 So, this is the, now this is the VN diagram as per another regulation. What is the difference in this diagram compared to the previous one? The previous one was from AP 970, this is from FAR 23. What difference do you see between this diagram and the previous diagram? No, do not worry about numerical value because that comes from the regulatory body whether it is 3 or 9. Look at the, look at the figure and tell me is there a difference in the figure compared to last time. So, what is the difference? The point, point D. So, what happened in the previous one? There was a cut given, correct. So, between C and D there was a point, between D and F there was a point and there was a cut given. So, the question is there is a cut in this on the bottom, but not on the top. So, do you think other things remaining same that means the aircraft class remaining same therefore NZ maximum will be the same and that minimum will remain the same. Do you think it is more difficult to design as per AP 970 or FAR 23? So, the numerical value of the NZ max and min will remain the same whether you do AP 970 or FAR 23 these numbers will come from the aircraft you are designing. So, in both the cases which one will impose more constraints and why? Which one will impose more constraints and why? Anybody who can answer this? Let us, let us get your point of view. Please take a mic constraints. Yeah, the answer is right, but why? Correct. The portion that has been cut off and thrown away in AP 970 means that you do not have to show compliance in that area which means at a speed between VC and VD in AP 970 you do not have to show that NZ equal to NZ max will occur. So, it is a concession you are right here basically the aircraft could be operated at any point inside this diagram okay. This diagram represents the limit of operation. Take any point let us say there is a point which is A. At point A you have some VA and you have NZ maximum that means the designer has to show that at a speed VA if the net load factor is equal to whatever 2.8 or whatever as this figure the aircraft structure is safe. So, any point in this diagram should be structurally manageable by the aircraft. So, if I give a cut and if I exclude some portion I am giving a concession. So, yes AP 970 is giving a concession, but why are they giving a concession and why are they not giving a concession? The answer is that AP 970 is meant for military aircraft and this is meant for other aircraft general aviation etc. etc. AP 923 is normally for small aircraft. So, it so happens that the regulatory body who has given permissions for this class of aircraft they feel that this is an area in which a rookie or a unskilled pilot may take the aircraft by mistake. So, we do not want to give a concession whereas the fighter aircraft pilots are generally very trained pilots. Secondly, we will see very soon you can answer the question actually when we go little bit towards the end. Now, let us look at the various parts of the VN diagram. We have this part which is O2A. So, O2A is a parabolic curve and it refers to the stalling angle of attack. How can we say that? Why is it referred to stalling angle of attack? Because it represents the maximum permitted load factor at the lowest possible velocity along the line. Now, in that we have marked one line called as VS. VS basically stands for stalling speed. So, do you think flight is possible on the left of the VS line? Sustained flight is not possible. Aircraft cannot maintain a speed lower than VS it will fall down. So, technically speaking there should be a vertical line at the VS line and the area on the left should be exempted because you cannot be there. So, that is the actual case that is what it is. So, VS is a numerical value of the stalling speed but the point which is shown is at NZ equal to 1. So, that point corresponds to level flight stalling speed. So, when the aircraft is flying at the minimum, now hang on a minute, the minimum permitted speed of flight is slightly more than stalling speed from safety point of view. It is normally 1.1 times stall speed, 1.15 times stall speed. So, let us ignore that that is the operating limitation. Technically speaking the aircraft can fly at V equal to V stall and now remember the x axis is equivalent airspeed. So, this is at any speed at any altitude. At any altitude there is a same equivalent stalling speed that is the beauty of equivalent airspeed. So, the pilot does not remember at what height I am should I have this speed. The pilot has only one speed to see in the indicator the true airspeed or the indicated airspeed which is the. So, the aircraft will stall at the same equivalent airspeed at all altitudes. So, there will be this point which is V equal to VS and N equal to 1. So, we call it as a 1G stall speed. You will see this in many aircraft documents. What is the 1G stall speed? That means what is the stall speed when the aircraft is in level flight. We have this speed called VA. What is special about this point VA? VA