 Hello friends, one of the most interesting and popular lighter than air system that we come across is a hot air balloon and today we will look at how we do the sizing of a hot air balloon. But as an example we will take an indoor hot air balloon so that if any student or a team of students is interested they can actually build this as part of their exercise. So let us start exactly what is a hot air balloon it is a member of the family of lighter than air systems. There are various types of hot air balloons but the ones that we normally see are these ones which are the hot air balloons used for adventure purposes. As you might be aware a hot air balloon has a single degree of motion it does not have any mechanism to control its flight it can just go up and down and one can control the buoyancy of a hot air balloon by the lighting of neoprene burner on the bottom of the balloon. As you saw in the picture the cold air is heated by firing that burner and once there is enough hot air inside the balloon it generates buoyancy required for it to be able to lift itself and the payload which is mounted on it or the people who are carried by it as payload as you can see in the extreme right of the figure. Now you also have a possibility of indoor hot air balloons such as the ones shown in the bottom two figures the one on the left is a series of hot air indoor balloons which are deployed for decoration purposes and the one on the right is a indoor hot air balloon which is touching the ceiling of a mall or the covering for an indoor arena. So we can even carry a reasonable amount of payload in these indoor hot air balloons. Today we have to understand that the working principle of a hot air balloon is the Archimedes principle which tells us that the force of buoyancy FB acting on any body is the product of the density of the fluid in which the body is suspended the gravitational acceleration G and volume of the fluid displaced. So these are the only three parameters which affect the value of buoyancy. So just to sum up Archimedes principle tells us that if you consider any body which is immersed in fluid it could be a balloon containing hot air or any other LTA gas suspended in ambient air or it could be any other enclosed volume suspended in any fluid it could be partially or fully submerged in the fluid. Now when you have a situation like this then the fluid exerts an upward force on the body this upward force is uniformly acting at all the points at which this body is under contact with the neighboring fluid and Archimedes discovered through his very famous experiment in the bathroom that this force equals the weight of the fluid displaced. So this also applies to fluids immersed in other fluids too it is not just necessary that it is meant for a body in a fluid for example if you look at the bubbles air bubbles inside water etc. they all work on the principle of Archimedes ok. As you are aware an elective course on LiDAR thermo air systems is being taught at the aerospace engineering department of IIT Bombay. In fact the recordings that you are seeing are mostly the recordings taken during that course being conducted. As part of this particular course we give many assignments and one of the first and the most popular assignments is the assignment on sizing of rehab which is what I am going to take you through today. So rehab stands for relocatable indoor hot air balloon. Here is a summary of the problem statement. In this assignment teams of students are required to design fabricate and test an indoor hot air balloon which meets a particular requirement. We have a three story indoor fire in our lecture hall complex which is approximately 60 feet high. So the requirement is that we need to do the sizing of a reusable hot air balloon incorporating the effects of varying various parameters. First of all envelope shape. So no specific envelope shape is specified. The team members are allowed to choose whatever shape they are interested to work on. They can also choose any kind of envelope material that they wish to use and they can also use different kinds of fuels to create the hot air inside the balloon. What is the requirement? The requirement is that you should have a balloon which can have a minimum payload fraction of 15%. By payload fraction we mean the mass of the payload divided by the mass of the entire system including the payload. So for example if the hot air balloon itself weighs 200 grams and if we mount a payload of 50 grams then the payload fraction is 50 grams divided by 250 grams. So that is the meaning of payload fraction. So the balloon should have a minimum payload fraction of 15% higher, better and in fact the team that wins the competition is the one that has the highest payload fraction and also meets all the requirements. So what are the requirements? From the time the team is given the go ahead within 4 minutes the balloon should develop enough buoyancy to start lifting from the ground and it should travel and hit a ceiling of that fire within 2 minutes. The fire is located at a height of or the ceiling of the fire is located at the height of 65 feet or approximately 20 meters from the floor. So once we give the go ahead within 4 minutes it should become buoyant and