 This is the 8th lecture which happens to be the second of capsule number 4 and today our focus will be on determining how airplanes really fly. By fly I mean essentially how lift is generated. We will look at some theories which have been proposed for generation on our lift and then we will try to proceed on to a term called lift coefficient and then other coefficients which are commonly used in aeronautics. The material for this particular lecture has been prepared by an undergraduate student of our department named Karthik Mahesh who underwent this course AE 152 last semester. So I am thankful to him for helping me out during this summer to prepare this material. Our first question tonight is how do wings generate lift? And to answer that let us look at some theories which have been proposed. The first theory is theory number 1 from the Glenn Research Center of NASA. As per this theory lift is generated because of curvature, curvature of a cross section called as aerofoil about which we studied last time. So this theory states that two particles one along the blue streamline or the upper streamline and the other particle along the red or the lower streamline they are coming in with the ambient wind which is supposed to have the same velocity. And the shape of the aerofoil is such that the top side has more curvature than the bottom side or as in this case the aerofoil is placed at a slight angle therefore the path which the particle along the blue streamline has to travel is slightly longer than the path that is taken by the particle below the streamline. As per this theory the two particles which come in the front at any given point of time they have to meet at the back because there cannot be any mass loss there cannot be any momentum flux loss also. So the two particles which are ahead of the aerofoil they have to meet at the backside. So this is called as a equal transit theory or a longer path theory. The particle on the top side because it travels at a faster rate than the particle on the bottom therefore it should have a higher velocity and as for Bologna's principle incompressible flow which can be assumed for this case because they are assuming loss no shock wave etc. are present. The higher velocity produces lower pressure on the top and the difference produces lift. This is one theory. Number two theory is called as a skipping stone theory or also called as the bullet firing theory. As per this theory the wing shown here as a cross section of the aerofoil is basically an obstruction to oncoming flow. So there is some air which is hitting the bottom of this particular aerofoil or wing and because it hits it transfers its momentum and that momentum is transferred back through Newton's third law as a reaction. So as per this theory lift is the result of a simple action equal and opposite to reaction. Air molecules strike the bottom of the aerofoil and imparting momentum to the file as a result there is a upward force and hence we have lift. There is also a third theory which is called as a Venturi theory. In the Venturi theory we see that the fluid particles going above the aerofoil go undisturbed and because of the presence of the body the shape of the body is such that the upper surface behaves like a Venturi. Venturi means an continuously changing area with a reduction in area height and then increase in area. So since the upper surface of the aerofoil behaves like a Venturi nozzle the flow is constructed and because the inflow and outflow masses the flow rates have to be the same. If you give a smaller area for the air to go through it is going to accelerate. Again Bernoulli's principle is applied the place where we have higher speed you have low pressure and therefore you get an upward flow. So these are the three theories which are proposed by NASA Glenn Research Center to explain lift and there is only one issue. The issue is that all these theories are wrong they are incorrect ok. So in fact I have done little bit of mischief here. If you go to the NASA Glenn Research base they are called as incorrect theory 1, incorrect theory 2 and incorrect theory 3. I actually used Microsoft Paint to remove that incorrect thing because many textbooks even pilots operating manuals so many encyclopedia they propose anyone or a combination of these theories. But they are all wrong they are not true. What they propose is not wrong the air above the aerofoil does flow faster than the air below that is a fact. But the reason given and hence application of Bernoulli's principle is wrong. So we will look at what is wrong with them one by one ok. So let us debunk each of these theories one by one. So to start with let us look at the equal time theory. So can someone tell me what do you think is wrong with the equal time theory? Should I show you again the theory? Ok let me just show you the theory once again. So tell me what is wrong with this theory? Now you know it is wrong. So in the multiple choice question you cannot say all questions or answers are right ok all three are wrong. But now you need to explain what is wrong ok. So let us lake one by one yes. My name is Vinay. Yes. And it has been shown through observation that the same streamline passing over the top and the bottom never reached the trailing edge at that same time. Ok let me interrupt you. You cannot say same streamline top and bottom. You cannot flow across streamline that is the first fundamental part about the streamline. I know what you are saying you are saying that observations