corresponds to the lowest speed at which N equal to NZ equal to NZ max. Do you agree? So, it is one of the corners of the VN diagram but it is the most important corner. Once again lowest speed at which N equal to NZ maximum. So, what is special about this point? Remember the formula for tightest turn and fastest turn. And I have stressed in the slides and I also asked a question in the quiz. What is the condition at which you have the tightest turn and the fastest turn? Highest load factor, lowest speed. That is the point. So, what will happen when you fly at VA? You are allowed to do the tightest turn. If you go tighter than that you are going to exceed the structural limit. So, you cannot do that. So, that is the corner speed. Now, why do you say that the lift coefficient is maximum? Why is it maximum? It is the least speed. So, lowest speed comes only when you are having CL equal to max. What are the implications? Implications are smallest turn radius, fastest turn rate, best turning performance. So, this is such an important point that sometimes we use it to compare two aircraft. Somebody says, how does F16 compare with let us say LCM? There are many parameters. We saw it last time also. One parameter is what is the corner speed? So, whichever aircraft has a lower corner speed, it will be better than the other from the point of view of maneuverability. Because if I can do the same turn rate and the same turn radius at a lower speed, I have an advantage over you because you have to fly at a faster speed to do it. When I am at a lower speed, I can quickly point my artillery towards you. So, two aircraft or let us say two versions of the same aircraft, F16, A, B, C, D, whichever has a lower corner speed is more maneuverable. And the chances are that in a combat situation, it will win over. In a dogfight situation, it will win over. So, just check out yourself, look for two combat aircraft, look for their corner speeds and then find out which one has one. It does not mean that the one with the lower corner speed will always win because there are other things armaments, pilot skill. More important is nowadays there is no need for a dogfight. You have fire and forget weapons. So, let us say I want to bomb this television. I can go this way, I can go this way and fire the missile and then go that way. The missile will turn and hit the television. Why should I come towards the television? Dangerous because I will not be welcomed by my enemies here. Ajao, please come and hit. They are going to be ready with their artillery. So, nowadays we have FNF weapons so all this discussion is all meaningless. But suppose there is a situation where you have an enemy aircraft coming and we want to now intercept it and now you have this dogfight, then this corner speed becomes an important. So, we also call it as a design maneuver speed, but more common word is corner speed. Now the vertical, the horizontal lines A, A, C, D that line and the bottom horizontal line, this is not something natural. This is something which is externally imposed. We call them as the placard limit. What is my placard limit? In every aircraft there is a small placard saying do not exceed NZ equal to 3 and NZ equal to minus 1.8 or 1.5. It is listed. It is a document. So, this is not natural. Flight on the left of O and A is impossible. Naturally you cannot fly below low A. If the pilot wants to fly at a speed less than V stall, cannot. I cannot be operating at this point. Even if I want to, I cannot. Because aircraft will stall. Similarly, negative, I cannot. It is a negative, let us say inverted flight you stall you cannot do. But upper and lower limits are not natural. We will see how they are imposed and what happens if you exceed them. Then there is one speed called as a cruising speed. So, cruising speed is a speed which is a function of the wing loading of the aircraft W by S and a function of also the power and the thrust produced. And then you have a design diving speed. For VC cruise speed there is no number given. It depends upon the aircraft design and engine and all that and aerodynamics. But there is a maximum dynamic pressure which the aircraft can take from the structural point of view. After you design the aircraft for some structure. So, half rho V square is the dynamic pressure acting on the aircraft. Beyond a particular V, the aircraft structure will fail. So, that V is called as that. Normally you get that speed in a dive. Because if you can fly at some Mach number in level flight, you can fly faster than that in a dive. So, the maximum speed you can ever attain will be only in a powered dive. Imagine diving with engine full on, with afterburner on. So, you might exceed this speed because power plant is very powerful. However, you do that, the structure fails. So, therefore, one limit is imposed by the designer himself, not by the regulatory bodies. That typically this number is 20% higher than the cruise speed, typically for transport aircraft. For military aircraft it