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Exam Problem by Dr. Judy Wood: Space Shuttle Columbia Disaster by @mes on 3Speak
In this video, I go over an exam problem that Dr. Judy Wood gave her Mechanics of Materials class on February 6, 2003, in which she solved the cause of the Space Shuttle Columbia disaster that had ...
Tags: #math #science #physics #space #nasa #scifimultiverse #chessbrothers #drjudywood #engineer
Hi, it's time for another math. Easy solution. Today I'm going to go over a pretty epic tutorial, and this is actually an exam problem by Dr. Judy Wood, and it's on the Space Shuttle Columbia Disaster. And yeah, before I get to that, I just want to do some quick housekeeping. So I've been taking some time with ClaudeCode AI, basically revamping all my webpages and so on, and also taking the Hive notes that I usually do in the Hive blockchain, but then also mirroring them onto my website so I can make it ultra-fast and do some a bunch of stuff with it as well. So for example, you go to MMS.fm slash math, so I have it that looks all pretty neat and tidy here. click on the live streams, you can go at different tutorials here, and I'll be adding more and more on there. For example, here's vector functions. You can see the vector functions, here's the list here, and you can go list views, see all the screenshots, and so on. So, for example, the latest one at Problems Plus, here's all the notes in here, and here's all those sections of it as well, of the playlist for separate videos, and you can also see there's links to going to each separate chapter on it, and so on. And you can also collapse all of these. Yeah, you can collapse, this right here, it will basically collapse all these. You can go problems plus questions, there's the solutions, and so on, different ones over there, problem one, two, three, four, five. And also, as always, you can open up the playlist, and then you go into each individual one, and I also take the notes associated with that specific section of that full notes. And again, you can see this, and so on, all the videos there, and so on. All right, let's go further. And again, yeah, the video notes, they're all going to be in the timestamps, PDF, and Hive article notes. We'll all be just on this link right here. I'll update this. when I basically publish this video and then move these notes onto high blockchain in the mirror, and then do a bunch of stuff there. So, I mean, ms.d.fm slash space shuttle, space dash shuttle, Columbia, and that'll be the notes where basically that you're looking at right here will be all on there. And also, I also made some browser extensions. So you can play back videos fast using this word here, MAS. FM slash video speed. And again, I always recommend that because your brain gets used to faster speed. And also, again, back, with the time stamps, you could skip this intro and so on, and also make, I'll make short clips of all this giant video. Anyways, let's jump right in, so introduction. So this is a problem for mechanics of engineering course EM304, the Dr. Judy Wood, author of the famous book, Where Did the Towers Go, and where I also put a link to it, basically, in all my math tutorials there. And yeah, highly recommend that. Yeah, so she gave to her class in Clemson University on... Yeah, on February 6, 2003. And she has sent me the test problem and solutions keys so that I can make this tutorial, and you can view and download the PDF right here, this right here, if you go to MES.fm slash EM-3 -04, dash problem 1, dash Judy Wood. So I upload the PDF over there, and also here's the notes and article format, again, after I finish this video. If you click on this one, it should open up again using a cloud and put it on my website. and there it is, there's the full thing, you can open in full screen. Yeah, and yeah, you can go over and read that and how she scores the problems there was actually four problems. but in this one, there's this problem one of this one right here, but there's other problems are not shown, and also that she does an honor pledge I've neither given or received any unauthorized help on this exam. It's a pretty epic stuff there. So there it is, there is the full problem. You can go and scroll through it, and there is the solution key and so on, and some notes from basically test results from Scott Hubbard that was investigating the Space Shuttle Columbia, which I'll get to later in this epic long video. All right, so let's jump right in, so topics to cover, so we'll go over live footage of the Space Shuttle Columbia disaster, and then Problem 1 of EM 304, test number 1, February 6, 2003. Keep that date in mind, because the Submish Shuttle Columbia disaster was February 1st, 2003, so literally five days later. So solution review of strain and thermal expansion. I'll do a bunch of review here just because it's been a long while since I covered this, but also I think it'll be, yeah, worthwhile. And then we'll also cover 2014-T6 aluminum alloy. Yeah, yeah, that's what the tube was used in the wing. of the space channel. So I'll go