.

Can you pass me that paper airplane please, who has built a paper airplane before? Okay, I see at least two people who didn't raise their hands, right? I need to do an exercise in class if you haven't filled out a paper airplane. It is very important that you do it as a general childhood experience. Here you have a paper airplane. Thank you, you know, for building it for me. If we took this paper airplane instead of This is so fancy, this fancy airplane and made a cross section of this wing, what would it look like? Yeah, you demonstrated it with your hands, but shout it out, yeah, maybe the same thing at the top of the bottom, from the top to the bottom, it's just a piece of paper exactly, it's like a little flat rectangle, so instead of this fancy shape you have here, we have red knees for bad, okay, it's like a little rectangle, this is what the cross section of its paper airplane wing looks like, surprise, surprise like you said it's the same thing at the top and bottom, so the distance that an air molecule would have to travel over the top and bottom is identical, so in reality the transit theory still falls apart completely, but a paper airplane still it flies, so why is it like this?

Again, remember that the real reason is that if this paper airplane is tilted, it is pushing air down, so the rising air collides with it and is pushed down, and therefore by deflecting the molecules air down, conservation of momentum, wing lifts, right? So now we're going to break this down in a little more detail and we'll go back to the slides, so one thing that's important, like I said, you don't really need a very detailed mathematical description to fly an airplane or become a pilot, the FAA. It doesn't require some of these details, but it's important to know them 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 most important things is simply that for a climb you have to increase the downward momentum of the air and the sheets of air have this shape called an airfoil, it's a type of shape that is very efficient at increasing that downward momentum, now who knows what Bernoulli's principle is, who you've heard. of Bernoulli's good, everyone has heard of Bernoulli, can anyone articulate Bernoulli's principle?

Yes, since D plus half of MV squared equals indifferent constant squared, so when the pressure drops somewhere, the speed of the particle has to increase. Yes, absolutely, absolutely. So what Bernoulli observed was the In the case that when there is a decrease in pressure there is an increase in speed, that is the core concept that you have to understand, so when we think about an airfoil, we see that and I will draw another airfoil for us to talk about when If you have air moving very fast over the top of the wing, that means you know that an increase in speed means there is a decrease in pressure, so this is the measure in which you really need to know for the FAA exam, so this statement relates to Bernoulli's principle.

I'll let you read those answers, so is it B or C? Shouts C good job, well done, okay, we'll discuss a little more detail, although for any wing to generate lift it has to be in a fluid. If this plane were in space or a vacuum and no fluid was passing through, then there would be no molecules deflecting downward and therefore the wing could not be pushed up, but fluid doesn't always do that. to be air, you might see similar underwater designs for underwater drones, it just has to be a fluid passing through the object. So when you have this airfoil in fluid, when the fluid is not moving, when it is stationary, then all the fluid exerts pressure. on the airfoil, so you get all these little normal forces that exert pressure when the fluids are not moving and the airfoil is stationary in the fluid, then all that pressure forces all those normal forces or forces with a sum perpendicular to zero because there is no net force, it's just sitting there. in the fluid, but when that fluid moves, it generates a force, so that is the force that generally generates when the fluid moves forward, the force is a vector, so it has direction and magnitude, so They are the vertical and horizontal components.

Component to that, so we call the vertical component the lift. Does anyone know what we call the horizontal component? Drag. Good job. Well, here's a dumb question. What part of the plane generates lift? Yes, the entire plane. A good job. Many people might have the mistaken impression that it is only the wings that generate good lift, in reality the entire airplane generates lift and it is not just the airplanes, all objects that move through a fluid have this phenomenon and, sometimes Sometimes, it's not a good thing, so what? Is this a photo of a racing car?

Let's go guys. I know we're on some kind of airplane, but hey, who can tell me what that thing sticking out of the back of the race car is? A spoiler. What is a spoiler? It spoils the air flow. So when? a race car is driving on a race track and it is passing through air, that fluid is air, actually only the race car is generating lift and that lift can make the race car rise upwards and have no so much traction with the ground and when you are a racing car you want to go very, very fast, you want to have very good traction with the wheels against the ground to be able to go as fast as you can, that's why you have a spoiler in the back. actually to counteract the lift that the race car generates, so it's not just airplanes and wings that generate lift, but anything that moves through a fluid can generate lift.

