 Hello, let us have a look at how we carry out refined sizing of a military aircraft. And as an example we have taken our F16C which you may recall is a theoretical aircraft loosely modeled around F16C. So we will follow a color scheme in this presentation, instructions for you which are general in nature will be shown in this brown color. The values of certain parameters regarding our F16 which have been taken from a standard source or the so called specified values from the mission profile will be shown in the black color. There are a few values which we have assumed those will be shown in the blue color. The calculations that you have to do will be shown or pointed out in the red color with question marks and there will be this pause symbol next to it. So wherever you see this pause symbol it is expected that you will pause the video and do those calculations. Once again I would like to reiterate that aircraft design is done and learnt only by doing calculations just by nodding your head or going through the video you will not learn it unless you actually do the calculation. So please pause the video do the calculations and then you can check the values with our values and the values that we obtain after calculating will be shown in this dark blue color. So the basic source of data for our F16C aircraft is this textbook by Brandt, Stiles, Burton and Wittford. In this textbook there is a section that talks about the aerodynamic analysis, constraint analysis of F16C. So we have taken our basic parameters from there and also we have assumed a mission profile. Let us do a quick recap on what is meant by refined sizing. At this state I would like you to go and watch the video about the methodology of refined sizing if you have not done so because this is just a tutorial and it assumes that you already know the procedure. Here we are only going to apply the procedure to sample problem. So if you have not watched the videos regarding refined sizing this is a good place to stop and to go back locate and watch those video clips about refined sizing how it is done what is the procedure and then come back here. So here after we assume that you know the refined sizing procedure so here is a quick recap. There are some steps to be followed in the sizing. First we finalize the design mission profile. Then we assume some parameters like the wing aspect ratio, the specific fuel consumptions or SFC in the various mission legs, the crew weight and the payload weight. Then we carry out initial sizing using these parameters and using the mission profile. You may recall that in initial sizing we estimate empty weight fraction WE by W0, fuel weight fraction WF by W0 and finally after an iterative procedure we estimate the design gross weight W0. Then we can do the estimation of aerodynamic characteristics especially the zero lift drag coefficient CD0 and K1 during each mission segment. For a refined sizing we will only need the value of CDO during the various mission segments. Once we have been able to do the aerodynamic analysis and initial sizing we can then look at the methodology for a constraint analysis through which we determine the values of the design wing loading W0 by S and the thrust to weight ratio under sea level static condition. This also has been taught and an example has been already demonstrated. So, once we have the values of W0, W0 by S, TSL by W0 etc. then we can carry out the refined sizing which will be demonstrated now in the next few slides. Remember one thing that the value of W0 obtained in the initial sizing is just the initial estimate. At that point of time we did not have much data about the aircraft. So, we had to use lot of formulae and procedures from the historical data. Even now we will use a few of them, but the number that you get there would be only the first estimate. You could use that as a starting point in this analysis if you wish. Let us have a look at the assumed mission profile of our F-16C aircraft. So, that is the ground. The aircraft is expected to take off from a base which is located at mean sea level. It is then undergoes an accelerated climb to a height of 2.5 kilometers. The end Mach number of the accelerated climb is 0.85. So, from approximately 0.2 Mach number when it is at the end of the climb or at point number 1, it accelerates to Mach number 0.85 in a accelerated climb. Then there is a cruise of 200 nautical miles at the same critical cruise Mach number MCR a 0.85 at the same altitude. Then you come down to the combat zone. So, you descend to a height of 1 kilometer. Then you dash for about 50 nautical miles at Mach number 1.05. This is the fastest you fly in this mission with afterburner on. So, a large amount of fuel will be consumed because you are flying for quite some time at a Mach number of 1.05 with afterburner on. So, please notice and remember in the