over elastic constant, constants, Yong's, modulus, modulus, shear stress, shere stress, posons, ratio, and then look at strength limits, allowable stresses, and as well as show off my calculator made with the clot code code, so it's pretty epic. So MES mechanics of materials calculators, so definitely check. that out so solution to part a will go to maximum temperature without failure candidate one aluminum tube and compression that's point C then candidate two plate bearing at the tube and point and again I'll read the full thing here again because you can skip in the timestamps and so on but I'm gonna read for completing the sake so candidate three shear at the plate connections we're gonna basically check different candidates for where it fails It's aluminum 2, plate bearing, or we got the shear at the plate connection. And then solution to part B, where it fails first, and solution to part C, stress state at the failure temperature, and then solution to part D, volume, element sketches, and then summary of the engineering logic. And, yeah, going further, so Dr. Judy Wood solved the space shuttle Columbia disaster right away. and the C-A-I-B investigator, Scott Hubbard, is basically Columbia Accident Investigation Board. Scott Hubbard, the investigator on April 15th, 2003 presentation, he confirmed Dr. Judy Wood's analysis. So she did this in February 6th, this exam, and then in April 15th, he does a basic presentation saying, yeah, exactly what she did, but again, they didn't communicate out. I don't think it was just, yeah, basically NASA slash the sky investigators, they solved it after Judy Wood gave her presentation, you know, gave her test problem in her university, which is quite remarkable. And also go over further, so we'll look at the space shuttle disaster, the Columbia Accident Investigation Board, and I'll put this C-A -I-B. Like that. And then CNN anchor, this is just pretty mind-boggling. The CNN-Woodruff, transcript of CNN's February 6, 2003, Live Columbia Memorial, yeah, footage there. And it's literally at the same time that the Dr. Judy Woods is... giving her test to her students on that same day. So, news footage of the Columbia disaster as well. All right, yeah, I'll cover that then, but also now at the beginning, I'm going to cover this live footage, just so we get some context of the exam problem. So live footage of the space shuttle, Columbia disaster, and I think I spelled this wrong disaster, or Z. So, yeah, so footage from February 1st, the... 2003 of the disaster can be seen at the two-minute timestamp as the space shuttle is disintegrating upon entry through the atmosphere. And you could go on here. This is Fox News live footage. NASA loses touch with shuttle just before landing. And I'll click this right here. Yeah, and here's the video right here. And actually, I'm going to go back 11 seconds because a pretty interesting sound by here. Play it right here. And the windows shook in their house. They thought it was a sonic boom going overhead. Another guy described it like a tornado, very loud and intense, shook his whole house. It was loud enough, and it was low enough, he thought, that it shook his building, but still, is so incredibly high in the air. It could have been an explosion rather than a structural failure, so, you know, that'll have to come in the analysis later on. You know, Captain Lovell, you know better than anyone, really, what these astronauts on board were experiencing as they were coming in for a landing. What's it like on board 16 minutes before you're supposed to land? I can imagine that everybody must be, is it tense, or is it exciting? Well, I've never been on a shuttle of the orbiter, so I don't really know, but I was suspect there's sort of a side relief that coming back home, there's only 16 minutes from landing at the Cape. And, you know, we've had well over 100 of these flights, and the vehicles have worked perfectly. And so, you know, actually, if you look at the analysis, all of our shuttle accidents have occurred inside or near, or in the atmosphere. So it's the atmospheric part of the flights that are probably the most critical for any kind of a failure. Yeah, so it's pretty well. I'm going to close this right here. Yes, you can see disintegrating. They're not talking about it. not live or not, anyways, it's pretty interesting. So then also at the 4331 time stamps, the thermal tile damage is mentioned as a possible cause. If I go over to, yeah, 4331. All right, here, over here, 4331 or just a second's behind, I'm going to place. because it could expose them to toxic propellants, so they're telling people instead to call 911. Shortly after launch on this mission, the launch on January 16th, it appears the piece of foam insulation broke off the external fuel tank and struck the shuttle's left wing, possibly damaging heat-resistant tiles designed to protect the shuttle during re-entry. That impact was on the left wing. and certainly we have all the indications that Milt talked to you about were on the left wing. We can't discount that there might be a connection. Okay, so