 So to understand this particular process and to get an idea about how to do it, here is a case study that will allow you to understand the nuances of the design. So in this case study, we are going to follow a particular color scheme for your convenience. All the instructions regarding the hot air balloon are going to be given in brown color. All the specified values which are given by the user are going to be shown in the black color. All the values that you assumed for your calculations will be shown in this light blue color. Wherever there are some calculations to be done, either you see some red colored symbol or you see this pause symbol. The purpose of the pause symbol is to tell you that whenever you see this symbol in the video, you should pause the video there. Do the calculations which have been asked and then play the video and see what answer is given by other students. And then whatever values you calculate will be shown in dark blue color as shown here. So general instructions in brown, specific values given by the customer in black, assumed values in blue, calculations to be done in red and whatever you calculate finally will be shown in dark blue color. So looking at the color of the slide and the entries, you will be able to figure out to which category it belongs. Let us see what is the required data. So what we need is ambient air temperature. Now we do not really know how much it is. So I am assuming 28 degrees centigrade but if you have a thermometer and if you are able to measure the temperature, this thing will appear in black color and it is there. Similarly we have to assume up to what temperature we are going to heat the air inside the balloon. So based on certain discussions, assumptions, online search, literature survey, we came to the conclusion that if the ambient air temperature is 28 degrees centigrade, then 180 degree centigrade is reasonably high to ensure that there is no major combustion but it keeps a tab on the people working in this particular project and supplying water. Then you will calculate the available net lift as lift minus weight but I would advise that you keep some margin. Do not work totally on the brink because once you make the balloon, you really cannot make any changes. So it is good to have a margin and we are recommending 5% margin in the lift. Similarly, you will estimate the weight of various components based on some calculations before you design but if you keep a 5% margin that means you know that the actual weight will come to be less than what was planned earlier. This I already told you that the minimum payload fraction has to be 150% percent. So for a balloon which has got a total self weight of 100 grams, you should be able to at least lift a payload of 15 grams. Then there are some values which are given to you as the numerical values of gas constant, calorific value of the fuel or kerosene. This is a number which comes from the person who supplies the fuel and specific heat capacity of air under normal temperature conditions is around 1 kJ per kg degree Kelvin. So we select the second method in which we fix the shape first and then we start with the sizing. As regards material selection, as I mentioned there are many choices. One could use aluminum wire on the bottom to hold the small container to mount the fuel. Envelope was considered to be best from butter paper in this exercise but you could change it to your requirement and the fuel that we used is the industrial kerosene. But we have done enough experiments in other universities where we look at the domestic kerosene and it has worked almost equally good. So you should also assume that you can use this kind of fuel for your calculations. Let us look at some geometrical specifications of the hot air balloon. So as I mentioned to you we are going to look at a balloon which has got a hexagonal pyramid at the top and hexagonal cylindrical shape which is the body and on the bottom there will be a frustum of a pyramid so that you are not very much away from the actual balloon. You are reasonably close. So what is the procedure to be followed? So you will get material from the shopkeepers in the case of the paper that he has selected. You will find that they will have some value of x and y. So we also went to the market and did a survey and we found that these dimensions are a particular standard available generally. So what you do is you create some basic templates and then if you join the balloon at those template areas they will become a joint balloon. Now let us look at how we can go ahead and do this. So basically what we do is in this case because there is hexagonal panel we make 6 panels and fold them along the dotted lines and then you put a propellant on the bottom and then you can ignite it and with that you will be able to get the hot air. In this case we have shown a blower to create hot air but the air cools very soon and you will not be able to really sustain the buoyancy. So it so happened that when we went to the market we found that the butter paper in our area is available only about 51 centimetres by 150 centimetres. So the best way to create a large side shape was to glue 2 pieces with an overlap. So 2 sheets of 51 by 76 they were joined together. So the availability of the sheet is 51 by 76. You join them together to get this large sheet of 150 by 51. Then there is an overlap as I mentioned and if you repeat this 6 times you will get 6 sheets. Then on these sheets you can draw the templates like this for the cut on the sides and then so this particular measurement is 30 degree centigrade 30 degrees at the top and 60 degree at the bottom and what you do is whatever is the excess paper you can just cut it off after folding it along those lines and you should measure that the bottom material is at least 120 degrees at the bottom okay and then you can just throw off the excess paper. Then since you have 6 pieces like this so you attach the panels along the edges so