 So, we have reached the end of capsule number 9, today we will look at three questions as a tutorial and the first one of them is on the range payload diagram. So I will spend little bit more time on range payload diagram and then we will take up two questions regarding the performance. I have not put any questions regarding takeoff and landing, I have only put questions regarding the cruise and endurance. So the first question that you will solve is on the range payload diagram, this I have discussed briefly in the class but today I want to take a live example and to show you how this diagram is constructed. So you are going to consider the diagram with me, I hope all of you have calculators with you, okay. So take them out, we will look at the example of a very interesting aircraft, a small jet engine aircraft which has got four jet engines, okay. So let us have a look, this is the aircraft when it is on approach at an airport, wind 330s, 42 knots that is what the ATCO has told. So everything looks normal, everything looks ordinary, okay. The plane is going from your left to the right hand side but interestingly the video has been shot from the runway where it is supposed to land, okay. So the aircraft is on a what is called a right hand circuit to come into land, there you can see now it starts banking and starts meeting the trajectory for the arrival. It is a very unique aircraft, when it comes into land I want you to look at some interesting features and I will point them out to you one by one, okay. So there you go now the aircraft is almost pointing towards us, notice a small aircraft but four engines, okay. So one question I want you to answer is and also notice only one light is working on the starboard wing. So the aircraft is in its final approach now, flaps are in the landing configuration or the approach configuration. The aircraft has a T tail, four small engines and look at the rear of the fuselage you will find an interesting thing, those are the air brakes which have been deployed and then there are spoilers deployed just after touchdown, we will roll it back slightly. At this point you do not see spoilers deployed, see they are up, they are down rather, the path is fully down, just after touchdown you will notice the spoilers have come on and those air brakes were also in the approach condition, right. So one question I have which I do not want you to answer right now but I want you to look up an answer is why is it so that such a small jet engine aircraft with approximately 110 seats, why does it have four engines? From the airline point of view, operational point of view obviously if you need four engines that means you must have four serviceable engines available to you, it is a maintenance problem, it is expensive, okay but then why have they gone for a design, it is not driven by power requirements because you can easily meet these requirements with two engines. I can understand that more than one engine is required from safety point of view but you could do with three engines, you could do with four, you could do with five, etc., but what is the need for four engines? So this is something that I would request people to study about this aircraft and answer on model. Let us look at the weight buildup, now the numbers that you see are the actual numbers for this particular aircraft, okay. So the max takeoff weight MTOW is around 44 tons, landing weight is around 4 tons less 40 tons. So in case the aircraft has to land immediately after takeoff from safety and from the structural strength point of view, you will be required to dump around 4 tons of fuel. Then you have maximum zero fuel weight, this is a very interesting term in aircraft operations. The maximum zero fuel weight means everything else except fuel. So what is there above maximum zero fuel weight to get maximum takeoff weight, you have the payload which consists of passengers, their baggage and cargo and crew operating items, okay. So maximum zero fuel weight means the only thing you can add to this to hit maximum takeoff weight is fuel. Operating empty weight stands for the aircraft structure, aircraft systems, no passengers, no cargo, but the pilot, co-pilot and the crew are all there and so are the operating items, the beverage is the food, the newspaper, everything is there, it is operating empty, okay. Fuel is not there, payload is not there, so you add those two items. This aircraft has a maximum fuel capacity of 11,000 odd liters and the maximum number of passengers can carry 112, okay. You don't need to copy anything because when we do the question you will get these numbers there again. So the maximum payload weight that you can carry would be the maximum zero fuel weight minus the operating empty weight because the difference can only be payload, right. So the maximum payload weight is 11,822 kgs and the maximum fuel weight is just a multiplication of the liters of fuel with the density of fuel, okay. So therefore the summation of two quantities payload and fuel can be only the maximum takeoff weight that you can carry minus the minimum operating empty weight that you need to have. As I said on the operating empty weight you just add payload and fuel to hit maximum takeoff weight. So