 Let us see the corrections first. So there is something called as a indicated airspeed. The indicated airspeed is what the pilot sees in the instrument. It could be 0, it could be infinity. Suppose the tube is broken, suppose the needle is jammed, the needle which is supposed to move, there is a breakage and now the needle has fallen to 0. Now whatever speed you fly it will show 0, correct? If the instrument is faulty, if the instrumentation has got some mechanical or electrical disconnection it will show 0 because it is not sensing anything, it is not working basically. So the indicated airspeed is what the pilot sees but that is not the actual aircraft speed because this instrument has been calibrated based on pressure on the ground. So there are some errors in the instrument, for example the dial has got some friction. So under some pressure it should move to 38 degrees but it is moving only 30 degrees because there is a friction or there is some error or there is some permanent elongation. So these are called as instrument errors including breakage of the link. So on ground when you do the maintenance of the instrument, you say let us give it a dynamic pressure and see what it shows. So in every aircraft there is a small placard which shows if the instrument says 300 read 290, if it shows 350 read 320, if it shows this read this, okay? Because and that card is changed by the maintenance people every time that is a simple calibration of the instrumentation. This is what you do in experiments also. Before any experiment that you do you should do calibration, same thing we do in the instrument. So let us assume that now we remove the instrument errors. So then the speed which the instrument shows is called as the calibrated airspeed. That means a perfectly working airspeed indicator should show this particular speed when so much dynamic pressure is acting on the system. That means so much, now the instrumentation basically does not worry about what is the total pressure, what is the static pressure. It works only on the difference because on one side you put static pressure, on one side you put total pressure, the difference is what moves it. So now we come to a speed called as the calibrated airspeed. So can I say now that a calibrated airspeed is the speed that an error-free instrument should show, clear? This is very important because when we do aircraft performance in the post mid-semester portion you will have to understand and correct the values otherwise you will be getting wrong answers. I am warning you right now. Many people will simply take the numbers and start punching them without processing it. And I am going to give you a very interesting assignment where you need to know how to convert the things. So the calibrated airspeed is what an error-free instrument should show, any doubt on that? Okay, so now let us assume a theoretical scenario that the errors in the instrument are 0. So what you see is what you should have got, which is the calibrated airspeed. But is that the true speed? It is not. For that we have to understand the working. So the working is very simple. The dynamic pressure in an incompressible flow can be shown as to be half rho v square. So p total is half rho v square plus p static. So if you subtract p static then you get half rho v square. So half is the constant. But rho is the density. Density of what? Of the air. And as we know the density of the air does not remain constant as we go from one altitude to the other. So what does it depend on? What does density of air depend on? Yeah, Saurabh you can speak. What is it depend on? Depends on temperature, humidity, temperature, altitude from the ground, anything else? Anything else will affect the density of the ambient air? Perhaps these are the only things. Something new? Yes. Speed of air. Right. Even the Mach number. Even the Mach number. There is a relationship between the density and the Mach number also. So whatever it is, it is not the same at all altitudes. So when you calibrate the instrument on the ground, see I cannot do the calibration of the instrument at various altitudes. I will calibrate only on ground. So what do I do on the ground is I apply some pressure into the, I apply some pressure into the total port and I open the static port to atmosphere on the ground. The instrument reads the differential pressure. So that is equal to half rho V square. But which rho is it? That rho is actually rho 0 or rho at the test condition. So if I test at Mumbai, it will be rho at Mumbai and that too rho at Mumbai will not be the same in summer or winter, there will be minor changes. So assume a condition when you are calibrating the instrument under perfect ISAC level conditions. Density of the air is going to be 1.2256 kg per meter square. That is the ideal C level value. So you tell, you do the calibration so that if there is so much pressure which is being put into the instrument that pressure is equal to half rho V square. So that V it should show, let us say it is 180 knots. Then you change the pressure and you make the instrument such that it shows that one. So remember that rho is constant at C level or at testing condition. So it is V square versus pressure. So you keep on adding more pressure and it should show velocity as a function of square and then you seal the instrument. So when the pilot is flying this aircraft now in New York at a height of 2 kilometers under a very cold condition, the air which is coming in the instrument is not at the same density as the air which came when the instrument was calibrated. The instrument was calibrated at Mumbai at C level but so much pressure equal to so much velocity. Now the same pressure if it is occurring in New York at 2 kilometer altitude at much more speed because that half rho V square is equal to this half rho V square, what will the instrument show? No, not different. See, understand. I gave some pressure to the instrument at Mumbai at C level. I have removed the instrument errors. It shows 180. The same pressure is exerted by an aircraft flying in New York at 2 kilometer altitude at some speed. If the pressure that is coming in is same as what was here, the instrument will show again 180, correct? But the speed is not 180. The speed corresponds to 180 only under that density. The density there is not the same. So just imagine a situation, forget about New York and other things. Let us say in Mumbai only you fly the aircraft at 2 kilometer altitude, will your density be lower or higher? Are you sure? My name is lower. Okay. Density of air at 2 kilometers in Mumbai, is it lower or higher than the density at C level? Lower. 