 Envelope sizing and fabrication, the first important task to be done is to select the envelope shape and for that we look at geometrical considerations. Now the best shape for an air for an airship purely from the point of view of itself weight and volume is spherical because a spherical shape has the least surface area per unit volume but the problem is that it has also a very high drag coefficient and because of that when you fly the spherical airship you may actually see lot of resistance and also there is unsteady shedding of vertices and therefore you can get oscillations behind the envelope. But if you look at aerodynamic considerations then the best shape is the one which has got high lift over drag or L by D ratio. This will give you a longish envelope because higher L by D means more length and less diameter. So you will have more surface area per unit volume that is a problem because it will be heavy but it will give you lower area of the stabilizer because now you have a larger moment arm for a given area of the stabilizer. So you can even reduce the stabilizer area. So these are the two considerations but ultimately we need to have a compromise solution. We need to look at geometrical considerations also and aerodynamic considerations also. So this is a graph which can be helpful to you in the first cut volume estimate. So in this graph various commercially available airships have been selected and their data have been plotted in volume, you know the payload in kilograms versus the volume. So on the y axis we have the payload ranging from something like 0 to 20, 22 kilograms. On the x axis we have volume ranging from almost 2 cubic meters to maybe 55 cubic meters. So if you just flat a straight line fit you get the formula as listed below and this formula can be used to get a first cut estimate of the volume of the airship. And we will use this in the tutorial that will follow. As far as envelope geometry is concerned we have few choices from the standard shapes. One of the most popular and most well known low drag shape is the NPL shape given by the National Physical Laboratories of the UK. This shape consists of 2 ellipses and the ratio of the semi-major axis of these 2 airships is root 2. So if A is the semi-major axis of the front ellipse then root 2 times A is the semi-major axis of the rear ellipse and they both meet at the point of maximum diameter where both of them have the maximum diameter as B. So this shape has a L by D length to diameter ratio of 4. Another shape that is very popular although it is more suitable for aerostats it is very popular in the country in India is the shape given by the late professor GNV Rao of IISC Bangalore called as the GNVR shape. This shape is construct between ellipse, parabola and arc of a circle all of them intersect. So therefore the beauty of this shape is that for any given maximum diameter you can get mathematically explicit expressions for the coordinates because the front portion till max diameter is ellipse. The last portion is parabola and in between there is an arc of a circle. So very popular shape mostly used for aerostats first employed by ADRD Agra the DRDO laboratory in India that is the lead of LTA systems in the DRDO sector and then subsequently many people have also built airships including we have also built airship in IIT Bombay using this particular shape. Although GNV Rao has also given another shape called as a modified GNVR shape for an airship in which he extends the you know he basically puts a constant diameter portion at the intersection of ellipse and circle so that the L by D of the airships is increased to nearly 4.5. The next shape which I will like to talk about is a shape which has come from China it is the Xeon 1 airship was built by a university in China and they have also given some shape and the equations of this shape are available in open literature. So if you look at it is also possible to have a double ellipsoid shape where there are 2 ellipses joined together. For a double ellipsoid shape as I mentioned to you L by D is 4 and it can be shown that the location of the center of buoyancy is 48% of the length from the nose and there are other parameters which are already listed there. So double ellipsoid shape also is a very popular shape for indoor airships. Let us look at the features of the envelope material. So first of all one of the desirable features of the envelope is it should not weigh a lot per unit area. So that parameter is called as its surface density or specific weight and normally it is measured in grams per square meter. How much is the weight of 1 square meter? How much weight in grams is 1 square meter that is GSM. The typical paper that we use for photocopying is around 70, 80 GSM and the material that we use for airship envelopes could be from 40, 50 GSM to about 200 GSM. The second important requirement is that the permeability to the lifting gases should be low. Permeability is generally explained or expressed in terms of how much gas leaks out in liters per square meter of the envelope material per day. So the desirable value of permeability would be less than around 3 liters per square meter per day and there are fabrics available today which can give you much lower than this. But if you have 3 liters per square meter per day or lower it is good enough for you to plan for an airship. The tear strength should be as high as possible because that helps it to resist the tear. It should be flexible, the envelope material should be flexible because we need to deflate and inflate the airship several times. But one of the most important thing is the material should be sealable. One should be easily able to seal the material whether you use heat sealing or whether you use some other special technique like impulse sealing or RF sealing or you use simple glue to join the material. But sealability should be good and this becomes a very important criteria. Many materials who may be otherwise quite good, good from permeability point of view, from GSM point of view, from tear strength and flexibility point of view but they may not be sealable and hence they are not suitable for our work. So for indoor airships what are the candidate materials available in India easily in the market. The most common and the most popular material is metallized polymer, metallized nylon which comes in rolls and of various kinds of widths and generally it is 65 GSM or 150 GSM or in between. Then you can use PVC coated nylon, this is quite strong and we have built airships of this particular material, basic PVC coated with basic nylon coated with PVC okay and you can also use simple PVC, just a PVC sheet but PVC sheets tend to be slightly heavy. Some of the first airships that we built not indoor but outdoor they were of simple PVC but then we shifted to PVC coated nylon for outdoor airships. Indoor airships in IIT Bombay are mostly metallized polymer of various types. So sizing of the envelope I have already shown you, first thing you need to determine is what is the critical length of the envelope that is the length at which the buoyant lift is equal to self rate because up to this particular length the payload will be equal to 0 or negative okay. Beyond the critical length you start getting some payload and payload actually increases exponentially in airships when you increase the length okay. So the envelope length has to be definitely more than the critical length to get adequate payload. Okay you can say that the critical length puts the absolute lower limit on the size of the airship and after you achieve this number when you