 So let's see if this video works. By sweeping the wing, we actually delay the supersonic flow and raise the critical Mach number by tricking the wing to make it feel like it's flying slower than it really is. We do this by creating two different components of airflow. The cord wise component travels perpendicular to the leading edge along the cord line. That's the only component that accelerates and since it's less than the total amount of our flow, we're only accelerating part of the air, which means we can fly faster before we have supersonic flow. However, we're also creating a span wise component of flow which moves parallel to the leading edge from the root to the wing tip. And as you move out to the wing tip, that span wise component stacks up, making the wing tip feel like it's flying slower than it actually is. Okay, so remember one thing that you may have swept the wing and created a normal component lower than free stream. But by the span wise component of flow, you actually create problems. Because the ailerons, the control surfaces, et cetera, okay, there are flaps also there but flaps will not be deployed at high speeds. But you might deploy the ailerons. And these control surfaces which are mounted towards the tip now get sideward flow. So their effectiveness is also decreasing. So their effectiveness is also decreasing, which is not desirable. So sweeping back has its own problems. In fact, if you talk to an aircraft design specialist, you will get this particular answer. Sweeper provides sweep unless it is essential from the aerodynamic considerations. Because everything else about sweep is bad. Nothing else is good. It makes the wings more flexible. It makes the wings heavier. It creates control surfaces less effective, okay. Everything else is bad about sweep back. Even sweep forward, okay. The only problem is that when you want to fly fast, then ability to fly fast and hence have a lower wave drag is the primary consideration and other things are going to take a back seat. So even in transport aircraft where weight of the wing is very important, where controllability is very important, since the benefits of sweep back in delaying critical mark number are so high, you are forced to provide sweep back. So the moment you have to fly beyond mark number 0.7, 0.75, etc., you grudgingly provide sweep, okay. Grudgingly, because unfortunately other solutions are not as elegant as sweep. So this is what it is, just a repetition. You have an aerofoil which is at mark number of 0.7. So you have no sweep, therefore the two speeds are same. The moment you sweep it, then you have a component and that component along the normal is going to reduce, okay. So effectively the mark number, the free stream mark number which was 0.7 was critical mark number earlier, it will become 0.808 by a simple approximation, this is only for indication. Actual story is very complicated. So actually when you provide sweep back you get a large amount of complexity, you get lot of 3D flow. But our assumption, okay, is a sweeping assumption, it is okay but still it works. So whatever we discussed in the class saying that when you sweep the wing behind, you have such reduction, that is a very simplistic explanation. In reality you may not get exactly that much improvement because the moment you sweep you bring in span wise component and the span wise component is going to create a very complex 3D aerodynamic pattern and hence the benefits of the sweep back may not be as pronounced as the simplistic explanation. So do not say that always if the free stream mark number is M infinity for unswept wing, it will be M infinity upon cos theta for swept wing. That is just a simple approximation, just an indication but not the total story. The actual and critical is actually a function of many, many, many, many things. So now there are other solutions which have been given but we do not see them very often, okay. It is actually very weird and that is why we do not see it but it is highly beneficial, okay. Let us have a look. So one intern who came and worked with me during the summer and his content will come after Midsom because he worked mostly on performance. So I will introduce you to him later but right now I will show you a small video. So this is a small video that introduces the concept of oblique wings. In 1958, Artigerm suggested that the aircraft with asymmetrically swept wing which we call as the oblique wing will offer higher advantage at higher transphonic speed and lower supersonic speed. You can see the oblique wing in this aircraft. This is a small glider model which I have made on using balsa wood. The span-wise length of this glider is 8.5 inches whereas its width is only 1 inch. So why do we prefer oblique wing instead of a normal swept wing? The answer is clear that the minimum lift dependent wave drag actually will be achieved when the lift is elliptically distributed along the span length on the wing and it has been seen in the supersonic flight that the lift gets distributed over twice the length which means which is the effective length becomes twice which will actually help in reduction of minimum lift wave drag by a factor of 4. Adding on to it, the single pivot in oblique wing will provide the structural advantage over the two pivots which will carry the bending load in a variable international sweep aircraft. So there were some challenges such as the significant variation in rolling moment with the change in angle of attack and the unusual inertial coupling and the aero elastic characteristics which made the dynamics of such an aircraft complicated as well as there was a problem with the propulsion integration of such an aircraft. How was it solved? With the help of modern computational methods and modern pride control system technology which now makes a strongly coupled and more stable physical aircraft system. Okay, so this is the video which just gave us some gyan about what this is. Let us look at his experiment. So what he did is he actually fabricated a small oblique wing aircraft just to see how it performs. So now here I have an oblique wing glider which is made out of a balsa wood and as you can see the span wise length of this oblique wing glider is 8.5 inches whereas it is width is 1 inch. With the help of sandpaper the edges has been made curved upwards and using water we have just banded this upwards because the slight bending will actually help in smooth gliding. Only things that need to be taken care of is that excessive sanding do not just remove the extra part of this glider as well as