like this here you can see 2 centimetre glue overlap so panel 1 to panel 2 is attached and then you attach number 3 and such like that 4, 5, 6. So 6 panels are attached and now when you glue the top angles to each other you will find that it becomes a first time of a cone so it becomes like this yeah. So the length of the butter paper is available so the paper length is 145.6 then breadth is 49.2 surface area it has to be calculated. So how do you find the surface area best by multiplying the 2 so please multiply and check your answer my answer is 7163.5 to square centimetres then if you cut the area of a single sheet after cutting the desired shape we found that the area of the useful sheet is 6041.5 to centimetre square right then the volume estimation is assumed that height of the envelope is assumed to be the length of the paper minus the cutoff. So 145.6 is the length of the paper and cutoff was 42 centimetres so the height is 103.6 centimetres the hexagon side was measured as 49.2 they have mentioned 49.5 but actually it is 49.2 and there is a simple formula for volume of hexagonal shape which is shown on the screen so using that formula one can easily calculate the value of the volume of the envelope so of the hexagonal shape only by the way ok. So it will be 3 root 3 times maximum a diameter square into H ENV upon 2 and I have given you the numerical so please put it in the equation and try to get the answer. So the answer is 651522.03 centimetre cube that is the volume of the balloon so you will get 0.65 cubic metres ok. So what is the left lift estimation how much will be this balloon lift itself it weighs 0.65 kilometres a few metre cube. So first we calculate the range of the embed air which is P upon RT0 no economics here or no assumptions here this is simple logic this formula simply gives you the value of the density of air as a function of the ambient air pressure gas constant and the temperature. So with that you can get the density of the ambient air. So if you want to use the charts you can just say ok I will determine this value graphically so for example if you are operating at this particular altitude there is an arrow that goes to the air density and from there it goes to the value. So you could use this or you could do the calculations I would prefer if you use both to validate your own calculations. So let us see how hot air density is calculated. So rho air or rho hot is equal to P by RT hot now P is going to be the same as atmospheric because it is an open throat balloon so there is no pressure difference but T hot is going to change. If you recall T hot was assumed to be 180 degrees it is an assumption based on the study of areas types of fuel how much they can increase the temperature of hot air. But if you do not have this number you have to take some reasonable estimate like we have taken. So the rho hot is going to be 101325 divided by 287 gas constant into 273 upon 80. So if you put these numbers correctly you get the density of 0.77 I think you might have to use G here also the expression due to gravity you might have to use. Again one can do it in the court by saying that this book is present the amount he claims is not correct or you can do the calculations yourself using this particular graph. So in this graph you can see that at a temperature of 180 degrees the density of the hot air happens to be nearly 0.7 and we have taken it as 0.77 anyway if you should live with 10% error in your life then how are we going to go further. So once again the same formula so rho A is known rho G is known V in V is known so you get this value can you tell me what is the value you got please calculate this number and the lift will going to be into G. So therefore it will be almost 0.26 kg or 260 grams. Now we calculate the drag of the bullet this is a very challenging exercise drag is equal to half into rho A into V square into SRF into CD here D is the drag rho A is ambient air density V is the velocity SRF is the reference area and CD is the drag coefficient. The interesting part is that reference area in case of buoyant systems is not taken as the cross sectional area or frontal area or any other area top view etc. So there is going to be a method to calculate the coefficient of drag which is the component built up method as you know in this method we calculate the drag as a product of 3 components the next thing is to calculate the skin friction coefficient for that we use the formula CF is equal to 1.32 weight divided by root of RE so you need to calculate the renounce number. So let us calculate the renounce number it is rho V L by mu okay so if you look at the formula for CF you will find that it needs only a renounce number which we have got earlier so with that we can calculate the value of CF. Then we look at form factors a simplistic formula for form factor estimation which just requires fineness ratio which is length upon diameter ratio so length is 103.6 centimeters grade is 91.2 centimeters so simple ratio is 1.12 okay that is the fineness ratio and with that if you put the values in this equation you will get the form factor please calculate it yourself remember that just watching the assignment will not make you learn anything you will learn only by doing it yourselves. Now aspect by SRF is a parameter that contributes a lot firstly it contributes in the drag. So there is a formula available for estimating aspect by SRF if you do not know already which is 3.8 bit into root of your third root of FR okay let us go ahead this way already seen so aspect by SRF can be calculated as a ratio of 2 numbers this value comes to 4.02 which means the embedded area of the envelope is roughly equal to 4 times the reference area and then we calculate the drag which is CD actually there is a sigma sign there which is missing is the sigma of CF into FF into aspect by SRF so CDF will be equal to 0.360 drag again the same formula and by now you know all components the value of drag comes