 Let us have a look at how we can use the methodology for sizing of an indoor airship for a practical example and for that I will take you through a small tutorial. So we are going to follow a particular color scheme in this presentation. So anything that you see highlighted like this in yellow color means this is something that we this is something very out to pay attention because that is something new in the tutorial. The general instructions will be given in black color. The specified values also will be in black color. The values that we assume for some parameters are going to be in this blue color. The calculations to be done by you are going to be indicated in red color mostly by question marks and there will be a pause button where you are requested to pause the video, do the calculations and then continue because we will give you the answer after that. If you do not pause the video, if you continuously watch the video without pausing, you will not be learning anything because in any design exercise you learn by doing things. So we want you to learn, so therefore we want you to do these calculations with us, stop the video when you see the pause button or the red color, do the calculations and then compare with your numbers and then finally whatever values we calculate are going to be shown in this dark blue color. This is something which I have already shown you in the previous lecture about the motivation. We also know what is our problem. We know that we want to design something for capacity of 250 grams payload less than 4 meters in length and it should be electrically powered and look like a typical airship and these are the requirements which have been discussed in great detail. So if you have not watched the video regarding the sizing methodology, I would request you go back and watch that before you do this assignment. This is something new, input data and requirements. So what is the input data payload to 50 grams and let us assume that you want to design a airship which can fly at around 8 meter per second, quite a good speed. But we want to limit the endurance to 15 minutes and the calculations will be done under ISA conditions at sea level. So you can do these calculations at conditions which are appropriate to the place where you are flying the airship. What are our requirements? We want length to be less than 4 meters, we want volume to be less than 1.4 cubic meters because we want to use one cylinder of helium or hydrogen available in the market at 7 cubic meters about 4 times. Okay. The gas could be hydrogen or helium, we will see what happens with both of them and we want to go for 3 motors, trimotor configuration, one motor on the back for yaw force and one for forward thrust and one on down for giving us thrust vertical force if needed. This also I have already covered that we need to understand. I will skip this, let us go to the methodology. This also you know this methodology I have explained in detail. So we are going to envelope design which is the first thing is to assume the envelope length. We assume the length of the envelope. So let us say it is 3.5 meters, why? Because maximum limit is 4 meters I just said let us take 3.5 meters. First thing is envelope shape selection, you have already been told that there are many considerations okay but and also I mentioned to you about the standard shape which are available and also we have selected the envelope profile to be NPL for this particular exercise. Now for NPL this is as I mentioned to you L by D is 4. Now you can get numerical expressions for surface area and volume. If you define a parameter Xi which is the max diameter upon maximum length. So here D stands for max diameter and L stands for the total length okay. So you can calculate the eccentricity of the envelope using the formula given on the bottom and then with the eccentricity you can get the value of the surface area okay. The formula looks very very confusing, very complicated but do not worry it is not a big problem okay. So let us do surface area estimation for the envelope profile length 3.5 meters. We know that the diameter length diameter ratio is 4. So first you calculate the value of this Xi which is D by L. This is the first calculation that you have to do. So if L by D is 4 what is D by L it is 1 upon 4. Then we have to calculate the eccentricity of the envelope. Accentricity is given by this formula root of 1 minus 1.457 Xi square Xi already know as 0.25. So this is the second calculation for you take a pause calculate the number and then when you are ready you can play the video and you can compare with the number which we have calculated. Volume is given by this formula you know the value of L 3.5 meters you know the value of Xi 0.25 it is very simple just calculate the value that is the answer. Surface area yes this is a fairly fairly complicated question but remember the value of E is to be considered in radians when you calculate this number okay. So when you take sign inverse you have to take a sign inverse in radians that is a very common mistake many people do. So this is of course a very nasty formula. So I am for your ease I am putting all the numbers there and I would like you to calculate the value. So you can pause the video calculate the value and then compare with the value that we have got 7.755 square meters your numbers may differ slightly in the third or second decimal place does not matter. First cut volume estimate using the graph which I showed you last time and using this formula. So in our case the payload is 0.25 kg we put the value of payload and you can get volume is equal to payload that is 0.25 plus 0.5739 divide by 0.3093. Calculate the