the total of payload and fuel is going to be 18,626 kgs. This is what the airline can play with. But remember entire fuel is not available to you, there is some reserve fuel which you cannot touch from safety regulatory requirements. So there will be some amount of fuel which is the mission fuel and payload, okay. So therefore if you now see the buildup of weight graphically, this is just for your understanding, you have the aircraft weight consisting of structure, propulsion, manufacturing, empty weight, etc., etc., all the item. The manufacturer does not always make engines, okay. They normally buy the engines from the engine manufacturer. They also buy the seats, they also buy the other equipment. So operating empty weight will consist of what the aircraft company makes plus what are the standard and operating items which are to be put on the aircraft. Without that you will not be allowed to operate, okay. But there is no fuel, there is no payload. Now you add passenger plus baggage and you add cargo, total of that is a payload. So that you add fuel, so first compulsory reserve fuel, then you have a trip fuel, trip basically here in this definition trip only means the flight from airport to the other. And taxi fuel, taxi out fuel is a small amount which they have added, normally we put taxi out fuel and trip fuel together as mission fuel, you do not do this distinction, okay. This is how the aircraft weight is built up, okay. So now you have something called as maneuver allowance, this is a slightly misleading term because people think this is the fuel required for doing maneuvers etc., no. This is basically the fuel required for doing other than the cruise, climb and cruise. So before every flight the aircraft undergoes some pre-taxi checks during that time the engine is normally switched on because you are ready for takeoff. So there is some fuel for engine starting and pre-taxi, this aircraft consumes around 18 kilograms, then taxi all engines that means you are going from the terminal to the beginning of the runway, you will consume around 89 kgs of fuel. Then takeoff you will lose 50 kgs of fuel and when you come to approach and coming to land and then taxi in all that will be around 143 kg. So this aircraft incidentally consumes around 300 kgs fuel in other than climb, cruise and descent, okay. This number is as high as 650-700 kgs for 747, alright. So let us look at the weight breakdown. Now we are assuming that the airline wants to fly with maximum possible payload. So there is something called as ramp weight. Now ramp weight is maximum takeoff weight plus fuel required for the taxiing etc. and warm-up and takeoff. So you know if you want to be very particular you can say the maximum takeoff weight is the maximum permitted weight when the aircraft will leave the ground or when they clear the obstacle height. All the fuel before that when you add to the max takeoff weight you get what is called as a ramp weight that is the maximum weight that the aircraft actually can have. So it is nothing basically you just remove the 300 kilograms odd in this case, okay. So the takeoff weight is 44226. Then in this case as I mentioned there are 112 passengers. So there are certain standard norms for how much weight to assume for a typical passenger plus baggage. So 95 kgs is the industry norm. Some of them take 100 kgs etc., okay. So since the maximum payload in this case is 11822 kgs you can carry 10640 and then there is some place for cargo. So fuel I am assuming that reserve fuel is 15%. So total fuel I have just taken 15% of that. So therefore the fuel weight available will be 6804. The operating empty weight as given by the manufacturer is 25600 which consists of just for your information, some structure, some crew and some operating items, okay. So this is the actual weight breakup of this aircraft in its typical operation, right. So the blue line that you see is the trade off between range and payload and these two purple lines or sand lines, the horizontal one is the cut because of the limitation on the maximum structural weight and the vertical one is the cut because of the maximum fuel capacity of the aircraft and the inclined line in between is the permitted operational trade off between range and fuel. So in this case the range payload diagram is a horizontal line, inclined line and a vertical line. This diagram was obtained assuming some numbers. One number that you need is what is the specific range of the aircraft that means how many nautical miles per kilogram of fuel the aircraft can travel. This number as you know will not remain constant because as the aircraft becomes lighter it will travel more distance on the same amount of fuel but for assumption purposes we have assumed that there is a constant value of 0.19 nautical miles per kg. So that is how this diagram was drawn. Now there are two important points. You already know this point that all the fuel is not usable, you have to keep it for various items and secondly we also know that the specific range also does not remain constant, correct. So moving ahead, keeping in mind the range payload diagram and the operation there are three types of ranges which are defined. We have only studied one range in