 sizing procedure for indoor remotely controlled airships. Let us first look at the motivation for developing this sizing procedure, we are looking at indoor remotely controlled airships which are a special class of airships. We want that these airships should look like an actual airship, we do not want to go into any odd shaped envelopes which may be easier to fabricate or any fancy shape. Also it should not be that it does not carry anything, so although it will not be used for any heavy payload because they are going to be small in size since they are indoor, it should definitely have some decent payload capacity so that at least a small camera or any other payload can be carried by the user. Also we want the airship to be fully functional, it should have proper 3 axis control in the pitch, in the yaw and in the roll domain. Let us first define the problem, we are looking at a situation when there is no systematic design approach available in open literature. Although there are textbooks, there are papers, there are handouts and various procedures available for sizing of an outdoor airship, whether it is remotely controlled, whether it is manned or autonomous but to the best of our knowledge there is no systematic design procedure available for sizing a small indoor airship. So this particular exercise helps to bridge that particular gap. So what do we need? We need a design and fabrication methodology for a non-rigid indoor airship. As you all know, airships can have various different internal structural configurations, they could be non-rigid which have no moving parts inside, they could be rigid which have rigid framework or they could be semi-rigid. In our case we are going to focus on the first and the simplest type which is the non-rigid indoor airship. As I mentioned, although it is meant for only indoor work it should have some decent payload capacity and in this exercise we are looking at approximately 250 grams of payload. It should be electrically powered because that is the most appropriate propulsion system for such small indoor airships. And to ensure that we can operate it from small and limited space available in indoor environment, we are putting a restriction that the length should be less than 4 meters. Anything more than 4 meters can be considered to be large enough not to be able to be handled easily indoors. Although there could be indoor stadia which can handle more than 4 meters airship very easily but generally we thought let us keep it within 4 meters. And that is why the testing area of this particular airship is expected to be any indoor hall or a classroom. So looking at the requirements we came up with the list of some parameters which have to be kept in mind. For it to be portable, see non-rigid airships the beauty is that they can be packed and they can be the envelope can be I mean once you detach the fin the gondola and the other avionic components when you have just the envelope you can deflate the envelope and you can fold it roll it and save it inside a box. So a typical suitcase that is carried under the birth of a railway train in India fits within the length of 68 centimeters, 49 centimeters and 28 centimeters. So we wanted that all the components of the airship perhaps except the fin maybe which can be just packed and kept standing we should be able to fit all the components inside this particular box. And then when we go and do a demo of this airship at some location at max within an hour we should be able to put it together. So it should have features which will allow it to be quickly dismantled. Since we want it to be maneuverable we would like it to be able to move in all directions and also it should be able to do a spot turn. By a spot turn I mean that the airship should be able to do an almost a 360 degree turn right at the place where it is without necessarily needing a large area or volume to do that. So the reason is that we are going to look for a typical demo arena as a enclosed area auditorium and sometimes you may be required to do a spot turn to bring the airship back towards you. The payload 250 grams could comprise of any onboard sensor or disposable items in many cases one can install a small box containing chocolates or cards which can be dropped on the people below just for fun or for sending a message. So that is why we wanted to have sufficient volume in the gondola of the airship to carry these small items totally about 250 grams in weight. Now whether you use hydrogen or you use helium for the lifting gas the commercially available cylinders come in about 7 cubic meter capacity. So if we buy one cylinder we should be able to use it for 4 fillings. So therefore the volume of the airship was constrained to be approximately 1 fourth of 7 cubic meters so that we can have 4 refills using one cylinder. Please note that the actual amount of gas which is generally available from a cylinder is not 7 cubic meters but around 6.5 cubic meters. So therefore at least it will allow more than 3 fillings. The endurance of the airship we wanted it to be sized the batteries to be sized such a way that it can at least fly for 15 minutes because when you do a demo if you do not do it for around 10 to 15 minutes it is not enough for the audience to understand and appreciate. The LTA gas could be either hydrogen or helium as you know hydrogen actually gives you more lift than helium around 7% higher lifting capacity but hydrogen is not very popular because it is combustible. Helium on the other hand is very inert however it is very very expensive and not easily available. So what we do is we size the airship for helium and then see if we can manage with with hydrogen you definitely get more lift than that. And very important requirement is the shape of the envelope it should look like a real airship and not some fancy shape. So let us start our calculations by a very simple look at aerostatics. So we need to understand the concept of gross and net lift. Gross lift is nothing but the product of density of the ambient air and the volume enclosed by the envelope of the LTA system that is a gross lift that is a total vertical force which will be created. So from the principle of buoyancy because we are displacing air due to the presence of the airship envelope therefore you will get gross lift is equal to rho A into V ENV where rho A stands for ambient air density and V ENV stands for envelope volume. The net lift is equal to the gross lift minus the mass of the lifting gas enclosed inside the volume. So it will be L gross minus rho G into V ENV or if you just take L gross formula it becomes rho A minus rho G into V ENV. So therefore