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 INDEX S. No Topic Page No. Week 1 1 General Introduction: Airplane Performance Characteristics 1 2 George Cayley: Concept of Lift and Drag...

 INDEX S. No Topic Page No. Week 1 1 General Introduction: Airplane Performance Characteristics 1 2 George Cayley: Concept of Lift and Drag 9 3 Introduction to airplane and its components 14 4 Hansa 3 Aircraft and its Primary Systems 24 5 Concept of Lift Aerofoil: Wing : Complete Aircraft 34 6 Drag Polar 46 Week 2 7 Revision 58 8 Standard Atmosphere: Description and Modeling 73 9 Measuring Instruments: Altimeter, Airspeed Indicator 88 10 Equations of Motion: Static Performance 99 11 Thrust Required, Power Required: Cruise 115 12 Excess Thrust and Power: Climb Angle and Rate of Climb 134 Week 3 13 Review 153 14 Thrust Required: A Closer Look 160 15 Modeling of CL: Dimensional Analysis 167 16 A Closer Look: Point Mass Model, Dimensional Analysis 177 17 Estimation of Drag Polar Through Flight Test 189 18 Estimation of Rate of Climb 202 Week 4 19 Revision. 211 20 Range and Endurance 219 21 Range and Endurance: Continued... 227 22 Gliding Flight 235 23 Accelerated Flight 247 24 V-n Diagram 259 Week 5 25 Revision.. 266 26 V stall: Cruise and Manoeuvre 283 Flaps:High Lift Devices to Reduce Take off / Landing 27 Distance 295 28 Take off: Warm-up Lecture 303 29 Take off Performance 321 30 Take off Performance:Continued... 331 Week 6 31 Revision... 348 32 Landing Performance 361 33 Landing Performance: Continued... 369 Challanges in Takeoff and Landing: Single and Twin 34 Engines 379 35 Introduction to Static Stability 388 36 Positioning of Center of Pressure for Static Stability 398 Week 7 37 Revision..... 410 38 Stability and Control: Designers Perspective 426 39 Stability and Control: Designers Perspective Continued... 439 40 Longitudinal Control: Elevator 454 41 Contribution of Wing and Tail: Stability 466 42 Stability: Wing and Tail Contribution 478 Week 8 43 Control: Elevator 500 44 Control: Delta-e Required 512 45 Control: Delta-e Required continued... 522 46 Design Basics: Wing Loading & Thrust Loading 535 47 Design Basics: Sweep & Dihedral 549 48 Revision. 560  NOC: Introduction to Airplane Performance Prof. A. K. Ghosh Department of Aerospace Engineering Indian Institute of Technology, Kanpur Lecture - 01 General Introduction: Airplane Performance Characteristics Welcome students, as you understand the title is Introduction to Airplane Performance. (Refer Slide Time: 00:31) And before I start this course, I try to share what I have learnt, let me tell you a story. I was staying in Delhi during my childhood in a place called Humayunpur which is very close to the airport. And every morning I have to see airplane flying over my house and at the best, I could think, I could wish was, can I get a chance to board this airplane. Can I get a chance to travel using this aircraft? It was a very difficult wish, because so far till that time I have seen film actor, actresses they are moving in airplane, rich industrialist moving in airplane. So, the almost like, you will get never a chance to board an airplane, but the destiny has something else to say. One fine morning I joined IIT Kanpur in 77 in Aerospace Department and I thought, I have got a golden chance to board an airplane and it was in 78, first time I could sit in an airplane and that airplane is still with us in our hanger which is flight laboratory at IIT, Kanpur and that 1 aircraft was Cessna 182. We will show you that airplane, but let me tell you honestly all those excitements were not there. This airplane did not have airhostess, did not have a steward, did not have all those luxury which use to see in a movie. More over it was a course flying that is we have to, we are supposed to do an experiment. So, the pressure was on doing experiment, the fun part was missing and after that I joined Defense Research and Development Organization, where no were aircraft was seen, where I was working. It was missiles, it was rocket artillery rockets, aircraft bomb, so I was too far away from aircraft and I was sure that my desire to be near aircraft was almost vanishing. Again as destiny has to have plays its role, one fine morning I found I have become faculty in an IIT Kanpur and I was the faculty in charge of this hanger, which is flight laboratory and we have 4, 5 aircrafts surrounding me. And for the first time I realize after doing B. Tech, M. Tech and Phd, I hardly understand the aircraft. I nothing surprising that is common thing happen with most of the Aeronautical Engineer who are getting degree. So first lesson which I learnt as a student, as a teacher are you must see an aircraft closely and try to appreciate, what has gone into an aircraft in terms of systems, in terms of components, in terms of instruments. So, we will have one demonstration to you, where we will be showing you all the, the aircraft with all the parts, explain you why they are required. But, before going to that, I come back again to this topic Introduction to Airplane Performance and I will underline two words, one is airplane another is performance. Let us go back to the fundamentals, what whatever we have learnt at the class 11th or 12th. If you recall, if there is a body of mass m and if I eject it with a velocity V at an angle theta (𝜃), I know that this is typically an example of a projectile in motion and I will be, smartly you can draw this path and we say the projectile or the mass will follow this path and this is typically a projectile motion. What actually happens here? As I launch this body, there is a gravity which is m g (𝑚𝑔)which tries to pull this body and this body has a velocity V. What is the effect of this force on this velocity? Let us again go back an example, it is a very popular example. When I move a stone using a string, you see that this body will move in this direction. What is happening? The velocity vector, this velocity direction is changed and who changes the direction, the tension in the string. 2 So, now, if I again come back, there is the velocity vector and there is a force, gravity force pulling this body down. So, you expect as happened here, the velocity vector changing direction, at some point it will hit the ground, right? But, if I want to design an airplane, I do not want this scenario. What do I want? I want, it should go something like this, sustain for some time and come down, this typically, I will look for such a motion of the body. If I want to do like this, what should I have? Whatever gravity force is trying to pull this velocity vector, I need another force which should counter this velocity or counter this gravity force, right. Somehow, I have to generate this force, if I could generate this force comparable to this force, then turning of this velocity vector will be minimal. And if I balance it, then there would not be any turning, it will go straight right, with this idea to generate a force, so that I can move a longer distance. (Refer Slide Time: 07:10) Initially a concept came which is the body, I put some blade here, some propeller and that propeller will generate force (𝐹) and this should be able to compensate the gravitational force or force of gravity (𝑚𝑔) acting on the body of mass m. This is typically the concept behind, what. This is a concept behind designing of helicopter ok. But, most of the part when you talk about airplane performance we will not be talking about helicopter, we will be talking about fixed wing airplane. 3 (Refer Slide Time: 08:11) We will be talking about fixed wing airplane. We have now introduce another new term, wing. So, we have got three terms, one is airplane, another is performance and third one is wing. Let us first see, what do you understand by the term performance. (Refer Slide Time: 09:03) Let us think, suppose you want to buy a motor bike. If I want to list out the performance of a motor bike, what we should look for. Number 1, it’s speed, second it’s mileage or we say fuel 4 consumption, third one maneuver, fourth a young man will like the word pick up. How fast it can speed up and of course, most importantly cost and if I add few more, I would like to see this maintenance aspect. There could be many, many other performance parameter a young man will try to look for. (Refer Slide Time: 10:36) If I now translate this into airplane, how do I translate this requirement, performance requirement of speed for an airplane? For a motor bike, we will be telling what is that speed at which the I get the maximum mileage that is the fuel consumption is minimum. I can also ask myself, what is the maximum speed I can run this machine, drive this motor bike. Similarly, for an airplane I will have a similar question which I called cruise speed that is, what is the speed at which I can efficiently cruise from one point to another point in air? We will explain you, what is the meaning of cruise, we can also think of V max (𝑉𝑚𝑎𝑥 ) that is, what is the maximum speed. Then, for an airplane I can also say how fast I can reach a particular height, loosely I will be calling it as rate of climb. There will be many such questions will come to our mind as we evolve this course. When coming to fuel consumption for an air craft, for fuel consumption, think of a motor cycle or a car. If you want to have a best fuel consumption or then there is a speed, a define speed, at that speed if you drive your machine you get the best fuel consumption or the minimum fuel consumption. 