 Hello and welcome to my talk. I'm the research Associated the chair of aerodynamics and fluid mechanics at the technical University of Munich and today I try to explain why an airplane can actually fly so what carries the airplane? And I speak to her, okay So I try to explain the aerodynamics in 15 minutes by using Three formulas, but today I have a special offer for you by using only one formula Let's try this First of all, I'd like to explain which forces are acting on the aircraft here. You see a pretty realistic Picture of the aircraft and of course, there's some gravity which Tries to pull them airplane to the earth So we need another force which should carry this airplane This is the lift force each acts upwards and Can overcome the gravity But when the airplane is moving through the air there appears some drag so the drag force tries to pull The airplane backwards and we need some another force which can overcome this drag And this is the thrust produced by the engines of the airplane So we have our four forces acting on the aircraft, but I heard about another four important forces acting on the aircraft These are the dreams of the engineers trying to get the airplane fly The reality tries to prevent them from from doing this The real willion here is the regulating authority and if there's enough money then Every problem can be solved and the airplane can fly So before I Explained the lift force. I have to introduce some basic concepts in order to make it easier for you to follow my explanation again, we go back to our airplane and This a really simple concept which can Explain almost every effect of aerodynamics. So we have only To look at the cross-section of the wing. So let's cut through the wing and Here you see the cross-section of the wing. We call it airfoil and The other important concept which should be understood is It doesn't matter whether the airfoil is flowing through the air or the airfoil is standing and the free stream It's just flowing over the airfoil. So we have our free stream and we can define some angle This is the angle between the free stream direction and the mid-quart of the airfoil and we call it angle of attack So pretty easy actually another concept. We have to understand are the streamlines These are just the tracks of the air particles which are flowing along the airfoil and We can depict it like this. So again pretty easy The third but really important concept for our explanation is the Bernoulli law Maybe a lot of you will learn this in the school and here you see a pipe with a varying cross-section It has a really big cross-section at the beginning and At the end and the narrow part in the middle of the pipe. So you can imagine when the Water or some fluid is going through this pipe It is accelerating in the middle because the same volume has to pass through the narrower Cross-section, so the velocity increases actually in the middle and the Bernoulli law tells us that when velocity is getting higher the pressure is getting lower. It's pretty easy and in the second part of the pipe the Velocity of the fluid is getting lower So the pressure is getting higher. I Simple as that. So now we have all the tools to understand the lift force We go back to our airfoil. You see this tracks of the air particles and Here we have two particles which are starting at the leading part of the airfoil and They want to go to the backward part of the airfoil Of course, everybody would agree So you can believe me that the upper surface is longer than the bottom surface It's it can be measured and it's actually true So the upper air particle has to carry up to meet the bottom one again. It's easy to understand So the velocity at the upper surface is higher And Bernoulli law tells us that the pressure is lower Again, it's pretty simple now we get some pressure difference between the upper and the bottom surface which generates some lift I can Show you my palms and if I pushing with the upper palm a little bit weaker Towards the bottom one Then some overall force tries to put my palms higher so the lift appears A really simple explanation of lift So now we are actually done But wait, so let's be real scientists and question this theory Here we have a really simple airfoil. This is a plate just a simple plate. We have some free stream What do you think would this airfoil produce some lift or not? anybody So everybody agrees and if we put this airfoil In the wind tunnel or if we are carrying out some experiments, we would really experience What you just answered we would We Would actually get no lift generation there So we wouldn't measure any force at this plate, but let's rotate it a little bit What about this situation so we increase the angle of attack? What do you think would we get some lift or not? According to our theory, so do we have some brave scientists here who would Okay, so I can tell you if we carry out this experiment we would get actually lift So our theory is starting to get some cracks It is it isn't predicted by our theory So the airfoil is it's not so bad actually so we can build an airplane by using this airfoil But what about this super airfoil now we increase the upper surface the bottom surface is pretty short It's great. So it would produce a lot of lift. What do you think? Yeah, I hear some voices of engineers, but Actually our theory would Predict some lift, but you're right It would only generate some drag and no lift at all. So the airfoil is bad So our theory is simply wrong. What's wrong in this theory? The air particles don't have to meet. That's what I claimed, but it isn't true and In general Bernoulli law can be applied to several streamlines. That's what we tried a couple of slides ago So this theory is pretty prevailing, but it isn't true and that's That's what I don't like that's why I talked to you today But don't worry. We need only one Equation which can explain everything we just have to understand this equation to solve it And we would know everything about the flow over an airfoil and this equation looks just like this Okay, it's a little bit complicated I agree It's so complicated You can get one million dollars only for a proof that there exists some unique solutions of this equation So you don't have to provide the solution actually you just have to prove there are some solutions So mathematicians are crazy people. They give one million dollars for a proof of there exist some solutions But no problem We actually solve this equation in an approximate way We use computers in order to solve these equations, but it's important to understand we get an approximate solution it's okay for us as engineers and scientists and Better our computer should look like this This is the supercomputer Which is located to the north of Munich and We're using it to solve actually of these equations As you see it isn't actually as simple as the first explanation But I tried to give you an idea about the lift generation by a simple concept We can look into a flow here you see again the stream lines and they're curved so we have some curved flow and There's air particles which are moving along the stream lines experience some Force this is the centrifugal force And it acts like this. This is the same force. I have my keys here So if I rotate my keys, you see this keys are pulled Outwards of my hand. This is actually the same force which strains this stripe So it's an easy concept and maybe it helps us to explain the lift generation What I did I solved the equations you just Have seen and I tried to look into the whole picture. Let's do it together Here you see