our lecture but here I want to clarify that there are actually three type of ranges. The first one I mentioned is called harmonic range. That is how far you can go without compromising on maximum payload because an airline wants to make money and to make money they want to carry maximum possible payload. It could be cargo, more cargo less passengers, more passengers less cargo does not matter. The total payload capacity they want to utilize without compromising on that they want to go as far as possible. So that range which corresponds to point number A in the range payload diagram is the harmonic range. Then you have ferry range. In ferry range the aircraft is now to be transported to a supplier, to an airline. So let us say Airbus constructs an aircraft and they want to deliver it. How far can you go without refuelling? So in this case what you do is you assume that you will consume the entire fuel including reserve fuel, okay. This is not a normal operation, this does not happen every day. So these activities are very very carefully planned. So the entire weather map is very carefully studied, there are no passengers in the aircraft, okay. In some cases they also install some temporary fuel tanks inside the aircraft to increase the range. But we will not take that case, we will assume that there are no fuel tanks inside the aircraft. There are no passengers, aircraft is empty, there is no payload. Now the entire fuel is being used to travel, so that distance is called as a ferry range. It is the largest distance that is theoretically possible without refuelling. And in between or just a theoretical definition is called as a gross still air range. Now this is a very peculiar, very peculiar quantity, okay. So I wanted to imagine some things before you understand what it is. Imagine that you have some kind of a magical crane which can lift the aircraft to the cruising altitude and throw it at the cruising speed. So you have somehow by magic reach the cruising altitude and you have achieved the cruising speed. Now how far can you travel with the full fuel? With no enroute winds, that is called as a gross still air range. Still air means no headwind, no tailwind. Gross means really gross value. No fuel consumed in takeoff, warm up, taxi, climb, descent. The entire fuel is used only in cruise. At the cruising altitude at the cruising speed, that is the gross still air range. This is just a theoretical number, okay. But it is still there. So this is the range payload diagram and this is what we are going to calculate now, okay. So point A corresponds to harmonic range and point C corresponds to the ferry range. And point B has to be determined. So basically if you look at how to draw this diagram, the first thing is you will draw a vertical line representing payload and the horizontal line representing range. And the first point you will mark will be this point called PA, this is the theoretical point. This is like aircraft is completely ready, pilots are there, everybody is there, okay. Payload is also loaded up, but there is no fuel. So now you add some fuel and you will travel some distance, add more fuel, you will travel more distance. So that is the theoretical point which is zero range point, max payload zero range. Any line on this operating point from PA to A corresponds to more and more fuel being added, hence more and more distance being traveled till you hit a point A where you will have maximum takeoff weight. Now you cannot add more fuel because you cannot, sorry, you cannot add more fuel simply because you have space in the fuel tank but you have already hit the maximum takeoff weight. If you want to travel further, you have to reduce some payload, so then you go along line A to B, you are trading off payload for fuel, payload for fuel, payload for fuel till you hit a point B, at point B in the fuel tank is full. So payload bay is not full but fuel tank is full and you have hit the maximum takeoff weight. Now you cannot add more fuel. After that you normally will go only along line B to RB, normally. Now some people say no, no it is possible to travel more distance because aircraft is lighter. So a lighter aircraft will travel more distance. So you reduce the payload further and because it is lighter it will travel more distance. So some people assume there is a line B but normally we assume this line to be vertical and point C is a theoretical point which is the ferry range, okay. I think it is clear to everybody, alright. So max payload line, max takeoff weight line and max fuel line, okay. So let us see how do we calculate these points. First point is very straightforward. So this table later on you will make for your aircraft, okay. Yeah, yeah it is not RC. The name I have given RF is because I want to distinguish between RF and RC. RC is the range which you can get more than RB because the aircraft is lighter. But RF is a theoretical point, the line is misleading, RF is a theoretical point which corresponds to reserve fuel also consumed for range. Along RC you do not consume reserve fuel. So when you go from B to RC, you are travelling more distance by reducing payload but reserve fuel is untouched. But when you go from B to RF, actually you do not go from B