more bending can result in stalling of an aircraft rather than the smooth gliding of this aircraft. Another major issue that I have been facing on this aircraft is the CG balance of this glider. This angle is 135 degree. You can see there are rolling moments introduced and that is what he was saying and that is the problem with oblique wings. It is very difficult to create oblique wings which have a perfectly balanced rolling moment. So that is the reason. So we did an experiment and it was successful. We were able to fly this reasonable distance but it is not really very common. So there are some benefits, there is a lower structural mass. The center of mass and lift is not shifted because on one side it is set forward on one side it is set back. As against either sweep back or sweep forward the center of gravity is completely shifted ahead. Here it is not shifted. There is a lower wave drag. Let us see if our video works let us see how the wave drag is lower. So this is the CFD analysis, a real time CFD analysis of a wing at various angles. So the colors you can see the solution time is increasing in seconds. So it is 7, 8, 7 seconds, 8 seconds and the color coding is such that when you go towards the blue you have higher values and when you go towards the red you have lower values for the pressure coefficient as well as for the Mach number. So you see the graph that you see on the bottom figure it shows you how as a function of time the value of CD is changing. So this I will, but there are some problems. One problem I already showed you in the flight when it was flown by Udit you realize that is asymmetric stall. So when the aircraft stalls you do not have both the wings stalling at the same time. That would be easy for the pilot to handle. What sometimes happens is that only one wing will stall before the other. So then you have this kind of a problem. Now to recover the aircraft from this kind of a motion as you saw in this video is not very easy. And if you have one wing swept forward one wing swept backward there is a very good chance that there will be an asymmetric stall whenever stall happens. So that is why oblique wings are dangerous. Then the whole wing is going to hinge at one particular point. So there will be a lot of load on that point. So that point will be heavily loaded and the place where you are going to, so imagine you have a wing which carries fuel and then you are moving the whole thing along the hinge. So that is a serious problem. Sometimes we have something called as inertia coupling. Now I would like to cover this, it is a flight dynamics problem but I found this very nice animation of inertia coupling. So inertia coupling happens when two modes of the aircraft start getting coupled and then one of them causes the other to accentuate and then it becomes completely uncontrollable. This is on a simulator, this is on a simulator. So you can see, okay, right. Now let us look at forward swept wings. Forward swept wings are better than rear swept wings actually speaking because as you can see the span wise component is along the, along the root. So therefore actually the flow is being gathered by the wing on the root and you can make it flow over a control surface and make it very very effective. But there is a problem, there is a problem regarding forward sweep and that problem was encountered by during flight testing. That problem is called as torsional divergence. So what happens is, let us say this is, let us first have a look at some videos of forward swept wings. So here is an example of a forward swept wing. So the initial. In the years of the X-29 as a test vehicle, engineers will be able to explore the forward swept wings unique mixture of speed, agility and slow flying qualities. They will also explore the interaction of the wings with the forward canards and rear strike flaps. In this design all control surfaces are linked together by computer. Walter Sepic, NASA's program manager for the X-29. All three of these surfaces are tied into a digital computer and their deflection or movement during flight is optimized by the flight control computers. When the pilot makes a stick input to the airplane, these three surfaces all react simultaneously to give the optimal response to the airplane, to minimize drag and maximize performance. The forward swept wing concept was first explored during World War II when the Germans built a test bomber with 15 degree forward swept wings. The bomber had a limitation which is inherent to all forward swept wings. It is called structural divergence and is illustrated here. As soon as higher speeds are realized, the wingtips experience tremendous twisting loads which flex the wings and can literally tear them off. The X-29's wing is crisscrossed with 750 composite tapes of such material as carbon, kevlar and glass. The materials are woven in a way to counteract the twisting forces encountered by the wing at transonic and subsonic speeds. So this torsional divergence one has to understand. Since the wing is located ahead of the center of gravity, as the angle of attack increases, the loads on the wing will increase and the increase of the loads will be such that the tips are deflected upwards more than the root. Why because the wing is flexible and the distribution of load is ahead of center of gravity. So as alpha increases, load increases. So something increases ahead of the center of gravity so the wing will deflect upwards. When wing deflects upwards, its angle of attack increases. When angle of attack increases, the load increases. When load increases, the wing flexes upward. So very soon you have what is called as a torsional divergence and there are been examples in which the wings have been torn off during flight. So this concept was started, experimented and then people said this is very dangerous because the wings are breaking away during flight. So it was kept in the cold storage. What was the advantage? The advantage was that the span wise component coming towards the root is beneficial. You can use it to energize the control surfaces. On the other hand with sweepback you are making flow bad over the control surfaces. So then when we developed expertise in composite material, we were able to provide flexural strength in the direction we want. So it is called as aeroelastic tailoring just like a tailor stitches a shirt or a suit matching with your dimensions, providing more material where needed and less material where not needed. Similarly, using composite material because you have layups and you have various orientations of