5 Similarly, for an aircraft, form a fuel consumption point of view you have best speed, loosely we will see we will talk about some ratio called lift to drag ratio. Meaning there by, if I really want that my fuel consumption should be low, I need to fly at a particular speed which will correspond to the one of the typical lift to drag ratio, which will be discussing as we progress. As for maneuverity concern, for a motorcycle maneuver you mean, you are going straight like this bank, the motorcycle take a sharp turn, like a young man or a young lady will do. For an airplane, the maneuver typically you mean I am going like this, now I have to take a turn, I bank the airplane and take a turn, I can go to the pull up, I can roll, all such things I should be able to do and there should be pre specified right. And this acceleration, pick up all are linked to this maneuver. Finally, it comes to the cost, cost is a deciding factor depending upon how much you can sell out and how efficiently you can sell it out, how efficiently you can use your money for a particular mission requirement. Because, do not forget, motorcycle you can drive in any type of road conditions. For an airplane, depending upon it is way, depending upon type of airplane, you need additional thing called takeoff distance. Takeoff or landing, airstrip that is you need to have, for takeoff your landing you need to have a airstrip dedicated. Made for the airplane, you need sufficient length, it need sufficient length of the airstrip for takeoff and also for landing also you need sufficient length. You may have a big airplane or you may not have an airstrip, so for you that airplane is of no use, because you cannot take it off or you cannot land right. So, whenever we are talking about performance, we will be actually talking about these things in a systematic manner. What are those things? Let us see. 6 (Refer Slide Time: 15:41) Let me draw this, lets say the aircraft is here, from here to here we have… We will be talking about takeoff and warm up distance, that is I will be switching on the engine, I’ll doing taxing then I’ll, will have start increasing a speed. After a certain speed I will start climbing, I go like this, I roll the plane, start climbing. So, this phase is basically climbing and this is where we are talking about cruise. This is where, suppose I am over an airport and there is no space on the air strip. So, what do I do? So, I need to loiter, I need to stay in particular altitude, a loiter till air traffic controller give a permission to land and then, I land and need minimum distance, so that once I apply the break, the aircraft comes to a stop. 7 (Refer Slide Time: 17:03) So, in performance also first thing we will be doing the cruise performance, second will be climb, third maneuver, fourth landing. In cruise performance, we will be also talking about range, then endurance, loosely what do you mean by this. Range is, given a tank of fuel, how long I can fly in air right. Endurance, how long means in terms of distance and endurance is for how long in terms of time. For a given tank of fuel, I can fly, I can be airborne. Climb, you know that for a particular height how much time I need to climb that altitude, what is the best speed at which I should climb. Maneuver, what sort of turn rates, what sort of pull up I can do. Landings, what is the landing distance, I need to have, to land the aircraft safely. So, in my lecture we will go along with, these are the guidelines. But, before we take up these things in detail, we will first go into simple concept, how does an airplane fly. Airplane means fixed wing, talking about fixed wing. One word of caution to you that, we should not try to see how a bird fly. It is not you are going to relate how a bird fly to, how does an airplane fly, a fixed wing airplane fly ok. 8  NOC: Introduction to Airplane Performance Prof. A. K. Ghosh Department of Aerospace Engineering Indian Institute of Technology, Kanpur Lecture - 02 George Cayley: Concept of Lift and Drag Good morning dear friends, I welcome you for this course titled introduction to airplane performance. And, you could see that I am standing inside our flight lab hanger which is one of the unique facility of IIT, Kanpur, Aerospace department. And, you could see that I am surrounded by so many aircraft. (Refer Slide Time: 00:36) This is the pride of India, the Hansa 3 aircraft designed, built and fabricated by national aerospace laboratory in association with so many private people, private companies - one of them Taneja aerospace. And, you could see there that plane is Cessna 206. It is named as STATIONAIR, wonderful aircraft. And, farther there we could see which is a motorised glider which is sinus 123. And, we have such more aircraft here. And, I will be showing you those aircraft as the lecture progresses. But, what is our basic aim for this course? The basic aim is if you see this airplane, Hansa 3 aircraft, there is engine, incidentally it has rotax engine. As I switch on the throttle, the propeller rotates; it generate thrust. So, it gives it a forward velocity. But what is more important that I need to take, I do need to generate lift which should lift the aircraft 9 upwards. And, for that we have which is the wing, the large huge surface where once the pressure acts beneath this wing surface it generates lift and we cruise. OK!. And, now we will explain you what exactly you mean by cruise? And, if we see at the end, if you come along with me here, you could see there are control surfaces which are deflected as and when required to turn the plane right or left like this. And, similarly, we have here elevator, is also a control surface which is used to pitch up or pitch down the airplane. And, similarly, we have rudder here which I can turn this way or that way to turn the plane towards right or towards left. All this will be explained in this course by one of our quality control manager Miss.Rekha. We will have soon; we will find one module will be dedicated for this part only. What is our basically aim? We would like to know, how do I utilize this area to generate lift, ok? Now, we will go back the olden times when George Cayley gave us this idea that if I put a flat plate at an angle of attack that is I move the flat plate like this and the pressure acting on the lower surface will be responsible to not only generate lift, but also it would try to drag the plate. So, we need a engine to overcome that. All this detail will be in our discussing in the classroom. The same time you do not forget this the cockpit; there will be dedicated lecture on the cockpit where we will see what are the instruments available in the cockpit which helps the pilot to know what is his status, what is the speed with which he is flying, what is the altitude he is flying, what is the bank angle he is flying, what is the throttle level - all this details engine details he will be getting, so that he is comfortable and used all the information to complete a mission requirement, right; thank you. 10 (Refer Slide Time: 04:18) So, now, you go back to the classroom and you start asking a question, how does an airplane generate lift and how manage this lift for our useful purpose, right. Before we go to the classroom let us have a closure look on the wing structure. If you see this portion we call wing leading edge. And, tip of the wing is decided by this ribs which forms very important part of the wing and we call it aerofoil. At every, if I take every cross section I will be seeing a shape like this. And, depending upon the cross section the quality of lift will be dictated. And, you could see that here there is a strut. This strut is because to support the weight of this wing. And, one of the important aspect once you put a strut is that ok, it is fine, it will withstand or take the load of the wing, but same time it should not create drag. So, you could see that even the covering of this strut is having a aerofoil shape, ok. So, aerofoil shape and knowing about aerofoil will be extremely important when you think about airplane performance. 11 (Refer Slide Time: 05:26) Also, you could see that these are the landing gear, and they are not retractable type. We have Piper Saratoga where the landing gear goes in. So, once it is flying in air, landing gear is out, then that offers enough resistance. So, that is unavoidable for such airplane. But, for bigger airplane or even for Saratoga what happens; the moment I take off, the landing gear goes in, so the drag part is reduced. So, we have aircraft where we have got a fixed landing gear; we have got a retractable landing gear with the purpose that once you have cruising I want to fly at a drag minimum. So, I prefer that the landing gear should be taken inside the belly of the fuselage so that overall drag reduction is there, right. You could also see, this is a Piper Saratoga airplane. Here in the other airplane you have seen the part of the surface moves as an elevator, but here the whole tail moves as an elevator, but this is called all movable tail. So, you will have 2 types of airplane – one, in which part of the surface moves as elevator; unlike other airplane, this airplane Piper Saratoga where you will see we have seen that this, as I was mentioning this is the whole tail moves as an elevator unlike the other airplane where part of the surface moves as an elevator. So, these are the basic important points we need to know before you start discussing about the airplane, how does it fly, how does we control an airplane. So, now from here we now go back to the classroom. And, keep back of your mind 2 important things when I am talking about wing - that wing and aerofoil they have got 12 implicit relationship. A good aerofoil will ensure that a wing is highly lift effective. So, we will be starting from this in the next session. Thank you. 13  NOC: Introduction to Airplane Performance Prof. A. K. Ghosh Department of Aerospace Engineering Indian Institute of Technology, Kanpur Module - 01 Lecture - 03 Introduction to airplane and its components (Refer Slide Time: 00:09) This is Sinus 912 aircraft which is a motor glider and its manufacture is pipistrel. So, we will today we will discuss about the structure and the instrument panel of this motor glider. This is an all made its construction is of composite material. This is the spinner of the aircraft having a 2 bladed propeller which is vario. Then, it has a rotex 912 engine installed in it which is a 4 cylinder engine and it is a piston engine 4 stroke. Moving ahead we come to the wing. This is the starboard wing of the aircraft which is containing a pitot tube. This is the pitot tube which senses the pitot pressure and the static pressure from the static veins located just beneath it. It senses the dynamic pressure and gives to the pitot instruments like ASI, altimeter and vertical speed indicator. 14 (Refer Slide Time: 00:59) Then, it has a wing span of 15 meters. Further this wing contains a flaperon. Normally all aircrafts have either aileron and a flap, but in this very motor glider the 2 control surfaces are combined in one and then that is of flaperon which consist of a flap and aileron that helps in rolling and as well as at the time of takeoff and landing. 15 (Refer Slide Time: 01:24) So, this is the empennage section of the aircraft that is the tail section which consist of the vertical stabilizer, the horizontal stabilizer; attached to it is the moving part that is the elevator and the rudder. Elevator gives us a pitching moment of the aircraft while moving up and down, and rudder gives us the yawing motion to the aircraft. So, this complete section gives us the tail section of the aircraft. Beneath this you can see, there is a skid, tail skid which consist of a hole which is moving for tying the aircraft when it is parked on the ground. 16 (Refer Slide Time: 02:05) So, further we will move towards the port side of the wing that again contains a flaperon. And, as you can see on top of this glider here we have antennas. These are VHF antennas - one is for communication and one is for receiving. And, on top of, for this very aircraft we have an optional parachute installed in it which can be served as an emergency equipment which is being installed over here. So, this was the basic of the motor glider. And, on top of the wing you can see that curve shape part; that is the fuel tank cap which is used for filling the fuel tank which is installed in the wings. 