 In this video, I'd like to prepare you for a project, an upcoming project, in which you will fly, analyze, and then reverse engineer a Tian Deng. Tian Deng is a Chinese fire lantern, and when you receive it, it will come in a package where it will be nicely folded in a piece of paper looking something like this, although it may vary a little bit depending on the version that you get. First thing we want to do is go ahead and unwrap the package, and what we'll see as we unfold this is there's a fair amount of paper here, and we'll carefully sort of unfold the entire thing, and you can wait perhaps until you get to the field where you're going to fly it before you unfold it completely, but I'm going to go ahead and unfold this one and show you the parts that we're interested in. Okay, first of all, you have the large paper casing here. It's a large paper casing that's going to fill with air. Well, that won't work, but it's going to fill with hot air and sort of expand, and that's what's going to create our buoyancy. The other two parts, your second part here, is a frame that's made out of a very light wood. Okay, that's pieced together to make a square down here at the bottom, and then attached there by four small strings is the fuel cell, and this is the part that you're going to light on fire and try to hold the rest of the lantern very carefully away from it as it burns and heats up the inside. Okay, so there's a couple of measurements you want to take, well actually there's one particular measurement you want to take pre-flight. Before you fly the Tian Deng, and preferably when it's still folded, I probably should have said that, is what you want to do is go ahead and see if you can get a measurement of the mass of the entire lantern. Although I am going to suggest for the best accuracy, there is a light piece of tissue paper here that I'm going to remove. That's sort of a protective casing for the fuel cell. Remove that, toss it away, you won't need it again. Okay, and then measure the entire mass of this particular thing, of the whole lantern, and record that information, because you will need it later in your analysis. Then, part two, is you're going to prepare for a flight. Now the directions on preparing for the flight will be available for you in a document. However, there's a number of things that you want to actually measure during the flight, things you're going to want to capture, information you're going to want to capture during the flight. The way the flight is going to work is you are actually going to take the lantern, and you're going to create a tether. Now most of the time when you fly lanterns like this, you do not tether them, you do not want them staying to the ground, you want them to rise as high as possible, where they will eventually burn out, extinguish before they land to the ground. In this case, we want to do an analysis that will require that you tether the lantern with a twine that will be sort of wrapped around and sitting on the ground. So, over time, what's going to happen is the lantern is going to rise. Let me draw it over here, although hopefully it will rise mostly straight up. The lantern will rise, and as it does, it will add more tether off the ground, adding more weight. So, there will be a point where it stops rising and reaches what we call neutral buoyancy. And then, after it reaches neutral buoyancy, after a period of time it will start to sink, it will start to come down. When you're pretty clear it's not going to go any higher, you can go ahead and bring it back down using the tether very gently to bring it back down to the ground, and then as soon as you do so, you're going to take the flame that's inside it, by the way there's flame burning inside it there, and you're going to extinguish that flame. So, that's actually three points in time that we would like you to record. The time being the launch time when you first started on fire and you're about to release it, and even if you're not quite releasing it, even if you're holding it and waiting for it to get enough to launch, you still want to record when you first started on fire. So, we're going to record that time when we first ignite it. Then we're going to record to our best estimate a neutral buoyancy time, and when we reach that neutral buoyancy time, you're to put a little tag, a piece of tape, or something on there to measure the point at which the tether left the ground, and so we know where to cut the tether later, we're going to cut that line off there and measure the mass of that tether. And then again, when it comes back down, when you reach this point and you're spraying it out and putting out the flame, record that time as the extinguish time, the time when you're done. So, when you're done, you're going to have those four pieces of information, a marking for the tether and these three times, and then the other thing you'll need to record is an ambient temperature. Do your best to get a value for the temperature outside on that day when you launch the lantern. Now part of the process for launching the lantern, when you bring it back down, you're going to cut out the fuel cell and you're going to have a burnt fuel cell, hopefully that you stored in a jar or something like that to bring home for measurements. So now we're assuming at the point you've flown the lantern, you've gathered the flight information, you've gathered the pre-flight information, and now we're going to gather some additional information so that we can analyze the lantern. So the first thing you're going to do is you're going to note here, this piece here, this mass will be all burnt and crispy, much less mass than it was before of this fuel cell. You're going to take that and measure it using a balance to figure out what its mass is. In this case, you might have to measure the jar that it comes in the entire thing and then dump it out, measure the jar and determine what, measure the jar alone, and then determine the mass of the burnt fuel cell. So you're going to look for the remaining fuel mass. You're not doing the mass it's burnt, you're really recording, we'll calculate that later, you're really recording what's remaining there, but that will have been clipped out and cut so it will not be part of your lantern, it'll be set aside. So then you'll have a lantern that's hopefully not too toasted, that's still all in one piece. However, we don't want to measure it all in one piece, we're going to disassemble it. To disassemble it, you're going to look very carefully there along these pieces of wood and you should see, if you look carefully it's sort of hard to see where you are, but you'll be able to see that it's sort of glued around here, you'll want to use a scissors or an exacto knife or something to do your best to cut and release the wooden parts from the paper without destroying the paper too badly. I've done that to another lantern over here that I'm going to turn around and pick up. Here I have the disassembled pieces, notice there's a little bit of paper on there but that's not too meaningful, and I have this sort of square piece of wooden pieces that we're making the base of the lantern. I really only need two measurements from this. I can take this entire piece, put it on my balance and find the wooden frame mass. I'd like to know the mass of this wooden frame because we are interested in designing something like this a little bit later and we'd like to know basically how much weight there was involved in this. The other thing I would like to do is measure the length of this wooden frame. Now