Okay, so we'll talk a little bit about the equations that you don't understand. Scared here, we'll just dive into this step by step so that we have F equals MA. Hopefully, this isn't the first time you've heard about that equation. Can someone shout out what is acceleration and change in velocity? over time, very well, so velocity again is also a vector, so velocity, being a vector, has magnitude and direction, so you can change velocity by changing magnitude or direction, in the caseof an aerofoil, we are changing the direction of the air. so the air has velocity, it comes in, we are changing the direction of that air and that creates lift, so because we change the direction of the velocity that creates a force which is our force F, so f is actually here representing the rate of change of The previous impulse pushes those air molecules down and generates a force that creates the airfoil that will rise, so we discussed it again and that transit theory is still false because even a paper airplane with a completely flat cross section of its long wing. since it is tilted up so the air is pushed down it will fly fine so here is another question about which one moves the wing faster through the air or the air past the wing, well you are very quiet, what moves faster, yes, the air on the wing that we have. one for the air over the wing moving faster than the wing through the air someone else yesDepends on what part of the wing you are talking about yes since you consider air to be the air that is immediately thanks to what is on contact with air, yes, it depends on the air you are talking about, okay, it's true, actually, what we do.

The discussion is about the frame of reference, so depending on your frame of reference, if your frame of reference is the airfoil, you can consider the airfoil to be stationary and see that the air is the wing stationary in the air . passing by you, if your frame of reference is here, you might see that the air is stationary and the plane is moving through it, so depending on what your frame of reference is, you can get the result identical, so the answer is that it is The same, depending on your frame of reference, it is exactly the same speed of the air passing over the airfoil versus the airfoil moving through the air and the reason why Which one wants to delve deeper into that, who is familiar with this concept? of the frame of reference, yeah, a lot of head movements, okay, cool, so the reason this is important is that as we learn about lift and study this, we could actually create a bunch of different sheets of air and then build airplanes and then fly them through airing them and measuring them, but that's very expensive, so 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? It has a couple of people. Hey, we saw that more than 60 of you were aero-astro, you need to go to your Wright brothers' wind tunnel. It's actually being upgraded right now in its 33rd building, so it's exactly identical the air going over the airfoil or the airfoil moving. through air it's much cheaper to put the airfoil on a stick in a wind tunnel and then shoot air through it and then take measurements rather than continuing to take off planes and make them fly through the air, so let's talk We talked about that a little bit, so the question is what factors affect lift.

There are many things that affect lift, so one has to do with the object itself, so I was talking about the shape of the airfoil, so you know, we talked. over a different shape that is just a flat sheet of paper or a rectangle as a shape, you can have a thinner shape and the way you modify the shape can significantly affect your lift, so for example one of the modifications can back here in the In the end, if you were to make your airfoil longer this way and it pointed even further down, then it would push the air in a slightly different way, so it would affect the lift that airfoil could generate, it would also affect the drag inducing, well another aspect is just the size of the wing and the shape of the wing, so we see a lot of different types, so you know this is a large rectangular wing on an airplane, you might see a swept wing, there are different types of shapes and then there is also just the area.

So regardless of whether you know if this is yours, if you're looking down at an airplane, these are kind of wide, flat wings or you could have very thin, skinny wings that you might see on a glider, regardless of whether there's a surface Of the area of ​​the wing also affects lift quite a bit and the aspect ratios we just discussed and shape can affect lift, something else besides the object itself, other than the motion of the wing itself, can affect lift, so the air speed and the The most important thing is what is called the angle of attack, so it is the angle that this profile has with respect to the air, so if you had a profile that pointed upwards like this versus another one that was the same but If it were not tilted upwards, this profile would have a higher angle of attack or angle to the wind than this Now, this may seem like a very fancy description, but who has been in a car driving down the road and taken the hand out and if you tilt it up? a little bit you'll see that the wind pushes your hand up and if you push it, you tilt it down and you know your hand pushes up and you slide your hand out the window, so okay, I'm getting a lot of nods, so that's really what angle of attack is all about.

If you tilt your hand up, it pushes up much more, if you tilt it down, it pushes down, that's the angle of attack and we're there. I'll define it more specifically when we talk about the terms associated with an airfoil and the shape, but it's good to understand the general concept first and then another factor that affects lift is the air and the fluid it's in, so the actual mass of the The flow of air comes around you, so there are many aspects that you already know, we talked about whether you are in water or whether you are air or the density, the density of the air, another component of that air is the viscosity, does anyone know? what viscosity is, yeah, resistance to flow, as I like to think of it, is if you've ever baked brownies and you have your mixing bowl and your spatula there, and if you just have those, you know water, oil, and eggs. and you're mixing it, you know you can, you can mix it pretty quickly and it doesn't stick to the spatula as much, but if you were mixing molasses or once you have all that brownie batter there, it's actually harder to do. and it sticks to the spatula, so that's what we're talking about when we talk about viscosity, so it's the tendency of these molecules to stick together and just stick to the object that's moving through them, in the case of the airfoil that we're talking about and we were discussing this a moment ago about what air we were talking about, so some air that might be very close might stick to that airfoil or stick to the wing instead of just passing smoothly through.