17 (Refer Slide Time: 02:38) Now, we will move inside the cockpit to just have a brief view of the instrument panel and the controls. So, this is the instrument panel of the motor glider which we were discussing about just a few minutes back about the composite motor glider sinus 912. This complete is the instrument panel which consists of an alpha m f t installed in this center which gives us the readings of various engine instruments; and, apart from that various airframe gauges. And, for standby instruments we have some analog gauges like we have airspeed indicator which gives reading in knots about the airspeed, then we have the turn coordinator and the level indicator which tells that aircraft banking towards left or right the turn of the aircraft. Then it tells about the altimeter, the height of the aircraft in feet. Then we have temperature gauges and the manifold pressure gauge. Along with these along with the readings which comes in these analog gauges we also get those same readings in the alpha m f t. And, below you can see the control stick like in some aircrafts you have the control column, in some we have control wheels and in some we have control stick, but the function of all is same. It is used to control the primary motions of the aircraft that is when you are moving left or right the flaperons of the aircraft of this aircraft is moving. Normally when you move towards left or right the ailerons move, but for this sinus 912 flaps and ailerons are combined. So, when we move it towards left or right the flaperons on install on the wing moves. If you pull it or if you push it then the elevator comes in action. 18 And, there you can see the rudder pedals. When the left pedal is moved, when the left pedal is pressed the rudder moves accordingly the action is transferred to the rudder towards left or right, and if you press the right pedal then the motion is transferred towards the moment of the control surface towards right, and if you press both of them together that gives the braking action that is feasible on the ground. So, this is about the motor glider of very light aircraft; weight is approximately around 550 kg. And, these are the engine controls - the choke and the throttle. It has fixed seat arrangement in this. And, it has a magnetic compass over here to give the heading of the aircraft in which direction it is moving. (Refer Slide Time: 04:50) As far as of now we have learnt about the conventional gauges that was been introduced in the earlier aircrafts, but nowadays the modern cockpit is being introduced that gives a display, a screen and a display on that screen inside the cockpit. Earlier we used to have gauges like we have in this aircraft that is airspeed indicator, the gyro instrument and the altimeter. But in addition to these gauges we also have the display on the screens. This is the part of the modern cockpit. You can see, also see a glass cockpit that gives us a glass screen on which the display comes up. We can see this is the primary functional display, this is the multifunctional display. There are various items on it to be displayed. These settings are made by the pilot at the time of flying whichever reading he wants to see. 19 This is, there is a gps in this, we have nav and com readings in this, there is a volume controller, this is the remote for the that, this is the heading control, this is the various nav and headings switches for this, then we have the range over here, then this is the multifunctional display that gives us the reading for fuel quantity that is the fuel quantity in both the tanks here tanks installed in the wing of the aircraft. We have the EGT the exhaust gas temperature, we have the CHT cylinder head temperature the oil temperature. the oil pressure and the fuel flow that is in gallons per hour. So, these 2 screens all together gives us the position of the aircraft, the heading of the aircraft, various engine instrument readings and how it goes about and it helps pilot to flying the aircraft. (Refer Slide Time: 06:22) So, as of now we have covered about the airframe of the fixed wing aircraft. Today we will cover something about the engine of the aircraft. The engine installed on these fixed ring aircraft is the piston engine. Here, is a picture of a piston engine that is a 6 cylinder as you can see 1, 2, 3, 4, 5, 6; these are the 6 cylinders horizontally posed piston engine. Engine is the heart of the aircraft because it provides power to the aircraft. And, these are the cylinders in which the valves run. This is the 4 stroke piston engine. On top you can see this is the oil inlet point of the engine, here is the propeller governor; this is the alternator of the engine which provides electrical power. In front, is the propeller, a 3 bladed propeller and, this is the couple crankcase in which the crankshaft runs, operates the cam lobes and thus operates the intake and exhaust valves 20 inside this 2 operator, the opening and closing valves to operate the engine. These are the sparkplug installed and, similarly we have a sparkplug on the other side of the head. This is the cylinder head and, these are fins, with the cooling fins use to cool the engine. Then, these are the lines for the fuel lines going to the various cylinders which supplies the fuel. Behind this you can see these are the mounts on which the engine is mounted. the mounts of the engine. Then we have the coolers for the engine; then, this is the hydraulic brake fluid which operates the brake. So, this is about the piston engine. Behind this valve is installed the magneto which supplies power to the engine in; it power to the engine it is connected to the battery; battery cranks starts the engine and then engine supplies power to the aircraft. This is the jest of the piston engine that you can see. Piston engine is a 4 stroke engine which powers fixed wing aircrafts. On higher aircrafts you have turbo engines, turbo fan engines, rotary engines. This arrangement is of various types on different aircrafts. In this aircraft you can see it is a horizontally opposed that is engines are opposed in a horizontal manner to each other. We also have a vertical opposed engine, we have a radial cylinder engines in which the cylinders are aligned in the radial way, but this is a kind of a horizontal opposed piston engine. (Refer Slide Time: 08:46) 21 As of now we have studied about the aircraft structure and aircraft engine. Today we are going to see about something about the landing gears that is used to balance aircraft on the ground. And, so, we have 2 types of landing gears - one is fixed and one is retractable. Fixed type of undercarriage is this which you can see; this does not have a retracting mechanisms. This is the short strut on which the landing gear is balanced. This is the nose wheel; the inner 2 are the main wheels. So, this fix landing gear takes the load, absorbs the load and when the aircraft lands. And, at the time of takeoff and the aircraft machine is in air these wheels creates drag which is an advantage added advantage in type of retractable landing gear like where I will show you just. In piper saratoga we have a retractable landing gear in which this the air oil oleo strut takes up the landing load and bends inside at the time of takeoff and a machine is in the air. So, now, we will move up to another kind of fixed landing gear that is being installed on Hansa 3 aircraft. So, we have just seen fixed landing gear of sinus 912 motor glider. This is another type of fixed landing gear that is being installed on Hansa 3 aircraft. Here you can see, this is a strut, a steel strut which takes up the load. And, inside other usually landing gears have an oleo air and oil combination kind of a strut to bare up the load. But this vary undercarriage in Hansa 3 aircraft has a piston and just above and below the piston there are rubber pads to take up the load being imposed for this aircraft at the time of landing. Rest all a same as compared to the aircraft when this aircrafts land. The load on the machine is being taken up by this strut, transferred on to the shock absorbing mechanism that is the piston and the rubber pads. This is Cessna 206; as you can see it is also having a fixed landing gear or fixed undercarriage; that is also having a an air and oil combination kind of a strut, this is a strut. At the time of regular maintenance check we need to check the extension of the strut. There is a limitation for this extension. And, there is a centering camlock just behind this strut. If that is being locked then the aircraft cannot stay left or right. So, this strut takes up the load at the time when aircraft is landing; this is the combination of air and oil and hydraulic oil, and it is a fixed landing gear, it creates a lot of drag in the air, and it is also having an air conditioning system installed in this aircraft. So, this is the complete thing about the fixed landing gear for Cessna 206 h aircraft. 22 So, as of now we have studied about the fixed landing gear. This is a kind of a retractable landing gear; you can see a torque link and air oil oleo strut which helps in shock absorbing of the aircraft while the aircraft is being touched on the ground. At the time of landing here is the spring which helps the aircraft landing gear to retract upward and low and keep it locked. These are the landing head doors which when the wheel is retracted upward these doors close and provides an complete aerofoil, a smooth surface to the aircraft structure, thus preventing a lot of drag which is an disadvantage in case of fixed undercarriage. 23  NOC: Introduction to Airplane Performance Prof. A. K. Ghosh Department of Aerospace Engineering Indian Institute of Technology, Kanpur Lecture - 04 Hansa 3 Aircraft and Its Primary Systems (Refer Slide Time: 00:09) Student: Today, we will learn about Hansa 3 aircraft, which is an NAL manufacture Aircraft, Hansa 3 is an all composite low wings single engine aircraft, which is equips with fixed tricycle landing gear. It consists of a conventional primary controls, namely aileron, elevator and rudder and secondary controls, which are flaps and tabs. The primary controls are manually operated by a dual interconnected set of controls sticks, which can be seen inside the cockpit and a rudder pedal, which is also located inside the cockpit, where our secondary control has a manual and an electric operation. 24 (Refer Slide Time: 00:49) There are two integral side by side seats for pilot and co pilot. The aircraft, this aircraft is powered by a Rotax 914 F 3 engine, which is a four stroke four cylinder horizontally opposed piston engine. The aircraft is equipped with a variable pitch two bladed constant speed Hoffmann composite propeller, the length of this aircraft is 7.6 meters and it is height is 2.6 meters. It is maximum takeoff weight is 750, 750 kg it has a fuel tank, which is fitted behind the pilot seat, with the tank capacity of 91 liters of which 85 liters is usable. The aircraft is equipped with a variable pitch two bladed constant speed Hoffmann composite propeller, the length of the say aircraft is 7.6 meters and it is height is 2.6 meters. It is maximum takeoff weight is 750 kgs it has a fuel tank, which is fitted behind the pilot seat with the tank capacity of 91 liters, of which 85 liters is usable, so this is a brief introduction of Hansa 3 Aircraft, which is an NAL manufactured. Now, whenever we think about the aircraft description of the structure, we intend to say that the internal structure, comprising of the item of equipment and the various instruments on the cockpit panel and the external structure, which consists of the wing, a primary control surfaces, the secondary control surfaces, the landing gears, engine and the propeller. 