value please the value is 2.66 cubic meters but we got a much different volume when we did the calculations in the previous slide. The reason is that we are looking at the extreme bottom of the graph which is for payload from 0 to 20 kg whereas ours is only 0.25 kg. So actually this graph may not be directly useful for you. So therefore it is just an initial estimate. Young has gone for shape classification. So young was a scientist who worked on various kinds of airships there is one very famous series called R101 series. So he got this equation of for area and volume for a class of airships as a function of D and L. So he plotted so if you plot some existing airships like from aero drum or RC blimps you find that they are slightly higher young surface factor compared to what he has got. Similarly if you plot the young's volume factor you also find that these airships have a slightly higher value. So does not matter. Let us look at the aerostatic lift estimation. So we have the envelope volume 1.403 cubic meters we have the density of ambient air under ISA conditions. If we assume hydrogen as a lifting gas we have the gas density under ISA conditions. So therefore the lifting capacity will be obtained directly by subtracting 1.2256 minus 0.0841 we will give you 1.1415. That means for every cubic meters of hydrogen inside the balloon you can get a vertical force of around 1 kg and 140 grams. So can you calculate the net lift which is the lifting capacity into the volume of the envelope. So what is the net lift available from the airship that we have chosen of 3.5 meters length it is 1.602 kgs. That means the entire weight of the airship minus the weight I mean including the payload should be less than 1.6 only then we will be able to get lift. If we repeat the same calculations for helium which has a gas density higher than that of hydrogen the lifting capacity is lower it is around 1.0594 kg per meter cube. So once again can we calculate the net lift that can be obtained by 1.403 cubic meters worth of volume of the gas the value is only 1.486 kg. So you can see that there is a difference between the lifting capacity of hydrogen and helium. And now we look at the surface area and envelope material selection and the weight estimation. So you already know the features of an envelope material I do not have to repeat it. We also know what are the candidates available this also I discussed in my previous lecture. Let us go for specific material so if you choose a material of 65 GSM which has all these advantages it is flexible it has got low gas permeability light weight and heat syllable these are the positive features so this material is suitable. So if it is metallized nylon citric GSM area comes to 7.756 already calculated and we need to assume a 15% margin for joints and patches because you are going to join the petals you will along the length of the airship there will be some overlap and therefore there will be joint weight then there are going to be some patches to put hooks etc. So therefore you need to give margin of 15% for the additional weight of the material due to patches and joints. So therefore the envelope mass could be estimated as 15% margin included surface area into the envelope GSM. So can you calculate this value please it is 579.73 grams so close to 580 grams is the weight of just the envelope and this is the finished envelope that we got going ahead let us go to get the gondola. As you know there are several materials which can be used for gondola we want to look for a lightweight material. In our case we assume that the gondola is made from HDP high density polyethylene which has got a material density of 20 kg per cubic meter like a thermocall piece. So basically if you take material of length 0.26 meter, width 0.25 meters and thickness 5 centimeter that block of that particular sheet can be cut into pieces and joined together to create the gondola. So with this you can calculate the gondola weight in grams 20 kg per cubic meter will become 20,000 grams per cubic meter. So with that can you estimate the gondola weight? It is just 65 grams so it is a very very lightweight gondola. We have to attach the motors on the gondola as discussed now let us come to fin sizing. So for fin sizing as I mentioned we use standard parameters which are available in literature based on a survey of existing airships. So let us estimate the fin area the envelope area is known to us and there is a area ratio of 0.0594. Therefore the area of the fins total that is S fin comma t is going to be by this expression. Can you estimate the value please? The number is 0.4607 square meters. Then you can calculate the value of b which is the span semi span. For that we use the aspect ratio of the fins factor. So calculate the value please it is 0.2754. Then to calculate the root chord because we know the span to chord ratio from the table and we also know now the span you can get the root chord. Can you calculate the value 0.4896 meters. Then CT or the tip chord is nothing but root chord into taper ratio. Already you know root chord value so you can calculate this very quickly 0.4896 into 0.7083. The value is 0.3468 meters. So once you know the value you can calculate the value of each fin. Each fin will be obtained as a trapezoidal so a simple formula of trapezium where b will be the span and CT and CR will be the two edges. So this is the area of each fin 0.1152 square meters and if you make it 4 times you will get the weight of the total fin area. So fin mass estimation so total fin area is already known to us you multiply by fin material density. So for fin material we have assumed HDPE or some kind of a sheet of weight 250 grams