and experiments are shown that particles along the blue and the red streamline in this figure do not meet at the end right that is true. So if they do not meet at the end does that debug the theory? The theory only says that there is a lower pressure on the top and higher on the bottom because in the same time the particles which meet at the front of the aerofoil have to reach at the back and you have said that based on some experiments and observation I will show you some experiments also. I agree that is a good observation but how does that debunk the theory? Yes. My name is Ashwari and here it is written that from Bernoulli's equation we know that the flow above aerofoil is has some velocity gradient and hence have some rotation. So we cannot apply Bernoulli's theorem in rotational flow and viscous flow. We cannot apply Bernoulli's principle in rotational flow and viscous flow and also we cannot apply Bernoulli's principle across two streamlines. Yes sir. Ok sorry that is it so that I agree. So therefore this particular theory which is very popular is wrong. What is wrong is not the phenomena of higher speed at upper surface, lower pressure upper surface but what is wrong is the explanation. Now if the equal time theory was correct then what would happen to a body like this? It will generate some lift in which direction downward or upward but do you think if I put a particle like this in flow I will get lift? So let us have a look. If you find that others still support the equal time argument ask them to generate lift from this surface. If they are too lazy to do so we will do it for them. Some experiment. So they are keeping this particular shape particle in a string. So this particular string is basically representing the flow direction ok. And Newton's third law analysis predicts direction of the lift in different ways. So here you can see the string is bending. We have even conducted a high quality CFD analysis to prove the same thing. If you understand what we have discussed so far here is one brain. So basically equal time theory can be debunked because it is not going to work ok. One more example of equal time theory is this. So if an aircraft is flying upside down inverted then how can you get lift by equal time theory? The lift in this case will be downwards and the lift is downwards how can it maintain level flight? It will keep on coming down ok. So interestingly even though it is flying inverted the lift is still upwards and it is overcoming the weight and that cannot be explained by equal time theory because if the plane can fly level inverted it cannot fly level in normal condition and vice versa. So therefore that is not true. One more example is shown in this video. It is often said the lift in a wing is generated because the flow moving of the top surface has a longer distance to travel and therefore needs to go faster. This common explanation is actually wrong. This video shows that the air on the top does move faster but it does not reach the end of the wing at the same time as the air along the bottom. Here we use smoke to visualize the stream lines around an airfoil. We can pause the smoke by briefly interrupting the supply. This gives us lines that travel through the flow as we can see here. And if we now slow the video down you can follow those lines and that gives you an idea of how fast the flow is in different parts of the airfoil. Here you can see it speed up as it approaches the airfoil and it moves faster over the top compared to the bottom. You can see that it reaches the end on the upper surface much earlier than it does on the lower surface. In fact by the time it reaches the end on the lower surface the flow has already gone a long way past on the upper surface. This shows very clearly that the flow does not take the same amount of time to reach the end of the wing. So this is basically a proof of what our friend mentioned that experiments have shown that the flow on the upper surface definitely moves faster than that on the bottom surface. On that there is no argument but the argument is on the justification for that particular theory. Another example which will completely debunk the equal transit theory is thin airfoils like these which were used. Now if the equal time theory is correct then such airfoils can never produce lift because there is nothing like now more curvature on top and less on the bottom. The curvature is same on both top and bottom but they do produce lift. In fact Wright brothers flew the aircraft for the first time using an airfoil like this. So they cannot be wrong they did produce lift. So in other words this is not a correct theory. Let us proceed to another example. So for this I am going to use this piece of paper as an example. So here is a piece of paper. I keep it horizontally in front of me and I blow air on it. Look at what happens to this piece of paper. Usually I am putting pressure on the paper it should go down but it is going up. Can you see? So even though the flow of air is on the paper and normally the momentum from my breath should push it down like this but when I blow it it is actually floating up. So why is it happening? This is happening because the fast moving air across the paper actually it creates a lower pressure on the upper surface. Is it because of Bernoulli's principle? No it is not. This is not Bernoulli's principle. This is quanta effect. So a large number of sources in literature on YouTube and even at many other places explain working of the aircraft