mission segment 4 to 5, although the distance is very small because of the afterburner there will be a huge fuel consumption. Then you spend about 20 minutes loitering at the territory where you are supposed to go and do your payload drop. So, about 1 kilometer above mean sea level, you are loitering there for 20 minutes. So, during this time the aircraft is going to look around for the targets and then it is going to drop the dropable payload. After that it will do an unaccelerated climb to a height of 10 kilometers. So, this is a very slow and very relaxed climb. Then when you go to a very high altitude you are now reasonably away from danger. You can comfortably cruise back that 200 plus 50 nautical miles back to the home base. So, you fly at a comfortable Mach number of 0.6 at 10 kilometer altitude. So, the consumption of fuel will be very less even though the range is 250 nautical miles you will notice that the fuel consumption in this cruise will not be very high. Then for about 45 minutes you are loitering at a comfortable altitude of 10 kilometers at a most optimal speed for loiter. This is so that you are ready for any other requirement if there be. If not, you come back, descend and then land. So, this is the assumed mission profile of our F-16C for which we will do the refined sizing. Earlier we have already completed a tutorial for the initial sizing of this particular mission and from there we got an estimate of the initial gross weight of the aircraft. Also remember that the reserve fuel fraction is 10 percent which has to be. So, the fuel of the fuel consumed in the mission you have to multiply by 1.1 to get the total fuel to be carried. Let us look at some useful data about our F-16C aircraft. It may be a good idea for you to note down this data in a notebook because you might need it in the calculations ahead. The maximum payload weight of this aircraft is specified as 7575 kg and here we make an assumption that around 25 percent of that would be the droppable payload 1895 kg which corresponds to 4 bombs of 1000 pounds each and little bit for the bullets that are carried. So, we assume that some of the bullets are gone and the 4 bombs have gone. Remaining payload remains with the aircraft. We also assume that the mass of the pilot and the G-suit would be total about 100 kilograms. This is also an approximation. The specific fuel consumption during cruise is already given as 0.8 per hour during loiter as 0.8 per hour and during dash because of the afterburner it is almost 3 times more more than 3 times more 2.46 per hour and the wing aspect ratio is known to be 3 and so is the tail aspect ratio. So, this information is used to calculate the numbers and the maximum mark number of the aircraft is given as 2.05. This number will be used only while estimating the empty weight fraction. So, may be a good idea to note down these values or remember them. Then there are some quoted values of CDO for our F-16C aircraft in the textbook by Brand, Stiles, Burton and Bittford. For the subsonic flight that is Mach number 0.6 in the return cruise segment CD0 is given as 0.0193. For the transonic flight Mach number 0.85 which is in the first cruise segment we are given CD0 value as 0.0202 and for the supersonic level flight dash at Mach number 1.05 which happens as shown in the segment from 4 to 5 15 nautical miles at Mach number 1.05 afterburner working. The consumption of fuel is very large it is 0.0444 so roughly it is and the value of CD0 is also almost double of the transonic value. So, once again these 3 numbers may be noted down because we will require these values when we calculate the fuel consumed in each of these missions. We also look at some data about our F-16C which we obtained earlier in the constraint analysis. So, we have obtained the thrust loading to be 0.98 and wing loading to be 431 kg per meter square. We are converting them into dimensionless units and in Newton per meter square here for our calculations. The Oswald efficiency factor was determined using the aspect ratio and the Mach number as 0.9086. So, we keep it like this. Let us look at the first step in refined sizing which is the takeoff weight built up. So, as per refined sizing procedure the aircraft weight is considered to be consisting of these elements. There is a crew weight there is a fixed payload and the droppable payload there is a fuel weight and the empty weight. The empty weight consists essentially of the weight of the structure, the engines, the landing gear, equipment, avionics, etc. All that comes under empty weight. W crew and W payload are known. They are known either from the user specified requirements or from regulations. So, which means that WDP which is the droppable payload and WFP which is the fixed payload are the 2 things which are available from the specifications. So, W crew is known, WFP is known, WDP