Demo a Course Session
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Demo Video Transcripts
00:00:15:15 OK, how are we doing?
00:00:19:11 How are you?
00:00:23:09 Maybe the snow's going away. That's a good thing. One can hope. Could be worse. We could be back East. I hear it's really bad.
00:00:33:11 Ready? We have virtual attendance. See, that's not bad.
00:00:36:15 And then it's ice. And I just-- I talked to a-- was supposed to meet with the guy for lunch today. And he's stuck in Columbus, Ohio. He's not even sure if his flight's going to get-- plane's going to get out today. So, OK, questions?
00:00:57:01 I'm going to say this probably poorly, but is there something called a indemnification clause about being-- from contract-- your contract-- I know I'm saying it wrong.
00:01:09:17 No, indemnification, so in general, it's whoever is indemnified, they're protected against legal actions under certain circumstances. So it's like indemnified and hold harmless. So that if a client-- I mean, we're-- I'm trying to give a decent example.
00:01:40:25 If you're in a contractual relationship but the other party behaves in a certain way that's reckless and irresponsible, there would be, presumably, clauses in the contract that would indemnify you from harm if things were brought forth. So I mean, just things like contractors are responsible for putting together storm water, erosion control plans. We would review those. But if it wasn't properly maintained, we'd be indemnified, I guess.
00:02:21:16 Was this a particular-- just something that popped into your mind? I was reading contract docs this morning. And part of the construction fitting, construction-- I think contract docs that said we'd do some observation had that clause in there at the end. So that way, I think if there's something wrong, we, as engineers, wouldn't get sued. The city would pay for our indemnification of that. I was trying to figure out what that--
00:02:45:05 So it would just be protecting and holding harmless for actions by others that we wouldn't be held responsible for, outcomes that happened. And it may come up again as we-- as we get more into the general conditions. Let's make sure we try and maybe catch that. OK, good. Other questions.
00:03:15:24 So I was going to share with you the Lewiston project here. We'll just go to overhead. I'll show a few things. As I've already told you, it's Lewiston, so that-- so here's the bid form, just to kind of get a sense of it. You can see in this case, your opening bids. There were four addenda. so when it was received, the number, initials, those types of things.
00:03:41:17 But what went South in this project is this particular language here. So this is under vertical turbine pumps. So a water pump, this was a water booster pump station. Under work included, so this is a technical spec, we haven't arrived at technical specs yet, but we will. And so they say in here, work included, "as a bid alternate, the contractor may propose vertical inline pumps."
00:04:12:04 And then the spec points the bidder to a particular section for the 50 and 100 gallon minute application only. If selected, the inline pumps shall be installed over the can. So these were pumps, cans that were already in place at the pump station, which should be covered with a blind flange as shown in the drawings.
00:04:33:15 The base-- so then it does say the base bid shall be for providing vertical turbine can pumps, which was the original spec one. And then any costs associated with providing and installing inline pumps shall be borne. So you read that, so you say, first you say, as a bid alternate, and then-- but then it clarifies then it says, well, but the base bid is for the vertical turbine can pumps, not the vertical turbine inline pumps, so slightly different.
00:05:08:01 So does allow for that. Not language I would have chosen. It led to, let's see, so here's the bid. So it was just it-- it was a lump sum project. Yeah, so the bidder shall list below the total lump sum bid prices. So this was a $1.8 million lump sum project, which is beyond my comfort range. That's a lot of money for a lump sum.
00:05:42:28 But no opportunity. It doesn't speak to base bid. It doesn't speak to alternate. But the technical specifications, which are part of the bidding documents, did speak to that. So they wrote in there their dollar amount. Then they said deduct $98,700 if vertical inline pumps are used. So they just wrote it in there because it was referred to in the technical specification.
00:06:07:18 So the bid form didn't account for a base bid. Didn't list alternates. And we've looked at the bid form in your document. And it's got that type of structure. So contractor, a very creative smart contractor, saw that opportunity. If we look at the total prices here, I'm not going to give you the names, although it really doesn't matter. This was several years ago.
00:06:33:19 And so you can see, so there's the-- there was their bid. It took them down to $1.719 million. You can see two other contractors observed the same, but they were not-- it wouldn't have dropped them to low bid. But you can see, so this is low bid, the apparent low bid with the deduct. Contractor 2 didn't deduct. And so you can see $1.818 versus $1.750. So this is number one, versus number two. Number one didn't list that. Number two did, these ones.
00:07:07:00 So now they're in a pickle, right? Because the technical specifications stipulated base bids, stipulated alternate. The bid form didn't include for it. Contractors address that, some of them. I won't-- I'll just read you from the letter. So during the bid process, so this is a letter from the contractor to the city, because they're hearing the bids might be rejected.
00:07:34:27 During the bid process, we conducted a thorough analysis of the bid contract documents provided by the city and project engineer of record, which again, is required in the instructions to bidders, in the bid form, thorough analysis. In the case of this project, the contract specification stated a bid alternative at the contractor's choice. It was clear at the contractor's choice.
00:07:55:00 This is clearly indicated in spec section, as copied below. And then the specs acknowledge the alternate is that the contractor's choice and not a requirement for the bid proposal. They found it in the best interest of the city. So they tried to make the compelling argument, you opened the door, you stipulated it, and then-- and then you're in this-- now you got yourself in a bind, because the bid form doesn't account for it.
00:08:21:07 And they didn't stipulate in the instructions to bidders how they might address that. So all of those things should have been covered. This is construction bidding 101 quite frankly. And the outcome was a rejection of all bids on basically a $2 million project. My understanding is the next time around, prices went up. And so it costs the city. And that low bidder, I mean, there are several good contractors out there.
00:08:48:26 That one in particular is a very good contractor, didn't bid. Walked away from it. And so there are consequences to our failures in putting together bid documents. And so, again, that's just 101. If you're going to develop a tech spec that allows for an alternative, you need to immediately put a note in your bid form somehow to catch it later on as you're developing that.
00:09:14:04 So that was a pretty bad one. And it cost-- it cost the city money. It cost the engineer money. So anyway, interesting one. So I'm sure there's more out there like that, unfortunately. So questions? Yeah.
00:09:32:11 What do you think is the leading factor for having-- for spec? Do you think is the transportation costs, like hauling equipment, or labor shortage?
00:09:45:29 So let me-- so we better understand your question, and I'll try and repeat for EOC. What actually in--
00:09:51:16 When bidding out a job, what is the biggest factor that makes it cheapest compared to more expensive?
00:09:58:23 Like for a contractor? I mean, it's going to vary by type of project, street project, underground utility project, where you're located. Mobilization costs are obviously expensive. Pipe materials can be expensive. Excavation is pretty fixed, probably. It's just equipment and labor. Pipe materials can vary substantially.
00:10:22:10 In today's world, I mean, who knows? Asbestos-- or asphalt concrete, any of the materials for road construction. So I'd say it's highly-- it's going to vary project to project on what drives the costs. And proximity-- certainly mobilization costs can affect things. Although we, again, we typically cap that as-- and most contractors will come in at, say, 5% pretty close to the cap on mobilization, et cetera, demobilization.
00:10:56:14 There's no one thing, though. So I'm not I'm not waffling. It's just highly variable, depending on the project. And these-- but these are the things that we do our best to stay on top of. It's one of the many hats we wear as engineers. Is we're doing the technical design, technical specifications, contract, thinking about pricing.
00:11:16:26 Making sure we're not gold-plating projects. I mean, this situation, this project in Colfax, now we're finding out that with new energy efficiency requirements in the state of Washington, it's requiring pump suppliers to upsize motors in order to get in the motors of a similar efficiency curve. And they're not maximum efficiency at maximum horsepower.
00:11:41:28 And so here we are, we've pulled out a system that's 75 horsepower. And unless we want to derate the capacity of the well, which really isn't desirable, we're probably going to have to bump to 100 horsepower, because you don't-- there isn't an 80 horsepower or 85 horsepower motor. It's 75 to 100.
00:11:59:09 So now we're in this-- we hadn't seen this coming. It was-- and trying to-- first thing you do is you let the client know, hey, energy standards in Washington might bump us to 100 horsepower. But then we got to go back and we got to look at all the electrical equipment. And what sort of domino effect does that have on the design and the cost, right?
00:12:22:29 It's a difficult-- it's an increasingly difficult environment to project design projects. OK, other questions? OK, so we left off here on this slide 29. This is unit pricing and contract management.
00:12:50:04 And this is one, I'm going to do my best to explain or give you an example on cash allowances. I'm going to-- you don't need to bounce to 14.03, but I will really quickly. If I go to instructions to bidders, get rid of that. 14.03, there's a little-- so in the instructions to bidders, for cash allowances, the bid price shall include such amounts as the bidder deems proper for contractor's overhead, et cetera.
00:13:23:15 So they're stipulating what's in a cash allowances piece. And then are there extra handouts? You want to pass one back to the back? Just pass one, just float one back. Oh, OK, OK, good. So it was here, and then gone, and then here? Somebody saved it for you? OK, that's good. That's good.
00:13:50:10 You got some friends back there. That's good. Because I wasn't going to pay one for you. And you can't ask for it in the next class either. I'm kidding. So here, so it's spelling out to the contractor, if there is a unit price contract, a line item for allowances, you would spell those out in your technical specifications.
00:14:14:24 And then it's also further covered. And we will spend some time-- I'll hit on Article 11 right now. But we'll come back to it more than once, because there is a lot of information there. But if we go to 11.02. Again, you don't need to bounce around here. Shortly, maybe we'll jump there for a while.
00:14:34:14 But this cash allowances contractor agrees. So in there, yeah? Sure. So I jumped to general conditions article 11, 11.02. sorry, I was-- it's one of the challenges, slides, I don't want to cut a whole bunch of stuff from the EJCDC into the slides. So we have to bounce back and forth. And I feel like Logan's still hasn't tapped his.
00:15:01:16 I honestly don't know what to do--
00:15:04:19 What time is it?
00:15:10:04 Yeah, so here's where it's spelled out, everything. And actually, article 11 in the general conditions, we'll come back to. Because one of my former grad students shared with me a really useful story about how to-- experience on how to deal with things like this. But here, contractor agrees that cash allowances include the cost to contractor of materials, equipment required by, to be delivered to the site, and all applicable taxes, and contractor's costs for doing all these things.
00:15:39:27 So it's right there in the general conditions on everything that needs to be the contractor if there is something for cash allowances. And so, sorry, we'll bounce back to the slides for a minute. What is it? It's a lump sum that you would put. You would just have a line item and a unit price contract. You would pay it off typically on a lump sum basis you can pay percent of, I suppose, that provides the owner with a general item to pay contractor for extras.
00:16:12:17 Maybe there's some uncertainty during the design, the contractor-- the owner's not quite sure what they might want to purchase, so funds to buy stuff later. And it could be-- I mean, it could be instrumentation. Hey, they'd like to-- we had a-- when we were closing, I wasn't involved with it, when the wastewater treatment plant project in Culdesac was being closed out, they had some money left over.
00:16:41:07 And so I helped the engineer work to buy some instrumentation. So they could do some of their own analytical work. They bought a spectrophotometer for nitrogen testing, which was pretty useful. They had some funds left over. So those types of things, you could envision that. Maybe you put it as an alternate in your bid.
00:17:01:26 But it's just that-- it just gives you some, if the owner wants, if there's maybe some things that might be desired, it allows the owner to have the contractor buy stuff, whatever that stuff may be. Now, that all being said, I mean, not that I've bid out hundreds of projects, but I've never used cash allowances.
00:17:24:17 But it's there. It's there. It's nice to know. It's good to know that you have that flexibility, that you could write that into a contract. And the general conditions cover that. So you're well covered if you want to do that.
00:17:41:08 Let's see, go to the next one, OK unbalanced bid. So this is an interesting one. And this is the handout. We'll take a glance at that. So what is it? So this is overpricing one or more items in a unit price bid. So this wouldn't be in a lump sum, because a lump sum is one number.
00:18:02:23 It's often called penny bidding. And we'll see an example where it literally was penny bidding. Why might a contractor do this? They might employ unbalanced to conceal some pricing strategies from contractors. Maybe there's-- they see an opportunity where they can frontload something, where they get a lot of money out of-- they sort of-- basically, what they're doing is they're putting together their whole bid, putting together their bid with all the unit price items.
00:18:36:06 And then they might end up-- they might see up front that there's maybe some uncertainty in quantities, the engineer screwed that up. So they can put a large number by that. And then-- and then balance it out somewhere else by putting a low unit price for an item that they then can be compensated. So they'll actually make a lot of money out of one particular item. So it's unbalanced. It's not equitably bid.
00:19:05:19 Again, believing the quantity estimates are inaccurate. So there might be a windfall. So you jack up that particular price. But in order to secure the bid or hopefully win the bid, they would elsewhere put in a really low price on an item. And there is some case law, we're not going to jump into that, other than just a case study.
00:19:26:19 Now, one of the things is, it's obviously-- if you go look at IB 19.01, and I'm not-- I'm not going to drag you there, I'm going to go there myself, but just point something out. It's minor, but it's I've covered it in the slides. If we look at 19.01, owner reserves the right to reject any and all bids, including unbalanced.
00:19:54:27 So we are-- so it's stipulated in the instructions to bidders if it's unbalanced, that the owner can reject based on that. Yup?
00:20:07:26 How do they determine whether it's unbalanced?
00:20:12:21 No, no, so good question, how do they determine? So not from the engineer's estimate, you just look at it. So let's just take a minute and look at this one I gave you. See if you-- just kind of-- anything look-- take a few minutes and just look at this handout here, this transmission line project. We've got five bids in there, plus the engineer's estimate. So obviously, I was not penny bidding. So you can ignore the engineer's estimate.
00:20:44:07 But-- So you think item 16, additional cost for--
00:20:54:27 He estimates $200, but you put $24.
00:20:59:06 So you're saying I was penny bidding? You think I'm unbalanced?
00:21:02:17 No, I thought it would be-- jacking down that one.
00:21:05:20 But remember, so this is-- so this is a good one to point out. So Rock ex, we didn't this-- I gave that example earlier. We didn't know if we would have rock ex. We had 2 and 1/2 miles of pipeline. We wanted to be able to pay the contractor if they encountered-- so we just said, gosh, we think there's 100 cubic yards of rock excavation.
00:21:27:11 And let me further clarify, in the payment section, in the measurement and payment section, it is made very clear what is rock excavation. There is certain equipment that has to be used if the rock is to-- so if the rock can be just-- rock excavation isn't rock, isn't just all rock. It's very specific to-- it would spell out the type of equipment necessary to excavate said material.
00:21:56:09 That would qualify under rock excavation. So we throw-- we just throw one in there. And rock ex can be expensive, because it's expensive equipment. And so remember Logan, the point is-- so here, this would be a situation where you might interpret penny bidding or unbalanced bidding, so maybe they would increase the price substantially, right?
00:22:24:04 Because they're like, wow, we actually think that it's going to be a lot. And so we see an opportunity to make some money. And so then elsewhere, they would reduce the price. In this case, given the uncertainty, we hadn't-- we hadn't shown on the drawings. If you knew somewhere where there was rock, you would spell it out.
00:22:42:15 You would provide that information in your supplementary general conditions. You would provide that information. You would provide geotechnical information in the bidding documents. We didn't do that. We just sort of put it out there as speculative, just to cover it. So in this case, it wasn't deemed unbalanced. And we didn't see anything that would suggest penny bidding elsewhere to-- because the low contractor was Skyline there.
00:23:11:25 They were at $20. That's, wow, that's cheap. You want to rock ex for us for $20, we're OK with that. That's a good price. It's on the contractor. It's not our fault that you underbid or underpriced that particular item. Anything else sort of jump out?
00:23:33:13 I was looking at item 22, buried 2 inch diameter conduit. Seeing a little bit of a misbalance there on Skyline and Mesa compared to everyone else.
00:23:45:02 So again, so what we're looking for then, so at $8, I mean, 2 inch diameter conduit, I mean, that's-- that we said there was 1,000 feet. We had good numbers on it. That's just what they thought it was going to be. So then you would look elsewhere. So you're saying maybe that's low. So did they did they counterbalance somewhere else to make money up front?
00:24:10:19 And again, we didn't see anything. And one of the takeaways here is just because the engineer's estimate and all the other numbers, the unit prices, are different and widely variable doesn't make it unbalanced. Doesn't make it penny bidding. So hold on a second, David. I think I had-- Willow were you?
00:24:29:18 No, I rethought that.
00:24:32:19 Would it be the control valve vault 13.
00:24:35:18 Number 13, OK. So we said 30. I mean, they're all about the same, really, and expensive. That was a particularly expensive-- and one way to-- one sort of the-- one value of the engineers estimate is, again, we aren't penny bidding or unbalanced bidding when we put together an engineer's estimate. So if they're in the ballpark, pretty close, if they're similarly seeing an expense, then you're OK with that.
00:25:04:13 And so number 13, we're at $30k, lowest-- the low bidder was $40, $40, you work away across. Particularly, what you're looking for-- I mean, just looking at Skyline, because they were the low bid. So I wouldn't-- Jade had one.
00:25:21:26 Oh, I was going to say Stanley contracting seems a little odd with all of their numbers. They're all weird dollar values. And then you get to a very large amount, I guess not large.
00:25:34:09 Yeah, you know, I honestly never quite-- I mean, although actually, if you look at the prices, I mean this is one, there's not a huge $872 to $928, not a huge range. I mean, they-- however, I've never been on the side of putting together an actual bid for construction. I've never worked for a general contractor. I mean, yeah, their numbers were-- I think one thing you would do is you would look at your two low bidders, thank goodness we didn't end up with low bid, change order low bid king there.
00:26:15:28 We were very grateful for that. Because this is the contractor that would go out and buy equipment when he found a project that he liked, and then sell it when the project was over, and was a true pleasure to work with. But you just get these-- you get-- oddities doesn't mean unbalanced or penny bidding. You're always going to see variable. And different contractors are going to employ different approaches.
00:26:41:19 And there might be-- it might be subtle, but it's been really hard to prove. It would have to be-- and when we look at a case study, it would have to be really egregious. So one more.
00:26:52:25 I was just looking at line 15, because Mesa's, their estimate was $15,000, and then the next highest was $3.
00:27:00:29 Yeah, that was abandonment. I mean, that does seem like a lot of money. And so-- but you think about, OK, I'm trying to remember where the phasing-- that was later stages of the project. So one of the things we're looking for in unbalanced is have they-- are they trying to get a lot of money upfront at the initial part of the project, and then balanced their bid to be competitive by lowering a price elsewhere.
00:27:35:01 So really, they're getting a whole bunch of money out of item 4, whatever it might be. But really, that's going to cover the cost of item 12, which comes later in the project, different strategies. So I will tell you, I've never seen it. I've never had it happen. I've never seen an unbalanced bid. I've never seen penny bidding.
00:27:55:25 I don't know that it's really actively pursued by contractors. But if we go back to the slides, so it's just good, because it's-- one of the things is looking at-- you're looking at these, you've got a couple of bid tabs now. You've got that one and the one I gave the other day on the pumping station.
00:28:15:10 You can see the difference in prices. It's just-- they just are. And you don't know what's going on behind the scenes. And as long as-- one of the things you do look for in pricing, particularly for the low bid, is it-- are there particular items that are significantly lower than everybody else and the engineer's estimate?
00:28:39:03 Again, because we're really trying to think through. We're not trying to get creative in the engineer's estimate to get some frontend money, or move things around, or whatever, look at the quantities. We're trying to literally predict what we think it's going to cost. And so if you get some that are significantly different, that could be a red flag.
00:29:03:26 But the red flag in that case is maybe they don't understand what the work entails. That would be a red flag, if they've really underbid something that you have illustrated and described in the drawings, and in the specs, it is really significant, whether it's equipment, I mean, whatever it might be, that would be a red flag.
00:29:29:22 So if we kind of go back to the slides here. So this is one, this was several-- obviously, several years ago. OK, this was in Boston. We had two bidders, $18 million, $20 million. The low bid had this literal penny bidding, a penny per square foot for temporary sheeting. And again, just as we've got in our instructions, the bidders commission could reject an unbalanced.
00:30:02:25 Boston went ahead, low bid, I mean, $2 million, that's not chump change. I mean, but then the Department of Labor and Industry for the state said the bid had to be rejected. Said it was-- they did find, though, so what was interesting is they said it's unbalanced. It's not unbalanced-- because there was no-- when you see a penny, you've got to go look for a counterbalance, because it's somewhere there.
00:30:33:15 And there was no counterbalance. But the Department of Labor and industry had a policy, that word's key, had a policy against penny bidding. And said that's not realistic. I mean, you can't accept that, because that's not really what it's going to cost. Boston said whatever the words they chose and moved forward, right? Went to a judge, judge determined that the low bid was not unbalanced or front loaded.
00:31:08:01 Judge concluded that Boston could not move forward with that. Again, we're talking $2 million, that's not a small amount of money. So it goes to a higher court, because that's what happens. And the higher court is ruling over policy. DLI can establish policy. They can't make rules.
00:31:27:17 So a policy and a rule are different. Legislature in this case hadn't given them that authority. All the rules come from the legislature. And then the departments enforce the codified rules. And ultimately, the judge said, look, that's fine, that's your policy. But it's a policy. It's not a rule.
00:31:51:13 Another appeal, claimed the judge had the power to prohibit penny bidding. And ultimately in the end, low bidder was just more creative, saw an opportunity. Wasn't unbalanced, wasn't frontend loaded. So those would be grounds for rejection. She had a more creative contractor, didn't think that temporary sheeting was going to be all that important somehow.
00:32:17:14 Maybe they'd factored it in elsewhere, but it wasn't obvious. And DLI and second low bidder had confused equal footing, which is a principle in contract law, with creative bidding to all bidders. So everybody had an equal footing. One got more creative. Why are you penalizing the more creative bidder?
00:32:37:29 And you could almost apply this case study here to the Lewiston situation. You had three contractors that were more creative, and it would have saved the city money. Unfortunately, the city hadn't properly-- or the engineer hadn't properly developed the bid form. So yeah, I've never seen it. Looking for-- I don't know how many of these are actually out there. But it's good to know.
00:33:06:09 I mean, it's one thing. I mean, we do scrutinize prices. We look for things that could be a red flag, that we think could cause problems should the contract be executed. And I think one more important one is-- I mean, the pricing is important. So it can be-- I wouldn't call it necessarily penny bidding, but low bidding, or underappreciating the required work, not that they have an unbalanced or loaded elsewhere, they just didn't actually understand the work. Those are the things that we look for. OK, Logan.
00:33:41:12 Talk about frontend loading. Is there anything in the sense of backend loading?
00:33:46:25 No, I mean, I've not heard of it. A frontend would make-- I think, the things where contractors are-- they're looking to exploit, perhaps, is underestimate of quantities, which is why we have to get our-- if we're going to do unit price, we need to measure super careful and very clearly articulate how measurement and payment. And then get it right in the bid form.
00:34:10:05 Because if we don't, a contractor might see that, they might jack up that price, but it's a low. It's a low quantity. But then when the real quantities come into play, boom, lots of money. But backend, I don't think there's really any-- I don't know why a contractor would necessarily do that. They're looking more for exploiting weaknesses in the bid form, and maybe getting some money upfront so they're less up bank during the project. Other questions? Yeah, Alex.
00:34:43:14 You may have hit on this. But how-- how are items-- in a lump sum contract, how is a contractor paid off of that? They're not going to get it all at once, I know they're going to slowly stagger it. But the unit price is pretty obvious. However much you put in, you keep quantities, you pay them that amount. But lump sum, I'm a little unsure how they get paid.
00:35:05:29 How does a contractor get paid under a lump sum contract? Excellent question. It's percent completion. It's a judgment call. But we'll see that. So we'll get to that later as well. But yeah, no, good point. I mean, how do you pay? You pay on percent complete. But the-- it's going to be subjective. It's going to be subjective. And the engineer has some weight in that.
00:35:32:17 Yeah, I mean, I much prefer unit price contracts for so many reasons. I mean, it's just-- one is it gives you the flexibility to add work if the bids come in low, which nowadays, they really aren't. But there was a time when they did. And you could add work to a project. And then it's so much easier to pay. And you're not getting into disputes.
00:35:59:11 OK, let's see where we are here. So different type of contract, so we've talked about lump sum. We've talked about unit price. This would be a cost plus contract. This is where you're paying for the actual work. You're paying-- you're actually paying for the labor, the materials, and supplies, plus a percentage or fee, that fee basis, that's the overhead and profit.
00:36:23:25 So you're actually pulling them apart. We're going to just pay you for the work. And then we're going to have an agreed upon percentage or fixed fee that's your overhead and profit, rarely used, more emergency project. Where you just say we need to get a contractor on board. We had-- during some flooding in '96, there were-- the city of Amity in Oregon, the whole Yamhill water-- or Yamhill River went over its banks.
00:36:52:24 And ended up totally silting in their raw water intake for their water plant. And so we had to bring a contractor on board in that situation. And we didn't have time to bid it. We were able to just hire a contractor, under a structure like this. We'll just pay you for the work you do. And then we have an agreed upon percentage or fixed fee. So those types of-- that's where you would use it.
00:37:17:00 You could use it in difficult or unique projects. We had-- that was actually the same contractor. It was the city of Hood River. It was actually design build project. So the engineer was partnered with the contractor. But sort of similar, we'll talk about that more later, and then I have a guest lecturer at some point later in the semester who's very knowledgeable in these alternate delivery methods, including design build.
00:37:46:19 But this was a situation where we had springs that the city had developed back in the early 1900s. We knew next to nothing about what we were going to see. And so as the-- we were doing preliminary design with the contractor for the city. And then there came a point where then the owner was able to work with the contractor to negotiate a sort of a similar cost plus type contract, given all the uncertainties.
00:38:18:29 Because we didn't know what to expect. And thankfully, one of our myriad designs is what we used. Not the one we put on the drawings, but one of the ones we'd actually talked through, which was useful. It was actually a lot of fun. If you can get into a design build project, that can be with a contractor, it can be a lot of fun.
00:38:39:04 OK, so here's-- I'm going to just talk about-- and we'll go look at some general conditions here to walk through this. So again, an engineer friend of mine had a project up in northern Idaho. They were-- it was a sewer project. It was a cured in place. So this was a special-- very specialized work. It was a contractor that would-- it was-- I don't know if it was Insituform or Gelco. I don't know who or what the contractor was, but-- who it was.
00:39:08:28 But they're pulling a liner. They're repairing a pipe in place, cured in place. So they're not excavating or removing the pipe. They're not-- they're not pipe bursting, pulling a new one in. They're just pulling a liner in. And then they actually can-- it's a particular chemical structure. And then they heat it up. And it creates a whole new pipe, if you will.
00:39:33:19 So they went to the contractor and said, hey, we'd really like to add some work to the project. But the project didn't have line item unit price on some excavation. So they had the contractor, again, was not an excavation project, had to go find a sub. And then they submitted a price. So they found a subcontractor who can do the excavation. They went, submitted the price to the owner.
00:40:01:25 And then the general contractor passed along the cost, so it was a cost plus type contract, but a 20% markup for overhead, admin, profit, et cetera. So the question is, do you just-- do accept it? Do you pay them the 20%? So this is where we need to go-- I'll let you get to general condition.
00:40:24:19 Actually, we'll go to Article 12 in the General Conditions, which is change of contract price or change in contract times. I'll let you find that. So this is page EJCDC C-700 page 46, at the bottom. So here's one. I mean, this is a real situation. And this engineer had to navigate it.
00:40:56:20 So if we look at 12.01.C, 12.01.C.1.a, that's where you start. So here's a change of contract price. That's what this was. You were asking for a change order. The contract may be only changed by a change order. So that's a formal document. It's in capital letters purposely. It's defined in Article 1 of the General Conditions.
00:41:23:14 Contractor's fee, that's what we're speaking of here, the contractor's fee for overhead and profit shall be determined as follows. So the general conditions in the contract that have been signed for allows-- I mean, it gives you clarity on how to deal with that. You can be a mutually accepted fixed fee, which wasn't the case.
00:41:48:12 If a fixed fee is not agreed upon, then a fee based on the following percentages of the various portions of the cost of the work for costs incurred under 11.01.A, et cetera, shall be 15%. Well that's not 20%. Contractor just did 20%, didn't adhere to the contract at all, 15%.
00:42:14:09 But then if-- so if we look at-- so C-- that's C.2.a, right? But then, it gets a little more gray. For costs incurred under 11.01.A 1 and 2, it's 15%. But if it's A.3, it's 5%. So it's either 15 or 5. But now, we have to go look at 11.01.A.1, A.2, and A.3.
00:42:54:20 So A.1 gets into some great-- spells it out in great detail, the cost of the work means the sum of all costs. You get all these-- one of the things you're seeing is it doesn't repeat. It says except as those excluded in 11.01.B. So you have to look at 11.01.B. So you're doing a little bouncing around, which can be frustrating.
00:43:20:11 When the value of any work, covered by a change order or a claim, which is different than a change order, is based on the cost of the work, the cost to be reimbursed will only be those-- will be only those additional or incremental costs required because of the change because of the event giving rise to the claim, except as otherwise may be agreed in writing, such costs should be the amounts no higher than those prevailing in the local.
00:43:49:18 That's subjective, right? Shouldn't be those that it would not exceed prevailing. So we've got payroll costs. I'm going to scroll through this really quickly. A whole bunch of them, costs excluded. But then C, so here's-- when all the work performed is performed on the basis of cost plus, so we have two different ones-- so it was 15% if it was A.1, which is payroll costs, what was it? A.1 and 2, I forget? Or yeah, A.1 and 2, right?
00:44:32:28 So it's 15% on top of what the contractor is proposing if what the contractor is proposing is payroll costs and materials and equipment, furnished and incorporated into the work. So that's 15%. But then, if we look at C, as set forth in the agreement. So all sorts of-- I mean, it's clear but not clear.
00:45:06:28 So again, the first part deals with payroll costs, materials. So the challenge that he faced was what do you do, right? Clearly, it's not 20%. Right from the get go, it's not 20%. But is it 15%? Or is it 5%?
00:45:26:12 His conclusion, based on the contract that was in play, is that the general conditions indicated 5% was the right number. Now, the contractor is not required to execute the change order. You invite-- you ask for a change order. You ask them to perform extra work. But if the price isn't agreed upon, it doesn't happen. So nothing is-- nothing is requiring the contractor to accept the terms.
00:45:54:05 Of course, the contractor in this case wasn't super thrilled about 5% for whatever reason, especially, it wasn't really their expertise. They had to really-- they had to bring on a sub. They'd have liked to get a little bit more out of the deal. And they countered with 12%. And they ultimately did settle on 12%.
00:46:16:16 So a little bit of negotiation, owners involved on that. They decided there would be some direct coordination work in the field and the office. So direct payroll costs, so there would have been-- it would have required payroll costs of the general contractor to, actively in the field, oversee the work performed by the subcontractor that was being brought into play. And so that would lean you toward the 15%.
00:46:47:06 But 15% didn't feel quite right. And they settled on 12%. So you could see where, depending on what you're asking, it could go either way. But the nice thing is, at least the general conditions cover us. And they allow for a discussion and a negotiation. We're not held to whatever dollar amount the general contractor wants to do.
00:47:18:11 And so I'll just-- I'm going to read this verbatim. So this is what he said. The rest of the story here that you won't find guidance on in EJCDC, and that I'm sure you're familiar with, from my experiences, is the give and take of construction and the need to pick battles. He goes, I didn't want to be too much of a stickler, because-- I'm going to make sure he's not using inappropriate words, anything I don't want to put on tape, didn't want to be too much of a stickler, because they were are really helping the owner by taking on the subcontractor and agreed to do so even though they typically don't.
00:47:54:07 Again, this was a very specialty contractor that they don't do excavation. So this was very much a favor to the owner. They'd also done some additional TV work on the lines that we thought we might add to the project that we ultimately didn't based on-- so there were some-- apparently some work that they didn't get paid for that was originally part of the bid. They weren't planning on claiming that additional work anywhere else. So even though they had some time.
00:48:25:23 So it was ultimately in the best interest to not make this a big deal. The city didn't pay a premium for the markup. But our generals still came out with something. So ultimately, it was a win-win. So that's the general conditions give us a lot of direction. But there is still that negotiating with contractors. A win-win, you want it to be a win for the owner.
00:48:48:04 And the other way to think about it, because again, the contractor could have said, no, it's not it's not our bailiwick. It's not in our world. We don't want to do this. So then you would have to prepare bid documents, go out to bid, bid the work, and then go through that whole process.
00:49:05:11 So all the engineering costs, so there's a lot of extra costs that would have been incurred if the general contractor said no, we don't like your terms. We're not going to do this. So you have to factor that in, as well. What's the alternate approach? And is that more expensive? Or is this a very expedient way, and so you compromise.
00:49:29:26 So I think those kind of stories are interesting to share. Let's see where are we at on slides? I got beeped. I'll let you look at-- I would encourage you, because I fully expect to have at least a question on the exam that speaks to 11.01, our general condition 11 and general condition 12. So you should be looking at those as you think about the exam. And we will pick up right there on Monday. Have a good weekend.
00:00:21.550 -- OK, a couple things as we get started. The first one is we
00:00:26.828 -- have the last lab assignment.
00:00:31.670 -- And so this one is going to be a bus differential protection lab
00:00:35.349 -- and so the on campus students is pretty much going to be a
00:00:39.028 -- similar setup to what you did before. You just need to read
00:00:42.424 -- through this and then work with the TA. As far as if you're
00:00:46.103 -- going to, I think you all of you have groups that you've been
00:00:49.782 -- doing the labs with the TA. If you want to stick with those
00:00:53.461 -- groups in those times. If you wanted to negotiate a different
00:00:56.574 -- time, then you just need to communicate with him about that.
00:01:02.040 -- Until you have a system and you're going to look at fault
00:01:05.628 -- at a couple of different places, this is actually
00:01:08.319 -- should be a little bit shorter than the last, quite a bit
00:01:11.907 -- shorter than the last lab.
00:01:14.920 -- And so you're really just going to look at several
00:01:17.710 -- different cases.
00:01:19.710 -- Look at the behavior with this.
00:01:22.940 -- The Engineering Outreach Lab is going to be similar.
00:01:26.730 -- So this is just the description of the entering outreach lab.
00:01:31.580 -- And so it's a little bit more complicated system, but it's
00:01:34.616 -- still the same basic idea.
00:01:36.980 -- And also you have some information about the CT
00:01:40.410 -- ratio that's was used for this.
00:01:44.480 -- And then this is using that.
00:01:47.590 -- Relay model that the differential relay model we
00:01:50.462 -- talked about. So again this is a low impedance restrained
00:01:54.052 -- differential element, so it's not. It's not a high
00:01:57.283 -- impedance differential element.
00:02:01.530 -- If anyone has fair time and wants to create their own
00:02:05.369 -- creative all the create this, it wouldn't be that hard to
00:02:09.208 -- create a lab for the restraint for the high impedance
00:02:12.698 -- differential elements. We just haven't had a chance to put
00:02:16.188 -- together the simulation files.
00:02:18.800 -- So anyway, it's the same idea you read in the data files.
00:02:24.470 -- Very similar to the handout that we talked about with the lecture
00:02:28.310 -- last week. All of this stuff we're reading the comtrade file,
00:02:31.830 -- and so where this really starts to differ a little bit is
00:02:35.670 -- towards the end of it. Once we've got the phasers, so we've
00:02:39.510 -- got the things where we're looking at the voltages in the
00:02:43.030 -- currents, and then we have the operating restraint current, and
00:02:46.230 -- so one thing that's different from the handout before is now
00:02:50.070 -- the. In this case, there's no.
00:02:53.660 -- Nothing where you put in a multiplier to imitate
00:02:56.297 -- saturation. The simulation data that you're using for this now
00:02:59.227 -- actually has saturation in it.
00:03:01.850 -- And the case is that you'll be doing for the on campus
00:03:05.450 -- students in the lab. You're actually going to be doing
00:03:08.450 -- these with an RTS simulation instead of using the model
00:03:11.450 -- power system, and so that the RTS will have setae. Models
00:03:14.750 -- that include saturation, but you're still going to be
00:03:17.450 -- setting the actual physical relay.
00:03:21.310 -- And then one of the things that this is going to show is the
00:03:25.664 -- basically the how they operate. Quantity changes. So basically
00:03:28.463 -- as it reads through samples, this thing is moving and then it
00:03:32.195 -- works its way up and then it has some final value it goes to and
00:03:36.860 -- so you can as you look at these different cases once you enter
00:03:40.903 -- the slope setting you can actually look at a little bit
00:03:44.324 -- how the how the value evolves and when you look at the case
00:03:48.367 -- with the saturation you can actually see how it.
00:03:51.300 -- Now the saturation changes what it's what the relay
00:03:54.171 -- element is seeing too, and so this was a case for an
00:03:57.999 -- internal fault, so it grows quickly.
00:04:02.860 -- So any questions about that?
00:04:09.170 -- Hey are there any questions from the last lecture?
00:04:12.680 -- Yeah, so in the last lecture when you talk about the high
00:04:16.832 -- impedance plus differential protection, you mentioned that
00:04:19.254 -- for an external fault. Once one of the see T starts to saturate
00:04:23.752 -- it will dive deeper into saturation, right? So my
00:04:26.866 -- question is how will that?
00:04:29.160 -- To how will that city begin to saturate? Like because?
00:04:33.660 -- The currents are all balanced, right? I mean based on the
00:04:37.972 -- culture of slow, so part of it's too far into this into the
00:04:43.460 -- hand out so.
00:04:47.760 -- That's the internal fault. So for the external fault part of
00:04:51.148 -- it's going to be the case that.
00:04:54.690 -- We've got this one. This is 1 heck external fault, right? So
00:04:58.338 -- this is seeing the current from all of the other feeders or
00:05:01.986 -- other lines going through it, and so depending on what the
00:05:05.330 -- burden is for this one.
00:05:07.800 -- Oh that 'cause there's going to be?
00:05:12.460 -- The relay and the and some of the winding resistance is going
00:05:16.084 -- to be dominant. Burden that affect saturation in this one in
00:05:19.406 -- a lot of ways.
00:05:21.210 -- So if this one, if there's a fault with a lot of DC offset,
00:05:25.088 -- especially then this one is going to start to saturate.
00:05:27.858 -- 'cause this is seeing the most current. I thought there is only
00:05:31.182 -- one button then that's the one at the end. Well, remember that
00:05:34.506 -- the burden and we look at ACT when we look at burden.
00:05:40.260 -- Mr Lead wire.
00:05:48.530 -- So the first thing we're going to have is the CT winding
00:05:51.338 -- resistance. And it's so. So in this case the Siti
00:05:54.649 -- winding resistance is going to be the most significant
00:05:57.088 -- one, because once we get to the terminals of the see T.
00:06:07.470 -- We're basically connecting each of the CTS.
00:06:12.750 -- In parallel on the secondary side, right and then once
00:06:16.320 -- they once we have this parallel combination, then
00:06:19.176 -- that's going. Then we have the rest of the lead wire.
00:06:25.200 -- And we have the relay out here.
00:06:30.540 -- But there's the secondary current on the secondary
00:06:33.404 -- winding, and the CT is still going to see.
00:06:37.340 -- All that current, right? The current when they sum
00:06:40.328 -- to 0 between.
00:06:44.320 -- We put in a third CT just to kind of.
00:06:49.030 -- Illustrate this a little bit more.
00:06:58.680 -- When I talk about connecting them together right, this is
00:07:01.940 -- where they sum to 0, right? So if it's if it's an
00:07:05.852 -- external fault.
00:07:12.350 -- So let's say that this is the one with.
00:07:18.870 -- The external fault, right? So that's going to have.
00:07:23.100 -- Let's say we have current going this way and this one. Each of
00:07:26.948 -- these are going to have their share feeding it right, so this
00:07:30.500 -- one is going to be the sum of this plus this and so at this
00:07:34.940 -- point here. They're going to sum
00:07:37.224 -- to 0. But this one, each one of these is going to have its own
00:07:42.072 -- fault current share the fault current, it's it's
00:07:44.628 -- carrying. It's going to go
00:07:46.048 -- through this resistance. And so basically what's going to
00:07:49.888 -- drive that start driving in this one in the saturation is
00:07:53.936 -- going to be a combination of the voltage drop across this
00:07:57.984 -- plus the ACE asymmetric current due to the DC offset.
00:08:03.130 -- Remember that as we talked about with on the BH
00:08:07.030 -- characteristic, the DC offset is shifting you in One
00:08:10.540 -- Direction and the BH characteristic.
00:08:17.450 -- And so when we look at this.
00:08:21.080 -- So under normal conditions.
00:08:23.650 -- It's going to be doing something like this, right? And
00:08:26.760 -- if we have a fault with no set without significant saturation?
00:08:31.480 -- It's going to be doing some like this, and so if we have well
00:08:36.324 -- size CTS we may only see behavior that looks like this.
00:08:40.730 -- But for a bus situation, sometimes it's hard to get
00:08:44.380 -- around that, but if we add.