I'm at the left wing there and the thermal and howl damage there. I can find the footage in them showing it, but that's again, that's the same day or a day or day after, depending on the time zone. And here is a thermal tile damage during the launch on January 16, 2003, in which a piece of foam from the rocket booster breaks off and strikes the left wing. You see it a bit here. I'll draw this in blue here. So here's that tile right here. So apparently it's like a foam tile somewhere there. It falls over there. So it's floating in the into sky right there, and it's going to hit this wing and it's going to like literally... dustify according to the doctor. So I'm going to go back here. All right, so here's that video where I'm going to play this right here. Space Shuttle, Columbia, Debris strike, January 16,0003, mission STS 107. And this should be enhanced side view of the foam strike to Columbia's left wing, 81 .9 seconds after lift off from camera E212. So you can see right here. Here's the frame with that. You can see it flying and hits it. it dustifies across. So, strikes it there, and yeah, just basically 81 seconds during the launch. And then they flew all the way up, and then during re-entries, and when you're going super fast, and all that writes through it to it. And there's a foam strike. This is, we'll show that later. This was when they're doing analysis on seeing a foam can damage stuff. So I'm going to start closing some stuff, and let's get back into the show. So there it is, there's a little piece there. And yeah, so Dr. Drew Wood saw that during the day and the days, and so on news coverage, and then thought might as well do a problem on this. All right, so now let's jump right in. So problem one of EM or mechanics of materials, 304, test number one, February 6,003. Yeah, and also test from one, because Dr. Jew would give, I think, different versions of the same tests so that people, if they're trying to cheat. If they try to get the right, yeah, copy the person's answers, the numbers might be all off, so they'll get it wrong because they're copying the wrong test. That's pretty genius there. So last, so here's from her book, I mean, from her test. So last Saturday, February 1st, 2003, the space shuttle Columbia disintegrated during re-entry through the Earth's atmosphere. One possible cost could be the loss of thermal tiles. So here is how this setup there. There's the main gear and so on. And then if you zoom into this part right here, so they have like these thermal tiles there to prevent overheating and so on. So yeah, so if you zoom in there, you're going to have a little thingy like this. That is the support. It's aluminum tube. So if you go to the wing there, so wing, skin, stringer covers, web, and trust supports. 11 honeycomb covers, interesting. Anyway, so it looks like this, so you have these plates, these are metal plates, and now you have this aluminum tube across, that's basically holding up the top and bottom of this wing there, so that's holding up a skin there, so looks like that, that's this part, so now we're told, assume tiles were lost in the localized zone shown below or shown above, actually, yeah, so assume that there's a thermal tile right here. and this is all that was removed. So basically, that foam hits it, and now this is gone. So basically, it strikes this, disintegrates it, or dustifies it, and that's gone. Yeah, so we're told, Assume tiles were lost in a localized zone shown below, exposing just one of the many aluminum stiffening tubes connected to both the top and bottom framework of the wing. And then assuming, yeah, assume the remaining structures completely insulated from heat and remains at zero degrees. So basically, it's saying that this is gone, but still assume everything else, including this part here, is all going to be 0 degrees Fahrenheit. Just assume that, yeah, it's all of 0. This is the only thing that's being heated, this tube from this zone. That's all that's being heated. These plates, assuming everything is just going to be 0. So just for simplicity purposes. Yeah, so assume the remaining structure is completely insulated from the heat and remains at 0 degrees Fahrenheit. Assume the one exposed tube is heated uniformly, so just heats completely at all throughout it once. So at 0 degrees Fahrenheit, the aluminum tube is stress-free and there are no gaps. All right, yeah, basically, yeah, there's no gaps anywhere, it's completely covered, and at zero degrees, there's no stress on it. So basically, the only stress that's going to happen is when it's heated and expands, and then that causes the resulting stress on, basically, where, on the supports that's holding it in itself as well, because it'll be compressed as it's trying to expand. So heat shields, insulate the structure from temperature various and jazz zone below, and assume the top and bottom of the framework is made of a solid plate. So these are solid plates, top and bottom, like that. and you just have thermal shield, thermal tiles, and so on. And yeah, this length L is between here. So this