is known. The only 2 unknowns are W fuel and WMT. These are the ones which have to be determined in the refined sizing procedure. Let us look at the equations for refined sizing. So, once again W0 as a summation of these 4 components crew, payload, fuel and MT. For payload we have seen there are 2 terms a fixed payload and droppable payload. So, for MT weight we have empty weight fraction into W0. So, it becomes a equation of iterative nature because on the LHS we have W0, on the RHS also we have W0 and this ratio is to be determined. So, now the 2 unknowns remaining only are WF and WE by W0. They are the only 2 unknowns remaining. If you recall in the initial sizing, the 2 unknowns were the fuel weight ratio and the empty weight ratio. But in refined sizing, since the method is able to handle payload drops or sudden reduction in the aircraft weight except other than the fuel consumption, we directly calculate WF not the ratio but directly. The empty weight still we go by the ratio. So, look at the payload and crew weight of F16 or F16C. For crew weight it is very simple. We have a single seat jet fighter. So, therefore the number of crew members is 1 and we also assumed that the pilot and the G suit together will weigh approximately 100 kg. This also includes anything else that the pilot takes with him or her. For example, the helmet etc. All of that comes under 100 kgs. As far as the payload weight is concerned, it is given in the specifications that the maximum payload is 7575 kg. So, we assume that 25% of that is droppable and the remaining 35% of that is fixed. Let us start with the estimation of the empty weight fraction. For this, we will use the assumed or obtained values of parameters. So, first let us see how we can get a slightly better estimate of empty weight fraction compared to the earlier one. In the initial sizing, the value was A into W0 power minus C, where A and C were constants on the basis of aircraft type. But now since we have more idea about the aircraft, we know for example, W0 estimate. We know the maximum Mach number. We know the wing loading. We know the thrust loading. So, therefore, there is a slightly more accurate estimate which is in terms of the 5 constants C1 to C5, which are inserted as powers to the variables W0, aspect ratio of the wing A, T by W0, W0 by S and M max. So, in the textbook by Rehmer 6th edition, we have this table that gives you the formula for empty weight fraction versus these 5 parameters. And for various aircraft types, military aircraft types, you know you have for example, we are looking at a jet fighter. So, the coefficients of all these parameters are given, but it may be noted that this formula works in FPS system. So, therefore, the value of W0 by S is going to be, the value of W0 is going to be in pounds. So, here is the formula. So, based on this formula and assuming that the aspect ratio is 3, the thrust loading is 0.98, the wing loading is 4226.817, Mach number as 2.05 and variable sweep constant is 1.0, you can estimate the empty weight fraction value. Now, the design glossary is not known, so it remains as it is. So, what we get is finally an expression. So, I think we need to calculate this expression. So, this is the place where you should pause the video and calculate these numbers. The answer will be minus 0.02 plus 1.221 into W0 power minus 1.10. Let us look at the estimation of the mission fuel weight. We use the approach of refined sizing in this particular case. So, we will go segment by segment and we will start with a guess value of W0, this whole process will be started by a guess value of W0. We will then obtain the fuel fraction of each segment as an initial sizing, but we do not remain to the fuel fraction, we then calculate the fuel consumed by using this formula where Wfi is the fuel consumed in the ish segment, which would be 1 minus Wi by Wi minus 1 into the fuel consumed till the previous segment. So, the total mission fuel weight is going to be the summation of all these fuels and then you have to just put 1 plus RFF to get the total fuel to be carried with the reserve factor included. Let us estimate now the mission segment weight fractions. So, for the warm-up, takeoff and landing weights fractions, we use historical trends like before. For the descent segments, there are two descent segments here. We assume that the fuel consumed and the distance travelled is ignored or it is considered to be 0. And therefore, these are the four standard values that we will be using in our calculations as specified by Raymer. So, the formulae are the same for warm-up, taxi out and takeoff. The ratio also is similar. The descent and landing, cruise and loiter, same formulae. The difference is that there will be a much better formula for accelerated climb, level flight acceleration and for the combat, using the combat time or the