 So we move on now to a special kind of aerofoils called as the LRN aerofoils. Aerofoils designed for very low speed aircraft because they will be operating at very low Reynolds number. Now we know about Reynolds number, we know that it is a ratio of inertial and viscous effects. So when viscosity is predominant Reynolds number is higher, when viscosity is less predominant Reynolds number is lower but viscosity is always there. So you may have a flow with low Reynolds number. So there was a question raised in the Moodle and I am very happy that so many questions are being asked. It is very nice to see that the students are thinking over the questions. Coming up with arguments about what they think is the correct answer, quoting literature, it is amazing, it is very interesting and as you saw we also found a mistake in one of our examples to do with the swing bowling. So I have referred to some sources and based on those sources I had some understanding but my own understanding became better because of clarification that was given yesterday. So this is something that I would encourage you to continue doing. So similarly here also what you have to see now is that if you have a low Reynolds number you will have drag or stream wise resistance and the maximum lift is going to be limited and we know that the Reynolds number, now for Reynolds number we need to have a defining characteristic length or dimension. So for the wing it is the chord of the wing. So look at aircraft like Gossamer, Albert Ross. Do you know about this aircraft? What is special about this aircraft? This is the human powered aircraft. The pilot is peddling the aircraft. Essentially there is a propeller behind and you can see there is a pilot who is sitting in the cockpit and the pilot is actually like a bicycle. So can you tell me what is the typical energy that a human being can produce in cycling? How much energy can you produce by the let us say a very fit in not like me a very fit individual an experienced cyclist who goes long distance cycling etc. people who do tour the France etc. How much energy can they produce? Can you guess? Is it 1 horsepower 747 watts? Do you think we can produce a power of a horse? I do not think so. We can produce probably half an horse power 200 watts to 250 watts is the maybe 300 watts that is a maximum energy. So with 300 watts of energy capability that means the engine can produce 300 watts. You have to fly an aircraft that can carry the aircraft and the horse and the person who is flying it. So it is a very tall challenge with 200 250 watts of power available or muscular power generation of 200 watts to fly an aircraft. Obviously this will not be a high speed aircraft. It is a very low speed aircraft. So the the aerofoil to be used for the wing of this aircraft is also an aerofoil that is suitable for a load in awesome of light. So the Gossamer-Albertros aerofoil you can see the cross section here I think it is not very clear but this will give you a better idea these are 10% thick Epler 193 aerofoil. So such an aerofoil is used for low Reynolds number flow. As I mentioned to you in the tutorial we will look at the shape of the aerofoil and corresponding it to its lift and the drag capability. Right now I am not going to go into that detail just wanted to give you some idea. This is another aircraft which is designed for low speed flight okay. So where is it used this aircraft? Looking at the aircraft can you tell me something? What kind of plane is this? What do you think? Yes what is your name? Yes Atharva. On what basis do you say that? For resting you share. It has a large fuselage so that it can show water. That is an assumption that it is a large fuselage. So there are a few distinctive shapes in this aircraft which can give you an idea. I agree that the fuselage shape is large but just because something is large does not mean it has got water inside to quench the fire. So this is not a fire extinguishing aircraft okay. Sir is this an amphibian aircraft? Yes it is an amphibian aircraft why do you say that? Downside of the wing. Below the wing? Below the fuselage? Below the wing. The yellow color. What is it? Basically it is a float. It is a float. This yellow color device now the team who has done the assignment on aircraft nomenclature okay. They have I saw the assignment that they have submitted they have looked at very interesting components. Which team is that by the way? Team number the team that did assignment on the only you are there in the class representative of the team. Oh there is one more person there that is all two of you. I saw your assignment and you have given some very interesting things like small parachute behind a bomb which can be used for retarding the bomb etc. Those are not part of the aircraft they are special things on special things. This is a part of the aircraft which I would have been happy if I do not know whether you have done it but such things is what I was looking for it is okay. So yes this is a float but apart from the float which is here is there anything else in this aircraft that makes you think it should be something that goes on water. Raise your hands if you have some idea by the looks of the aircraft. Yes anybody yes. So my name is Vinay. Vinay yes. And the engine is mounted on the top. Right. So if it was somewhere on the wing as in conventional aircraft then the amphibian like water landing might not have been possible. Right. So you are right that the engine is mounted high but it is on the wing like any other aircraft but the wing itself is high so that you can keep it away from the water level agreed. Okay but not every high wing aircraft is water aircraft. So something else which is distinctive yes your name first. Right that is right very good observation the bottom of the aircraft. So you can see from here to here and there is a sudden jump here which is not very much visible here. This is the shape of a boat. So this is a flying boat or an amphibian aircraft. Okay. So now why should they have low enough number of aerofoils because