00:08:47.510 -- The.
00:08:52.590 -- The DC offset.
00:08:54.830 -- I did not draw that very well, sorry. So we may start out with
00:09:00.248 -- something like this. Then the
00:09:02.183 -- next cycle. It's going to be working like this and it's going
00:09:06.480 -- to be following that DC offset, so it's going to push it into
00:09:10.302 -- saturation. Discuss. The flux loops are being pushed this way
00:09:13.242 -- by the DC offset.
00:09:15.870 -- And in some cases with a combination of the of a large
00:09:20.286 -- current and going through this resistance in a DC
00:09:23.598 -- offset, this one may start to go into saturation an.
00:09:29.390 -- Lessina cycle.
00:09:31.800 -- Possibly quite a bit less in the cycle.
00:09:35.790 -- And so that's why that's why even though you on the surface,
00:09:39.606 -- you would say that there shouldn't be much voltage across
00:09:42.786 -- this, because these current sum to zero and the voltage drop
00:09:46.284 -- across this should normally be negligible. But what's going to
00:09:49.464 -- happen is that the combination of that fault current going
00:09:52.644 -- through this winding resistance and the DC offset starts this
00:09:55.824 -- one into saturation. And then that mismatch current through.
00:10:00.130 -- That saturation goes through this, and because of that
00:10:03.577 -- compensating resistor that's going to drive this voltage up.
00:10:08.730 -- But because this is the one that's already starting to
00:10:12.290 -- saturate and has a lower impedance than it's, it's
00:10:15.494 -- going to tend to make this voltage collapse and keep
00:10:19.054 -- these from rising.
00:10:28.560 -- Like I said, it's not. That's a very good question. 'cause it's
00:10:32.280 -- there's a lot of things that are not intuitively obvious when we
00:10:36.000 -- look at the high impedance bus
00:10:37.860 -- differential. Because we're basically using something that's
00:10:42.662 -- inherently nonlinear to work.
00:10:57.580 -- Any other questions for my son?
00:11:06.790 -- OK, so then we're going to start on. Next, we're going to start
00:11:11.223 -- talking bout transformer protection and I talked to I did
00:11:14.633 -- a very quick introduction to some of the some of the issues
00:11:18.725 -- and the difference.
00:11:20.960 -- Things were gonna talk about.
00:11:21.870 -- We're going to talk about. Fall protection of the
00:11:25.190 -- transformer itself for faults inside the transformer.
00:11:29.680 -- And then we're also going to look at protecting the
00:11:32.850 -- transformer, firm external conditions, and
00:11:34.435 -- this can include faults external to the
00:11:36.654 -- transformer. Boy, the transformer is carrying
00:11:38.556 -- the fault currents that goes that go to it.
00:11:47.680 -- And then there are Transformers introduce a number of unique
00:11:51.640 -- challenges that we'll talk about as we go through this.
00:11:56.550 -- So in some ways it will start out looking at a concept similar
00:12:01.308 -- to what we looked at with the bus protection. So we're going
00:12:05.700 -- to a lot of the internal fault protection for Transformers.
00:12:09.360 -- Starts with the idea of restrained low impedance
00:12:12.288 -- differential element, so it's kind of build time. We start. I
00:12:16.314 -- started with the bus protection.
00:12:29.630 -- And so one of the things that the bear in mind as we talk
00:12:35.748 -- about transformer protection is when we talk about bus
00:12:39.681 -- protection. Fast protection has a bus fault or misoperation
00:12:43.614 -- where a bus gets tripped when it shouldn't can have very severe
00:12:48.858 -- operational. Consequences for our power system. So bus faults
00:12:52.556 -- are actually fairly rare.
00:12:54.760 -- Fat faults that cause were and the bigger concern is as
00:12:59.028 -- generally going to be external faults that caused the bus
00:13:02.908 -- protection to miss operate.
00:13:06.160 -- And so that's why the restrained differential element, the high
00:13:09.640 -- impedance differential element, have so there so much efforts
00:13:12.772 -- gone into developing and optimizing those at the relay
00:13:15.904 -- vendors is because they are very high consequences operationally
00:13:19.036 -- to the system in the short term.
00:13:24.130 -- Transformer failures, on the other hand.
00:13:44.050 -- Can have longer time consequences.
00:13:54.730 -- And that's because there are longer replacement times.
00:13:59.700 -- And in most cases, if an internal fault happens in a
00:14:04.560 -- transformer.
00:14:06.370 -- There is a good chance that it's going to evolve to the point
00:14:10.348 -- where it's not something that's very simply repaired. In some
00:14:13.408 -- cases there are still a number of cases where they're caught
00:14:16.774 -- fast enough, or it could be repaired simply, but if it gets
00:14:20.446 -- to severe faults and you'll have a fire in the transformer, then
00:14:24.118 -- it can be very severe.
00:14:27.950 -- And so there are a number of things. The number of strategies
00:14:32.750 -- that try to minimize the impact of transformer faults.
00:14:49.760 -- So one of the big ones is finding ways to reduce the
00:14:53.252 -- likelihood of them happening.
00:15:05.320 -- And so part of what a lot of this comes down to is.
00:15:10.900 -- Track external events.
00:15:31.620 -- And it's really the life of the installation. That's a
00:15:34.010 -- big issue.
00:15:35.620 -- So one of the things that I mentioned is that we have two
00:15:39.741 -- directions. We're gonna go to, and they actually are related to
00:15:43.228 -- each other. So one of the big things that is a has a
00:15:47.349 -- consequence for Transformers is.
00:16:06.620 -- Meeting of the installation will have a big impact on
00:16:09.700 -- how the life or how long that installation is going
00:16:12.780 -- to be good.
00:16:23.030 -- Transient overvoltages is another another issue.
00:16:44.770 -- So what are some of the things that are going to
00:16:47.168 -- cause a transformer? Cause heating in a transformer?
00:16:51.350 -- So let's think about a transformer for a second
00:16:53.690 -- we have.
00:16:56.970 -- So I'm just going to draw a single phase core.
00:17:01.570 -- So as we've talked about where we have a single phase core
00:17:05.410 -- and have the low voltage winding on the inside, an will
00:17:08.930 -- have a higher voltage winding wrapped around the outside of
00:17:12.130 -- it, right? And then we'll take those out to the bushings.
00:17:16.690 -- And as I mentioned earlier, we don't. You don't see a
00:17:20.397 -- transformer core just sitting out open in the air, right?
00:17:24.360 -- And so usually this is going to be.
00:17:32.140 -- In a tank.
00:17:37.710 -- Anna's tank is going to be.
00:17:45.730 -- Filled with oil, right? So usually it's going to be some
00:17:48.271 -- sort of a dielectric oil.
00:18:02.600 -- Is also used as a coolant.
00:18:08.650 -- And so you may look at a name plate for a transformer, an it
00:18:13.914 -- may say that you have a transformer that's rated at 15
00:18:18.050 -- MVA, 20 MVA.
00:18:20.300 -- 25 NBA
00:18:23.920 -- so why would why would there be 3 MVA ratings for the
00:18:27.712 -- same transformer?
00:18:34.120 -- Different cooling stages. It's different cooling stages, so
00:18:37.424 -- this is going to be.
00:18:40.720 -- Basically, entirely passive cooling.
00:18:45.100 -- So there is going to be there will be radiator fins or on the
00:18:49.510 -- side of this case on the side of
00:18:52.030 -- that tank. This is going to be.
00:19:03.070 -- Going to be pumps used to circulate oil to cool the
00:19:06.029 -- transformer or cool the oil so it's going to circulate because
00:19:08.988 -- there are going to be.
00:19:11.010 -- Different spots in the winding that are hot spots said certain
00:19:14.156 -- certain points are going to be
00:19:15.872 -- hotter than others. And so if you don't circulate the coolant,
00:19:19.424 -- there will be a little bit of natural convection, but you're
00:19:22.262 -- going to. Those hot spots are not going to be cooled as well.
00:19:26.580 -- And then this is going to be pumps.
00:19:31.090 -- Plus
00:19:32.920 -- running cooling fans that are blowing error basically across
00:19:36.997 -- the radiator so that the radiator works more efficiently.
00:19:45.810 -- So depending in some cases people will just run these
00:19:49.220 -- all the time. In some cases they'll based on the load
00:19:52.971 -- conditions, they'll start and stop this equipment.
00:19:56.890 -- And if you have a transformer that's always lightly loaded,
00:19:59.290 -- they may not. Run it as. Run to run them very much at all.
00:20:15.100 -- So other things that could cause heating.
00:20:23.270 -- So I want to be carrying harmonic currents.
00:20:38.460 -- Do you know external loads?
00:20:48.380 -- So for example, if we have a transformer that one of
00:20:52.153 -- the loads.
00:20:54.110 -- Is.
00:20:59.190 -- A dialed dialed rectifier.
00:21:04.740 -- And then we have a voltage source converter.
00:21:09.580 -- Anyway, have an induction motor.
00:21:17.060 -- If.
00:21:19.260 -- This doesn't have any compensation.
00:21:28.570 -- The current strong by this drive are going to look
00:21:30.800 -- something like this.
00:21:34.920 -- And so this is going to have 5, seven, 1113 and
00:21:39.463 -- basically multiples of 6 plus or minus one.
00:21:47.670 -- Is there going to have other loads here? But this
00:21:50.100 -- transformer is going to be carrying this current plus
00:21:52.287 -- whatever loads are here.
00:21:57.000 -- And carrying those harmonic currents increases Eddy current
00:22:00.808 -- losses in the transformer core.
00:22:04.480 -- And so that the transformer is going to run hotter.
00:22:23.280 -- And so they actually you can actually get.
00:22:27.470 -- K factor rated.
00:22:35.920 -- So basically these K factors are more of a derating factor.
00:22:41.170 -- And so if you have, if you know you're going to be supplying
00:22:45.642 -- harmonic loads, you can buy a transformer that has basically
00:22:49.082 -- an extra factor in its MVA rating to be able to deal with
00:22:53.554 -- harmonics. If you're not, if you don't have a transformer
00:22:58.028 -- that has any K rating an you start supplying harmonics,
00:23:01.848 -- then usually you can. There's there are formulas from the
00:23:05.668 -- IEEE standards that talked about how you derate the
00:23:09.106 -- transformer, so instead of being a 15 MVA transformer, it
00:23:12.926 -- may actually be a 12 MVA transformer due to the extra
00:23:17.128 -- heating from the harmonics.
00:23:19.820 -- And so when someone buys a transformer, usually you're.
00:23:24.470 -- Part of the data for when you sign the contract with the
00:23:28.019 -- supplier and stuff like that is saying well, this is. This has a
00:23:31.568 -- 30 year design life for this as a 25 year design life.
00:23:35.850 -- If you routinely overheat the transformer, you may take years
00:23:39.750 -- off of that life.
00:23:41.870 -- So we had an outreach student awhile back that worked at an
00:23:46.334 -- industrial facility that was basically with zinc smelter.
00:23:50.010 -- And so they had a lot of very large rectifier loads and so
00:23:54.924 -- they had Trent. They bought Transformers that had.
00:23:59.340 -- 30 year old designlife
00:24:01.880 -- Then they push them kind of right. It may be a slightly
00:24:07.520 -- beyond their NBA ratings.
00:24:10.240 -- And then they gave this heavy harmonic loading. So they
00:24:13.060 -- lasted about 10 years.
00:24:18.790 -- An that fit and when I say lasted about 10 years, they had
00:24:24.237 -- a fault, and so if I did so by heating the insulation, you end
00:24:30.103 -- up causing the you decrease the lifespan of the installation and
00:24:34.712 -- your moral an it's more likely to fail by having our fault. And
00:24:40.159 -- so that's why this external event, external condition stuff
00:24:44.349 -- matters from the from the transformer Protection POV.
00:24:52.670 -- So transformer protection will usually track the loading on a
00:24:56.900 -- transformer an if the transformer is overloaded, and
00:25:00.284 -- then there are formulas you can use to figure out how much
00:25:05.360 -- that's affected the life.
00:25:10.980 -- And so some other things that will go into this are going
00:25:13.776 -- to be over excitation.
00:25:23.720 -- So on a transformer over excitation basically means
00:25:26.400 -- a steady state.
00:25:34.200 -- However, voltage that means you're partially saturating.
00:25:57.850 -- Angene why the transformer is going to produce more
00:26:01.478 -- harmonics because of this? Because this is a steady state
00:26:05.438 -- sinusoidal condition, these will be only odd harmonics.
00:26:11.110 -- And often the 5th harmonic is usually going to be the one
00:26:14.674 -- that's used as sort of the main detection detector for that.
00:26:21.140 -- But again, because you're saturating the core.
00:26:26.070 -- What does that? What does it mean when you saturate
00:26:28.960 -- the core more deeply?
00:26:35.050 -- More excited, you have more expectations, well over
00:26:37.938 -- expectations. We have more expectation right? But what
00:26:40.826 -- losses go up?
00:26:44.480 -- The winding losses go up, or so we're going to increase
00:26:50.200 -- hysteresis losses.
00:26:54.180 -- Remember, hysteresis losses are basically proportional to
00:26:56.672 -- the area of the hysteresis loop it follows, so if you're
00:27:00.588 -- over exciting the transformer, your loop has a bigger bigger
00:27:04.148 -- area, so the losses are going to be higher.
00:27:24.780 -- Another one that's a big factor are through faults, which means
00:27:29.345 -- that the transformer.
00:27:52.160 -- So basically, one of the things that also gets tracked is how
00:27:56.120 -- many, how many faults is this transformer supplied? What is
00:27:59.420 -- the magnitude of the fault
00:28:01.070 -- current bin? Because. Oh through fault can cause very substantial
00:28:05.092 -- heating. It may not. It's not going to last very long, but
00:28:08.764 -- it's going to take a long time. It's going to take awhile quite
00:28:12.742 -- awhile for the transformer to cool down from that.
00:28:37.870 -- So even frequent large motor starting or if the transformer
00:28:42.020 -- is supplying current to energize other Transformers.
00:28:48.500 -- So for example when.
00:28:53.020 -- I think their procedures have changed a little bit, but at
00:28:56.771 -- Grand Coulee there's a pumped hydro storage facility that
00:28:59.840 -- has very large synchronous Motors. They generally only
00:29:02.568 -- start those Motors once a day because the thermal shock on
00:29:06.319 -- the Motors every time they start them is so much that
00:29:10.070 -- they can't start them more often.
00:29:14.040 -- They redid that facility.
00:29:17.610 -- And within the last.
00:29:20.130 -- Eight years, so I think they've redone it, so
00:29:23.019 -- it's not quite as harsh.
00:29:26.260 -- But so basically all of these things get tracked.
00:29:45.910 -- They predict lifespan loss and we're going to. We're going to
00:29:48.814 -- come back and talk about the over some of these issues and
00:29:51.982 -- how and how this factors into the transformer protection later
00:29:54.622 -- in the course. I want to talk about internal faults. First,
00:29:57.526 -- we're going to come back to
00:29:59.110 -- this. That a good resource for this. Our textbook does a pretty
00:30:03.945 -- good job with this, but also the IEEE 30 C 3791.
00:30:08.770 -- Also another good one for this and or there's some
00:30:11.730 -- other references. We'll talk about a little bit later.
00:30:21.310 -- And So what I want to start talking about is now protection.
00:30:27.370 -- For internal faults.
00:30:33.170 -- And will be going through this over the next couple
00:30:35.320 -- of lectures.
00:30:45.020 -- And so I guess that's one other sort of structural
00:30:47.990 -- thing. When we look at.
00:30:51.370 -- Large Transformers again.
00:31:13.460 -- I felt it evolved to the point where there's
00:31:15.485 -- a fire can cause long.
00:31:19.490 -- As I said, long repair times.
00:31:23.550 -- And so some of the things that you'll see in a substation, for
00:31:29.205 -- example for large transfer transmission substations
00:31:31.815 -- especially often you'll see single phase Transformers used,
00:31:35.295 -- and so you'll see.
00:31:40.310 -- Three single phase units, and actually they are often going
00:31:43.810 -- to be 3 winding Transformers as we talked about earlier in
00:31:47.660 -- the semester.
00:31:49.800 -- And so they're going to have their own individual tanks.
00:32:00.700 -- And when you look at the substation.
00:32:04.490 -- You'll see a wall that's been placed.
00:32:09.980 -- Between the Transformers.
00:32:13.120 -- So what's the purpose of that wall?
00:32:16.130 -- Prevent fire from cleaning, so these are.
00:32:20.530 -- Firewalls raise more of the archaic usage of the term
00:32:24.070 -- instead of the one that's now everyone uses when they talk
00:32:27.964 -- about software.
00:32:29.990 -- And so this is basically if this one has a fault, and as
00:32:34.072 -- a fire, the idea is that this is that this is going
00:32:37.840 -- to basically make it less likely for any for the heat
00:32:41.294 -- in the flames to get to this transformer, so it fails to.
00:32:49.730 -- And a lot of utilities will
00:32:52.352 -- have. A limited number of spare Transformers that they
00:32:56.392 -- can put in to replace a failed transformer.
00:33:00.350 -- So.
00:33:03.620 -- This was probably almost 15 years ago. Now there was a
00:33:08.328 -- transformer fault at a 500 kva. Think it's a 500KV substation in
00:33:13.464 -- the Southwest. An they did not have.
00:33:18.530 -- Firewalls between the single phase transformer, so they lost
00:33:22.364 -- all three phases. They had their spares close enough that it
00:33:27.050 -- actually scorched the paint off of the tanks, but they actually
00:33:31.736 -- didn't lose the spares.
00:33:36.820 -- But because they lost all three and they only had three spares,
00:33:41.392 -- then they had to scramble to try to get spares from other people.
00:33:46.345 -- And I know that one of the utilities in the northwest
00:33:50.536 -- sentence pairs and they had all sorts of issues because these
00:33:54.727 -- were 500 kva Transformers, Oran, high MVA ratings. Just
00:33:58.156 -- transporting them was difficult.
00:34:04.410 -- And I think even transporting the spares
00:34:06.867 -- took like several months.
00:34:17.190 -- So then actually one of the things that the.
00:34:21.070 -- US Department of Energy in the Department of Homeland
00:34:24.814 -- Security been working on in the last several years, is
00:34:28.974 -- basically trying to form a kind of a national database
00:34:33.134 -- of transformer spares and also trying to increase the
00:34:36.878 -- inventory of spares so that if there is something like.
00:34:42.950 -- High energy electromagnetic pulse from a nuclear weapon or a
00:34:47.550 -- major Geo Geo magnetic.
00:34:50.070 -- A disturbance for the gym geomagnetically induced currents
00:34:53.454 -- caused transformer failures that they've got something that they
00:34:57.261 -- can go to restore power in some
00:35:00.222 -- areas quickly. Relatively quickly.
00:35:05.270 -- OK, so let's now start talking a little bit more about the
00:35:08.798 -- Internal fault protection.
00:35:16.340 -- Really, the first line for this is going to be
00:35:19.390 -- differential protection.
00:35:27.600 -- So as I said, much like what we were just talking
00:35:31.285 -- about with the.
00:35:33.640 -- Boss protection for the restrained low impedance
00:35:38.078 -- differential protection.
00:35:42.100 -- So let's start out looking at a transformer that.
00:35:47.170 -- We have a YY connection.
00:35:51.350 -- And so, let's say it's.
00:35:55.330 -- 3:45 KV. 2.
00:36:00.110 -- 138 KV.
00:36:07.700 -- And so for the moment, let's just say it's a.
00:36:11.870 -- 2 winding Transformers. So we're going to have
00:36:14.102 -- three leads coming out.
00:36:34.210 -- Now I have see T is on each phase and will just look at one
00:36:38.110 -- phase for the moment.
00:36:47.100 -- And so we start out saying, OK, well, this looks a lot
00:36:50.436 -- like what we talked about when we anytime we talked
00:36:53.216 -- about differential protection. So we're going to
00:36:55.162 -- have current if we have current going this way.
00:37:02.630 -- Then we're going to have.
00:37:06.340 -- Secondary current. That's going to circulate like this, and.
00:37:12.870 -- I op should be about 0, right? That would be. That's
00:37:17.666 -- what we would expect.
00:37:23.200 -- Now, unlike the virus protection, we've got a number
00:37:27.574 -- of factors that complicate this.
00:37:44.360 -- So what do you think? Some of the complicating factors
00:37:46.660 -- might be?
00:37:49.540 -- Configuration. Well, let's say they will stick with the
00:37:53.020 -- YY for the moment.
00:37:56.010 -- If it's why Delta that, that will add, that will be the next
00:37:59.195 -- challenge, will talk about after we finish this one.
00:38:03.450 -- CD accuracy. Find CD accuracy.
00:38:07.640 -- So ciety accuracy, but there's actually something
00:38:09.831 -- before that. One is going to be the CT ratios.
00:38:37.200 -- So we may not get apart. We may not get a perfect
00:38:40.284 -- cancellation of.
00:38:42.410 -- So let's say that just for making this easier, let's say
00:38:46.172 -- that this was a 2 to one ratio.
00:38:54.770 -- So let's say that this was 500KV and this was 250KV just
00:38:58.598 -- for nice numbers. Even though the 2:50 is not something
00:39:01.788 -- you'd run across much.
00:39:04.660 -- Then we would say OK. Well then this. Let's say that
00:39:07.608 -- this is 1000 to one CT and this is going to be what?
00:39:15.290 -- Or 1000 to 5C T, and that's what would this
00:39:17.760 -- would need to be then.
00:39:24.010 -- Remember, this is.
00:39:26.200 -- Two to one is the effective voltage transformation
00:39:28.680 -- ratio, so the current goes the opposite, right?
00:39:32.170 -- So this one would need to have 500 to 5 setes.
00:39:37.110 -- So that would be one that would be an example of a
00:39:39.894 -- good cancellation. So let's say that this was.
00:39:44.450 -- 500KV to 250KV.
00:39:50.810 -- And the cities were.
00:39:53.330 -- 1000 to 5
00:39:56.690 -- in. 500 to 5 so that's something that you could pretty easily.
00:40:00.320 -- Fine cities.
00:40:03.260 -- To cancel that right?
00:40:06.340 -- If we look at 3:45 to 138.
00:40:13.080 -- That's not going to be so easy to find CTS that give
00:40:16.572 -- you a good cancellation on that. So even if this was
00:40:19.773 -- even if these were still.
00:40:22.920 -- Thousands of five.
00:40:27.930 -- This would need to be basically 1000 times.
00:40:33.640 -- 38 / 345.
00:40:37.240 -- To five.
00:40:43.830 -- And chances are that's not going to be a nice stock
00:40:47.108 -- number that you're going to be able to buy in. SNS ET.
00:40:56.510 -- And so it's one that we're we'll talk about a solution for that,
00:41:01.424 -- but this is basically going to
00:41:03.692 -- be. Having
00:41:06.760 -- taps on the relay.
00:41:10.600 -- So watch mechanical relays. What they had was they had multiple
00:41:13.625 -- tap points where you could
00:41:15.000 -- connect. The inputs from the transformer for the differential
00:41:19.010 -- and you could partly correct for that mismatch to a degree you
00:41:23.690 -- couldn't. You could not connect 4 correct for it perfectly, but
00:41:27.980 -- you could. You could go a long ways towards correcting it.
00:41:33.160 -- What we'll see in probably not today. We may. I don't know if
00:41:37.697 -- we get to the example today, what you'll see in
00:41:41.187 -- microprocessor relays now that's just a number, so it's just a
00:41:45.026 -- scaling factor, so you can. So basically you as you enter the
00:41:49.214 -- stuff into the relay for setting it, you're entering the
00:41:52.704 -- information so the relay calculates that tap and you
00:41:55.845 -- don't even have to answer. Calculate it yourself so you say
00:41:59.684 -- OK, here is the MVA rating. Here's the voltage rating.
00:42:03.680 -- And then at the relay says OK and this is the rated
00:42:06.980 -- current and just basically calculates it for you.
00:42:11.830 -- And then you also put the seat. The actual CT ratios 'cause it
00:42:15.444 -- puts that in as a correction to.
00:42:27.670 -- Another thing you'll see in a lot of large power Transformers
00:42:31.080 -- is they have taps, right?
00:42:34.410 -- So we may see.
00:42:37.830 -- 500KV to 250KV.
00:42:42.510 -- Anne, this could be we could
00:42:46.392 -- have. Plus 2 1/2% + 5%
00:42:58.620 -- And these could also have some different apps. So if
00:43:01.930 -- you start putting.
00:43:04.060 -- If you and so in some cases, these maybe.
00:43:08.340 -- For lower power ones, these may be on load. Tap
00:43:11.695 -- changing Transformers where they can be changed. In other cases
00:43:14.745 -- the transformer has to be D energized for crew to come in
00:43:18.405 -- and change that tag.
00:43:22.870 -- What is that tap change due to the differential current?
00:43:32.540 -- You just change the ratio of the transformer, right? So you've
00:43:36.984 -- gone to the effort of correcting for compensating for this, this
00:43:41.428 -- ratio and the CT ratios. Now you just threw that off because you
00:43:46.680 -- changed the transfer. The power transformation ratio by 2 1/2%.
00:43:59.070 -- Then another one would be.
00:44:25.660 -- The transformer is always going to draw some magnetizing current
00:44:28.480 -- if it's energized right.
00:44:32.250 -- And this is something that's.
00:44:34.160 -- Going into the transformer and not coming out.
00:44:44.190 -- And as we talked about last time, this might be 2 to 4%,
00:44:48.948 -- maybe 5% of the rated current.
00:45:07.230 -- It will be higher if the transformer is over excited.
00:45:13.210 -- So there's really two things that you need to look at with
00:45:16.414 -- over. Excitation is going to be.
00:45:18.830 -- If the over excitation is severe enough and last long enough you
00:45:23.114 -- want to trip the transformer.
00:45:25.910 -- But you don't want to trip it because you think it's an
00:45:29.414 -- internal fault, so you don't want to trip at the instant it
00:45:32.918 -- happens. So there's some tradeoffs on that, and the
00:45:36.460 -- harmonic content of that's going to be a factor in how
00:45:39.595 -- the relay responds to it.
00:45:44.120 -- Now there's another issue that you have to worry about
00:45:46.480 -- with magnetizing current.
00:45:51.280 -- What would that be?
00:45:58.370 -- So we have magnetizing inrush current.
00:46:09.250 -- So if you energize a transformer.
00:46:23.570 -- You're going to see a current that's going to
00:46:25.568 -- start out looking like this.
00:46:28.260 -- And it may take a second or two
00:46:31.508 -- to. One at one to two seconds to get down to the normal
00:46:36.314 -- magnetizing current.
00:46:40.990 -- So are people familiar? Why Transformers exhibit
00:46:43.867 -- this behavior?
00:46:52.120 -- So it goes down, it goes back to our hysteresis characteristic.
00:46:57.400 -- So the transformer is going to when it's operating is
00:47:00.650 -- going to be.
00:47:03.580 -- Following something that looks like this, right? So if this is
00:47:07.507 -- B versus H.
00:47:10.670 -- This is proportional to voltage. This is proportional to current.
00:47:15.790 -- So every time you go through a sinusoidal cycle, it's going to
00:47:18.982 -- trace this curve, right?
00:47:22.010 -- And so when you deenergize the transformer, you deenergize
00:47:26.042 -- nearer at a current 0, right?
00:47:29.630 -- And so when the current goes to zero, you're going to be
00:47:32.654 -- somewhere up here. And so there's going to be some trapped
00:47:36.706 -- flux on the core.
00:47:38.830 -- When it's deenergized and depending on where you were in
00:47:42.030 -- that hysteresis cycle, when the breaker contact cleared or what
00:47:45.230 -- the power factor of the current
00:47:47.150 -- was. Usually the final invoice and normal routine operation
00:47:51.948 -- when I want to Transformers.
00:47:54.940 -- D energize you open one side, then you open the other ones
00:47:59.476 -- you're interrupting, basically just magnetizing current with
00:48:02.122 -- the final. The energizing of the transformer.
00:48:06.540 -- When you re energize it.
00:48:09.140 -- How is voltage related to flux in a transformer?
00:48:13.830 -- So V is equal to NDF DT, right? So the flux in the voltage or 90
00:48:19.014 -- degrees out of phase with each other. But you can so that the
00:48:23.226 -- voltage here at some point in a sinusoidal voltage waveform you
00:48:26.790 -- can map that the flux when you energize it. So when you're when
00:48:31.002 -- you close a circuit breaker, there's going to be some
00:48:34.242 -- basically effective flux that you're you're trying to impose
00:48:37.158 -- on that core. So if you're lucky and you and you pose a circuit
00:48:41.694 -- breaker in the effective flux for the point on waiver, you're
00:48:45.258 -- closing. It's about what you trapped on the core.
00:48:48.680 -- Then there's not really going to draw any current.
00:48:53.430 -- If you're unlucky and you had trap works up here and you're
00:48:56.562 -- closed when you're somewhere down like this, now the
00:48:58.911 -- transformer is going to draw a lot of current to try to
00:49:02.043 -- equalize that flux. And after magnetizing inrush current.
00:49:06.320 -- And it's very nonlinear current.
00:49:09.000 -- And so this has a lot of harmonic content. The
00:49:12.210 -- generally it's going to be dominated by second and
00:49:15.099 -- then 5th and so on. But it's going to have more
00:49:18.630 -- even harmonics where the over excitation is only
00:49:21.198 -- going to be odd.
00:49:25.610 -- How's the modern steels that they're using in newer
00:49:29.615 -- Transformers? Do not have a sharper second harmonic
00:49:32.839 -- characteristic. They still draw big magnetizing currents, but
00:49:35.135 -- now there's not as clear a second harmonic, and we'll talk
00:49:38.292 -- about some of the issues with that later in the.
00:49:42.650 -- Not this, not later today, but next week or
00:49:45.570 -- the week after next.
00:49:49.040 -- So you've got these very large currents again, they're just
00:49:51.940 -- going into the transformer.
00:49:57.860 -- And so you know, if you're doing
00:49:59.764 -- a normal. Registration of the transformer. Not something
00:50:02.364 -- following like Re closing in a fault. You might have this side
00:50:06.312 -- open and you energize this side and so now you're seeing current
00:50:10.260 -- San people have measured currents as high as 15 per unit.
00:50:16.260 -- If there are a lot of lights, limits that is partly whether
00:50:19.596 -- the surrounding power system can supply that much current.
00:50:22.098 -- If there's too much impedance in the power system that won't
00:50:25.156 -- supply it.
00:50:28.120 -- And so you're doing. You have a differential element. You're
00:50:31.140 -- going to see. Let's say it's something more normal, like 5 to
00:50:34.764 -- 7 per unit for a second.
00:50:37.980 -- So in electromechanical relays.
00:50:41.570 -- One of the things that they did initially was basically turn off
00:50:46.274 -- the differential element until the inrush current period was
00:50:49.802 -- over. They still had issues where if you had two
00:50:53.199 -- Transformers that were close together and you energized one
00:50:55.638 -- when the other one was on, sometimes you had a sympathetic
00:50:58.619 -- trip of the different of the differential element for the one
00:51:01.600 -- that was already energized.
00:51:07.180 -- Professor, I have a question on this one, so
00:51:09.952 -- there is no saturation really, it's just the.
00:51:13.740 -- The core trying to reach that
00:51:15.876 -- flux level. But there's no saturation, so as.
00:51:21.150 -- It face it, it started has sort of a saturation effect because
00:51:24.966 -- of where it pushes the flux, but there really isn't any true
00:51:28.782 -- saturation of the core in this.
00:51:31.560 -- So why isn't it sinusoidal?
00:51:35.990 -- So when you think about the iron in the core right, you
00:51:40.423 -- basically have a bunch of magnetic domains that want to be
00:51:44.174 -- in random directions, right? So let's say that because of the
00:51:47.925 -- trap flux, they're all pointing
00:51:49.630 -- this direction. And for the inrush you're trying to flip
00:51:53.712 -- them all to go back. Basically you want the flux to go this
00:51:58.249 -- way, so you need to flip all
00:52:00.692 -- these domains. And.
00:52:03.920 -- They don't, simply.
00:52:06.420 -- Follow a nice thing in sinusoidal behavior as they flip
00:52:09.250 -- on this. So there's some resistance. I'm really
00:52:12.652 -- oversimplifying this, but basically it's it's a
00:52:15.186 -- magnetic. The nonlinear magnetic behavior of the core
00:52:18.082 -- that keeps it from looking sinusoidal.
00:52:25.980 -- And this harmonic, and So what we're going to see in a little
00:52:30.426 -- bit, is that to try to minimize
00:52:32.820 -- this effect. The second harmonic is often used as a
00:52:37.252 -- as a signature, so if the second harmonics above a
00:52:40.942 -- certain threshold.
00:52:43.030 -- Then it's got the relay will block the differential
00:52:46.189 -- element, so you can either do harmonic blocking or harmonic
00:52:49.699 -- restraint, which is basically making the slope steeper.
00:52:53.590 -- Now, this raises an interesting thing. From a relay point of
00:52:57.572 -- view. We talked about digital filters, right? So here we
00:53:01.192 -- talked about second harmonic. I talked about fifth Harmonic when
00:53:04.812 -- I talked about over excitation detecting over excitation.
00:53:09.520 -- So remember what we talked about with digital filters? If
00:53:12.270 -- we're using cosine filters.
00:53:14.730 -- Well, the is the what is a cosine filter due to harmonics.
00:53:19.866 -- What's the gain about cosine filter 0, right? So the relay
00:53:24.574 -- needs a separate.
00:53:26.820 -- Cosign filter that if you want to measure second harmonic or
00:53:30.582 -- you want to measure 5th harmonic or any of the others, you need
00:53:35.028 -- to have some separate filter elements that are going
00:53:38.448 -- to calculate those.
00:53:40.160 -- Because the normal cosine filter using for your protection
00:53:43.400 -- calculations is going to have a gain of zero and block those.
00:53:49.450 -- And when you start getting up to 5th or 7th, now you're
00:53:52.450 -- starting to get up to the range where the low pass filters,
00:53:55.450 -- anti aliasing filters also going to have an effect on
00:53:57.950 -- them.
00:54:03.460 -- So when you talk about residual magnetism, why doesn't it die
00:54:07.387 -- out? So if I'm.
00:54:09.370 -- I'm switching off or closing opening the breaker in front of
00:54:13.286 -- the transformer at equals to zero. Eventually the residual
00:54:16.490 -- magnetism should die out, right? If I'm not energizing it back in
00:54:20.762 -- let's say days or weeks. So does it die out and not? It does
00:54:25.746 -- decay OK, so basically it's a it's a thermal process. So
00:54:29.662 -- basically these are going to try to randomize if the car is warm
00:54:34.290 -- when you demagnetize it, then they tend to randomize faster
00:54:37.850 -- than if the core is cool as the core as a transformer cools that
00:54:42.834 -- slows down the rate.
00:54:44.460 -- That randomization OK, but even if it's gone to zero an you
00:54:48.900 -- closing your somewhere up here still we're going to have
00:54:52.970 -- some issues on that.
00:54:57.930 -- Awhile back, well actually one of the Masters students here who
00:55:01.989 -- works at Sweitzer. Now guy named Doug Taylor looked at using a DC
00:55:06.786 -- source to preflex the transformer so you could put
00:55:10.476 -- the trap flux at a known at a known point and then if you have
00:55:16.011 -- Breakers with individual phase control then you can control
00:55:19.332 -- when you close them.
00:55:22.220 -- They also are using variations of that an like.
00:55:28.760 -- There's been a lot of stuff looking at that in Europe, for
00:55:32.324 -- example, in some of the offshore wind farms where they basically
00:55:35.591 -- are in a system that can't supply that magnetizing current
00:55:38.561 -- to magnetize the core, because there isn't a source strong
00:55:41.531 -- enough to provide it out there.
00:55:44.090 -- And so they want to be able to close the Transformers with no
00:55:48.276 -- inrush. And so rather than pre flexing the cores, they're
00:55:52.692 -- looking at trying trying to dissipate the flux in the
00:55:56.960 -- core so that they can bring it to zero, and then they do
00:56:02.004 -- individual phase control on the Breakers to minimize the inrush.
00:56:07.670 -- Also the whole pre fluxing minimize trying to get the
00:56:10.730 -- known side of inrush makes a big difference. If you have a
00:56:14.402 -- five legged core versus the three legged core.
00:56:18.190 -- So when you see the anticipated, basically they figure out at
00:56:21.644 -- what time or what voltage at what point in the voltage the
00:56:25.412 -- breaker was opened, and then based on that they calculate the
00:56:28.866 -- residual magnetism and the decay, and then they open
00:56:31.692 -- individual phases at different times. Or they close them, they
00:56:34.832 -- close them at specific times. OK, so the Breakers are always
00:56:38.286 -- going to try to open it. A natural current 0. Sure, an
00:56:42.054 -- there are actually some big problems if you don't open it in
00:56:45.822 -- natural current 0, because then you can get very big.
00:56:49.350 -- Transient response if you do a current shopping.
00:56:53.590 -- So the parasitic capacitance of the winding will interact
00:56:56.560 -- with the magnetizing branch, and you can see like 2 / 2
00:57:00.520 -- per unit voltage.
00:57:03.600 -- Even if you're chopped like half an amp.
00:57:11.700 -- That's a topic more for you. See 524 though.
00:57:20.290 -- OK, so any other questions related to the magnetizing.
00:57:24.950 -- Current behavior.
00:57:27.630 -- So these are all things that need to be accounted for in
00:57:31.758 -- creating the differential element an in setting like
00:57:34.510 -- the slope and the minimum operate current.
00:57:39.090 -- The other one to look at is going to be the transformer
00:57:42.342 -- phase shift.
00:57:49.760 -- So I started out drawing a YY transformer.
00:58:00.000 -- So the other thing we have to look at is Delta Y.
00:58:04.150 -- Or why Delta Transformers?
00:58:22.310 -- And so in North America there's an ANSI IEEE standard so that
00:58:27.926 -- the phase shift is generally very predictable, right?
00:58:33.330 -- And what's the standard?
00:58:37.720 -- Sorry. The high side is leading by $30.
00:58:59.020 -- So V line the neutral in the high voltage side leads
00:59:01.902 -- vilanda neutral in the low voltage side by 30 degrees.
00:59:06.370 -- The Power systems textbook I used when I was an undergrad
00:59:10.055 -- gave the impression that whenever you had a Y Delta
00:59:13.405 -- transformer or the Y side always led the Delta side by 30 degrees
00:59:17.760 -- because the author in.
00:59:20.620 -- All the cases he had run across the Y side was always
00:59:24.328 -- a high voltage transformer, 'cause he'd always worked in
00:59:27.109 -- transmission and never worked in distribution.
00:59:38.430 -- And so. So one of the effects were going to have
00:59:42.274 -- obviously is the 30 degree phase shift this also.
00:59:58.400 -- The Delta Y connection also
00:59:59.820 -- impacts the. Turns ratios right. So now you've got this other
01:00:03.574 -- sqrt 3 that gets put in there in addition to having.
01:00:11.110 -- The voltage transformation ratio.
01:00:14.910 -- That sqrt 3 shows up in the current so that reflects
01:00:18.320 -- back to the CTS.
01:00:23.620 -- And let's say that we have a Delta Y grounded transformer.
01:00:28.640 -- So this side.
01:00:41.830 -- When we're measuring the phase currents, there's going to be 0
01:00:45.537 -- sequence current on this side, but there won't be on this side.
01:00:53.200 -- And so even some Even so, one of the things that you have to be
01:00:57.550 -- careful of his solutions to try to fix this phase shift.
01:01:01.490 -- And fix this also after account for this. So I said that they
01:01:05.871 -- are one of the solutions that people did for less mechanical
01:01:09.578 -- relays. Had to have an extra step added to it because of
01:01:14.094 -- the zero sequence kind.
01:01:26.250 -- So if we have a transformer.
01:01:47.130 -- So we can look at the CTS.
01:01:51.140 -- So for electromechanical relays.
01:02:00.880 -- The common solution in this for this was going to.
01:02:06.860 -- To use the CT connections to help cancel for the cancel this.
01:02:12.520 -- And so.
01:02:16.250 -- So one option.
01:02:31.830 -- Would be to connect the CTS on the Y grounded side in Delta.
01:02:38.340 -- And the CTS and the Delta side and Y.
01:02:57.440 -- You need to make sure you connect the Delta properly to
01:03:01.092 -- cancel the shift. But So what that means is that the that the.
01:03:07.110 -- Phase currents that the Delta phase currents.
01:03:12.580 -- Well, include the zero sequence current that's going
01:03:15.148 -- to circulate in that Delta, but then the line currents
01:03:18.358 -- coming off the Delta which go to the differential relay
01:03:21.568 -- will not have.
01:03:23.640 -- That current
01:03:29.600 -- morning your device is running low on memory.
01:03:37.470 -- So one of my colleagues has a sledgehammer. He brings the
01:03:40.737 -- class for people whose cell phones make noise during class.
01:03:47.100 -- The new phone is trying to shut it down.