number of sustained turns, we are going to get a formula to directly estimate the value of fuel. So, we are now looking at the first segment shown in the red colour, which is the takeoff segment. So, W0 to 1 would be 1 minus W1 by W0 times W0, guess this is the basic formula. The data is you have to guess the design gross weight as a starting point. You could use the value calculated by you in the initial sizing or you could take it approximately 4 times the payload. So, what will be the value just multiply 4 with the maximum payload of 7575 and you will get 30300. So, this will be a good guess for the starting value. The fuel weight fraction in the takeoff is assumed to be 0.970, this is for warm-up, taxi out and takeoff. So, therefore, the weight of the fuel consumed in this segment will be W0-1 and that would be 909 kilograms. So, therefore, the weight at the end of the segment would be 30300 minus 909. Please calculate the value. So, from 30 tons, the aircraft weight becomes around 29 tons 391 kgs when it comes to the beginning of the accelerated climb. So, to calculate the fuel fraction in accelerated climb, we first identify what is the Mach number at the end of the climb. Then we use this equation to get the value if the climb is if the climb is subsonic supersonic and if there is subsonic there is another formula available. With that you estimate W2 by W1. For our F16C aircraft, the Mach number at the end of climb is 0.85 which is the cruise Mach number. So, therefore, in the graph which has been given by Nikolayan character in their textbook, you start the value of 0.85 on the x-axis, go to the line and you can read out the value of WFWI or you could actually use this formula and calculate this value. The number comes out to be 0.9788. So, I hope you had paused the video and you had calculated this number. Moving on to the accelerated climb segment, which is segment from 1 to 2 shown in the red color. So, this is the standard formula for every segment. Fuel consumed in a segment will be equal to 1 minus weight ratio at the beginning of another segment into the weight at the beginning of the segment. So, we know that for this aircraft, the weight at the start of the accelerated climb is what we got earlier as the weight at takeoff weight minus the fuel consumed during takeoff and warmer. And we also know the value of fuel weight fraction, we have just seen it in the chart or done the calculation. So, therefore, the fuel consumed during this segment will be 1 minus 0.9788 into 29391. Please calculate the value, the value is 623 kilograms. So, at the end of the segment, the weight will be 29391 minus 623. It will be this value which is at the beginning minus the value which is available at the end of the segment. So, the difference of these two is going to give you the fuel weight at the end of this segment. And that value is 28768 kilograms. So, we have gone for an approximation here, we are not looking at any values beyond decimal point, we are looking only at whole number values. So, we are rounding up the numbers up to the 0th decimal place. Now, we come to the first of the slightly complicated segments. It is actually a simple cruise segment, but the methodology for estimating the fuel fraction is little bit complex. So, for the cruise wheel weight fraction, we again take records to the Brighay range equation, which has V cruise, C cruise, L by D cruise and the weight ratios in the calculation. So, here R cruise is the cruise range in meters, C cruise is the SFC during a particular phase during takeoff, during landing, during climb. The cruise velocity also has to be calculated. So, the first three are cruise, C cruise, V cruise, they will come from mission profile, but the last one has to be estimated. Earlier, we took the last one, we took L by D as equal to the 0.866 times L by D max I think because it is a jet engine aircraft in a cruise. But now what we do is, since we know the value of CD naught W by S and E and AR and hence we also know the value of Q, which is half rho V square. You can actually get the value of L by D for level flight as 1 upon Q CD naught by WS plus W by S by Q pi AER. So, we need some data regarding the first cruise segment. The first cruise takes place at a height of 2.5 kilometers, the Mach number is 0.85, the range travelled is 200 nautical miles, which is 370400 meters. The speed because of the Mach number of whatever specified value of Mach number is there, at that Mach number is around 0.6 I think. You will get some speed and then you have the SFC at that particular speed, which is already specified as 0.80 per hour. You know the density of air at 2.5 kilometers from the tables and the parasite drag coefficient is 0.020, because the aircraft is going to be flying in the transonic regime and the wing loading can be calculated from the constraint diagram for that