of square meter plus you need to give some margin for velcro that you put on the bottom of the envelope and also ropes etc. So let us say 10% margin. So W fin is going to be 1.1 into 0.4607 into 250. Please calculate the value the value is 126.7 grams. Coming to the drag computation now drag estimation we have to use the formulae available in literature because one option is as I said you can do CFD analysis and get the value that takes time and effort and that is not very straightforward. We can look at literature and try to get some values of the drag coefficient. So bare hull drag can be estimated based on the Reynolds number for various kinds of airships and you have to multiply it by 2 because it is generally seen that drag of the whole airship is twice the drag of the envelope. So you can get now there is a confusion many people have between CD volume based and CD area based. So normalized with area will be D upon half rho V square A and normalized with volume will be D upon half rho V square V power 2 by 3. So be very careful. We looked at some data in open literature for small airships. There is an airship called Lotte which was the first solar powered airship developed in University of Stuttgart and we got some data regarding its drag coefficient. There is one number for bare hull and there are numbers for various deflections. So you can get the value from there. You can also use the Horner's formula which depends only on finest ratio that is the length upon diameter and also the Reynolds number. But the problem is this is completely independent of the envelope shape. So all shapes which have the same finest ratio and the same Reynolds number are going to have the same drag. So let us just check. So if you check this formula, if you check this formula against the Zeon data where L by D is 4 and Reynolds number is 7.3 million, you get the value of CDV as 0.029 whereas Horner's formula gives 0.025, which is a fairly close match, 13 percent error. So let us calculate the Reynolds number. So the length is 3.5 meters, velocity is 8 meter per second, viscosity 1.46. So therefore you can get Reynolds number as 8 into 3.5 divided by 1.46 into power minus 5. Calculate the value please. The value comes out to be 1.917 million. Remember whenever we mention about Reynolds number we normally speak in millions. So it is around 2 million. So we know the envelope L by D ratio. We also have the Reynolds number. So using the Horner's equation one can easily calculate the CDV value. So that number I would like you to calculate now. It is 0.03097. So now let us calculate the drag and thrust. We know that the envelope volume and the CDV values have been already calculated. Enveloped drag will be half into rho into velocity square into envelope volume power 2 by 3 into CDV because that is how we define the CDV. All numbers are known to us. So can you please insert the value and calculate? The answer is 1.5 Newton. Total drag will be twice because this is only for the envelope. So it will be around 3 Newton. That comes to 310 grams. So that means we need to put motors which can give thrust of at least 310 grams to be able to get 8 meter per second with this particular airship. Coming to the last part of the methodology, we look at the electrical motor selection and weight estimation. So thrust required is known to us 310 grams. We have this graph which has got a formula for motor weight. So from there you can estimate the motor weight. Please do the calculation and get the number. The answer is 38.6 grams approximately. Then number of cells required are available from that expression in terms of thrust required. Thrust required is 310.38 grams. So it comes to 2.31 which means it has to be more than 2 and less than 3. So you can go for 2 cells or 3 cells depending on what you think is appropriate for your airship. Then we go for current and propeller estimate diameters. Current has to be calculated and remember we have to increase by 20 percent. So this is the formula for current which requires you to put only inside the value of thrust required. So what is the value you get? 6.28 amperes. Put 20 percent more you get 7.52 amperes. So 7.52 amperes is the current rating of the motor and now we need to get propeller diameter. So again we use the same equation on the right hand side and you get the value. The value is 6.66 inches. Battery and ionic selection. So to estimate the capacity of the battery we start with the endurance of 15 minutes and the current is 7.52 amperes. So the capacity will be 2 into current into 100 into endurance. So that would be basically calculated and that is 3760 milliampere. So you require a battery of 3760 milliampere hours. So battery capacity is known. Should we go for 2 cell or 3 cell? Well let us check both of them. For 2 cell batteries there is a formula which has to be used. So please pause the video and calculate the battery mass for 2 cell battery. It is this grams. For 3 cell battery you have a similar formula. Please insert the values and calculate. It is 404 grams. So we prefer a 2 cell battery because it is coming very heavy. 404 grams is quite heavy for the battery. So we go with 2 cell battery. So now we need other equipment on the airship to be able to be remotely controlled. So there is a receiver which is around 30 grams. You need a battery which we have found at 2.66 grams. Then there are thrust motors and the lift motor. We assume them to be the same, 37, 38.7 grams. There is a yaw motor which is 19.3 grams. Then assume some wire weight. Then there are 3 speed controllers. Each of 15 grams can be assumed. So 45 grams. 