01:03:52.290 -- And so this is so, you still will run across substations that
01:03:57.018 -- have the CTS wired this way from the electromechanical relays.
01:04:03.920 -- And then a second option.
01:04:16.440 -- Would be the connect.
01:04:18.660 -- This it is an Y and this it isn't Delta.
01:04:24.240 -- So yes, there's a problem with this one, right?
01:04:30.810 -- So now the.
01:04:35.270 -- The differential element on this, the current that goes to
01:04:38.140 -- the differential an element from this side, it's going to include
01:04:41.297 -- zero sequence current. The one in this one won't, right.
01:04:45.970 -- So this one is going to need.
01:04:55.020 -- So basically this one needed an auxiliary set of current
01:04:58.210 -- Transformers that would block the zero sequence current by
01:05:01.081 -- basically circulating it in the auxiliary Transformers and
01:05:03.633 -- not have a go to the differential element.
01:05:26.570 -- So now if you go to a substation where it's new
01:05:31.553 -- construction and it's designed not anticipating
01:05:34.271 -- that there's going to be microprocessor relays
01:05:37.442 -- protecting this.
01:05:47.680 -- Now the seats are going to be why on both sides and there
01:05:51.632 -- will be a ground reference in the seat path.
01:06:19.860 -- And it will also the CTA will basically perform calculations.
01:06:24.340 -- To compensate for the phase shift an it's going to
01:06:28.920 -- perform another calculation to remove I 0.
01:06:35.480 -- And these are actually going to be matrix multiplications.
01:06:48.380 -- So I have a handout that.
01:06:51.350 -- Maybe I will pass it out today. You need to
01:06:53.950 -- remember to bring it.
01:06:57.250 -- Don't be sorry.
01:07:13.600 -- And so.
01:07:18.360 -- This first calculation is basically.
01:07:23.660 -- Typical calculation that you would see.
01:07:27.220 -- Done in the relay.
01:07:29.840 -- For the.
01:07:32.120 -- As an intermediate step for going to the
01:07:35.264 -- differential element.
01:07:37.540 -- So you're gonna have.
01:07:40.570 -- You're going to have the primary currents. Then they're going to
01:07:44.112 -- be divided by the current
01:07:45.722 -- transform transformation ratio. Remember, these are
01:07:48.686 -- why connected.
01:07:54.000 -- And then there's also going to be this tap calculation, and
01:07:57.744 -- the other hand out goes into more detail about the how this
01:08:01.488 -- tap is calculated. And then there's going to be a correction
01:08:06.020 -- matrix, so the correction matrix the output is going to be the
01:08:09.920 -- secondary current with the phase and zero sequence correction.
01:08:16.110 -- And so the current from both windings are going to. So this
01:08:20.190 -- is actually. This would be the primary side, and then we're
01:08:23.930 -- going to secondary sidewinding. So this is actually.
01:08:27.470 -- The power transformer primary.
01:08:53.070 -- And then the correction matrix, or a number of correction matrix
01:08:58.240 -- we can do. And so when I say matrix zero, that is using the
01:09:04.820 -- IC Clock terminology. So if we think about o'clock, we're going
01:09:09.990 -- to have 12369, etc and then 12.
01:09:13.890 -- 12 is also equal to 0, right?
01:09:19.820 -- And so if we have a Y connection with, if you say
01:09:24.212 -- that we have basically our phase, a voltage is going to
01:09:28.238 -- be here at an angle of 90 degrees. That's our zero
01:09:32.264 -- position.
01:09:37.340 -- And so the Matrix Zero is assuming we have a Y
01:09:40.783 -- connection and we're not trying to do any reversal of
01:09:43.913 -- the voltages, so this will be just the identity matrix.
01:09:53.370 -- And then where matrix one is the one o'clock position and this is
01:09:59.129 -- one that in.
01:10:00.540 -- South America is often referred to as the DAB and
01:10:03.490 -- this would be a Delta.
01:10:08.250 -- AV connection so that means that the first winding of the
01:10:11.583 -- Delta is connected from A to B. The second line will be to
01:10:15.522 -- see the third one will be see to a. This gives you remember
01:10:19.461 -- North America. You're limited to either plus 30 degrees or
01:10:22.491 -- minus 30 degrees when you're going from Y to Delta. So all
01:10:26.127 -- we care about in North America is going to be the D1
01:10:29.763 -- in the D11 connection.
01:10:33.240 -- And then we have the D11 connection, and so if we
01:10:37.398 -- compare these all it's doing is exchanging
01:10:40.044 -- which rows are have the.
01:10:43.410 -- Then have the different column combinations.
01:10:47.840 -- And so, well, we'll talk about this a little bit more, applying
01:10:52.172 -- it in the other example.
01:10:54.970 -- And then, as I mentioned, we have that we need that zero
01:10:58.054 -- sequence removal matrix too.
01:11:03.900 -- And so that's what this one does.
01:11:08.460 -- And so this is mathematically reproducing
01:11:10.410 -- the effect of the current circulating in the Delta.
01:11:20.750 -- Anworth this what this is coming from?
01:11:24.700 -- A very good reference for summarizing this is.
01:11:31.420 -- A paper that was written by.
01:11:35.230 -- I group from Basler Electric John Horack.
01:11:37.659 -- Actually, I have a link to on their class links web
01:11:41.476 -- page. I have a link to webpage it he's got put
01:11:45.293 -- together an extensive web page was protective
01:11:47.722 -- relaying. Related links.
01:11:51.260 -- And so I did not. I gave you copy. It's, uh, some of the
01:11:54.676 -- pages from this paper. I have links to the whole paper on
01:11:57.604 -- the course web page. That's the on campus students. There
01:12:00.044 -- were some of the pages that I'm going to talk to talk
01:12:02.972 -- about today and next time.
01:12:06.810 -- So this is just showing sort of the connection information
01:12:10.070 -- as a reference for the rest of this paper.
01:12:16.410 -- So.
01:12:18.450 -- He has uppercase letters to indicate the primary lowercase
01:12:22.635 -- to do the secondary.
01:12:25.520 -- And then he has the third of the terminal ends an the.
01:12:31.060 -- So this would be the polarity end of the wine,
01:12:33.656 -- and this is the nonpolarity end of the winding.
01:12:40.150 -- And so. This is one of the things that you go through.
01:12:45.030 -- You're going to find different people in different places, use
01:12:48.580 -- somewhat different notation so we see UV WABC.
01:12:52.070 -- And so on.
01:12:59.290 -- And so if we wanted to build a YY transformer in a typical
01:13:05.166 -- North American connection so when we see the W1W 2W3, those
01:13:10.138 -- are referring to the winding.
01:13:14.330 -- The windings of the six windings that produced the
01:13:17.372 -- three phase transformer.
01:13:21.590 -- And then it's not very obvious, but these are his
01:13:24.910 -- polarity marks for those windings.
01:13:28.910 -- And so H1X1 this is high voltage. This is
01:13:31.664 -- low voltage and so on.
01:13:34.330 -- And so mapping these this is how they would map.
01:13:39.870 -- Tell the two winding sets.
01:13:47.510 -- And so winding one and winding 4 on the same course.
01:13:50.282 -- So these two are going to be in phase with each other.
01:13:55.700 -- And so you can use this to build the diagram for how
01:13:59.168 -- the transformer ones relate to how the windings relate
01:14:01.769 -- to each other.
01:14:06.900 -- And so then he goes on to look at.
01:14:15.830 -- So the basically the Y zero is the one that's most
01:14:19.669 -- common in North America.
01:14:24.100 -- And so we can look at things that change polarities by so
01:14:27.556 -- the Y four is now we're shifting things down to the
01:14:30.724 -- 4:00 o'clock by putting winding one connected to Phase
01:14:33.316 -- V.
01:14:35.850 -- White and then we can just look at all these different
01:14:39.546 -- combinations. WHI Six is just reversing the polarity so the
01:14:42.906 -- polarity marks reversed unwinding one.
01:14:47.440 -- And so this is another one that is more of an industrial
01:14:51.076 -- power systems one, but you'll sometimes see Transformers
01:14:53.500 -- with wired opposite of the polarity marks.
01:14:57.580 -- Then he goes through the same thing with Delta windings.
01:15:02.450 -- So the. And so next time we'll go back and look at
01:15:06.270 -- this in terms of a Y Delta transformer. How we do the
01:15:09.054 -- plus 30 if the Y is a high side, how we do the minus 30?
01:15:12.534 -- If the why is the low side?
01:15:17.010 -- And so this paper goes on to kind of lead into deriving
01:15:21.402 -- those connection matrices.
01:15:24.560 -- And so we'll finish talking about this paper next time, and
01:15:28.014 -- then we'll talk about the.
01:15:31.130 -- Example handout so that we're going to apply these
01:15:34.622 -- connection matrices to measurements for a fault.
01:15:38.450 -- We can look at an internal fault or an external fault. We
01:15:42.458 -- can also look at what happens if somebody accidentally left
01:15:45.798 -- ascete shorted in the substation and how that plays
01:15:48.804 -- through these connection matrices.
01:15:51.560 -- So with that, well, any questions before we stop.
01:15:55.730 -- OK, and just a reminder for the outreach students.
01:15:58.115 -- There is no class on campus next week, so there will be
01:16:01.295 -- no new lectures for a week.
01:16:05.650 -- OK, that's all done.
Hi everyone. Welcome to EM 513. In our session today, we're going to talk about great by choice by Jim Collins and it really is a good follow on to the last session we had where we talked about.
Way by choice, and hopefully you're going to see some similarities of the concepts. But there's also a little different twist that I'd say comes out of the research that was done for this book. And hopefully, though, you'll see how those things really do hang together pretty well. And.
Seemed to make a lot of sense.
Here we are again in our overall course framework. We are in this last session on leading organizations. After today, we'll have two more sessions that will where we will focus on the concept of.
Execution and really applying good discipline to getting things done within the broader organization, which of course will be an extension to a lot of the concepts we talked about in leading others. And then the final session of the class will be focused on building the leadership pipeline within your business. We'll talk at that point about transitions you may be going through.
As, as even you yourself move from.
Or move along a management career path or leadership career path and we'll talk about how you can do the right things to invest in your team and really make sure that you have a leadership pipeline that's going to set you up for.
Having good successors, and we talked about that in the last session. And if you do have the chance to read rate by choice, there's some great stories in there about how people did in fact set themselves up for.
Succession planning, if you will.
I wanted to at least start with, as a refresher, the good to great framework that we talked about last time and I'll I'll try to make references here.
Where I think it's appropriate, and if you recall the high level framework that came out of the research in good to great was this notion of having disciplined people, disciplined thought and disciplined action. And we talked about 2 concepts within each of those areas and hopefully you'll see the connections as the work is extended to the research done for great by choice.
Here is a little bit of background on the research that.
Took place for great by choice. It was a 9 year research project.
That was started in 2002, and it was based on the question why do some companies thrive in uncertainty, even chaos, but others do not?
The high performing study cases that were examined in the book were called 10 Xers.
The research done for built to last you know if you recall really looked at companies that had been successful over this 15 year time frame.
In good to grade, the research was similar, but it also looked at another dimension. It looked at the extremity of change that was happening in the particular environment that these businesses were in and that was a critical element that was explored along with the performance of each of these companies.
What is A10 xer in the context of this book?
It is a company that has sustained what Conn's calls truly spectacular results for an era of 15 plus years relative to the general stock market and also relative to its own industry.
The enterprise achieved these results in a particularly turbulent environment.
Full of events that were uncontrollable, fast moving, uncertain and oftentimes harmful to the businesses.
The companies studied began their rise to greatness from a position of what they describe as vulnerability.
Where they were either young or a pretty small company at the start of this journey.
They started by examining over 20,000 companies. They had a set of criteria and ultimately cuts that they used to continue to whittle down the list. In fact, they went through 11 layers of cuts to get to this final set of 10 experts.
It didn't include the list here because my assumption is you're all going to.
Read this book.
On Page Six of the book identifies the final set of business cases, and quickly here I'll read these Amgen, Biomet, Intel, Microsoft, Progressive Insurance, Southwest Airlines, and striker.
Many of these of course are very familiar to us and they certainly are in businesses that we would say are either.
Very competitive. I'm tech. Lots of competition.
Significant changes, etc.
And that those things all contributed to their ending up on this final set of TENEX cases.
Interestingly enough, the TENEX cases during the comparison time frame.
Or during the timeframe assessed and with the comparison companies, they performed 30 times better.
Which is really pretty phenomenal.
The framework that Collins is going to use as a result of the research done here is really this triangle I have in the center of the slide I put in just as a starting point again the framework that we saw in good to great and.
The three key areas there were disciplined people, disciplined thought, discipline, action.
Level 5 leadership of course was a critical element discussed as a part of disciplined people and you can see they carry forward this level 5 leadership. They are calling it level 5 ambition in this case and what they really highlight the most or maybe in addition to the characteristics we saw discussed last session are this idea.
Or is this idea of inspired motivation?
In a particularly turbulent environment where there's a lot of change happening.
00:00:30.200 -- Yes.
00:00:33.030 -- So today we will continue discussion about the
00:00:35.870 -- modified, all the method and Runge Kutta methods. So we
00:00:39.420 -- will talk about the formulas and then accuracy and so on.
00:00:43.325 -- So I give you hand out and the problem. I'll use it
00:00:47.585 -- today so that we can cover a little bit faster. And then
00:00:51.845 -- I'll spend time on other material. OK, so.
00:00:58.460 -- In there you remember in all this method in order to go from
00:01:03.751 -- point X&YN to point XN plus one 1 + 1, essentially with another
00:01:09.042 -- next index, we only use information from the previous
00:01:12.705 -- point. So in a modified or leave use information from 2 points
00:01:17.589 -- and we use oil as step to go to the point X N + 1 NU N +
00:01:24.915 -- 1. This is predicted point.
00:01:27.950 -- And then be available slope at the predicted point and we use a
00:01:33.059 -- slope at initial, not initial. But the point that we start
00:01:37.382 -- start from and then we average these slopes defined slope
00:01:41.312 -- alone, which we find essentially construct line right tangent
00:01:44.849 -- line and then we find approximation at the next step.
00:01:48.779 -- So I also wrote this method last
00:01:51.530 -- time. So you can either define predictor which is the Oilers
00:01:57.000 -- step and then this is slope at.
00:02:01.370 -- .1 right and here we have slope at .2 and then we average slopes
00:02:07.082 -- and this is how we find the next. The next point all we can
00:02:12.794 -- write down these slopes explicitly. So K1 is a slope at
00:02:17.282 -- point. XNYN and then we use it to March to find point you and
00:02:22.907 -- plus one. Then we find K2 slope at the second point and then we
00:02:27.793 -- take every to the slopes defined. And if you don't want
00:02:31.632 -- to use K1K2 and just write this in terms of an even without you
00:02:36.518 -- N + 1, then you just write explicitly all the expressions
00:02:40.357 -- for you and plus one. So this is a first step. Predictor
00:02:44.894 -- does not change and in the second step in the character.
00:02:48.970 -- You have your own plus one equals UN plus H / 2, so you
00:02:53.702 -- take average. This is your slope at point XYN. This is your point
00:02:58.096 -- and you X N + 1 right here. This is your predicted point. U N + 1
00:03:03.842 -- essentially just written
00:03:04.856 -- explicitly. OK.
00:03:09.510 -- Modified the oldest method uses two term approximation from the
00:03:13.990 -- Taylor series right. The constant term and the linear
00:03:18.022 -- term. The modified Euler method uses. Also next terms uses
00:03:22.502 -- quadratic term in the Taylor expansion, so if we go back to
00:03:27.878 -- their tail expansion then modified Euler will use up to
00:03:32.358 -- age squared term. So this means that the first time that you
00:03:37.734 -- neglect will be proportional to
00:03:39.974 -- H cube. Right next will be age to the 4th. Each of the 5th and
00:03:45.450 -- if H is small then this will be a dominant term. So air local
00:03:50.070 -- error over one step will be proportional to H cube.
00:03:54.290 -- And then you find cumulative error after multiple steps right
00:03:58.000 -- after. If you're going from zero to X final, then the error will
00:04:02.823 -- be proportional to age squared, so similar usually you lose one
00:04:06.904 -- order when you sum the errors you find cumulative error. So
00:04:10.985 -- since modified term all this but it matches the 1st three terms
00:04:15.437 -- in the Taylor series up to and including termination squared,
00:04:19.147 -- the local area is proportional to each cube, but the cumulative
00:04:23.228 -- error is proportional to age
00:04:25.083 -- squared. So if air is proportional to H squared
00:04:28.998 -- and instead of H, you take H / 2, what would happen
00:04:32.910 -- with the error?
00:04:35.610 -- As will decrease by approximately 1 force, right? So
00:04:38.265 -- if you see so, this is a way how you can check that your method
00:04:42.690 -- is quadratic. So this means that your method is quadratic,
00:04:45.935 -- so your error is proportional to each squared. Let's say you
00:04:49.180 -- write a program and how would you verify that? Yes, the method
00:04:52.720 -- is programmed correctly. So what you can do you take you take a
00:04:56.555 -- test problem for which you know exact solution, so you can look
00:05:00.095 -- at the error because error would be the difference between exact
00:05:03.340 -- solution and numerical solution. So you go from.
00:05:06.430 -- Initial time to some final time final point, and you compute
00:05:11.457 -- solution at the final point.
00:05:14.530 -- And you look at the error right? And then you decrease error by
00:05:18.391 -- half and look how the error will change. So if error bill
00:05:21.955 -- decreased by half, this means that you have a linear method.
00:05:26.250 -- If it decreased by quarter, than its accuracy is quadratic.
00:05:32.310 -- OK. So this is a way to verify that your program is correct,
00:05:37.448 -- and then once you verify your code then you can change
00:05:41.034 -- equation. You can change function, then you can more or
00:05:44.294 -- less thing that your program is reliable, computes correctly, so
00:05:47.554 -- this is what happens with the error. Is H decreased by half
00:05:51.466 -- then the arrabelle because by a factor of four and just for
00:05:55.704 -- comparison. Again for all this method it's a linear
00:05:58.638 -- convergence. So if you decrease age by half your error will also
00:06:02.550 -- decrease approximately by half.
00:06:05.710 -- OK.
00:06:11.410 -- And so essentially we know the methods we just. I can just
00:06:15.442 -- rewrite it may be in the way that is more convenient for
00:06:19.810 -- programming. So if we want to solve initial value problem with
00:06:23.506 -- some initial condition. So what do we need? We need initial
00:06:27.202 -- condition right? So X not, why not? We also know we need to
00:06:31.570 -- know the step size and how many steps we have to perform right
00:06:35.938 -- function F is known. So once you have equation you can find
00:06:39.970 -- function F so again.
00:06:41.420 -- Then before you need to compute 'cause you have some homework
00:06:46.051 -- that you have to actually implement by hand or using
00:06:50.261 -- Calculator. So write down the formulas before you substitute
00:06:54.050 -- values right so?
00:06:56.320 -- You can, we can use either write this in terms of predictor
00:07:00.256 -- corrector or we can use this slopes K1K2 to write the method
00:07:04.192 -- so XN plus 1 = X N plus H. So every time you increment by H
00:07:09.440 -- right and also we can write
00:07:11.408 -- that. H is X final minus X starting divided by number of
00:07:17.326 -- steps right or number of steps is X final minus 0 / H right?
00:07:23.150 -- So if you know number of steps you know initial point
00:07:28.142 -- terminal point then you can find step size or vice versa.
00:07:32.718 -- If you know step size you can find number of steps.
00:07:39.730 -- OK, predict this step is just the oldest method.
00:07:43.490 -- Right and then corrector? So predicted allows you to find
00:07:46.940 -- this predictive point you N + 1 and then corrector will find
00:07:51.080 -- slopes at both points and average them to find exponent.
00:07:55.210 -- OK, and again Alternatively this is using the K1K2 and but
00:07:59.687 -- essentially the same.
00:08:01.550 -- OK, so whatever way you prefer, you can use.
00:08:08.170 -- OK, any questions here.
00:08:14.070 -- So let's look at the example.
00:08:16.890 -- So in this example you have to implement modified order in.
00:08:23.520 -- And solve the problem in 2
00:08:24.972 -- steps. So equation is Y prime equals X + y -- 1 squared.
00:08:30.250 -- Initial condition by 0 = 2. So find Y at. So you start from X
00:08:35.575 -- equals. O you go to X = 0.2 in two steps means that step
00:08:42.728 -- step sizes. 0.1 right again, it's a 0.2, so H is 0.2
00:08:49.380 -- -- 0 / / 2 zero point 1 which is written here.
00:08:56.710 -- Initial condition X00Y0 stole from here number of steps two
00:09:02.050 -- and then H you find.
00:09:06.260 -- Their function function F function F is the right inside
00:09:09.760 -- of your equation.
00:09:12.550 -- OK, and I know it's tempting to write down right away their
00:09:17.230 -- solutions, but take some time. Just write down the formulas in
00:09:21.520 -- terms of X&YN, it's easier than to substitute. I mean, if you
00:09:26.200 -- program something then you just program with indices and then it
00:09:30.490 -- computable repeat, write your computations. But when you do by
00:09:34.390 -- hand then you have to keep track of X0X1Y0Y1 and then here you
00:09:39.460 -- have you also UN to worry about.
00:09:43.700 -- So you write down the formula. So this is your next.
00:09:46.850 -- Approximation of X. This is your predicted value just
00:09:50.540 -- using the Euler's method, because this is your function
00:09:54.230 -- F at X&YN and then.
00:09:57.420 -- This is your next approximation.
00:10:00.110 -- By using the previous and the average of slopes.
00:10:04.030 -- OK.
00:10:06.520 -- So for all this method to go from one point to another, you
00:10:11.109 -- do one is 1 stage method because you only use one point for the
00:10:16.051 -- modified order, it is 2 stage because you have predictor an
00:10:19.934 -- you have character. So each step has two parts.
00:10:24.160 -- OK.
00:10:26.920 -- So if we take so here, we have N equals.
00:10:33.010 -- Zero, so when N = 0, I have X 1 = X O plus H. We find 0.1,
00:10:40.462 -- which is what supposed to be predicted point Yuan Yuan plus
00:10:45.016 -- one. Will you one and then it's Y0 plus HX0Y0 and you substitute
00:10:50.398 -- values you get 2.1. So this is your predicted value and then
00:10:55.366 -- you can use it in the next stage
00:10:58.678 -- defined. Correction, OK, so this is your essentially. This is the
00:11:02.650 -- same as what you have here.
00:11:05.450 -- So it might be more beneficial to use key one key two if you
00:11:10.014 -- want to reduce time on writing because you have to rewrite
00:11:13.600 -- this. And this is your slope at the predicted point. Again, just
00:11:17.512 -- write down X0Y0X1U one before you substitute values, because I
00:11:20.772 -- mean you see that becomes messy.
00:11:29.940 -- OK, so then we substitute values and we obtain approximation. So
00:11:33.845 -- so we did two stages, but this is the first step.
00:11:38.670 -- OK, it's not 2 steps first step. So now we use N = 1 and
00:11:45.525 -- this allows us to find X2U2 and Y2. So X2 is exam plus H, so
00:11:52.380 -- we have you too is a prediction using the Oilers step from Point
00:11:58.321 -- X one U-1 and then you do is correction with average of
00:12:03.805 -- slopes. Again as you see, right down X one U1X1X2U2 and so on.
00:12:09.880 -- And then approximate and then substitute values.
00:12:16.130 -- So finally so this is our approximation of a solution at
00:12:19.639 -- 0.2, and again this is not exact value, right? It's only
00:12:23.148 -- approximation because we use out of infinitely many terms in the
00:12:26.657 -- Taylor series, we only use 3.
00:12:29.290 -- So H is finite, right? So definitely we have an error. OK,
00:12:33.442 -- so schematically what is going on here? You start. Your initial
00:12:37.248 -- condition was at 02 right? This is your point.
00:12:42.180 -- Predictor brings you to point X one U-1.
00:12:47.560 -- You find slope at this point at X1. You want you find slope at
00:12:54.224 -- X0Y0. You average corrector gives you point X1Y1.
00:12:59.420 -- This is your first step, but
00:13:01.412 -- still stages. Then again from point X1 U one you find
00:13:06.648 -- predictor X2U2 right YouTube means has index as Y two. So
00:13:11.510 -- please different letter. But it is the same index and then
00:13:16.372 -- you've added slopes at X 11X2U2 average them and this
00:13:20.792 -- gives you correct correction point X2Y two again two stage
00:13:25.212 -- but it's one step.
00:13:31.180 -- OK.
00:13:33.760 -- Any questions here?
00:13:36.930 -- So example have either Euler or modified Euler method to
00:13:40.870 -- implement by hand, which means the step size will be generously
00:13:45.204 -- large, maybe like one or something that doesn't require
00:13:48.750 -- because you cannot use calculators for the test there
00:13:52.296 -- 'cause I don't know which device you bring mini. Something
00:13:56.236 -- computer that has access online and so on. So the algebra will
00:14:00.964 -- be simple enough that you can do
00:14:03.722 -- by hand. But for me, even if you have to perform 2 steps.
00:14:08.650 -- I need to see that yes, you know what is initial
00:14:11.411 -- condition. What is the next point and so on. So it will
00:14:14.423 -- not be a lot of steps, but at most Euler or modified Euler.
00:14:18.810 -- OK, your homework has more steps to perform, so you're welcome to
00:14:23.358 -- use whatever calculators computers to get the values, but
00:14:26.769 -- you have to write down. Then you can probably minimize number of
00:14:31.317 -- things that you write.
00:14:33.600 -- OK, your project Modeler project is based on
00:14:36.888 -- implementing these methods actually not implementing.
00:14:39.354 -- Using them to solve problems because the
00:14:42.231 -- programs functions are available on the course
00:14:45.108 -- websites. You just have to.
00:14:49.070 -- Maybe on Monday I'll bring the laptop so I'll show you where
00:14:52.646 -- files are and how to use them.
00:14:57.500 -- OK so next method.
00:15:00.250 -- To consider is so called 1st order on the quota method.
00:15:06.320 -- And the idea here is the falling. So we saw from their
00:15:10.880 -- modified all the method that if we use information from two
00:15:15.060 -- points then we get more accurate
00:15:17.340 -- approximation. Right, so can we use more points to get the even
00:15:22.577 -- more accuracy and the question the answer is yes. So in this
00:15:27.101 -- case we use four points.
00:15:29.560 -- So we go from .1.
00:15:32.980 -- 2.2 Essentially this is your order step. We get point .2.
00:15:38.645 -- Then we use this slope K2 to go to .3.
00:15:44.670 -- We use the .3 slope. Do you go to .4 and then we take weighted
00:15:50.790 -- average of the slopes at this
00:15:53.238 -- point? OK, so OK.
00:15:57.250 -- Um?
00:16:00.400 -- So which points we use? We use
00:16:03.529 -- point X. We use point in the middle of this interval at X N +
00:16:08.925 -- H / 2 and here we have two points to use and we also use
00:16:13.050 -- point at X = N + 1.
00:16:16.350 -- So do we? Do we give the same weight essentially the sum of
00:16:21.316 -- slopes over 4? No, we give twice more weight at points
00:16:25.518 -- in the middle.
00:16:36.200 -- And this is last page that you have an I I did not print. I
00:16:42.095 -- have a few more pages, but.
00:16:45.910 -- I'll explain what we have here. So if you have.
00:16:51.170 -- Probably let me use, maybe this so you don't
00:16:55.094 -- have this page, but this is a recap of the last page, so you
00:16:59.672 -- have to want to solve the 1st order equation with some given
00:17:03.596 -- initial. So I'll bring a copy of
00:17:05.885 -- this next time. So what you do you find the slope at .1. This
00:17:11.178 -- is where you start.
00:17:13.540 -- Then you match half step to .2 using this slope.
00:17:19.110 -- So you have you have X N + H over to you. This is your X
00:17:25.462 -- displacement an in. Why you do Oilless step with step size H of
00:17:30.623 -- it but slow K1.
00:17:33.320 -- So once you have this point, you use this point
00:17:37.380 -- to evaluate slope.
00:17:39.970 -- So I compute slope K2 and I find
00:17:43.858 -- .3. By marching again from KXAN half step and using alone Def
00:17:50.700 -- line with slope Cato.
00:17:53.650 -- OK, this gives me point X 3.3, so from .3 then we match full
00:18:00.090 -- step to find point for using Slope case 3.
00:18:05.020 -- Once you have all these four slopes, you have weighted
00:18:08.630 -- average so you have you give weight 1 to the first point and
00:18:13.323 -- to the last point, but two weights to the .3 and two and
00:18:18.016 -- three. So overall you have for slopes six slopes. So you divide
00:18:22.348 -- age by 6.
00:18:24.130 -- So this is your average weighted slope.
00:18:28.090 -- OK, and then you can write this slope like even if you don't
00:18:32.640 -- know this. So you use information from four points. OK
00:18:36.140 -- to find, so this is a full stage
00:18:38.940 -- method. Anne.
00:18:43.250 -- In order to go from X&YN 2 X N + 1 one plus one, it is still
00:18:49.098 -- using only one previous point, right essentially, but it does
00:18:52.538 -- it in four in four stages.
00:18:55.260 -- OK.
00:19:01.760 -- OK, So what I can say here is there wrong accoutre
00:19:08.756 -- force order matches there?
00:19:14.230 -- The local error in their own decoder 1st order method is of
00:19:18.406 -- order H as a power 5.
00:19:21.980 -- OK, but when you find cumulative error then you lose one order
00:19:27.476 -- and then overall the error is.
00:19:31.300 -- Proportional to H is about four and you can. You can appreciate
00:19:35.116 -- it if H is let's say 0.01 to 10 to the point is the power of
00:19:40.204 -- negative one right? All this method will have error also of
00:19:43.702 -- the order of 10 to the minus
00:19:45.928 -- one. Right modified order will have error to the order 10 to
00:19:50.999 -- the minus. Two but longer code will have error of the order 10
00:19:56.205 -- to the minus four right? So you see that it's occasionally.
00:20:00.180 -- Logic difference in the in the accuracy. So all this method in
00:20:03.744 -- order to get the same accuracy.
00:20:06.480 -- You need to use smaller H. Ruby code allows you to use larger
00:20:11.992 -- step size. Because the error is small and So what you save,
00:20:17.542 -- you save the number of steps. But again, remember that one
00:20:21.634 -- step of the longer quota has
00:20:23.866 -- four stages. So at each stage you have to evaluate function
00:20:28.565 -- and function evaluation may be consuming, so that's so. That's
00:20:32.015 -- why it's not very cheap method because at every step you have
00:20:36.155 -- four function evaluations.
00:20:39.020 -- OK.
00:20:40.850 -- How do we check that method is first order accurate? If we
00:20:45.686 -- decrease H by half, their level decreased by a factor of.
00:20:55.410 -- If H is replaced with H / 2, so the arrabelle decreased
00:20:59.622 -- by a factor of.
00:21:03.430 -- 22 to the power. 416 right so this is, you see, is a
00:21:08.929 -- significant difference between this method and that method OK?
00:21:14.650 -- Which method you would like to use if you have
00:21:17.570 -- to solve your problem?
00:21:22.740 -- So you have a choice. You have three methods and you have to
00:21:27.095 -- implement MCF thread programs, foiler for modified or Lefranc
00:21:30.110 -- equal to which method you would start with.
00:21:33.900 -- If you want to solve the problem that you don't know
00:21:36.595 -- solution about anything about.
00:21:39.660 -- Probably oil it while it's easy to implement, its lately least
00:21:43.037 -- accurate, but it's easy to implement, and for example, if
00:21:46.107 -- you programmed at an, you see that it doesn't work. Maybe
00:21:49.484 -- there is no point of investing time, right? But if you know
00:21:53.168 -- that yes solution exists, an that gives you what you need,
00:21:56.545 -- you can start with all the method just to get a feeling of
00:22:00.536 -- what solution is going to do. But then if you need to have
00:22:04.527 -- more accuracy, or let's say if you have to compute for long
00:22:08.211 -- time and maybe. Many points then you probably would use on
00:22:12.492 -- GeForce order method. Matlab in fact has so called variable
00:22:15.782 -- Force 5th order method ricotta which allows us to change the
00:22:19.401 -- step size depending on the estimate of the error. So they
00:22:23.020 -- have some estimate of the error in air is small. Then
00:22:26.639 -- you can use largest largest step. If estimate becomes
00:22:29.600 -- large then you decrease the time step so it's not
00:22:32.890 -- constant, is not the same method that would be
00:22:35.851 -- considered here.
00:22:37.550 -- OK, I mean whatever Matlab built-in function solver.
00:22:42.500 -- OK, so an example and I'll have this available on the course
00:22:47.564 -- website and then I'll give you a hand out next time just to show
00:22:53.472 -- you what is going on in this ricotta method. So if we
00:22:58.958 -- want to solve this initial value problem starting from .12 and
00:23:03.600 -- finding oh at 1.4 in two steps using force ordering decoder
00:23:08.242 -- method, so two steps means that.
00:23:11.460 -- What is H we go from 1 to 1.4.
00:23:15.900 -- Each is.
00:23:19.750 -- So age is 1.4 -- 1 / / 2, so this will give us.
00:23:27.190 -- Zero Point 4 / 2 will be 0.2, right? So this is your step size
00:23:32.515 -- capital N number of steps is 2 inside of each step. How many
00:23:37.130 -- stages do you have?
00:23:39.330 -- Four stages right? So 4th function evaluations. So for
00:23:42.480 -- each stage you have to write K1K2K3K four and then the
00:23:46.330 -- weighted average to find next
00:23:48.080 -- approximation. So K1K2K64 will be different for
00:23:51.738 -- inside of each step.
00:23:55.390 -- OK, so H with no envy, no initial condition. X Zero is
00:23:59.626 -- one, XY0 is 2 OK, what is a function function is X + sqrt y.
00:24:04.921 -- This is your function F so F of XNYN is X N + sqrt y N.
00:24:12.780 -- OK, and then you carefully substitute these values, right?
00:24:16.263 -- I mean it's OK for demonstration purposes, so you probably want
00:24:20.520 -- to have this done by computer right? Unless function is simple
00:24:24.777 -- that you can, you can do it. OK, so gave one is a slope at first
00:24:30.969 -- point. In this case at X0Y0, right? You find Cato is you
00:24:35.613 -- March, you replace X with 0 + H to point in between and Y zero.
00:24:41.418 -- You follow The Cave one slope.
00:24:45.130 -- Right, so this is your X value. This is your why value once you
00:24:48.882 -- have them, you substitute them in the function, so you replace
00:24:51.830 -- X with this. Why is that?
00:24:54.140 -- Annual value it so this gives you slope K2 then use K2 here to
00:24:59.768 -- find .3 again. X is just half step away while zero plus K 2 *
00:25:05.798 -- H / 2 This is your ex. This is your Y value you put in the
00:25:12.230 -- function you evaluate. Finally K 4 you much full step.
00:25:16.890 -- Use slope case 3. This is your X value. This is your.
00:25:20.694 -- Why will you find slope K 4? You take weighted average.
00:25:24.181 -- You get next approximation.
00:25:31.380 -- OK, so now what you found you found.
00:25:37.130 -- X1 is 1.2 and Y one is 2.5201.
00:25:45.570 -- So now you use this.
00:25:47.540 -- To do another step so we have two steps here to do.
00:25:51.350 -- Right, so we have this and then again K1K2K3K four. But now
00:25:56.990 -- instead of X0Y0 you have X1Y1.
00:26:00.690 -- Just indexes shifted and so on, so I'll have this online and
00:26:05.034 -- I'll bring this on Monday.
00:26:09.020 -- OK, any are there any questions yes.
00:26:14.720 -- This is based on.
00:26:17.670 -- Next one you just. Right, you found this one from the previous
00:26:22.220 -- right step and then you just keep it the same, but you keep
00:26:26.640 -- adding. So what I do OK, I have formulas dependent on X&YN
00:26:30.720 -- right? So here I had to use.
00:26:34.040 -- My end was zero.
00:26:37.050 -- So I replace end with zero everywhere before I try to
00:26:41.285 -- compute anything. So in the next stage I have to use N equals.
00:26:46.910 -- 1.
00:26:48.560 -- OK so I replace.
00:26:51.160 -- SNV X1 Y end with Y1 and similarly everything else but
00:26:56.011 -- K1K2K3 will be different now from the previous case from the
00:27:00.862 -- previous step. So I have F of X1Y1 compared to.
00:27:06.930 -- F of X0Y0 I have for K2 I have F of X1 plus HY one plus K 1 * H
00:27:14.250 -- / 2 I have here with HO, but this key one and escape one of
00:27:19.740 -- the same. OK, so at every state at every step you
00:27:24.894 -- K1K2K3K four will be different, so he probably
00:27:28.142 -- technically we have to write down another index an, but
00:27:32.202 -- it just will increase. It will be very cumbersome. So
00:27:36.262 -- so all slopes are different. So for each step you
00:27:40.322 -- recompute your slopes.
00:27:44.870 -- OK, that's why.
00:27:47.280 -- Write this before you implement your substitute values.
00:27:52.260 -- OK, right X 0X1YY1Y2 and so on.
00:28:00.600 -- This will not be on the test.
00:28:04.540 -- OK, but it is in the homework so you have to do it.
00:28:10.850 -- OK, any other questions?
00:28:16.150 -- So more about numerical methods. So we teach a
00:28:20.236 -- course which is now taught between three department's
00:28:23.868 -- mathematics, physics, and engineering is typically
00:28:26.592 -- chemical genius teaching and then so this method are
00:28:30.678 -- studied in more details, but not only this, but also
00:28:35.218 -- root, finding methods, argon values, eigenvectors,
00:28:37.942 -- solving linear systems. So maybe I should write so.
00:28:47.210 -- More about.
00:28:58.720 -- Anne.
00:29:01.050 -- 428 and there's also so this physics for 28 and engineering.
00:29:07.850 -- So it is the same course. I mean, of course the also
00:29:12.602 -- graduate version.
00:29:15.760 -- 529 I think and physics.
00:29:20.070 -- 528 So it's slightly dependants who is teaching, but we cover
00:29:24.437 -- the same material, so professors from different departments POV
00:29:28.010 -- alternate, but we have the same syllabus to follow.
00:29:36.920 -- No, normally you choose whatever flavor you want on
00:29:40.664 -- your transcript, but that's the only difference.
00:29:46.810 -- OK questions.
00:29:51.800 -- So.
00:29:53.810 -- I'll start Chapter 3, which is linear equations of
00:29:57.689 -- higher order.
00:30:16.410 -- So far we've dealt only with first order linear equations,
00:30:20.940 -- but we will look at their methods that will allow us to
00:30:26.376 -- solve equations of high order and linear equations do not
00:30:30.906 -- require. Coefficients to be constantly constant, but we will
00:30:35.444 -- for simplicity we will start with questions of miss
00:30:39.656 -- constantly efficients. OK, so let's just recall the definition
00:30:43.868 -- of the linear equation of ends order so linear.
00:30:51.720 -- And order.
00:30:54.120 -- Differential equation. Has function derivative, second
00:30:58.768 -- derivative, and so on up the derivative order NPL linearly in
00:31:04.675 -- the equation so?
00:31:07.440 -- Hey Ann.
00:31:13.720 -- Plus a N -- 1.
00:31:21.670 -- Loss etc plus a 2X.
00:31:25.550 -- D2Y T X ^2.
00:31:29.040 -- Plus a one of X.
00:31:34.190 -- Plus a 0 times function Y
00:31:37.382 -- equals. Some function that does not depend on why.
00:31:44.150 -- So remember.
00:31:46.460 -- How, how, how we define linear function we defined in a
00:31:50.673 -- function is a X + B right? So your independent variable AP is
00:31:55.652 -- linearly means raised to the power one. So now in the linear
00:32:00.248 -- differential equation you have the same but for the function
00:32:04.078 -- derivative, second derivative and up to the ends of the
00:32:07.908 -- derivative. These are the functions of X only.
00:32:11.540 -- Right then they don't involve why dependence are
00:32:14.716 -- of X is right inside.
00:32:18.020 -- Can be 00 but linearity means that you don't have y ^2.
00:32:22.604 -- Don't have y * Y prime and so on so they appear linearly
00:32:27.952 -- same way as X appears in the linear function.
00:32:32.770 -- In this case, we multiply by constant in the equation. In
00:32:36.268 -- the case of, the equation, coefficients can be functions
00:32:39.130 -- of X at most.
00:32:41.960 -- OK. So if.
00:32:46.070 -- Oldest coefficients.
00:32:51.390 -- Constants.
00:32:57.190 -- Then we have equations with constant coefficients.
00:33:00.960 -- Then differential equation is.
00:33:05.460 -- A linear.
00:33:08.260 -- Differential equation with.
00:33:13.190 -- Constant.
00:33:18.560 -- Coefficients. And these are, these equations are
00:33:23.016 -- typically easier to solve. Otherwise equation has
00:33:26.103 -- variable coefficients.
00:33:36.630 -- This differential equation is.
00:33:41.680 -- Linear, viz.
00:33:48.200 -- Variable coefficients.