So, the Viscosity and then compressibility also affect the lift, so the compressibility of the air. I turned off my microphone, so certain types of fluids are compressible, so you can take an air balloon and you can move it to a cold environment and have it. shrink or in a warm environment and have it expand while having the same amount of mass inside the balloon, so I get a lot of head shaking, which just shows the compressibility of air, while some types of fluids are not compressible. They are incompressible and they affect lift in a different way, so although I have told you all these things that affect lift, one thing I will admit to you is that calculating lift is difficult, it is very difficult, in fact, we don't really know how. do it.

Well, this is a snapshot from Wikipedia of all the different theories of lift, so there are many different ways that people try to calculate lift and it turns out that it is very difficult to do it, one of the ones you see there is is Navier- Stokes, so Navier-Stokes is a set of equations that does a very 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 There are a lot of things like thermal conductivity and a lot of considerations, but the problem is that solving those equations is very difficult.

You know, we try to use supercomputers to estimate every little aspect and it's very difficult to do and we really can't. Solve those equations to determine precisely what the lift will be. Let me talk about some of the limitations we have in solving these equations. Firstly, it has to do with how the air flows over the wing if the air is moving very much. It passes smoothly beyond the airfoil, then it is very easy to climb, it is not easy, but it is easier to approach. You know, we can predict what a particular air molecule is going to do, but as you see there, when it starts to spin and become turbulent, if you start.

See a particular air molecule that moves and becomes turbulence and does not form a laminar flow but a turbulent one and moves and collides with other air molecules and then predict what that molecule does and what all the molecules around it do. around it becomes very, very difficult, in fact, We have a hard time doing that and instead we basically assume that that doesn't happen and propose limitations or conditions on the airflow that are not actually true, but help us with lift approximate, so one of them is the Kutta condition. what you see on the bottom left is this smooth flow, so you're basically saying that no turbulence is happening and the air is moving very cleanly and you also have a couple more specific requirements, like no air molecules coming out of the upper part. towards the bottom and no air molecules from the bottom go towards the top and they are just assumed to move smoothly so Kutta condition is actually very useful to approximate lift, we also make other assumptions that there is no viscosity or that the fluid is not compressible sometimes these assumptions are appropriate and sometimes they are not something else that is really critical about our ability to estimate lift is that, as I have been talking to you here on the board, I have talked to you about a section transversal, right? you just cut the wing and you just look at a cross section, so since we're talking about a cross section, we're talking in a two dimensional space, well we can actually do a pretty good job of estimating lift in a two dimensional environment, but the gist The point is that wings are not two-dimensional and the wing goes out to the classroom and comes back to the blackboard and really estimating how all these air flows work at the edge of the wing is very difficult.

Has anyone heard of tip vortices? A couple of head nods. Okay, so we have an image there that shows a jet to show a little bit about what the air does when it comes off the edge of the wingtip that we're going to use. We talked a little about tip vortices, but the problem is that it no longer adheres to all of our conditions. Now we don't have a smooth flow. We definitely have a turbulent flow. We have a rotating flow and we have air molecules hitting other air molecules. It becomes extremely difficult for us to model all those air molecules, we can't really do it, so going from two dimensions to three dimensions is really a limitation of many of the equations that we have to approximate lift, so what do we do right?

First of all, we go to our two-dimensional surface and we talk about all these normal forces, so when you have all the fluid that passes through it has pressure and it supplies all these forces perpendicular to the airfoil around it, how do you do it? approximate elevation while you say oh okay, you just add up all those forces well, that's great if you know what all those forces are, but it's not great if you don't know what all those forces are, so what's the solution we have? What we do is basically we calculate what we can and then we measure the rest experimentally, so in this lift equation, for example, we have Ellis for lift, some of the other terms you have there, Rho is the one that looks like a P, so Rho is talking about the density of the air, you have velocity and a is the wing area that we talked about and then we have this fancy little symbol there C sub L or the lift coefficient and we basically say you know, no.