25 (Refer Slide Time: 02:21) The most important part of an aircraft is the wing that is a lift producing device. The wing of Hansa 3 Aircraft is a single piece wing with three spars, the leading edge spar, main spar and the rear spa. It is of composite construction, because span are around 10.5 meters consisting of a primary control surface. Aileron attached to a wing and a secondary control surface flap, which is located in both side of each wing. Flap is located in both side of each wing, which is secondary control surface used at the time of landing and as well as the time of takeoff. So, after the wing the main plane comes the tail plane, which consists of a horizontal stabilizer, that is a fixed surface to which, is attached a movable tail surface that is an elevator and a vertical stabilizer, which is again a fixed surface, to which it is attached a movable surface that is called rudder, this is the elevator movement and this is the rudder movement. 26 (Refer Slide Time: 03:22) Now, when we get to know about the elevators, elevators are the primary flight control surfaces, which are usually at the rear of an aircraft. Elevators are usually hinged to the tail plane or horizontal stabilizers, which is a fixed surface, which control the aircraft pitch that is, movement of aircraft about the lateral axis. (Refer Slide Time: 03:58) And, when we talk about the rudder, rudder is a directional control surface, the rudder is usually attached to the fin or the vertical stabilizer, which is a fixed vertical surface. They control the yawing motion of the aircraft, that is movement of aircraft about the vertical 27 axis, the movement of the rudder is provided by means of rudder pedals, which is provided in the cockpit. A forward and aft movement of pedals is transmitted to the rudder pedals to the rudder controls by means of bell cranks, levers and push pull rods. Pressing the right rudder pedal, turns the controls surface towards right, thereby which an air pressure acts upon it, which in turn forces the tail left and nose of the aircraft towards right. All primary controls are mass balanced and are provided with stops to limit the respective range of the controls. The primary control surfaces, which is attached to the wing is known as aileron, it is the hinged flight control surface usually forming part of the trailing edge of each wings of a fixed wing aircraft. Aileron are used in pairs to control the aircraft in roll, that is the movement of aircraft about it is longitudinal axis, which normally results in a change in flight path due to the tilting of the left vector. Movement around the axis is known as rolling or banking, the sideward movement of the controls stick transmits motion to ailerons by means of lever, bell cranks and push pull rods. The normal range of the movement of aileron for Hansa 3 Aircraft is 20 degrees up and 20 degrees down. As we can see, when the controls stick is moved towards left, the left aileron raises up, whereas the right aileron goes down. The left aileron, which is going up creates drag whereas the right aileron increases the surface area and hence raises the right wing, whereas the left aileron goes down, lowers the lift towards the left wing and hence the aircraft rolls towards the left. Wing flaps are, manually operated by means of a control handle provided in the center pedestal located in the cockpit. The movement of the control handle it is transmitted to the flaps through torque tubes, bell cranks and push pull rods, wing flaps and in this aircraft is a single slotted fowler type flap, it has a 10 degree and 20 degree down position. Flaps can be used at the time of take off and as well as the time of landing. Trim tab, which is located on the left elevator provided to aid the pilot by assisting in operation of primary control surfaces and also to keep the aircraft balanced. It is operated by an irreversible electrical actuator, which is located inside the horizontal stabilizer, which is directly attached to the operating lever of the tab and it is located on the LH side. This is all about the controls and the structure, external structure of Hansa 3 Aircraft. 28 (Refer Slide Time: 07:07) Here comes instrumental panels of Hansa 3 Aircraft, we can see the various instruments installed on instrument panel, will start with the primary flight instrument, that is air speed indicator, this is air speed indicator, which gives the reading in knots. Then, we have altimeter, which tells us the height that is the vertical speed indicator also known as rate of climb indictor, which tells us the feet per minute. ASI (Air Speed Indicator) altimeter and vertical speed indictor these three are the pitot static instruments out of which, altimeter and vertical speed indicator, inputs the static pressure whereas airspeed indicator, take the total pressure the dynamic pressure and does the static pressure. Then, we have the gyro instruments, gyro horizon, we have engine instruments that is the manifold pressure gauge this is the tachometer, also known as RPM indictor, which tells us both the RPM, of the engine. The static RPM, for this engine on ground is around 2250 RPM. Then, we have the ignition switch over here, we have various indictors for CHT that has cylinder head temperature indicator, we have an oil temperature indicator, we have a oil pressure indicator. Also, we have a turn coordinator aligned with it is a level indicator, which tells us the aircraft is aligning towards left or towards right, can see the markings on the cage as L or R. So, this is a turn coordinator, then we have various switches for lights, for electrical panels this is the radio communication set of this aircraft, above you can see the magnetic compass and just this is the outside air temperature gauge. 29 So, magnetic compass gives us the heading, where the aircraft is moving outside air temperature tells us the free air temperature of the air and the various gauges gives us the reading, which helps a pilot to maneuver the aircraft properly. (Refer Slide Time: 09:12) Below here, you can see the various controls that is the throttles control and the propeller control. Here is the choke activate, then we have this is the flap lever, this is the choke, which is used to activate the engine, we have the throttle controls, we have the propeller controls. Propeller controls to make the make the propeller pitch fine or coarse it is having a constant speed propeller, which can be changed this, the throttle which can be set on idol on 100 percent and 115 percent that is the max RPM. 30 (Refer Slide Time: 09:48) This the lever for flap, which has three positions UP, 10 degrees and 20 degrees, UP is when flap is fully up, 10 degrees is, when flap is instructed downwards to 10 degrees and 20 degrees, when flap is retracted fully towards downwards that is 20 degrees, 10 degrees is use at the time of takeoff to increase the surface area of the wing and to increase lift, twenty degrees is used at the time of landing to increase more drag, and thus provides safe landing in a minimum distance. (Refer Slide Time: 10:23) 31 This is the controls stick, which is used to operate the primary flight controls, the aileron and the elevator. Moving it towards left or right gives the movement to the aileron and thus a rolling motion to the aircraft, moving it forward or aft gives the pitching moment to the aircraft, that is to the motion to the elevator and thus and aircraft pitching takes place. Below, you can find the rudder paddles here, this are the paddles moving towards left or right and when this are used in ground both of them are together to give a breaking action to the aircraft. And air these serve as yawing motion this gives a yawing motion to the aircraft, pressing the left rudder pedal, gives the motion of the aircraft motion of the control surface towards left. Pressing the right rudder pedal, when right rudder pedal goes forward the rudder move towards right and accordingly gives the yawing motion to the aircraft. (Refer Slide Time: 11:30) As I, mentioned behind the pilot and co pilot seat there is a fuel tank, tank capacity of ninety one liters this is the location of the fuel tank, this is fuel tank its tank capacity is 91 liters out of, which 85 liters is usable fuels and 6 liter is unusable. Whenever, an aircraft passes through the lightning atmosphere is a protection provided on the aircraft to protect it surface from lightning ill effect… 32 (Refer Slide Time: 12:01) So, on this Hansa 3 Aircraft there are 6 lighting arrestors, which arrest charges and passes on them to the two ground the charges. There are 6 lighting arrestors two, in the form of a triangular plate, which are located on both side of the wings one on top of the fuselage as aluminum rod and three on the three under on the three landing gears to main wheels and the nose gear these six arrestors in all carries away the charges and ground them to the surface, so that the surfaces aircraft surfaces is rotate from any lightning strike. If, the aircraft flown in day time as well as in night there are certain light, which are provided on the aircraft surface to aid the pilot, to fly the aircraft and also to aid the pilot of other aircraft, which are flying in the air space in or around the aircraft. So, we have navigation lights located on the wing tip the left side that is a both side it contains a red light the right side contains the green light on top of the rudder there is a light, which is blinking all the time and that is known as an anti-collide that is anti-collision light. 33  NOC: Introduction to Airplane Performance Prof. A. K. Ghosh Department of Aerospace Engineering Indian Institute of Technology, Kanpur Lecture - 05 Concept of Life Aerofoil: Wing: Complete Aircraft (Refer Slide Time: 00:10) See for a symmetric aerofoil, if this is the v, this is the v, and this is the chord line and if I join this, this is the chord line. What do we notice here? Remember, chord line we defined as if we join leading edge and trailing edge by straight line that becomes the chord line. So, when here the leading edge and trailing edge are joined and that become the chord line for a cambered aerofoil, this is cambered and this is symmetric. Now, what is in your mind? If the air is coming like this, do you think this will produce any lift? The answer is no, because we remember as far as George Cayley’s guideline to us, On the Concept of Generation of Lift. Lift will be generated when there is an angle between the velocity and the surface. In this case, it this there is no angle, so it will not generate any lift. So, if I draw C L which is nothing but, lift divided by half rho v square 1 S, 𝐶𝐿 = (2 𝜌𝑉 2 𝑆) versus angle at alpha (𝛼) equal to 0, I will also get a 0 lift or a 0 CL. But, for cambered to see, you verify this chord line, it is no more parallel to the velocity vector. 