particular point. So, keeping all this in mind, you can calculate the fuel fraction in the first cruise. So, Q is half into rho into V square, rho is 0.957 at 2.5 kilometers and V is 280.95 at a given Mach number. So, Q is 37769 per square meter. Again the same formula. So, insert the values of Q, CD naught, W by S, W by S and also the value of Q and pi E R. So, plugging in these values and calculating the numerical value, we get L by D as only 4.937. Previously, this number was very high because we assumed that the aircraft will fly at the optimum condition. But now we are flying their craft at a given condition. So, therefore, the L by D max is much lower than that. Fuel in the first cruise segment. So, once the ratio is known by inverting both sides, you can get W by 2, W 3 by 2 would be equal to E power minus R cruise by V into L cruise, L by D cruise. Just put in the values of the various parameters that you have already calculated and you get W 3 by W 2 as 0.943, 0.943. Now, we want to actually write the fuel weight. So, fuel weight in the second and third segment will be the fuel weight in 3 by 2 minus 1 into times times how good a person is scaling up based on W 2. So, it is 1 minus 0.968 plus. So, with that you can get the estimation of weight in the cruise segment and that weight is 1660 kg. Now, let us look at the descent segments. Remember that in descent segments we have ignored the distance travelled and the fuel consumed. So, weight at the start of the descent segment is the weight at the end of the previous segment which is 2868 minus 1060 kg which we know is 27108 kg. Now, from this you subtract whatever is consumed during the descent. So, in the descent we can assume that certain components of the system like the sensors etc. are working. So therefore, W 4 is equal to W 3 is equal to 27108 kg because there is no reserve needed for any mission specific information. So, the weight at the beginning of the next segment also will be the same as weight at the beginning of the previous segment 27108 kg. Now, dash occurs at 1.5 kilometers. The Mach number during the dash is given as 1.05. The range is 50 nautical miles. The speed is 353.22 because you are flying at supersonic Mach numbers. The SFC is 2.46 per hour which is very high. It is more than 2 times that of the these 2 aircraft during peacetime. The density of error at 1.5 kilometer also plays a role. And of course, there is a parasite drag coefficient which is twice the normal value. And the wing loading in screws is given as 385.6 from the initial sizing. So, after completing the initial sizing and the constraint analysis, we can now calculate fuel fraction in the dash segment which is a low altitude accelerated flight. So, the Q is half rho dash v square dash. So, the value of Q is available by multiplying by density and the velocity that is 69368 Newton meter square. And then you can estimate the L by D using this formula. So, putting in the numbers. So, the L by D in this condition is very, very poor. It is only 1.2. Whereas L by D can be as high as 20 during an optimized cruise and we also got it around 12. But here it is 10 times less. It is just 1.218. So, remember in the fuel fraction, because of very low L by D, it will come in the denominator here. There is going to be a large value of the fraction in the dash. Let us look at the fuel weight. So, the formula is known. This already we have calculated 0.8632 is the weight fraction. So, 23 percent of the aircraft is gone in just one mission which is the dash mission. So, the weight of the aircraft at the end of the program would be the, what we are spending is actually this ratio. This is what is the actual price of the purchase of the frame. So, however, we took the challenge to calculate what is WF, W4 by W5. And we find that the value of W that gives you convergence is 5.05. So, let us look at the weight at the end of the dash segment. That would be the weight at the beginning of the dash segment minus 370. So, notice the fuel consumed in dash is very, very high is 3.7 tons in a 15 nautical mile dash. So, 27108 minus 3708 23400 kg is now the weight of the aircraft at the end of the dash segment. After that we do a combat for 20 minutes. So, it is given that the SFC is 80 per hour or 0.0002222. Thrust loading in combat is known from the previous initial sizing calculations. The time for combat is specified at 20 minutes or 1200 seconds. So, the weight fraction in the combat would be 1 minus SFC of the combat into T by W of combat into D. So, it turns out it will be 0.9686. Similarly, for the combat segment, once again the weight would be just 1 minus the ratio into the old weight. So, 1 minus ratio then to the old weight or the weight at the beginning of the segment that is 735 kg. So, you can see in combat we have spent additional 735 kg. Now, the payload to be dropped in the