 Welcome to lecture number 16, which is the second lecture of capsule number 8. Before I start this lecture, I want to share with you some interesting things about the person who has created the content for this course. This is Dr. Rahul Goyal, who is currently a research assistant in University of Houston. He was one of our very distinguished undergraduate students, joined in 2004, and after one semester of staying in IIT Bombay, when most students want to go home, he came along with his friend and said, I do not want to go home because all my friends have gone to various engineering colleges, medical colleges, there is nobody at home. I want to do something, so I said, you are so fresh, just fresh into engineering, forget about arrow. But he was highly enthusiastic, he insisted, so I said, okay, go home for a week so that your parents can see you and your friends and relatives can see, then you come back. He came back with his friend and the content that you are going to see today was first initiated in 2004, so it is very old. As a winter intern, it was done, he did many things. One of the things was to prepare this presentation. Now today, PowerPoint is very common, it is available everywhere, we do lots of animation etc., etc., video insertion. Go back in 2004, PowerPoint was very new, it was the latest sensation software in the market and we had not explored PowerPoint, prior to that we were using transparency sheet. So this presentation was created by Raul and his friends using my transparency sheets for this lecture and inserting some more material. So take it from the point of view of some historical approach also. After completing his graduation in IIT Bombay, Raul went to MIT on a fully funded master's program. After completing master's he did many interesting things, he went to Germany for a space program etc., etc., and interestingly, just about, what today is 13th, about 7 days ago he defended his PhD at the University of Houston, okay. This is Raul and his wife Supriti, I had the pleasure of attending his wedding last year and he is now an expert in space physiology. So the topic of his thesis is sensory motor mechanisms underlying postural control for the astronauts, okay. So I present to you the presentation, the PPT made by Raul and his friends on VN diagram, okay. So these are the contents of this particular presentation and one more interesting fact, the entire content of this presentation have also been recorded as a video lecture. So back in 2001 I think or two, we had one education technology cell in IIT Bombay, ET cell. I can call it as the father of C.Deep basically, C.Deep has formed basically out of ET cell and ET cell approached us, young faculty members, at that time I was quite young, 2001 to record video lectures. So I volunteered to record this lecture, it is available in the library on a VHS cassette and I think it is also available as a soft copy. So the same lecture is already recorded, you will find me a very young person with lot of hair and also darker in black presenting this lecture, okay. If I locate that I am not getting that DVD somehow, if I locate it I am going to share with you. So what we are going to look at is definition of VN diagram, we are going to look at load factors acting on the aircraft, what are the limits on them, remember, limits, upper limits are not necessarily just positive upper limits, there are also negative upper limits. I do not call them lower limits, I call them as a positive and negative limits. There is a concept called as corner speed, which is very important and in the lecture that you attended on turning flight, we have discussed some formulae and methods to calculate turning rate, tightest and fastest turn. I will come back to that, the VN diagram is of many types. One of them is called as operational VN diagram and then we move on to the effect of gusts or disturbances acting on the aircraft and how they generate load on it. We will look only at vertical gusts in this particular presentation and then look at some regulations on how the gust velocity is specified and finally how these impose limits on the VN diagram and make a limit combined envelope, okay. So this is the VN diagram of an aircraft called HF-24 Maruth, which was one of the first transonic fighter aircrafts designed in the country. It was designed by a team led by Dr. Kurtz, tank from Germany and Dr. V. M. Ghatge from India and his team. At its time, during the time when it was designed, it was censored to be one of the best aircraft in the world in its category. So what is the VN diagram? Basically we see we have an x axis which is load factor, on the y, x axis we have the velocity, on the y axis we have the load factor, okay. Now the velocity on the x axis is not a normal velocity but a special velocity and the load factor on the y axis is also not the y load factor but the z load factor as we will see and I want to show you the diagram first and then we will see how to derive it. So you see there are two curved lines from origin OA upwards and OB downwards. These are the two lines. There are two horizontal lines on top and bottom which are the limits of the maximum vertical positive and maximum vertical negative load factors and then we have a vertical line here which is the maximum speed and then there are some cuts here and AP 970 stands for the British regulations, they were called as aviation publications that is AP, AP 970. AP 970 was a regulatory document provided by the Britishers for military aircraft and they gave a procedure and calculations and methodology to calculate the VN diagram. Similarly there are other agencies who also give the requirements. So let us take a typical aircraft in flight and although we have shown level flight here but it could be at any particular angle but consider level flight. You have thrust, drag, lift