they will not fly at very high speeds. They are operating from they are operating from sea or from lakes. Okay. So therefore they will not fly at very high speeds. So the Reynolds number of these aircraft will tend to be small compared to other aircraft. So therefore they are fitted with special aerofoils which are suitable for loading all number. So this is a Lisman 7769 aerofoil distinctive shape and the holes in the center are basically holes for lightning it. So this is another example of an aircraft with low. Now surprisingly if you look at L by D or CL by CD maximum versus Reynolds number you find that rough aerofoils are very good at low Reynolds number and then there is an area of intersection of both of them 10 power 5. Beyond that the smooth aerofoils start having high L by D. So this depends on whether pressure drag is more important or the skin friction is more important. So from there you come to know. Okay. Moving on let us look at aerofoils designed for aircraft that fly very fast faster than the speed of sound. So what will we have when you fly at a speed more than speed of sound? You will have a shock wave. So you have to have provisions in the aerofoil to handle the shock waves. This is an example of shock wave. We have already seen this. We have seen videos of this so nothing great here. So basically high speeds it is very difficult for the flow to remain attached because there is a shock wave and there is a shock wave boundary layer interaction. So typically aerofoils which are used for aircraft that fly supersonic are double wedge or biconvex. What do we observe here? Anything special which is not there in the other aerofoils? Leading edge is sharp. Trailing edge is sharp in both of them but leading edge also is sharp in these aerofoils okay. But now the problem is that an aircraft that flies supersonic will also fly subsonic. They will be very bad in that condition but they will still produce some lift just by the angle. So however they will be inefficient. They will be more efficient when you go for. So if you do not make it sharp, if you make it rounded and fly at high speeds what you have is you have a detached bow shock and that is a very very strong shock. It creates a loss of loss. Lots of loss behind. Temperature rises and pressure falls. So it is not a desirable thing. Total pressure remains the same of course okay. Now let us go to the supercritical aerofoils. This is for one very specific condition and this is an attempt to now the question is do you really have to fly supersonic in order to encounter sonic conditions? Okay. Do you mean to say that you can see shock waves only when you fly more than mark number one? Yes or no? No? You can see shock waves and mark number one even in subsonic flight? Okay. So I will show you a small video which shows a transport aircraft Boeing 737. Recently somebody is putting a camera on the window and you can see there is a line and that line is the transition line. That line is the line at which the sonic conditions are achieved. Okay. So even though just because of the acceleration from the top of the surface. So you have shock waves. You have a you can see these shock waves on the top surface. This is the line on the wing that shows you where the shock wave is sitting. So this is a so under special conditions of weather the water condenses and you can see such phenomena. Okay. So the purpose of a supercritical aerofoil is to delay the onset of the wave drag because there will be a very strong shock at that. So we want to delay it. This particular speed okay. At which you start getting these high drag. So there are two speeds there. There is a critical Mach number and then there is a drag divergence Mach number. The critical Mach number is the free stream Mach number at which the sonic conditions are first seen onto the wing anywhere. And just behind that or just slightly more than that is the critical is the drag divergence Mach number because the drag will suddenly increase because of the presence of the shock wave. So to delay this. So I want to fly faster and faster without encountering sonic conditions. So for that the aerofoils are called as the supercritical aerofoils and you can see the feature of these aerofoils. Okay. They have a flat upper surface. They have a rounded leading edge and they have a reflex on the back. Okay. There is a large leading edge radius. There is a high cambered arch section and there is a flat upper. These are the three features of supercritical aerofoils. And they so again in the tutorial I will show you how this curvature leads to pushing of the sonic conditions. So it is the flat upper surface. There is thus the magic basically. So many of these aerofoils have been designed by NASA. So you can see slotted, integral, thickened, trailing edge. All kinds of aerofoils are available for this application. And the main person behind this particular aerofoil is a scientist called as Richard Wittcombe. So Richard Wittcombe is the person who actually came about the supercritical aerofoils and essentially how they work. Now let us look at let us look at some aerofoils which are even for lower speed. Lower than Lord Noll's number. So now the question is what are the applications? Where will you have aerofoils on aircraft for very low speed? Even lower than what we have seen so far. What would be UAVs? Unmaterial vehicles. So we have seen that flying aerofoils for that purpose. So these are called as the VLS aerofoils. Very low speed aerofoils. So you want to provide lift but the speeds are very low. So these are very common in the modern aircraft which are solar powered aircraft. Because we would like to have ability to fly with least possible ambient power because it depends on solar power. So one example is a solar challenger, a recent aircraft and the aerofoils used in solar challenger. They have a flat surface on the top so that you can mount the solar cells nicely. And the solar cells work very well when they are flat because of the incipient radiation. So they have a flattish bottom surface, a