00:33:53.330 -- OK.
00:33:55.070 -- If you have a linear equation an if right hand
00:33:59.190 -- side is identically zero, then we have linear
00:34:02.486 -- homogeneous equation and in fact homogeneous equation
00:34:05.370 -- only can be introduced for linear equations. I mean
00:34:09.078 -- sometimes can be introduced for nonlinear, but typical
00:34:12.374 -- is for linear equations.
00:34:15.830 -- Then
00:34:19.440 -- linear differential equation.
00:34:22.060 -- Is homogeneous.
00:34:29.190 -- Otherwise.
00:34:35.270 -- Linear differential equation is.
00:34:42.490 -- Nonhomogeneous
00:34:47.710 -- let's look at some examples that we've just trying to classify
00:34:51.593 -- and then to analyze the order if it is linear. If it is
00:34:56.182 -- homogeneous or non homogeneous.
00:35:01.010 -- So Y double prime plus X y = 0. So what is the
00:35:05.716 -- order of this equation?
00:35:09.740 -- 2nd order.
00:35:12.000 -- Is it linear or nonlinear?
00:35:16.800 -- Linear right? Because XY is multiplied by a function of
00:35:21.040 -- XY, double prime is multiplied by one. So linear is a
00:35:25.704 -- sensitive linear. Is it homogeneous or non
00:35:28.672 -- homogeneous?
00:35:32.050 -- Homogeneous because there is no function that only depends on X
00:35:36.428 -- rated 0 so homogeneous.
00:35:42.100 -- Coefficients are constant or variable.
00:35:46.930 -- Variable because we have X right? So this.
00:35:55.180 -- Variable coefficients. OK.
00:35:59.730 -- What about this equation?
00:36:03.530 -- X ^2 y double prime minus two XY prime plus Y to the XY equals
00:36:10.640 -- two X -- 1.
00:36:13.550 -- Order
00:36:15.760 -- 2nd. Is it linear or nonlinear?
00:36:25.740 -- OK, so we have Y times each of the XY prime times minus two XY
00:36:30.630 -- double prime times X squared. We have termed it depend on why
00:36:34.868 -- is it in this form?
00:36:38.870 -- That you have derivatives multiplied by at most
00:36:41.350 -- functions of X.
00:36:43.760 -- Yes, so it is linear, right?
00:36:46.730 -- Is it homogeneous since it is linear or not homogeneous?
00:36:51.860 -- None, because we have to explain this one.
00:36:56.590 -- So, nonhomogeneous? And coefficients are variable
00:37:00.892 -- variable right? Because we have functions so this.
00:37:07.660 -- Variable coefficients.
00:37:12.280 -- OK, next example.
00:37:15.440 -- Is 2 Y triple prime minus three Y prime plus seven Y equals
00:37:22.499 -- luxury four X ^2 -- 1?
00:37:26.490 -- OK, the order of the equation is 3 third order.
00:37:35.940 -- Is it linear or nonlinear?
00:37:42.440 -- Huh?
00:37:43.970 -- Linear or nonlinear?
00:37:47.530 -- Why is it nonlinear?
00:37:52.610 -- We have function multiplied by 7 derivative multiplied by
00:37:57.002 -- negative three, so the order to multiply by two.
00:38:03.220 -- Linear.
00:38:07.420 -- What is in here an is 3.
00:38:10.950 -- Look for linear equation. You have function multiplied by at
00:38:14.430 -- most, so this may be
00:38:16.518 -- constant. Or maybe some function of X. This functional effects
00:38:20.159 -- may be nonlinear, but we look at the look at the YY prime Y
00:38:24.373 -- double prime up to the highest order derivative, not in terms
00:38:27.684 -- of X in terms of Y.
00:38:30.880 -- OK. So equation is.
00:38:34.260 -- Linear.
00:38:36.670 -- Since it is linear, is it homogeneous or homogeneous?
00:38:41.910 -- Non, because of the logarithm of X ^2. So nonhomogeneous
00:38:46.250 -- and coefficients are.
00:38:48.580 -- Constant rate with constant coefficients.
00:38:54.990 -- OK and last example.
00:38:59.640 -- White triple prime my plus 2Y double prime
00:39:04.216 -- minus y * Y prime +7.
00:39:08.920 -- The order is.
00:39:11.750 -- So the order. 3rd order.
00:39:16.710 -- Linnaean olenia.
00:39:21.560 -- Nonlinear because we have y * y prime right nonlinear.
00:39:28.920 -- We cannot say if it is ominous nonhomogeneous because we don't
00:39:33.980 -- have linearity to say this.
00:39:38.200 -- OK.
00:39:40.660 -- So big chunk of this course will be devoted on the 2nd order well
00:39:45.924 -- probably not sister going to order, so essentially it's
00:39:49.308 -- easier probably to solve 2nd order equations, especially when
00:39:52.692 -- you consider with variable coefficients. But the method
00:39:55.700 -- that we will develop for equations with constant
00:39:58.708 -- coefficients can be easy.
00:40:00.470 -- Applied to the 2nd order first Order 5th order intense order I
00:40:06.086 -- will have 19th order example to consider. So yes.
00:40:15.070 -- It is defined only for linear for linear equations, so.
00:40:21.530 -- I've seen some definitions that say if identical is zero
00:40:24.950 -- solution satisfies equation, then you can think of this as
00:40:28.370 -- homogeneous. In this case it won't be because if you have
00:40:32.132 -- zero then this is 0. This is non 0 but typically homogeneous is
00:40:36.578 -- only for linear equations because you have some relation
00:40:39.656 -- to linear algebra. So linear systems, linear equations so
00:40:42.734 -- that's the reason. So once you may have a question on the
00:40:47.180 -- test to classify equation equations and then so similar
00:40:50.258 -- like we we've done here.
00:40:52.400 -- You look at the order if it is linear then you can think
00:40:56.716 -- it's homogeneous, nonhomogeneous, but if it's
00:40:58.708 -- not linear then you just stop.
00:41:01.720 -- OK.
00:41:06.820 -- OK, so let's start with second order linear
00:41:10.396 -- homogeneous equations so.
00:41:15.190 -- So we consider 2nd.
00:41:19.420 -- Modern.
00:41:24.600 -- Linear homogeneous differential equations.
00:41:30.280 -- We will first address the problem when we have none of
00:41:34.031 -- them, we have homogeneous equation. Once we know how
00:41:37.100 -- to solve homogeneous then we will study how to solve
00:41:40.510 -- nonhomogeneous equations because there are different
00:41:42.556 -- methods how to address this problem. OK, so in general,
00:41:45.966 -- if you have second order linear equation then you can
00:41:49.376 -- write it in just using some coefficients which are
00:41:52.445 -- functions of X.
00:41:55.200 -- A1 of X.
00:41:57.440 -- Divide the X + A zero XY homogeneous. This means very
00:42:03.776 -- inside is 0.
00:42:15.190 -- And so let's look at example and then we will try to establish
00:42:20.546 -- some properties of solutions to the homogeneous equations.
00:42:25.750 -- So example is.
00:42:38.500 -- Let's let's let's do 2 examples, so example a.
00:42:43.530 -- X ^2 D two YG X ^2 -- 2 X divided X.
00:42:51.680 -- Plus plus two y = 0.
00:42:54.760 -- So you can see it is second order, right?
00:42:58.620 -- It is linear 'cause you have y * 2 divided you exams minus 2X and
00:43:03.480 -- this is also linear term and it is not just homogeneous because
00:43:07.368 -- there is no function that only depends on X and not multiplied
00:43:11.256 -- by wire derivative and.
00:43:13.310 -- My first statement is that the X ^2.
00:43:17.680 -- Is a solution of this equation.
00:43:21.770 -- How do we? How do we verify that this function is a solution?
00:43:27.300 -- We have the substitute and check if you get identity right. OK,
00:43:30.840 -- So what do we have? If X squared is a solution, what is the
00:43:34.970 -- derivative of this solution?
00:43:37.500 -- 2X and 2nd derivative will be 2, so we have X ^2 * 2 -- 2
00:43:44.572 -- X times. Two X + 2 times function. So do we have 0?
00:43:51.430 -- We have two X ^2 -- 4 X squared plus two X squared
00:43:55.863 -- right, so cancels so 0 = 0. So this means that X squared
00:44:00.296 -- is a solution of the equation. What happens if we?
00:44:05.020 -- Multiply this function by constant.
00:44:09.370 -- By some arbitrary constant.
00:44:13.130 -- The claim is that this is also a solution.
00:44:18.740 -- So C One is an arbitrary constant.
00:44:25.870 -- Indeed.
00:44:27.990 -- 1st Order derivative will be 2 C 1X and 2nd order derivative will
00:44:32.839 -- be 2C1, right?
00:44:35.290 -- So we have X ^2 * 2 C 1 -- 2 X times 2C. One X
00:44:43.162 -- + 2 * y C One X ^2.
00:44:48.260 -- C1 is present in all the terms, right and otherwise
00:44:51.760 -- you have two X ^2 -- 4 X squared X squared, so this
00:44:56.660 -- is also zero. So again, if you take a solution of a
00:45:00.860 -- linear homogeneous equation multiplied by arbitrary
00:45:02.960 -- constant, you still get the solution, so this will be
00:45:06.460 -- still a solution.
00:45:08.850 -- So similarly.
00:45:11.370 -- And you can verify that X is a solution.
00:45:18.240 -- The first derivative is.
00:45:20.930 -- One second derivative is 0, right? So we have X ^2 * 0
00:45:26.819 -- plus. I'm sorry minus.
00:45:32.040 -- Minus two X * 1 + 2 times function you can see that
00:45:37.318 -- this is 0.
00:45:40.060 -- And if I multiply this solution by an arbitrary constant, I also
00:45:44.452 -- get a solution.
00:45:49.450 -- Let's say C 2 * X is a solution.
00:45:55.110 -- And we can verify this by substitute and so again, second
00:45:58.883 -- derivative will be 0, so we have X, y ^2 * 0 -- 2 X times C 2
00:46:05.057 -- + 2 * C Two X.
00:46:07.860 -- Zero and finally, if you consider linear combination of
00:46:12.225 -- these two functions.
00:46:14.860 -- In linear combination is you multiply function by constant by
00:46:19.410 -- different constant and you add
00:46:21.685 -- so C1. X ^2 + C two X is.
00:46:27.720 -- Also a solution.
00:46:33.150 -- OK, let's let's verify, because probably those cases are easy to
00:46:36.560 -- see. This one is a little bit tricky. OK, so we have X squared
00:46:40.900 -- times second derivative. What is the 2nd derivative here?
00:46:45.460 -- To see one right plus zero.
00:46:48.830 -- Minus two X times first order
00:46:51.908 -- derivative 2C1X. Plus C2.
00:46:56.020 -- And plus two times functions, so C One X ^2.
00:46:59.830 -- Plus it 2X.
00:47:02.870 -- Do we have here?
00:47:06.240 -- So if I look at terms with C1.
00:47:10.270 -- I have two X ^2 -- 4 X squared, two X squared, they cancel.
00:47:18.040 -- In terms with C2.
00:47:21.470 -- Minus two XY2 plus to exit to
00:47:24.837 -- also cancel. Right, and this is here.
00:47:29.070 -- So 0 = 0.
00:47:36.510 -- So what we showed here is that if you have linear homogeneous
00:47:41.178 -- equation an if you have solutions, you form linear
00:47:44.679 -- combination. So you multiply by constants and you add and you
00:47:48.958 -- have you keep them arbitrary. Then result is also a solution
00:47:53.237 -- to this equation.
00:48:01.930 -- So maybe just another example be.
00:48:05.740 -- G2Y G X ^2 +
00:48:09.486 -- 3. Divide X + 2 * y = 0 again. This is second
00:48:17.322 -- order equation. Linear homogeneous coefficients are.
00:48:22.880 -- Constant variable so 2nd order.
00:48:29.390 -- Linear homogeneous.
00:48:34.050 -- With constant coefficients.
00:48:39.860 -- And the claims here are that E to the minus X is a solution. So
00:48:44.615 -- at this point I'm not saying how we find them, we will. We will
00:48:49.053 -- know this soon, but let's just check. So if you have it to
00:48:53.491 -- the minus X derivative will be minus E to the minus X second
00:48:57.612 -- derivative will be with the plus sign, right? So you have either
00:49:01.416 -- the minus X + 3 * E to the minus X minus sign plus two times
00:49:06.488 -- function E to the minus X.
00:49:10.010 -- You get 0 right, and similarly if you multiply by constant.
00:49:16.900 -- Is a solution.
00:49:20.190 -- That I will not verify, but you can see that this is also
00:49:23.284 -- straightforward to do.
00:49:27.080 -- And then another solution here available is E to the minus, 2X
00:49:32.864 -- is a solution.
00:49:38.360 -- And if we multiply by constant, it is a -- 2. X is a solution.
00:49:45.230 -- And finally, linear combination is.
00:49:50.340 -- Also a solution.
00:49:53.260 -- OK.
00:49:56.540 -- So the result is how much time do I have left?
00:50:05.830 -- One minute. OK, so I'll I'll write the just result
00:50:09.690 -- so theorem.
00:50:12.320 -- So principle.
00:50:15.760 -- Of linear superposition?
00:50:22.460 -- It only works for linear homogeneous equations, so given.
00:50:28.790 -- 2nd order equation.
00:50:39.160 -- 2nd order.
00:50:42.280 -- Linear.
00:50:44.550 -- Homogeneous equation.
00:50:51.200 -- If. Why one of XY2 of X?
00:50:56.650 -- Our solutions.
00:51:01.250 -- Of this differential equation.
00:51:05.810 -- Then
00:51:08.050 -- their linear combination.
00:51:15.580 -- C1Y one of X + y two Y2FX is also solution
00:51:21.212 -- of the same equation.
00:51:37.400 -- See once you're here.
00:51:41.630 -- C1C2 are arbitrary constants.
00:51:50.360 -- And similar result holds 4th order equations, right? So this
00:51:54.430 -- doesn't change. OK, so I guess I'm out of time, any questions?
00:52:01.690 -- OK, thank you and drive safely.
00:00:21.260 -- Alright, good morning.
00:00:22.202 -- Welcome to class city.
00:00:23.460 -- You got your homework turned in?
00:00:25.340 -- How was the assignment? Do OK with it.
00:00:29.170 -- How was the airfoil problem the long?
00:00:34.050 -- But solvable.
00:00:34.688 -- Just kind of have to be patient
00:00:36.921 -- as you work your way through it.
00:00:39.240 -- OK, so since you're here right now,
00:00:40.970 -- I will tell you next time we
00:00:42.503 -- have a midterm next Thursday.
00:00:43.930 -- We have mentored.
00:00:45.007 -- There will be an airfoil problem on the exam.
00:00:48.200 -- So study that up.
00:00:49.276 -- We'll review it a little bit later on today,
00:00:51.830 -- OK? Alright I have.
00:00:54.616 -- I have colleagues here at the university
00:00:57.292 -- and some friends in the law school.
00:00:59.620 -- That's probably a bad sign,
00:01:01.420 -- right that I have lawyer friends.
00:01:05.130 -- And I always ask, you know,
00:01:07.130 -- do you do you bring up current
00:01:09.265 -- events in your classes?
00:01:10.790 -- You know they're always the Supreme
00:01:12.854 -- Court litigation stuff going on?
00:01:14.450 -- I hear no all the time.
00:01:16.450 -- It takes too much work.
00:01:18.120 -- We do not do that in gas tax.
00:01:20.780 -- OK, just to be clear,
00:01:22.450 -- so.
00:01:25.150 -- This is. The seven minutes of terror.
00:01:29.460 -- OK, the perseverance Lander
00:01:30.888 -- that landed on Mars last week.
00:01:33.030 -- So I thought that I would go through
00:01:35.854 -- step by step to let you know what's
00:01:38.812 -- going on and then watch a video of it.
00:01:41.950 -- Just 'cause I'm the teacher, right?
00:01:44.096 -- And I say we could watch videos,
00:01:46.590 -- we're going to watch videos, all right.
00:01:49.092 -- Let's check this out.
00:01:50.520 -- So 10 minutes before landing,
00:01:52.300 -- the shell comes off and this
00:01:54.346 -- is what the Lander looks like,
00:01:56.590 -- and you can see that it maneuvers itself.
00:01:59.850 -- OK, now it's 8 minutes to entry.
00:02:01.870 -- Gets balance right here.
00:02:02.958 -- What kind of body would we call that right
00:02:05.550 -- there, that kind of rounded surface?
00:02:09.750 -- That's a blunt body. OK,
00:02:12.520 -- that's how that's how any kind of spaceship.
00:02:18.460 -- Enters the atmosphere with a blunt body and
00:02:21.100 -- we'll see that once it starts to enter.
00:02:23.630 -- Look at this, although they
00:02:25.170 -- don't draw it as a shock.
00:02:27.180 -- We know because we are experienced
00:02:29.352 -- gas dynamicist that is a
00:02:31.554 -- shockwave that occurs right there
00:02:33.274 -- and notice that's a peak heating.
00:02:35.290 -- OK, let's look at some of these numbers.
00:02:39.140 -- Here it is 78 miles in altitude
00:02:42.262 -- above the Martian surface.
00:02:44.430 -- Look at this velocity 13,000.
00:02:47.670 -- Mph. Let's move in.
00:02:52.573 -- That is about 5900 meters per second, OK?
00:03:00.730 -- And let's see here.
00:03:02.322 -- So I did a little bit of calculation here.
00:03:06.760 -- The Martian atmosphere temperature.
00:03:08.512 -- Obviously it ranges like
00:03:10.264 -- every other atmosphere,
00:03:11.870 -- but kind of a standard temperature
00:03:15.272 -- is 60 degrees Centigrade below 0.
00:03:18.410 -- Minus 60 pretty cold, so that is 213
00:03:22.210 -- Kelvin enters at 5900 meters per second.
00:03:25.730 -- It's Martian atmosphere is primarily
00:03:28.170 -- carbon dioxide is about 95% carbon dioxide,
00:03:31.548 -- and so it's gamma is about 1.3
00:03:34.831 -- and its molecular weight is 44.
00:03:37.930 -- So we can calculate RA 314 divided
00:03:41.038 -- by 44 and it works out 'cause you
00:03:44.993 -- know how to calculate Mach numbers.
00:03:48.430 -- This works out to be a Mach number of 25.6.
00:03:53.910 -- Entering the atmosphere.
00:03:58.570 -- That's moving. That's moving OK,
00:04:00.990 -- so one of the one of the one of the
00:04:03.975 -- primary designs for this blunt body is that
00:04:07.951 -- you're traveling on Mach number of 25.6.
00:04:10.940 -- Tell me do parachutes work
00:04:12.895 -- very well in a lot #25.6 no.
00:04:15.720 -- OK, we will talk actually a little
00:04:18.303 -- bit later on in the semester that
00:04:21.516 -- there are some supersonic parachutes.
00:04:24.050 -- OK, there are some,
00:04:25.506 -- but this is not designed to do that.
00:04:28.390 -- So what the blunt body does is
00:04:30.721 -- that it absorbs that kinetic
00:04:32.582 -- energy and slows it down.
00:04:34.550 -- OK, so it's moving that amount #25.
00:04:37.080 -- Here's where it heats up that peak
00:04:39.460 -- heating and then it starts to decelerate,
00:04:42.150 -- and then finally finally it starts
00:04:44.244 -- to slow down and what it can do
00:04:47.223 -- this hypersonic aero maneuvering
00:04:48.731 -- what it does is kind of vibrate.
00:04:51.200 -- So it goes like this and it
00:04:53.657 -- converts that kinetic energy into.
00:04:55.650 -- Thermal energy and slows down.
00:04:57.510 -- That's what this maneuvering is.
00:04:59.360 -- And then finally.
00:05:00.803 -- Begins to deploy a parachute.
00:05:03.210 -- Does that at 400 meters per second.
00:05:05.980 -- Now, if you think in air that's
00:05:08.696 -- a little over Mach one,
00:05:10.730 -- it turns out for the Martian atmosphere and
00:05:14.098 -- these times it's a little bit over Mach one,
00:05:17.470 -- so it turns out that this supersonic,
00:05:20.240 -- but not real high,
00:05:21.820 -- not like hypersonic.
00:05:23.010 -- A parachute begins to deploy,
00:05:24.990 -- then the heat shield that
00:05:26.970 -- protected the spacecraft.
00:05:28.160 -- Right here, drops off.
00:05:29.988 -- OK falls off and then over here.
00:05:33.290 -- This is kind of neat.
00:05:35.210 -- The shell drops off and then there's
00:05:37.975 -- a little radar system right there
00:05:40.454 -- in that beams down to the surface to
00:05:43.756 -- determine the best place to land.
00:05:46.150 -- So it's like an autopilot.
00:05:48.140 -- It's like it's like an auto,
00:05:50.530 -- an artificial intelligence system.
00:05:52.602 -- That search arounds figures
00:05:54.674 -- out the best place to land OK?
00:05:57.420 -- Starts to collect that data and
00:05:59.706 -- then this shell drops off right
00:06:02.030 -- here and the Lander starts to
00:06:04.190 -- descend to starts to descend.
00:06:06.280 -- Excuse me, comes down,
00:06:07.776 -- it's got 4 little rockets right here
00:06:10.480 -- and these are called cold gas thrusters.
00:06:13.210 -- That's pressurized gas there,
00:06:14.902 -- so it's not necessarily a combustion
00:06:17.507 -- process starts to descend right here and
00:06:20.020 -- then it deploys what's called a sky crane,
00:06:22.830 -- so this hovers right here with those rockets,
00:06:25.910 -- and what the sky crane does.
00:06:28.380 -- Is that it lowers the Lander CABI
00:06:30.606 -- wires so that the Lander lands,
00:06:32.790 -- and then it cuts those wires in the sky,
00:06:35.840 -- crane falls away and you have
00:06:37.730 -- soft landing on the surface?
00:06:41.890 -- First off, if you're an engineer,
00:06:43.400 -- you can't look at that and say
00:06:45.213 -- that is not absolutely awesome.
00:06:47.230 -- To see that in action OK Now is actually.
00:06:49.980 -- That's kind of a complicated process if you
00:06:52.188 -- think of everything that's going on there,
00:06:54.550 -- you know one of the few seniors here that
00:06:57.016 -- learn about the Kiss principle, right?
00:06:59.125 -- Keep your design simple so that they work.
00:07:01.570 -- This is actually a pretty
00:07:03.090 -- complicated process.
00:07:03.700 -- Past Mars Landers.
00:07:06.030 -- Past Mars Landers actually have a
00:07:08.022 -- kind of a balloon on the outside
00:07:10.452 -- number of balloons that cover this in,
00:07:12.870 -- so that when it lands,
00:07:14.580 -- it actually bounces on the
00:07:16.230 -- surface of Mars until it stops.
00:07:18.340 -- Then the balloons deflated, opens up.
00:07:20.390 -- Then you have a Lander,
00:07:22.100 -- so spirit and opportunity landed like that.
00:07:24.500 -- OK, so.
00:07:26.460 -- That the pretty complicated
00:07:27.820 -- sort of landing process.
00:07:29.180 -- Now let's watch the video.
00:07:30.880 -- They actually in fact I heard
00:07:32.896 -- this on the news is that is that
00:07:35.661 -- in part of the design process,
00:07:37.680 -- they told a couple of engineers say hey,
00:07:40.400 -- listen,
00:07:40.804 -- would it be kind of cool to take high def?
00:07:44.890 -- Pictures,
00:07:45.179 -- High resolution pictures of the
00:07:46.624 -- landing process so they actually went.
00:07:48.450 -- I want to see RadioShack that kind
00:07:50.585 -- of dates me so they went to off
00:07:53.100 -- the shelf cameras and were able to
00:07:55.232 -- put it on the Lander so that you
00:07:57.360 -- can see the landing in process.
00:08:00.400 -- Dumb question, would you like to see it?
00:08:03.570 -- I thought so, so here we go.
00:08:05.630 -- So now that you know.
00:08:07.100 -- So now that you know the landing process,
00:08:09.450 -- let's see what we got here and fly
00:08:11.482 -- right maneuver where the spacecraft
00:08:13.007 -- will jettison the entry balance
00:08:14.612 -- masses in preparation for parachute
00:08:16.198 -- deploy and to roll over to give the
00:08:18.563 -- radar a better look at the ground.
00:08:23.330 -- Public it indicates she's deployed.
00:08:26.610 -- The navigation has confirmed that
00:08:28.390 -- the parachute has deployed an.
00:08:30.170 -- We're seeing significant
00:08:31.235 -- deceleration in the velocity.
00:08:32.660 -- Our current velocity is 450 meters
00:08:34.658 -- per second at an altitude of about 12
00:08:37.545 -- kilometres from the surface of Mars.
00:08:42.310 -- He tilts up. Perseverance is now,
00:08:45.000 -- so she was dropping off these
00:08:47.010 -- and then literally on Mars.
00:08:48.750 -- Just allow both the radar and the
00:08:50.920 -- cameras to get their first look
00:08:52.991 -- at the surface current velocity
00:08:54.771 -- it 145 meters per second at an
00:08:57.263 -- altitude of about 10 Columbia 9
00:08:59.321 -- 1/2 kilometers above the surface.
00:09:03.160 -- Now that's pretty cool to see that close.
00:09:06.420 -- Picture in that sort of definition of
00:09:08.667 -- the Martian surface. That's pretty neat.
00:09:14.260 -- And if you look on the bottom,
00:09:16.470 -- you can kind of see it's.
00:09:18.370 -- It gives the step filter contract about
00:09:20.540 -- players entry .3 meters that there
00:09:22.546 -- should come out altitude 7.4 kilometers
00:09:24.574 -- now has radar lock on the ground.
00:09:26.580 -- Current city is about 100 meters per second,
00:09:29.110 -- 6.6 kilometres of the surface.
00:09:35.220 -- President is continuing to
00:09:36.888 -- descend on the parachute.
00:09:38.560 -- We're coming up on the initialization of
00:09:41.507 -- terrain relative navigation and subsequently
00:09:43.641 -- the priming of the landing engines.
00:09:46.060 -- Our current velocity is about 90 meters per
00:09:49.724 -- second at an altitude of 4.2 kilometers.
00:09:53.320 -- Now, whether or not your geologist,
00:09:55.090 -- you could look at that surface
00:09:56.692 -- and say that there's windblown.
00:09:58.340 -- You can see the guys mentioned
00:10:00.086 -- that the reservation system has
00:10:01.595 -- produced a valid solution here,
00:10:03.060 -- and part of strain out the navigation water
00:10:05.500 -- or liquid that was there be a nominal.
00:10:07.780 -- We have timing of the landing engine's.
00:10:15.160 -- Back Shell survival at sea is 83
00:10:17.589 -- meters per second at about 2.6
00:10:19.838 -- kilometers from the surface of Mars,
00:10:22.110 -- we have confirmation that the
00:10:23.940 -- back shell has separated.
00:10:25.410 -- We are currently performing
00:10:26.870 -- the divert maneuver.
00:10:27.970 -- Travelocity is about 75 meters per
00:10:30.256 -- second at an altitude of about a
00:10:32.874 -- kilometre off the surface of Mars.
00:10:34.920 -- Here, in safety Bravo.
00:10:38.090 -- We have completed our
00:10:39.770 -- terrain relative navigation.
00:10:41.030 -- Current speed is about 30
00:10:43.130 -- meters per second altitude,
00:10:44.810 -- about 300 meters off the surface of Mars.
00:10:50.680 -- We have started our constant
00:10:52.570 -- velocity accordion, which means
00:10:54.084 -- we are conducting the skycrane,
00:10:55.970 -- so this is where the sky Crane
00:10:58.616 -- maneuver deploys at it drops,
00:11:00.510 -- there's the Lander right there?
00:11:02.400 -- I mean, that's that is totally cool,
00:11:05.040 -- 20 meters off the surface.
00:11:13.220 -- And you see that in the top view,
00:11:15.220 -- that's the that's the sky cream.
00:11:16.720 -- Rocky go delta.
00:11:18.148 -- Captain confirmed persevered
00:11:19.576 -- safely on the surface of Mars,
00:11:22.130 -- ready to begin seeking
00:11:23.930 -- the sands of past life.
00:11:29.220 -- There you go.
00:11:32.380 -- How great is that?
00:11:33.828 -- And that is pretty cool.
00:11:35.640 -- And since you are,
00:11:37.088 -- since you were all gas dynamicist's,
00:11:39.260 -- you know you could figure out the
00:11:42.186 -- aerodynamics of a good portion
00:11:44.444 -- of everything that we saw there.
00:11:47.210 -- In a couple of weeks actually,
00:11:49.100 -- starting next week,
00:11:50.528 -- we'll learn about rocket nozzles.
00:11:52.910 -- OK, and how they work good.
00:11:56.780 -- Any questions at all for get going?
00:11:58.950 -- Is it not a beautiful day
00:12:00.600 -- for gas at the office today?
00:12:02.670 -- It is awesome, OK?
00:12:05.420 -- Thursday is an exam at the end of class.
00:12:08.480 -- Today we will have a little review
00:12:11.360 -- an what's going to be on the exam,
00:12:13.920 -- but I want to just rehash
00:12:15.780 -- expansion waves to make sure
00:12:17.462 -- you've got that down expansion,
00:12:19.360 -- which are very important concept.
00:12:21.400 -- OK so.
00:12:23.500 -- Recall that an expansion wave
00:12:25.810 -- occurs when you have a supersonic
00:12:28.231 -- flow that turns away from itself,
00:12:30.650 -- so it's coming down this way
00:12:32.828 -- known as the mod numbers.
00:12:35.010 -- One goes through goes through
00:12:36.995 -- a turn away from itself.
00:12:38.980 -- There are some questions
00:12:40.568 -- last time after class,
00:12:42.160 -- so I just want to clarify
00:12:44.542 -- this that this line,
00:12:46.130 -- this leading Mauchline in this
00:12:48.205 -- trailing Mauchline constitute
00:12:49.450 -- what's called an expansion fan.
00:12:51.290 -- OK, those are expansion waves that.
00:12:53.810 -- That occur when a supersonic
00:12:56.005 -- flow turns away from itself.
00:12:58.200 -- OK, this leading Mauchline,
00:12:59.992 -- then that's the front edge of that fan,
00:13:03.470 -- and it occurs at this Mach angle.
00:13:06.540 -- Musa one OK?
00:13:09.470 -- It's it's the air turns through this
00:13:11.990 -- fan once it leaves the fan then it
00:13:14.769 -- falls the wall as it comes down here OK.
00:13:17.890 -- In the turning angle Delta OK,
00:13:20.590 -- recall a number of things.
00:13:22.840 -- The flow is isentropic.
00:13:24.640 -- No losses.
00:13:25.540 -- That means the stagnation pressure
00:13:27.790 -- remains constant across that turn,
00:13:30.040 -- their model number goes up.
00:13:33.190 -- It accelerates,
00:13:33.940 -- in fact,
00:13:34.690 -- I mentioned nozzles rocket nozzles will learn
00:13:37.357 -- how expansion waves work in rocket nozzles,
00:13:39.870 -- and that's how they that's how a
00:13:42.201 -- nozzle can produce supersonic flow.
00:13:44.320 -- Since the model number goes up,
00:13:46.550 -- the pressure goes down,
00:13:48.030 -- static pressure goes down,
00:13:49.510 -- static temperature goes down,
00:13:51.350 -- so these temperature and pressure ratios
00:13:54.182 -- right here are both less than one.
00:13:56.420 -- OK, again,
00:13:57.056 -- as you're going through problems,
00:13:58.650 -- make sure that you've got that.
00:14:01.850 -- That when you calculate those numbers
00:14:03.602 -- that your pressure and temperatures are
00:14:05.476 -- all trending in the right directions.
00:14:07.450 -- OK, if you haven't seen it already
00:14:09.445 -- in your homework problems,
00:14:10.870 -- but I've seen it all the time in exams.
00:14:13.670 -- You're under the pressure.
00:14:14.878 -- You gotta get the problem solved and
00:14:17.060 -- you accidentally invert a number.
00:14:18.640 -- Or you read it wrong.
00:14:20.200 -- OK,
00:14:20.540 -- check and make sure that all those
00:14:22.920 -- pressure temperature Mach number
00:14:24.332 -- values are going in the right direction.
00:14:26.670 -- OK.
00:14:28.710 -- Good we showed then what the
00:14:31.032 -- Prandtl Meyer angle was and it is.
00:14:33.400 -- It's a fictitious angle.
00:14:34.828 -- OK so it's not like as an angle.
00:14:37.740 -- You can take your protractor
00:14:39.540 -- out and measure it in the flow.
00:14:42.070 -- It's a mathematical construct that occurs
00:14:44.590 -- for every Mach number greater than one.
00:14:47.480 -- OK,
00:14:47.824 -- and as you learn in your in your homework
00:14:51.004 -- that you could go through the book
00:14:53.573 -- or go through com prop and be able
00:14:56.444 -- to figure out what that value of
00:14:58.840 -- Theta is that parental Meyer angle.
00:15:00.970 -- And this is the big relationship right here.
00:15:04.580 -- That the turning angle.
00:15:06.292 -- Right there is related to the
00:15:08.946 -- difference in the parental Myer angles.
00:15:12.100 -- OK. Alright, and this is this is
00:15:14.564 -- the key relationship right here.
00:15:16.420 -- When you're solving expansion weight
00:15:17.885 -- problems, you know any two values.
00:15:19.650 -- If you know the downstream Mach
00:15:21.360 -- number and the turning angle,
00:15:22.870 -- you can get the upstream Mach number.
00:15:24.920 -- If you know the upstream Mach number
00:15:26.901 -- in the downstream Mach number,
00:15:28.440 -- you get the turning angle.
00:15:29.900 -- If you know the turning angle
00:15:31.562 -- in the upstream Mach number,
00:15:33.120 -- you can get announcement number.
00:15:34.590 -- OK, so you'll be able to deduce
00:15:36.522 -- two pieces of information and
00:15:38.168 -- from this relationship right here
00:15:40.043 -- you can get the third OK.
00:15:42.030 -- Straight forward there.
00:15:46.230 -- OK, shock expansion theory.
00:15:48.054 -- You use this when you solve problems, OK?
00:15:54.360 -- So again, I don't want you to use
00:15:57.120 -- the airfoil function on com prop.
00:15:59.500 -- I want you to be able to look at
00:16:01.831 -- an airfoil like this and determine
00:16:04.504 -- if you have oblique shockwaves.
00:16:06.840 -- If you have expansion ways all
00:16:09.420 -- based on the geometry of the turn
00:16:12.395 -- right here and the angle of attack.
00:16:15.120 -- OK, let's let's, let's talk about.
00:16:17.160 -- Let's talk about a problem here real
00:16:19.505 -- quickly to make sure you've got this down.
00:16:22.260 -- 'cause this is, this is an issue
00:16:24.514 -- that comes up many times here.
00:16:26.680 -- Let's say you have a triangular
00:16:28.720 -- shaped airfoil.
00:16:29.400 -- OK, and then we'll just put
00:16:31.494 -- this at an angle of attack of 0.
00:16:34.160 -- So looks like this.
00:16:35.520 -- It's a symmetric airfoil.
00:16:39.930 -- Looks like this here and you have some
00:16:42.314 -- Mach number that's greater than one.
00:16:44.400 -- And let's say that we have a
00:16:46.647 -- turning angle here of 10 degrees
00:16:48.601 -- just to pick a number, OK.
00:16:50.590 -- K alpha is equal to 0,
00:16:53.290 -- so zero angle of attack there.
00:16:55.290 -- What kind of waveform do
00:16:56.955 -- you see at the bottom?
00:17:01.400 -- Nothing. What's the pressure that
00:17:03.725 -- acts on the bottom right there?
00:17:06.620 -- It's whatever your that's greater than one.
00:17:08.730 -- It's whatever your piece
00:17:09.934 -- of one is right there.
00:17:11.440 -- Whatever the atmospheric pressure is.
00:17:13.770 -- OK. Right, what do you see on
00:17:17.368 -- this top surface right up here?
00:17:21.580 -- Well, big shockwave.
00:17:22.555 -- The flow is turning into itself.
00:17:24.510 -- Changes 10 degrees,
00:17:25.740 -- so in oblique shock.
00:17:27.380 -- Forms right there and what's
00:17:29.240 -- the direction of the flow?
00:17:31.100 -- Flow follows the wall.
00:17:34.730 -- So it goes up this way.
00:17:36.790 -- OK, so here's where the here's
00:17:38.680 -- where the messed up part happens.
00:17:40.830 -- What occurs around the turn here?
00:17:44.510 -- Expansion wave.
00:17:46.340 -- OK, here's the question.
00:17:47.572 -- What is the turning angle
00:17:49.112 -- across the top there?
00:17:53.090 -- For me. 20 degrees.
00:17:59.000 -- Everybody see why that is.
00:18:01.140 -- If not, let's talk about it.
00:18:03.400 -- OK, if this is where the mistake comes in.
00:18:06.970 -- If it were 10 degrees.
00:18:09.810 -- Then what would be the direction
00:18:11.904 -- of the flow coming out here?
00:18:13.990 -- It would be horizontal.
00:18:16.970 -- If that turning angle 10 degrees
00:18:18.938 -- 'cause it goes down this way goes up
00:18:21.458 -- 10 degrees and so it's going to turn
00:18:23.919 -- another 10 degrees just to go horizontal.
00:18:26.330 -- OK, however the flow is not
00:18:28.772 -- horizontal on that side.
00:18:30.400 -- It goes down this way another 10 degrees.
00:18:34.230 -- OK, so this turning angle.
00:18:37.910 -- Right there. 20 degrees.
00:18:42.960 -- OK. Alright.
00:18:46.690 -- OK, you can calculate the
00:18:48.475 -- pressure in this region.
00:18:49.910 -- You can calculate the pressure
00:18:51.700 -- on this plate right here?
00:18:53.490 -- Can you calculate the pressure
00:18:55.280 -- in this region right here?
00:18:57.070 -- Absolutely OK with those three pressures.
00:18:59.910 -- Determine what the force is.
00:19:02.860 -- And then some of the forces.
00:19:05.930 -- In the vertical.
00:19:08.090 -- And the horizontal directions
00:19:09.534 -- get the lift in the draft.
00:19:11.700 -- OK.
00:19:12.160 -- Good.
00:19:12.620 -- OK, this is not so critical in
00:19:15.840 -- your calculations of lift and drag,
00:19:19.470 -- but an actually an oblique
00:19:22.250 -- shockwave forms here.
00:19:23.920 -- And the reason that is is because
00:19:26.188 -- the flow now comes down this way
00:19:28.809 -- and it's going to turn horizontally.
00:19:31.180 -- Across here.
00:19:31.922 -- So the float turns into itself,
00:19:34.150 -- and so there's going to be
00:19:35.890 -- an oblique shockwave,
00:19:36.760 -- but you don't have to worry about that
00:19:38.864 -- for to calculate the lift and drag.
00:19:41.090 -- OK, so it's this turning angle right there.
00:19:44.010 -- That causes problems.
00:19:45.102 -- I wanna make sure you got that down OK?
00:19:48.280 -- Excellent.
00:19:50.460 -- OK.
00:19:52.370 -- Overhead,
00:19:52.728 -- alright,
00:19:53.086 -- so actually all this is just a
00:19:55.592 -- review of what we talked about here
00:19:57.736 -- that the lift is equal to the sum
00:20:00.230 -- of the vertical components of all
00:20:02.150 -- the forces that act on the plate.
00:20:06.740 -- Very good. The lift coefficient
00:20:08.890 -- often used in the in determining
00:20:11.560 -- what kind of airfoil you want to
00:20:14.570 -- use and over what flight regimes.
00:20:17.590 -- OK is just the lift lift force.
00:20:21.340 -- Divided by 1/2 rho V squared,
00:20:23.660 -- this is the dynamic pressure.
00:20:26.230 -- Multiplied by the.
00:20:28.420 -- Multiplied by S here,
00:20:31.340 -- that is the area of the wing.
00:20:35.170 -- That's what S is there.
00:20:36.980 -- OK, and we showed in class in
00:20:39.101 -- the past that 1/2 rho V squared
00:20:41.245 -- is the same as one half P Mach
00:20:43.857 -- number squared right there.
00:20:47.600 -- OK.
00:20:50.040 -- So let's look at some.
00:20:51.890 -- Let's look at some things.
00:20:53.730 -- Let's let's just solve for L for
00:20:56.999 -- this relationship right here.
00:20:58.910 -- L and let's see what we can
00:21:01.101 -- do to generate lift here. OK.
00:21:03.381 -- We could have a better lift coefficient.
00:21:06.960 -- OK, so that's going to depend.
00:21:08.720 -- That's going to depend on
00:21:10.190 -- the shape of the airfoil.
00:21:11.660 -- OK, we could get better lift if you
00:21:14.212 -- have a higher freestream pressure.
00:21:16.990 -- OK, are you higher in the atmosphere,
00:21:19.430 -- lower in atmosphere that governs that?
00:21:22.880 -- But look at this right here. The lift.