to RF, RF is a very special point. This line actually should be removed. RF is just one theoretical point which is how far can you go with all fuel plus reserve fuel consumed? Yes. The definition of ferry range is complete fuel consumed including reserve fuel for distance. Alright. So if you want to calculate this point is very straightforward. In the payload column you put maximum payload weight. In the fuel weight column you put 0, hence range will be 0, okay. And in the takeoff weight column you will put maximum 0 fuel weight because what does it contain? It contains operating empty weight plus maximum payload, 0 fuel. So this is maximum 0 fuel weight. For point number A, what you should do is since it is on the inclined line, the takeoff weight is maximum takeoff weight. Since it is on the horizontal line, payload weight is equal to the maximum payload weight. So to get the fuel weight you just subtract from the maximum takeoff weight, take out the payload weight, right and take out the operating empty weight. Remaining is only fuel. So that fuel is available to you for the mission and for the reserve. So if you subtract from that the reserve fuel, you get the mission fuel, multiply this by the specific range you get the range can be traveled. Clear? You are going to do this now. So you better understand what it is, okay. Point number B, point number B you can fill up the column for maximum takeoff weight and the maximum fuel weight, a fuel weight because for point B intersection of two lines fuel weight is maximum fuel weight, takeoff weight is maximum takeoff weight. So therefore the payload will be what you can carry maximum that is max takeoff weight minus operating empty weight which is minimum minus the fuel weight remaining is payload. It will be less than maximum payload and from the maximum since your fuel tank is full. So maximum fuel weight minus reserve fuel that is available for the mission into the specific range gives you the range. Point number C payload is 0, takeoff weight is going to be operating empty weight plus maximum fuel weight payload is 0, fuel weight column you can fill in advance and the range now this is not C actually this is actually F, this is F because we are saying range is equal to the total fuel in the specific range so this is actually F point, correct. Now the point C actually yeah so the point C is change with point F, alright. So this is a summary. Now I want you to spend just one minute looking at this and if you have any doubts you can ask me you should be able to appreciate this table. So the best way of doing this is whatever things you know the blue ones by definition you fill them first and other things you calculate, okay point A is on the two lines so therefore both of them are maximum payload and takeoff weight point B is on two lines takeoff weight and fuel point C is on the fuel line maximum fuel and calculate the other things, alright, right now let us look at Avro RJ 100. So first assumption is specific range and these numbers are given, okay. These numbers we fixed we fill in because we know them you can check you can check from the table above and see if you are okay with these definitions. So from PA to A you will have maximum payload from A to B you have maximum takeoff weight from B to C you have maximum fuel so therefore those columns get filled up. Now you have to fill the remaining so this is your job now, so now you make this table and fill in the blanks there are just seven calculations you have to do, seven numbers you have to calculate so when you finish calculating all seven quantities just raise your hand so I know that you are through all the weights are in kgs and the range I want in nautical miles then all seven, okay, okay. So here is the table which is filled in now you can check your numbers, all correct will we go ahead, okay. So this is the actual range payload diagram of this aircraft from the operating manual from the aircraft manual and these paneer tanks basically are those additional fuel tanks that you can fit inside the aircraft for delivery purposes. So you can see that with 112 passengers at 95 kg each this is your range payload diagram there is no line it is just increasing. So you can see this is estimated versus quoted so whatever numbers we do in the class they are very similar to what are actual numbers just one more figure I want to show you effect of winglets effect of winglets on the range payload diagram this is a very interesting report which has come from an economist there is a magazine called as aircraft monitor which is the magazine of aviation economists. So one aviation economist has done some calculation and he has shown what is the effect of putting winglets on a 737-800 so it just tells it concludes that if you put winglets you get 130 nautical miles more range or 5800 pounds more payload so the airline has to weigh this against the cost of getting the winglet installed it will not be free of cost the manufacturer or the company there are some companies also who do it there are third party companies who make winglets for an aircraft so you do not have to go to Boeing or Airbus only you can go to some other company okay one of our alumnus is working in such a company.