out to be 4.04 into 10 to the power 3 minus 3 newtons very very small amount of drag. Now let us look at the weight estimation so for weight estimation the first is the envelope weight so we measure the GSM or the grams per square meter of the envelope and we found that it is around 34.8 to 35 grams so we looked at the data we found that the required area of the envelope was 3.62 square meters so the weight of the envelope is going to be simply multiplication of these two quantities so 34 by 3 approximately 125.9 or 130 grams approximately is the weight of the envelope alone. Remember I have not put the weight of the glue here but I think it can be included when you look at the wire or the base which is also going to be installed by you to mount the payload or the amount of fuel. So let us assume that weight of the wire is about 0.05 grams per centimeter or 5 grams per 100 centimeters very light weight wire we require about 496 centimeters. So weight of the wire is basically nothing but length of the wire into wire GSM which is 496 into 0.05 then we come to the required heat because mass of the air M air is equal to rho ambient into V infinity it contains ambient air which is 0.76 kg. So the heat required by the balloons to create the temperature is given by this particular simple equation where T hot is the hot temperature of the gas and T 0 is the ambient room temperature Cp is a parameter that is used for pressure coefficient calculation. So with that you can calculate the value it comes to around 116,000 joules wow that is good energy fuel weight. So mass of the fuel required to produce 1 kilo joule of heat can be obtained as 1 by the calorific value that is the definition of calorific value actually okay. So mass of the fuel required to produce the and the minimum weight comes out to be 2.5 grams only. Let us estimate the mass of the payload now. So mass of the payload is basically expressed as a fraction of the as the fraction of the total weight correct. So it is 27 grams if the total weight if the structural weight is 2.5 and 150.8 grams then the mass of the payload keeping in mind 15 percent is 227.05 grams the total mass of the system is the mass of the payload plus fuel plus structure which is the addition of these three items and that comes to 180.35 kg okay. So static lift we calculated a 256 grams lift margin was 5 percent available lift was 5 percent lower than actual available lift. So therefore percentage lift available will be 1 minus 0.05 times 260 which is 247 grams and the margin is 5 percent. So the available weight will be 1 plus margin total mass. So we know that the net lift is equal to 64.64 kg. Now the question that I want to keep open-ended to you is how will you calculate the time for heating because we must finish it within 4 minutes and the upward travel time of maximum 2 minutes. So this is an exercise which I want to leave it to you. I will just give you a hint that you can use in Newton laws of motion which is simply force is equal to mass into acceleration. So if the balloon has to go against gravity and rise up then the buoyant force acting on it should give you the acceleration okay. I will show you now one of the experiences of making this balloon by our students. Here is a group of students working on petal cutting and making the trial of the system okay. You can see that they are working on their own inside a room. Then they use butter paper as I mentioned so it is translucent and this is the kind of system they used. You can see that the balloon is very hot in the bottom and finally the balloon was held by upper surface released very soon. So this is the final design. There is a small dish to control to control the to hold the fuel in the center you see a simple rectangular hot air balloon and I can now show you the video of a successful trial that took place. You can have a look at this particular video. You can see that the fuel is ignited by a mastic on the bottom and one of the team member holds the balloon apart allowing the air to get heated and slowly it is going to come to the top. So we were given 4 minutes to do this but looks like this team is able to manage to get enough buoyant lift not in 4 minutes but much better. You can see once they leave it it is going up as it goes up its speed slightly reduces and that is the ceiling of the fire at 65 meters. So this is what happens it gets stuck in a structure just below and then good luck that there was a side breeze because of which the balloon came unstuck and it went and hit the ceiling. So you should carry only so much fuel that the balloon hits the ceiling after that the buoyancy should start decreasing and because of the decreased buoyancy the balloon should automatically have the tendency of coming down. In this case because there was too much buoyancy available the balloon went to the ceiling of the fire and stayed there and now you can see so you can see now slowly the balloon is going to now start descending as it loses buoyancy because of the consumption of the fuel its buoyancy reduces and when the buoyancy reduces it starts slowly sinking there you see coming down and the team going and collecting it. So this is an example of a successful experiment. So I would like to end by acknowledging the contribution of some people the first experiment in this area was done by two interns by the name Amitwani and Chitandusane both of whom are now designers in their own right they have gone for higher studies in design masters in design to be very specific. They were the first interns to work on this in the December of 2014 and then we launched this in the course on 2015 and then 7 and then 19 and then 20 and I also want to help my teaching assistant Namanuddin for help in preparing this presentation. Thank you so much and I hope you will take advantage of this recording and make hot air balloons and you will share your videos with us so that we can also get some information from you. Thank you so much.