a picture of an airfoil I just used a symmetric airfoil for the sake of simplicity So the upper surface and the bottom surface have the same length and You see some beautiful colors. It's actually the same situation as with the weather forecast the blue color denotes the lower pressure and the red color or green color denotes some higher pressure as you see Our stream lines I actually curved because they try to follow the airfoil They're curved here. So they there because of this Curve a chair appears a force and This forces they are acting outwards of the airfoil and they produce this regions of lower pressure on the upper and on The bottom side of the airfoil But because our airfoil is a symmetric and we don't have any angle of attack These forces are equal and the airfoil is in equilibrium and Doesn't produce any lift in this situation, but let's look in time a graph So we are real scientists. We want to Make a beautiful graph. So we put our angle of attack It's zero and our lift is also zero, but let's increase the angle of attack So now we have an angle of attack of five degrees and as you see the curvature of the stream lines isn't The same anymore the curvature is here higher at the upper side then at the bottom side because of this curvature and Region of lower pressure occurs only on the upper side. That's why This region produces some force which is acting upwards So we are starting to get some lift in this situation as you hear as you see here We go to our beautiful graph. We put some new data point five degrees and some lift occurs Okay, let's increase the angle of attack again. Now you see it certainly the stream lines here are Getting much more curvature than at this side and the region of lower pressure is getting bigger This causes the lift to increase so we get we get even more lift here and Here we have our new data point and as you see it's a pretty nice Dependency it's a linear dependency. What does it mean if we double the angle of attack the lift doubles as well? It's pretty easy but let's Increase the angle of attack again We are greedy now We see some limit Because the angle of attack is too high the air can follow the airfoil anymore at this side So here appears some region. We call it separation bubble Here the air is just Recirculating over and over again and this bubble disturbs actually the whole flow over the airfoil and our lift is Getting lower unfortunately So let's The the lift is actually lower here, so let's Look into our graph another data point and now the lift is getting lower Now we try some really high angle of attack Here you see the separation bubble is really huge That's why this airfoil produces only a tiny amount of lift and we can't use this airfoil anymore By such a high angle of attack. It's pretty difficult and this situation Is pretty dangerous We call it stall and the stall can be compared to the wheel of a car Which loses Contact to the street if it's raining or it is icy out there So the driver of the car can steering the wheel As intense as he wants, but the vehicle wouldn't respond to his Steering and the car is driving However it wants the same appears here We get our new data points, so the lift is pretty low And now we are designing some aircraft so the What we are interested in is this region actually this green region Where the lift is linear? So we are trying to use the airplane with such Flow around the airfoil And this region is pretty dangerous for the civil aircraft But this region can be used by military aircraft for example fighter chats are flying Also at higher angle Angles of attack like the here now I hope you have a little bit more clue about the lift generation and Here a small brief conclusion, so the newly law is great But unfortunately it can be used for the explanation of the lift force in general It is valid only for one single streamline Lift can be explained by the courage of the stream lines centrifugal force Lift depends on the angle of attack and in our nice region. It's a linear dependency and Once the angle of attack is too high the stall occurs. So this dangerous situation we don't like and Especially this effect constraints the lift force generation. So there are always some limits in our lives Thank you for your attention. That's thank you very much blood Any questions It was just Coincidence actually so I've chosen only 20 colors in order to depict the whole situation here and Yeah, I could have taken much more colors But it doesn't No meaning actually I It appears nicer It's a great question It works exactly in the same way you can just turn the picture and you will get the opposite situation So there are some airplanes. They can fly another way around. So It works pretty well Hey, I have a following question I quite often I used to observe birds and I have come to the following conclusion that they Do fly in a completely different way considering the airplanes and to be precise they wave with their wings Why don't the engineers construct their airplanes so that they wave with their wings? Okay, it's a Great question Actually as engineers we can do it much easier We can use some engines and birds unfortunately don't have any engines at the wings So they have to wave in order to produce some force Forward which push pushes them forward and we can just use Engines for it or propellers Thank you. Any other questions About this huge equation actually It was solved Approximately, but what was the meaning of like what did the solution? What is the meaning of the solution? It's it's again a really great question So actually these equations are just laws of Newton everybody know this laws They describe the conservation of mass momentum and energy. So nothing else. It's pretty easy so the the concept is easy, but This solution or the way to solve this equation is pretty hard So the math behind this equation is hard, but the physics is pretty easy. It just okay the the mass Can't actually disappear. So if we put one liter of Fluids in a pipe we get one liter again. This is the first equation these three equations are The conservation of momentum so the the law of Newton and the third equation is just the conservation of energy So the energy or the heat is flowing From the hotter region to to the colder run That's what this equation actually explained but the math again the mass the mathematics is ugly and how Do you mean this solution you you can get one million of us dollars Yes, so we we don't have to carry out any experiments anymore So if if I want to know the lift of this airfoil, I just showed you I just have to carry out some simulation by means of a computer and I don't have to go to the wind tunnel then I Don't get any Dirty hands, so it's better Yeah, that's right. Yeah So there are some simple setups for example a pipe or something simple there You can find a solution just by by the hands. It's pretty easy, but there are really complicated regimes of flowing or of the flow and In these regions, nobody knows what what's actually happens. It is an unsolved problem So the physicists are fighting against these equations and are trying to to get more Insights but it's pretty difficult Yeah, that's right, it's these equations are really non-linear they're really complex so some chaos occurs there and Nobody knows whether you It's a coincidence that you get especially this solution or this solution It depends on everything so okay. Yeah, okay. Thanks. Thank you very much blood Please feel free. Thank you very much for a talk. Please feel free to approach blood with your questions during the coffee break Thank you again