I know how We come up with the idea of ​​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 kinds of things and that's why we say that you know how to measure things. that we can and then We'll calculate or calculate what we can and then we'll be in a wind tunnel where we'll put this guy on a stick, we'll measure the lift coefficient and that's how we actually calculate lift these days, using a lot of measurement to report what's really happening because it's very complicated, you know speed is squared, so if you go twice as fast you get four times as much lift,that's the absolute ratio and the other thing that's really important is that lift coefficient.

It's measured for a given angle of attack, so we talked a little bit about the angle of attack with your hand outside the window, so let's look at it in a little more detail, so to describe it I have to think of some more terms. which have to do with the airfoil, so we talked about the front of the airfoil or the front, the front of the wing is called the leading edge and then the rear part is the trailing edge, and we talked a little bit about the exit. A little bit when we were talking about the condition of the cutter that there is no air center, it is assumed that no air molecule can cross the trailing edge to the other side, so the curvature is there, so that's just talking about actually representing the curvature of that airfoil and then a chord. line that goes in the middle so you can measure what it is like, so try to do your little zoom with the fantasy that you were doing.

I'm just going to point it out so that this is the chord line of the wing so you can see that it's a complete line. airplane, the airfoil is right here and you see this line of cable going from back to front, someone trying to get in the door, okay, cool, and then we'll talk about some of these terms, one of the most basically important things. What you have to think about is the angle of attack. Thanks for checking the door. Well, we talked about how we can control lift. Some of the things we can do have to do with the design of the airplane so we can build an airfoil and we can talk about, you know how curved that airfoil is, you know the curvature at the top, how curved it is, we can design the wing area when we fly we can control the air speed and then the angle of attack is something you can control. when you are in the airplane doing some type of pitch down or pitch up and I will describe pitching and how you control an airplane in more detail.

Another thing that's relevant is the flaps, which I talked about in this drawing right here where I added this white part of the trailing edge that moves down and that's really similar to the flaps, so when the flaps are up, they're on. line with the rest of the wing, but when the flaps are down. It's the most effective, like pushing and pulling a piece of your trailing edge down, which again causes 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 us.

I also talked about spoilers, for example, it's something that a car can like that can actually disrupt lift by disrupting the airflow and when we talk about the four forces of flight, if you're doing steady flight, you're not climbing or you're descending but you are just flying straight that means your lift and your weight basically cancel each other if your lift is greater than your weight then you can go up and if your weight is greater than your lift then you go down but if you are just flying in a line straight, you are in an equilibrium where those two forces cancel each other.

It's good, very good. I have a more detailed diagram of the angle of attack so you can see the chord line here. You can also see the relative wind and the same things I drew. Here, the lift and drag and then the resulting force vector, okay, so you can control the angle of attack in several ways. One of the ways we talk about is pitch down, so pushing the yoke forward causes the plane to descend and it does this by shifting the elevator at the back of the plane. We'll describe it in more detail, but the other things that can affect the angle of attack you can affect before you even take off, so it has to be done. with the weight of your plane for example and the center of gravity as well as your airspeed when you are flying so here are a couple of diagrams showing how lift changes with the effective angle of attack and then there is an angle critical attack, so that's when you know you can keep going up for a while, but if you get too steep, what happens?

Who knows what happens when you go too steep, you stall, that's right, so the air can't really get over the wing and it starts. separating and then you are no longer effectively pushing the air down and you lose the lift that you were generating and one thing that I also want to point out here in these diagrams is that you see with these little colored lines the air just coming in and out and you can see which in this case the blue lines show that the air that passed over the airfoil was faster and actually came back faster than the air that passed from below, so again please don't fall for the transit theory same, okay, so practice the question, okay, B or C.

Hey, okay, so the angle of attack is defined there and one thing I would like to point out is that this is also the case. a propeller, so its propeller also looks a lot like an airfoil or a wing that is on its side and rotating, so also the angle of attack of a propeller is a symbol that is defined basically the same way as the angle between the chord line of the propellers and the relative wind is fine, so let's define the center of pressure to be basically the point on the wing where the lift is centered and it can actually move as you can see in this figure based of the angle of attack of the center.