then within the next 2 minutes it should hit the ceiling and then after hitting the ceiling we expect the balloon to cool down and come down and we want it to be recoverable without any damage so that it can be reused. So these are the critical requirements for this particular assignment. If a balloon travels only 10 meters or 15 meters and comes down then some marks are deducted, some marks are awarded for the distance that the balloon travels. So we look at first floor, second floor, third floor and ceiling. So I think you should have a mental picture of these requirements because all of these are going to affect the sizing of the balloon. Let us go ahead. What are the candidates for envelope shape? So one can look at several different shapes. For example, one could look simply at a rectangular cylinder with some frustum of a cone on the bottom, below which you put some kind of a wire and in the center of that wire ring you can mount the fuel which can be ignited and the payload can be stuck anywhere on the top or on the side of the balloon or maybe on the bottom of the balloon. You could also go for a hexagonal cylinder, these are the shapes which many students have preferred in the past or you could go for something which has got a conical hexagonal top and bottom as a frustum of a cone. The conical top allows you to pierce the air and go up quickly because remember there is a requirement to be able to reach the height of 65 feet within 2 minutes and sometimes if you have a very flat top then there might be some problem, there might be massive resistance of the balloon in the vertical flight. So therefore some teams have gone for the conical top and that is the one that we are going to use in the tutorial that we will do today to just get a firsthand feel of the sizing of the hot air balloon. One can also look for any miscellaneous shape that you are interested in, it is up to you. When you do this assignment there are no constraints on the material or the shape, you can choose what you want. What are the candidates for the envelope material? Well any material that is lightweight which can hold the hot air which can withstand the temperature and also be sturdy enough to be able to take all the loads acting on it and of course since we have to build the balloon it should be easy to seal it up. So one can use newspaper because newspaper is very easily available, it is lightweight, it can hold the gas in fact it meets all requirements except perhaps newspaper is easily combustible. So by any chance if the flame comes near or on the newspaper because of some drift or because of some sideward motion of the balloon then it will catch fire and then it will not become reusable. One can use plastic bags or the bin liners as we call them which are easily available, they are very lightweight, they can hold the gas and also they have some resistance towards temperature and in fact we have seen in our trials that some of these plastic bags are flame retardant. So therefore if a small amount of flame touches it can even sustain it for some time. One can also use kite paper, this is very popular, it is again paper but it is a special kind of paper which is used for kites which many students have tried. In fact if you place an order for a hot air balloon called as Akash Kandil during Diwali it is very commonly used. If you look at on Flipkart or Amazon you will find that one of the most commonly available balloons are the ones using kite paper. Another discovery is that a butter paper which is the translucent piece of paper is also very popular and it can be used to make the envelope. But in short there is no limit, there is no restriction, anything that you feel is meeting the requirements can be used by you. Every material has its own benefits and its own disadvantages. All right, to create hot air you need to heat it and one of the common ways of heating is to burn some fuel and collect the heat that is generated by it. So what are the candidates for the fuel? One could think of kerosene, so you can as shown in this particular example, you can soak a wick with kerosene and then just use a matchstick or any other device to lighten that. You can use a candle and that will create a lot of heat and hence generate the hot air. Remember you need fuel that creates very large amount of heat because you have only 4 minutes to make your balloon buoyant. The other option is petrol, highly inflammable, much better than even kerosene but very difficult to handle and also as you all know it is very very expensive nowadays. You can use candles because candles have wax which allows it to burn for a very long time. So you might be able to locate some light weight candles which give a large flame sufficient enough to create the hot air for the buoyancy or one can use highly ignitable components like camphor. But there are various other modes of heating, you can think of an electrical coil, you can think of any other method, so we do not impose any restriction. We allow you to be innovative and experimentative in these methods and you can choose your material, you can choose your shape and you can choose your fuel. The bottom line is that it should be able to generate buoyancy within 4 minutes, it should be able