is L, this is our L there. And these are structural support surfaces, thermal tiles, and then we're asked, what is the temperature at failure right here? So in Fahrenheit, and it's a heat shield removed in this zone only, and there's the thermal tiles, and so on, L is constant. So let's say it's constant height there. I mean, L is just constant, it's not changing. Yeah, so if it's not changing, basically, it wants to expand, but then it's going to be being shrunk at the same time. So basically, the thermal and compression strain has to be well equal. All right, and now we have the zoomed -in portion, so we take this and then zoom in like that of this aluminum. tube there, so we have over here and we have three different sections to look at inside there, basically the elements inside. The first one's part A, and this will be later in the video we'll see, we'll be making use of this. So this part here, this element right here, is at the connection point, just on this along this. plane there. So as this is expanding upwards or wanting to expand, it's going to be putting a bunch of shear stress along this thing over here. So it's going to be sheer like that, and it's going to be, and you have to draw the corresponding diagrams like that. So it's going to be shearing, and then you have to be the equilibrium, because it's not moving there. So you just put them accordingly and so on, so we'll do that later in this video. So that's part A, and then, again, these are the structural support surfaces. and this is going to be a thickness of sport plate is 0.25 inches, or a quarter inch, and now we have Part C is basically on this element over there, move it over there, so it's going to be like that, and this is on the tube itself. So as it's expanding, as one expands, but it's not going to be allowed to because the plates can be forcing it not expand, just due to thermal expansions, and this can be compressing it, so you can have a bunch of compressive stress along the C. yeah, along this C element is basically indicating basically all them can be in compression like that, and assume it's uniform, really heated, and so on. So that's that, and then part B is this part right here, and that's actually on the support plate, but instead of shearing like that, it's going to be like, yeah, basically within this, or actually just in here, somewhere around there. So basically, in compression. So we're going to have this as it as is expanding, as it's pushing on it, now we have to compare this stress on this actual. yeah, the support plate, and that's going to be also in compression and so on, and find where it fails, and so on. And here we're told that it's an end connector, quote, rivet, and yeah, so that's useful, well, that's used for in this part here, so that's the center of this cylinder, right, there's tube. So center portion, we're told as part of end connection, so this center one is connected to this right here, so this is the internal one, it's connected to this. and we're basically told to assume it's a quote rivet and does not support connections. Basically, just there just to keep these together, but it's not supporting load. All the load is based on this tube, this outer tube there. So then when we do our compression, the calculations, we all need to consider this outer area there. Yeah, so we're also told right here, now we're told the diameter inside, that's going to be, this is one inch. So this is from here to here. So we're ignoring the center there. Diameter outside is 1.2 inch. That's by 1.2 inch. And basically, the area of this yellow part, we're already given, is going to be 0 .11 pi inch squared. All right, so we have that. And now let's go further. Now we'll look at the material property. So we're given L is constant. So this is going to be constant right here, this length right here. So this L is constant, this is going to always be constant. So even though it's wanting to increase in thermal stress, it's going to be compressed from the support plates. And from there, we can obtain a formula and so on, because the displacement is going to be zero. So note, this is the length of the aluminum tube within the structural support and surface, yes, structural support surfaces, or support plates as shown in the earlier figure above. And also, now we're told the delta Tmax, or the change in temperature, equals to 3 ,000 degrees, and it's maximum possible. And then from Wiki, if you just go over that, says, during reentry, the thermal protection system TPS experienced temperatures up to 3,000 degrees Fahrenheit. or 1,648 degrees C, but had to keep the orbiter's vehicle's aluminum skin temperature below 350 degrees Fahrenheit or 180 degrees Celsius. All right, yeah, so basically the whole setup that this is given the maximum to deal with. We're not going to be dealing with any temperatures higher than that. That's during re-entry, but it had to keep it within this range there. All right, so let's take a look at the top and bottom plates. Yeah, and take a look at the material…
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