The pressure can act in a different location and it is very important to also understand that you know that it is not that the elevator always comes right in front, depending on where you are, it can be pulling you in different directions and that can affect the capacity of your plane and we will enter into that in more detail, so we talked a little bit about the flaps, which can actually increase the lift you can produce, but it's a trade-off because it also increases drag, so when you're in the course of the flight takeoff cruise or landing When do you use flaps, does anyone know the takeoff and landing? landing yes the reason you are especially on landing many times people also use flaps on takeoff but the reason is just that you like make your airplane set that in case you don't take off you can land without doing many dramatic changes.

The reason you do this is basically that by increasing your lift but also increasing drag, you know that drag affects you. it knows how fast you are moving forward and therefore it can make the air speed higher with the lower forward speed, so without what it does is it allows you to go very slow without stopping and that It really helps you land. airplane, so it basically allows you to go into sort of a steeper angle to land while maintaining the speed that you need to do it and you'll notice that there are different flap settings so you can have flaps. you know, 10 degrees 20 degrees 30 degrees, we'll discuss that in more detail and Philip will talk about it in terms of performance.

I think also thrust, so we talked about forward force thrust in this type of airplane, a single-engine propeller. airplane, it's the spinning propeller that actually produces the thrust and like I said, the propeller blades are like the wing of an airplane, it's a good way to think about it, they just spin and spin and generate lift, but In this case, it is about moving air fuels from the front to the rear of your plane and although this is also just a force, instead of talking in pounds, we usually talk about the horsepower needed to drive the propeller, so let me also talk about resistance, so there are a couple different ones. types of drag, so a drag is what is called parasitic drag or parasitic drag.

Basically, when the plane moves in the air, 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 a lift, so this is backwards D and then you can see in this figure that the total drag is a sum of that induced drag in the parasitic drag that we do, we also call the induced drag just lifting in an undesired direction lifting in a direction unwanted direction sure whatever you can do that associate induced drag with lift that's the drag created by lift okay ground effect does anyone know what ground effect is just a couple of you , okay, so let's talk about it a little bit, basically, when you're very close to the ground, within a wingspan of the ground, you actually have some of the airflow that happens with your airplane and it's blocked by the ground, so that the induced resistance decreases now that the induced resistance decreases, is actually the case. that your plane may fly at a slower speed than it's supposed to, so what you might notice is that when you're on the runway taking off, it's probably the first part of your flights after doing your pre-flight with the engine running.

Above, you are now out on the runway and will have determined in advance what airspeed you should turn at. That's really important with a Cessna 172, for example, it's about 55 knots and you want to look at your airspeed indicator. because if you just sit with yourself, you may notice that it's 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 it and you might want to just know. , pull back on your yoke to take off, you won't be able to maintain flight and that's why ground effect is really important, because you can hover above the ground because you're so close to the ground.

The ground is blocking some of the effects of the air, so What you really want to do is make sure you continue your tour on land. It continues even if you are a little in the air. Stay low to the ground until you reach your speed. up to that rotation speed, in this case 55 knots and then you pull back on the yoke to take off, so again, when does ground effect occur? When you're close to the ground, when you're within a wingspan of the ground. Okay, so, talk a little bit about stability and we'll start by talking about the three axes of flight, so there's a longitudinal axis that goes basically from the nose to the tail of your airplane and then there's a lateral axis that goes from the tip. of the wing. to the tip of the wing and then vertically across the plane so you have the ability to control those three axes, so the elevator that I keep talking about is like your yoke where you push it forward or pull it back, allowing you head. the plane, so pitch the nose up, pitch the nose down, that's what you control the back of this tail.

The elevator, which allows you to have movement in this direction, so tilt the nose down so you can hear it a lot in case you're about to stall. because its angle of attack is getting too high, you could say nose down or nose down, it also has an orange that's on the side of its wings and those ailerons control the roll, so it turns along. 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 movement, so when you're turning, you actually do a turn and yaw usually for in the enacted turn, okay there are some cases where you really want to have an adverse yaw or actually an adverse yaw basically means that you're using the yaw direction and maybe the opposite direction that you are trying to turn with the turn. or other angles of your airplane and this only talks about adverse yaw is when you are not turning the rudder in the same direction that you are using your ailerons and this is where you talk about coordinated flight or uncoordinated flight when you are in an airplane, the rudder or The yaw are controlled with your feet so you have pedals that control the rudder and the yoke that you hold on to or a joystick that you hold on to fore and aft control the pitch and then turning it like on a car steering wheel only controls the roll, so you actually use your feet for that third yaw direction as well, so just talking about stability in general, this isn't going to work. dive into the whole discussion about Diffie Q or anything else, but generally something that is stable, so it's just a little bowl, if you have a ball and a bowl, even if the ball is pushed, it will go back to the central point, it would be unstable.