00:21:26.392 -- Goes like the Mach number squared.
00:21:30.870 -- So what does that say about how fast you fly?
00:21:33.580 -- What is that going to generate?
00:21:36.120 -- More. Lift.
00:21:39.910 -- OK, so that means you can have
00:21:42.570 -- some very poorly shaped airfoils.
00:21:45.090 -- OK, so this Isabelle.
00:21:46.890 -- This lift coefficient might be bad.
00:21:49.590 -- But if your Mach number is high enough.
00:21:52.050 -- You can generate a lot of lift.
00:21:54.650 -- My number squared.
00:21:56.045 -- Also says that the that the wing
00:21:59.398 -- area S the larger the wing area,
00:22:02.320 -- the greater the lift you have.
00:22:05.290 -- OK, now this actually works well.
00:22:07.580 -- Not this relationship right here,
00:22:09.480 -- but this relationship.
00:22:10.953 -- If we wrote this is 1/2 Rho
00:22:14.496 -- v ^2 s think about a glider.
00:22:17.250 -- Moves very slow, right?
00:22:19.790 -- V is pretty small.
00:22:21.042 -- How does a glider make up for the
00:22:23.660 -- lift that it has to generate?
00:22:25.640 -- Was it have?
00:22:28.740 -- Lots of wing area.
00:22:30.344 -- Wings are very, very long,
00:22:32.350 -- so as if we wrote this as rho V squared.
00:22:36.080 -- Just substituting this right here.
00:22:37.940 -- If V is small then you could have
00:22:40.428 -- a large wing area right here to
00:22:43.223 -- generate whatever list you have nice.
00:22:45.770 -- OK, so that's the balance.
00:22:47.640 -- In aerodynamic design there OK?
00:22:50.770 -- We we've seen this diagram a few times and
00:22:53.920 -- showing the difference between a subsonic
00:22:56.374 -- airfoil you seem kind of nice rounded,
00:22:59.390 -- symmetric airfoil right there.
00:23:00.958 -- This is subsonic.
00:23:02.140 -- Speeds is getting close to transonic
00:23:04.408 -- here at the transonic regime.
00:23:06.450 -- Remember we said that now all the shockwaves
00:23:10.146 -- start to form right up there in the top.
00:23:13.870 -- And then that subsonic airfoil
00:23:15.900 -- has a bow shock here when it's
00:23:19.414 -- traveling supersonically,
00:23:20.810 -- whereas whereas a supersonic airfoil
00:23:23.765 -- like we see right here very thin.
00:23:27.830 -- OK, here you can see the shaded area right
00:23:30.827 -- here is going to give you it's roughly
00:23:33.616 -- related to the amount of drag that you see.
00:23:36.700 -- OK, so this shaded area right here
00:23:39.129 -- is smaller compared to its companion
00:23:41.223 -- there at the top same Mach number,
00:23:43.520 -- but different airfoil has
00:23:45.388 -- a nice rounded shape.
00:23:47.260 -- And then Supersonically right here,
00:23:48.920 -- you see, an oblique shockwave that forms.
00:23:51.870 -- Across that very thin airfoil,
00:23:53.290 -- whereas whereas you would have a bow shock
00:23:55.714 -- if you have a subsonic airfoil there.
00:23:58.250 -- OK, so again subsonic airfoils are great.
00:24:01.640 -- Flying subsonic Lee, they're awful.
00:24:04.060 -- Supersonically supersonic airfoils
00:24:05.512 -- are awful subsonic Lee,
00:24:07.450 -- but very good supersonically OK.
00:24:09.870 -- And then we talked a little bit
00:24:12.894 -- last time about these airfoils.
00:24:15.670 -- Here you see,
00:24:17.764 -- it's very thin.
00:24:19.860 -- K very thin right across here.
00:24:21.620 -- It's got a little curve there at the
00:24:23.764 -- bottom gives a little camber little
00:24:25.599 -- curvature so that you can generate lift.
00:24:27.800 -- Subsonic Lee.
00:24:28.722 -- This is the Russian.
00:24:30.570 -- This is the Russian aircraft that didn't
00:24:33.125 -- have that crashed really bad.
00:24:35.550 -- That's our 71 and then we talked about this
00:24:39.042 -- plane and F15 that flew with only one wing.
00:24:42.450 -- OK, Why was able to fly with one wing?
00:24:45.890 -- Well,
00:24:46.273 -- if we went back to our CISA Bell right?
00:24:49.720 -- He already went over it.
00:24:53.180 -- Right here, so it loses a wing.
00:24:55.880 -- So that means this area S decreases.
00:24:58.240 -- But as you increase the
00:24:59.920 -- Mach number right there,
00:25:01.270 -- you can generate the lift that you
00:25:03.552 -- need in order to fly in order to
00:25:06.088 -- in order to stay straight and level
00:25:08.430 -- roughly straight and level OK.
00:25:13.130 -- So actually before we get to that, here is.
00:25:19.100 -- So Mr Castle, sorry it's a Navy plane.
00:25:21.560 -- You OK with that? OK good.
00:25:24.310 -- So this is an F18 Hornet right here.
00:25:28.120 -- I want you to look. At the wings.
00:25:34.040 -- Can you get an idea for what that
00:25:36.152 -- for those wings look like right?
00:25:38.100 -- There? You see how thin those are?
00:25:40.870 -- It's got a very sharp leading edge.
00:25:44.130 -- OK, very thin all the way across there.
00:25:47.850 -- OK, now this actually has a really,
00:25:51.100 -- really cool design to fly.
00:25:53.430 -- Subsonic Lee. We saw F-14.
00:25:55.750 -- Tomcat had the swing wings.
00:25:58.080 -- Variable variable, swept wings.
00:25:59.860 -- If you look closely on
00:26:02.085 -- this airplane right here.
00:26:06.620 -- There is a hinge there and
00:26:09.608 -- the hinge right there. OK.
00:26:11.979 -- So what this plane does this is this
00:26:15.011 -- is awesome engineering as well.
00:26:17.960 -- OK, what this plane does with
00:26:20.234 -- this hinge here and the ailerons
00:26:22.601 -- here in the back. What it does?
00:26:28.420 -- OK, so as you say,
00:26:30.290 -- unhinged is probably a little bit unhinged,
00:26:32.900 -- so OK, so there's a hinge right there.
00:26:36.530 -- Flat plate for the surface of the wing
00:26:39.210 -- and then the other runs here in the back.
00:26:42.240 -- OK, so there's a kind of a classic
00:26:44.456 -- real thin supersonic airfoil.
00:26:46.270 -- What this leading edge hinge
00:26:47.965 -- does when it flies subsonic Lee.
00:26:49.970 -- Is that this actually bends down a little
00:26:52.906 -- bit and I'm just going to exaggerate
00:26:55.447 -- it so you can see what's going on.
00:26:58.450 -- So look like this.
00:27:01.320 -- Then the wing comes across here.
00:27:04.430 -- And then either on comes
00:27:05.855 -- back down there a little bit.
00:27:07.580 -- You see what that does to the wing?
00:27:11.290 -- Provides a little bit of curvature
00:27:14.170 -- little camber to the wing there so
00:27:17.438 -- that subsonic Lee you can take off and
00:27:21.124 -- land relatively relatively safely.
00:27:23.780 -- OK, that's that's pretty cool
00:27:25.880 -- design right there.
00:27:27.140 -- OK, will show some pictures a little
00:27:29.975 -- bit later on in the semester,
00:27:32.600 -- but one of the one of the research areas
00:27:35.750 -- that Aerodynamicists are working on now.
00:27:38.900 -- So let's say you're in the class,
00:27:41.840 -- which you really like materials.
00:27:43.940 -- OK, your control systems,
00:27:45.620 -- and not necessarily interested in that.
00:27:48.140 -- Fluids in the aero part they're
00:27:50.660 -- working water called smartwings.
00:27:52.340 -- OK, so smart wing.
00:27:55.400 -- So it has a surface like this cake
00:27:57.480 -- kind of a classic subsonic airfoil,
00:27:59.740 -- but this airport is actually
00:28:01.770 -- made up of a bunch of sections.
00:28:04.930 -- Right here. OK, on the wing.
00:28:08.774 -- So kind of looks like this,
00:28:11.390 -- and so those sections and
00:28:13.010 -- I'm just putting a squares.
00:28:14.630 -- I think they're hexagons.
00:28:15.926 -- I don't recall right off hand,
00:28:17.870 -- but you get the idea.
00:28:19.490 -- OK,
00:28:19.804 -- each of these little sections and
00:28:21.688 -- what they what they do depending on
00:28:24.008 -- the flight regime that you're in,
00:28:25.970 -- flying really fast or really slow,
00:28:27.920 -- it actually changes the shape
00:28:29.535 -- of the wing or your fly.
00:28:33.950 -- OK, so there are little.
00:28:37.460 -- Their little devices, little little motors,
00:28:39.530 -- little servos here on the inside that can
00:28:42.322 -- move up and down and change the shape of
00:28:45.297 -- the wing to make it the most aerodynamic
00:28:48.091 -- and the most the most efficient wing
00:28:51.070 -- for that particular flight regime.
00:28:54.050 -- That school engineering. OK.
00:28:59.040 -- Good, here's a here's another
00:29:01.895 -- little bit of supersonic design.
00:29:04.750 -- OK, I don't mean to.
00:29:06.570 -- I don't mean to brag on
00:29:08.682 -- this little guy right here.
00:29:10.570 -- Here's the X one.
00:29:11.966 -- We mentioned that it did break.
00:29:14.580 -- The sound barrier didn't have swept wings.
00:29:17.130 -- Not not the best compressible flow design.
00:29:19.670 -- Here's another part that Aerodynamicists
00:29:21.884 -- didn't understand at the time,
00:29:23.680 -- but is not a good design here is
00:29:27.192 -- that if you look at the tail.
00:29:30.490 -- OK, if you look at the tail right there,
00:29:33.700 -- notice it's got cut.
00:29:35.256 -- Classic tail design tail here and you see
00:29:38.286 -- you see here these tabs here in the back.
00:29:41.200 -- In the back there so that when this
00:29:43.816 -- is flying this remains flat and
00:29:45.979 -- then those back parts go up and
00:29:48.565 -- down again so that can maneuver
00:29:50.791 -- the plane going like this.
00:29:52.696 -- Turns out that Supersonically that is
00:29:55.054 -- not a very good way to maneuver in aircraft.
00:29:58.680 -- OK, so let's see why.
00:30:00.390 -- If this is flying super fast or if it's
00:30:03.261 -- flying this in the in the supersonic regime,
00:30:06.220 -- there were going to form there at the front.
00:30:12.230 -- Oblique shockwaves OK,
00:30:13.565 -- so an oblique shockwave forms there and
00:30:16.755 -- then these fins go up and down like this,
00:30:19.700 -- and so another shockwave is
00:30:21.665 -- going to format that side.
00:30:23.630 -- So you get 2 shocks that would form
00:30:26.014 -- and what aerodynamics is found is that
00:30:28.404 -- you could get a shock interaction
00:30:30.724 -- between those two shockwaves that
00:30:33.329 -- form their supersonic aircraft.
00:30:35.420 -- Nowadays will go back to
00:30:37.385 -- our F18 Hornet right here,
00:30:39.350 -- and you look at the tail.
00:30:42.720 -- Right here, OK, notice that there's no.
00:30:45.740 -- There's no part in the back there
00:30:49.408 -- that the whole tail moves up and down.
00:30:53.600 -- Like this or like this OK?
00:30:56.020 -- And it turns out that aerodynamically
00:30:58.438 -- again when this, when this turns,
00:31:01.363 -- say down like that.
00:31:03.650 -- Shockwave's going to form there at the
00:31:06.037 -- top and then you get smooth flow all
00:31:08.703 -- the way across the rest of the elevator.
00:31:11.420 -- OK, so that's another sign that you
00:31:13.583 -- could tell of what a supersonic
00:31:15.632 -- aircraft looks like if that whole
00:31:17.750 -- tail moves as opposed to just the
00:31:20.057 -- just the back portion of the tail.
00:31:24.300 -- Alright.
00:31:26.960 -- Aren't you gonna glad
00:31:27.896 -- you came to class today?
00:31:29.070 -- I'm glad that you came in class. OK.
00:31:33.690 -- Alaskan, so one of the things that now
00:31:36.554 -- that we've got this here, so let's see.
00:31:39.450 -- Did you send this to me?
00:31:41.610 -- Yes, so I got an email from Samantha.
00:31:44.490 -- He ran. She said that you should check
00:31:46.826 -- out this particular design and it's
00:31:49.187 -- called a coleopter Anna Coleoptile.
00:31:51.330 -- If you notice there that it has a,
00:31:54.210 -- it has a rounded wing on it.
00:31:57.880 -- That's that's kind of cool
00:31:59.755 -- right across there.
00:32:00.880 -- So here's the rounded wing.
00:32:02.760 -- Now it turns out that when
00:32:05.268 -- you have a finite wing.
00:32:07.520 -- Like you have here,
00:32:08.820 -- the pressure on the bottom of the
00:32:11.148 -- wing is higher than the pressure
00:32:13.014 -- on the top of the wing does.
00:32:15.150 -- That's how you generate lift.
00:32:16.740 -- But what happens is you have
00:32:18.504 -- what are called end effects.
00:32:20.240 -- So in end effect occurs when
00:32:22.052 -- the air on the bottom of the
00:32:24.311 -- wing kind of leaks out here,
00:32:26.280 -- and so you have high pressure air on the
00:32:29.133 -- bottom and low pressure air on the top.
00:32:31.690 -- And what that does is generate
00:32:33.826 -- these vertical structures go like
00:32:35.582 -- this and that causes a lot of drag.
00:32:37.730 -- It's a parasitic drag problem.
00:32:39.590 -- End effect drag problem OK in in
00:32:43.545 -- aerodynamics class you'd learn about how
00:32:46.926 -- wings can be shaped to minimize that.
00:32:50.610 -- The Spitfire that flew in World War
00:32:53.263 -- Two has elliptical shaped wings.
00:32:55.390 -- Beautiful beautiful aircraft but those
00:32:57.545 -- elliptical shapes right there minimized
00:32:59.759 -- the formation of those tip foresees.
00:33:01.750 -- OK so menace and minimizes
00:33:03.740 -- the drag flights faster.
00:33:05.340 -- OK so one of the nice things
00:33:08.028 -- about this design over here of
00:33:10.389 -- the coleopter is that it's got a
00:33:13.105 -- rounded wing so that there are no
00:33:16.024 -- tip effects that go across there.
00:33:18.489 -- Alright so you might think well.
00:33:20.910 -- How the heck does that generate
00:33:23.046 -- any kind of lift?
00:33:24.470 -- OK,
00:33:24.817 -- well it turns out that the angle
00:33:27.246 -- of attack is also related to the
00:33:29.756 -- amount of lift that you have,
00:33:31.950 -- so the higher angle of attack that you get,
00:33:35.150 -- the more lift you can generate.
00:33:37.290 -- Now for those that are paper airplane.
00:33:40.370 -- Enthusia STS
00:33:44.170 -- is it cold after I hear? Ever seen this?
00:33:48.130 -- And you can fly it. We'll see,
00:33:50.858 -- maybe we can catch this in slo-mo
00:33:53.266 -- from our from our from the cameras
00:33:55.583 -- here so you can fly this like this.
00:34:00.800 -- Not very good. Not very good.
00:34:04.260 -- But the idea is that you can generate lift.
00:34:07.500 -- Now you might think how can you
00:34:09.803 -- generate lift from something like that.
00:34:12.180 -- And again notice that in the picture
00:34:14.812 -- here it's flying at an angle of attack.
00:34:17.580 -- OK, so an airplane like this right here.
00:34:21.240 -- OK, actually has a slight angle of attack
00:34:24.008 -- built into it so that when it takes off.
00:34:26.710 -- In fact, if you if you look at it
00:34:29.374 -- straight and level right here, that Wing
00:34:31.812 -- has a little bit of an angle of attack.
00:34:34.760 -- OK, so that angle of attack is going to
00:34:37.460 -- create a small shockwave on the bottom.
00:34:39.920 -- Slight expansion wave on the top
00:34:41.852 -- so it generates lift.
00:34:43.140 -- OK, now it also answers the age old question
00:34:46.632 -- of how can a plane like this fly inverted?
00:34:50.330 -- OK, again, if this plane and you'll
00:34:52.283 -- notice it notice any aircraft when it
00:34:54.374 -- flies upside down screen level like
00:34:56.233 -- the Blue Angels and the Thunderbirds
00:34:57.871 -- when they do a flight show like that,
00:35:00.422 -- there's always a little bit of an
00:35:02.957 -- angle of attack as it goes down so
00:35:05.253 -- that it generates lift. OK, good.
00:35:10.130 -- That's your area lesson for today.
00:35:12.980 -- Alright. Got any questions?
00:35:14.924 -- Any questions? Anything we've seen so far?
00:35:18.570 -- OK.
00:35:21.500 -- So let's see here what we'd like to do now is
00:35:24.903 -- to figure out what we know for turning angle,
00:35:27.980 -- you can accelerate the flow.
00:35:29.600 -- What is the maximum turning angle?
00:35:31.540 -- How much can you turn?
00:35:33.810 -- And then what is the associated
00:35:35.670 -- Mach number associated with that?
00:35:37.230 -- OK, so here's our parental Meyer angle.
00:35:39.410 -- Theta of M is equal to this relationship,
00:35:41.900 -- right here it's got an arctangent of
00:35:43.972 -- the Mach number there and arctangent
00:35:45.881 -- of the Mach number right over here, OK.
00:35:48.439 -- So this is this will harken
00:35:50.353 -- back to your calculus days.
00:35:52.400 -- I know that was three or four years ago,
00:35:54.870 -- right so?
00:35:57.110 -- We're going to take a limit.
00:35:59.800 -- And what we're going to do is we're going
00:36:02.500 -- to take the limit as this angle as Phi.
00:36:05.330 -- We want to know what that
00:36:07.988 -- maximum turning angle is.
00:36:09.760 -- Of of our flow here.
00:36:11.500 -- So notice that in these arc
00:36:13.480 -- tangents right here we have gammas.
00:36:15.660 -- Cagamas are going to be constant for the air.
00:36:18.780 -- The only variable that we
00:36:20.515 -- have is the Mach number.
00:36:22.250 -- So we want to say if this
00:36:25.029 -- Mach number goes to Infinity.
00:36:27.460 -- What's the turning angle going to be?
00:36:30.510 -- OK, so just from mathematics right here.
00:36:33.560 -- The arctangent of Infinity is π / 2.
00:36:40.720 -- So we figure that one out.
00:36:43.170 -- Arctangent of Infinity is π / 2.
00:36:45.917 -- Let's go to the overhead here.
00:36:49.080 -- So have a triangle.
00:36:52.060 -- OK, and this is fi right here.
00:36:56.910 -- What's the tangent of Phi?
00:37:01.070 -- Say X. Why? Z what's tangent feet?
00:37:10.090 -- Tangent of Phi. The rise over the run. Y / X.
00:37:16.840 -- OK, alright, so let's let's
00:37:19.200 -- expand fi a little bit here.
00:37:26.040 -- Here is why an X.
00:37:30.280 -- 10s if he's going to get bigger
00:37:32.555 -- there right? 'cause your eyes.
00:37:34.314 -- Why is large and X is small here?
00:37:37.390 -- What happens when you have
00:37:38.560 -- a triangle look like this?
00:37:46.200 -- Look at this rise divided by
00:37:48.858 -- that teeny tiny run right there.
00:37:51.840 -- And then eventually.
00:37:53.553 -- You just have a straight line.
00:37:56.980 -- This is 90 degrees right here.
00:37:59.530 -- Which is the same. Is π / 2?
00:38:05.520 -- So the arctangent.
00:38:07.371 -- A fee from our little trigonometry
00:38:11.073 -- bit right there is π / 2.
00:38:14.287 -- That's why the limit as
00:38:16.972 -- fee tends to Infinity. OK.
00:38:21.280 -- Net fee is just the rise over the run.
00:38:23.900 -- That's why are y / X here is equal to π / 2.
00:38:27.653 -- OK, so if we take that limit then
00:38:29.757 -- Theta taking the limit here as
00:38:31.596 -- N goes to Infinity here an as N
00:38:34.053 -- goes to Infinity here substituting
00:38:35.528 -- in π / 2 to both of those terms,
00:38:38.160 -- we get that Theta is equal to π /
00:38:40.780 -- 2 times the square root of gamma
00:38:42.803 -- plus one divided by gamma minus one.
00:38:44.850 -- All this minus one right here.
00:38:47.720 -- So you can actually get a turning
00:38:51.066 -- angle of 130 degrees.
00:38:53.440 -- If you could turn that flow 130 degrees,
00:38:55.910 -- you would accelerate it to Infinity.
00:38:59.920 -- Obviously that's not going to happen OK,
00:39:02.030 -- Anna 130 degrees.
00:39:02.930 -- I mean, if you think about it,
00:39:05.040 -- it's got not just 90 degrees,
00:39:06.840 -- but now it's coming back
00:39:09.105 -- in the opposite direction.
00:39:10.920 -- Not an actual physical limit,
00:39:12.320 -- but a theoretical limit on what
00:39:14.474 -- the term could be in your flow.
00:39:16.940 -- OK, little bit of mathematical
00:39:20.750 -- gymnastics there OK?
00:39:23.040 -- This is the problem that was
00:39:24.912 -- cancelled in your homework assignment,
00:39:26.850 -- but I want you to make sure that
00:39:29.258 -- we've got shock tubes down so that you
00:39:32.133 -- understand how a shock tube works.
00:39:34.460 -- OK, so again,
00:39:35.264 -- this is 1/2 of it as a rehash from
00:39:38.039 -- when we did normal shocks and moving
00:39:40.909 -- normal shocks in a shock tube.
00:39:43.110 -- You have a driver section.
00:39:44.840 -- OK, high pressure gas right?
00:39:46.570 -- Over here there's a membrane that
00:39:48.856 -- separates this high pressure region
00:39:50.786 -- from a low pressure region right over here.
00:39:53.520 -- And this is what the pressure
00:39:55.986 -- profile looks like.
00:39:57.220 -- So you have a high pressure
00:39:59.542 -- region in the driver region.
00:40:01.740 -- A low pressure area right
00:40:03.795 -- here in the DRIVIN region.
00:40:05.850 -- OK then we break the membrane
00:40:08.406 -- and what that membrane does is
00:40:10.967 -- that it creates a normal shock
00:40:13.277 -- and that normal shockwave then
00:40:15.692 -- propagates down from left to right.
00:40:18.810 -- OK,
00:40:19.214 -- and so this stuff that we talked
00:40:22.042 -- about in class when we did
00:40:24.901 -- normal shops right across here.
00:40:27.350 -- Right across here,
00:40:28.307 -- we figured out what the pressure
00:40:30.602 -- profiles the Mach number is.
00:40:32.200 -- The Mach number of the wave, and so on.
00:40:35.225 -- We figured all this stuff out and we
00:40:38.262 -- ignored the things on the left hand side OK.
00:40:41.780 -- Kate, now that we know about expansion waves.
00:40:44.930 -- What's going on here between 3:00 and
00:40:47.450 -- 1:00 is an expansion wave problem.
00:40:50.330 -- Just like we talked about before.
00:40:53.610 -- OK,
00:40:54.067 -- so what's happening here is that again
00:40:57.266 -- you have a high pressure region here.
00:41:00.780 -- There is a lower pressure region
00:41:02.898 -- right across here in Region 3.
00:41:04.980 -- In fact,
00:41:05.714 -- if you look at the pressure
00:41:07.916 -- profile here it is.
00:41:09.180 -- This is the driven section
00:41:10.930 -- has a low pressure,
00:41:12.330 -- goes across the shock.
00:41:13.610 -- That's what this region is right
00:41:15.597 -- across here and then that pressure
00:41:17.727 -- remains constant to what's called
00:41:19.582 -- the contact surface right here.
00:41:21.430 -- And that's where Region 3 contacts Region 4.
00:41:24.230 -- And then there is a gradual
00:41:26.606 -- increase in the pressure right up
00:41:29.075 -- here and then the driver section.
00:41:31.480 -- OK,
00:41:32.021 -- so this gas this high pressure gas
00:41:35.808 -- begins to expand. As it goes across.
00:41:40.872 -- OK.
00:41:41.640 -- Draw that out, drawn out process out here,
00:41:44.900 -- OK?
00:41:46.430 -- So.
00:41:52.870 -- So here's the membrane.
00:41:54.442 -- Here's the high pressure section.
00:41:56.410 -- Here is the low pressure section here.
00:41:59.160 -- OK, when the membrane breaks.
00:42:03.680 -- Creates a shockwave.
00:42:06.900 -- Propagates down this direction here,
00:42:09.680 -- and an expansion wave
00:42:12.464 -- forms as this gas expands.
00:42:15.950 -- Into this region right over
00:42:18.695 -- here so that wave propagates.
00:42:21.440 -- Starts out small here,
00:42:23.416 -- gets a little bit larger.
00:42:25.890 -- And then that distance increases
00:42:27.525 -- right across there as this high
00:42:29.536 -- pressure gas region expands
00:42:30.820 -- and goes across this way.
00:42:35.040 -- As a as my kids say, you know fun
00:42:39.299 -- fact fun fact about expansion waves.
00:42:42.140 -- OK, this behaves exactly like.
00:42:46.240 -- A traffic jam or traffic
00:42:49.620 -- flow at a red light. OK.
00:42:54.940 -- But how could that be OK?
00:42:57.100 -- Think about this.
00:42:58.180 -- You have a red light right here.
00:43:04.440 -- We want to make this authentic,
00:43:06.310 -- so there's a red light right there.
00:43:08.480 -- OK? And there are cars lined up.
00:43:11.840 -- And it's all bumper to bumper, right?
00:43:13.897 -- I'm sure all of you keep a safe
00:43:16.593 -- distance right when you break.
00:43:18.520 -- In traffic, especially,
00:43:19.669 -- the traffic jams here in Moscow ID OK,
00:43:22.620 -- so looks like this and you can have a line
00:43:26.893 -- of cars that go all the way back here.
00:43:30.670 -- OK, so the red light then turns green.
00:43:35.490 -- Green light right here.
00:43:40.130 -- There's a green light OK,
00:43:42.170 -- and now the cars go do all seven of
00:43:45.050 -- these cars move at the same speed and
00:43:48.453 -- propagate through their drive-thru light?
00:43:51.150 -- No, what happens?
00:43:52.809 -- First car goes it's here.
00:43:55.580 -- And there's a larger distance
00:43:57.390 -- between that one and the next one,
00:43:59.880 -- and then that distance gets a
00:44:01.890 -- little bit smaller and smaller,
00:44:03.810 -- and the way in the back here is that,
00:44:07.040 -- and I've had this happen to me before.
00:44:09.900 -- Is that you see the green light here,
00:44:12.760 -- but the distance when I'm parked
00:44:14.710 -- way back here the distance between
00:44:16.863 -- me and that car hasn't changed.
00:44:19.210 -- Heckuva lot for 1015 seconds,
00:44:21.000 -- however long it takes to
00:44:22.790 -- propagate that through these cars.
00:44:24.580 -- Driving through here.
00:44:26.062 -- It turns out have the same
00:44:29.026 -- mathematical modeling associated
00:44:30.809 -- with expansion ways right there.
00:44:33.820 -- Same modeling process here.
00:44:35.308 -- This membrane breaks the gases expand.
00:44:37.540 -- This wave goes faster than this one,
00:44:40.140 -- which goes faster than this one and so on.
00:44:43.490 -- So as this as this pressure wave
00:44:46.381 -- propagates there through the back
00:44:48.431 -- has the same properties as cars
00:44:50.645 -- parked not part but in a in a
00:44:53.369 -- traffic line right across there.
00:44:57.160 -- There you can tell your folks
00:44:58.984 -- over the break that you learned
00:45:01.030 -- something here in gas dynamics.
00:45:02.940 -- OK, like I said, fun fact.
00:45:05.720 -- OK, shock tubes in let's go and here is
00:45:09.374 -- what happens after the membrane breaks.
00:45:13.010 -- OK, so let's look at the
00:45:15.920 -- expansion wave process.
00:45:17.380 -- OK, so here again these waves
00:45:19.840 -- propagate back and as they propagate
00:45:22.606 -- back eventually this high pressure
00:45:25.216 -- region is going to completely expand.
00:45:28.560 -- OK, so the initial state of our
00:45:32.179 -- of our shock tube right here.
00:45:35.730 -- Of this pressure difference
00:45:36.918 -- across here from one to two,
00:45:38.700 -- we have a high pressure region
00:45:40.380 -- in a low pressure region,
00:45:41.970 -- right across here,
00:45:42.858 -- that's called the diaphragm pressure ratio.
00:45:46.930 -- OK, right across there after that
00:45:49.348 -- diaphragm or the membrane breaks,
00:45:51.510 -- then the pressure in Region 3 is the
00:45:55.190 -- same as the pressure in region 4.
00:45:58.840 -- And the speed in Region 3 is the
00:46:01.216 -- same as the speed in region 4.
00:46:03.520 -- So if we go back to our
00:46:05.627 -- little drawing right here,
00:46:06.950 -- these two pressures are the same.
00:46:08.820 -- Cross this contact surface and the speed
00:46:11.004 -- of the air or the gases between those
00:46:13.570 -- two regions are the same as well. What?
00:46:16.176 -- What do you think would be different?
00:46:19.580 -- Speeds the same pressures the same.
00:46:21.010 -- What do you think would be
00:46:23.380 -- different across there?
00:46:24.570 -- What happens to the temperature
00:46:27.760 -- across a shockwave?
00:46:29.680 -- It goes up what happens to the
00:46:32.214 -- pressure downstream of this expansion
00:46:34.112 -- wave as it starts to expand.
00:46:36.320 -- Goes down. OK, so there's a.
00:46:38.530 -- There's a temperature difference between
00:46:40.365 -- 3:00 and 4:00, right across there.
00:46:42.586 -- OK, T4 is going to be higher than T2,
00:46:45.890 -- and T3 is going to be higher than T1.
00:46:49.830 -- That's really what defines that difference
00:46:51.882 -- right across there is that temperature OK,
00:46:54.380 -- but the pressures in those
00:46:56.130 -- two regions are the same.
00:46:57.880 -- The speed in those two regions of the same.
00:47:01.030 -- OK, so again, across an expansion wave,
00:47:03.480 -- the flow is isentropic.
00:47:04.764 -- So we can use our isentropic relations here.
00:47:07.680 -- P3 or P1 is equal to T3 over T1 to
00:47:10.572 -- the gamma over gamma minus one power.
00:47:13.630 -- Or we could write that in terms
00:47:16.843 -- of the densities as well.
00:47:19.090 -- You know this is nice because
00:47:20.590 -- once we get it in this form,
00:47:22.390 -- we can write this in terms
00:47:24.412 -- of the speed of sound.
00:47:26.330 -- So now P3 over P11 minus gamma one.
00:47:30.120 -- Over 2 times V 2 /, 81 squared.
00:47:33.334 -- So this is the Mach number.
00:47:36.680 -- OK, in the expansion region right there to
00:47:39.272 -- the two gamma sub one over gamma minus one,
00:47:42.260 -- right across there.
00:47:43.769 -- OK if we solve for V then.
00:47:47.290 -- We can solve for V2.
00:47:48.760 -- We can solve for the speed and region 2.
00:47:52.260 -- Right across there and it is just
00:47:54.808 -- a function of the speed of sound.
00:47:57.450 -- He said one and this pressure ratio,
00:48:00.050 -- the diaphragm pressure ratio P2 over P1 OK.
00:48:04.450 -- What it gives us here is that since gamma
00:48:07.105 -- minus one this power right over here,
00:48:09.410 -- gamma minus 1 / 2 gamma is less
00:48:11.658 -- than one as PP1 tends to Infinity.
00:48:14.060 -- This term is going to go to zero,
00:48:16.540 -- and So what this does is you
00:48:18.990 -- can generate a maximum.
00:48:20.780 -- Speed in region 2.
00:48:22.528 -- From this term right there twice,
00:48:25.150 -- the speed of sound divided
00:48:26.930 -- by gamma minus one.
00:48:28.360 -- OK, enough gammas for air,
00:48:29.850 -- that's one point 4 -- 1 or that's two
00:48:32.588 -- times the speed of sound divided by .4.
00:48:34.920 -- What it tells you can do is you
00:48:37.608 -- can generate pretty high speeds.
00:48:39.820 -- With the shock tube.
00:48:42.040 -- OK, they don't last for very long.
00:48:44.230 -- OK,
00:48:44.522 -- but you can get hypersonic flows from a
00:48:46.858 -- shock tube that comes right across here,
00:48:49.240 -- OK?
00:48:51.270 -- Good,
00:48:51.614 -- so that was the problem
00:48:53.334 -- that was cancelled is
00:48:54.781 -- to figure out the expansion portions
00:48:56.983 -- of the flow. OK, any questions? Yes.
00:49:04.810 -- OK, I'm getting to that,
00:49:06.520 -- so I answer part one.
00:49:08.220 -- No shock tube questions,
00:49:09.572 -- no moving shock problems on the exam.
00:49:14.180 -- What's that? And an airfoil
00:49:18.041 -- is not a shock tube, so yes,
00:49:20.052 -- so there is an airfoil problem.
00:49:21.770 -- There is not a shock to problem.
00:49:23.780 -- OK, I just want to make sure that
00:49:26.068 -- you understood kind of the basic
00:49:27.825 -- workings of what a shock tube are.
00:49:29.810 -- OK, not answer your question here.
00:49:31.530 -- Exams are open book.
00:49:33.690 -- Open notes OK.
00:49:37.600 -- And it's also open laptops if you
00:49:40.414 -- choose that you've got a laptop to use
00:49:43.203 -- com prop that is OK to use as well,
00:49:45.950 -- but there are no communications
00:49:48.122 -- with the outside world or the
00:49:50.278 -- inside world on your laptop.
00:49:51.870 -- So if you have a phone 'cause you
00:49:54.558 -- want to use your app, that's OK too.
00:49:59.430 -- OK, so open book, open notes, open com,
00:50:02.910 -- prop, or if you've got some other,
00:50:05.960 -- you know if you use some other device
00:50:08.848 -- for your compressible flow tables,
00:50:11.610 -- that's OK as well, yes?
00:50:17.110 -- Open Book open notes.
00:50:24.070 -- There are five problems on the exam,
00:50:25.450 -- so if you spend all your time looking
00:50:26.946 -- at your notes, you're not going to
00:50:28.408 -- have time to solve the problems.
00:50:32.510 -- OK, so be sure that your
00:50:34.682 -- your laptops are charged.
00:50:36.130 -- We don't have a whole lot of.
00:50:38.660 -- Let's see. Do you have?
00:50:40.470 -- Do you have plugs underneath?
00:50:44.200 -- Not sure what you got there. OK.
00:50:48.770 -- And you will have the hour and 15
00:50:51.746 -- minutes to solve the exam as well.
00:50:54.520 -- OK, I will talk to the greater today and we
00:50:57.548 -- will try and get this graded by tomorrow.
00:51:00.370 -- So if you want to pick him up
00:51:02.818 -- tomorrow you could come by my
00:51:04.854 -- office and pick up the exams.
00:51:06.870 -- That's fine.
00:51:07.616 -- The solutions are also will
00:51:09.481 -- be available this afternoon.
00:51:11.310 -- So even though even if you don't
00:51:12.689 -- have your homework assignment,
00:51:13.750 -- if the greater can't get it back in time.
00:51:17.120 -- Can you can always look online on TV learn?
00:51:21.160 -- OK. Good, so let's see here.
00:51:24.980 -- I would say that the exam problems
00:51:26.807 -- are going to be very similar to what
00:51:28.959 -- you see in the homework problems.
00:51:30.830 -- Let's just let's just review.
00:51:33.610 -- Write reviews 'cause then you
00:51:35.720 -- can see how intelligent you have
00:51:38.277 -- become over the last one week.
00:51:40.500 -- Six now, let's see what we've discussed here,
00:51:43.740 -- OK?
00:51:45.680 -- Just going through just going through the
00:51:49.460 -- going through the table of contents here.
00:51:53.280 -- OK, let's see here.
00:51:54.708 -- You probably won't have any problem that
00:51:57.396 -- just discusses the continuity equation.
00:51:59.780 -- You probably won't have a problem
00:52:02.222 -- that just has the ideal gas law,
00:52:05.050 -- but you could certainly use it.
00:52:08.650 -- OK,
00:52:09.065 -- some fundamental aspects
00:52:10.310 -- of compressible flow.
00:52:11.560 -- You know how to calculate the speed of sound?
00:52:16.350 -- OK, and you know how to calculate
00:52:18.380 -- Mach numbers and Mach waves.
00:52:19.950 -- I would say that's going to
00:52:21.840 -- be something to study up on.
00:52:23.550 -- Make sure that you understand what
00:52:25.224 -- a Mach wave is and how different
00:52:27.348 -- it is from an oblique shockwave.
00:52:29.250 -- What is the difference?
00:52:32.300 -- What's the difference between an
00:52:33.910 -- oblique shockwave animac wave?
00:52:37.280 -- A Mach wave is an infinitesimally
00:52:40.880 -- weak oblique shockwave.
00:52:42.680 -- OK. Good. Uh, now?
00:52:49.560 -- You probably won't have a problem.
00:52:50.820 -- It says, just calculate the speed of sound,
00:52:52.500 -- but you will likely have a problem.
00:52:53.970 -- You'll have to calculate the speed of sound.
00:52:56.440 -- OK, so this is all fundamental
00:52:59.068 -- stuff right here.
00:53:00.390 -- OK, in chapter four we learned about
00:53:02.938 -- isentropic flows and the difference
00:53:05.251 -- between stagnation conditions,
00:53:06.980 -- static conditions and critical
00:53:08.732 -- conditions right there, OK?
00:53:12.020 -- You probably won't have a problem
00:53:14.138 -- that says what is the stagnation
00:53:16.500 -- temperature of such and such.
00:53:18.680 -- You might OK, but you'll be able to.
00:53:21.820 -- You'll need to calculate what stagnation
00:53:25.144 -- temperatures are and pressures.
00:53:27.360 -- Pretty straightforward using
00:53:28.542 -- the tables using comp.
00:53:30.120 -- However you want to do it OK.
00:53:32.880 -- We learned about shockwaves.
00:53:35.072 -- OK, and you'll probably see some problems
00:53:38.584 -- that have a normal shocks in him.
00:53:41.890 -- OK, that's very important in gas dynamics.
00:53:46.210 -- OK, pitot tubes. Are also important,
00:53:51.190 -- so make sure you got those down.
00:53:54.150 -- Don't worry bout moving normal shocks.
00:53:58.200 -- OK.
00:54:00.360 -- Are oblique shock waves are important?
00:54:02.620 -- Make sure that you've got those down
00:54:05.147 -- and expansion waves are also important.
00:54:07.520 -- Make sure that you've got that down.
00:54:12.350 -- And make sure that you've got
00:54:14.702 -- the reflection part of oblique
00:54:16.895 -- shockwaves down pretty well. OK.
00:54:21.310 -- Again, as you learn in your problems,
00:54:23.570 -- a lot of it's just the geometry.
00:54:25.830 -- Make sure you've got the
00:54:27.890 -- direction of the flow right. OK.
00:54:32.670 -- Just to re clarify. We're going to
00:54:36.557 -- go back to our normal shocks here.
00:54:42.040 -- Region 1. Region 2 flow goes
00:54:44.950 -- this way comes out this way.
00:54:47.930 -- This is the region that is upstream.
00:54:53.590 -- It is also ahead. Of the shock.
00:54:59.930 -- OK, this is the supersonic flow.
00:55:03.280 -- Regime this is the subsonic flow.
00:55:07.240 -- Regime this is. Downstream.
00:55:12.700 -- Of the shock, this is also behind.
00:55:17.250 -- The shock there means the same thing.
00:55:21.530 -- OK, sometimes a problem will ask
00:55:23.396 -- what's the temperature and
00:55:25.004 -- pressure just downstream of the shock?
00:55:26.870 -- Where does that where you where?
00:55:28.750 -- Are you looking to calculate that?
00:55:31.280 -- Right there.
00:55:34.070 -- Just downstream so you don't have to
00:55:35.876 -- worry about any of the flow anywhere else.
00:55:38.000 -- What's the temperature and pressure?
00:55:39.310 -- The Mach number just downstream of the
00:55:41.564 -- shock just in that region right there?
00:55:44.080 -- OK. Excellent. Any questions?
00:55:52.850 -- OK, have a wonderful day study
00:55:55.724 -- up for the exam and we'll see
00:55:59.529 -- Thursday bright and early.