34 You could see actually effectively it has an angle with velocity vector, even if it is at alpha equal to 0, similar condition, Ok. So, in this case what we will see that, even at alpha equal to 0, there will be some lift. I repeat this, one way to explain is this chord line and there is an angle between the chord line and the velocity vectors. So, what we talked about alpha equal to 0, a same velocity condition it will produce a 0 lift, but here because of this camber, because the camber is there, the some angle some surfaces is there, which is making the angle with the velocity vector. So, even the alpha equal to 0, it will produce lift. As I increase this angle, what will happen? As I increase this angle what will happen, there will be more lift, because from this George Cayley explanation, the lift will be function of angle for a given area, given other conditions. So, as I increase the angle the lift will increase, so you will find upto certain point lift will go on increasing as alpha is increased. But, beyond this certain point you will see that, beyond a certain alpha you will see that lift is no more increasing. In fact, it is going down like this, similarly for here going down like this. What exactly is happening? Typically, here if I see there is a limit which you called alpha stall (𝛼𝑠𝑡𝑎𝑙𝑙 ) and this value you called C L max (𝐶𝐿𝑚𝑎𝑥 ). Similarly, here you call it alpha stall (𝛼𝑠𝑡𝑎𝑙𝑙 ), and this CLmax (𝐶𝐿𝑚𝑎𝑥 ). What do you say that beyond a certain angle called alpha stall the flow will no more remain attached. There will be a separation and there will be a stall and the lift will reduce and drag will increase, right? Flow will no more remain attached or there is some sort of a flow separation. What is actually, loosely happening? 35 (Refer Slide Time: 05:17) If you see, if an aerofoil is an angle, now see what is happening here. The air flow is coming like this, now as it comes backward, it’s relative air. What again you are seeing that, if I take a control surface? I see here, as the air particle moves in the backward direction, the area at 1, 2, 3, 4 all these stations, the area is going on increasing for a given control surface. So, area increasing means the velocity V1, V2, V3 (𝑉1 , 𝑉2 , 𝑉3 ). So, V1 is greater than V2, V2 is greater than V3 (𝑉1 > 𝑉2 > 𝑉3 ) , that is as area is increasing as, so maintain the same amount of fluid flow, the velocity has to reduce. So, V2 will be less than V1, V3 will be less than V2, V4 will be less than V3 and this implies, the pressure at 3 is greater than pressure at 2, pressure at 2 greater than pressure at 1 (𝑃3 > 𝑃2 ), (𝑃2 > 𝑃1 ). So, it will experience an adverse pressure gradient, ok! or at this stage, we only talk about adverse pressure and this adverse pressure will try to discourage the fluid particle to move in the direction and moreover, because of skin friction already some part of energy of the fluid is taken out. So, there will be an angle at which the, the flow will not be able to move backwards, at some point it will separate, right! and that is, we say the flow is no more attached. Stall is much more than this, but we need to know that when we are talking about this zone, where it is almost linear. I am talking about attach flow and when I am talking here, I am talking about separated flow. There is a subsidiary aerodynamics to explain all these things, we are not going deep into it. 36 We only need to understand one thing, that for symmetric aerofoil I can write model CL as dCL by dalpha into alpha. 𝜕𝐶𝐿 𝐶𝐿 = ( )𝛼 𝜕𝛼 What is dCL by dalpha? DCL by dalpha, because it is linear, straight line, almost straight line, right? so here this is a slope. What does almost straight line in practice will find? Beyond 6, 7 degree some sort of a non-linearity comes. So, but we are assuming here, after this point this is straight. So, I can write CL as slope of this into alpha, but for cambered, for cambered aerofoil I will write CL as CL0 plus CL alpha into alpha. 𝐶𝐿 = 𝐶𝐿0 + 𝐶𝐿𝛼 𝛼 This is just a question of, because for cambered aerofoil I will be actually doing it like this, that alpha equal to 0, there is some CL which is I will be referring to as CL0, so I can model CL as this. In text book, when we try to distinguish between CL because of aerofoil and CL because of wing, we use strict nomenclature. (Refer Slide Time: 09:05) For aerofoil, we use C small l (𝐶𝑙0 ) and for wing we use C capital L (𝐶𝐿0 ) of course, in aerospace there is confusion, even for only moment we write Cl. So, let us be very clear, 37 we are talking about lift coefficients. So, for aerofoil I will write Cl equal to Cl0 plus Cl alpha into alpha, 𝐶𝑙 = 𝐶𝑙0 + 𝐶𝑙𝛼 𝛼 where Cl0 equal to 0 for symmetric and Cl0 not equal to 0 for cambered 𝐶𝑙0 = 0 ∶ 𝑆𝑦𝑚𝑚𝑒𝑡𝑟𝑖𝑐𝑎𝑙 𝐶𝑙0 ≠ 0 ∶ 𝐶𝑎𝑚𝑏𝑒𝑟𝑒𝑑 and for wing, I will write CL equal to CL0 plus CL alpha into alpha, 𝐶𝐿 = 𝐶𝐿0 + 𝐶𝐿𝛼 𝛼 again CL0 is 0 for symmetric and CL0 not equal to 0 for cambered, right? 𝐶𝐿0 = 0 ∶ 𝑆𝑦𝑚𝑚𝑒𝑡𝑟𝑖𝑐𝑎𝑙 𝐶𝐿0 ≠ 0 ∶ 𝐶𝑎𝑚𝑏𝑒𝑟𝑒𝑑 Why this is important? You will soon realise that as far as flying the machine is concerned, if I have to maintain lift equal to weight, I need to fly at a particular CL which will be governed by the weight, speed, etcetera, etcetera. But, a question is how do I generate this CL when I am flying, the pilot how will you generate? That answer will come from here, if I know what is the CL0 of the airplane, if I know what is CL alpha of the airplane, then I know if I have to generate CL which I know priory, then I know how much angle of attack I should fly. So, I know how much I should turn the airplane right, so this is the, that is why in performance this is important, the back of your mind, please. Now, I am talking about aerofoil and wing, for the whole aircraft we will try to find out, for whole aircraft we will try to find out, for CL aircraft, what is CL0 of the aircraft and what is CL alpha of the aircraft into alpha. 𝐶𝐿𝑎⁄𝑐 = 𝐶𝐿0 + 𝐶𝐿𝛼 𝛼 𝑎⁄𝑐 𝑎⁄𝑐 Please, see the distinction. First one is aerofoil, second one is wing and third one I am talking about aircraft. But, now what is the difference between aerofoil, wing and aircraft? Why we are using these three terms? Let us see that. 38 (Refer Slide Time: 11:31) When I am talking about aerofoil, imagine aerofoil is basically a 2D concept, 2D that is imagine this is ,you have seen this aerofoil shape and imagine this having a span infinite, that is infinite here, infinite there. So, what is the basic message is, as the flow is coming like this, it has no way to go towards cross, right or left. So, always the flow is over the each aerofoil section. So, there are no flows around right or left, because these are infinite span. So, that is why you called aerofoil is a 2D concept, but in actual practice what happens. See, when I come to the wing from, so this, from here when I come to the wing, many text books used a word called finite wing. This finite comes from here, the aerofoil, they are infinite span. So, no cross flow is allowed, only all the flows are along the chord of the aerofoil, right. Now, when there is a finite wing; that means, this is not infinite, let us see what happens. If it is flying at an angle like this, the pressure here is more than the pressure on the top that is why there is a lift. As I come near the tip of the wing here, what happens? There the pressure is more and pressure is less, so air will try to come from the bottom to the top and they go on forming a vortex, vortices like this, right. And since, they go as a rotational; they go into a rotational motion, the vortices are formed. So, rotational kinetic energy is required and that comes at the cost of the energy of the airplane, so we call this actually induces drag. 39 So, that is why in the finite wing we have wing tip vortices. If I draw the diagram, if you see this is the wing cross section I am drawing, this is the span, right. Let us say, this is the fuselage, now what is happening. Because, if there is a lift; that means pressure at the bottom they are more as compared to pressure at the top. So, what is happening at the tip, because it is high pressure, so flow will go like this and they form vortices, which draws rotational kinetic energy from the energy of the airplane and hence, energy is lost and it affects the speed, so we call it drag, because of this vortices or we call these are induced drag. Induced drag, because of these vortices, so many times we are called vortex drag, many time they are called lift induced drag. Why lift induced? Because, these vortices are formed, because of the lift, because of the lift there is a pressure difference and because of finite wing, there is a vortices form at the tip and so it gives a vortices drag, induced drag, lift induced drag. Note here, if I make it infinite, then this situation will not come, so it becomes 2D or it becomes an aerofoil. That is why aerofoil will never encounter conceptually any such vortex or lift induced drag, right, so that is why it is finite wing. (Refer Slide Time: 15:24) Then, we use for this aircraft, CL for the aircraft. So, we started with aerofoil where infinite span, wing, finite wing, we found there is the vortices and because of vortices, there is a drag and because of the vortices, we will find the vortices will be coming like this. So, 40 there will be inducing a downward component of velocity to the local angle of attack at the wing or even at the tail will be changed, will be reduced, so effectiveness will go down. So, in a language of airplane, aerodynamic modelling, we can always say that the lifting characteristic gets changed because of downwash or the CL alpha may also changed because of downwash, right. Now, for CL alpha of the aircraft or CL of the aircraft we write CL, because of wing, CL because of fuselage, CL because of tail plus CL because of miscellaneous component, that is to say. 𝐶𝐿𝑎⁄𝑐 = 𝐶𝐿𝑤 + 𝐶𝐿𝑓𝑠 + 𝐶𝐿𝑡𝑎𝑖𝑙 + 𝐶𝐿𝑚𝑖𝑠𝑐 If I know what is the CL alpha of the wing, if I know what is the CL alpha of the fuselage, if I know what is the CL alpha of the tail and assume that, all of them are based on same reference area. Then, if I simply add these things together, then I am expecting that, that will be CL alpha of the whole aircraft, you may not be correct. In fact, we are not correct if we are deal like that. For simple reason there are many such reasons, but one of those, see this is the CL. When I compute the CL alpha of the wing, this is the wing in isolation. But, in the actual practice, what happens? When there is a fuselage, it gets let us say if this is the fuselage, then I am attaching it like this on the wing. So, there is a body to wing interference here, right. Similarly, if I calculate for body alone, when I bring near the wing there is a wing body, body wing interference, same thing happens with the tail. So, when I am talking about total CL of the aircraft, I need to take care of body wing, wing-body. Similarly, for tail interference factor which modify the overall CL of the aircraft. So, that is why we use three terms distinctly. 