Otherwise, if you have a convex surface, if the ball moves even a little bit, it's really going to get out of control, so the reason we talk about this is basically when you're flying in an airplane and you're talking about stable airplanes, For example, the reason I really love flying a Cessna 172, even though it's kind of a training plane, is that, as people call it, it flies itself, so if you notice the planes doing something strange and spinning, It's almost the best thing you can see. What I can do is just let go and the controls will normalize and then the flame will fly straight andlevel, which is really cool.

There are other types of airplanes that are inherently unstable, so we're referring to her and Roxanna, who are here doing Arab aerobatic flights. and Mark is going to talk about that tomorrow, so that's where you really want a plane that's not so stable so you can make it do all kinds of crazy maneuvers and turns very easily that you pretty much can't do with a Cessna. If you really want to fly straight and level, then there are also other aspects that can affect stability, like the center of gravity, so how you load the plane will have a specific lecture that only talks about weight and balance, but one thing.

What you need to keep in mind is that you know that when people sit on your plane or when you put bags in the luggage compartment, you are loading the plane and therefore if you have too much weight behind the CG or behind the center of gravity, you can cause the airplane basically goes like this, which is not very helpful when you're flying if you have things too far forward, it actually pushes the nose down in general, the nose down is a little more stable from a lift perspective and having the air fly over you you don't want something that keeps trying to stop every time you release it and then similarly you can talk about the stability in the lateral direction in that turn in the direction of the turn and some of these things like The swept back wings, like you see on an airplane, can affect that type of stability and finally there is a stability in the vertical axes, generally this will be something fixed for the airplane you are on, but you can't.

It affects it as you design an airplane, so we've already started talking about stall, so when your angle of attack goes above the so-called critical angle of attack, it can cause the air to basically no longer be able to flow over it and no longer. You will be able to effectively divert the air downwards, so the air separates and you can stall, so it is very important to know that you can actually stall at any air speed, even at full power, you can stall. loss, in fact, in one of the maneuvers that What you will have to do to obtain your pilot's license is a loss of power so that you can stop both when the engine is idling and when you are about to land and reach a position very steep, but you can also stop at full power and it just simply made your angle too steep, so it's really affecting that critical angle of attack and again, once that angle of attack is too steep, there's a loss. very significant lift, which is not good when you are flying an airplane, so when can you? you stop at any airspeed and any power setting and it's really based on the angle of attack, so if yes, forward, yes, it's basically not generating any lift, right, you can look at this like with a paper airplane, a times, if it stops and crashes, we'll see how I mean, actually your paper airplane works here, well, I definitely had that one. a low angle of attack, so it flew very well, let's see if I can get it to stop or if it's too stable an airplane, basically, after it stopped, it basically stayed nose down, which is good, It has a little more The paper folds in the front so the nose goes down, but it's really bad, basically, if you stop, it can go that way.

The other thing that can happen after you stop too much usually is that you can go into a turn, which is actually, the next case is when you are not coordinated in your stall, so what I mean by uncoordinated is what I was talking about before, where you are your role and your yaw is not going in the same direction and here There may be a situation where both wings have stalled, so the airflow has separated over both, but a It can be more stationary than the other and that makes the plane have a very, very dangerous condition or an intentional condition if your ox is there. and you are trying to spin your plane to do a fancy trick, it is very dangerous near the ground as you will hear that you only do this and certain types of planes intentionally when you are carrying parachutes in certain airspace when you are very very above the ground, you don't want to do this and in fact if you're just getting your private pilot license or your personal you're not going to practice a turn because it's a pretty dangerous thing to do. in a lot of airplanes, but you have to learn about it and make sure you don't spin, so let's talk a little bit about flight maneuvers, so basically that means that when you're flying straight and level it's like when you're in balance where your lift and your weight cancel out and the planes just go 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 De In fact, your forces are still in balance, so remember that F is equal to M a, so a is acceleration, which is a change in velocity, so if you're not changing your velocity and you're on a constant climb , then you are not accelerating now either.