100 percent sure. Positive? Then do not worry. You say yes. It is lower. That will be lower obviously. I am just trying to scare, sorry. It is lower. Okay. So if the pressure which is acting on the instrument at 2 kilometer, tell me, I ask you a question now. Assume that the instrument is showing 180 knots. The instrument calibrated at Mumbai at C level is now flown at 2 kilometers. It shows 180 knots. So what is the pressure acting in the instrument? The pressure acting in the instrument is the same, which was acting at the same instrument at C level when it showed 180. So that pressure is half into rho 2 kilometers into V 2 kilometers square and this pressure was half rho 0 into V 0 square, V 0 was 180. So this 180 will not be the same because rho 2 kilometers is not same as rho 0. So since rho 2 kilometers is going to be lower, the velocity will be higher. In other words, whatever this is how you remember it, you get confused sometimes. So basically, you always tell yourself, the pilot always sees a velocity which is lower or equal to the actual. The pilot always sees a velocity which is lower or equal to the actual because the density of the air at any altitude is going to be definitely lower than density at C level under ISA conditions. So therefore, the true air speed that means at 2 kilometer, I was flying at 190 knots but the pressure that was created, half into rho at 2 kilometers which is lower than rho 0 into 190 square is equal to half rho 0 into 180 square. Instrument only measures pressure. So when I tell students about working of the, working of the calibrated air speed, I always say the calibrated air, listen to my words, the calibrated air speed is the reading that an instrument will show when the pressure acting on the instrument will be same as the pressure acted on the instrument when at that reading it was at C level, is it clear? So therefore, the true air speed is always going to be either equal to or lower than unless you have a rare situation in which the density of the air at 2 kilometers is more than C level density. Can it happen? Is it possible? Is it possible that density of air at 2 kilometers at any place in the world is more than density at C level? Where is it possible? Yes? So is there a place on earth where the mean C level is 2 kilometers or 2.5 kilometers unlikely right? You cannot have a place which has, I can understand 100 meters, 200 meters difference but to find a place where the C is at 2 kilometer altitude from C at Mumbai is not generally possible but let us not talk about all these things. We are saying that in general the indicated air speed is going to be always more than or less than the true air speed. So then you have true air speed, you account for the changes in temperature and density then you get the true air speed. Now this true air speed is what actually the pilot wants to know because the pilot the aircraft will not stall or will not behave or will not do anything based on the integrated air speed. For all you know instrument is blocked IS could be 0 or infinity, it does not matter aircraft works on physics not on instrumentation. So therefore for all phenomena where you need to know the actual speed you need to have a correction between the IAS and the TAS. So from IAS you get CAS, removing instrument errors, from CAS to TAS you get the true air speed. Now we forgot one small thing here which is called as the position error that is the error in the readings because of the location of the pitot static tube that could come also under the IAS to CAS conversion. So when I say instrument error you can say instrument error because of the mechanical instrument and because of the location. Remember all discussion is applicable right now only in subsonic flow where the other effects are not yet modeled. When we go further we will look at modeling of. Now the other thing is ground speed so now come to your point you are flying at 100 knots and the wind is coming at 100 knots, opposing direction. So now what is going to happen is you are actually flying at 100 knots physically but to an observer on the ground you are stationary because for the observer there is no relative motion now. So the ground speed is the speed of the aircraft with respect to the ground and remember the ground speed can be negative also. If the oncoming wind is at 20 knots and you have a small UAV which is flying at 5 knots then your ground speed could be minus 15 knots possible. So ground speed is used for what purpose? What is the advantage of ground speed? Who will need ground speed? Yes. Hello my name is Dinesh. Yes. It is air traffic control in airport they use the ground speed. Why? For landing purposes and takeoff purpose. In what way you mean to say no they tell the pilot that the headwind is so much, crosswind is so much, tailwind is so much that I understand but why will the air traffic controller what will you do with the ground speed? I do not think it is the ATC. No ATC is not concerned about ground speed. The ATC else, yes now let me just see if you have the answer. Who wants