plies available to you, you can actually strengthen the wings such that it is without heavy weight. It is strong in the flexural direction and not that strong in the direction where we do not expect the load. So with the limited or with the lower weight of the structure, we were able to provide sufficient strength. So when that technology was available, the forward swept wings have come back. But as the testing of X-29 shows, the net result of the forward swept wing experiment was that it is too complicated, requires very very accurate and precise flight control system. It is prone to other problems of controllability and hence the technology is demonstrated and kept but it is not popular because the problems that are encountered are actually more than the benefits. So all these are benefits. However, the problem was in the instabilities. So there is a phenomena called as a Dutch roll. So this is the coupling between aerodynamics and structures. The structure of the aircraft provides damping to the oscillations and disturbances provide oscillation. So there is a frequency at which the aircraft generates disturbances because of its aerodynamic configuration and the atmosphere and depending on the structural configuration there is a frequency at which those are damped. Now if they are not matching, then you get a phenomena of Dutch roll. So you can see now. The speed of the motion itself and there is the roll to your ratio which is a measure of how much roll, how much bank angle to how much side step and those are the three aspects that you have to assess and they are all important in their own way. This is a Dutch roll when the aircraft starts oscillating in roll and yaw and this is a very common problem. This problem is more pronounced in forward swept rings. I have already talked about horizontal divergence. So then the answer to that is variable sweep, variable swept rings. So basically you provide whatever sweep is needed at whichever condition. So this is an example of an aircraft. The first aircraft to provide the ability to sweep the wing at whatever angle you want at whatever speed you like is the F triple 1. So let us see F triple 1 in action. It is a very old video because it is a very old aircraft. You will see a very interesting control on the left hand side of the pilot which is the control of the sweep. So during takeoff and low speed flight you have low sweep and that is the one. So in this aircraft any location or any sweep position was possible. It is a truly variable sweep aircraft. The pilot can actually lock the handle at any point right from the starting, starting to the end at any point and then you can take it forward also at any location and lock it. Notice that there is a chase aircraft which is filming this particular aircraft. Notice that as the wings sweep forward and backward you do not have any great speed changes. The idea is not to make it fly faster or slower but to present the aircraft in the best configuration at various speeds. So during low speed flight lower sweep is better because you want to have high aspect ratio. During high speed flight better to have delta wing or a fully swept wing. So you go into whatever position is appropriate for your flight profile. There is the air break coming down during landing. But during landing you will find the sweep will be always the lowest possible sweep. Okay. In India also we have dealt with two aircraft. Now I have worked on this aircraft for one and a half years so it is very close to my heart. The MiG-27 M Bahadur. This particular aircraft had three sweep positions. It was not a continuous sweep aircraft. The pilot had a choice of 16 degree, 45 degree and 72 degrees. These are approximate number. Actually it is 16 degree and 43 minutes and all that. So three possible positions. The lowest sweep position was during takeoff, during landing and low speed flight. The 45 degree sweep is during transonic maneuvering, during combat. At transonic speeds because that is the most appropriate one. And high speed flight when you are basically coming back home after doing the damage. This is a bomber aircraft. MiG-27M is a ground attack bomber. So you go and do your work and then you simply run behind, run back to your safe territory. At that time high speed flight with no external stores attached. You just move it to the maximum sweep and rush back home or dash back home. Okay. But there are severe limitations and problems because of this. Drag is lowered, lateral stability is improved. Okay. Same thing like what we have seen earlier. But they are not popular today. You do not see many modern aircraft having very well sweep because they make the aircraft very heavy. And that is a rough approximation that an aircraft is 4% heavy if you make it sweep back, variable sweep. And it is a huge penalty. Okay. So MiG-27M weighs approximately 20 tons, 4% to 20 tons. It is a large amount of weight. I could carry fuel or I could carry armament instead of that. Then there are serious issues of maintenance and we were always having a problem in the maintenance. This is not MiG-27 sweeping mechanism. This is for I think F1111 or Tomcat. I think it is Tomcat. But just look at the size of the bearing because the whole wing has to swing along one bearing, one on each side. I remember the bearing for MiG-27 was taller than me in height. I could actually go inside and stand with the race on top and bottom. That is the size of the bearing. And it was at least this much diameter. So such a thing has to now rotate. And if there are two wings and if they do not rotate equally then you have this balance. So we always faced a problem in the maintenance of this particular component. And the largest number of problems which we encountered during maintenance of the aircraft was on the maintenance of the bearings. Remember the wing is not, it has got a slight anhydrous. So you need to also balance. You have to be sure once it comes from maintenance the wing is removed. You do many things. When you put it back then you find that the bearing is not moving smoothly. Or it is giving imbalance and it was a nightmare. So all in all people say it is not worth it. Then you have a higher radar cross section because you are providing variable sweep. So under some condition it is going to have low sweep and therefore it will have a much larger cross section. And in some condition it will have a lower one. So if you have a constant high sweep you have a lower cross section. So in the next class we are going to look at types of drag and what do we do to reduce them. Thank you.