41 (Refer Slide Time: 18:17) One was CL alpha of the aerofoil, understanding very clear this is 2D, 2D flow that is no cross flow like this, right. Second thing, where we use small l CL capital alpha for a finite wing, because of the finite wing there will be vortices, that will affect the drag and the lift curve slope depending upon the size and third one this is CL alpha of the whole aircraft which will be summation of sum of CL alpha of the wing plus CL alpha of the fuselage plus CL alpha of the tail plus any other components are there. But, we should be very careful that we have an appropriate be taken, no interference factors between body wing, wing body, tail body, body tail all in together, right. (Refer Slide Time: 19:17) 42 If I come back to CL again, I said this lift by half rho V2 free stream into S reference. 𝐿𝑖𝑓𝑡 𝐶𝐿 = 1 (2 𝜌𝑉 2 ) 𝑆𝑟𝑒𝑓 𝑓𝑟𝑒𝑒𝑠𝑡𝑟𝑒𝑎𝑚 Similarly, you said CD as drag by half rho V2 S reference, again this is freestream. 𝐷𝑟𝑎𝑔 𝐶𝐷 = 1 (2 𝜌𝑉 2 ) 𝑆𝑟𝑒𝑓 𝑓𝑟𝑒𝑒𝑠𝑡𝑟𝑒𝑎𝑚 We have being using the word free stream, right, I am talking about S reference, let us understand what are these things. Let us draw an aircraft and lets say, this is the relative air speed. Text book, always you see V infinity is written to explicitly mention that is the free stream condition. What is the meaning of free stream condition? We are tried to adjust that. If I come close to these bodies, so here, here, here, here, what will happen, you see or here, for that matter. If this is V, 1 and if I take this point 2, will the velocity at point 1 and point 2 to be same or speed at point 1 and point 2 to be same. We could see very clearly, at point 2 because of the contour of this fuselage, there will be a change in speed here, because you could see at this point, again the area goes on decreasing if I take contour surface. There is a natural tendency for the flow to accelerate. I am talking about low speed flow, right. So, local velocity and the velocity of air further away from the body are different, similarly if I come here, I come here by the time flow reaches here, there is a viscous effect on it, what about the contour effect and then, the velocity will never remain same. So, when I am try to non-dimensionalised , this lift or drag which velocity should I take? Because, at each point the velocities are different, that is why we take the freestream velocity and the understanding is this, it is at a very far away from the body. So, that there is an influence on the speed of the freestream, so it remains constant, that is why we talk about free stream, so that we can define a non dimensional quantity consistently. Now, S reference for aircraft, S reference is the wing area. Wing is the primary component, which produce the primary thing the lift and wing area is the S reference for aircraft and for a missile, you will find, missile is wingless missile. Just it has got like this, you may 43 find this maximum cross-sectional area max that sometime becomes reference area. But, coming back to aircraft let us not forget when I talk about S reference, it is the wing area, ok. (Refer Slide Time: 22:57) So, what we have very quickly learn that, when I try to model lift, I will model it like this half rho square S, S means S wing, V means free stream. 1 𝐿 = ( 𝜌𝑉 2 ) 𝑆 2 Half rho V2 is freestream dynamic pressure into CL, ok? and CL is basically lift by half rho V2, 𝐿𝑖𝑓𝑡 𝐶𝐿 = 1 (2 𝜌𝑉 2 ) 𝑆 𝑓𝑠𝑡𝑟𝑒𝑎𝑚 which is the free stream into S, which is wing area. 44 (Refer Slide Time: 23:40) There is another observation on freestream, dynamic pressure, if I draw an airplane again, if you see a tail here and this is a V. The freestream pressure here, here, here and here could be different, because the flow, the energy might have lost. However, if I have an engine here, mounted here, this propwash can create or augment, change the freestream dynamic equation on the tail. So, that is why we need to be very, very careful when I am talking about lift and drag, that when I try to finally, talk about overall CL of the airplane. Then, it has to be non- dimensionalised with the free stream dynamic pressure ok, but local lift could be on the local dynamic pressure. 45  NOC: Introduction to Airplane Performance Prof. A. K. Ghosh Department of Aerospace Engineering Indian Institute of Technology, Kanpur Lecture - 06 Drag Polar See, we were discussing about George Cayley’s explanation for generation of lift. (Refer Slide Time: 00:18) We just quickly revise, so that we can understand few things better. Remember, this is the plate and if I move this plate at an angle with respect to the speed. And this angle, because of this angel that there will be a pressure from the air outside as we moves like this and that will get translated into force, because of this area and there will be normal force acting on this body. So, I represent this as, this is the pressure, because of air as it moves through the air and resultant of this I can write this is R, the reaction and one component perpendicular to velocity, we call it lift. Another component which is opposing the velocity called drag and this lift is supposed to balance the weight and if I put an engine which gives thrust. So, this thrust is supposed to balance the drag, so that I can move like this which is typically we will see soon, we will be defining this flight as a cruise flight. But, let us understand first that if lift has to balance the weight. Then, what is this lift? This lift is generated, because there is an angle between the velocity vector and the surface and this angle we 46 call let say alpha, this lift definitely will depend upon the speed, it will depend upon the area of this plate. When it comes to the area, we also now let us investigate one thing. If I move this plate like this or I move the plate like this, both are having the same angle, but which case you think more lift will be there, this way or this way. You see this way or this way? It is obvious that lift will be more when I moving it like this; that means, it is not only the area, but also how the area is laid out with respect to the velocity vector. If you see, soon we will be defining some term of that, of this piece in terms of aspect ratio. Watch out for understanding, what is the meaning of aspect ratio and before we go for aspect ratio, we will have a relook here and try to see, how do I translate this to a pilot in terms of flying the machine. Because, I always said whatever aerodynamics, whatever flight mechanics we do finally, I have to translate this in terms of a language which pilot can understand, right. Then, from here we realize that we will be operating in terms of CL which is nothing but, lift getting down dimensionalized by dynamic pressure into S reference. And when we say the dynamic pressure, we talked about freestream dynamic pressure, because we realised that the velocity at different points will be different. If it is the aircraft, if it is moving like this, velocity here, velocity here, velocity here or the dynamic pressure here, here, here all will be different. So, when a non-dimensionalise this, which dynamic pressure I take. So, for that we choose freestream condition, the meaning thereby that at this condition, is not affected by the presence of the body and that is what is half rho V2 freestream dynamic pressure and S is the reference area. 𝐿 𝐶𝐿 = 1 (2 𝜌𝑉 2 ) 𝑆 𝑓𝑟𝑒𝑒𝑠𝑡𝑟𝑒𝑎𝑚 By now, you know that S is the wing area for aircraft. Similarly, CD we have drag, non dimensionalized with dynamic pressure, again freestream and wing area. 𝐷𝑟𝑎𝑔 𝐶𝐿 = 1 (2 𝜌𝑉 2 ) 𝑆 𝑓𝑟𝑒𝑒𝑠𝑡𝑟𝑒𝑎𝑚 47 (Refer Slide Time: 04:17) Now, let us see if I want to fly a machine and if I decided to operate in terms of CL (𝐶𝐿 ), then I will say for a given weight (𝑊), given rho or given altitude (𝜌) and given speed (𝑉). This lift equal to weight (𝐿 = 𝑊)and lift is nothing but, from that expression I see it is half rho V2 S C L equal to weight or C L equal to 2 W by rho V2 S. 1 ( 𝜌𝑉 2 ) 𝑆𝐶𝐿 = 𝑊 2 2𝑊 𝐶𝐿 = 𝜌𝑉 2 𝑆 So, what I know, for a given weight, if I am to maintain lift equal to weight, I must fly at this CL. But, then how do I generate this CL? I will be turning this plate at an angle or turning the airplane at an angle, so that total CL of the aircraft is, what is dictated by this CL and how do I do that. Because, I know the airplane have wing, has tail and at angle of attack, they produce lift, the fuselage produce lift, the total lift and total CL should be equal to the CL required. This part we have already covered, in covering this we also have spoken about the finite wing and quickly, I go through that finite wing we understand. 48 This is typically a finite wing, where this is the span, this is the chord here, we have already discussed that. If I joining a line, the leading edge and the trailing edge, the straight line is the chord and this is the span and if it is a finite wing, then what is happening that, at an angle of attack when there is a lift this bottom portion is high pressure compared to the top portion. So, there are vortices will be formed and that has two effect. One is, because it is carrying out rotational kinetic energy and that energy is come from the energy of the machine. So, the machine will lose energy or say increase drag and that is termed as vortex drag or lift induced drag and second thing, as the vortices form like this, they induce a downwash in the downward direction. The meaning thereby, if this is the freestream velocity, as it comes close to the aircraft it’s velocity vector gets tilted, because of downwash component. So, if I try to draw that… (Refer Slide Time: 06:45) So, finite wing before I draw anything, quickly I should have my thinking clear. One is vortex drag or lift induced drag, another component is it induce downwash. So, so the local velocity is tilted, right ok, just to draw a diagram on this. Let us see, this is the wing and this is the free stream speed or velocity, as it comes close there is a downwash. So, the velocity vector no more remains straight like this. They also get tilted like this and this tilt if I try to draw that is nothing but, this is the freestream and this is the downwash denoted by w, then this is the resultant velocity vector which comes because of the downwash. 