 So, today's talk is going to be quite different from what you have seen so far. Today we start doing our analytical calculations and there will be 2 or 3 such presentations. Today we look at only the prediction of static lift and then we will look at in the next presentation estimating how static lift variation can be estimated. So, this presentation has been made from the reference textbook, one of the reference textbooks for this course by John Taylor and we have the authors permission to freely use the book for this course. So, I am thankful to John for permitting us to use the book. The material covered today is going to be part is based on 3 or 4 chapters of that particular book. So, let us first look at the basics. I hope all of you remember what is meant by gross static lift. So, can someone help me by starting? What is meant by how will you define gross static lift of an LTA system? One of you, gross means total, complete and static lift means because of buoyancy. So, gross static lift imagine there is a small bubble of air in the atmosphere, this is not a balloon, this is a bubble of extremely low weight so we ignore the weight of the bubble. This bubble is stationary in the air so therefore, there is the upward force of buoyancy acting on it that will be on the bottom, there will be force active on the top of the bubble because of the ambient pressure. So, as this bubble is taken to higher altitudes, the value of FT will keep on reducing. And then there is weight of the air of the bubble. So, since the bubble is in equilibrium because it is a bubble of air in air, it cannot be under any dynamic condition, this is static lift prediction. So, therefore, if you apply a complete principle, you can easily say that the force FT plus the mass will be equal and opposite to the force of buoyancy. And hence, weight of the air can be considered to be the difference between the buoyancy force and the pressure acting. Now, this is weight of the air inside the bubble. Let us repeat the same thing, now we have a bubble of gas, identical dimension but now will it be in equilibrium, it will not be because the weight of the fluid displaced is not same, is not equal to the weight of the gas. Gas is lighter. So, this is going to rise up, as it rises up the force FT will fall because of ambient pressure reducing, correct. So, it is not, the net force is not 0, there is some net force and that net force will be weight of the gas plus the pressure acting minus the force acting. So, therefore, the net force will be the gas weight minus the air weight. Actually this FT is a difference between the pressure acting on top and pressure acting on the bottom. But if you are assuming that the bubble is in free atmosphere and it is basically enclosed, then the pressure acting on this bubble is only going to be the pressure that is because of the column of the air above this particular bubble. So, therefore, when it is in equilibrium, the force acting on the from the top will be just the because of the pressure acting on the bubble because of atmosphere. Why? Agreed, but as I said air bubble is in equilibrium, it is air bubble inside air. The gas bubble is not in equilibrium, therefore it is rising that is because the forces are imbalanced and the net force acting on the gas bubble is exactly what we are looking at which is the difference in the weight of the gas minus weight of the air. Sir, if we look at only the force picture and not take the gas into the above, then the FT that should be called as force because like if you take the difference between the pressure, it is basically T into A. No, no, hang on a minute. If I understand what you are saying, but if there is an enclosed column of air which is in equilibrium, I understand that you are talking about the atmospheric effect that is as you go up, there is some pressure below, some pressure up, but if there is an air bubble which is in equilibrium, then because of the weight of all the air above it in the atmosphere, there will be a force acting on that bubble. So that is what I am saying, there is this FB force from the bottom, then there is a rate of the bubble and then there is the force FT, we take the equilibrium and we equate the forces. Yes, FT is negligible as compared to, that will depend on at what altitude this air bubble is in equilibrium. Air outside is same. Right. So FT is nearly 0. So correct, so we are trying to bring in this concept by saying that if there is a air bubble in equilibrium, the 3 forces which will be acting are as follows. So will FT be equal to 0? No, it is the same air, it is the same air, I am not putting gas inside, I am taking an atmosphere which consists of general air, the density of the air will change from various altitude to altitude. For any particular altitude, I capture some gas, some air in a weightless enclosure let us say. So it is a bubble, it is infinitesimally thin membrane which captures this control volume. So the atmosphere, the pressure of the atmosphere acting on the bubble will be balanced by the force acting and if it is in equilibrium, then the downward forces will be equal to the upward forces. Yes, I am not calling it as a buoyant force or something, I am saying the forces acting will be in equilibrium, the buoyant force will come only when you have a gas. For the weight of air that has been displayed, so that downward force has to be compensated now by FT, now there will be some force acting, but just right now like in this picture, does FB, if you remove FT, then it is W, air and FT both acting downward. It cannot happen, then how will there be equilibrium? Exactly, so FB here is FB 0. See, understand one thing that we are trying to bring the concept of buoyancy by showing that there is no force if it is air in air and there is some force if there is gas in air. So I am not commenting on the numerical value of any of these forces, I am just saying that if there is a bubble stationary, then the air inside the bubble has displaced there both have the same mass, so you are right there is no buoyancy. But now when I replace, this is only for illustration purpose that now when I replace, I when I replace that air inside with gas, then there is going to be an upward force. So, suppose we go ahead and look at now two important concept, now this is the gross lift. So, the gross lift is basically difference in the weight of the displaced air and the gas.