 So, the statistical data was established to answer specific questions. One question is how much should be the ballonet volume to meet the trim requirement about the requirement for the pressure altitude correction. So, what we did is first we tried to arrive at a theoretical formulation using the formulas that we discussed. Then we collected data of various airships. You can see this AU-11, 12 and these are all airships which have either been designed or they were somewhat under design and the data was available in reports, websites, papers etc. And we said okay, assume our theoretical calculations and look at the data actually available. Now the same information here, so I just wanted to look at this line which says that for a height of 3,500 meters which is what we are expecting the airship to operate, the estimate ballonet percentage was 30%, let us say 9.6% and the average value of all these is around 2.2%. So, therefore we said let us take it as 2%. The same information that you see is projected now in a graphical form. The red triangles are the points corresponding to the actual ballonet volume ratio as published by them in the reports versus their pressure altitudes and the blue dots and the open rectangles are the mathematical estimates using our formulae for the ballonet percentage needed with altitude, pressure altitude for either ISA conditions or ISA plus 15 conditions. So we notice one thing that the numerical value of ballonet needed is not too high if it is ISA plus 15, which means temperature does not play that much of a role. It is the altitude which plays that much of a role because of the pressure loss. And we see that the red dots some of them have higher than what we need, some of them are trying to follow on the trend line that we got. So it is a very encouraging result for a person doing this work for the first time, which is what we were. We had no prior experience of working on airships. When we plotted our theoretical lines against the actual red dots, we were very happy to see that the trend that we have got is somewhat relevant, however some airships you can see have far higher ballonet percentage than what we expected. So the reason for that is the technical requirements, the mission profile are not released by companies for public consumption. So we are assuming that they go from sea level to a height of 2,000 or 3,500. But they may be going from some altitude to some other altitude, we do not know. So that is why actual practical data will never fit perfectly along the line, but at least the trends are very encouraging. So this gave us some confidence that we will be able to capture roughly how much is the ballonet needed, percentage ballonet needed for a particular operating requirement. Then we wanted to also investigate what is the effect of the ballonet volume ratio on payload. Suppose I make it more than needed, that means suppose I make a larger ballonet than needed, what is the big deal? If you make a ballonet larger than needed, first of all you have extra dead weight. So those of you who did the calculation, do you remember the numerical value of difference in weight between an integral ballonet and the, what do you say spherical ballonet? How many cases is the effect? Some of you have answered the question. In fact, one student uploaded within 15 minutes or 20 minutes of the lecture. That means he went home to the hostel and did the calculations, scanned it and put it up. Very nice. That is very good. So what is the numerical value? 20 kg lighter. 21 kg lighter. So I think somebody said 50 kg lighter. So yeah, these numbers can be checked but even if it is 20 kg lighter, it is 20 kg for nothing. So just for little bit of manufacturing ease, will you go for 20 kg heavier airship? Imagine that means you can have 20 kg more payload or 20 kg more fuel compared to what you can have with the integral ballonet. So similarly, empty air will be more because you have a bigger ballonet for no reason. Now if the ballonet occupies more volume than needed, it will also give you a problem with the lift. So here is the output of our analysis. So that the line on the top with rectangular, dark rectangular boxes indicates the change in the empty weight in kilograms. So if I have 10 percent extra, if I have 10 percent extra ballonet. Now why do you want to have more ballonet other than the pressure height requirement? Why should you even think about it? Why not do 1 percent? Why should you have more than, you know that ballonet is needed basically for ability to provide you the delta H, pressure altitude from a ground altitude, operating altitude, right. Liger the difference, more will be the ballonet volume needed. But suppose that number is 20 percent, should you have more than 20 percent? For what? Recall our discussion from last time for trim conditions. So you should need something more for trim conditions, okay. Because you can also use, if you have two ballonet front and back, you can also use them differentially to provide trim. And that trim can reduce drag during flight a lot, okay. Now how much should we give? Correct. We, I just told you that we have used 2 percent but here is the logic and justification. I can use it 10 percent, 8 percent, 6 percent, 2 percent. I saw that as long as I go up to 2 percent, so I have, this particular figure tells you how much is the change in the empty weight, okay. So up to 2 percent ballonet, the empty weight changes only about 2 kgs approximately. But if I have 10 percent ballonet, it becomes almost like 8 to 9 kgs. This is for the demo airship, the small airship that we designed with the envelope of 1000 meter cube. But look at these two lines which indicate the change in the payload which is the rhombus and change in the lift which is the delta or the triangle. So we see that if you accept up to 15 percent or 15 kg difference in, not percentage, 15 kg, percentage, 15 kg difference in empty, in payload and 15 kg in the lift, then 2 percent is the limit beyond that there is a drastic reduction. So I can give more ballonet, I can give 10 percent more ballonet, let us have more margin for trim. But the penalty I will pay is 8 kg in the empty weight and around 70 kg in the lift and around you know what 65, 62, 64 kg, 64 kg in lift and around 70 kg in payload. So my payload capacity was only 77 kg and I would compromise 70 kg of that in giving extra ballonet. So you have to be very careful, percentage ballonet should not be too much additional. So that is why we said okay we will keep 2 percent. We also confirmed that most airships have around 2 percent. So it is a double reason based on what others have done and a confirmation that more than that is going to be very harmful. So design decisions are normally driven by analysis results. It cannot be and should not be arbitrary okay right. Now there is one more small contribution that many people have used and that is so you have this question always okay I decide the envelope shape. Now should I do a detailed stability analysis for every shape I investigate to find out the area of the fins that is actually too much of an overkill for conceptual design. So what we did is we just looked at the statistical data. So the logic is that if 30, 40 airships which are flying have fins located at some place or some portion from the nose of some area we also should not go too much away from that. We should not give too less or too more than that. So what we did is simple analysis of statistical data. So we parameterize the geometry of a fin in these standard symbols. So there is a root chord, tip chord, half