wing generating lift using this example and then they say Bernoulli's principle as I blow air on top of it the speed is large so pressure is low and hence it lifts up that is not the reason. The explanation for this particular phenomena is coming from the quanta effect. So Bernoulli versus quanta conundrum is very common. Similarly if I place a spoon with a curved surface in a stream of water at a reasonably slow speed so that I do not create too much turbulent flow you will notice that the water follows the curvature and more important there is a force acting on the spoon in the direction opposite to the curvature. So when the fluid in this case water flows along the curved surface such as the fluid flowing notice I was always keeping it like this so that it remains little bit curved if I make it stiff okay and if I do not allow curvature it may not lift up let me try difficult but it will not it won't lift up it will lift up only if I allow it to have curvature okay. So when I have curvature and when I make the air flow along the curvature a force will act opposite or perpendicular to the direction of curvature and that force will make the spoon move towards this side and this is very important so the jet of the water follows the spoon curvature and the spoon feels the force opposite to the deflection okay that is more important. So certain things about this particular theory are right. Number one quanta effect which says that a jet of flow attaches itself to a surface which is curved and also the jet deflects due to a force and also because the jet deflects towards one side there will be an equal and opposite force on the other side. So these three points are correct about this explanation but there are also three wrong explanations one is the flow past a wing is not a jet because there is flow above it there is flow below it and it need not be only at a very high speed it can be at a reasonable speed or low speed also but it is not a jet it is not that only on one side you have a flow it is a it is a uniform jet. So flow along a long airfoil actually is like this it is above and below both. Second point is the flow underneath the wing does not remain stationary it also moves and thirdly you cannot use quanta effect here because it is not always having curvature even a flat plate at some angle can give you lift. So let us see yeah the equal transition time theory was proposed by some people for attempting to give a simple explanation to school kids and to other people general public about how lift is generated. It is very convenient to say there is something called Bernoulli's principle in which when there is a velocity increase there is a pressure decrease and you know so it was not proposed by any scientific argument it was proposed simply to go for these are called as hand waving arguments. So you try to just convince somebody by giving a general argument which are wrong. So the repercussion of the argument or the justification that there is low pressure that the upper surface fluid speed is faster is correct but the reasoning is wrong that is why we are debunking the theory. Sir my name is Samyit my doubt is we are saying that we cannot apply Bernoulli's principle for two different stream lines but the value of p plus half rho v square plus rho gs is almost equal for both of them. And p1 plus rho 1 v1 square plus z1 is equal to c1 and p2 plus rho 2 v2 square per z2 is equal to c2. So along the stream line the constant c1 remains the same across stream lines you have two constant they are constant but not equal. Sir almost equal. Almost is not acceptable in science. Sir means pressure is almost same in both of them and velocity of both of them are almost equal. They are not equal just now I showed you. No when they were attached here before hitting the foil. So when they approach the body the velocities are almost the same but when they went towards the end the velocities were different. So when the velocities were different the pressures cannot be the same. However you cannot apply Bernoulli's across two stream lines because the two constants are different. Scientifically you cannot apply Bernoulli's principle across two stream lines. If that is a case I can apply Bernoulli's principle at a stream line which is 1 kilometer above the aerofoil 1 kilometer below the aerofoil and I can say the two pressures are equal I cannot. So you cannot say they are so near we can assume it to be constant. No along the stream line yes but across stream lines you cannot you just cannot apply. So that is what I am saying do not apply a principle or a scientific tool wrongly to explain something simply that is why we are trying to debunk these theories they are not scientifically correct. Now yes. My name is Aamun but in case of Bernoulli's theorem we can still write two different equations and manipulate them right above and below the aerofoil. You can but then you will have not the same constant. Yeah but initially the constants are same right so. No when you apply them at one particular point can you apply the can you apply the principle exactly just think about it. As it is we have been told the flow is not irrotational so you cannot apply Bernoulli. As it is we have been told the flow is viscous so we cannot apply it. On top of that we cannot apply Bernoulli's across two stream lines so that is why let us not try to explain some phenomena by application of a principle in a wrong manner. There are simpler methods available which we will see just now.