49 Please note that, this is the freestream velocity and this freestream velocity gets super impose with the downwash, because of wing to vortices and the velocity vector get tilted. So, local velocity vector is different than the freestream velocity vector. Now, the question is, when I try to find lift on this wing, the lift will be perpendicular to the local flow condition. But, we define drag and lift for the whole airplane based on freestream condition, this is very important. This is to be noted down, the lift on the wing or any component will be perpendicular to the local velocity. However, CL of the whole aircraft when I try to write, the CL or the lift when I try to model it, I should ensure that, that lift is perpendicular to freestream velocity. And by now you know, the local velocity and freestream velocity they are not in same direction, because of downwash near the wing or near any other component. In this case we are discussing downwash, because of the wing to vortices that is, as these vortices go like this, they induced the downwash, right. So, let us try to use this understanding and try to get an approximate expression for the induced drag. (Refer Slide Time: 09:49) Let’s say, this is the lift of the… This is the wing and this is your freestream velocity direction and because of downwash, this direction has changed the local, v local. Now, here if I try to draw lift, I know this will be perpendicular to the local flow condition. This lift seen by the wing will perpendicular to the local flow condition, not to v infinity and 50 this angle is called… This angle that tilt in the velocity vector which is called induced angle of attack. Who has induced this? It is induced by the downwash. Why downwash has come? Because of the vortices. Why vortices have come? Because of pressure difference in the bottom and the top position and why do we need a pressure difference, because I want lift, right. So, it is alpha induced. Now, since I want to define lift and drag, see if I want to write lift I have to resolve this lift which I will call it local, for clarity that should be perpendicular to the freestream direction for the overall aircraft. So, if I take the component, so this is the lift and this is the drag, ok, so if I now try to write the drag, you see this will be L sin alpha i, (𝐷 = 𝐿 𝑠𝑖𝑛𝛼𝑖 ) this component. I write Di this is nothing but, L sin alpha i (𝐷𝑖 = 𝐿 sin 𝛼𝑖 ) and for a small angle, I can write this as L alpha i that is of course, for small angle you know sin alpha i approximately equal to alpha i. 𝐷 = 𝐿 sin 𝛼𝑖 = 𝐿 𝛼𝑖 ; sin 𝛼𝑖 = 𝛼𝑖 (𝑓𝑜𝑟 𝑠𝑚𝑎𝑙𝑙 𝑎𝑛𝑔𝑙𝑒) Similarly, if I, I can write this equivalently CD equal to CL into alpha i, where C D when I am writing like this, please understand I am talking about induced drag coefficient, because it is coming from the lift. 𝐶𝐷 = 𝐶𝐿 𝛼𝑖 Where 𝐶𝐷 ∶ 𝑖𝑛𝑑𝑢𝑐𝑒𝑑 𝑑𝑟𝑎𝑔 51 (Refer Slide Time: 12:29) And from theory of incompressible flow, for elliptic distribution one can show that alpha i can be approximated as CL by pi aspect ratio e. Of course, e is 1 for elliptic distribution of lift per unit span that is, if I draw it, you’ll find This is typically elliptic distribution of lift, any standard textbook you can get this information in detail and the bottom I am writing that downwash component and that denoted by w, right. And of course, e is less than 1 for anything which is not non elliptic. 𝐶𝐿 𝑒 = 1(𝑓𝑜𝑟 𝑒𝑙𝑙𝑖𝑝𝑡𝑖𝑐𝑎𝑙 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑜𝑓 𝑙𝑖𝑓𝑡 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 𝑠𝑝𝑎𝑛) 𝛼𝑖 = ; 𝜋𝐴𝑅𝑒 𝑒 < 1(𝑛𝑜𝑛 𝑒𝑙𝑙𝑖𝑝𝑡𝑖𝑐𝑎𝑙 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛) Mostly, we have non elliptic distribution. 52 (Refer Slide Time: 13:49) Now, if I substitute this here, so what I get, CD equal to CL into CL by pi aspect ratio e and that is equal to CL square by pi aspect ratio e, ok. 𝐶𝐿. 𝐶𝐿 𝐶𝐿2 𝐶𝐷 = = 𝜋𝐴𝑅𝑒 𝜋𝐴𝑅𝑒 So, this is nothing but, CDi, C D induced. So, now, for a wing what we see. For a wing if I want to find total CD, I know total CD will be what. One part is induced because of lift, which is given by CL2 by pi aspect ratio e and what about the other part. Suppose, this is the wing or further we might have, this is the airplane. As I am along the air to flow over the wing at alpha equal to zero, so there will be lot of resistance because of skin friction. Depending upon how stable it is, the skin friction value will change. There could be flow separation at different points, so there will be, pressure drag because of flow separation, so a typical resistance which will be at alpha equal to zero and typical resistance because of lift and the typical resistance for alpha equal to zero. We call parasite drag, which are dependent on the flow condition, which is a subsonic, low subsonic, supersonic, very high speed depends upon, what is the geometry of the airplane. You will know, the aerodynamic something called Reynolds number, which talks about ratio of inertia of the viscous force, that is if it is a low Reynolds number, then we expect to have more viscous effect, right. So, accordingly to that, this CD0 will be decided and once we say CD0, this ‘0’ means that CD at zero lift. 53 For a symmetric aerofoil, it is good enough to say CD at alpha equal to zero. For cambered aerofoil, we define this you write CD at CL equal to zero and as we progress you’ll see that, some time we try to represent this drag coefficient using CD minimum also. Those are matter of detail, at this present only understand that the drag coefficient will have two component. One because of parasite drag, zero lift drag and another lift induced drag and this representation is known as drag polar. 𝐶𝐿2 𝐶𝐷 = 𝐶𝐷0 + ∶ 𝐷𝑅𝐴𝐺 𝑃𝑂𝐿𝐴𝑅 𝜋𝐴𝑅𝑒 Whenever you finalize the design, when aircraft is flight tested, everything is done, then this has to be estimated and every aircraft is bench marked with a given drag polar under different, different fight conditions, right? So, this is one of the contribution of finite wing, that because of finite wing there is vortices, because of vortices there are drag, induced drag and because of vortices, they downwash which will also change the lift curve slope or CL alpha of the wing. Let us see, how that happens. Let me draw this diagram. (Refer Slide Time: 17:20) So, this is typically let us say this is a wing and this is a freestream velocity. As it comes near the wing there is a downwash, because of wing tilt vortices, the velocity vector gets tilted downward. So, this is the local velocity direction and this is the chord line, all these thing you are now familiar and this is the angle, which I call it alpha effective (𝛼𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 ). Because, as far as this wing or the body is concerned, all the lift generation will happen 54 because of this angle, because come back to the John George Cayley, that the lift will depend upon the angle between the velocity vector, local velocity vector and the surface or the chord line in this case. So, this is alpha effective and alpha i is the induced angle of attack. So, now, we understand one thing if I denote a0 (𝑎0 ) as 2D lift curve slope, that is lift curve slope which is typically C l alpha represented by C l alpha (𝐶𝑙𝛼 ). What is the meaning of this 2D lift curve slope? That we are assuming that span is infinite, so there are no alpha i, because if it is infinite; that means, there are no wing tip, it is not a finite wing. So, there won’t be any wing to vortices, so there won’t be any downwash, so there are no alpha i, ok, so that is what is a0. So, if I now write dCL by dalpha minus alpha i, this should give me a0. 𝜕𝐶𝐿 = 𝑎0 𝜕(𝛼 − 𝛼𝑖 ) Because, I have taken out alpha i from the angle, this slope when I am writing CL versus alpha effective, which does not take alpha i, or alpha here has been taken out, the effect is taken out. We are talking about this, so this should be the a0, if that is a0, then I can write CL equal to a0 alpha minus alpha i plus constant. 𝐶𝐿 = 𝑎0 (𝛼 − 𝛼𝑖 ) + 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 So, CL I can write as a0 alpha, for alpha i I put the expression which I have written earlier 𝐿 𝐶 which is CL by pi aspect ratio e (𝜋𝐴𝑅𝑒 ). I multiplied by 57.3 to convert this value from radian to degree, right, then plus constant. 𝐶𝐿 ∗ 57.3 𝐶𝐿 = 𝑎0 (𝛼 − ) + 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝜋𝐴𝑅𝑒 So, if I now manipulate this, I do some algebraic adjustment, I can find that CL equal to a0 alpha by 1 plus 57.3 a0 by pi aspect ratio e, ok or I can write dCL by dalpha equal to a 0 divided by 1 plus 57.3 a naught by pi aspect ratio e. 𝑎0 𝛼 𝐶𝐿 = 57.3𝑎 1 + ( 𝜋𝐴𝑅𝑒0 ) 55  𝑎0 𝐶𝐿𝛼 = 57.3𝑎 1 + ( 𝜋𝐴𝑅𝑒0 ) Let us see, again you come back here. What was a0? A0 is the lift curve slope for an aerofoil, that is 2D value; that means, the 2D value does not have any alpha i. So, when I try to find the slope CL and angle of attack, I am eliminating or taking out the contribution of alpha i. So, if I take this slope, this should a0, right. Now, from here I write CL equal to this and I get an expression CL equal to this a0 not alpha plus 1 plus 57.3 a naught by pi aspect ratio is e, 57.3 I put to convert radian to degree. What is the message here? If I have got aerofoil lift curve slope, let us say 0.1 per degree, it is degree that is per degree I am talking about. If I want to really calculate CL, what I have to do, I have to use that value, put alpha in degree and add such value a0 here, so from 2D value I will get 3D value. In this whole expression, there is one term which I am being writing AR that is the aspect ratio. We need to know, what is this aspect ratio? Remember, we will go back again, if this is the plate ((Refer Time: 23:08)) and I am flying like this, as per as George Cayley the lift will be… Because, there is a angle between the velocity vector and the surface and the lift depends upon the reaction which depends upon velocity, area, density, etcetera, etcetera. If it depends upon area, then whether it goes like this or it goes like this they should be same, but they are not same. We know that lift, for generating lift I should fly like this. Very simple way to get an understanding of it, remember when I am flying like this I can assume that it is composed of so many aerofoils like this. But, if I am flying like this, aerofoil which are not as large as aerofoil like this, because why aerofoil, because the pressure difference will come because of contour of the aerofoil. and here, if I am flying like this, so many aerofoils, so the contour will get, effect will get added and we get lift. To make sure that you are flying like this, we also define some term call aspect ratio and that gives us a feel, which way I am orienting this way or this way. For example, aspect ratio if I draw a wing, if I call this b as span and this c as chord, aspect ratio will define as b square by S wing (𝐴𝑅 = 𝑏 2 ⁄𝑆𝑤𝑖𝑛𝑔 ). For a rectangular wing, it automatically becomes b square by b into c, so it becomes b by c, for rectangular planform wing, rectangular wing which I mean planform. 