span area of the control surface that is SC deflectible area. SF is the area of the fin which is the fixed portion so total area will be SC plus SF. This is the height which is equivalent to the I mean this is not exactly equal to the half span because half span has is a function of the geometry and this is the tip chord. So there will be a taper ratio for the fin, there will be aspect ratio for the fin, there will be area ratio. Now if you are doing this analysis I want to get from you how will you obtain a correlation or what will you use as a correlation parameter for the area of a fin. So you have data of n number of airships and you want to develop a correlation so that you can size the fin of your airship. How would you proceed? What geometrical parameter of the airship will you take for scaling up or scaling down? Is the problem clear to everybody? You have geometrical data of n flying airships. By that I mean you have the envelope diameter, envelope length, envelope surface area, you have their fin area, number of fins are all 4 for everybody. Let us assume all of them are plus fins so you know their fin area then all that. You have now a new shape or some shape. You want to estimate what will be the fin area that I will need for my airship. What will you do? Let us see if you can think like a designer. So normally what people answer is I am going to calculate the center of buoyancy, center of gravity, calculate the moment arm acting, calculate if the moment that is generated by the control surface is matching with what is needed but that means you will do a basic stability analysis. You could do that but there will be so many imponderables there. So there is a simpler way of doing it and still not being too much away from reality. So let us think and let us see if you can suggest a solution. So what you will do is you will find the ratio of area of one fin upon envelope surface area for all these airships. So each airship fin area upon its envelope area is a ratio then what do you do? Provided this number is somewhat same for all. So interestingly we did the same thing and we tried to find a correlation right. So that means you are saying that the area of the envelope decides the area of the fin yeah you are right we did the same thing. In reality it would only be the side area of the envelope because you take two airships of the same volume one spherical and one longish one. The longish one will require smaller fins because they are farther located. So the moment arm will be smaller a sphere would actually need a long stick and then a big area so that you can get some moment arm. So that we thought was now our airships for all axisymmetric bodies with large L by D. So we said anywhere the side area will be a function of the envelope area only. So we did the same thing as you said just divide and obtain the ratio. Similarly we did the same thing for other parameters also. Find the paper ratio of all these airships. So find it will be 5, 6, 5.29, 5.73, 5.63, take the average of that typically it came to 0.596. So what we have done is looking at the statistical information for many many airships. We got these ratios and will be surprised that these ratios are now being used by many people all over the world to size fins. Many people have quoted our paper and said the main thing we have taken is the sizing of the fin because it is a big headache to do a stability analysis. Then we thought this tail volume ratio, do you know what is tail volume ratio? How do we do the sizing of the aircraft vertical tail or horizontal tail? We define something called as a tail volume ratio and that tail volume ratio apparently is a very small band for aircraft. So what is tail volume ratio? It is a ratio between 2 multiplicative terms in the numerator for the aircraft. In the numerator you have the distance between the aerodynamic center of the wing and aerodynamic center of the tail it is called as a tail arm into the area of the tail divided by the mean aerodynamic called C. So like that you can create certain ratios from grammatical data for airship we found that there is a huge spread between the tail volumes. So we could not take a tail volume ratio as a fixed number because you can see from 3 L by D equal to 3 to L by D equal to 5 and a half it spreads from 0.03 to 0.07 more than double. So there is no great correlation so we could not take some number and go with it. What should be the propulsive efficiency assumed for an typical airship mounted engines? So for that I got some data about generalization aircraft from the book by Stinton. So he has given this particular chart which relates the propulsive efficiency eta with the airspeed and he gives it in kilometers per hour in the top and in knots in the bottom and also Mach number. So what he says is that the total propulsive efficiency of fans never goes beyond approximately 80, 81%. Propelers can have up to 85% also but there is a band in which they lie and propellers or unducted propellers are useful if your Mach numbers are approximately beyond 0.2 or speeds are beyond 200 kilometers per hour which we will never achieve in an airship. We will actually hit the maximum at 90 to 100 kilometers per hour perhaps 120 kilometers per hour that would be the tops you will go. So we learn that it is good to have a ducted fan, fans are better. The efficiencies may be slightly lower compared to the peak efficiency of the propeller but they are much better. So he himself says that fan is the best for speeds below this and propeller is the best for speeds beyond this. So with this information we are okay we will use ducted fans if possible but as I said ducted fans are going to be heavier as well as they will cost more but they are safer. So operationally they are better safer and they are also having a better efficiency. So then looking at the data of some existing airships like Skyship 600 was in front of us as a baseline airship we got the propeller ratios by you know so these are some correlations for you to be able to size the airship with the requirement. Now there are many many more things but I have left them out because they are too detailed and of course the papers have been already uploaded. On the module page this morning I uploaded 2 papers. One is the conference paper which was written in 2003 and the next one is because the paper got heavily referenced and many people wanted to be publicly available. I got several requests from people all over the world asking me to mail the paper. So then we actually wrote a technical note in Journal of Aircraft in 2008 after correcting the data and making a few changes. So both the papers have been uploaded onto the module page and it is important for you to note that they are not there just for fun they are part of the course notes. So I expect you to understand everything that is mentioned in those papers. I expect you to be able to use the formulae not mug up but as a reference material the paper is a variable you should be able to use the procedure and formulae to do the calculation. So read them very carefully I thought it is very futile for me to copy and paste the formulae from here and show it to you. You should do some self-reading this is the master's course so you should do some reading on your own and we have the module page for clarifying any question that you may have. So it is very important and very desirable that you should read those two papers carefully. I want you to learn how to read technical papers and extract useful information. If you find any mistakes or errors you should bring it to my notice.