and force, do not worry about the point of action of the forces. The points are not collinear but in the direction along the thrust line or in the forward direction if we ignore the thrust mounting angle we have the force T minus D. So that force T minus D upon W aircraft weight will be Nx. Similarly you will have lift acting on the wings plus or minus lift acting on the tail mostly it will be plus lift acting on tail because tail has down load. That divide by the aircraft weight would be called as NZ or the vertical load factor and if there is any turn with acceleration then there is also going to be side force. So that side force divide by aircraft weight will be NY. So an aircraft typically has 3 load factors Nx and Zny. So this already I have covered yes yeah net force upon net force acting on the aircraft external force accept weight it is accept weight it is a net force acting on the aircraft accept the weight. So let us see some general points. First point is that VN diagram when we talk about VN diagram we are only looking at symmetrical maneuvers in the vertical plane. So can you name or describe any symmetrical maneuver in the vertical plane that you have heard of. Barrel roll is it in the vertical plane what is the barrel roll that is not the way it is barrel roll is this way. So some people are moving their fingers now there is a name for moving fingers yes anybody here knows yeah. Pull up maneuver, pull up maneuver, we have studied that maneuver you have answered a question in the quiz based on that. So why is it only for the symmetrical maneuvers in the vertical plane that means we cannot use this VN diagram for barrel rolls or for flip rolls or for anything that are not in the vertical plane there is one maneuver called as a nice edge pass so you go like this and then you turn like this and you go like this ok. And then if you turn it will create side force apart from the load. So we do not consider those maneuvers only symmetrical maneuvers that means not even this symmetrical maneuvers in which the wings remain level and in the vertical plane. So basically dive pull out or a loop. So why only for these what do you think this is a question I am not going to give the answer I want the answer to come from you. What do you think yes what could be the reason. So the question actually can be answered in many ways. One way to say is that you already told that VN diagram has NZ as the y axis so that means you should have pure NZ pure NZ will come only when you have a symmetrical maneuver ok. The other reason is someone can say ok then let us make one more VN diagram for NY versus VNX versus V. The answer is that NZ has the highest numerical magnitude in a symmetrical maneuver in vertical plane NX and NY remain constant. And the numerical value of NX and NY generally are much lower than NZ. So NZ is the real difficult thing the larger so we worry only about NZ we do not worry that much. So otherwise if you do a turn the engine may be thrown away by the aircraft if you do not take care of enough side force but those numbers are far lower ok. This is the reason numerical values are much higher for NZ ok. Now we have to see now the line in the VN diagram if you notice was parabolic of NZ versus V. So we have to prove that NZ is proportional to V square only then the line is parabolic and also to the angle of attack. So let us see how we can prove it ok. So here is the typical CL alpha curve for an aerofoil and this is the cambered aerofoil just for generality the same argument also applies for a symmetrical aerofoil. So the load factor N normally shown as a small N not capital N that is L by W L is equal to half rho infinity V infinity square S into CL where S is the ring reference area. But CL comes from lift curve slope into the angle of attack assuming that it is linear and assuming that we do not go into the areas where the curve is non-linear ok. You would never fly the aircraft beyond or near alpha stall. So the operational angle of attack range will be probably 5 degrees or 4 degrees below alpha stall. So it is a linear area. So L is proportional to V square because density of air is constant if you ignore density change in one small height ok. S is the ring reference area it remains constant. Angle of attack is going to remain constant because you want lift equal to NW you cannot change that. And lift curve slope is a parameter that is married to the aircraft geometry and aerodynamics so that is also constant. So in other words other things are constant and hence N that is proportional to rho into V square. So now there is a problem. When I do the maneuvers at 3 kilometer altitude although the maneuver may be only 100 meters height but density at 3 kilometers is far lower than density at sea level ok. So the problem is that N that is proportional to rho and V square and also to the angle of attack. That means the pilot can actually be required to do a vertical maneuver at any altitude you cannot say please do not do vertical loop at 3 kilometers do it only at 2 kilometers or lower we cannot say that correct. You might say does not matter take the highest density which is at sea level. So if the aircraft is safe at sea level it will be safe at higher altitude ok. But still it is important for the pilot to know whether they are within the limits of operation or not. So now how do you solve this problem? This will be a nightmare right 25 different VN diagram for each altitude. Remember you had a curve which said power variation with altitude and we saw that the curve tilts towards the right and moves up. So that kind of drama we have to do now for VN diagram also which is not a good idea. So can you suggest something how do you take care of this? So is the question clear to you? The question is how do we remove the dependence of NZ and V on rho and have only