choose the envelope length to be higher than critical length you are guaranteed to get some payload you have to appropriately increase the length to get the required payload. Now another important thing is okay we can build the envelope we can fabricate the envelope but then the material used is flat sheet whereas the envelope is the 3 dimensional body. So to create a 3 dimensional body from a 2 dimensional flat sheet you need to use a method called as a petal profile generation. I will explain to you little bit about how so for example take the location which is at the maximum diameter of this airship as an example and look at the cross section at that place you will see that the cross section is actually a circular cross section. So most airships actually have a circular cross section for the envelope okay. Now this envelope can be divided into sectors. Now what you are seeing you should not get confused by looking at these as the sectors at the cross section consider this to be the front view consider the cross section of the envelope to be the front view of the airship and in the front view of the airship you will see that you are joining various petals with each other to create this particular shape. So these petals are shown as dotted line in the figure on the right. So now we need to work out how to get the dimensions of the petal. So what you can do is you can first decide how many number of petals are you going to put. So typically we have seen that if you have 6 petals or 8 petals then you get a reasonably good shape but if you get more number of petals let us say you make 10 petals or 12 petals normally they are all even numbers then there is a problem you have to work more although you will get better accuracy in the envelope shape but you have to work harder because each of these petals have to be joined all along its length okay. So let us say an example as shown here we have a 6 petal airship. So what we will do is we will calculate the angle between the so the angle will be 360 upon 6 so 60 degrees okay. So the petal will start and end at e 60 degree as we go along the cross section. So the width at any point of the petal will be 2 pi r divided by np because 2 pi r is the entire width and np is the number of petals. So the width of each petal is 2 pi r by np. So the cross section of the envelope is shown on the right hand side and on the left hand side we show the top view of the airship or the plan view of the airship showing the petals as you can see in this case there are 6 petals okay. So each petal looks somewhere like this so as we go along the length of the envelope in the side view there is a parameter called x at every location x there is some r or the width or the radius of the petal. So the width of the petal corresponding to the location x will be the maximum width will be 2 pi r by np or the width will be 2 pi r by np at every place okay. So for a length l at any length l along the petal where you have the length x along the curve of the petal okay you can see that the width will be 2 pi r by np okay. So because the length of the petal comes along the curved length of the envelope okay. So if you look at this you will find that so how do you get this particular length so is you take a small section and then at that point the radius is r1 length is l1. So you can get this dimension now you can see that there is a difference between the length of the red hypotenuse of this triangle and the black line that is the error between the actual and the estimated length then go to the point number x2 and this way you can keep on doing it and by this you will be able to get the entire so the total length when you get match is equal to the length of the airship you can stop. So this is how we generate the geometry of the petal so how do you get the profile so this is the cross section at any point the width is 2 pi r by np so you cut the petals down as shown in the photograph below this is the photograph of one metallized nylon airship you can see that the petals have been drawn and they have been cut this is the template that we use so first we make one template for a petal and then we cut it I will show you a small video also another example of a petals cut for an airship made up of black epoxy coated PVC material. Now there are 3 methods available to join 2 petals with each other one method will be what is called as a butt joint in which you take 2 petals and you create a butt joint as shown okay one over the other or you can have a lap joint so you keep them touching each other and you put another small strip on it you could have a cusp joint also in which it comes together and there is a joint at the edges. So lap joints are always preferred over the cusp joint because cusp joint is going to create a change in the length of the airship so that has to be factored in when you create it okay so we always recommend that the lap joint type 2 is always preferable for envelope the one that is shown in the center that means you join the 2 envelope petals and then you put a small strip over it and then just join that strip to both the edges that normally gives us better shape and also it gives better resistance to internal stresses because of the gas pressure. So we recommend lap joint number 2 shown in the center of the figure also it reduces the leakage of the lifting gas considerably because there is a very solid proper joint between the outer fabric and the inner patch or the outer patch. So what you do is you cut the hull profile on an HDP mounting board then you place the petal edges together on the mounting board and then you can heat seal the joint by use of some small strip there are strips available which you can iron onto it and heat it. There are many other ways of doing it you can do it by glue also but this is a method which is easily doable in the laboratory provided the material is heat sealable on both sides or at least one side. Then you provide a self pressure sealing air filling duct so you make a small duct and by back pressure it becomes vacant and this at the top at the front and the back you end you where the petals are converging you actually put one end disc to avoid the leakage. So if you look at PVC or PVC coated fabrics you can use what is called as a RF sealing machine. We have one machine in our laboratory which we purchased many years ago and if you do not have this machine because this is very special although it works only on a certain class of fabrics then you can go for another machine which is not very expensive. It costs around 10 to 15,000 rupees it can be used for heat sealing of polyurethane, metallized polymer and nylon sheets something like this is used by shopkeepers also to seal the milk or any other grocery envelopes. So it is a very commonly available machine not very expensive. So let me show you a small video of the envelope fabrication. So you can see there is a white colored petal and on that we have marked the blue line which includes the margin for the assembly or fabrication of the envelope. So the petals have been cut now these petals are going to be joined to each other by a heat sealing machine in our case. So it is a very simple process but it needs 2-3 people to be working together. For glass leakage testing we have special tools available this particular tool actually is a helium sniffer. So we release small amount of helium in the envelope and wherever there is a leakage when it comes out you can sniff it and you will come to know that there is a leakage there. So here is an example of the finished envelope how it looks when you fully assemble it.