notice it's four parts so you could just measure one of them but you need to be very clear whether you're measuring one or all four parts. The length of the wooden frame pieces measured as well so you just measure that length. In this case we're not really going to care about the other two dimensions of this particular length. We're going to assume that they are relatively consistent and so we're going to have a specialized density measurement which isn't going to be based on mass per unit volume but instead just on mass per unit length because we'll assume a consistency of the thickness of this particular piece. So these two pieces will help us create a mass per unit length term. Okay, so we're done with this particular part. Now we need a couple other measurements. Here's the paper. You'll notice the edges have been a little bit sort of torn so I could actually release them from the frame but now I have this large piece of this large paper casing and the paper casing is actually divided into four parts that have been attached together. One, two, and then there's one on this side and one on the other side. So there's these four pieces that make up this paper frame. One of the things we want to do is do our best to refold this into something relatively small and then place it on our balance and try to balance it. You may need to take something, since it's so wide, you may need to take something like a plastic cup or something, set it on the balance, tear it with the plastic cup there and then set this on top so you can see underneath and actually read the values but we're going to find a mass value for this paper casing. Notice the paper casing we're also basically interested in how much mass it has per, well it's density effectively but in this case it's very thin and figuring out its volume is going to be difficult. The volume of the paper itself is going to be difficult. So what we're interested in is we're going to do some measurements so we know what the area of this particular thing is and then we'll get a value of mass per area for the paper so then if I design something using any given area I can work backwards and figure out what the mass will be as part of my design. So we're looking for two density values but there are densities that are based on some simplifications of volume where we either do density by length for the wooden frame or density by area for the paper. Well, how do we calculate the area of this paper when we have such a strange shape? I haven't memorized a formula for the shape of a truncated pedal. Whatever that actually shape is, there's probably a better mathematical term for it than I have no right now. But what we are going to do is we're going to use a process of measuring that will allow us to approximate this using what's called numerical integration but we're just going to take the measurements now. So what I'm going to ask you to do is take your large piece, lay it out, flatten it out so one of the sides is showing, we can always multiply by four. There is a symmetry here where all the sides are the same and what you're going to do is you're going to lay this down and do some measurements. Now it's difficult for me to sort of demonstrate this in the video so I'm going to assume that this drawing over here is what I see as I take this and I lay it down on a table to do my measurements. Okay, so take this, lay it down and get yourself a tool to measure the length a yardstick or some sort of tape measure. So here I am with my yardstick and I'm going to use it to measure the length that's along or to measure this entire sort of area. But here's how I'm going to do it. I'm going to go ahead and slice this into a number of different parts and it seems to me the best way to go about doing that is going to be to sort of slice it along the horizontal in slices that are as even as possible. Now they do not have to be a hundred percent even but I like to make them as even as possible. If I look at this particular length there it looks to be, okay, on this scale this is roughly about 45 centimeters so I'm going to do it about every five centimeters or so. Actually five centimeters or two inches is actually a pretty good measurement for doing the full lantern as well. But I'm going to take and try to do my best to draw a vertical line from the tip of the Tian Deng down to the base, trying to make it perpendicular with the base. Now that I've created that line I'm going to measure off intervals as evenly as possible but they don't have to be perfect, as evenly as possible except for maybe the last one. So in this particular case I'm going to mark off relatively easy intervals. In my case it's every five centimeters or so. Turns out mine actually goes almost exactly to 45 but that last one may be a little different for you so that's okay if it is you can mark what it is. And then what I'm going to go ahead and put here is make a little chart, a chart for the height and the width of each of these markings. Now this might be a little confusing because I'm starting from the bottom and then measuring up okay but I'm going to start with my first data point actually being at a height zero from the bottom. I should put my units up here and then I'm going every five centimeters, 15, 5, 10, 15, 20, 20, 30, 35, 40, 45. Now that I've established those vertical locations I am then for each of those locations going to measure horizontally do the best I can to go perpendicularly horizontal across, whoops that was not quite high enough. If you feel insecure about your ability to draw horizontal lines you could even measure some, make another set of measurements along each side and help line yourself up there. So now that I've done that I would like to get a value for the entire width across the lantern face. So I will measure across the lantern face here, here I estimate something as being 25, we'll say it's 20.5, I'm sorry 20.5 centimeters so I will go ahead and record that width here. Now notice since I said 20.5 centimeters there I'm going to the nearest, actually I could probably do even better if I wanted to because I do see the .5 but let's say I decide to go to only that sig fig, I should probably note that since I measured these out I am confident in the ones digit and that my fuzzy digit, my estimated digit is in the 10th place. So I'm going to say I'm happy with 20 centimeters and I have an estimated digit of a half. And then I'll measure the next one I would say 24 and probably .4 centimeters. So 24.4 centimeters. Similarly moving up all the way I get an estimate here of 28.3 etc. Notice your last value will have a width of zero although it is still important to record that as we will use it later in our calculations. So with that we have recorded our paper case geometry which is information we'll be able to use later to calculate a couple of important things namely the area, the surface area of the lantern and the area of each face which will help us determine the mass value to use for the paper or a density value to use for the paper. And then there's one more thing you have to measure before you're done with measurements and that will be the mass of the tether. So that long string that you had there, you'll take a scissors and cut it off wherever you marked it. You will separate it as well as with the sort of connecting mechanism from the lantern. It will have already been separated from the lantern and you take that and find the mass of that. And that would be the last piece you would need to have all the information you need for a successful analysis of the Tian Deng.