00:00:27.640 -- Alright, for today we're going to start in Chapter 3. We're
00:00:31.336 -- going to go over. Some were basically kind of reviewing at
00:00:35.032 -- this point, so a couple of things to show everybody on the
00:00:39.064 -- website. Is if we go to I have to move this up here. Sorry I
00:00:45.806 -- forgot I have a preview in a program one so up here the
00:00:50.928 -- lectures we have. Intro class review so for this I have been
00:00:55.656 -- an I will continue to do so. Uploading my intro class of
00:01:00.384 -- lectures. Hopefully most of these links should work OK good
00:01:04.324 -- and they were working on the right files. That's even
00:01:08.264 -- important. Super important
00:01:09.446 -- actually. So there's the.
00:01:13.100 -- And.
00:01:14.470 -- Basic Intro class review lectures. Like I said, I'll
00:01:16.882 -- be putting up a whole bunch more, especially as we run
00:01:19.830 -- into more stuff that's more pertinent to the stuff we're
00:01:22.510 -- looking at and or reviewing.
00:01:25.260 -- And on today's we are going to be in Module 3 which just from
00:01:28.550 -- correspond to chapter three. I'm not quite sure why use the term
00:01:31.370 -- module, but I did and there it is, so we're using it.
00:01:35.560 -- So here my links are working. Yeah, I have a few more links
00:01:39.408 -- for other things to look at, so my central limit theorem we're
00:01:42.960 -- going to talk about that today review that I have two
00:01:46.216 -- different lectures for that. One of 'em actually shows a
00:01:49.176 -- simulation which will be. I don't know. I always enjoyed
00:01:52.136 -- this simulation. Once I finally thought so it was kind of nice
00:01:55.688 -- to see. And we're also going to go through this probability
00:01:58.944 -- distributions handout. I wasn't actually going to put this up
00:02:01.904 -- and I'm going to do most of it on the document camera, but.
00:02:07.070 -- I decided to at the last minute and it literally is a last
00:02:10.567 -- minute hand out, so don't expect anything gorgeous. No pretty
00:02:13.257 -- colors, sorry, no pretty colors here. Have a couple of nice
00:02:16.216 -- looking tables or just not sitting where I want them to,
00:02:19.175 -- but the handout itself will work just fine, and that's actually
00:02:22.134 -- primarily we're going to go through today and then we'll see
00:02:25.093 -- if we get a chance to look at least one of these central limit
00:02:29.128 -- theorem. Handouts, so today we are going to look at this, but
00:02:33.546 -- we are going to walk through all this, so we want to do most of
00:02:37.836 -- this on the document camera, but I wanted to show something
00:02:40.982 -- first, because, well, this thing can graph so much nicer than I
00:02:44.414 -- can. So alright first.
00:02:49.140 -- We need to review some basic terms from
00:02:53.228 -- probability and we want to.
00:02:57.150 -- Zoom in just to hear will come back to the computer in just a
00:03:02.358 -- bit. So remember, we're going to be talking about is
00:03:06.078 -- probability distributions.
00:03:10.950 -- We'll start out with this simple case just to work through. Now
00:03:14.826 -- that we're going to get into a super highly complex one, but
00:03:18.702 -- will start out with a simple case. Alright, so we have this
00:03:22.578 -- hypothesize data, and that's what this worksheet that I made
00:03:25.808 -- is going to basically following through it. Oh, sorry
00:03:28.715 -- hypothesis. Can you tell that to normal term? I use hypothesized.
00:03:36.740 -- Population.
00:03:41.420 -- And it's an old example. It's probably not extremely current
00:03:45.010 -- in terms of its probabilities. Fitting it is OK. It will still
00:03:49.318 -- work. So here we have the number of TV sets that are owned.
00:03:55.960 -- Per household.
00:04:01.570 -- Nowadays it might be more interesting to look at
00:04:05.960 -- phones or computers, but everybody's got something
00:04:09.033 -- alright. So in this population, well, we can
00:04:12.545 -- either have the TV's can take on values of 0123 or four. Do
00:04:18.252 -- I have for USF 4?
00:04:21.920 -- And then we have some probabilities associated
00:04:23.845 -- with those.
00:04:26.400 -- P of TV's.
00:04:29.250 -- So the probability of those.
00:04:31.860 -- So I'm just going to write
00:04:33.006 -- another wreath. We can make a nice pretty table here
00:04:35.404 -- when we're done.
00:04:40.190 -- Alright.
00:04:42.870 -- OK, so this example is at least.
00:04:46.220 -- Now might be over 10 years old, but it's at least 10 years old.
00:04:50.100 -- So the probability that probably not quite so accurate anymore,
00:04:53.140 -- but that's OK for what we want to do here. So this is the
00:04:57.396 -- number of TV sets owned per household. And if you want to
00:05:01.044 -- think about it this way for remember what this term is
00:05:04.692 -- the number of TV's this is going to be a random variable.
00:05:10.630 -- Which remember is kind of like a function of valued function.
00:05:15.910 -- So a specific value of our distribution has a specific
00:05:19.610 -- probability associated with it.
00:05:23.440 -- Alright.
00:05:25.470 -- So actually, let's make a nice table. I should have done that
00:05:28.350 -- to begin with, but whatever.
00:05:30.770 -- I do things the hard way sometimes, so TV's
00:05:34.991 -- probability of TV's.
00:05:43.660 -- Your attentive and you want to redo it, go
00:05:45.928 -- for it, I understand.
00:05:48.120 -- Probably not necessary, as long as you got all your information,
00:05:51.442 -- but nice little table.
00:05:54.160 -- I could have done it vertically, whatever it however you want to
00:05:57.280 -- look at it. Either way, this will get us the basic idea.
00:06:02.790 -- And that's where my graph comes into play and I totally draw it.
00:06:06.287 -- But really, my little – my little handout can show so much
00:06:09.515 -- better than I could ever draw it. So if you want to look at
00:06:13.281 -- that real quick on the computer that is distribution TV's.
00:06:17.910 -- Thought about playing with colors, but I just left alone.
00:06:20.390 -- Figured you could get the gist of it. So we got our 20% here at
00:06:24.110 -- zero and two 40% at one and then our 10% at three and four.
00:06:28.490 -- Alright. So back to our examples here.
00:06:35.110 -- So one of the things, well, we have many things of interest
00:06:38.254 -- that we'd like to look at about. One of the major things
00:06:41.398 -- we want to look at is to look at some of our summary
00:06:44.804 -- statistics, and while looking at this, it would probably be
00:06:47.424 -- nice to know on average, how many TV's are owned per
00:06:50.306 -- household. So we want to find a mean.
00:06:53.970 -- And we also call this here in. With this we call this
00:06:58.134 -- an expected value.
00:07:02.070 -- Expected value alright, so an expected value is a mean, but
00:07:06.756 -- unlike our continuous distributions versus discrete
00:07:09.312 -- and this is more of one of those discrete answers 'cause you
00:07:14.424 -- can't own. 1 1/2 television sets. You could on average but
00:07:19.110 -- not. Literally.
00:07:22.380 -- You probably don't want broken ones. I think they think they're
00:07:26.208 -- counting functional TV's not nonfunctional TV's as well, so
00:07:29.340 -- this would be discreet.
00:07:33.200 -- So basically you want to think about it that your variable
00:07:36.344 -- in our book uses why a lot versus X, but pick a letter. It
00:07:40.012 -- doesn't really matter. I'm going to use why just because their
00:07:42.894 -- book does, but what was I going with? This whole number values?
00:07:46.860 -- That's what these things can take on.
00:07:50.850 -- There's an S there. There we go.
00:07:54.640 -- So this mean here the way we're going to compute it is because
00:07:59.359 -- it's basically it's a weighted average, so not every value of
00:08:03.352 -- our random variable TV's.
00:08:05.560 -- Takes on equal probabilities, they don't have equal
00:08:08.240 -- probabilities, so we have a weighted average that we're
00:08:11.255 -- going to do.
00:08:13.440 -- And.
00:08:15.690 -- Since we're dealing with the population, this is what we
00:08:18.900 -- call deductive because we know exactly what's going to
00:08:21.789 -- be happening in the population versus a sample,
00:08:24.357 -- and most of our exploration there is going to be
00:08:27.567 -- inductive, but this ones deductive, because we can
00:08:30.135 -- actually see what's actually happening, so we're going to
00:08:33.024 -- call this thing mu the population mean of the
00:08:35.913 -- distribution, some other notation E of Y, like
00:08:38.481 -- function notation.
00:08:41.180 -- And to calculate this is the
00:08:44.180 -- sum. So Sigma sum at each Y times its
00:08:50.164 -- corresponding probability.
00:08:53.320 -- They just calculate about products and add them all up.
00:08:59.830 -- Alright, so why not? We're here. We should do this, for example.
00:09:05.870 -- So to calculate our expected value of Y or mean for this
00:09:11.258 -- we would take zero times its probability.
00:09:15.950 -- Plus one, so I was trying to parenthese ahead of time times
00:09:19.922 -- the probability of 1.
00:09:22.890 -- Two times its probability plus three times .1.
00:09:30.060 -- There's four times by 1.
00:09:33.490 -- There's also and then we get a lovely 1.5.
00:09:38.590 -- Oops, sorry, papers got broken.
00:09:42.410 -- So on average, we could expect a household to
00:09:45.830 -- have about 1 1/2 TV's.
00:09:49.290 -- It's like the 1 1/2 kids thing, though obviously we can't have a
00:09:51.994 -- half a TV or a half a kid, but it's an average, even if it's
00:09:55.114 -- not a part of the original
00:09:56.362 -- distribution. And that's OK.
00:09:59.780 -- So. This, unfortunately, you're going to have to torture with my
00:10:03.740 -- drawing anyways. If I drew out our little distribution.
00:10:09.860 -- So this will be our probability.
00:10:12.750 -- We have wide on the X axis.
00:10:16.310 -- Let's see here.
00:10:18.840 -- So I'm just kind of guesstimating I'm not an artist
00:10:22.290 -- by any stretch of the imagination. I can draw a decent
00:10:26.085 -- Bell curve. And occasionally decent rectangles.
00:10:31.040 -- Pretend those are both .1 and the other ones are point 2.4,
00:10:35.348 -- point 2.1. .1 there we go.
00:10:40.090 -- So if we imagine where we put the mean, that would be right
00:10:43.639 -- about here. Well, this is basically what we would consider
00:10:46.369 -- this center of mass. So if we actually try to balance this
00:10:49.645 -- thing on, that's exactly the point where it would balance the
00:10:52.648 -- center of mass right there. And that's where that mean is.
00:10:59.580 -- I think I just wanted to touch you with my drawing.
00:11:01.395 -- That's not what I think I needed to do here.
00:11:04.750 -- Right, and of course we love measures of location. That's
00:11:08.310 -- what the mean is. But we also love measures of spread so we
00:11:12.938 -- can see how much variation we actually have. So this is our
00:11:17.210 -- measure.
00:11:19.070 -- Of spread.
00:11:21.380 -- Variation.
00:11:27.190 -- It's one of 'em, but this one in particular.
00:11:31.040 -- The variance.
00:11:34.270 -- Is the average.
00:11:40.050 -- Important work here squared.
00:11:43.820 -- Distance.
00:11:46.410 -- Each point is from its mean.
00:11:53.280 -- Remove there.
00:11:59.540 -- So we can see how much variation we have in our data. Points were
00:12:03.670 -- in relation to the center.
00:12:05.750 -- Of the distribution.
00:12:11.170 -- At see here it's units.
00:12:14.290 -- R-squared units.
00:12:22.720 -- Measurement but yeah.
00:12:25.130 -- But it's not on the same scale as the mean, so not all the
00:12:29.568 -- time. Is this the one we want to directly deal with? But we still
00:12:34.006 -- have to calculate it. So to do that it's it's Greek symbol is a
00:12:38.444 -- Sigma squared. Yeah, my Sigma is mostly OK.
00:12:42.810 -- And one of my friends used to draw it and it looked like a
00:12:44.896 -- Theta and I was like Theta
00:12:45.790 -- squared shoes. Now it's a Sigma. OK, mine supposed to be a Sigma
00:12:50.030 -- at mostly kind of looks like one. You can also use via Y. Now
00:12:54.930 -- this V here is going to denote the actual true variance.
00:12:59.660 -- And of course, since we're dealing with the population,
00:13:01.694 -- that's OK. 'cause that's what we're going to be looking at.
00:13:04.180 -- But that reason I brought that up is that will come into play
00:13:07.118 -- here in just a bit, so.
00:13:09.070 -- Keep that in the back of your
00:13:10.183 -- head, all right. So what we're going to do
00:13:14.456 -- is look at Y minus mu.
00:13:18.550 -- Quantity squared times the probability of Y, so we'll take
00:13:23.300 -- each squared difference of each value between it and the mean.
00:13:29.170 -- Look at that squared distance and multiply it by the
00:13:32.280 -- probability of that data point and that gives us.
00:13:35.970 -- What we're looking for in terms of the variation.
00:13:42.290 -- Alright. So of course we're going to do that.
00:13:48.350 -- And I got a little carried away on my hand out, which is OK and
00:13:52.910 -- carried away in a good way, sort of. It might be a little
00:13:56.862 -- redundant for you, but I did actually expand some of these
00:14:00.206 -- formulas a little bit more, but I did show the actual work later
00:14:04.158 -- on, so we will actually do this. So Sigma squared is the variance
00:14:08.110 -- of Y. So we're going to take the first data point, which is a 0.
00:14:13.780 -- Minus the mean.
00:14:15.750 -- Squared and the probability of zero was a .2.
00:14:21.720 -- And we get to do this for all
00:14:23.704 -- five values. So next one 1 -- 1 1/2 ^2 * .4.
00:14:33.350 -- I have the right table. I'm just making sure I have the
00:14:35.318 -- right values OK.
00:14:37.450 -- And the next one 2 -- 1 1/2 ^2 * .2.
00:14:43.550 -- I have to move it down page or move it down the line.
00:14:47.400 -- 3 minus the mean squared times .1 and the last one 4 -- 1 1/2
00:14:53.715 -- squared times point. That's a two up there. Sorry times .1.
00:15:01.080 -- Well, you know this stuff and all these lovely little.
00:15:06.550 -- Squared differences in products all add up to 1.45.
00:15:14.620 -- Ann, if at anytime you're working through this on your own
00:15:17.887 -- and you get a different number than I do, don't hesitate to say
00:15:21.748 -- something. It happens, unfortunately, but it happens
00:15:23.827 -- and I won't be offended.
00:15:27.730 -- I used to wonder why I was like
00:15:29.498 -- why. How is it so easy to make mistakes? And I think it's
00:15:33.506 -- actually really easy on this end 'cause you get caught up in what
00:15:36.665 -- you're doing. You don't think about something that you're
00:15:38.852 -- dealing with right this moment when you're trying to talk about
00:15:41.525 -- something 5 minutes ahead of you know and think 5 minutes ahead.
00:15:44.441 -- Yeah, it's interesting, alright, but if I do make a mistake,
00:15:47.114 -- don't hesitate to let me know.
00:15:49.900 -- So. Of course, the variance leads us to the next one, which
00:15:55.212 -- is the standard deviation anisur standard measurement of spread.
00:16:02.230 -- And.
00:16:04.320 -- So it's a again a measure of spread.
00:16:09.480 -- Variation that's an R in there, sorry.
00:16:12.890 -- It is the average distance.
00:16:17.670 -- Without the squared.
00:16:20.910 -- Each point is from its mean.
00:16:23.690 -- Oh, there's an end in there.
00:16:32.600 -- So.
00:16:36.450 -- It's just the square root of the variance, and since it's
00:16:39.365 -- really what we end up wanting to do because its units of
00:16:42.545 -- measurement are the same as the mean, so they have single non
00:16:45.725 -- squared units of measurement.
00:16:47.830 -- It has seem.
00:16:55.120 -- Units of measurement azzameen
00:17:00.870 -- which is good? Want to keep things on the same scale?
00:17:06.180 -- And it literally is just the square root of the variance.
00:17:14.510 -- The positive square root, of course.
00:17:19.220 -- Remember, standard deviations invariances cannot be negative.
00:17:21.789 -- They can be 0.
00:17:23.810 -- Which is not very exciting, but they can't be negative.
00:17:27.280 -- 'cause if there is zero, you
00:17:28.678 -- have identical data points. Which I suppose is not
00:17:31.805 -- necessarily that it's not super exciting. There could be
00:17:34.550 -- a good case for it, but it might not be that exciting to
00:17:38.515 -- look at. So Sigma without the squared is our notation.
00:17:43.890 -- So SD of Y.
00:17:46.650 -- Probably, but as of why, but that might mean something else
00:17:50.005 -- in a different class, so I use SD and so we just take the
00:17:54.275 -- square root of our variance.
00:17:56.910 -- Or the square root of Sigma squared. Either way for us in
00:18:01.962 -- this example, is sqrt 1.45.
00:18:05.720 -- Which is fire Mario 1.2?
00:18:13.770 -- Or something close.
00:18:22.100 -- Alright, this would be great if we could always get population
00:18:25.070 -- values and we would never have to worry about doing. You know
00:18:28.310 -- we'd always be able to know everything about the population.
00:18:32.020 -- Not always the exact case in life. Unfortunately, there's a
00:18:36.010 -- lot of unknown.
00:18:38.650 -- And it's a two point 1.20 that some decimals off the end, but I
00:18:42.458 -- just found it to 1 decimal place as far as your work goes most of
00:18:46.538 -- the time using significant digits is not a horrible idea,
00:18:49.258 -- but I would say except in a rare case when we get to the last
00:18:53.338 -- chapters, you probably don't need to carry it more than two
00:18:56.330 -- to four decimal places are last chapters or there are some
00:18:59.322 -- concepts where we're going to have a small value, some sort of
00:19:02.586 -- density value which is very similar to like a growth or
00:19:05.578 -- decay rate, so you'd probably more like a decay rate, so you
00:19:08.842 -- probably want to make sure you might want to carry those out a
00:19:12.378 -- little bit further, but.
00:19:13.640 -- The most part significant digits or two to four decimal places
00:19:17.457 -- will be more than sufficient for what you need.
00:19:22.630 -- But unfortunately we don't have.
00:19:26.030 -- Population values all the time. He did. Life would be simple and
00:19:29.510 -- then we wouldn't probably need a whole discipline called
00:19:32.120 -- statistics for all this stuff because we wouldn't know the
00:19:35.020 -- entire population. But since we don't, we have to use
00:19:37.920 -- statistics. So what we're going to do is take samples and that's
00:19:41.400 -- really what you're doing. Here is looking at the samples from
00:19:44.590 -- surveys and what have you and trying to make estimations. Our
00:19:47.780 -- main estimations are going to be
00:19:49.520 -- a mean. A total which you may or may not have dealt with in your
00:19:55.123 -- intro class and a proportion. There are others, of course, but
00:19:58.764 -- those are our main.
00:20:00.180 -- Three statistics of interest while we're here in this course
00:20:02.840 -- and those would be the main three statistics of interest in
00:20:05.766 -- surveys as well. So.
00:20:08.360 -- And of course with that we always want to have a variance,
00:20:12.284 -- so we getting back to calculating this all right now.
00:20:16.590 -- You've probably seen that there are different.
00:20:20.540 -- Calculations formulas for population versus sample values.
00:20:25.880 -- So let's kind of take a peek at
00:20:28.336 -- the differences. Population.
00:20:33.650 -- Versus sample.
00:20:36.980 -- So population value for a mean.
00:20:40.470 -- Is mew. I'm going to write the word meaning here so we know
00:20:44.698 -- what this is at first case. It's been a little while since you've
00:20:47.402 -- seen some of these. So if we knew every single value in the
00:20:51.642 -- population, we would sum all of those up. So I'm going to use.
00:20:55.516 -- Not that you can tell the difference, but that's supposed
00:20:58.496 -- to be a capital Y versus a small way. Usually my capital wise are
00:21:02.668 -- straight just lines and my lower case. Why is usually kind of got
00:21:06.542 -- a curve to it?
00:21:08.830 -- I'll usually remind you as we get there, so we take every
00:21:12.514 -- value of the population.
00:21:14.700 -- And we divide it by. Now we have a new symbol, big End. Big N
00:21:19.875 -- represents population size.
00:21:22.480 -- I'm actually going to write that on my previous sheet of
00:21:25.351 -- paper that I'm going to bring down Tuesday here, so an is
00:21:28.483 -- always your sample size.
00:21:32.560 -- And Big N is going to be your population size.
00:21:37.320 -- Which is actually important. In this course we need to
00:21:39.380 -- know that for the surveys and stuff that we were analyzing.
00:21:45.350 -- Alright.
00:21:48.520 -- Before a sample.
00:21:51.400 -- Ala carte, why bar could be X bar. Yeah, Brooke. Uses why
00:21:54.856 -- we're going to stick with guys. We would take the sum of all of
00:21:58.888 -- our sample. Observations and divided by the number of
00:22:03.687 -- observations in our sample.
00:22:06.980 -- Depending on how we draw a sample, these could be
00:22:10.090 -- identical. But it's not going to happen terribly often, except in
00:22:14.340 -- my example. Today it was coincidence. I swear I actually
00:22:17.390 -- do a random sample, and the thing we're going to look at
00:22:21.050 -- today, and it turned out that the sample mean is going to end
00:22:25.015 -- up being exactly the population mean, but that doesn't always
00:22:28.065 -- happen, but it should be most of the time, pretty close.
00:22:33.250 -- Alright, variance.
00:22:36.060 -- So we call it Sigma squared.
00:22:40.420 -- I'm going to actually give you two different derivations
00:22:43.183 -- of the same formula.
00:22:46.410 -- There's one you've seen before.
00:22:47.860 -- Maybe sort of. So why that should be an eye for each
00:22:52.895 -- individual observation minus mu?
00:22:55.150 -- Quantity squared divided by big N.
00:22:58.680 -- Or in the discrete case, what you saw earlier?
00:23:04.730 -- That was the sum Y minus mu quantity squared times the
00:23:09.427 -- probability of Y.
00:23:15.730 -- Alright.
00:23:19.650 -- S squared following the same sort of formula over here.
00:23:24.040 -- It's going to be.
00:23:27.980 -- The sum why I -- Y bar quantity squared. We divide that by
00:23:33.661 -- little N -- 1.
00:23:36.370 -- Because it came from a sample and we're losing
00:23:38.773 -- some information. If you look there at the formula
00:23:41.176 -- I have. Why bar versus mu, since we don't know mu, we
00:23:44.380 -- lose. We lose our information. A degree of
00:23:46.516 -- freedom. So that's why we're dividing by N -- 1
00:23:49.186 -- little N -- 1.
00:23:51.980 -- But in the population case, we wouldn't actually lose any
00:23:55.010 -- information because we have it all. So, and we're using
00:23:58.040 -- the real mean.
00:24:01.050 -- This one here. Technically we still use via why, but it's more
00:24:05.154 -- ha with a hat on it, so anytime you see a hat on something
00:24:09.942 -- that's usually called an estimator and you're actually
00:24:12.678 -- going to see a hat on a V. More often than not. So this one
00:24:17.808 -- implies that we actually do
00:24:19.518 -- know. All the values and population. Here we are
00:24:23.030 -- estimating the variance, so it's the estimated variance of Y.
00:24:27.750 -- And it really isn't going to look hugely different.
00:24:36.970 -- As well, calculate the expected
00:24:38.450 -- value of Y. Or mew hat.
00:24:42.130 -- Yeah, this book likes to use hats on things, so if you
00:24:44.962 -- haven't seen that too much before, we're going to have
00:24:47.322 -- hats. Lots of hats.
00:24:51.340 -- Standard deviation, well, that's actually.
00:24:57.180 -- Not that exciting or different than what we were used to. So
00:25:01.212 -- Sigma is the square root of Sigma squared and over here S is
00:25:05.580 -- sqrt X ^2.
00:25:11.650 -- Alright.
00:25:15.800 -- Trying to keep my pages and pages in line here so in our
00:25:21.065 -- statistical studies we love to take samples and we make
00:25:25.115 -- inferences from those samples about the larger population. So
00:25:28.760 -- we want to make.
00:25:30.980 -- Well, it's an inference is an educated guess, but we're using
00:25:34.126 -- data and facts to back that up. So it is an educated guess.
00:25:37.844 -- Guess sounds so. I don't know Willy nilly versus.
00:25:42.350 -- An educated statement I don't know, but that's what we're
00:25:45.690 -- going to do. So a lot of times we want to make inferences about
00:25:50.366 -- unknown population parameters. So what do we do? We use our
00:25:54.040 -- sample statistics, so we're going to get back to our TV
00:25:57.714 -- example. 'cause it's completely exciting an in our TV example.
00:26:04.140 -- TV simple. Let's say I took a sample an it's not a very
00:26:09.301 -- big sample, it's only a sample size 4.
00:26:13.970 -- An out of this sample, we knew that we could have values that
00:26:18.169 -- were 0123 or four, but in this particular sample my values
00:26:21.722 -- were. Those are my sorry. These are supposed to be my curly
00:26:25.598 -- braces, but I suck at drawing them, so that's what it is.
00:26:30.900 -- These were my data points.
00:26:34.650 -- There we go.
00:26:37.580 -- 2013
00:26:42.340 -- now just for reference, our population had a sample or
00:26:44.780 -- had a size 4 as well, but we're going to take a sample
00:26:47.952 -- of size 4 and it could have been any values Now notice.
00:26:52.870 -- We actually had five different values that could happen. We
00:26:55.460 -- only chose for actually so big N is. I have a big I have a typo
00:26:59.604 -- on my thing. I gotta fix it big and is actually 5 here, alright?
00:27:04.520 -- So let's estimate mu. So mu hat. We usually just
00:27:07.920 -- call that Y bar X bar.
00:27:11.360 -- Pick a letter well, minus a few of 'em till pigsie.
00:27:17.060 -- But here it is. When we use the sum of our values
00:27:21.296 -- divided by your sample size. So we can do that.
00:27:27.960 -- Divided by 4, why are we doing it this way? Well in this case.
00:27:33.280 -- We're kind of assuming that they didn't have different
00:27:36.286 -- probabilities from our sample when we actually went to those
00:27:39.626 -- probabilities were different based on numbers in a
00:27:42.298 -- household, but from our sample, each of these had an
00:27:45.638 -- equal chance of being chosen.
00:27:48.740 -- So we do this and like I said before.
00:27:54.130 -- We actually get.
00:27:56.190 -- The same number, or pretty close to it, 6 force. I don't know.
00:27:59.986 -- Today is one of those days.
00:28:02.510 -- One of my favorite teachers in the math Department, so some
00:28:05.370 -- days are Calculator days, even for the most simple things like
00:28:08.230 -- 1 1/2. Which I already told you it was the same, but all of a
00:28:12.991 -- sudden my brain said no, you must test it again. So even
00:28:16.195 -- though I calculated it 2 hours ago, evidently I needed to do it
00:28:19.666 -- again. Alright now your sample mean is not always going to be
00:28:22.870 -- equal to your population mean. It should be relatively close
00:28:25.540 -- most of the time this just happened have been one of those
00:28:28.744 -- samples that I happened to draw and I did actually honestly draw
00:28:31.948 -- it randomly. And it just happened to be that this sample
00:28:35.507 -- mean was the same as a population mean, which is OK,
00:28:38.290 -- that's not a bad thing.
00:28:41.470 -- But now we're going to get into calculating our variance
00:28:46.070 -- and standard deviation.
00:28:49.020 -- So here's our variance. We can call it Sigma squared
00:28:52.170 -- hat or Sigma hat squared, probably Sigma hat squared.
00:28:56.380 -- Or you just call ask word that works too.
00:28:59.750 -- We're going to use the other formula, the second, well, the
00:29:02.335 -- first one I drew out, but not the first one we actually used.
00:29:06.540 -- Why I -- Y bar quantity squared divided by N -- 1?
00:29:12.260 -- That's the one we're going to use.
00:29:16.480 -- Amazon to all this lovely fun stuff.
00:29:22.350 -- And we got a zero. Remember using the values from the sample
00:29:25.878 -- and not the actual population.
00:29:28.710 -- 1 -- 1 1/2 squared and 3 -- 1 1/2 ^2.
00:29:38.620 -- Bye bye oh I was gonna say 4 -- 3. Now the answer is
00:29:42.904 -- three 4 -- 1.
00:29:47.900 -- We had five thirds or 1.67.
00:29:53.010 -- Versus what was it before 1.45?
00:29:58.000 -- So a little more variation in
00:29:59.842 -- this. Particular sample, then there wasn't a
00:30:01.996 -- population, that's OK.
00:30:05.390 -- And then for the standard deviation.
00:30:08.780 -- Sigma hat or S just take the square root of your S ^2.
00:30:15.100 -- Anne will get.
00:30:17.490 -- Our standard deviation 1.29.
00:30:22.170 -- As probably.
00:30:28.010 -- Alright.
00:30:30.940 -- Not very exciting, but I thought we do a nice little nice
00:30:34.816 -- overview. Just remind you so for random samples from infinite
00:30:38.046 -- populations, which is what we're kind of doing. The expected
00:30:41.276 -- value of the sample mean.
00:30:43.670 -- Is usually the true meaning that leads us toward what we're
00:30:47.850 -- looking at next, which is not just probability distributions,
00:30:51.270 -- but distributions of statistics.
00:31:02.590 -- Sample statistics so distributions of sample
00:31:05.278 -- statistics, or in other words, sampling
00:31:07.966 -- distributions. That's usually the more common
00:31:10.654 -- terminology.
00:31:16.340 -- So just a reminder, what a sampling distribution is that
00:31:21.235 -- it looks it's the distribution.
00:31:28.200 -- Of all possible samples, Whoops, there's 2 S is there?
00:31:37.310 -- Of a sample statistic.
00:31:46.050 -- We like that we have a specific theorem that we really really
00:31:50.106 -- like. And I need to go find that real quick here now. We probably
00:31:56.269 -- going to look through one of these on the computer up here,
00:32:00.985 -- but it didn't want to go
00:32:03.343 -- through. Well, I wanted to show I didn't want to necessarily go
00:32:06.891 -- through both of 'em 'cause the other one really just kind of
00:32:09.663 -- summarizes this whole thing together. So that's something
00:32:11.511 -- you can look at the other link for. It's called CLT 2.
00:32:15.230 -- But we're going to do is we're going to look at the sampling
00:32:18.961 -- distribution an. I actually have a couple of examples to
00:32:21.831 -- show through simulation how this actually works and why
00:32:24.414 -- we're still able to actually use a normal model. Most of
00:32:27.571 -- the time for analysis, and we're going to do a normal
00:32:30.728 -- model in this classroom as well for this course.
00:32:34.600 -- Not all your surveys are going to have variables that follow
00:32:38.131 -- normal models. OK, not all of 'em, but provided we look at we
00:32:42.304 -- have large enough samples and what have you most of the time
00:32:46.156 -- we should be OK, but not every time. There are exceptions to
00:32:50.008 -- that rule always. So first thing you should always do graph your
00:32:53.860 -- data if you don't know what your data looks like visually, then
00:32:57.712 -- you're only getting probably about 1/3 to half of the
00:33:00.922 -- picture. So alright, so we're gonna look at the central Limit
00:33:04.453 -- theorem. And for that one, our sampling distribution of the
00:33:08.129 -- sample mean is approximately normal with a mean mu and
00:33:11.539 -- standard deviation of the sampling distribution of the
00:33:14.267 -- sample mean. Is Sigma divided by square root of N. So since
00:33:18.359 -- we're looking at the distribution of the sample
00:33:21.087 -- mean, we don't just use our variance, we take the variance
00:33:24.838 -- divided by N or the standard deviation divided by the
00:33:28.248 -- square root of N. We call that Sigma over square root of N.
00:33:32.681 -- We used to call that a standard error.
00:33:36.760 -- That is provided that N is sufficiently large. This theorem
00:33:39.570 -- can also apply to other statistics, which is really,
00:33:42.099 -- really handy because we're going to be using those other
00:33:44.909 -- statistics as well. The sample proportion an one of 'em I
00:33:48.000 -- didn't actually have on here. The sample total which could be
00:33:51.091 -- used in case I don't know if you guys have ever dealt with the
00:33:55.025 -- total before, but it could be nice, say for an airline we need
00:33:58.678 -- to know how many passengers are boarding the plane right? And
00:34:01.769 -- the other thing we do is we weigh how much your bags weigh.
00:34:05.810 -- We need to know the weight of your bags, how much junk
00:34:09.002 -- you're taking with you on the plane, in addition to the
00:34:11.928 -- weight of everything else on the plane, the humans on the
00:34:14.854 -- plane, everything.
00:34:16.640 -- So it might be nice to know what the average weight per person
00:34:20.085 -- should be. The maximum average weight per person, but that's
00:34:22.735 -- not the only thing of interest. It could actually be of interest
00:34:25.915 -- to look at the entire plane full of people's total weight. That's
00:34:29.095 -- just one example. It's not the only one, but it's one of the
00:34:32.540 -- few examples that you could use a total for, and so that's how
00:34:35.985 -- that's going to play in when we start getting to that.
00:34:39.770 -- Alright, so for the most part, the sample size should be
00:34:43.752 -- approximately at least 30.
00:34:46.100 -- If your distribution wasn't already normal to quote
00:34:48.956 -- unquote, guarantee the normality I say and kind of
00:34:52.169 -- using that term guarantee a little. Loosely, there's no
00:34:55.382 -- guarantees, but to get us the approximate normality,
00:34:58.238 -- we should have a sample size of at least 30. Now, if your
00:35:02.879 -- original distribution you already know is inherently
00:35:05.378 -- normal, that sample size stipulation is not required.
00:35:08.234 -- You could have a sample size is smallest 2.
00:35:12.850 -- But if you don't know anything about your original
00:35:15.613 -- distribution, always safer to take a sample size of at least
00:35:18.990 -- 30. That being said, in surveys we take, sample size is usually
00:35:22.674 -- of probably at least 10 or more times than that than 30, so.
00:35:27.480 -- And we're going to sample proportion. We usually want to
00:35:30.000 -- sample size of at least 60. Most of your information from sample
00:35:33.024 -- surveys, alot of time, not most or all. But a lot of times are
00:35:36.552 -- going to be percent, so that would be of interest.
00:35:39.800 -- And again, I said here, if you're just distribution is
00:35:42.520 -- already inherently normal, your sample size stipulation can be
00:35:44.968 -- ignored. It's not that you're ignoring it, but it's not. It's
00:35:47.960 -- not relevant to what you need to worry about it, alright?
00:35:52.040 -- This one sorry. The book I was using used pie instead of P for
00:35:56.184 -- the proportion. Now it should be like most. I'm an intro books,
00:35:59.736 -- they always use P, but as soon as you hit like our 431 class,
00:36:03.880 -- that book uses pie 'cause everything else uses a Greek
00:36:06.840 -- letter. Why not? So why not intro class? Well unfortunately
00:36:09.800 -- will never find that answer out but we still go back to P in
00:36:13.944 -- this book. This book uses P for that terminology just to kind of
00:36:17.792 -- let you know. But you can interchange it with pie. It is
00:36:21.344 -- the same basic thing.
00:36:23.990 -- Alright, so in shorthand notation. Our sample mean X bar
00:36:28.110 -- or why bar is distributed normally with a mean mu and the
00:36:33.054 -- Sigma sub X bar is another notation for that standard
00:36:37.174 -- error. Sigma over square then.
00:36:41.150 -- Same thing for the one for the proportion and the total would
00:36:44.042 -- work as well. I thought this was my updated file that showed.
00:36:47.630 -- Totals so all this is nice and interesting in review. You'd not
00:36:51.950 -- be calculating Z scores in here.
00:36:54.890 -- So if you're hoping to see Z&T scores in here, I'm actually
00:36:58.454 -- going to see those, but that's OK, Alright? This is the
00:37:01.721 -- important part, so we actually see how this distribution works
00:37:04.691 -- and how the central Limit Theorem helps us to look at
00:37:07.958 -- normality. So we're actually going to look at a distribution
00:37:10.928 -- that's already normal, so it's not going to be that exciting
00:37:14.195 -- when we take the look at the sampling distribution, it's
00:37:17.165 -- still going to be normal. There are going to be some
00:37:20.432 -- differences, but then we're going to look at an exponential
00:37:23.402 -- distribution, which is obviously
00:37:24.590 -- not. A normal Bell curve distribution and a binomial
00:37:27.672 -- distribution, just so you can see how the central Limit
00:37:31.062 -- theorem works on even the non normal distributions.
00:37:35.200 -- You don't ever have to reproduce this unless you want to, and
00:37:38.608 -- which case if you want to borrow my code, just ask me, But what
00:37:42.584 -- this does is I'm basically going to take this is in our command,
00:37:46.276 -- so our norm. And you plug in how many values you want into that.
00:37:50.969 -- That will give you random numbers generated from a normal
00:37:53.659 -- distribution. If you don't specify the mean and standard
00:37:56.080 -- deviation, it will assume the mean is 0 and the standard
00:37:59.039 -- deviation is 1, just like the Z
00:38:00.922 -- distribution. So we needed.
00:38:04.070 -- And in this case I actually gave it a different mean in a
00:38:08.256 -- different standard deviation than the Z distribution. So I
00:38:11.154 -- took a sample of 500.
00:38:13.810 -- Out of a normal distribution and I set the mean at 100 and the
00:38:18.612 -- standard deviation at 10 and I said, oh, let's look at the mean
00:38:23.071 -- so mean for that particular sample was 100.25.
00:38:26.970 -- So close.
00:38:29.170 -- And here's our histogram. So the spread on this one goes from
00:38:33.898 -- about 65 to 135, give or take.
00:38:39.630 -- And another random sample just to show the mean change
00:38:42.480 -- to her. But we're still right around that 100 mark.
00:38:46.440 -- And then. For some silly reason, I decided I need to put a curve
00:38:51.432 -- on it. I hardly ever put curves on my on my distributions like
00:38:54.890 -- this, but this one was like I'm going to put that curve on
00:38:58.348 -- there. So there it is. So it is a normal distribution still
00:39:01.540 -- spread out between 65 and 135 center right about 100.
00:39:05.510 -- Oh, rest of my code fell off, sorry.
00:39:09.260 -- Alright, so for this simulation process I'm setting the mean and
00:39:12.714 -- the standard deviation. I'm going to take samples of size
00:39:16.232 -- 5 and I'm going to do that 500 times. We're going to have 500
00:39:20.236 -- samples of size 5, so we can look at the means of all of
00:39:24.240 -- those, and that's what I'm calculating here.
00:39:28.350 -- And then we look at histogram and there is the distribution of
00:39:32.898 -- the sampling distribution of the sample mean. So the spread
00:39:36.688 -- changes 'cause we're dividing it by the square root of N. So it's
00:39:41.615 -- now spread from about 85 to maybe 115 versus 65135.
00:39:46.160 -- So the curve got skinnier and a little bit taller and that
00:39:50.324 -- happens. But it's still a normal distribution, but
00:39:53.151 -- this is now the distribution of X bar versus X.
00:39:56.910 -- And they are just kind of arbitrary values. I guess I
00:39:59.968 -- just. Grabbed grabbed a mean in a standard deviation and
00:40:03.884 -- just used it so.
00:40:05.900 -- Normal spread change though.
00:40:08.720 -- That's important to look at.
00:40:10.480 -- Exponential distribution. I don't know why I really like
00:40:12.919 -- this distribution. If you took 201 or 251 then chances are you
00:40:16.171 -- probably didn't see this. You may have heard about it, but you
00:40:19.423 -- probably didn't see this. If you take 301, they may have seen
00:40:22.675 -- this, but don't stress it if you
00:40:24.572 -- haven't seen it. I'm not going to test you on this formula,
00:40:29.394 -- but this just shows you the formula I'm using, so it's an
00:40:33.786 -- exponential distribution. Exponential is really great
00:40:35.982 -- for modeling the waiting time between events.
00:40:39.620 -- Other processes too, but that's one of its big draws.
00:40:43.920 -- Now let's see. Here we are going to be looking at this with this
00:40:47.784 -- one. We're going to use a distribution with a rate of 1.
00:40:52.180 -- Alright, so random number again, a different
00:40:54.595 -- distribution R has told whole bunch of different
00:40:57.355 -- distributions. You can randomly generate numbers
00:40:59.425 -- out of which is great.
00:41:03.170 -- We need N.
00:41:05.160 -- Anna rate. So with this one we're going to sample size 500.
00:41:10.040 -- We will find the mean.
00:41:11.880 -- That's pretty close to 1.
00:41:14.470 -- That sample #1 sample #2.
00:41:18.450 -- Actually knows same sample. This sample number one.
00:41:21.362 -- Sorry, obviously not a normal distribution.
00:41:25.370 -- And do it again. This time the mean was to even just a hair
00:41:28.968 -- lower. But we're still pretty close to the one mark.
00:41:33.720 -- There we go. Being silly had to add that curve in again. So
00:41:37.984 -- there's our curve or exponential curve and the
00:41:40.936 -- regular distribution of it.
00:41:43.260 -- So now we're going to do the same thing, except for I'm
00:41:46.776 -- going to be taking samples of size 30 and I'm going to
00:41:50.292 -- take 500 samples of size 30 to calculate. 500 means joy.
00:41:54.530 -- It's kind of fun to do. Well, this is the first time so.
00:41:58.840 -- This one, a sample size of 30 almost gives it the normality.