to travel a distance of 65 feet in the indoor fire in about 2 minutes and at the end of this it should touch the ceiling and then it should slowly come down and be recoverable that is all we need. Moving ahead, for example in one of our experiments we have used necron wire to generate heat but you know it becomes very heavy to have an on board system. Let us see how we can estimate the lift generated by a hot air balloon. So the simple formula is the difference in the density between the ambient air outside and the gas inside and the envelope volume which is the volume of the displaced fluid into G. So the density of air rho A will be equal to the local prevailing atmospheric pressure P A divided by the local temperature T A and the universal gas constant R and if you use P A upon R T A you will get the answer in kg per meter cube. Then similarly you can use P G upon R T G for calculating the rho G or the density of the lifting gas. Now the question is how do you calculate these parameters P A, P A and P G and T G. So for this you have to now devise some simple formula as well as some procedures which can be used by you. And also how do you calculate the envelope volume? This is from pure geometry so it should not be a big problem for you. Let us see when you go for the weight estimation because it is important to know the system weight and also the self weight. There are the total mass of the system consists of 3 components the mass of the payload which is decided by you. The only requirement as you know is that this total weight the payload has to be at least 15% of that. Mass of the fuel depends on what is your assessment through experimentation of the amount of fuel required to be able to generate buoyancy within 4 minutes and to rise within 2 minutes and hit the ceiling. And M structure is the mass of the envelope mass of the material and mass of any other thing that is mounted on the envelope. So 15% is the payload required and hence it can be shown that if the structure mass is considered as the mass of the envelope material and the base at which you put the fuel and ignite it. So then the first thing that you need to calculate is how do you estimate the M fuel. Or how much mass of fuel needs to be carried. So for that we need to first look at the sizing procedure. There are 2 possible approaches in doing this assignment. The first approach is that you assume some volume. So let us say you say okay I will start with a volume of say 20 cubic feet okay some number. So you assume some volume you select a candidate shape and then you do geometrical sizing that means you estimate the size of this particular envelope based on the shape and on the assumption of the material density and then you know the self weight. Then you start with lift estimation I will show you in a few minutes drag estimation weight estimation and then you calculate whether the lift is equal to or more than the weight and the drag. If you find that your estimated lift is going to be less than or equal to weight minus drag that means you have very little buoyancy available to pull the balloon up. So the payload weight is going to be basically lift minus weight minus drag. So the payload weight should be calculated. In fact the net lift written here is equal to the payload. If you feel that you have taken the correct volume and you get W payload is matching then you can just go ahead and fabricate. If you feel that it is too much higher you can reduce the volume or if you feel that I am getting a negative payload then you go ahead and increase the volume. So it is up to you okay the other way of doing it is you have to assume the fixed size that means you say okay I am going to make this particular shape of this particular size. This could be a limitation from the size of the material available in the market. For example if you are going to use butter paper as a material to build the envelope. Now butter paper is available in the market in some standard sizes right. There will be some particular width some particular length. Sometimes you have very long length you have roles available. So where you can say the length is quite large. But still depending on the width you will hit up with the limitations. So you assume some size of the balloon, you assume some shape of the balloon and then you calculate the volume. From the volume you estimate the lift from the shape you estimate the drag on the velocity using the velocity that it has to travel in our case it is 2 meters per second upwards. Calculate the weight then you just calculate okay what is my net lift that will be equal to lift minus weight minus drag. Then you can say okay is this enough for my payload? No please change the size. If it is much larger you would make it smaller. Generally you get a negative answer for payload so therefore you say okay we have to increase the volume. You keep on doing this till iteration and then you say okay we have finished the iteration. Now we have a balloon which has got enough payload the fraction is what we were planning. So then you can start fabrication. Remember you should keep some margin in your calculations always because when you actually fabricate the system you are going to encounter larger values of parameters.