combat was assumed to be 25% only that is 1895 kg. So, that can be released now. So, the weight at the end of the segment will be that with that value minus 1895 kgs. So, it will be substantially lighter now. That means it will come to 20770 kg. Now, we go to the peaceful and relaxed unaccelerated climb to the height of 10 kilometers. The end mark number is 0.6. So, once again the formula remains the same, but the data would be as follows. The weight at the start of the climb is 2076, 9.8 or 20770 actually. The fuel weight fraction in unaccelerated climb is given as 0.985. So, therefore, you can just put 0.985 in this expression and W06 in this expression and you will get the W627 that is the fuel consumed. How much is it? Can you please calculate 1 minus 0.985 whole bracket into 2.070. It is just 1 312 kgs. So, the fuel spent in loitering for 20 minutes is 312 kgs. Weight of the aircraft at the end of the unaccelerated climb is as follows. First thing is you should know the self-weight. So, it will be 20770 minus 312. That means you have to provide a cater for this weight in case it is required for us to relocate to Mumbai. So, let us look at the fuel weight. The fuel weight is very simple. 20770 was the weight or the bidding of the climb at the end of the previous phase and the value now is 312 kgs has been estimated as the fuel consumed during the unaccelerated climb. So, therefore, the difference is going to be the simple weight addition during the segment. We look at the return cruise now which is happening at a comfortable marker of 0.6 at a height of 10 kilometers. So, the range is 46300 meters that is 250 nautical miles. The speed is 179.66 that is from mark number 0.6. The SFC is given as SFC in cruise as 0.0002222 per second. The density of air at the altitude of 1.5 kilometer under ISA would be sorry, density of air would be 1.44 kg millimeter cube. The parasitic occupation is 0.0193 because you are at a very benign low speed flight and the wing loading as determined by the initial sizing for this segment is given. So, therefore, dynamic pressure being half rho into V square gives you this value. So, calculate the value of Q half into rho into V square turns out to be 6681 Newton per meter square. Same formula applies here also and putting in the numerical values I would like you to note down these values pause the video and check whether your number matches roughly with my number. You can do this in MATLAB or any other software also. The L by D value we get is 10.519 for the return cruise segment and the value of the empty weight fraction is obtained by the endurance equation in which W8 by W7 is 0.87, 0.947. So, putting in the values in the formula you can get the weight fraction as 0.947 and then the same formula applies even here. So, this is the weight fraction in this segment and this is the weight at the bidding of this segment do calculate the value of W7 by W8 it is 1084 kgs. So, in the return cruise segment, although we have traveled more distance the total fuel consumed is less than that one third than that are consumed in this in dash because dash is a very time very very fuel guzzling kind of a mission after burner is on and you are there for 20 minutes. So, W8 would be 20458 minus 1084 because at the end of cruise there is this nasty divergence segment for which we are going to do the calculations separately. So, what is the value of W8 here? 19374 kgs. Finally, we come to the loiter segment at the end of the flight. So, for that we have been told that the loiter is happening for 45 minutes at the speed that we choose to be the optimum speed for the SFC would be 0.00022222 for per second density at 10 kilometer is 0.414, paraso-dry coefficient is 0.0193 as well efficiency sector is 2702.65. And finally, the efficiency sector E is also needed in the calculation it is 0.9086. So, with this you can calculate dynamic pressure at the cruise as 4 times or sorry half rho V square. What is the value of this expression? Please calculate the value is 3839.37. Remember this number will be in Newton per meter square then when we put density in kg per meter cube and velocity in meter per second we do not get dimensionless value. You get meter cube per second something like that very awkward units. So, therefore, we need to be careful we have to use if you use kilograms and kg per meter cube then you get units in terms of actually no units are needed then but that is the value. So, L by D same formula the expression is similar only the numerical values have changed slightly. So, please do calculate this number L by D loiter is 9.123. Now, let us go to the loiter segment again we use the Brighi endurance equation 9 by 8 this is the equation for the weight remaining w 8 to 9 this segment we are having a vacancy in weight. So, the value of the fuel consumed is 1240 kg 20 minute loiter at 10 