one VN diagram applicable to all the altitudes. So let us see your suggestions. How do you take care of this? Yes let us ask if you are going to divide by half rho V square then the dependence of V also is gone, dependence of rho also is gone. Then how do you draw diagram between N and V? I want to graph between NZ and VZ. So what do I divide by half rho V square both are those equations. So L is equal to half rho. So that means you are saying divide take half rho V square on the denominator of the left hand side. Yes. So shield I think so shield has some point. Yes. Converting it to equivalent air speed. So yes that is the right answer. So let us see how to do it. So let us use the speed so that dependence of density on speed is gone and that is gone through equivalent air speed. So for the same dynamic pressure half into rho at altitude into V at altitude square is equal to half into rho at sea level into V equivalent square that is how you define equivalent air speed. So something to what you said something like what you said do not use V true on the x axis use V equivalent. Now if you use V equivalent then V equivalent is the same at every altitude because it takes care of the effect of density. So that is what is the solution okay using the pitot static this is all of you know but I just wanted to quickly repeat. So you take a pitot static tube that measures the dynamic pressure and that gives you that gives you the value of V infinity which is the true air speed. So the true air speed or TAS is indicated by the air speed indicator. Now this is not correct because the true air speed indicator shows IAS not TAS but interestingly I told you some many instruments are there which also have a TAS indication in the instrument. So I correct it for the errors and give you the true air speed. So this all of you know because we have already covered this right. So taking care of compressibility taking care of position error taking care of instrument errors if you have equivalent air speed and if you use that then the problem is solved by using equivalent air speed the variable rho can be eliminated. In that case NZ is proportional to angle of attack and NZ is proportional to V equivalent square only okay. The other thing is about limits on the load factor these limits as I said are specified by the regulatory bodies. So let us look at now two categories of aircraft the aircraft in which people like you and me normally fly these are the transport or commercial aircraft. So there are two important considerations in deciding the upper value of NZ. The first consideration is the strength of the aircraft obviously if I say that the aircraft is permitted to fly at load factor vertical of 10 and if the aircraft weighs 20 tons it means the structure has to be designed especially the wings to take care of a 200 tons of vertical load which is quite a lot. That will make the aircraft heavy. So the designer would like to design the aircraft for low load factor the designer is interested to sell you the aircraft the commercial organizations are wanting to sell you the aircraft. So they will design it for load factor of 1.2 but if you use an aircraft with load factor 1.2 and if the load factor increases in a slight turn the structure will break. So the regulatory bodies say no no no not permitted to design for 1.2 design for at least so much. So from our safety point of view the regulatory bodies insist on certain max value. So they say show us the compliance of the structure and other systems at higher load factor do not we will not give you certificate unless you show that the aircraft can take so much load factor. So please understand the limits are specified by the regulatory bodies left to the designers or to the aircraft manufacturers they will design them for low load factors because while competing with the competitor they will have a lighter aircraft it will meet the performance requirements but it will not meet the safety requirements. Second thing is high load factor also means more discomfort for the passengers. So let us look at this table. Now this table is taken from FAR 23 regulations as per these regulations typically the aircraft are divided into some categories the first one is called as a general aviation category again there you have three normal utility aerobatic. So I hope you know that general aviation basically means aircraft to be used by people who are not paying any fare, non fare paying passengers. So who are these people who do not pay any fare for the aircraft personal aircraft ok. So let us say he wants to go to his hometown after today's class so he just takes a taxi Ola Uber to Juhu gets into his aircraft takes off and lands. Personal use we had a very good panel discussion recently on why this category is not so popular in India the general aviation category then we have utility. What is utility aircraft? Can you give an example of a utility general aviation aircraft, what could it be used for? So let us say we have to drop some medicines at some place where there is a problem or we have to rescue some people. Now these are aircraft which are used by the agencies for non-profit non-commercial reasons but they are going to be subjected to slightly more loads compared to a normal aircraft that is why the load factors are higher. Load factors higher basically means compliance in design should be shown to that load factor. So if you are going to make or buy a general aviation aircraft the structure need to be only designed to maximum 3.8. Now 2.5 to 3.8 depends on the mass of the aircraft that is the formula so but nothing less than 2.5. So you can conclude that any aircraft has to be able to take two and a half times its max takeoff weight as the vertical load below that you cannot get certification but it could be 2.8, 3, 3.2, 3.5 or 3.8 for this category. If it is