the net lift that is available to you will be the difference of the density of the two gases outside and inside. This difference multiplied by the volume of the envelope will give you the gross, this difference will give you the net lift and that is what is available for you to lift the airship. So if the total mass of the airship is within this then you will get to be afloat otherwise you need to increase the volume. So the various factors which affect the net lift are listed as internal pressure, superheat, humidity, gas, purity, etc. But we are not going to really bother about that too much and also we have to understand that there are two important points the center of buoyancy and the center of gravity. Center of buoyancy is the volumetric center of the envelope where the net buoyancy force is expected to act and center of gravity is the center of mass and they both may not be the same. However in a good airship design we try to ensure the location of center of gravity to be right below the center of buoyancy so that we do not get any net moments when the airship starts moving. And then we need to understand the concept of static heaviness. Static heaviness is basically the amount of excess weight above the buoyancy that the airship has. So if I find that the net lift is say 100 units and the weight of the entire airship is 105 units then the airship is statically heavy by 5 units. So that is static heaviness. Normally when we fly airships we fly them statically heavy because if in case you lose control then you do not want them to drift up or stay in the air you want them to come down because of static heaviness. And also because as the airship develops lift when we make it fly forward some excess lift will be created and if it is not statically heavy then it will unnecessarily start climbing up so that also helps. Okay now let us look at the design methodology which we are going to follow. Envelope sizing is the first step that we need to do and envelope sizing is affected by many parameters. First of all it is the shape that you choose then the shapes will result in dimensions depending on the self weight of the envelope fabric which is a function of the material that you use for the airship and then the size of the envelope also depends on how much payload you carry. Larger the payload, larger will be the envelope size and also when we decide the material we also have to be careful that it should be easy to fabricate otherwise it will be theoretically very nice but very difficult to fabricate and ultimately this exercise is basically meant to teach you how to design an airship which you can eventually fabricate. So here is a broad overview of the design methodology that we will follow but I will take you through this one by one. So we start the process by an initial estimate of the envelope volume which we have to do it based on our past experience or based on some assumptions. Okay this is just a starting point because it is an iterative process and if this envelope volume that we have assumed is not enough you will be coming back to change it. If it is too large then you are going to have much higher payload than needed again you can reduce it. So this is iterative process. To start with you can assume the envelope volume to be one fourth of the cylinder volume because that is the constraint. So let us say you have assumed some number for the envelope volume the first thing that you do is you select the envelope. Now there are many criteria which are available for selection of the envelope we will discuss about them. I will show you a few typical envelope shapes I will talk about the merits and demerits of each of them. So you choose some shape remember our constraint is that we cannot choose some awkward or odd or fancy shape we need to choose a shape that looks like an actual airship which flies. Once we select the shape we can go ahead and do the geometric sizing. By geometry sizing what we mean is arriving at the dimensions like maximum diameter, length, surface area etc that is the next step. Once you estimate surface area of the airship you are then in a position to carry out the selection of the envelope material and hence you can estimate the weight because surface area is known to you. Once you do that you then go for tail sizing. Now a tail on an airship is required like on any aircraft to provide control and stability. So there are procedures available by which we can do what is the appropriate tail size for a particular shape of a particular dimension and because you have done the tail sizing you will be able to do the estimation of the weight of the tail. Then we create a CAD model of the whole airship because we would like to do some aerodynamic analysis. Now one other way of doing it is to make a wind tunnel model but then wind tunnel model is an expensive activity it is time consuming and how many models will you make because you may have to change the shape eventually. So generally what most people do is they create a CAD model and then they use standard computational dynamics techniques to estimate the drag and hence the power. Power comes from drag into velocity that is all. So you calculate how much power will be needed to overcome the requirements. Once you know the power then you can estimate you can select the electrical motors. Once you know the power that is available you can select the electrical motors which are appropriate to give that to meet the requirement and with that you can also get the weight of these electrical motors and the associated accessories which go with it. Finally we choose the avionics. Avionics are the electronic equipment that go on the airship for various purposes and with that once you choose the avionics you will get the avionics weight. Now since you have all the weights you can calculate the aerostatic lift because you have the envelope dimensions and the gas plus so and you also know the weight of envelope tail, electrical motors and avionics if you add that you get total weight. So the difference between the aerostatic lift available and the payload and total weight of the system if it is matching that means the payload requirement is met so you can stop or if you find that the payload requirement is not met you change the envelope volume either you can increase it or you can decrease it because if you have too much volume or if you have too much lift it is not good you will have to carry dead weight called the last to take care of it. So therefore it is good idea to maybe go back and reduce the volume and then this cycle keeps on iterating till convergence and once it is converged you get the output.