00:42:03.016 -- It's not perfect, but it's.
00:42:05.570 -- Close enough, that's the one thing that's hard to once you
00:42:08.309 -- get out. Intro class is looking at some of these
00:42:10.799 -- curves, and some of these they might not look normal to. You
00:42:13.787 -- might want to go. Some of these are going to be normal
00:42:16.775 -- enough. This one is actually good.
00:42:19.450 -- Obviously not exponential anymore and then binomial. So
00:42:23.266 -- remember binomial distribution is one of those discrete
00:42:27.082 -- distributions for absence or presence, so success or failure.
00:42:33.220 -- So this one is again 500 samples with a binomial
00:42:38.020 -- distribution. Its probability of success was .8 an. We did
00:42:42.820 -- sample sub size 10.
00:42:46.370 -- But this person will probably do 500, though again binomial. You
00:42:49.967 -- can randomly generate, so this first one is actually 500. Later
00:42:53.564 -- on when we do, the 500 samples were going to take 500 samples
00:42:57.815 -- of size 30. I think or is it 10, probably 10? I don't know. I'll
00:43:02.530 -- double check. I looked through it today and then I forgot.
00:43:06.200 -- So the eight the mean should be 8, so the mean for a
00:43:11.127 -- binomial is N * P, so 10 times .8 gives us 8 and this one's
00:43:16.812 -- pretty darn close 7.98.
00:43:20.370 -- Not even a continuous distribution.
00:43:25.820 -- There we go again, and this one that means just a hair over
00:43:29.668 -- eight. OK, so that was our second random sample and there's
00:43:32.924 -- our second. Histogram.
00:43:36.780 -- Same process we're doing samples of size 10, but
00:43:39.012 -- we're taking 500 of them.
00:43:42.220 -- And look at that all of a sudden. It's not the prettiest
00:43:46.084 -- thing I've ever seen, seen prettier distributions, but
00:43:48.660 -- it's still approximately normal.
00:43:51.700 -- Excuse me, centered right about 8:00, so that's what the central
00:43:54.989 -- limit Theorem does. Remember, when I took my intro course, I
00:43:58.278 -- was just like it was just kind of this concept. You had to just
00:44:02.464 -- think about it was like, OK, I'm sure I'll use it, but actually
00:44:06.351 -- saying it for me it made a huge
00:44:08.743 -- difference this other. Thing that you get Lord death right?
00:44:12.372 -- I zoomed in, sorry this other one that you can look at is
00:44:16.090 -- just moves a nice little handout that my 200 level class
00:44:19.236 -- professor had given to us. So I asked him if I could steal it.
00:44:23.240 -- Well, I said I asked him if I could borrow it so I said well
00:44:27.530 -- can I. Can I borrow it and give it to my class and you said OK,
00:44:32.106 -- that's fine so I stole it. There it is but I did I did put
00:44:36.396 -- his name down there so.
00:44:39.460 -- Alright. So we're looking at this thing. We're probably not
00:44:43.222 -- gonna be able to finish this up today, which is OK. We can
00:44:46.576 -- finish this up later, but we can kind of set ourselves up for the
00:44:50.188 -- end of this. So what we want to do?
00:44:54.510 -- Is we have our population at see here.
00:44:59.810 -- I left my pen open, sorry.
00:45:03.800 -- So this is our original population values.
00:45:08.530 -- And we're going to.
00:45:11.320 -- I think in this case just take samples.
00:45:19.530 -- Size 2
00:45:22.310 -- just keep simple.
00:45:25.620 -- Now.
00:45:28.390 -- In this case.
00:45:31.100 -- This is this is our population and this is the number the
00:45:35.132 -- sample size we're going to do. We want to actually look at all
00:45:39.500 -- possible samples for this so.
00:45:49.860 -- All possible samples.
00:45:54.600 -- From in this case, what we're doing is those were the number
00:45:58.344 -- of TV's in the House, but what we're going to do is we're going
00:46:02.712 -- to be looking at from 4 houses.
00:46:06.240 -- So let's say we have House 1-2, three and four.
00:46:13.590 -- So this has a population of four different.
00:46:19.210 -- Possibility so for houses small town. There we go
00:46:22.666 -- more than Moscow.
00:46:26.250 -- One of the things we got excited about when I was a kid
00:46:29.396 -- we were driving. I think we were driving to California and
00:46:32.058 -- we were driving through southern Idaho really late
00:46:33.994 -- tonight. My dad got all excited how to wake all of us up. It
00:46:37.382 -- was like 3:00 o'clock in the morning. 'cause one of the
00:46:40.044 -- towns we came from California so this was a pretty cool
00:46:42.706 -- concept to us. 'cause it was cute, neat. One of the towns
00:46:45.610 -- actually like listed on the animals and I can't remember
00:46:48.030 -- what town it is but listed all the animals, the cows, the
00:46:50.934 -- humans telling my dad had to wake us all up. Look, look at
00:46:54.080 -- this look at this.
00:46:57.060 -- Alright, so small town that was a small town, not as small as
00:47:01.038 -- this little town we're going to deal with, so we're going to
00:47:04.710 -- sample the houses. And then we're going to ask them.
00:47:11.280 -- How many?
00:47:13.980 -- TV's do you own?
00:47:20.060 -- All right, we're going to look at all possible samples.
00:47:25.100 -- So if we just line 'em up.
00:47:29.080 -- One and two can be one of the samples 'cause we're
00:47:31.621 -- taking samples of size 2.
00:47:34.540 -- Now we're obviously going to assume something here that's
00:47:37.528 -- going to be kind of important for us to talk about. Kind of
00:47:41.844 -- important. That's an understatement.
00:47:44.660 -- Is that we're doing this?
00:47:49.350 -- Without replacement.
00:47:52.210 -- So what I'm doing here is that when I choose a house,
00:47:56.086 -- it can no longer be chosen for the observation #2. So
00:47:59.639 -- if it's been chosen for observation number one, it
00:48:02.546 -- can't be chosen again for observation #2, so we
00:48:05.453 -- couldn't go to the House number one twice or House
00:48:08.683 -- number 2 twice, etc.
00:48:12.680 -- Now two and three can be chosen, and this is all
00:48:15.969 -- possible samples. It's not what we actually did, but
00:48:18.660 -- we're looking at the possibilities.
00:48:21.830 -- I don't know. I like Roman numerals. I always have it
00:48:24.888 -- thing from when I was a kid. I apologize, but I'm not
00:48:28.224 -- that sorry.
00:48:31.500 -- So these are all possible samples. We had six of them.
00:48:37.480 -- And that's where we get to pick
00:48:39.545 -- up next time. Figure out what to do with this thing.
00:48:46.780 -- And that's it, and we will finish this tomorrow or
00:48:49.910 -- finish this next class.
00:00:21.060 -- Audi so this is the 7th lecture and
00:00:25.486 -- we're going to continue on with work
00:00:28.634 -- related musculoskeletal diseases.
00:00:30.250 -- So when I talked about anthropometry
00:00:33.778 -- couple lectures ago I talked a little bit
00:00:37.595 -- about this one commercial where Shaquille
00:00:40.120 -- O'Neal is trying to get into a small car.
00:00:43.670 -- And I have found that video and I'm waiting.
00:00:46.270 -- I'm trying to find another video that I
00:00:48.310 -- want to show from anthropometry as well,
00:00:50.610 -- and I haven't located it yet,
00:00:52.340 -- but I want to show this video really quick,
00:00:54.940 -- and again it's throwback to
00:00:56.380 -- a previous lecture,
00:00:57.250 -- but it's pretty interesting
00:00:58.430 -- how they how they set it up.
00:01:12.700 -- I may have retired from the game.
00:01:14.870 -- But not from being big. Good thing.
00:01:17.104 -- One car gives me full size luxury and
00:01:19.916 -- 36 MPG which is nice because I've got
00:01:22.596 -- shoes that are bigger than most hybrids.
00:01:25.370 -- And more stylish too.
00:01:27.990 -- If you don't know the luxurious yet fuel
00:01:30.542 -- efficient across you, don't know Buick.
00:01:32.433 -- Get two years of premium services
00:01:34.359 -- with nothing to at least signing on.
00:01:36.520 -- The EPA estimated 36 Hwy MPG
00:01:38.416 -- lacrosse with the assist.
00:01:39.680 -- Consider it if you don't know the looks.
00:01:43.570 -- If you don't know the luxurious.
00:01:46.810 -- And more.
00:01:49.340 -- So I don't know if you see this self.
00:01:52.570 -- You along with me along with
00:01:55.096 -- this commercial but you can see
00:01:57.888 -- Shaquille O'Neal sitting here.
00:01:59.940 -- They've obviously put the seat way back
00:02:02.495 -- so he could actually sit in the car.
00:02:05.390 -- You can see where his knees are
00:02:07.693 -- in relationship to the dashboard
00:02:09.563 -- and the steering wheel.
00:02:11.190 -- It's obvious that he doesn't
00:02:13.235 -- fit into this car very well.
00:02:15.770 -- He is a a big person.
00:02:18.660 -- And it's just almost ridiculous
00:02:20.525 -- that they have him trying to look
00:02:23.146 -- comfortable in this car because he
00:02:25.192 -- could not drive this car comfortably.
00:02:27.710 -- It be like me trying to fit in
00:02:30.998 -- my daughter's Honda Fit which is
00:02:33.748 -- about the same as Shaq sitting
00:02:36.590 -- in this Buick Lacrosse.
00:02:38.740 -- So again from anthropometric standpoint,
00:02:40.570 -- it's a mismatch.
00:02:41.830 -- He would be very uncomfortable
00:02:43.930 -- and probably sore at the end
00:02:46.020 -- of a very short drive.
00:02:51.800 -- So. We're going to talk about work related
00:02:57.095 -- musculoskeletal diseases of the spine.
00:03:01.300 -- And.
00:03:06.060 -- Paratroopers, helicopter pilots,
00:03:07.296 -- other people in the Military,
00:03:09.360 -- Navy Seals that have to ride in
00:03:12.314 -- the Zodiac boats quite a bit,
00:03:14.730 -- all experience a high degree of back
00:03:17.376 -- injuries associated with their professions.
00:03:19.690 -- Now these are militaries standpoint.
00:03:23.300 -- People of all professions.
00:03:25.460 -- Office workers,
00:03:26.540 -- people that are working on shop floors.
00:03:32.000 -- All experienced back problems
00:03:33.784 -- at various times depending on
00:03:36.014 -- the type of tests are doing.
00:03:38.230 -- There's some genetic components to it.
00:03:40.720 -- The fact that sometimes are not moving
00:03:43.583 -- around and so they can experience problems.
00:03:47.170 -- So what we're going to talk
00:03:49.606 -- about in this today's lecture,
00:03:51.980 -- our spine anatomy and then spinal work
00:03:55.452 -- related musculoskeletal diseases?
00:03:56.940 -- I do have several videos,
00:03:58.890 -- again talking about very aspects
00:04:01.200 -- of various aspects of.
00:04:03.050 -- Dumb.
00:04:04.900 -- No musculoskeletal diseases of
00:04:06.440 -- this particular one talks about
00:04:08.365 -- the anatomy of the spine.
00:04:10.040 -- This is when I found it's truly it.
00:04:12.970 -- More educational and in nature,
00:04:14.810 -- and then we'll go through it in
00:04:17.134 -- detail as we go through the lecture.
00:04:23.150 -- Hi there, I'm doctor Gary Simmons
00:04:25.412 -- of Curling Clinic neurosurgery
00:04:26.980 -- and we're going to talk a little
00:04:28.877 -- bit about the human spine today.
00:04:30.810 -- We talked in the past about
00:04:32.712 -- the anatomy of the spine,
00:04:34.470 -- but what I want to talk about
00:04:36.661 -- today is what goes into the spine,
00:04:39.130 -- because really,
00:04:39.902 -- that's the most important thing
00:04:41.832 -- about your spinal column and that
00:04:43.874 -- is what's on the inside of it.
00:04:45.790 -- Well, what's on the inside of it are nerves,
00:04:48.790 -- and they are the main wiring of your body.
00:04:51.790 -- When your brain tells you to move your hand.
00:04:55.140 -- That has to go through a network
00:04:57.317 -- of wires if you will.
00:04:58.960 -- That eventually goes from the part
00:05:00.904 -- of the brain giving the command out
00:05:03.178 -- to the muscles that move your hand,
00:05:05.320 -- and the same thing goes for if you
00:05:07.688 -- touch a hot stove that the message
00:05:10.054 -- of wow that's hot has to go through a
00:05:13.033 -- series of wires all the way back up
00:05:15.496 -- to your parts of your brain that say,
00:05:18.040 -- you're you're putting your hand
00:05:19.770 -- on a stove that's incredibly high
00:05:21.847 -- and that all goes through the main
00:05:23.828 -- wiring of your body, which is housed.
00:05:26.233 -- Within your spine. Now the main wiring.
00:05:29.610 -- The principle wiring is in what
00:05:32.172 -- we call the spinal cord.
00:05:34.400 -- The spinal cord is a whole bunch of
00:05:37.360 -- wires bundled together basically,
00:05:39.620 -- and those wires run all the way from
00:05:42.996 -- the brain coming out of the head and
00:05:46.639 -- into the spinal column and run all
00:05:49.773 -- the way down through the canal of the
00:05:53.115 -- spine until it reaches somewhere in your.
00:05:56.230 -- Upper low back or your upper
00:05:58.834 -- lumbar region of your back there.
00:06:01.620 -- The bundling of the wires kind of
00:06:04.588 -- breaks up an each wires hanging down
00:06:07.724 -- from the end of the main wiring or
00:06:11.399 -- the spinal cord and almost looked
00:06:14.165 -- like a horses tail in the end part
00:06:17.784 -- of the spinal column.
00:06:19.580 -- In other words,
00:06:20.993 -- a whole bunch of wires just hanging
00:06:24.387 -- there off the end of your spinal cord.
00:06:27.900 -- Looking like a horses tail.
00:06:29.790 -- So in medicine we often use Latin
00:06:32.303 -- terms and that area of your spine
00:06:34.920 -- is called the cauda aquina and
00:06:37.196 -- that means horses tail in Latin,
00:06:39.590 -- and that's what that part of the
00:06:42.243 -- anatomy is now for all that main wiring
00:06:45.363 -- to connect out to your legs and arms
00:06:48.410 -- and lungs and all that sort of thing,
00:06:51.326 -- they have to get out of your spine somehow
00:06:55.255 -- and the way they do it is each time.
00:06:58.390 -- Two vertebrae,
00:06:59.404 -- 2 bones of your spine come together.
00:07:02.960 -- There's a little hole on the side.
00:07:08.980 -- We give that yet another fancy term
00:07:11.528 -- we call that the nuro foramen,
00:07:13.990 -- but it's basically the nerve whole,
00:07:16.300 -- and that's all neural foramen means.
00:07:18.610 -- It's a nerve, whole.
00:07:20.158 -- It's a hole through which a nerve
00:07:22.963 -- jumps out of the spinal column and
00:07:25.728 -- goes off to where it needs to go
00:07:28.736 -- off to an everywhere two vertebrae
00:07:30.928 -- come together from your neck,
00:07:32.850 -- and your thoracic region or the
00:07:35.064 -- chest region to lumbar region,
00:07:37.090 -- which is your lower back region.
00:07:39.510 -- Nerves pop out of these little
00:07:41.928 -- holes now once they get out of
00:07:44.621 -- the holes they tend to go into the
00:07:47.558 -- little Los Angeles freeway exchange.
00:07:50.250 -- In other words,
00:07:51.456 -- several nerves will come out
00:07:53.466 -- of several holes,
00:07:54.790 -- and then they'll go and interchange
00:07:57.112 -- for awhile and then spring
00:07:59.186 -- out is totally different.
00:08:00.990 -- Nerves and those nerves are
00:08:03.050 -- are called peripheral nerves.
00:08:04.700 -- The nerves inside the holes.
00:08:07.920 -- Are called nerve roots,
00:08:09.440 -- so will often talk about nerve
00:08:11.792 -- roots in my business,
00:08:13.270 -- and that's what they're talking about.
00:08:15.560 -- It's the nerve after it comes off
00:08:18.045 -- the spinal cord and comes out the
00:08:20.635 -- little holes before they go into the
00:08:23.299 -- Los Angeles freeway exchanges and
00:08:25.364 -- become what we call peripheral nerves.
00:08:27.776 -- So if you talk about some people
00:08:30.422 -- might talk about the median
00:08:32.271 -- nerve which gets caught in your
00:08:34.448 -- wrist in carpal tunnel syndrome.
00:08:36.570 -- That's what's called a peripheral nerve.
00:08:38.860 -- It's well far away.
00:08:40.700 -- From the spinal nerves that are
00:08:43.558 -- coming out of your spinal column.
00:08:46.540 -- Now again, this is important stuff.
00:08:49.550 -- This spine is designed to give
00:08:52.772 -- you stability and mobility and
00:08:55.440 -- all that sort of thing,
00:08:57.560 -- but really it's designed to protect your
00:09:01.039 -- spinal nerves and your spinal cord,
00:09:04.080 -- and it's obviously made up of tough
00:09:07.545 -- bone and surrounds that, nor the.
00:09:10.262 -- Spinal cord,
00:09:10.934 -- as much as it can to give it protection.
00:09:14.550 -- You might even argue that some of
00:09:16.769 -- the stuff on the backside here
00:09:18.870 -- was to protect you and Saber.
00:09:21.030 -- Tooth tigers were trying to bite
00:09:22.920 -- you in the old days or something.
00:09:25.460 -- But All in all,
00:09:26.920 -- the spinal column is a protective
00:09:29.185 -- element for these very delicate
00:09:31.335 -- wiring of your body.
00:09:33.060 -- We'll talk more about this later
00:09:34.860 -- and further episodes.
00:09:35.760 -- Thank you very much for listening today.
00:09:37.860 -- Bye bye now.
00:09:48.370 -- I don't need a school to just promise me
00:09:51.016 -- the tools for change. I need to school.
00:09:58.340 -- That's the problem about using.
00:10:00.020 -- YouTube is then all the sudden.
00:10:02.030 -- All these advertisements pop up or
00:10:04.208 -- or other videos start to pop up.
00:10:06.380 -- You can't download the videos where
00:10:08.252 -- you can and keep them yourself,
00:10:10.400 -- but it's not the easiest thing to do as well.
00:10:15.470 -- So when we look at the general
00:10:18.228 -- population for every five people in
00:10:20.754 -- a classroom or an office building,
00:10:23.280 -- 80% will experience significant back
00:10:25.925 -- pain at some point in their lives.
00:10:29.760 -- So four out of five people in a room
00:10:33.234 -- will experience some sort of back pain.
00:10:36.930 -- So when I was 20 years old,
00:10:39.290 -- I was working at a marine warehouse.
00:10:42.870 -- Truck driver pulled up.
00:10:44.686 -- Add 2/5 gallon buckets on the
00:10:47.498 -- back of the truck.
00:10:49.040 -- I assume that they were typical 5 gallon
00:10:52.176 -- buckets containing 5 gallons of paint,
00:10:54.290 -- so I grabbed both of them and pulled
00:10:57.794 -- him off the back of the truck.
00:11:00.970 -- And they turned out to be 100 pounds
00:11:03.666 -- of chain and each 5 gallon bucket.
00:11:06.300 -- And so I went straight down to the
00:11:08.836 -- ground and pulled my back muscles.
00:11:11.160 -- So do I tell anybody?
00:11:12.890 -- No, I was 20 years old.
00:11:14.980 -- This was a different era.
00:11:16.710 -- You didn't report every accident
00:11:18.445 -- that you had.
00:11:19.490 -- It was a small company.
00:11:21.220 -- I knew the owner well so you know,
00:11:24.000 -- I didn't report anything.
00:11:25.476 -- I didn't want anyone to
00:11:27.321 -- know that I had done this,
00:11:29.200 -- but that pain lasted for a couple
00:11:31.629 -- weeks and I still remember to
00:11:33.940 -- this day how painful it was.
00:11:36.310 -- And how long it took me to
00:11:38.907 -- overcome that pain?
00:11:40.020 -- At that time,
00:11:40.986 -- you really didn't even have things
00:11:42.918 -- like mottron readily available.
00:11:44.880 -- Ibuprofen there was Tylenol.
00:11:46.376 -- There was aspirin,
00:11:47.500 -- so I didn't really even have things to
00:11:50.588 -- help alleviate the pain at that point.
00:11:55.340 -- I'm lucky that I haven't had persistent
00:11:58.273 -- back pain since that point in time.
00:12:01.060 -- Other people have persistent
00:12:03.408 -- back pain their whole lives.
00:12:06.350 -- I've talked about my colleagues, husband.
00:12:08.581 -- You saw this.
00:12:09.694 -- The hardware that's in his back.
00:12:11.920 -- I have another colleague.
00:12:14.950 -- Who also her husband has significant
00:12:18.172 -- amount of hardware in his neck
00:12:21.375 -- and has constant back pain.
00:12:23.760 -- So back pain is second only to
00:12:26.350 -- the common cold for keeping
00:12:28.574 -- American workers from their jobs,
00:12:31.160 -- and this is from nine 2003 at.
00:12:34.200 -- The statistics still applies today.
00:12:36.380 -- Back pain is very significant amongst people.
00:12:40.040 -- As people get older generally
00:12:42.470 -- there they experience more back
00:12:44.980 -- pain for one reason or another.
00:12:47.450 -- Spinal stenosis is one of those things
00:12:49.823 -- that seems to crop up as people get older,
00:12:52.730 -- and that's where there's a narrowing in the
00:12:55.930 -- opening for the spinal cord to get through.
00:12:59.060 -- This final bones. So.
00:13:04.240 -- When we look at the spine.
00:13:07.240 -- Here's a couple.
00:13:09.490 -- Diagrams of it.
00:13:12.570 -- The diagram at the left.
00:13:14.710 -- Shows the various sections of the spine.
00:13:17.810 -- We have seven vertebrae
00:13:19.162 -- and the cervical spine.
00:13:20.520 -- The skull rests on top of the
00:13:22.550 -- top of the cervical spine.
00:13:24.590 -- They said, I think,
00:13:25.946 -- in the first day of lecture,
00:13:27.980 -- if you reach back and touch.
00:13:30.960 -- I'm going to stop sharing for a second.
00:13:35.720 -- If you reach back and fill that
00:13:37.869 -- lump on the back of your neck
00:13:40.246 -- right here, that's your C6.
00:13:41.915 -- Your cervical 6 vertebrae.
00:13:43.220 -- It's a really easy reference to find,
00:13:45.500 -- so you have one more cervical vertebrae.
00:13:47.780 -- Be a below that, and then it
00:13:49.971 -- starts the thoracic spine.
00:13:57.250 -- So the thoracic spine is the
00:13:59.950 -- least movable part of the spine.
00:14:02.740 -- There are 12 thoracic vertebrae
00:14:04.640 -- T1 to T12 as compared with seven
00:14:07.392 -- for this sort of cervical spine.
00:14:09.710 -- They provide some motion,
00:14:11.254 -- but they're more immobile.
00:14:12.800 -- The discs are not as thick in that region.
00:14:16.290 -- The cervical spine discs are fairly movable.
00:14:18.990 -- That's why we can move our
00:14:21.150 -- heads all the way around.
00:14:25.810 -- But the thoracic spine
00:14:27.710 -- is not as more moveable.
00:14:30.090 -- And then we have the lumbar spine.
00:14:33.090 -- Which is 5 vertebrae, L1 to L5,
00:14:35.860 -- and that's bears most of
00:14:37.835 -- the weight of our body,
00:14:39.810 -- and any load that we pick up.
00:14:43.340 -- So when we're talking about lifting tasks,
00:14:46.110 -- will talk about biomechanics
00:14:48.058 -- during the next couple lectures.
00:14:50.500 -- The server the lumbar spine is what
00:14:53.860 -- actually supports the load of our
00:14:56.602 -- bodies and anything we pick up.
00:14:59.020 -- And then the below the lumbar spine.
00:15:02.100 -- We have the sacrum,
00:15:03.632 -- and it consists of five fused
00:15:06.018 -- and modified vertebrae,
00:15:07.820 -- and with two ilium bones,
00:15:10.020 -- which completes the pelvic ring.
00:15:12.820 -- And then at the very end is the coccyx.
00:15:16.020 -- I know I've talked about a lot
00:15:18.533 -- of different injuries I've had.
00:15:20.300 -- I fell ice skating.
00:15:21.692 -- One time this we were skating on Hayden Lake,
00:15:24.920 -- outside Corda Lane which is in North
00:15:27.594 -- Idaho and all of a sudden we heard
00:15:30.387 -- a large crack of the ice through
00:15:32.750 -- the lake and we both took off.
00:15:35.250 -- A friend of mine and I both took
00:15:37.746 -- off on our skates skating as hard
00:15:40.410 -- as we could because of this crack.
00:15:43.330 -- And I fell and broke my coccyx
00:15:45.374 -- and that took several months to
00:15:47.435 -- to feel better again.
00:15:48.920 -- It's a really easy bone to break
00:15:51.839 -- if you fall on it. It doesn't it.
00:15:54.648 -- It heals by itself and less it gets
00:15:57.140 -- displaced and so it's it's just
00:15:59.234 -- something that a lot of people have
00:16:01.744 -- experienced in the course of their lives.
00:16:04.287 -- So in general we have this large
00:16:07.416 -- structure of bone and are back and in
00:16:10.671 -- between each of the vertebrae there's a disk,
00:16:14.430 -- except in the sacrum,
00:16:16.034 -- because again, they are fused bone.
00:16:22.630 -- So, interesting enough.
00:16:26.160 -- When we look at this final column.
00:16:29.270 -- And we just saw in that one video.
00:16:33.710 -- How the processes work?
00:16:38.600 -- On the back of the spinal
00:16:41.456 -- column and again if he filled
00:16:43.983 -- at C6 vertebrae in the back,
00:16:46.410 -- those Bony processes project out.
00:16:49.860 -- And they protect ingeneral the spinal cord.
00:16:55.020 -- But the discs and the bulk of the bone.
00:16:58.710 -- Are medial to the body versus the
00:17:01.538 -- spinal cord, which is more distal?
00:17:03.966 -- So when you think about it,
00:17:06.390 -- the spinal cord is out away from the
00:17:09.894 -- body compared with where the discs and
00:17:13.229 -- the majority of the vertebral bone is.
00:17:16.390 -- So in this diagram on this slide,
00:17:19.360 -- you can see we have the intervertebral
00:17:22.720 -- disc where the spinal cord is.
00:17:25.620 -- That's right here.
00:17:28.550 -- The cursor is being able to be seen.
00:17:31.260 -- We have these processes that come
00:17:33.342 -- out and the processes have a lot
00:17:35.838 -- of different small muscle groups
00:17:37.573 -- attached to him and they provide us
00:17:39.880 -- the movement that we have back and
00:17:42.106 -- forth that control our body moves.
00:17:44.140 -- There's a lot of these little
00:17:46.780 -- muscles that help us move our
00:17:49.472 -- bodies in a whole variety of ways.
00:17:52.420 -- So vertebrae are similar to
00:17:54.005 -- STACK children's building blocks.
00:17:55.280 -- Best way to sit.
00:17:58.460 -- They physically are not connected
00:18:00.715 -- to each other.
00:18:02.070 -- By bone other than in the sacrum,
00:18:04.840 -- but they are test, of course,
00:18:07.210 -- via the discs in the back.
00:18:10.140 -- And then have a course.
00:18:11.300 -- The spinal cord that goes through.
00:18:14.430 -- If you look at the bottom diagram
00:18:16.775 -- you can see the vertebrae.
00:18:19.200 -- You can see the disc in between,
00:18:21.770 -- which is that light blue color.
00:18:23.970 -- You can see how the nerves come
00:18:26.903 -- out in between the vertebral discs.
00:18:30.080 -- And they, as a video talked about.
00:18:32.580 -- They go out and they innervate
00:18:34.740 -- your whole body so that you can.
00:18:37.220 -- Your brain can talk to your arms or legs.
00:18:41.610 -- Body your skin,
00:18:43.176 -- your fingers,
00:18:44.220 -- everything within your body
00:18:46.760 -- has a connection to the brain.
00:18:50.570 -- So in an injury and will go back up.
00:19:00.620 -- Certain injury we've all heard about
00:19:02.804 -- people who broken their backs,
00:19:04.690 -- which is like crack in the vertebral
00:19:07.210 -- discs or severing the booty galore,
00:19:09.500 -- totally smashing a vertebral disc.
00:19:11.950 -- And then cutting the.
00:19:15.420 -- Spinal cord so dependent on where the
00:19:17.702 -- spinal cord is cut in an accident and
00:19:20.567 -- hopefully nobody ever watching this
00:19:22.451 -- video has not, but it does happen.
00:19:25.170 -- Determines where the body
00:19:27.010 -- is paralyzed or now.
00:19:28.570 -- You don't have that transmission of
00:19:30.820 -- the brain to the rest of the body,
00:19:33.630 -- or vice versa, because it's a two way St.
00:19:36.890 -- It's not just that the brain
00:19:39.260 -- sends signals out and also
00:19:41.425 -- collects signals coming back out.
00:19:43.930 -- So if the vertebrae or the spinal column.
00:19:47.960 -- Is broken twords the neck.
00:19:49.830 -- You may be a person will become
00:19:52.980 -- a quadriplegic versus if it's
00:19:55.272 -- lower down in the back and again
00:19:58.247 -- depending on where the break is.
00:20:00.630 -- Determines what level of paralysis
00:20:03.240 -- somebody might experience.
00:20:08.860 -- So again, we have the small bones
00:20:11.548 -- and project from each of the
00:20:13.998 -- corners of the vertebral disc,
00:20:16.020 -- and these processes, actors,
00:20:17.612 -- attachment points for muscles and ligaments.
00:20:23.960 -- So one of the interesting things is
00:20:26.508 -- this slide talks about in the morning.
00:20:29.150 -- You're about half an inch taller than you
00:20:31.862 -- are in the afternoon, and the reason is,
00:20:35.094 -- is why we're standing or sitting.
00:20:37.320 -- We compress those discs and
00:20:39.175 -- they tend to lose fluid.
00:20:41.030 -- If we're dehydrating,
00:20:42.488 -- we can lose fluid out of those discs.
00:20:46.550 -- People that are on the space station
00:20:49.399 -- astronauts actually become taller during
00:20:51.444 -- the period of time because their disks
00:20:54.069 -- along gate because there's no gravity
00:20:56.259 -- acting on the body and so they are.
00:21:01.570 -- They are a living thing.
00:21:02.960 -- I don't know how is this drive it.
00:21:05.170 -- Bone is a living thing also,
00:21:06.830 -- but disks actually change
00:21:08.250 -- during the course of a day.
00:21:10.380 -- So there are cushions of
00:21:13.445 -- tissue between most vertebrae.
00:21:15.900 -- Which absorbs shock and
00:21:17.744 -- protect the spine from impact.
00:21:20.050 -- So if you're going to be in a hard fall,
00:21:23.120 -- it's better to break a disc than
00:21:25.024 -- it is to break a vertebrae.
00:21:29.170 -- So they are an interesting
00:21:31.405 -- structure because they. The.
00:21:35.370 -- Connective tissue that they're
00:21:37.098 -- made up of are an annular rings,
00:21:40.230 -- and within each of these rings there's
00:21:43.457 -- a gelatinous substance we heard last.
00:21:45.980 -- Unless lecture people talked about something
00:21:48.746 -- similar to like crab meat consistency.
00:21:51.870 -- And that's basically what they're like.
00:21:54.400 -- They're not a solid thing.
00:21:56.500 -- They're not like a gummy bear,
00:21:59.030 -- though they probably are
00:22:00.938 -- closer to a gummy bear than.
00:22:03.800 -- Then a piece of steak.
00:22:06.030 -- But they are squishing,
00:22:07.726 -- but not like you could squish
00:22:10.350 -- him every different way.
00:22:12.270 -- They are hydrophilic,
00:22:13.728 -- meaning that water is attracted into
00:22:16.644 -- the disk versus going out of it,
00:22:19.410 -- and the whole idea is we want to
00:22:22.874 -- have water flowing into the disks
00:22:25.902 -- to keep the spine mobile and to
00:22:29.636 -- keep the spinal cord protected.
00:22:32.920 -- And the endplates of the.
00:22:36.750 -- Discs are covered in cartilage, so it
00:22:39.854 -- makes it a very strong stuff structure.
00:22:46.440 -- Interesting enough.
00:22:49.440 -- When you look at those the way the stone
00:22:52.887 -- spine is built and the vertebral discs,
00:22:56.110 -- you can see that generally the
00:22:58.456 -- posterior side or the structured
00:23:00.563 -- towards your back distal from the
00:23:03.317 -- body is compared with medial is less
00:23:06.313 -- strong than the frontal part of it.
00:23:09.132 -- And for whatever reason,
00:23:11.180 -- I think it adds more mobility so
00:23:13.805 -- that you can bend forward better.
00:23:16.690 -- But if you're going to rupture disc,
00:23:18.730 -- more than likely you're going
00:23:20.635 -- to rupture it towards the back.
00:23:22.960 -- So herniated or ruptured
00:23:24.784 -- disc basically are similar.
00:23:26.610 -- The walls, the disk have broken
00:23:30.096 -- down and the fluid bulges out.
00:23:33.820 -- So in this diagram you can see on the
00:23:36.835 -- right side there's a ball in there.
00:23:39.520 -- Basically,
00:23:39.875 -- that's not really a ball,
00:23:41.650 -- it's just demonstrating the way
00:23:43.430 -- that the disk works,
00:23:44.860 -- that the posterior side is weaker
00:23:46.996 -- than the anterior side.
00:23:51.780 -- So the nerves emerge from the spinal
00:23:54.468 -- canal through openings in each
00:23:56.539 -- vertebrae and potential problems of
00:23:58.654 -- nerves become trapped or compressed.
00:24:00.910 -- So I want to show this diagram
00:24:03.066 -- for a couple of reasons.
00:24:04.850 -- We see the spinal nerves,
00:24:06.490 -- how they come out and you'll notice
00:24:08.765 -- how they kind of wrap around the body.
00:24:11.410 -- So on the on the anterior view or
00:24:13.826 -- the front of the body you can see
00:24:16.315 -- again how they kind of wrap around
00:24:18.690 -- the legs and the nerves innervate
00:24:20.880 -- the body and in various locations
00:24:22.890 -- as the physician talked about.
00:24:24.530 -- In that short video that we
00:24:26.498 -- just saw the spine,
00:24:27.810 -- the nerves come out from the vertebrae
00:24:30.309 -- and they branch into much smaller.
00:24:32.640 -- Nerves,
00:24:33.171 -- and then there's secondary nerves
00:24:35.826 -- that are the peripheral nerves that
00:24:39.104 -- interact with these spinal nerves.
00:24:41.790 -- So if a nerve becomes trapped
00:24:44.196 -- because of a compressed disk.
00:24:48.810 -- Then the person feels the pain.
00:24:51.920 -- Sometimes in the whole length of
00:24:54.002 -- the nerve for the nerve innervates.
00:24:56.640 -- So if we see that towards the lumbar
00:24:59.313 -- part of the body lower part of the body
00:25:01.900 -- can see here this is the spinal
00:25:04.593 -- column and these nerves that come out.
00:25:07.062 -- If this if the nerve is compressed in
00:25:10.107 -- this location, the person could feel that
00:25:12.670 -- compression all the way down to their toes,
00:25:15.330 -- for instance, or part of their foot.
00:25:19.590 -- If somebody is developing sciatica because
00:25:21.972 -- the sciatic nerve is compressed either from
00:25:24.737 -- the spinal column or from sitting in a chair,
00:25:27.910 -- that's not designed well.
00:25:30.490 -- People develop problems from sitting
00:25:31.905 -- at trucks for a long period of time.
00:25:34.120 -- Truck drivers.
00:25:35.186 -- Then that whole length of that nerve.
00:25:38.920 -- Can become irritated and people wish
00:25:41.416 -- filled out shooting pain all the way down.
00:25:44.310 -- I talked in the first class about my
00:25:47.150 -- problem with compressing nerves in my legs.
00:25:50.110 -- And this is a good diagram that shows if
00:25:53.386 -- I'm have my wallet in my front pocket.
00:25:56.660 -- And I can press that nerve that
00:26:00.132 -- nerve wraps around my leg.
00:26:02.420 -- I fill it in my heel.
00:26:04.420 -- And until you look at a diagram
00:26:06.835 -- like this and realize.
00:26:08.570 -- That depending on where
00:26:10.250 -- the nerve is compressed,
00:26:11.930 -- where you might actually feel the sensation
00:26:15.017 -- of that compression of that nerve.
00:26:17.390 -- Nerves are sensitive.
00:26:18.590 -- Some people's nerves are closer to the
00:26:21.466 -- surface than other peoples, obviously.
00:26:23.789 -- Mine I am sensitive to pressure on
00:26:27.422 -- my nerves in my arms go to sleep.
00:26:30.730 -- Without much pressure on him, for instance.
00:26:34.730 -- And so again,
00:26:35.963 -- you want to protect the spinal column.
00:26:38.840 -- Make sure people are sitting
00:26:40.895 -- in the proper chairs,
00:26:42.540 -- not doing activities that can injure
00:26:45.630 -- the spinal cord or the discs so that we
00:26:49.849 -- we don't have this pain in the future.
00:26:53.320 -- The majority of back pain comes
00:26:56.002 -- from just muscular issues and then
00:26:58.896 -- secondarily it's nerve issues.
00:27:06.030 -- So within the body.
00:27:08.386 -- We have these antagonistic muscle
00:27:11.331 -- pairs so one muscle will contract
00:27:14.521 -- while the other one is relaxed
00:27:17.651 -- and depending on how we move,
00:27:20.820 -- determines whether or not we have a
00:27:24.131 -- a muscle that's that's compressing
00:27:26.922 -- or contracting versus one that's at.
00:27:30.750 -- A relaxed state, so the diagrams
00:27:33.414 -- on this side shows some of this.
00:27:36.410 -- We see the in diagram.
00:27:38.580 -- A healthy muscle is balanced,
00:27:40.760 -- it's normal and either both of them are.
00:27:45.870 -- Not being flexed at that time.
00:27:48.620 -- Sometimes if there's an imbalance,
00:27:50.230 -- the stronger muscle pull to
00:27:52.540 -- one side or another.
00:27:54.390 -- In some cases where people's
00:27:56.550 -- muscles are flexed a lot,
00:27:58.710 -- they develop that pain in their back.
00:28:03.480 -- The 10s machine sometimes is
00:28:05.605 -- used to help relax the muscles.
00:28:08.490 -- They'll give a pulse of electric electrical
00:28:12.564 -- energy so that the back will relax.
00:28:16.420 -- In the abdominal muscles,
00:28:17.720 -- one idea is that to keep your core
00:28:20.475 -- muscles strong because of the spine
00:28:22.695 -- movement as well as back muscles,
00:28:24.870 -- thousands of muscles of rack
00:28:26.570 -- participate in every move you
00:28:28.331 -- make and keeping muscle strong.
00:28:30.150 -- The abdominal muscles and the back muscles.
00:28:33.650 -- An imbalance is a key to help prevent.
00:28:38.360 -- Pain and injury to the back.
00:28:40.450 -- With weak muscles,
00:28:41.428 -- there's little back support and
00:28:43.058 -- when muscles are imbalanced the
00:28:44.609 -- entire spine can be out of balance.
00:28:46.570 -- If we see somebody sitting
00:28:48.735 -- in an awkward posture.
00:28:50.470 -- This is sometimes how people can get to
00:28:53.262 -- where one muscles stronger than another.
00:28:56.170 -- Muscle or muscles are used adequately.
00:28:58.610 -- They'll atrophy,
00:28:59.422 -- meaning they get smaller,
00:29:01.050 -- and then there's more of a
00:29:03.546 -- potential for back injury as well.
00:29:12.080 -- So at the end of the lecture,
00:29:13.410 -- what we're going to do is we're
00:29:15.013 -- going to look at a couple of
00:29:16.709 -- videos we looked at before.
00:29:17.900 -- But when we see something like this,
00:29:20.510 -- you know what are the potential work
00:29:23.856 -- related musculoskeletal disorders?
00:29:25.290 -- So the diagram on the left
00:29:27.654 -- you see a person welding.
00:29:30.060 -- They're bending over at the waist.
00:29:32.900 -- Their head actually is at about a
00:29:35.406 -- 90 degree angle with their torso,
00:29:37.800 -- but the torso is bent over
00:29:39.978 -- totally into 90 degree angle.
00:29:41.950 -- I mean the head is at a.
00:29:45.930 -- Correct angle to the torso,
00:29:47.490 -- but the back is bent at a 90 degree angle.
00:29:50.610 -- This is a very unhealthy posture and can put
00:29:53.418 -- a tremendous amount of pressure on the back.
00:29:56.660 -- On the right side we see that this
00:29:59.156 -- dental hygienist or dentist is
00:30:00.876 -- working on this person's teeth.
00:30:02.600 -- They're not only sitting cross.
