 Estimation of empty weight fraction, this is the first step in the initial sizing of the aircraft and unfortunately we do not have much leeway here, we have to rely almost completely on history here because as I mentioned the aircraft has not yet been designed, the aircraft is not in front of you, only what you know is the type of the aircraft and hence you have to go purely by historical information. But we have some help available from historical data, so according to the procedure suggested by Raymer, the empty weight fraction WE bar can be assumed to be a constant A times gross weight to the power C into another constant called KVS which stands for variable sweep. A and C are constants which are a function of a particular aircraft type, their values are obtained by a statistical fit of existing data. KVS is just a multiplication factor that tells us the effect of providing variable sweep. So KVS equal to 1.04 basically tells us that if you provide variable sweep in a aircraft which you would probably never provide in a transport aircraft then you have to have a weight penalty of 4 percent of the total weight. And if you do not provide variable sweep which is most commonly true for transport aircraft then you only have AW0 power C. The values of A and C for various aircraft types have been specified by Raymer in his textbook. So he categorizes the aircraft type under these various categories and for each of these categories there are suggested values of the coefficients A and C to be used. Please note that these values are to be used when the gross weight is in kilograms. There is a separate set of values which are specified in the textbook when the gross weight is in pounds. Now let us observe a few interesting things here. What we notice here is that the exponent C is always going to be a negative number for all the aircraft types. So what does this tell us? This tells us that as W0 increases for a given aircraft type for all aircraft as W0 increases the empty weight fraction reduces. In other words a smaller aircraft which weighs less will have a higher empty weight fraction, a larger aircraft which weighs a lot will have a larger empty weight but it will have a smaller empty weight fraction. The coefficient A is the one that tells you about the sensitivity of the gross weight to the increase in the size. So let us see this some information in a graphical fashion. So what we notice here is that the jet transport aircraft follow this particular line. Now I want to put in a word of caution here. In this particular graph you are seeing the figures where there are these symbols attached to each of the each of the lines and you may assume that these symbols correspond to actual points but that is not true that is not true. These symbols are just given to allow you to distinguish between the various types of aircraft because there are so many lines here so and we could not even use so many colors so we have just included a bunch of symbols. So please ignore the symbols but use them only as an indicator. So a jet transport aircraft typically has an empty weight fraction which can be starting from approximately 0.55 or 55% and it can go as low as around 44%. This is only based on historical data. What do we see here? We see here that the flying boats have the highest empty weight fraction never below around 0.64 and generally as high as 0.7172 and the military cargo aircraft they have the least empty weight fraction which can be as low as 35% when they tend to be very large. Another point to be observed is that this graph has a logarithmic scale on the x axis. It is not a linear scale bear in mind it is a logarithmic scale and the y axis of course is just a linear scale. So on a linear log plot the trend lines appear to be linear and we can use them to get an idea about what would be the expected empty weight. So how do we use this graph? Let us say you are designing a jet fighter aircraft and this jet fighter aircraft gross weight of this aircraft is expected to be some number let us say 10,000 kilograms then its empty weight fraction is likely to be around 0.65 by looking at this particular graph. So what you do is you come up on the line and then go on the x axis and read the number. This is how you use this particular graph but in our case unfortunately we do not have an estimate of gross weight. On the other hand we are actually going to estimate the gross weight and we need to know the empty weight fraction but empty weight fraction depends upon the gross weight. So therefore we have to use this formula which was shown. This particular point corresponds to this particular point shown in the graph. This particular point corresponds to Boeing 787-8 which has got an empty weight fraction of approximately 0.49. So therefore I told you that many transport aircraft they have an empty weight fraction roughly 50 percent which is very much true for Boeing 787. This graph taken from the book by Professor John Fielding actually gives you a better information about the spread. So we notice here that the aircraft do not fall along a straight line. These lines are just statistical inferences. You can see that there is a huge spread even if you look at one particular type of aircraft. Let us say for example we are looking at you know we are looking at large commercial aircraft. The large commercial aircraft again this is a log and linear graph. They do not follow a straight line it is not that they are all on this line. They are above and below this line different manufacturers they have solutions that you get are not exactly along the straight line. So therefore one has to keep in mind that there are bands and what we use in our estimate is only a number which has come from history. Thanks for your attention. We will now move to the next section.