flattish top surface and some curvature in the front. So first they started losing this aero, laminar flow aerofoils but the recent example is this aircraft called Sodar Impulse. How many of you know about this aircraft? Solar Impulse. So I have a very interesting video, a short video with which we will probably very soon we are going to stop this class. It is an amazing video which shows the version of Sodar Impulse. An aircraft with a wingspan larger than Boeing 72 meters long, covered in solar cells, ultra-light and a long solar impulse to fly day and night. This is the Solar Impulse wing. An extraordinary flight called for an extraordinary wing to be built. Rider than a Boeing 747, Solar Impulse 2 has a wingspan of 72 meters, an additional 9 meters from the prototype aircraft. In total there are over 17,000 solar cells across the wing, stabilizer and fuselage. Providing the power for Solar Impulse to fly day and night with no fuel, they act as an aerodynamic skin across this truly innovative wing. Such a large wing required intelligent design to make it as light and strong as possible. Swiss company Decision are normally more used to building high-performance sailing boats with rigid carbon-fiber sails as seen in the America's Cup. And these scales were reapplied to the Solar Impulse wing, developing carbon-fiber wing just 90 grams per square meter. So the most challenging time we had during the wing construction was the failure we had with the first wings for the wing testing. It was a big technical challenge but also a challenge for the team because many were a little bit pre-modulated and we had to do quite a lot of effort to bring the team together again. While the wing is different to any other airplane, we have a construction with a main spar in the middle of the wing and ribs on both sides and on top of it solar cells. So I've never seen a similar construction like that and it has to be very light and it is very light The wing spar is the carbon-fiber box structure that runs through the centre of the entire wing. A honeycomb structure, developed by Salve, is sandwiched between carbon-fiber layers providing the core strength required behind them. Attached to the wing spar are 140 carbon-fiber ribs. Spaced at 50 centimetre intervals, these give the wing its shape without adding excess weight. The underside of the wing is covered in a flexible fabric that's ironed onto each wing using hot melt glue. A thin solar skin made of the solar cells the power solar impulse to covers the top of the wing. To ensure good adhesion, a huge portable oven heated to 70 degrees Celsius was used to cure the entire wing. The wing is amazingly huge but amazingly light as well. So every single puff of wind is actually moving the wing. So we should put two people on every side of the wing to hold it. You can hang roughly two people on each handling mast under the wing but backward and forward we've got only 25 kilogram of forces which is very light. So therefore we have to... So can you imagine it's a wing which is 72 metres in span and the total weight is 25 kilograms. Total weight of the wing is 25 kilograms. Really an amazing structure. Careful is the aircraft that fights into the wind. Incredibly the wing is designed to be unbolted from the fuselage and split into three sections for transport. A process in which it's loaded into the hold of a cargo luxe bow in 7478. The largest of these sections is 25 metres long yet weighs only 350 kilograms. At the rear of SI2 is the horizontal stabiliser a much shorter wing that's also covered in the solar skin. At 14.4 metres the stabiliser is still larger than that of many hobby aircraft. Running the length of it is an elevator that gives the pilot pitch control. The main wing has a surface area of 271 square metres. Slightly larger than that of a tennis court. This massive area gives SI2 the ability to glide through the sky. They're standing at a minimum of 23 metres per minute with a glide ratio of 1 to 32. So the L by D max is 32. And the L by D max of a Boeing 747 is only 19. So for such very special applications you do need special aerofoils. So the aerofoil used here was very very special. Okay, very quickly let's move on to parafoils or aerofoils which get inflated with air. This is for a ram air parachute. So they have a cut in the front and they have a proper shape on the back and typically they are around 80% thick and as you bring it in the ambient wind the pockets get filled up and it acquires a particular shape or a parafoil shape. So this is a non-rigid textile aerofoil which is wind inflated. And then you have reflex aerofoils. These are aerofoils used on flying wings. So there is no tail here to give the stability. So the aerofoil also aerofoil itself has to have a reflex on the back to provide the moment. So the top will be S shaped and there will be a lifted up. Finally we go back to the most basic aerofoil which is the symmetric aerofoil. That means the chord line and the camber line are matching. There are some aircraft incidentally which fly with these kind of aerofoils. For example you can see NACA 0012, it is a flat aerofoil. It is a symmetric aerofoil and they are used on aircraft but mostly they are used for, they are mostly used for actually control surfaces because there you need to have equal force on both sides but there are also some aerofoils which are inverted. What is this inverted aerofoil? So basically if you look at a stabilizer you normally want to have down force. So what you do is you mount the aerofoil upside down. So the top surface is flat and the bottom has a curvature. So that you have an aerofoil mounted upside down. Therefore under all conditions it will give a down force except when you give it an angle. So that is all. In the next class we are going to look at part 2 of this particular capsule in which we will look at the mechanism used for the generation of lift and also to calculate the CP and the CL values. So the next class is about lift generation and many of the myths will be broken in that about how lift is generated.