00:30:05.960 -- Asymmetrically.
00:30:06.446 -- So there are twisted at the trunk.
00:30:09.850 -- His head is twisted and it's also bent.
00:30:13.330 -- When we talk about bio mechanics and
00:30:15.500 -- we get into these couple ergonomic
00:30:17.640 -- tools that are called Rula and Reba,
00:30:20.310 -- we'll talk about what the level of
00:30:23.145 -- stress that's actually putting on the body.
00:30:25.860 -- But in both diagrams,
00:30:27.668 -- the person could experience
00:30:29.476 -- Backcountry overtime on the right side.
00:30:31.610 -- The person could experience
00:30:33.254 -- neck injury on the left side,
00:30:35.720 -- not so much with neck injury because
00:30:38.597 -- the head is in a relatively
00:30:41.840 -- good posture according to.
00:30:43.770 -- The persons torso.
00:30:48.760 -- Not sure. This little video
00:30:52.412 -- talks about back pain.
00:31:00.170 -- Sometimes I want to pinch myself
00:31:01.796 -- 'cause I think I'm dreaming.
00:31:03.420 -- I've just been able to enjoy my life again.
00:31:06.070 -- It's a miracle I'm a miracle.
00:31:20.420 -- I had severe sciatica.
00:31:21.636 -- It was to the point where I couldn't
00:31:24.117 -- even get out of bed in the mornings.
00:31:26.500 -- I couldn't stand very long.
00:31:28.020 -- I couldn't sit very long.
00:31:30.760 -- Thing for a long period of time,
00:31:32.850 -- I mean more than five or 10 minutes
00:31:35.066 -- it had gotten to be that severe.
00:31:37.340 -- How's your pain today?
00:31:38.532 -- Zero pain.
00:31:39.130 -- That sounds very good.
00:31:52.290 -- She also had an unstable
00:31:53.815 -- condition or lumbar spine.
00:31:55.040 -- She had a condition called
00:31:56.830 -- spondylolisthesis where one
00:31:57.904 -- bone is slipped forward on top
00:31:59.829 -- of the other and that tends to
00:32:01.881 -- slowly get worse over the years
00:32:03.435 -- and it can cause a lot of pain.
00:32:05.750 -- It can even cause paralysis.
00:32:18.750 -- Of that operation, however,
00:32:20.042 -- is that in order to treat the problem,
00:32:22.780 -- we have to also cause a fair
00:32:25.076 -- amount of injury and damage
00:32:26.807 -- to the spine to the bones.
00:32:28.830 -- The muscles to the tendons,
00:32:30.510 -- which are all structures that are
00:32:32.484 -- very important in these patients
00:32:34.202 -- when it comes to recovery.
00:32:49.320 -- It's a 3 dimensional GPS system that
00:32:51.308 -- allows us to navigate very accurately
00:32:53.400 -- and very precisely within the spine.
00:32:55.760 -- Even though we're operating through
00:32:57.450 -- very small incisions, we equip the
00:32:59.487 -- tools that we use with little sensor.
00:33:01.860 -- You're operating on the patient,
00:33:03.560 -- but on the screen you see
00:33:05.636 -- exactly where you are.
00:33:07.020 -- Within the Spine 5 and then 14 millimeters
00:33:09.564 -- we're really at the forefront of
00:33:11.881 -- minimally invasive spinal surgery
00:33:13.501 -- patients benefit from this because
00:33:15.358 -- they recover now much faster from
00:33:17.332 -- these operations then they would have.
00:33:19.450 -- Maybe not a few years ago when I woke
00:33:22.186 -- up five hours after the surgery,
00:33:24.770 -- I had no more sciatica pain is scared.
00:33:28.290 -- 'cause I haven't been paying
00:33:30.110 -- free for over a decade.
00:33:31.930 -- Yeah, life is real good.
00:33:33.750 -- It's extremely good.
00:33:34.842 -- You know.
00:33:35.570 -- I'm blessed.
00:33:45.120 -- So grateful for this new technology
00:33:46.962 -- that the Doctor performed on man,
00:33:48.600 -- you know I got my life back and there's not
00:33:51.941 -- enough time in hours in the day. For me,
00:33:54.912 -- 'cause there's so much I want to do now.
00:34:20.230 -- So there's been quite a few advertisements.
00:34:22.620 -- It's usually around Christmas for teeters.
00:34:24.660 -- Hang up, teeter hang ups,
00:34:26.370 -- which basically you lock your feet in and
00:34:29.090 -- then you lean back and get to posture.
00:34:31.820 -- That feels comfortable for a person.
00:34:33.870 -- And that idea is the same thing.
00:34:36.260 -- It decompresses the spine,
00:34:37.624 -- takes the pressure off the nerves,
00:34:39.670 -- and people experience less back pain.
00:34:41.710 -- OK, so a couple of issues with
00:34:44.069 -- that before anybody ever uses
00:34:45.825 -- one of those types of devices,
00:34:47.850 -- they need to consult with their physician.
00:34:50.700 -- Because if you think about it,
00:34:53.570 -- you're upside down the pressure
00:34:56.610 -- and your pressure in your.
00:34:59.650 -- Brain increases because you're
00:35:00.958 -- in that inverted posture,
00:35:02.270 -- so you need to be checked out before
00:35:05.454 -- anybody uses it to make sure that
00:35:08.285 -- they're not a candidate for a stroke.
00:35:11.050 -- So no problems are commonly associated
00:35:13.024 -- with prolonged exposure to static postures,
00:35:15.210 -- typically as a consequence of
00:35:16.945 -- visual requirements of a task.
00:35:18.680 -- So we saw the dental hygienist,
00:35:20.770 -- and that one diagram a couple minutes ago,
00:35:23.540 -- and that person is at a higher.
00:35:26.980 -- Potential for.
00:35:29.494 -- Neck injuries and there is evidence
00:35:33.210 -- of flexion beyond 30 degrees.
00:35:36.780 -- Leads to more rapid onset of fatigue.
00:35:39.970 -- So if you're sitting in a posture again,
00:35:42.700 -- your natural posture for your neck is
00:35:44.702 -- about a three degree inclination forward.
00:35:47.130 -- If you're at a 30 degree inclination forward,
00:35:49.860 -- the idea is it puts pressure on the
00:35:52.612 -- nerves and blood vessels of the neck and
00:35:55.945 -- can increase your potential for fatigue.
00:35:58.630 -- People who use microscopes
00:36:00.498 -- for long periods of time,
00:36:02.840 -- like pathologists do experience potential
00:36:05.430 -- problems with fatigue and also the
00:36:08.496 -- potential for disc problems in the neck.
00:36:13.420 -- So disc generation.
00:36:15.121 -- Can happen and an older individuals
00:36:18.523 -- as well as younger individuals.
00:36:21.930 -- So we see here on this diagram
00:36:24.002 -- and this is pretty exaggerated.
00:36:26.300 -- On the left side we see a normal disc.
00:36:29.570 -- It's equal, it's not bulging out,
00:36:31.760 -- so it's not putting excess
00:36:33.580 -- pressure on the spinal cord.
00:36:37.520 -- The next diagram down is a herniated
00:36:40.586 -- disk and this is on the left side
00:36:43.786 -- and you can see where the walls.
00:36:46.550 -- Of the disc are starting to breakdown
00:36:49.154 -- and you see a bulging out and
00:36:51.988 -- putting pressure on the spinal cord.
00:36:54.450 -- So minor pressure is not a big
00:36:56.963 -- deal as it gets worse and worse.
00:36:59.970 -- It puts more pressure on and people
00:37:03.358 -- experience a higher degree of pain or
00:37:06.415 -- start to fill lack of use of a limb.
00:37:09.660 -- Or both legs, for instance,
00:37:11.530 -- both arms dependent on where
00:37:14.480 -- the disc is herniated.
00:37:16.840 -- A bulging disc is a little bit
00:37:19.073 -- different than a herniated disc.
00:37:21.120 -- It's the same idea.
00:37:22.488 -- Only in this case it's much worse,
00:37:25.050 -- and in this case the annulus outer layer
00:37:28.498 -- of the disc bulges into the spinal cord.
00:37:32.490 -- And then we have thinning discs and
00:37:35.535 -- this is on the right side as the disc
00:37:39.484 -- thins out that the spinal cord tends to.
00:37:43.270 -- Spinal column tends to compress more,
00:37:45.250 -- putting more pressure on those nerves that
00:37:47.966 -- are coming out of the various openings.
00:37:50.840 -- And then finally we have discussed
00:37:52.856 -- the generation and it's something
00:37:54.680 -- similar to osteoporosis where calcium
00:37:56.765 -- and phosphate or leaving the bone
00:37:59.079 -- making it much weaker and the bone
00:38:01.109 -- starts to get smaller and smaller.
00:38:03.160 -- So when you see somebody an older
00:38:05.575 -- person that maybe you haven't seen
00:38:07.715 -- for three or four years and before
00:38:10.200 -- they were your height and now you're
00:38:12.664 -- 4 inches taller and taller than them.
00:38:15.128 -- But two things could have happened.
00:38:17.240 -- Either you grew or the disks in this
00:38:20.320 -- person's back. Hands for table.
00:38:24.660 -- Vertebrae have started to degrade
00:38:26.760 -- and the person is actually getting
00:38:29.513 -- shorter overtime.
00:38:33.670 -- So here's a diagram. An X ray of
00:38:36.158 -- a herniated disk on the left side.
00:38:38.410 -- You can see where it's actually bulging
00:38:40.629 -- out and pressing on the spinal column.
00:38:45.040 -- And you can see.
00:38:46.208 -- So this is on the right side.
00:38:48.400 -- Is the posterior view and the
00:38:50.056 -- left side is the anterior view.
00:38:52.060 -- You can also see at the
00:38:54.778 -- bottom of the Lombard.
00:38:56.590 -- Vertebrae these are the lumbar
00:38:58.415 -- vertebrae right here, and these.
00:39:00.560 -- This is the sacrum.
00:39:02.660 -- How that curve is and you
00:39:04.436 -- can see here at the bottom.
00:39:06.490 -- This disk also appears to
00:39:08.080 -- start to have problems,
00:39:09.360 -- and usually if you have problems
00:39:11.154 -- in one disc it can lead to
00:39:13.432 -- problems and other disks.
00:39:17.960 -- So on the right side.
00:39:20.260 -- You see a ruptured disc.
00:39:21.970 -- This is what the actual
00:39:23.670 -- disc material looks like.
00:39:25.030 -- As they said in the one deal
00:39:27.354 -- about looking like crab meat.
00:39:29.130 -- That's kind of what it looks like.
00:39:32.830 -- They see the tear through the.
00:39:35.330 -- The cartilage area.
00:39:39.440 -- And the concentric rings of
00:39:41.010 -- the disk material itself.
00:39:42.270 -- And if you look closely,
00:39:43.840 -- you can see a tear in this area
00:39:45.992 -- that tare allows the fluid to flow
00:39:48.210 -- through from one area to another area.
00:39:50.740 -- Generally again it's hydrophilic,
00:39:52.000 -- meaning it's water loving.
00:39:53.260 -- But still,
00:39:53.886 -- when you start to break those rings,
00:39:56.080 -- it starts to release fluid out and
00:39:58.250 -- this is where the disk and bulge.
00:40:00.480 -- I don't think in this particular
00:40:02.208 -- case this person is going to notice
00:40:04.433 -- because obviously it's a cadaver,
00:40:06.130 -- but that's beside the point.
00:40:11.050 -- So we're going to show this video.
00:40:13.140 -- I don't think I keyed it up. Oh, here it is.
00:40:22.130 -- Hi there, I'm doctor Gary Simmons
00:40:24.260 -- of Curling Clinic neurosurgery and
00:40:25.969 -- I'm going to talk to you a little
00:40:27.785 -- bit about lumbar disc surgery.
00:40:29.520 -- You may remember from previous
00:40:32.800 -- discussions that there are times
00:40:36.189 -- where a cushion or lumbar disc.
00:40:39.420 -- Has problems.
00:40:40.410 -- The disc is tough on the outside,
00:40:43.880 -- squishy on the inside.
00:40:45.308 -- The inside looks like crab meat
00:40:47.522 -- and sometimes a chunk of crabmeat
00:40:49.508 -- will rip out and push backwards and
00:40:51.953 -- to the side exactly where nerve is
00:40:54.410 -- trying to get out of your spine,
00:40:56.860 -- and when it pushes up against the
00:40:59.212 -- nerve the nerve gets irritable and
00:41:01.377 -- you may feel pain, numbness, tingling,
00:41:03.542 -- have some weakness all the way down your leg.
00:41:06.690 -- Usually it's just one leg,
00:41:08.450 -- but it can be miserable now.
00:41:10.550 -- Luckily most get better.
00:41:12.154 -- All by themselves,
00:41:13.360 -- but sometimes they don't,
00:41:15.092 -- and when they don't,
00:41:16.830 -- and that nerve is continuously
00:41:19.005 -- being pushed on,
00:41:20.310 -- it can be absolutely miserable and people
00:41:23.621 -- can be totally laid up by the pain.
00:41:26.820 -- And if the pain doesn't go away,
00:41:29.850 -- we sometimes will resort to surgery.
00:41:32.460 -- Now sometimes we can get by with
00:41:35.071 -- shots in the back where a numbing
00:41:38.274 -- medicine is used initially.
00:41:40.270 -- But really,
00:41:41.190 -- a steroid medicine is put on the nerve.
00:41:44.870 -- Now, this isn't an athlete steroid.
00:41:46.830 -- This is an anti inflammatory steroid
00:41:48.810 -- and the idea is to calm the nerves down.
00:41:51.720 -- But it doesn't do anything for the
00:41:53.925 -- crab meat that's sitting there on the nerve.
00:41:56.610 -- So if the nerve wants to stay
00:41:58.647 -- irritable it will stay irritable.
00:42:00.520 -- So sometimes we have to resort
00:42:02.398 -- to literally going in there and
00:42:04.396 -- removing the disk,
00:42:05.410 -- removing the crab meat that's
00:42:07.035 -- pushing on the nerve.
00:42:08.340 -- Now one of the misconceptions is
00:42:10.080 -- that we take the entire discount.
00:42:12.250 -- That's not the case at all really.
00:42:14.540 -- What we're going after.
00:42:16.040 -- Is that chunk of crab meat that
00:42:18.788 -- ripped out created out?
00:42:20.470 -- Herniated discs slip.
00:42:21.469 -- This ruptured disc.
00:42:22.470 -- They all mean the same thing.
00:42:24.470 -- In fact, we've got another name,
00:42:26.460 -- herniated nucleus pulposus
00:42:27.795 -- all mean the same thing.
00:42:30.020 -- We go in there surgically and
00:42:32.786 -- sometimes take the chunk off the nerve.
00:42:35.920 -- The way we do it is usually through
00:42:38.464 -- a small incision in the back.
00:42:40.740 -- This can be done through little
00:42:42.804 -- tubes with TV scopes,
00:42:44.180 -- or could be done with a microscope,
00:42:46.580 -- but usually it's a relatively small incision.
00:42:48.990 -- There are gaps between the vertebrae
00:42:51.096 -- here and we sneak in through the gap.
00:42:53.810 -- Sometimes we make the gap a little larger,
00:42:56.560 -- but we sneak in through the gap.
00:42:58.970 -- Find the nerve that's being pinched.
00:43:01.030 -- Find the crab meat that's pinching it,
00:43:03.440 -- grab the crab meat and we throw it away.
00:43:06.650 -- Literally throw it away.
00:43:08.498 -- We give it to the pathologists,
00:43:11.270 -- the.
00:43:12.810 -- All for all intents and purposes,
00:43:15.320 -- that surgery is now done.
00:43:18.910 -- Our goal is to get that nerve
00:43:21.024 -- swinging in the breeze.
00:43:22.470 -- Have nothing pushing on it.
00:43:24.090 -- I can't fix the nerve.
00:43:25.710 -- I can't make the nerve feel better
00:43:27.992 -- I can't make it less irritated
00:43:29.898 -- but I can get it out of
00:43:31.964 -- trouble. I can get the pressure off
00:43:34.518 -- of it and if I get the pressure off
00:43:37.452 -- of it 9 * 99 times out of 1095 times
00:43:40.296 -- at 100 it will feel much, much better
00:43:42.927 -- off and it feels better instantly.
00:43:45.150 -- Patients can be wheeled out of the
00:43:47.285 -- operating room where they're going.
00:43:49.040 -- Oh my goodness, my leg is better already.
00:43:52.120 -- But it doesn't always happen that quick.
00:43:54.440 -- Sometimes it can take weeks for the nerve
00:43:57.032 -- to settle down while we're in there,
00:43:59.400 -- we usually will go into the disc itself
00:44:01.656 -- and try to grab any other loose pieces
00:44:04.152 -- so that another piece doesn't just
00:44:06.282 -- immediately follow the first piece,
00:44:08.340 -- but we don't take the whole disk out.
00:44:10.990 -- That's a misnomer,
00:44:11.980 -- is not what happens.
00:44:13.300 -- We don't take the whole disk app we leave,
00:44:16.280 -- we put everything back together and we leave
00:44:19.192 -- just trying to keep that nerve nice and calm.
00:44:22.140 -- But it often feels better
00:44:24.380 -- real quick afterwards.
00:44:25.730 -- Can you re herniated disc?
00:44:27.360 -- Can you have another chunk
00:44:28.985 -- of crabmeat come out?
00:44:30.290 -- Unfortunately yes,
00:44:30.942 -- 10 to 15% of people who have had one
00:44:34.002 -- herniated disc will go on and do it again,
00:44:36.810 -- either at the same place or there
00:44:39.092 -- slightly more prone to having it occur
00:44:41.408 -- somewhere else in the lower back.
00:44:43.330 -- So it's not a cure all.
00:44:45.290 -- But boy,
00:44:45.890 -- if you're in that desperate shape where
00:44:47.990 -- it's been going on for weeks and weeks
00:44:50.214 -- and weeks and you're feeling absolutely
00:44:52.328 -- miserable and nothing is helping,
00:44:54.420 -- it really can feel like a miracle within.
00:44:57.250 -- Within often a matter of hours or
00:44:59.574 -- days if it's not getting better.
00:45:02.020 -- If that nerve decides not to settle down,
00:45:04.960 -- well, there's other tricks up our sleeves,
00:45:07.530 -- but the majority of the time getting
00:45:10.064 -- that hunk of crabmeat out of there and
00:45:13.042 -- off the nerve will make you feel much,
00:45:15.970 -- much better.
00:45:16.656 -- Why don't we do it the first day
00:45:19.477 -- that you have a herniated disc?
00:45:21.840 -- Because 80 plus percent of people
00:45:24.102 -- who have a herniated disc will
00:45:26.400 -- feel better within a few weeks.
00:45:28.550 -- So you can be saved from having to
00:45:31.262 -- have surgery if you just take it
00:45:33.676 -- easy and let things settle down,
00:45:35.770 -- but when it's not selling down,
00:45:37.840 -- it really is a wonderful operation in
00:45:40.171 -- that it helps a lot of people will
00:45:42.742 -- talk about other types of operations
00:45:44.718 -- in the spine in future sessions.
00:45:47.130 -- Bye bye now.
00:46:10.790 -- So if you want to watch the rest of
00:46:13.814 -- the series, it's pretty interesting
00:46:15.899 -- this guys are a good speaker and does
00:46:18.834 -- a good job about explaining these
00:46:21.180 -- various operations that they do.
00:46:22.930 -- Obviously we saw two videos today and you
00:46:26.386 -- could see how well he explained things.
00:46:30.130 -- So there are other types of injuries,
00:46:33.160 -- and some of these you may have
00:46:36.044 -- experienced if you go into the workplace.
00:46:39.220 -- Many times you'll see these injuries
00:46:41.848 -- or these conditions of the spine.
00:46:44.420 -- Sometimes they're not injuries,
00:46:46.148 -- but they're just how people have
00:46:48.814 -- how their spines are basically,
00:46:50.910 -- so ideally we see that we have
00:46:54.529 -- our person on the left.
00:46:57.260 -- Who has his ears over shoulders,
00:46:59.260 -- shoulders over his hips,
00:47:00.588 -- hips over his knees,
00:47:01.920 -- knees over his ankles,
00:47:03.852 -- and the neutral posture?
00:47:05.790 -- The person that's diagram to the right of
00:47:09.334 -- him or her more likely him in this case.
00:47:13.360 -- You see that he's got extreme lordosis.
00:47:17.310 -- Meaning the upper part of the
00:47:19.842 -- spine is protruding out.
00:47:23.640 -- When we get into biomechanics two
00:47:25.578 -- and a couple of photos that I have,
00:47:28.200 -- this one person you can see has a
00:47:32.120 -- pronounced lordosis. Basically.
00:47:37.870 -- From working or kyphosis from working,
00:47:40.380 -- doing these laundry tasks
00:47:42.932 -- over a period of time.
00:47:46.130 -- So and somebody can experience a
00:47:48.446 -- couple of these conditions together,
00:47:50.650 -- kyphosis and lordosis and also
00:47:52.705 -- scoliosis at the same point.
00:47:57.620 -- If you've ever seen the movie Molly's game.
00:48:01.730 -- It talks about the star of the show,
00:48:04.170 -- so to speak, or what the story centers
00:48:07.018 -- around the person it centers around.
00:48:09.630 -- But she grew up and all the
00:48:11.933 -- sudden she developed scoliosis.
00:48:13.680 -- Severe case of scoliosis for spying
00:48:15.780 -- twisted and she had to undergo
00:48:18.007 -- surgery to straighten your spine out.
00:48:20.300 -- Scoliosis is,
00:48:21.401 -- I don't wanna say real common,
00:48:23.610 -- but it is relatively common.
00:48:25.450 -- And when somebody experiences at a young age,
00:48:28.400 -- what they normally do is put
00:48:30.320 -- the person in a back brace to
00:48:32.928 -- help the spine straightened out.
00:48:35.020 -- In very severe cases,
00:48:36.652 -- they do have to do operations.
00:48:39.100 -- And they have to pin the spine so
00:48:42.228 -- that it is more straight in nature.
00:48:45.690 -- And you see,
00:48:46.761 -- water kyphosis is for this
00:48:48.546 -- bulges out at the top,
00:48:50.120 -- a lordosis where the lumbar area bulges in
00:48:53.168 -- and then scoliosis for the spine is crooked.
00:48:56.630 -- So with the ideal posture,
00:48:58.350 -- the forces are evenly distributed
00:49:00.080 -- through the body and all the joints are
00:49:02.818 -- in their neutral zone and this results
00:49:05.091 -- in minimal wear and good muscle and
00:49:07.590 -- stable stabilizer muscle recruitment.
00:49:09.150 -- When they talk about the fact that.
00:49:12.510 -- Oh you know, just.
00:49:15.852 -- When you're growing up and they
00:49:17.676 -- say you know have a good posture,
00:49:19.780 -- keep your head up.
00:49:20.888 -- Keep your shoulders back.
00:49:22.000 -- That helps put you in that neutral posture
00:49:24.296 -- and helps prevent some of these conditions.
00:49:26.760 -- Poor posture,
00:49:27.402 -- the joints are out of alignment,
00:49:29.330 -- their type,
00:49:30.320 -- the muscles are shortened or weak.
00:49:33.290 -- Jason muscles are weak and important.
00:49:36.010 -- Stabilizers are inefficient.
00:49:42.450 -- So we do have disk congenic and neurological
00:49:45.418 -- types for conditions where the disc
00:49:48.338 -- prolapses there's nerve irritation,
00:49:50.440 -- nerve entrapment.
00:49:52.360 -- We have muscular ligament and tendon
00:49:54.952 -- problems which are caused by trauma,
00:49:57.450 -- strain, sprain and tear.
00:49:59.186 -- And then we have muscle weaknesses
00:50:01.867 -- which cause imbalances.
00:50:03.560 -- And then we have structural
00:50:05.970 -- and genetic type problems.
00:50:07.900 -- Real common and thank God knock knock.
00:50:11.100 -- I don't experience this,
00:50:12.852 -- but my family has a history of stenosis,
00:50:16.580 -- meaning and narrowing of the.
00:50:20.470 -- Vertebral vertebrae,
00:50:21.326 -- where the spine goes through,
00:50:23.470 -- and this put can put pressure
00:50:26.416 -- on the spinal column.
00:50:28.380 -- There's cartilage damage,
00:50:30.063 -- bone where osteoarthritis and osteoporosis.
00:50:36.420 -- So why do people get back pain or
00:50:38.748 -- New Years starting up a new activity?
00:50:41.240 -- If you've never shoveled dirt before
00:50:43.262 -- and today you're out shoveling dirt or
00:50:45.518 -- like what we've had to do this winter,
00:50:47.980 -- is shovel a lot of snow,
00:50:49.900 -- and this is the first time you do it.
00:50:52.790 -- People can experience back pain.
00:50:55.070 -- There's misuse cumulative effect of bad
00:50:57.494 -- body use over a long period of time.
00:51:00.660 -- So poor postural alignment or
00:51:02.545 -- pushing their body too far too often?
00:51:05.170 -- There's overuse repetitive use of one
00:51:07.276 -- group of muscles causing an imbalance,
00:51:09.480 -- and then diseuse lack of exercise
00:51:11.484 -- may cause a back problem,
00:51:13.430 -- but one can result when we attempt an
00:51:16.158 -- activity requiring a certain degree
00:51:18.023 -- of strength or fact flexibility.
00:51:19.890 -- So if you don't do something for a
00:51:22.530 -- long period of time and then you try
00:51:25.245 -- doing it with without proper training,
00:51:27.790 -- so to speak, to get into the shape,
00:51:30.660 -- to do that activity, you can cause an injury.
00:51:36.150 -- So again, I've shown this picture before.
00:51:39.010 -- This is hardware and a colleague
00:51:41.428 -- of mine's husband's spine
00:51:43.113 -- that keeps his back together.
00:51:45.130 -- You can see in this X ray how
00:51:47.730 -- those two vertebrae aren't
00:51:49.466 -- really lined up as well either,
00:51:52.470 -- but without this he would have tremendous
00:51:55.333 -- pain with this hardware in his back.
00:51:58.180 -- What he does is he lacks flexibility.
00:52:02.740 -- But you can do stuff.
00:52:06.240 -- So from an economic perspective,
00:52:08.360 -- what can we do? We can rest.
00:52:11.330 -- We can change the risk factors.
00:52:13.870 -- We can get physical therapy.
00:52:15.990 -- We can do hold your holistic,
00:52:18.540 -- natural path type things.
00:52:22.020 -- If we have pain,
00:52:23.228 -- we can use over the counter
00:52:25.115 -- medication or prescribed medications.
00:52:27.660 -- One of the things that many
00:52:29.148 -- physicians talk about now and again.
00:52:30.660 -- I'm not a physician.
00:52:32.464 -- But again, using topical type pain relief
00:52:36.220 -- rather than consuming Mot ran or Tylenol,
00:52:40.220 -- but putting on like asper
00:52:43.075 -- cream or Salon pass patch.
00:52:45.930 -- One of those things that are
00:52:49.842 -- a topical type pain reliever.
00:52:53.810 -- Steroidal injections basically what
00:52:56.062 -- they do is they reduce inflammation.
00:52:59.440 -- Of course they have to be done by
00:53:02.496 -- a physician cauterizing nerves.
00:53:04.960 -- So when you cauterize the nerve,
00:53:06.330 -- what do you do?
00:53:08.480 -- You basically are killing the nerve.
00:53:10.980 -- But in some cases.
00:53:12.920 -- If there is an irritated
00:53:15.345 -- nerve that can't be called,
00:53:18.020 -- they will cauterize it to prevent it
00:53:22.521 -- from rapidly firing or firing at.
00:53:26.060 -- Overtime.
00:53:27.740 -- And then disc fusion or disc replacement.
00:53:29.930 -- And really it's not disc replacement.
00:53:31.810 -- They are getting to the point
00:53:33.688 -- of replacing disks.
00:53:34.630 -- You can look it up and you can
00:53:36.654 -- see the material they use diagrams
00:53:38.611 -- on the right here in this slide
00:53:41.083 -- shows some of those things that
00:53:43.039 -- are used as disc replacements.
00:53:44.908 -- Again,
00:53:45.352 -- this is really radical surgery
00:53:47.572 -- and rather risky,
00:53:48.930 -- but in cases where a person
00:53:51.150 -- is in constant pain,
00:53:52.630 -- it may be what is required
00:53:55.132 -- to help alleviate that pain.
00:53:57.320 -- And then from an ergonomic perspective,
00:53:59.350 -- that's why we're here.
00:54:00.710 -- Prevention is the best solution.
00:54:02.410 -- Not getting to the point of pain.
00:54:07.630 -- So this video and I'm not
00:54:09.322 -- going to show it here.
00:54:10.860 -- Because it's quite long and
00:54:12.440 -- also it's more like goes over
00:54:14.562 -- preventing various types of work
00:54:16.957 -- related musculoskeletal diseases,
00:54:18.400 -- music, orgonomic solutions,
00:54:19.591 -- but wanted to provide it.
00:54:21.580 -- Here is a link that you can
00:54:23.932 -- watch at your own convenience,
00:54:26.340 -- again on the GBU learn website.
00:54:28.730 -- All these video links will be
00:54:31.526 -- there along with the original
00:54:34.063 -- videos that I'll be showing.
00:54:36.940 -- So what I want to do?
00:54:40.710 -- Just go back to some of these videos
00:54:42.494 -- that we've watched in the past.
00:54:55.880 -- And have you think about what
00:54:58.118 -- types of injuries somebody could
00:55:00.120 -- develop from doing this activity?
00:55:02.290 -- Some of these you haven't seen before.
00:55:05.150 -- Show these first.
00:55:06.452 -- No, I had some students several
00:55:09.056 -- years ago and do a project at a
00:55:12.007 -- lamb Weston potato processing
00:55:13.736 -- facility in American Falls.
00:55:16.140 -- And some of these videos
00:55:17.785 -- we took when we were there,
00:55:19.950 -- and it's a potato processor in handling.
00:55:24.190 -- This first one.
00:55:35.240 -- Is a logging operation.
00:55:36.768 -- You can tell that it's loud also.
00:55:39.510 -- But when their one machine breaks down,
00:55:41.690 -- they have to stack boxes manually.
00:55:45.110 -- I'd like you to watch it and
00:55:46.601 -- just think about the types of
00:55:48.140 -- injuries this person could develop.
01:00:03.570 -- So I went back a couple of steps.
01:00:07.670 -- And this is a good place to
01:00:09.336 -- stop for a couple of minutes.
01:00:11.240 -- So you can see that he's picking
01:00:13.102 -- the boxes off a conveyor line.
01:00:14.890 -- You can see that how he's twisted.
01:00:17.720 -- His back is twisted.
01:00:18.884 -- He's got 1 foot planted.
01:00:20.340 -- He's got the other foot
01:00:22.390 -- slightly off the floor.
01:00:24.030 -- He's reaching for the box.
01:00:25.610 -- This is a posture he always uses to take the
01:00:29.372 -- boxes off the conveyor belt to stack him.
01:00:32.800 -- So of course, when he's on the 1st
01:00:34.936 -- tear down at the bottom of the pallet,
01:00:37.230 -- he asked to lower the box down.
01:00:39.790 -- When he's at the top of the pallet,
01:00:41.650 -- he has to raise the box all the way up.
01:00:44.730 -- So if you think about this posture and
01:00:46.794 -- the other postures that he develops
01:00:48.592 -- during the course of doing this task,
01:00:50.760 -- what types of entries could he
01:00:52.938 -- experience in the long run?
01:00:54.740 -- So you can see that at the end of
01:00:56.900 -- the time that he's left in his boxes,
01:00:59.360 -- so move forward just a little bit.
01:01:11.440 -- So watch here and see how fatigued he is
01:01:15.067 -- lifting this last box up to that top tier.
01:01:26.200 -- So just standing there you can see
01:01:29.007 -- that he's getting very fatigued.
01:01:31.370 -- That he's tired of moving these boxes
01:01:33.477 -- now I don't remember exactly weight,
01:01:35.930 -- but I think it's either 40 pounds,
01:01:38.390 -- 35 pounds, forty pounds,
01:01:39.794 -- something like that.
01:01:40.850 -- It's not like a box of
01:01:43.292 -- potatoes that weighs £50.
01:01:44.920 -- But you can see the this posture that he has.
01:01:49.060 -- He's always twisting the same way.
01:01:51.500 -- You could develop the differential
01:01:53.885 -- muscle strength in his back.
01:01:56.270 -- With the muscles aren't pulling evenly
01:01:58.808 -- and he could develop a problem like
01:02:01.628 -- that doing this task all day long.
01:02:04.090 -- And again they this is.
01:02:06.050 -- This task is required when the stacking
01:02:09.291 -- machine breaks down the automatic stacker
01:02:12.112 -- so he has to stack things manually.
01:02:15.250 -- But it in this particular facility,
01:02:17.130 -- even though they had two of
01:02:19.386 -- these stacking machines.
01:02:20.520 -- They were breaking down quite frequently,
01:02:22.650 -- so one of the things we're looking
01:02:24.960 -- at is not only the ergonomics of it,
01:02:27.980 -- but also you know what was the
01:02:30.024 -- economical tradeoff of purchasing
01:02:31.459 -- another stacking machine,
01:02:32.950 -- or trying to find one that's more reliable.
01:02:37.280 -- OK.
01:02:47.310 -- This is not stocking
01:02:49.294 -- machine I'm talking about.
01:02:51.280 -- The two stocking machines.
01:02:53.920 -- So when they're working, they work great.
01:02:55.970 -- When they don't work,
01:02:57.782 -- they have to stack the boxes by hand.
01:03:01.320 -- So like I said, there's two of am.
01:03:03.110 -- You see the one on the left.
01:03:04.680 -- There's also one on the right
01:03:06.060 -- that's kind of out of you.
01:03:10.290 -- But they automatically palletized the boxes.
01:03:12.630 -- They stack a man.
01:03:14.242 -- Then they put shrink wrap or stretch
01:03:17.294 -- plastic around the outside of the pallet.
01:03:21.060 -- First four, then using a forklift
01:03:23.088 -- and then for putting in the back
01:03:25.428 -- of a truck so manually stacking.
01:03:27.270 -- They can't put the same number
01:03:29.094 -- of boxes on a pallet that they
01:03:31.415 -- can with a stack of machine.
01:04:30.810 -- And the third video is kind of interesting.
01:04:37.070 -- So these are £500 totes.
01:04:41.290 -- So when the one packaging
01:04:44.990 -- machine breaks down.
01:04:47.210 -- They would have to put the French fries
01:04:50.050 -- or tater tots in these 500 pound toes.
01:04:52.990 -- And so again, we were looking at.
01:04:56.730 -- What are the efficiencies or what's the
01:04:59.817 -- cost trade off on putting in another
01:05:03.287 -- packaging line versus storing these
01:05:05.862 -- spuds in these 500 pound totes?
01:05:08.750 -- So what happens with these 500 pound toads
01:05:11.342 -- is they are stacked up on top of each other.
01:05:14.400 -- You know, they're fairly rigid boxes.
01:05:17.450 -- And they actually the stuff inside
01:05:20.534 -- the product inside helps provide
01:05:23.321 -- structural stability as well.
01:05:25.900 -- But they lose about 10% of the French
01:05:30.418 -- fries when they use these 500 pound totes.
01:05:35.870 -- So also when you see the person doing it,
01:05:38.530 -- the motions that they have to
01:05:40.324 -- have while they're putting the.
01:05:44.030 -- Product into those 500 pound toads.
01:05:53.390 -- Then once they get the toe down,
01:05:55.670 -- when they start to fill the packaging again,
01:05:58.270 -- there's some activities that they
01:06:00.685 -- have to do for that as well.
01:06:03.930 -- It's one of those things whether it's
01:06:06.359 -- a cost tradeoff to lose in a £500 to
01:06:08.999 -- losing 10% of the product which is.
01:06:11.700 -- £50 of French fries that
01:06:14.490 -- are ground to a pulp.
01:06:17.280 -- Or do they get another packaging
01:06:19.134 -- line which is several $100,000?
01:06:20.950 -- So that's another one of
01:06:22.620 -- those things we looked at.
01:06:24.290 -- And of course you see the worker here
01:06:27.410 -- wondering why in the world we're videotaping.
01:06:30.650 -- But we're we're doing that look
01:06:32.696 -- at efficiency of the operation.
01:06:38.900 -- So there is a lot of operations
01:06:41.112 -- associated with this.
01:06:42.060 -- It's not real simple. Again,
01:06:45.095 -- once the tow gets to certain level,
01:06:47.790 -- they've gotta move the product
01:06:50.130 -- around inside there manually.
01:06:52.010 -- So that the product is evenly spaced
01:06:55.167 -- and doesn't collapse the box when
01:06:57.738 -- it's stacked up on each other.
01:07:57.730 -- So we're going to go back and watch
01:08:00.074 -- the life raft one again and then
01:08:02.371 -- it'll be time to complete this.
01:08:04.410 -- But think about this operation.
01:08:06.270 -- Now that you know more about work
01:08:08.965 -- related musculoskeletal diseases and
01:08:10.506 -- think about the types of injuries
01:08:12.432 -- that these people could experience.
01:11:14.040 -- So if this were alive class we talked
01:11:17.088 -- about this as a goat, do this task.
01:11:19.813 -- But just think of this stress again.
01:11:22.340 -- What they're putting on their
01:11:23.920 -- bodies and the type of injuries
01:11:26.006 -- that they could experience.
01:11:27.760 -- 'cause these aren't little
01:11:29.076 -- forces that they're using to
01:11:31.108 -- put these clamshells together.
01:11:32.810 -- They're using a lot of force to
01:11:35.323 -- try to get that thing compressed.
01:11:38.370 -- And where it's not crimping the.
01:11:42.010 -- The raft inside.
01:13:52.170 -- So also think about what other tools they
01:13:54.874 -- might use to if this task weren't changed,
01:13:57.740 -- which we know that it was changed.
01:14:00.170 -- The pods are bigger now and
01:14:02.606 -- the equipment is different.
01:14:04.230 -- But think about the tools that
01:14:06.120 -- would help this. Then do this job.
01:14:09.570 -- Better than like a rubber mallet
01:14:12.120 -- and a handle that they push in.
01:14:15.020 -- 5 minutes. Pushing for the raft.
01:16:01.150 -- So that's it today.
01:16:06.520 -- We'll talk a little bit about injuries,
01:16:08.760 -- the next lecture, and then
01:16:10.950 -- started in biomechanics. Thanks.
Good evening everybody.
I think we can start now. So basically what we're going to do today, we'll go through the lecture file that I posted last time but didn't finish because of the.
Early class release.
But today is not the case like that. So we are going to go up to what is the time 9.
That's dreadful. OK, we'll see what happens. Because when I feel like tired, that means it's time. It's time to go. Not you guys feel tired. Not that that time is not. Yeah, it's always advantage the instructor.
Correct. So anyway, of course if you have to go somewhere, you can always tell me that you have to go for some reason.
Extraordinary circumstances then you can, but otherwise, you know, just stick with me and see how far we can go. All right? So last time.
What we did was just going through chit chatting basically, and everybody got the syllabus.
Let me see. I was having few left with me. Do you need one?
Like commercial power reactors, are all thermal reactors OK? Fast reactors are generally the ones that we had before.
Like BR1BR2 then FF.
Fast, fast flux.
Or in that area where the Pacific Northwest National lab.
Is near that area.
But they are not operating anymore.
But other countries are doing that progressing now. If we don't have a fast reactor, we cannot do lot of irradiation work.
Faster, you know, we would like to have that and also we would like to know what happens with fast neutrons, right? So we would like to have that past reactor and that's where the versatile test reactor can help PTR.
Can anybody tell me some?
Overseas fast reactors.
That are operating. There are also mainly research reactors.
Russia has bore 16.
I don't know they whether they have a more advanced one now.
But that is 1 reactor. I can think of France as Phoenix.
Japan has jail.
Right something like that. So everybody has this fast reactors but the but we don't have so that's very important that we have we have DTR.
And recently I gave an interview.
To Idaho Statesman, it's a local Idaho paper.
Right. So they came up with a new system there, OK.
And the reported took like almost 30 minutes interview, OK. And they also told me that they are going to talk to final people.
So I said yeah, because you should talk to IRL people more because they know more than that, right? I don't know much. So when the item came out, I just got one sentence that Doctor Cherith, chair of the Nuclear Engineering Industrial management department, said.
That nuclear is great for baseload, the continuous electricity.
Not like solar range, that's my contribution to that news item. OK, that's good for me because it's OK. So what I said like I had little bit of contribution to that, OK, so.
Now basically you can see however it is important.
Important to have a break.
But I don't give a break like for long like 15 minutes. Actually, they want me to give you.
How many minutes you want break?
It will be very late, like 945, you'll go home.
How about you go home 9:30?
That's better. So I'll give you 5 minutes break. OK then. Right now it is 818. So if you add five minutes here, it becomes 823.
OK. You can come back 823, you have to take, you know, refresh yourself and then we'll continue.