kilometer altitude. So, the weight at the end would be 19374 which is the beginning of the loiter minus 1240 it is 18134. The next segment is the descent segment and recall that in descent segment we are ignoring the fuel consumed from the distance travelled. So, they are the same and also we assume that the aircraft comes back intact without dropping the payload also. So, you can get the value of W10. Finally, we come to the approach and landing segment which is again it is a standard from historical data the formula remains the same. These are the two parameters which are known to us a priori. One is that the weight at the start of the segment it has to be 18134 and also we know that the weight ratio in the approach and landing segment is assumed to be 0.995. So, just multiply 1 minus 195 into 18134 you will get the answer as so weight at the end of the mission will be equal to the weight at the beginning of this particular segment minus the fuel consumed in this segment which is 91 kgs. So, the answer is 18043 kg. Let us see how we calculate the fuel weight in all mission segments. So, for that we just sum up the mission sum up the fuel weight consumed in each segment. So, WFM would be just the addition of all the weights in each segment right from 01 to 1011 and these numbers are written here for your convenience W this number corresponds to 909 this corresponds to this this corresponds to this. So, notice that the onward cruise segment has more fuel consumption than the return cruise segment mainly because the aircraft is lighter much lighter it has knocked off 3708 pounds of cargo. The least segment the least fuel is consumed in the approach and landing segment we ignore the fuel consumption in the data in the sorry we neglect the fuel consumption in the both the descent segments and this is the big daddy 3708 the fuel consumed in the dash. So, fuel consumed in loiter and fuel consumed in return cruise are quite low but the main consumption of fuel is happens in the dash segment. So, if you add up these numbers I think you should do it yourself by pausing the video the total fuel comes out to be 10362 kg on this we have to slap an additional 10% because of the reserve fuel. So, therefore the total fuel weight will become 1 plus RFF times this value which will be how much please calculate this value turns out to be 11398 kgs. So, now once we know now the fuel weight for an assumed value of W0 let us see how we find the W0 in the refined sizing. So, once again the formula contains crew fixed payload trapeble payload fuel and MT, MT is replaced by ratio to W0. Now, the gas weight is 30300 kg. So, WE by W0 can be calculated how much is this please calculate this number 0.415. So, therefore the MT the MT weight will be 0.415 times 3030 that is 12575 kg. And the value of estimated W see we assume W0 as 30300 and we got all these values we got empty weight fraction also and then we put it back here. So, crew is 100 fixed payload is 5680 trapeble is 1895 fuel as estimated now is 11398 and MT is 12575. Now, if you add this number you will see that it will become more than the LHS it will become 31648 kg which is more than the left hand side. So, therefore we need to iterate we will take probably this value as the initial value do the whole process again. So, we keep on iterating till we receive convergence. So, this is the answer finally this is what you get. So, these are the symbols various segments in refined sizing we got these numbers and these are the numbers which we got earlier in the initial sizing you can go back and check there. So, we notice that there is a huge difference between the fuel consumed in refined sizing versus the fuel consumed in initial sizing. So, the difference is very large it is around 600% 550% in the case of dash segment and large in the so the net net you have a 27% additional fuel compared to initial sizing and this is the weight breakdown. So, we will look at empty weight fraction fuel weight fraction empty weight fuel weight and design gross weight these numbers you get in refined sizing these numbers we got in initial sizing you will notice that the values are away by about 24% 41% 31% 27% etc. But the design gross weight you get is roughly around just 10% away. Before I close I like to acknowledge Daniel Ramer for his seminal textbook in aircraft design brand styles Burton Bidford for their textbook which has become the baseline for us to use for getting the data of our F-16C. Nikolay and Karitman have given graphs for estimation of the fuel in the unnecessary line and also very good updates about the aircraft and Namanuddin the teaching assistant for helping creating this tutorial. Thanks for your attention and I hope that the numbers obtained by you have also matched with our numbers. If there is a discrepancy please bring it to our notice and we will take care. Thank you.