 Now, we have discussed the concept of ballonets but at the moment let us assume there are no ballonets which means you have a simple envelope which has got nothing inside. So, the volume occupied by the gas is equal to the volume of the envelope. In this case, the gross lift will be basically weight of the air which is rho A density of the air into V ENV. Now, I will use this symbol V ENV throughout for envelope volume and G will be the expression to do gravity. So, what will be the units of LG in SI system? It will be Newton's. Now, this is one mistake which many students will make. So, it is important for me to caution you right now. By a simple check of units where rho is kg per meter cube, V is meter cube and G is meter per second square, you will find that it is going to come in Newton's. So, be very careful. I keep warning people but people keep committing this mistake because they are in a hurry. They do not look at the units. At every point in this calculations units have to be confirmed. So, the force LG acting will be rho A into V ENV into G. This is the gross static lift and the net static lift will be the gross static lift minus the weight of the lifting gas and it out straight forward. Therefore, the weight of the lifting gas can be assumed to be rho G into V ENV into G. So, the difference between them. So, then we come up with the simplest formula, the most basic formula which you will use throughout your calculations. And that is the net lift which is available from any LTA system is the difference in the density between the ambient air and the gas volume times envelope volume into G assuming that the entire envelope space is occupied by the lifting gas. But this is never the case except under one condition. So, which is the operating condition at which this formula is perfectly applicable? For a typical airship, what is the operating condition at which this formula is correctly applicable? At the ceiling at the now the altitude at which this thing happens that means at the altitude at which the LTA gas occupies the entire volume. That altitude is when the balloonets are completely flush that happens at the ceiling and this altitude is called as the pressure height. So, this is important term which you can note down pressure height is the altitude at which the balloonets are flush is present and the complete volume occupied by the lifting gas is there in the full envelope. The envelope is fully occupied by the lifting gas there is no balloonet. Above this altitude it is not very easy to go you have to resort to dumping of the gas or some other measures. Now, we know that a typical airship has balloonets we have seen last time why we give balloonets. Do you remember what is the purpose of balloonets? Correct. So, to control the buoyancy to control its equilibrium and is that the only reason for pitch control and any other reason? Angle of attack basically is pitch only giving angle of attack means allowing it to pitch. One more important purpose is to relieve the stresses on the envelope. So, from structural considerations if you do not provide balloonet and if you take it to very high altitude then the delta P between inside and outside outside pressure will keep falling inside will remain same. Therefore, there will be a huge amount of tear. So, by using balloonet you are giving lesser or more volume for the same LTA gas and thus you relieve the pressure. So, pressure control buoyancy control and trim these are the three reasons why we have one or many balloonet. So, now if you have a situation which is most typical situation for a manned airship at least is that you will have one or many balloonet filled with air. So, if you define a term called as the infraction fraction, it is a very funny name infraction fraction and that is fraction of the envelope occupied by the LTA gas. So, 1 minus i will be fraction of the gas occupied by the balloonet. So, the value of i infraction fraction will be 0 to 1. It will be 1 if there are no balloonet or if you are at pressure height it may be 0.8, 0.7. Typically, typically the balloonet volume tends to be around 20-25% of the envelope volume but this is not a fixed number. If this number has to be calculated by you based on how much delta H you would like to provide. From which height you will operate and up to what height you will go. These important parameters determine the amount of balloonet volume that you need to provide. So, if there is air in the gas bag then the net lift will not be equal to LG minus WLG gross lift minus the lifting gas weight. There will be one more term to be subtracted which is the weight of the air in the balloonet. We call it the WBA and WBA will be volume of the balloonet at that particular condition times the density of air which will be same as density of air outside because balloonet is always in contact with the ambient air. It takes air from outside. However, at various altitudes when it takes in air it will have different density compared to say C level. So, note that WLG that is the weight of the lifting and now all these items you are not supposed to just see on the board and nod your head. You are supposed to note down because very soon you will be deriving expressions to use it. So, it is not a good idea to just watch. It is a good idea to I see some students are doing it. Just note down these expressions because the equation will become very very complicated after a few slides. So, weight of the lifting gas will be density of the gas into I into VENV where I is the infraction fraction times G and weight of the air in the balloonet will be 1 minus I into VENV times. The pressure inside the balloonet is very slightly more than outside to maintain its shape. So, you can assume it to be roughly same as outside because there is a direct communication through a fan or through an injector. But those walls are freely opening walls. So, the pressure is communicated. So, the balloonet is normally in touch with the atmosphere. So, the pressure inside the balloonet will be roughly the same as outside unless you close the whole system and then you push pump air inside then the pressure will change. So, the simple formula of net lift with the presence of balloonet it just gets slightly modified with this infraction fraction I. So, it becomes density of air minus density of gas times I minus rho BA into 1 minus I into VENV into G. So, with this you can calculate the net. So, if someone tells you that an air chip has 20 percent balloonet and the volume is 1000 meter cube and it is operating at some altitude with helium. So, you know rho G at that altitude you know rho A at that altitude infraction fraction is given you can easily calculate the net lift that will be available and this net lift is meant for you to utilize. So, the payload will be this net lift minus the self weight. So, net lift is what vertical force this whole system is going to give you. You can use that force to carry payload, but you will have some weight of the gondola fins and other things. So, that is a dead weight. So, payload available or I should say fuel plus payload or useful load will be net lift minus system weight and you can trade off that between fuel and payload. And remember you also have to also carry some ballast. So, ballast as I said removable ballast fixed ballast, decibel ballast all of them are going to be part of the empty weight. Some of which you can throw some of which you can temporarily adjust some of which will remain fixed for center of gravity control, but they will all be part of the empty weight. You have to carry that much.