to worry about the ground speed? The pilots because they will require to know that what is their speed with respect to the ground speed. Why do they want? They should know how much fuel they have so that like they will calculate that if I am going to land at a distance of 10 kilometers, the airport is 10 kilometers away so like they will need to know not see how much time they take for them. No. Honestly speaking pilots are not concerned about how much time it because they are flying the aircraft because when they reach the aircraft the ATC may say go for one circle then one more circle, 10 circles pilots cannot do anything. So it is the airline who is interested not the pilots, it is the relatives of the people who are coming in to receive you to pick you up. So for example, just as a theoretical example, if the aircraft is flying at 100 knots and the wind speed is 100 knots headwind, you can tell the relatives just wait for infinity because this plane will never come to you. It cannot, relative speed is matching so the aircraft is virtually stationary. On the other hand, I will talk about this when I come to range and endurance. I will give you a very beautiful example in which the presence of headwind and tailwind can create a time difference of 2 hours in flying between Mumbai and New York, 2 hours and it can save 12 tons of fuel for the airline. Then I will talk about this. Right now we will go ahead. So we have to apply the corrections and this is the sequence in which the corrections are applied. Okay. Yes. What is the pilot speed on this video? Indicated airspeed and true airspeed. So you can see this is the instrument that the pilot gets and that shows, it just shows IAS. No, I have never said that the indicated airspeed is 0 if the relative wind is 0. I never said that. I never said that the ground speed is 0, there is a difference. If the aircraft is flying, whatever be the headwind, there will be pressure acting on the instrument and that pressure will be read as a speed. So the indicated airspeed is the speed of the aircraft, whether it is flying in headwind or tailwind is not important. So what you are asking is the ground speed. So the indicated airspeed could be 100, ground speed could be 0. There is ground speed but then there is no airspeed. That means you are... The aircraft is the same reaction as the plane is time, the same velocity, the airspeed will show there is no... No, that is the tailwind. Yeah. Okay. Tailwind. So at that time what will happen? See, because the aircraft is flying, the instrument attached to it will face some oncoming wind. Now because it is flying. Now air from the back is coming and pushing does not matter, that is not really going to affect the instrumentation. The pressure will be read. The ground speed will change based on headwind or tailwind presence or absence. That is the lightest airspeed shown 0 in case... Not necessary. See, do not mix up indicated airspeed with the ground speed. Do not mix up indicated airspeed with the relative wind. The IAS is not reading relative wind. The IAS is reading the wind, the IAS is reading the speed of the aircraft based on the pressure that the aircraft is facing because of the oncoming wind. Okay. So the IAS or the integrated airspeed is what the pilot will actually see but it is dangerous for the pilot not to know the true airspeed. So therefore there is also a small scale inside you can see in the same picture called as TAS. It is hidden by the needle. So in this example, the true airspeed is approximately 140 but the indicated airspeed is only 105. 5, 10, 15, 20. So this is 105 indicated airspeed. True airspeed is actually 140. So as you can see the true airspeed is more than, so how is it more? How is it more? Is it going to be more? And what is the problem here? Okay. So the airspeed that the pilot reads is directly and there could be errors. So these could be the errors. Okay. So this is a small wheel which the pilots use is old instrumentation where dial type thing. So we can use the calibrator. So you remove it for the position and the instrument errors okay and this is in the aircraft operating handbook because they are designed for standard conditions. So you can get chart like this calibration chart. If the speed shows 110 actual value is little bit less or little bit more. So if this line is 45 degree that means it is correct instrument. If there is a slope more, slope less that shows the error in the instrumentation. So we normally do it with a handheld GPS because GPS will give you the actual location and you can have time and GPS time from a clock and the GPS location. You can use that to do calibration. This and then this is a detail which we will skip right now okay. So these are again instruments. I want to keep it for you for self-reading yeah because so now I want to ask you another interesting question which is what he has raised. Do you think the pilot is happy only to know the true airspeed or the what is the advantage of indicated airspeed for the pilot? That is the question that you are raising right. So now can someone tell me if we as engineers or instrumentation experts can do the corrections and tell the pilot this is your true airspeed. The job is over then why should we tell the pilot what is your indicated airspeed okay because the pilot has to apply corrections to that to get the calculated airspeed. So why is it needed for the pilot to know the indicated airspeed okay. This is the question I do not want to answer. I would like this to be answered by you and Moodle. So there must be some advantage. In today's technological world don't tell me that you cannot do the correction and tell the pilot because you are giving pilot both. You saw the dial the dial showed that the true airspeed was 140 indicated was 110. So don't tell me that is not possible but then why not show