This is a little complicated so I'll say it's a little complicated, these airplanes have a tendency to turn left and there are actually several things that contribute to this tendency to turn left and when you're in an airplane flying You may hear your instructor say right rudder and it's actually to counter some of these left turn tendencies, so we'll break them down and talk about them, but this can be a very deep topic so I will definitely refer to the P hack, which is the pilot's manual for aeronautical knowledge, chapter five covers all of these, so the first one is torque, so basically the issue is when you're sitting in the plane and you're waiting for its propeller. , most American engines actually have the propeller spinning clockwise, so you can see that arrow that says action, so that's the propeller spinning clockwise, and because To Newton we know that for every action there is an equal and opposite reaction, so because the propeller is turning to the right, the whole plane is trying to turn to the left, so that is the first tendency of turning to the left before to move on to the next.

Are there any questions about this left turn trend? Okay, great, so next is the P factor. which is 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 awkward, you have to do this in your flight training, so basically you have Your power setting is pretty high, but you've tilted the airplane up and therefore you don't get as much airflow over your control surfaces as the ailerons and the elevator, so they call on your soft controls, so it's hard to coordinate your airplane, but you sit in that environment to basically understand how difficult it is to control the airplane in that environment, so if you're leaning toward up and you have a high angle of attack and you are Climbing or in slow flight, you have this tendency that because you are at an angle to the wind, the descending right propeller blade cuts off the incoming air, so The rising propeller blade on the left side moves away from the wind coming towards it and therefore does not generate as much thrust as the left propeller blade. right propeller blade, which causes the center of thrust to move to the right and that creates a bit of yaw tendency of the airplane makes sense.

Great, lots of head nodding. The P factor was one that both Philip and I spent quite a bit of time understanding and Professor Hansman helped us with, so it's called another one. The corkscrew effect is sometimes called slip current or spiral slip current. It basically has to do with the fact that the propeller remember it's like a wing that rotates and it's basically a thrust, you know, pushing the air back and from the propeller it spins around the air coming back from the propeller spins around the plane. and as it turns when it comes to the rear, it pushes the vertical stabilizer on that tail piece and makes the plane turn to the left as well.

Yaw, does that make sense? Some good head nods. Yeah, why don't you roll too? The question might be, especially if it's hitting the wing, but generally what we've seen is you know and it can depend. It depends on whether you're on a high wing or a low wing, but the biggest thing that hits is here now, generally when you yaw to the left, you kind of roll, these are connected angles, but I think just what we've Mainly observed is that the air when it hits the vertical stabilizer is the largest surface area pushing on it and the angle it is at, so if you add it all up, yeah, I'm pretty sure you'll get something. roll, but the most important thing you notice is the yaw, okay, so let's see if we understood the P factor and we think we got it right with a B or C, uh, okay, good job.

In fact, I have my little clue there that the B actually is. Talking about torque, which is a different tendency of left turn, and finally we're going to talk a little bit about gyroscopic precession, it's a little complicated if you're not familiar with the gyroscope, but when Phillip talks to you about the different controls. In your plane you will have to learn about driver sights over and over again, but in general, what do you need to know about a gyroscope? Do you know what a gyroscope is? The gyroscope is something you can hold, it's spinning, you can, you can play. with them what they allow you to do is have rigidity and space and they also have this concept of precession and precession is basically that the resulting action of a rotating rotor when a deflection force is applied occurs 90 degrees ahead of that rotation and so on because From that you can consider that the propeller rotates and that causes the scopic precession of the driver and that basically causes 90 degrees out of that sink is this force that causes a kind of young pitching motion and a young in this case.

Once we talk more about gyroscopes and how they work, you'll also learn the different flight controls you see on the plane. Take advantage of these gyros and we'll come back to make sure we understand the key fundamentals of gyros. Yes of course. So let's go back to the P factor. So what we're talking about is the difference in the center of the thrust, so the thrust that you know when you're straight and level, the thrust is just forward, but what we're looking at is that when it is the right blade because when you are at a high angle of attack, the right blade generates more thrust than the left blade, so the center of thrust is slightly to the right, that is why it is to the right and not up . or down, up or down would cause a pitch up or down, but since it is to the right, that is why it causes the yaw action, so the precession is separate, it is generating its own factors and dynamics , so both things act at the same time.

So precession does indeed affect pitch as you correctly recognized, but this is an additional factor happening as the center of thrust is actually moving to the right, which makes the young people answer your question. No, do you want to intervene Phyllis? it is an external force rather than generated by the propeller it is a bit difficult I think so, we should introduce it and refer it to that physics book to see how it flies, which has some of that, but one thing I would add that the P factor is another thing to keep in mind: whether the propeller moves forward or backward with the wind, so if you think about it when the plane is level, the propeller doesn't move relative to the oncoming wind, but if you tilt it.