could be much higher than that. But whatever it is, there is a vertical line. Beyond this I cannot go. Even if I want to go, I cannot go. The structure will fail. On the left of this I cannot go because aerodynamics will not permit me. Above and below I can go. I can go but there is a problem. So, this becomes the operational VN diagram. The areas on the top right and the bottom right which are actually cut by the AP 970, they are cut because of experience. Because of the power plant limitations, you really cannot go there. So, these areas are not operationally possible. Structurally possible but because of the power plant limitation. So, we come back to the VN diagram as per AP 970 because in some cases there may be an assignment to do the calculation for this. So, it is just a method. It just says that there are these various numbers given. So, there will be some formulae for N1, N2, N3, N4 etc. In terms of, can somebody answer this question? His question is that we talked about dependency of VN diagram on angle of attack. But we have forgotten that now. We are only worried about speed. Yes, what is the answer? Yeah, what you say is true. If you are approaching, if you are flying at the highest speed, the alpha will be the minimum. But his question is that for any point inside the VN diagram when you fly at that speed and that load factor, what did you do about the angle of attack? So, the answer is very simple. The angle of attack automatically gets fixed when you have a fixed speed. Remember, CL is equal to alpha into DCL by D alpha. So, the moment let us say I am flying level, lift is equal to weight N equal to 1. So, depending on V, there will be some alpha. They are related. Let us say I am maneuvering N equal to 3, lift equal to 3 times the weight. So, L will be equal to half rho V square SCL. Equal to this weight. So, CL will be N times W upon rho V square, rho SV square. Once you have a V, you have some CL. That CL is only at some angle. So, angle is taken care automatically. So, NZ depends on angle, but we have replaced the angle by AOA, we have replaced the angle by CL. I am saying that when you have the calculation for NZ, that much lift has to be created by the aircraft with the given density, with the given area. So, the only variable is V. So, once you fix the V in the VN diagram, there is a corresponding angle at which L equal to NW. So, it is taken care. You do not have to say I want this V and this alpha. It is not possible. You cannot fly at different alphas at the same V. For a particular V, alpha is fixed at which CL equal to CL required. So, that is why we do not have to worry about angle of attack. That is why in aircraft, you do not talk about nobody ask the pilot at what angle of attack are you flying. You know, I do not know. My V is so much. So, my aircraft has automatically trimmed to an angle at which the lift I need is coming from this aircraft at the appropriate angle. The only thing is I cannot exceed angle of stop. Let us go ahead. Any more doubts? So, you see now this particular cut which you saw in AP 970, it is not a fluke. It is given because they know that that area you cannot go because the power plant is unable to give you that much NZ at that much speed. So, they give you a concession a priori. That is the maximum sustained. In the vertical direction. In the vertical direction. The gain diagram is for a particular aircraft. Yeah, let us say 4. NZ equal to 4. Okay. No, no, no. Not necessary. Okay. It can. The point is, the point is, yeah. If you fly, let us say the line A to C represents locus of operating points at which you are flying at the maximum NZ at various velocities. So, let us say dive pullout. You are doing dive pullout at V equal to 200 knots. NZ equal to 6. You do it now at V equal to 200 knots. NZ equal to 6. You do it at 300 knots. NZ equal to 6. But when you fly at speed 200, 300, 600 knots, alpha is getting fixed. So, that is what I told him. I said we do not care about at what alpha it is happening. Yes. AP 970 and FR, the difference I am talking about is this cut. This cut. This cut CD is prescribed or permitted only in AP 970. In FR 23, there is no cut there. So, these concessions are given by regulatory bodies. So, what a regulatory body says, this is a defense regulatory body. It says, we know that you will not be able to fly in this area anyway because power plant will start packing up before anything else. So, they give you a cut. There the regulatory body says there could be a pilot who is at a very high speed and pulls the G so that you come in this area. So, that is the difference. So, the regulatory bodies decide the pattern based on the aircraft type which they are dealing with. Somebody might say that I will not even give this cut. No, I will not give this cut. If you see the FR 23, they give a cut in the bottom because they have found out that it is very difficult for even a rookie pilot to be at negative load factor and very high speed and very high load factor. So, they have