him only the 140 only the true airspeed why show him the indicated him or her. So now that is a question which I want you to answer okay. So at low speeds and low altitudes yeah you want to answer the question okay you have another question that is good. Sir so true airspeed should always be higher than the highest right. What do you think? It should be higher. Always okay why should it be higher. Yeah so assuming that the density decreases every go up okay. So why was there an error in the picture you told. Which error? Because higher. No you think about it. The density is the density of the air at high altitude is lower. So the total sorry the pressure at which the instrument shows 110 the same pressure is acting when the density is lesser. So the speed has to be higher. So I only said that the indicated airspeed is always lower than that of the true airspeed. There is no error in the instrument it is working correctly. The true airspeed is more than the indicated airspeed which is typically the case. So at low speeds and low altitudes the three speeds oh now we have one more speed called as the equivalent airspeed. So now we are into a soup we have somehow skipped this. Why did we skip this okay. So equivalent airspeed sorry it is my mistake I thought I can skip but it is important. The equivalent airspeed is the airspeed when you remove the compressibility errors. Especially at high altitudes because the density change happens due to static due to altitude and also because of speed as my friend rightly mentioned that there will be a change in density because of altitude and because of speed that correction is the compressibility correction and that correction when you do it you can get what is called as the equivalent airspeed which is the airspeed that should have been shown on the instrument without. So this is for very important because the equivalent airspeed is actually the one that is the dynamic pressure acting on the aircraft. So from the loads point of view from stalling etc that is the so it is a function of dynamic pressure. So ES basically is equal to 2q by rho 0 remember I am not using rho altitude here okay. So suppose I replace rho 0 by rho altitude q is half rho v square. The q is half rho v square which is the rho at the altitude. But I am saying root of 2q divided by q0 rho 0. So rho 0 is the standard density 1.256 kg per meter cube. So that is why it is equivalent airspeed. This is the speed that gives the same pressure with the compressibility effects removed okay. So since the value of so you will get some more indication there. So at low speed flight they are all same. So the true airspeed will be the equivalent airspeed into rho 0 by rho. rho 0 is the density at sea level conditions rho is the density actual condition. So since rho is less than rho 0 therefore what is the which is more tas or eas. In high speed flight you have a function of Mach number also. So you have to have you have to put that Mach number function that is what our friend mentioned this a0 rho is the effect of the density okay. So this is the equation when you bring in temperature. So look we are not here to derive these expressions because in the introductory course of fluid mechanics or introduction to flight they are interested in just knowing what the relationships are. So you do not have to really worry about you know talking about. Let us go to ground speed the actual speed of the aircraft over the ground. So you correct the true airspeed for the wind effects headwind or tailwind. So if you have a headwind it subtracts headwind means coming from the head tailwind coming from the tail which one is better that is what you think. Takeoff distance will be less or more depending on headwind or tailwind okay. So we will talk about it okay. So this is how you do it see there is a resultant ground speed. So suppose there is a wind coming at an angle then you have to take a vectorial addition and get the value of ground speed okay right. Now let us look at the markings in the indicator. There are these regions you know green region yellow region and red region. So from pilot safety point of view. So obviously the white arc depicts the normal flap operating condition that means what is the speed at which the flaps can be operated because if you do not the flaps may break off. Flaps cannot take so much structural loading they are only meant to be deployed in takeoff and landing and in military aircraft we also have combat flaps but very small angle 5 degrees perhaps 15 degrees in some cases. So that is a different case but in general flaps are not to be deployed after you achieve the climb and before you come into land. So therefore there is a maximum speed at which flaps can be deflected. So that is indicated the green arc represents the normal operating range on the airplane and there is a cautionary range that is yellow color. So now if you are flying at the yellow color area and you have turbulent weather it can become dangerous because the loads will become very high. So the pilot is told if you are expecting disturbed weather conditions take it to the green region do not go in the yellow region and then you have a maximum allowable feed to the red line that should be never exceeded but can the pilot exceed that speed. Do you think it is possible for this pilot to fly beyond 230? How is it possible? What does the pilot have to do to fly at a speed more than the maximum permissible speed? Yes. Sir if engine is capable enough to go beyond that speed 240 the structural limit will be exceeded as a happen in the one air crash when the aircraft just plunge down with the speed more than the limiting speed and its flap and all the components were just cleared of that. So the pilot can exceed this speed either using the power of the engine if the engine can give that much power or you can go for a dive.