 Alright, the next thing is the tether profile estimation, very briefly we will discuss it although it is there in the paper in more detail. So what we do is, starting from the confluence point till the ground, you assume the tether to be broken into small small components, let us say 1000 segments, okay. So now let us take at any segment, so that this is i minus 1, this is i, this is i plus 1. So let us look at this i th and i plus 1, this is one segment of the tether. What are the forces acting on the tether? One is the self weight, the other is the aerodynamic load acting on it because it is a cylinder at an angle to flow. So again, there will be two components, one will be along the length, one normal to the length, so for that for cylindrical body at some renounce number, CD is available by empirical data or from internal testing. So DWI is the elemental weight acting and there will be dry force acting here and the tension will be more here and less here. The tension will keep on, change elemental, okay. Tension will actually be conveyed, so the rope will have the same tension but what will happen is because the weight, weight overcomes the tension, component of the weight is going to overcome the tension. So what will happen is after some time, the net tension acting on the tether will be 0. That is the place where you can assume that tether will not have any curvature after that. So this is how you calculate. You take the tension which will be the force acting into cos alpha plus sign here the dynamic forces acting on the tether and z force will be the weight of the tether minus buoyancy minus the two forces acting and you do this incrementally, calculate the angle of each element and at the end you will find this tension will become 0. That is the maximum after that tether will be, so if I leave the aerostat, it will occupy some curvature and then it will remain flat on the ground. So that is what is done and this is one of the results obtained, right. So now just to show you an example of thin size determination, again we have an M-tech student called Vijay Ram. He came for Zafar recently in the panel discussion also. So Vijay Ram has based on his M-tech, he has published a couple of papers. One of them is on aerostat design and in this particular paper, Vijay Ram has given the same method to calculate the fin area. So I encourage you to read his report and you can see this is the comparison. And then recently one intern who came for 6 months, he looked at all these formulas, put them together into one nice spreadsheet and developed a methodology for conceptual sizing of the aerostat. And he presented or rather I should say I presented his paper in the conference in Kuala Lumpur. So this particular paper is the one which is being quoted now by people. So there you will find the same figure which I showed you. You will find the calculations for moment and equilibrium, the profile after that you will find fin sizing and you will find some results which I will show you very briefly now. So finally, I will just show you an example. So this is one actual scenario for which we did some aerostat design. I cannot name the customer, they are not important for you. What is important for you is the requirements which were actually given. So payload of 300 kg plus 120 kg extra, 800 meter altitude from the ground of 200, wind speed 25, temperatures, temperature range and hood index deployment. We chose this particular shape for the aerostat. We chose helium gas and we chose the integral ballonet. We gave these constant parameters free lift, how much gas purity, gas leak rate, maximum speed, envelope mass, fin mass, tether mass, additional mass and we got the output. The envelope was 2662 odd square volume meter cube and the angle at which it came was around 7 degrees. So at around 7 degrees the aerostat is automatically trimmed. This is the figure profile. So notice that the aerostat is to be deployed at a height of 100 meters from the ground but because of this heavy wind of 25 meter per second, it is having a blow by of so much. So it is actually going much behind but that you cannot avoid. Then we did some analysis as to how the angle of attack. So you notice that when the diameter of the, so what is the diameter of the aerostat? The diameter of the aerostat is 11.31 meters. So it so happens that at 15 degree, 15 meters location XC and ZC, the angle of attack is around 7 degrees, 6 point something degrees and that is the location. If the alpha changes, the optimum conference point changes but at this, they both meet here. And this is how the blow by changes with the wind speed. So you notice that at 5 meter per second the blow by is only 150 meters but as the wind increases to 25 meters it becomes around 400 to 420 meters and as wind becomes more and more blow by is reducing but there is a substantial blow by. For a height of 800 meters, I have 400 meters of blow by which is quite large. And then some studies we did about, you can see the same methodology which I showed you. Similar results, we are trimming it at around 2 degree angle of attack. This is the wind speed versus angle of attack. And this is how the payload changes. It changes linearly. In the question I asked you about payload drop and I asked you justify your methodology. Some of you said that as shown in the class, the payload reduces linearly. That is what I want you to understand. The data in the question paper may be linear but that is not your reasoning. The reasoning is that payload drops linearly with altitude. It is something which is known to us. So even here also at a height of 700 meters payload is around 480, 1000 meters it is just 300 kg payload. So in conclusion, we have the methodology for sizing of the aerostat. It can be used for carrying out this analysis of sensitivity.