56  𝑏2 𝑏2 𝑏 𝐴𝑅 = = = (𝑓𝑜𝑟 𝑟𝑒𝑐𝑡𝑎𝑛𝑔𝑢𝑙𝑎𝑟 𝑤𝑖𝑛𝑔) 𝑆𝑤𝑖𝑛𝑔 𝑏𝑐 𝑐 Now, see if this is the wing, if the span is increased to infinity what will happen to the aspect ratio. So, aspect ratio also will become infinite. If aspect ratio becomes infinite here, what happens here? If aspect ratio becomes infinite very large, then this term will become 0, so in that case the CL will be same as CL what you get from 2D or coming here, the CL alpha of the whole wing will be same as CL alpha of the aerofoil, that is it will now behave like a 2D. So, if you want to get larger CL alpha, it is better to have larger aspect ratio. By there is a problem of larger aspect ratio, one of the problem is if it is very large aspect ratio wing, how do you balance the weight of the wing and there are other issues will come, as we progress we will understand. In the nutshell, whole effort here is towards making one thing very clear that, if you have a finite wing it will give induced drag and there, because of the induced drag your drag efficient will have CD parasite or zero lift drag plus K CL square. This typically follows a parabolic form and also the lift curve slope or CL alpha of the wing will also reduced as compared to CL alpha of the aerofoil. If you understand this, then we have understood, what is minimum required for and using this concept for performance analysis. Why do I need the relationship between CL and alpha? Remember, if we written CL equal to CL0 plus CL alpha into alpha, why do you require this, because to maintain lift equal to weight, we need some CL which will be given by the lift equal to weight equation. But, for a pilot he has to generate that CL, so he has to turn the airplane by some angle of attack, which will be dictated by this relationship. And finite wing, we were trying to understand with aspect ratio, how CL alpha of the wing is going to change, right? So, this is good enough of understanding for us to use this first performance analysis. We may most likely we have going to start with the cruise performance next. Thank you. 57  NOC: Introduction to Airplane Performance Prof. A. K. Ghosh Department of Aerospace Engineering Indian Institute of Technology, Kanpur Lecture - 07 Revision Good morning students, I hope you have good session in the first week. I was also going through these lectures and I have few questions in my mind. Incidentally, we are all aware our prime minister occasionally or regularly to be more precise announces a program called Mann Ki Baat. And in that, he tries to share his feeling about, what is happening in and around this world and more specifically, what is happening in this country. I also thought, let me also see all these lectures for last one week and let me share with you my Mann Ki Baat and the success will be decided by the answer, where whether my Mann Ki Baat has become your Mann Ki Baat or not, right. (Refer Slide Time: 01:17) So, I give this title Mann Ki Baat and it’s basically introspection, we will try to revisit, whatever we have studied in the first week and this will be a routine feature. The new week will start with the Mann Ki Baat, where we revisit whatever we have discussed and whatever I feel, that is these are the points where I should be more specific, I should give more stress. These are the area which I should not give you too much of stress at this time. 58 Because, we are going on pumping information to you and we do not have any eye contact with you. I do not get a feedback, whether I am able to communicate or not. So, it is better that we follow this practice and try to crystallize the basic foundation before we take off, right. If you go in the first session, you will find we have defined something called aerofoil and we have realized that aerofoil is basically a 2D concept that is it has a contour with an infinite span. The basic message here is that, we are restricting the flow to go in this cross section. There are no cross flows, this way or this way; that means, the flow will be more characterized by the contour of this aerofoil, that is if this is the aerofoil, then the contour of the wing and the flow over the wing will be decided by this contour and there won’t be any lateral flow or cross flows, right. In that we define something called streamline, we din’t define streamline, we want to define the streamline in a little bit of explicit manner, without going much into the details. What actually happens? Suppose the fluid flow is coming like this, what happens here? Here some fluid will go like this, some will go like this, right and this flow over this surface, both these surfaces will decide, what is the pressure difference, ok? Now, the question comes, why at all there should be a pressure difference? This question we need to ask, we need to understand little more and we will be addressing that part. First, if I want to represent this flow, which direction the flow is going. One of the ways is to define streamline. What is the streamline? You imagine those points in this flow and if I draw tangent at this point, that should give me the direction of the flow. So, this becomes your streamline, ok, that is another streamline that is any points you pick draw a tangent that should give you direction of the flow. This helps in visualising, it helps in modelling, ok. So, you can write like this, so many streamlines will be going like this. Infinite streamline I can draw, right?, because these are fictitious line. This only helps, to understand to represent the direction of flow, nothing more than that, ok. However, this concept will find aerodynamicist have used in developing analytical model of relevance to understand, what is the forces, how the force is acting, what will be the force behaviour with the orientation of the aerofoil, etcetera, etcetera, right?. 59 Forgetting about streamline and all, if I draw a symmetric aerofoil, symmetric we have defined that this distance from the chord line, they are same. Though, it is really not drawn properly, but I hope you understand, by now what is a symmetric aerofoil. What will happen without going into aerodynamics or anything very specialized? By natural justice we find, the half of the flow will go like this and half of the flow will go like this. Because, one of the, this half over a particular line flow will have a direction like this, the other part will flow go like this. So, there will be another line where the flow will be just like that, there would not be any flow at that direction. So, it separates lower as well as upper flow, this part separates upper and lower flow, I am not using any aerodynamic term. So, now see one thing, if it is symmetric aerofoil; that means, from here to here and from here to here. If I measure there length they will be same; that means, the flow over this, if we remain attach, it will travel from here to here. Flow here will travel from here to here and they will travel equal distance ok and this is another law of justice or natural law, is that whatever fluid is coming here, they have to come out. They cannot get stagnated at one point, they cannot get accumulated at one point which we call the continuity of the fluid particle motion, right ?. That is if you try to draw a pipe, if I allow fluid to flow through the pipe, I know that whatever is going here has to come out, ok. If that is true; that means, if they are travelling equal distance, upper portion as well as lower portion; that means, they will have same average velocity. And if the velocity, average velocity is same; that means, the pressure here and pressure lower has to be same, because you know Bernoulli’s p plus half rho v square has to be constant, right. 1 𝑃 + 𝜌𝑉 2 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 2 And since, both are having same average velocity, so the pressure remains same. So, the pressure, upper pressure lower will be same and hence there would not be any lift, this is one of the explanations, ok. There are many explanations and the explanations are designed or formulated to suit mathematical modelling. So, you see there are many ways of defining this, other than what I am explaining here. This is using a very fundamental common sense, ok. 60 (Refer Slide Time: 09:02) Now, think of, if this same symmetric aerofoil is at an angle of attack alpha (𝛼). Now, the question comes, what is the angle of attack? To understand what is the angle of attack, again revisit. If this is the plate ((Refer Time: 09:23)) and if this is the velocity direction, I am concentrating on the vertical plane and in vertical plane, whatever the angle between this velocity vector and the chord of the wing is called an angle of attack, ok. Now, what happens if I try to visualize like this? What you could see that, flow will something go like this and some flow will go like this, what is the difference between this picture and this picture ((Refer Time: 09:59)). Now, you could see that the upper part of this fluid, they will be travelling more distance than the lower fluid. Am I correct? This is going like this, so it will be traversing larger distance than this fluid particle. However, because of continuity, whatever has entered here has to come, at the same time that is fluid particle all will come at a same time here, that also tells us since this is to travel larger distance. The average velocity here has to be greater than the average velocity lower or I call it upper. Is this clear? 𝑉𝑎𝑣 𝑢𝑝𝑝𝑒𝑟 > 𝑉𝑎𝑣𝑙𝑜𝑤𝑒𝑟 If it is at angle of attack, now I could see this fluid stream has to traverse larger distance compared to the lower part of the fluid. 61 However, all the fluid has to come at same time; that means, the upper part has to hurry up, because larger distance. I say the average velocity of the top surface will be higher compared to the lower surface. And if upper part speed is higher and we know that p plus 1 half e v square is constant, (𝑃 + 2 𝜌𝑉 2 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡) that is the Bernoulli’s theorem. So, if this man is higher; that means, this man has to go down, if this increases this has to go down, that is why the pressure here reduces. Pressure upper now goes down compared to pressure lower or I say pressure lower is greater than pressure upper, so there is a lift. (𝑃𝐿 > 𝑃𝑈 ⇒ 𝐿𝐼𝐹𝑇)Is this clear, ok? I have purposely avoided technical term, which an aerodynamicist will use, they will define something called stagnation point, I am not using those things, right , ok. Then, we were discussing about cambered aerofoil. (Refer Slide Time: 12:11) And now that symmetry has been broken. Now, what happens? You could see here, from this geometry if the flow is coming like this, this part has to have higher speed compared to the lower part. Same theory will apply here and we will have pressure difference and we will have lift, ok. We also realize that if I plot CL versus alpha, for a symmetric aerofoil up to certain point it is linear and after we call it here. Strictly speaking we call it CL max that is the maximum CL, this wing or this aerofoil can generate. 62 And after that they drop in CL, increasing drag and that area we call stall. So, conventionally we call this angle, at which the flow separates we call alpha stall (𝛼𝑠𝑡𝑎𝑙𝑙 ). So, this two important term, one is alpha stall, but you could see also at alpha stall CL is C L maximum; that means, if you further increase the angle of attack beyond this alpha stall, you will not get additional CL (𝛼𝑠𝑡𝑎𝑙𝑙 ⇒ 𝐶𝐿𝑀𝑎𝑥 ). In fact, CL w