given a cut because otherwise the designer has to design the aircraft for such a high load at such a high speed. Hang on a minute. Half rho V square is the dynamic pressure acting on the aircraft. If V is more, load is more, that is only a ratio. You are forgetting that the load on the structure is not the load factor. Load factor is a ratio of maximum lift upon aircraft weight. But that lift comes from where? From dynamic pressure. So, if the structure cannot take that, if let us say the wing breaks at half rho V square equal to some value. So, that is why there is a condition that you do not. So, the vertical line ensures that you never fly at a speed more than V d. Basically that is from that point of view. Let us go ahead and see. So, now we look at what happens when the pilot wants to exceed the limits. So, this is the V-end diagram. Now we go back to FR 23 just to show you an example. Yes, what is the point? What this diagram is saying is that these are the lines indicate the maximum load that aircraft can develop during any maneuver. No, no, no. They are not telling what the aircraft can maneuver. They are telling what the aircraft should not exceed. This is a regulatory diagram. Do not exceed this. You can take it both ways. Regulatory body says prove to me that the aircraft can fly safely at any point inside this box. This is what the regulatory body is asking the designer. Show me that any point in this particular, inside this particular graph, inside or on this graph is attainable by your aircraft. Plus it also says do not exceed this. So, now let us look at this slide. This will tell you something. Let us look at when you want to exceed. This area is impossible to fly. I have already told you. Why? Aircraft cannot have sustained flight in that area because of stall. Between that V s and point V a, is there any mechanism we can cross that line or it will automatically come back to that line? It will come back. If you go from n equal to 1 and v equal to V s, which is this point, this point. Suppose you, suppose you fly at this condition. So, V is more than V s and n equal to this value but less than n z. Now, suppose you, suppose you want to fly at this point. V is equal to more than V s, but n is more than that value. You cannot because that line represents stalling. This whole line represents O a. The line O a represents flight at the maximum permitted angle of attack or CL max. Above this is not possible to operate sustainably. On the left of V s you cannot because you will stall. Above that if you go you will come back because the aircraft cannot sustain you. So, it has inherent tendency to come back to that line. Correct. You just cannot fly in that area. So, that is what I am discussing. In this region, even if you want to. What about this region? Why? Power plant. Power plant limitation. Because you have reached something like V max, thrust is equal to drag. Now you do not have more thrust to create more flight. Okay. What about regions above A d and below B e? Is it possible to go there? No. It is possible to go but sector might break. So, pilot can try to go and then experience. So, on the left and the right pilot cannot even go. Aircraft will not, will not cooperate little bit. Above A d and below B d, B e you can go if you have enough control power. You can go. Okay. So, let us see how. The problem is this if you have enough engine and control power. You can do that because what you need? You need to pull up very quickly or turn very quickly. So, if you have control power you can but there will be a problem. If you are passenger you will start vomiting and if you are a pilot then you can start experiencing structural damage. So, therefore that is why this dive pullout maneuver. Now look at many of the videos that are available on YouTube of aircraft disintegrating during dive pullout. Some very enthusiastic pilot pulls it into a dive and then it breaks. It has happened. That is why we call it as a checked maneuver. You have to check. So, the pilot simply cannot pull the control stick. Now, today's aircraft are such that the control system itself has an inherent limiter. So, that even a pilot who wants to commit suicide cannot do it. At least in the turn, you can take the aircraft to the ground. No problem. Because it is supposed to land. But if you want to do willful deviation of flight performance, the control system may come in way today. Especially if you have a flabber wire system, every input is an intention of the pilot which goes to the computer which says no, this is a sensible input. Sometimes it creates a problem also because the system misinterprets and we saw one crash happening. When the pilot wanted to bring the aircraft down to land but the aircraft thought it is a problem with the control system. So, the dive pullout maneuver is possible that the pilot may exceed NZ max but you do not allow the pilot to do it by training. So, this is a dangerous maneuver because you might be able to take it and cause a crash.