utility it is more 4.4. If it is aerobatic that means for shows etc etc then higher because they will be doing aerobatics so they will be doing a lot of maneuvers and hence they will be subjected to higher load so there you go to 6 values. Then there is one category called home built aircraft. Home built basically means as the kits are available you buy the kit assemble it together. So because it is expected that when you do home built you will not be able to do a very good job in the structure and also from enhanced safety the load factor is 5. Transport aircraft between 3 to 4 depending on the max takeoff weight so then that means this table is not for FF 23 only it is for all aircraft. If you go to military aircraft regulations are given by the military agencies like defense standard or death stand or earlier AP 970 or some other regulatory requirements ok. The FAA and the JAA requirements are not applicable for military aircraft they have their own requirements. In India we have something called semi-lac center for military aircraft airworthiness they specify the values. So typically if it is a strategic bomber that means an aircraft that is used for long distance travel heavy bombs for strategic applications not just go and kill whatever you see load factors are only 3 if it is a tactical bomber that means you have to go and await some enemy aircraft or if you expect to fight with some ground forces so just like A10 aircraft which I showed you there it will have 4 and if it is a fighter aircraft with lots of maneuvers it can go from 6.5 to 9. So the highest vertical load factor is for fighter aircraft who undergo very very tight and complex maneuvers which load the aircraft too much. Now let us go on the negative side when will you have negative load factors acting on the aircraft what do you think when will the load factor be negative when the lift force acts downwards. So when does it act downwards we have seen in the examination also there was a question in a vertical loop there are some situations when you go inverted and also when you come down inverted you have lift acting downwards so that is when the negative load factors come so the negative load factors are not equal to positive one they are nearly half because it will be very difficult to expect a person to be doing maneuvers while being negative there will be a requirement but not so much. So therefore concession is given it is a concession if the evidence agencies were cruel they would have said give us negative 6 also but then people said how do you achieve negative 6 you normally do not do maneuvers when you are having negative loads and then you do not do the acceleration. So that is why by now these numbers have come from experience they have not come from somebody's toss or just arbitrary they are coming on experience. People have fitted aircraft with load factor meters and measure load factors which occur in fact I have done that when I was in HEL Nasik we have fitted accelerometers on MiG-27 done flight testing because there was a requirement on MiG-27 to subject the aircraft to load factor of 5.5G with no armaments loaded and 4.5G with the drop tank loaded. So we used to do that we used to measure the load factor the flight recorder used to give us the data and we had to ensure I have a very interesting lecture on that which I will give sometime when we have it will be a general lecture for everybody in the department okay. So yes there are requirements for negative load factor but they are typically half of the ones. Now these numbers are generally non-negotiable, generally non-negotiable but if you go to the agency and say look I am designing a very special aircraft and I can prove to you that this aircraft will never experience more than NZ equal to 3.1 and if you can convince the agency by testing by calculation or whatever they demand they may give you a concession such things have happened for example there is a aircraft called Voyager. What is the famous thing about Voyager? What did it do? Why is it so famous? Do you know what is the Voyager aircraft? So why do not you check on Moodle and tell me? More importantly from today's lecture point of view I want to know what was the concession given to Voyager in load factor calculations or load factor estimate? Why was it given? It is a very unique aircraft. So these are guidelines so it is like unless otherwise stated you have to follow this table. If you want to if you want to go beyond this table then you need to make special provisions and prove yes, yes, yes because see as a passenger if the aircraft is subjected to vertical acceleration you are also inside the aircraft although there is a seat belt. But if the aircraft does like this you will not be comfortable as a passenger you will have this problem right. So if the aircraft is going in level flight let us say n equal to 1 and suddenly there is a disturbance which we will see very soon you will have some NZ and if the NZ because of disturbance is 4 that will get added to the level flight so it will become 5. So if delta NZ is 4 because of a huge jerk so you will get a force on your body which is 5 times your weight how will you feel? You will be highly disturbed. So if a passenger from the passenger point of view the load factor which the aircraft can be subjected to should not be very high but from safety point of view it should be sufficiently high because if those load factors come the aircraft should not break just to give you comfort I cannot say from comfort point of view the aircraft can take only 1.2 load factor if it is 1.4 aircraft will break I hope there is no problem so this you cannot say safety is paramount. So from safety point of view there is a limit but it cannot be that okay to make it safe make a transport aircraft also NZ equal to 7 safer but that will cause discomfort.