3 propellers each of 10 grams. So add up all of this to get the mass of Avionics. It comes to 487.8 kg. So envelope is 579.7. Avionics is 487.7. Finns are 126.6 and Gondola is 65. So the total empty weight if you add up comes to 1259.11 grams. Now we estimate the CG. So what we do for that is for each component we will calculate the weight and the CG location and then do a product of these two to get the moment arm. So envelope is located at 1.6 meters from the nose, the CG of the envelope and the weight is 579.73. Therefore the moment arm will be the product of 579.73 and 16. Similarly for Avionics they are located slightly ahead because they will be on the Gondola. Calculate the value please. Just multiply 487.8 with 1.3 is 374.14 grams. Then Finns are having a large moment arm because they are located very far away. So their contribution is 354.7. Gondola is very small 55 grams located at 1.3. So it is only 84.5. The total weight is 1259.11 and the total moment arm is 2000.93. So CG will be this number divided by the total weight. So CG of the whole airship is going to be at 1.589 meters or 1.6 meters. So envelope CG is where the total aircraft CG is lying roughly. Now we check the payload requirement. So the empty weight is known now. Assuming that we have to carry 90 grams of ballast for controlling and for margin. If we use hydrogen, net lift 1602, excess lift will be calculated by net lift minus empty weight minus ballast. How much is that going to be? That is 252.89 grams. Therefore our requirement of 250 grams is met with a margin of 2.89 grams. It is a very small margin but nevertheless it meets our requirement. If we use helium on the other hand, the net lift is 1486 grams. The excess lift is nothing but net lift minus empty weight minus ballast. So you put the numbers there. What do you get? You get payload as 136.89 grams. So although this airship can carry some payload, it is not 250 grams. So requirement is not met. So what do we do? Either we shift to hydrogen with the same length 3.5 meters and you meet the requirement or you have to increase the length and then use helium. So this is the final parameters of the airship. The envelope shape is NPL, the length is 3.5, payload is 250 grams with 2.8 grams margin, metallized polymer of 65 GSM, volume 1.4 and the lifting gas hydrogen. Now let us see what happens if you change some of the parameters. For example, we have chosen the length to be 3.5 meters and we got a payload of around 2, with the excess of around 2.5 grams, 250 grams plus a margin of around 250 grams. That was for the length of 3.5 meters and for the gas to be hydrogen. If we use helium, we were getting negative payload or negative, I mean not 250 grams. Then what happens if you change the gas? What happens if you change the shape? What if the material of the envelope is changed? So all these things they can be checked if you make create a spreadsheet using the formula which I have shared with you. So here is an example of that spreadsheet. So in this spreadsheet you will notice that we are going for the baseline case. So the payload is 0.25 kg, velocity is 8 meter per second, endurance is 15 minutes or 0.25 hours. We are at sea level under ISA conditions. And the lifting gas is 1 which means it is hydrogen, envelope shape is NPL and the length is 3.5 meters. So this is what I have done in the tutorial. And if you do the calculations for it, you will see that we get a net payload of 252.51 grams which is 2.5 grams margin at an excess payload. If I change the gas from hydrogen to helium by putting helium here, you will notice that you will get payload of only 137.32 grams. So the excess payload is negative because we want 250 grams of payload. So similarly, if I make the length of the envelope, suppose I make it 4 meters and I keep the gas as helium, I will get not 250 but 459 grams therefore the excess payload is 2.09. So therefore what I can do is I can find out what should be the length so that I get excess payload equal to 0. So for that I will do what is called as a goal seek. So in goal seek, you go to what if analysis, you go to goal seek and you say that this cell L10 which is the value, I want to set this cell to 0 and I want to change the length of the airship. I want to change the airship length. So if I do that, it calculates and tells you that 3.5 is not enough but 3.71 meters length if you do then with helium also you will get the payload of 250 grams. So this is an example of using the power of excel and spreadsheet to calculate. Similarly, I can say suppose I now make the lifting gas back to hydrogen and if I make the lifting gases hydrogen then what happens? So you can see the difference. So if I make this as, so earlier I was getting an excess payload of exactly 2.5 grams, now I am getting 137 grams. I put this back to 3.5, I will be able to recover the numbers that I have earlier. Now let us go to change of shape. So suppose you change the shape to GNVR and you go to 3.5 meters length and you go again back to hydrogen. So then what happens is you see if you take a GNVR shape you can get for the same length of 3.5 meters you can get payload of 719 grams that means your excess payload is 470 grams 469 grams. So GNVR shape is much better even though GNVR shape may have more self weight but its volume is much better. So like that you can do various kinds of what if scenarios to check. Let us see what happens if I change this lifting gas to helium. So with helium I will get slightly lower payload capacity compared to hydrogen but still I get 535 grams which is 285 is more than the double. So this way you can actually investigate various scenarios. Thanks a lot we will be open for any queries through our discussion forum where you can put your questions.