The plane goes up as the prop goes down, it actually goes into the wind and you get a little bit of an efficiency increase that way, whereas when it goes up it goes from the front of the plane to the back of the plane, so it goes backwards. , Yes and what? Philips describes why the right propeller blade generates more thrust on the left propeller blade, which is what moves the center of thrust, so I think the real thing to answer your question is that there is more than one effect happening. simultaneously, yes. I'm not sure you get gyroscopic precession from that action here because it generates lift by pushing air.

I'm not sure all the thrust really has to go through for P-factor, at least through the center of the rotating propeller. I know too. in helicopters, you know, the answer for physics 101 is 90 degrees, but the real answer for engineering is 72 degrees, so it gets complicated, luckily it's beyond the scope of what the FAA tests you because they themselves, I'm sure that no. Get it completely, yeah, how about we come back after we've talked about gyros in excruciating detail and then we have a set of terminology to talk about. Let's go back to discuss more things. Yes, just remember.

I hope she is happy with the power or thepropeller. the P refers to the propeller wanting the right propeller more than the left, it also tends to happen when you have higher power, so some flight instructors like you to think about when you have higher power and the airplane you will have to put. on more right rudder to counteract left turn tendencies, I'm actually almost done with it, so I think we can end there, so it's one thing to write it down, so we talked about ascending flight, you know F is equal to MA, so once you're done changing speed and you don't have a change in speed, your forces are in balance, so the same goes for a downward flight when you're actually turning, your forces are not in balance. balance because you're having this change in speed and So there's actually a series of changes going on and it's basically considered accelerated flight, which is the same thing you know when you're driving, if you're turning, when you're flying, when you're doing a turn.

When accelerating because you are constantly changing the direction of your speed, you also have a load factor which we will go into in more detail when we talk about the performance of an aircraft and how loading affects your performance, but another thing to think about when we are talking about that flight in zero gravity and of a plane that flies in a parabolic trajectory or of a roller coaster when you are at the top, but when you are at the bottom of the roller coaster you really feel like you are pressed against your seat in In fact, when we were on that zero gravity flight, even though at the top we had thirty seconds of weightlessness to be able to do our experiments, when you go to the bottom of the parabola, you basically get two G's or double what you normally feel, so you have to sit back and let that happen before you get back on, so when you think about load factor, think about you're at the bottom of the roller coaster and you actually feel twice that force on you and then just To finish, we want to talk about what you know, most of the time we are talking about the airplanes that you will fly, but another type of airplane altogether is a blended wing body airplane, so this is an example of that, so this is what What it means is that that fuselage or that kind of tube in the middle that you sit on is mixed with the wings so that the whole body generates more lift because the whole surface is designed that way, it's really kind of cool and since an aerodynamic perspective, it has a much better lift to drag ratio because you know that all of this is actually deflecting the air molecules down and generating that lift, so I'm just asking kind of a reflection question if this is so much.

Better, it is more efficient than an airplane and aerodynamically it has much better properties. Why do you think so? We've also found that you taste better in terms of fuel efficiency because you have less drag and more lift. Why do you think you know JetBlue and American Airlines doesn't fly planes that look like this, they don't have routes with a thousand passengers, well you could do it, you could make a smaller plane with blended wings, yes passengers like the windows, that's actually a big one, that's a big reason, honestly, yeah, it's very different from what's currently manufactured and they said the development would be very risky actually.

I think it's more than just the development because it's different from what's done today, the whole infrastructure supports the current format of an airplane with a tube and wings, so we're talking about airports, airplane bridges, the way People load food carts onto a plane. that passengers get on and off the fact that passengers don't have as many windows on this type of plane, unfortunately all the infrastructure around it is a big contributing factor to why, even though there is better design, we don't move towards that, so this was very important to me when I was a student at MIT, you know, aero-astro.

I'm thinking I'm going to design the next best awesome airplane, but even if you design the next best awesome airplane, it may not be widely deployed because of these other infrastructure aspects that really got me into systems engineering, but enough of that exercise. of thought for a moment. We'll just summarize, you know what we learned today? So we talked about how an airplane generates lift and we talked. About the different factors that affect lift, we also discussed that lift is very difficult to calculate, so we experimentally measured many aspects of it and discussed the different forces on the stability of an airplane and these types of left turn tendencies. and some of the different aircraft configurations, so are there any questions about that?

Yeah, okay, what do you think about the two questions, let's take a bathroom break and then yeah, do you think about I'm going to call the pizza people and give them my credit card?